A panorama of the current historiography on the Supernova of 1054 is outlined. Shklovsky (1968) [1], and Murdin (1985) [2] show how the interpretation of this phenomenon converged on a Su-pernova event. Here we reconsider the historical data, assuming a Gamma-Ray Burst (GRB) as its source. A Supernova correlated with the GRB explains well the fading time observed by the an-cient Chinese astronomers, in daytime and in night time, while the GRB power-law explains the present X-rays and GeV emission of the Crab. On the ground of recent understanding of the first episode of binary driven Hypernova GRB (BDHN GRB) in terms of the collapse of a ten solar masses core, we propose the possible identification of the real Supernova event at earlier time than Chinese chronicles. This work allows a new understanding of the significance of historical astronomical observations, including a fireball, due to gamma-rays air shower observation, and a plague of acute radiation syndrome, documented with several thousands of victims in the Eura-sian area (Egypt, Iraq and Siria).

Panel data of our interest consist of a moderate number of panels, while the panels contain a small number of observations. An estimator of common breaks in panel means without a boundary issue for this kind of scenario is proposed. In particular, the novel estimator is able to detect a common break point even when the change happens immediately after the first time point or just before the last observation period. Another advantage of the elaborated change point estimator is that it results in the last observation in situations with no structural breaks. The consistency of the change point estimator in panel data is established. The results are illustrated through a simulation study. As a by-product of the developed estimation technique, a theoretical utilization for correlation structure estimation, hypothesis testing, and bootstrapping in panel data is demonstrated. A practical application to non-life insurance is presented as well.

One of the oldest problems in physics is that of calculating the motion of N particles under a specified mutual force: the N-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and considerable progress has been made by considering the problem in one spatial dimension. Here I review what is known about the relativistic gravitational N-body problem. Reduction to one spatial dimension has the feature that gravitational radiation is absent, thereby allowing for a clear comparison between the physics of one-dimensional relativistic and non-relativistic self-gravitating systems. After describing how to obtain a relativistic theory of gravity coupled to N point particles, I discuss in turn the 2-body, 3-body, 4-body, and N-body problems. Quite general exact solutions can be obtained for the 2-body problem, unlike the situation in general relativity in 3 spatial dimensions for which only highly specified solutions exist. The 3-body problem exhibits mild forms of chaos, and provides one of the first theoretical settings in which relativistic chaos can be studied. For N4 other interesting features emerge. Relativistic self-gravitating systems have a number of interesting problems awaiting further investigation, providing us with a new frontier for exploring relativistic many-body systems.

Stueckelberg-Horwitz-Piron (SHP) electrodynamics formalizes the distinction between coordinate time (measured by laboratory clocks) and chronology (temporal ordering) by defining 4D spacetime events x^μ as functions of an external evolution parameter τ. Classical spacetime events x^μ (τ) evolve as τ grows monotonically, tracing out particle worldlines dynamically and inducing the five U(1) gauge potentials through which events interact. Since Lorentz invariance imposes time reversal symmetry on x⁰ but not τ, the formalism resolves grandfather paradoxes and related problems of irreversibility. The action involves standard first order field derivatives but includes a higher order τ derivative that while preserving gauge and Lorentz invariance removes certain singularities and makes the related QFT super-renormalizable. The resulting field equations are Maxwell-like but τ-dependent and sourced by a current that represents a statistical ensemble of instantaneous events distributed along the worldline. The width λ of this distribution defines a correlation time for the interactions and a mass spectrum for the photons that carry the interaction. As λ becomes very large, the photon mass goes to zero and the field equations become τ-independent Maxwell’s equations. Maxwell theory thus emerges as an equilibrium limit of SHP, in which λ is larger than any other relevant time scale. Particles and fields are not constrained to mass shells in SHP theory, and by exchanging mass may produce pair creation/annihilation processes at the classical level. On-shell evolution with fixed particle masses is restored through a self-interaction associated with the 5D wave equation.

Following Dirac’s notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc…Using the PBN, many formulas, such as normalizations and expectations in systems of one or more random variables, can now be written in abstract basis-independent expressions, easy to expand by inserting a proper P-identity. The time evolution of homogeneous Markov processes can also be formatted in such a way. Our system P-kets are identified with probability vectors and our P-bra system is comparable with Doi’s state function or Peliti’s standard bra. In the Heisenberg picture of the PBN, a random variable becomes a stochastic process, and the Chapman-Kolmogorov equations are obtained by inserting a time-dependent P-identity. Also, some QM expressions in Dirac notation are naturally transformed to probability expressions in PBN by a special Wick rotation. Potential Applications show the usefulness of the PBN beyond the constrained domain and range of Hermitian operators on Hilbert Spaces in QM all the way to IT.

We develop an action principle for producing a single fluid, two-constituent system with dissipation in general relativity. The two constituents in the model are particles and entropy. The particle flux creation rate is taken to be zero, while the entropy creation rate is non-zero. Building on previous work, it is demonstrated that a new term (the proper time derivative of the matter space ``metric'') is required in the Lagrangian in order to produce terms typically associated with bulk and shear viscosity. Equations of motion, entropy creation rate, and energy-momentum-stress tensor are derived. Using an Onsager approach of identifying thermodynamic ``forces'' and ``fluxes'' a model is produced which delivers the same entropy creation rate as the standard, relativistic Navier-Stokes equations. This result is then contrasted with a model generated in the spirit of the action principle, which takes as its starting point a specific Lagrangian and then produces the equations of motion, entropy creation rate, and energy-momentum-stress tensor. Unlike the equations derived from Onsager reasoning, where the analogs of the bulk and shear viscosity coefficients are prescribed ``externally'', we find that the form of the coefficients in the second example are a direct result of the specified Lagrangian. Furthermore, the coefficients are shown to satisfy evolution equations along the fluid worldline; also a product of the specific Lagrangian.

Developing new ways to estimate probabilities can be valuable for science, statistics, and engineering. By considering the information content of different output patterns, recent work invoking algorithmic information theory has shown that a priori probability predictions based on pattern complexities can be made in a broad class of input-output maps. These algorithmic probability predictions do not depend on a detailed knowledge of how output patterns were produced, or historical statistical data. Although quantitatively fairly accurate, a main weakness of these predictions is that they are given as an upper bound on the probability of a pattern, but many low complexity, low probability patterns occur, for which the upper bound has little predictive value. Here we study this low complexity, low probability phenomenon by looking at example maps, namely a finite state transducer, natural time series data, RNA molecule structures, and polynomial curves. Some mechanisms causing low complexity, low probability behaviour are identified, and we argue this behaviour should be assumed as a default in the real world algorithmic probability studies. Additionally, we examine some applications of algorithmic probability and discuss some implications of low complexity, low probability patterns for several research areas including simplicity in physics and biology, a priori probability predictions, Solomonoff induction and Occam's razor, machine learning, and password guessing.

We study the center of energy (CE) before and after the separation of superposed wave from a moving medium (MM). It is assumed that two out-of-phase mechanical transverse waves propagating from the opposite directions on a medium moving at non-relativistic speeds are superposed and the superposed portion (SP) is separated from the MM at that moment. We consider the CE of the SP before and after the separation from the MM. The location of CE (LCE) of the SP seems to be at the center of it at the moment of superposition. The SP rotates due to the separation from the MM since the velocity of each portion symmetric with respect to the center of the SP is equal in magnitude and opposite in direction. The magnitudes of velocities of the symmetric portions become different as soon as the SP begins to rotate with the separation from the MM. Then the energies of their symmetric portions are not the same, so the LCE of the SP is not at the center of it. As a result, the LCE of it looks different before and after the separation from the MM. We must find a solution to keep the LCE of the SP constant. We propose that two out-of-phase mechanical transverse waves (MTWs) propagating from the opposite directions on a MM originally have hidden difference in relativistic energy and it suddenly appears within the range observable in Newtonian mechanics when the SP starts rotating. This means that the point of view of hidden difference in relativistic energy is necessary to keep the LCE constant.

Relativistic shocks are one of the most plausible sites of the emission of strongly variable, polarized multi-wavelength emission from relativistic jet sources such as blazars, via diffusive shock acceleration (DSA) of relativistic particles. This paper summarizes recent results on a self-consistent coupling of diffusive shock acceleration and radiation transfer in blazar jets. We demonstrate that the observed spectral energy distributions (SEDs) of blazars strongly constrain the nature of hydromagnetic turbulence responsible for pitch-angle scattering by requiring a strongly energy-dependent pitch-angle mean free path. The prominent soft X-ray excess (``Big Blue Bump'') in the SED of the BL Lac object AO 0235+164 can be modelled as the signature of bulk Compton scattering of external radiation fields by the thermal electron population, which places additional constraints on the level of hydromagnetic turbulence. It has further been demonstrated that internal shocks propagating in a jet pervaded by a helical magnetic field naturally produce polarization-angle swings by 180$^o$, in tandem with multi-wavelength flaring activity, without requiring any helical motion paths or other asymmetric jet structures. The specific application of this model to 3C279 presents the first consistent, simultaneous modeling of snap-shot SEDs, multi-wavelength light curves and time-dependent polarization signatures of a blazar during a polarization-angle (PA) rotation. This model has recently been generalized to a lepto-hadronic model, in which the high-energy emission is dominated by proton synchrotron radiation. It is shown that in this case, the high-energy (X-ray and $\gamma$-ray) polarization signatures are expected to be significantly more stable (not showing PA rotations) than the low-energy (electron-synchrotron) signatures.

The philosophy of testing statistical hypothesis is a natural consequence and functional extension of mathematical analysis of Probability. Along with the concept of recurrence when applied to random sequences and functions, it leads to the analysis of a priori and posterior which implies testing statistical hypothesis. Testing statistical hypothesis also involves algebraic, functional and dimensional considerations, which are found in the works of Laplace. Aspects of mathematical analysis such as universality of solutions, Laws of Large Numbers, Entropy, Information, and various functional dependencies are the main factors explained in the five properties that lead to implication of testing statistical hypothesis. Various interesting examples with modern scientific significance from genetics, astrophysics, and other areas give methodological access to answers of different problems and phenomena which are involved in the logic of testing statistical hypothesis.

An analysis of the consistency of the Abraham and Minkowski momenta in the determination of the photon trajectory was carried out considering a new principle of conservation of the photon's mechanical energy, in which the photon conserves translational energy in orbital angular momentum when transiting between two media, introducing the relativistic energy wave (REW). The confrontation between REW and the recent theory of space-time waves (ST) was considered, pondering your differences. Throughout this study it was possible to verify that the Abraham momentum appears a relativistic photon ignition device in the transition between two media, acting as the hidden momentum of the Minkowski’s relativistic momentum. The wavy behavior in the matter is relativistic, and the relativistic trajectory appears with delays and advances, with points of synchronization between source-observer. The classical or relativistic trajectories are determined as a function of the angle of incidence and the relative refractive index, by one of two distinct non-additive torques, the classic by Abraham or the relativistic by Minkowski. It was found that the same analysis conducted under the principle of conservation of the mechanical energy of the photon can be treated by an new Doppler, Relativistic Apparent, that can be confused with other Dopplers in the treatment of redshift from distant sources. It was found that the conservation of energy in Orbital Angular Momentum (OAM), in the interaction with matter, explains that the synchronization instants are found in the inversion of the OAM, where the advances and delays of REW occur under negligible variations of the OAM, however, opposites.

Despite the availability of COVID-19 vaccines, the global pandemic remains a significant health challenge. Timely detection of the virus is crucial for effective containment efforts, prompting the exploration of machine learning (ML) models for COVID-19 detection. highlights the ongoing significance of COVID-19 as a global health crisis despite the availability of vaccines. To address the need for timely virus detection, the study explores the efficacy of machine learning (ML) models, including DNN, Voting, Bagging, SVC_rbf, SVC_linear, SVC_polynomial, and SVC_sigmoid, in predicting COVID-19 infection probability. With a dataset comprising 4000 samples split into 3200 for training and 800 for testing, the analysis reveals that DNN and Voting models demonstrate the highest performance, achieving an impressive accuracy of 89%. These results underscore the potential of ML techniques, particularly DNN and ensemble methods like Voting, in facilitating early COVID-19 detection and contributing to effective pandemic management. The study emphasizes the importance of continued research to further refine and optimize ML-based COVID-19 detection systems.

The rapid development of the Industrial Internet of Things (IIoT) has brought enormous opportunities to the industrial environment but has also posed significant challenges to network security, especially the physical layer security challenges,which is crucial for the reliable transmission of messages interconnected devices and sensors. Focus on the enhancing the physical layer security in the IIoT communication, this paper proposed a mechanism of Spatial Secrecy Outage Probability (SSOP) to ensure the secure transmission of data. The SSOP algorithm assumes that the location of legitimate device is known, while eavesdropper on the random distribution of device locations, forming the SSOP model related to device locations from the perspective of insecure regions (ISR) and secure regions (SR), and deduce the closed-form expression for its upper bound. Subsequently under the constraint of SSOP conditions, establish an optimization model with the objective of system throughput maximization based on Spatial Secrecy Outage Probability(SRM-SSOP). By optimizing the transmission rate of legitimate channels or controlling the transmission power, the maximization of system throughput can be achieved, thus reducing the consumption of communication resources. Through sophisticated modeling and simulation in the MATLAB, we verified the accuracy of the definition and derived upper bound of SSOP. The experimental results also show that SSOP algorithm gradually converges to a specific value as the number of antenna elements increases. In addition, we observed that when the receiver device is aligned with the normal direction of the transmit antenna array, the SSOP reaches a minimum value. These performance are crucial for understanding and optimizing the security performance of IIoT communication systems.

The Schwarzschild metric emerges independent of Einstein's field equations, offering a straightforward derivation solely reliant on Newtonian mechanics and Minkowskian proper acceleration. This approach provides a clear path to understanding the gravitational field around a spherically symmetric mass without the need for the complexities of Einstein's full theory of General Relativity. Transitioning to our exploration of the cosmic Friedmann equations, we adopt a novel perspective rooted in a Lagrangian formulation grounded in Newtonian mechanics and the first law of thermodynamics. Our investigation operates under the assumption that the universe is populated by either a perfect fluid or a scalar field. By elucidating the intricate interplay between the Lagrangian formulation and the cosmic Friedmann equations, we uncover the fundamental principles governing the universe's dynamics within the framework of these elemental constituents. In our concluding endeavor, we embark on the task of harmonizing the classical equations—namely, the conservation, Euler, and Poisson equations—with the principles of General Relativity. This undertaking seeks to extend these foundational equations to encompass the gravitational effects delineated by General Relativity, thus providing a comprehensive framework for understanding the behavior of matter and spacetime in the cosmic context.

The extremely high rotation of some SMBHs is the origin of their relativistic rotational energy that results in their relativistic mass. Relativistic mass creates their relativistic gravity which is a partial answer to the missing dark matter.

We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the previously stated entropies are derived in parallel. This formulates a quantum maximum entropy method for the purpose of inferring density matrices in the absence of complete information.

In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron–proton (e^- - p⁺) and electron–positron (e^±) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of "global" jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the e^- - p⁺ jet simulation recollimation-like instability occurs and jet electrons are strongly perturbed. In the e^± jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields.

This study delves into the intricate dynamics of classical mechanics, exploring the interplay between force, mass, and energy. Through fundamental principles and mathematical formulations, it elucidates key relationships governing physical systems. Beginning with an overview of classical mechanics, the study establishes the foundational principles laid down by Newton, emphasizing concepts such as inertia, acceleration, and the relationship between force and motion. Central to the investigation is Newton's second law of motion, highlighting the direct proportionality between force and acceleration, and the inverse relationship between acceleration and mass when acted upon by a force. The study extends to the concept of effective mass, elucidating how the application of force influences the inertial mass of an object and contributes to its effective mass through the acquisition of kinetic energy. Furthermore, the study examines the total energy composition of systems, emphasizing the holistic nature of energy as a combination of potential and kinetic forms. Through the work-energy theorem, a direct link between force and kinetic energy is established, revealing how mechanical work done on an object results in changes in its kinetic energy and effective mass. Mathematical formulations and conceptual analyses provide deeper insights into the intricate relationships between force, mass, and energy, shedding light on the underlying mechanisms governing classical mechanical systems. Through validation against empirical observations and experimental data, the study ensures the accuracy and reliability of derived equations, contributing to a richer understanding of classical mechanics and paving the way for further exploration in the field of physics.

We describe here the coherent formulation of electromagnetism in the nonrelativistic quantummechanical many-body theory. We use the mathematical frame of the field theory and its quantization in the spirit of the QED. This is necessary because of the manifold of misinterpretations emerging from the hystorical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions inspired from the classical electromagnetic theory of point-like charges. However, this later is known to be inconsistent due to the self-interaction. This way could not be continued further to include properly the magnetic forces between the charged particles and lead to a lot of confusion about the interpretation of the magnetic field in the Hamiltonian, as well as about the gauge invariance. We emphasize the importance of the distinction between the applied (external fields) and the field in the matter. All these problems are length properly solved within the non-relativistic QED, nevertheless the confusion dominates in all the problems related to the magnetic properties of the solid state.

From the theory of relativistic chemical kinetics [M. W. Baig, Int. J. Mod. Phys. B 31, 1750177 (2017)] relativistic thermodynamics and kinetics for electrode processes have been developed to explain time dilation for electrode processes. For a moving observer moving at fractions of the speed of light, cell potential is observed to decrease. This results in the slower oxidation and reduction of ions at the respective electrodes. The newly formulated Lorentz transformation of the electrode and cell potential is explained in terms of generation of spin 2-boson “gravitons” from fusion of spin-1 boson “virtual-photons” mediating electrostatic force of attraction between ions and electrodes. It is postulated that birth of spin 2-boson i.e. gravitons is followed by their eventual escape in any of higher 4+n dimensions. To demonstrate the effectiveness of the present theory, the Daniel cell is considered as a numerical example.

This paper discusses about the quantum energy levels of muonic hydrogen considering only Coulomb interaction. The computational analysis in this paper will help the reader get a good understanding of how different a muonic hydrogen is from its electronic counterparts. Energy eigenvalues are calculated by numerical method and the probability density distribution of muon around the nucleus is plotted for different quantum states using special functions. The code is written in python. A comparative study of emission spectra between the muonic hydrogen and hydrogen has also been discussed.

The extra precession of Mercury - 42.9 seconds of arc per century - explained by General Relativity (GR), is the result of a secular addition of 5.02 × 10⁻⁷ rad. at the end of every orbit around the Sun. We will analyze, the instantaneous precession and its addition along one orbit, determine the magnitude and oscillations around the mean value, comparing key theoretical proposals. This angular precession, should be the result reaction of Mercury to the gravitoelectric action produced by the geometric curve space-time at each single point of the elliptic orbit. The better we should know about this instantaneous precession, the better we will determine the external action and its quantum core nature, if that is the case. The Doppler tracking of the MESSENGER spacecraft, produces only 1 m error, enough precision to deduce the complete geodesic orbit of Mercury as an open free-fall path, isolated from other planets gravitational interference. The aim of this article is also to encourage JPL, IMCCE. and other scientific teams to do so because, as far as I know, it has not been entirely measured yet, by accurately tracking that motion.

It is discovered that the gravitational field on the surface of a neutron star is with a relativistic mass density of 2.65*10¹⁶~5.87*10¹⁸kgm^-3 which can be larger than the mass density of the neutron star (~10¹⁷kgm^-3). And, the total relativistic mass of the gravitational field of the Sun is ~10⁷ times the mass of the Sun. For different stars, the relativistic mass of the gravitational field is larger as the mass density of the star is larger. In the Milky Way, the total relativistic mass of the gravitational fields is much larger than the total mass of the stars, planets and gas. And, the relativistic mass density of the observed strongest magnetic field is 2.17*10⁸kgm^-3. This discovery should be a new frame to understand the fundamental problem of physics.

When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.

This article lays the foundation for Extended Relativity (ER) – a unified geometric approach to the electromagnetic and gravitational field and relativistic dynamics in them. We explain here the basic tenets of ER, including the influenced spacetime of an object and the Extended Principle of Inertia. These two new ideas enable a unified theory of these fields. We introduce local scaling functions for describing the geometry of a spacetime influenced by a field and construct a simple, universal local scaling function which unifies electromagnetism and gravity. We recover the full electromagnetic theory, including Maxwell’s equations. For gravitation, ER passes all of the tests of General Relativity. Despite the non-linearity of relativistic gravitation, we obtain a method of combining fields from multiple sources. Finally, we identify the differences in the relativistic treatment of the electromagnetic field by Special Relativity and of the gravitational field by General Relativity and indicate how these differences are resolved in ER.

The Eliezer and Gray physical interpretation of the Ermakov-Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov-Milne-Pinney equation and associated first integral. The special relativistic extension of the Ray-Reid system and invariant is obtained. General properties of the relativistic Ermakov-Milne-Pinney are analyzed. The conservative case of the relativistic Ermakov-Milne-Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered as well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov-Milne-Pinney equation has additional nonlinearities, due to the relativistic effects.

In recent years, with the rapid development of technology, artificial intelligence(AI) security issues represented by adversarial sample attack have aroused widespread concern in society. Adversarial samples are often generated by surrogate models and then transfer to attack the target model, and most AI models in real-world scenarios belong to black boxes, thus transferability becomes a key factor to measure the quality of adversarial samples. The traditional method relies on the decision boundary of the classifier and takes the boundary crossing as the only judgment metric without considering the probability distribution of the sample itself, which results in an irregular way of adding perturbations to the adversarial sample, an unclear path of generation, and a lack of transferability and interpretability. In the probabilistic generative model, after learning the probability distribution of the samples, a random term can be added to the sampling to gradually transform the noise into a new independent and identically distributed sample. Inspired by this idea, we believe that by removing the random term, the adversarial sample generation process can be regarded as static sampling of the probabilistic generative model, which guides the adversarial samples out of the original probability distribution and into the target probability distribution, and helps to improve transferability and interpretability. Therefore, we propose a Score Matching-Based Attack(SMBA) method to perform the adversarial sample attacks by manipulating the probability distribution of the samples, which can show good transferability in the face of different datasets and models, and give reasonable explanations from the perspective of mathematical theory and feature space. In conclusion, our research establishes a bridge between probabilistic generative models and adversarial samples, provides a new entry angle for the study of adversarial samples, and brings new thinking to AI security.

In this paper, we study the relativistic correction to Bekenstein-Hawking entropy in the canonical ensemble and isothermal-isobaric ensemble and apply it to the cases of non-rotating BTZ and AdS-Schwarzschild black holes. This is realized by generalizing the equations obtained using Boltzmann-Gibbs(BG) statistics with its relativistic generalization, Kaniadakis statistics, or κ-statistics. The relativistic corrections are found to be logarithmic in nature and it is observed that their effect becomes appreciable only in the high-temperature limit suggesting that the entropy corrections must include these relativistically corrected terms while taking the aforementioned limit. The non-relativistic corrections are recovered in the κ → 0 limit.

The relativistic effects of the dynamical properties of light at angular incidence were analyzed from the perspectives of Bohr indeterminacy and Heisenberg uncertainties and statistical dispersion. It was found that these effects report minimal uncertainties that agree with one or the other according to the angular range of incidence and that decrease with increasing refringence of the medium, constituting a specific relativistic uncertainty at angular incidence. An anomaly is indicated for the uncertainty principle in the Quantum Theory (QT) setting for small angles of incidence, where the accuracy of the angular position does not imply an increase in the uncertainty of the linear momentum. The anomalies arise because TQ does not predict the alternation between the classical and relativistic regimes of photon inertia at angular incidence. Specific relativistic uncertainty particularizes the uncertainty principle in the transmission of light between media pairs at angular incidence for the relativistic scenario, considering an observer that registers the relativistic effects of measurements that interfere with the observed system, in another inertial referential.

The geodesics on a relativistic manifold are given by the well-known equation involving the Christoffel coefficients. This equation can be solved numerically step by step and transposed into a quantization. We study here the effect of this quantization on the Schwarzschild spacetime, more precisely in the Kruskal-Szekeres map.

In ultra-relativistic collisions of heavy ions, the strongly interacting Quark Gluon Plasma (sQGP) is created. The fluid nature of the sQGP was one of the important discoveries of high energy heavy ion physics in the last decades. Henceforth the explosion of this matter may be described by hydrodynamical models. Besides numerical simulations, it is important to study the analytic solutions of the equations of hydrodynamics, as these enable us to understand the connection of the final and initial states better. In this paper we present a perturbative, accelerating solution of relativistic hydrodynamics, on top of a known class of solutions describing Hubble-expansion. We describe the properties of this class of perturbative solutions, and investigate a few selected solutions in detail.

Based on recent contributions regarding the treatment of unsteady hydraulic conditions into the state-of-the-art of scour literature, the theoretically derived probability distribution of bridge scour is introduced. The model is derived assuming a rectangular hydrograph shape with a given duration, and random flood peak following a Gumbel distribution. A model extension for a more complex flood event is also presented, assuming a synthetic exponential hydrograph shape. The mathematical formulation can be extended to any flood-peak probability distribution. The aim of the manuscript is to move forward the current approaches adopted for the bridge design coupling hydrological, hydraulic, and erosional models in a mathematical closed form.

Philippines as an archipelago and tropical country, which is situated near the Pacific ocean, faces uncertain rainfall intensities. This makes environmental, agricultural and economic systems affected by precipitation difficult to manage. Time series analysis of Philippine rainfall pattern has been previously done, but there is no study investigating its probability distribution. Modeling the Philippine rainfall using probability distributions is essential, especially in managing risks and designing insurance products. Here, daily and cumulative rainfall data (January 1961 - August 2016) from 28 PAGASA weather stations are fitted to probability distributions. Moreover, the fitted distributions are examined for invariance under subsets of the rainfall data set. We observe that the Gamma distribution is a suitable fit for the daily up to the ten-day cumulative rainfall data. Our results can be used in agriculture, especially in forecasting claims in weather index-based insurance.

This study presents a comparative analysis of length deformation in Classical and Relativistic Mechanics, specifically investigating 10-gram objects accelerating to 1% of the speed of light. By employing Hooke's Law in Classical Mechanics and the Relativistic Lorentz Factor, the research explores the implications of acceleration dynamics and the limitations inherent in Relativistic Mechanics. The results reveal significant differences in predicted length changes between the two frameworks, emphasizing the necessity of considering relativistic effects beyond velocity alone. This study underscores the critical importance of addressing the incomplete treatment of acceleration dynamics in Relativistic Mechanics to achieve a more accurate depiction of length deformation in high-speed scenarios.

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation, and for the first time the worldlines equations are given. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, especially the experiment with the accelerated Michelson-Morley interferometer is solved, and we described an experiment where a new relativistic paradox appears --- a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

The theories of quantum mechanics and relativity dramatically altered our understanding of the universe ushering in the era of modern physics. Quantum theory deals with objects probabilistically at small scales, whereas relativity deals classically with motion in space and time. We show here that the mathematical structures of quantum theory and of relativity follow together from pure thought, defined and uniquely constrained by the same elementary ``combining and sequencing'' symmetries that underlie standard arithmetic and probability. The key is uncertainty, which inevitably accompanies observation of quantity and imposes the use of pairs of numbers. The symmetries then lead directly to the use of complex \sqrt{-1} arithmetic, the standard calculus of quantum mechanics, and the Lorentz transformations of relativistic spacetime. One dimension of time and three dimensions of space are thus derived as the profound and inevitable framework of physics.

The discovery by the Large Area Telescope on board Fermi of variable gamma-ray emission from radio-loud narrow-line Seyfert 1 (NLSy1) galaxies revealed the presence of a possible third class of AGN with relativistic jets in addition to blazars and radio galaxies. Considering that NLSy1 are usually hosted in spiral galaxies, this finding poses intriguing questions about the nature of these objects and the formation of relativistic jets. We report on a systematic investigation of the gamma-ray properties of a sample of radio-loud NLSy1, including the detection of new objects, using 7 years of Fermi-LAT data with the new Pass 8 event-level analysis. In addition we discuss the radio-to-very-high-energy properties of the gamma-ray emitting NLSy1, their host galaxy, and black hole mass in the context of the blazar scenario and the unification of relativistic jets at different scales.

A relativistic positioning system is a set of four emitters broadcasting their proper times by means of light signals. The four emitter times received at an event constitute the emission coordinates of the event. Covariant quantities associated with relativistic positioning systems are analysed relatively to an observer in Minkowski space-time by splitting them in their relative space-like and time-like components. The location of a user in inertial coordinates from a standard set of emission data (emitted times and satellite trajectories) is solved in the underlying 3+1 formalism. The analytical location solution obtained by Kleusberg for the GPS system is recovered and interpreted in a Minkowskian context.

In previous papers we have shown how Schrödinger’s equation which includes an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The quantum behaviour was derived from Fisher information terms which were added to the classical Lagrangian. It was thus shown that a quantum mechanical system is driven by information and not only electromagnetic fields. This program was applied also to Pauli’s equations by removing the restriction of potential flow and using the Clebsch formalism. Although the analysis was quite successful there were still terms that did not admit interpretation, some of them can be easily traced to the relativistic Dirac theory. Here we repeat the analysis for a relativistic flow, pointing to a new approach for deriving relativistic quantum mechanics.

In a recent paper discussing Newton’s third law in the framework of special relativity for charged bodies, it was suggested that one can construct a practical relativistic motor provided high enough charge and current densities are available. As on the macroscopic scale charge density is limited by the phenomena of dielectric breakdown, it was suggested to take advantage of the high charge densities which are available on the microscopic scale. A preliminary analysis of this option denoted "nano relativistic scale" is studied in the current paper.

In this review article the study of the development of relativistic cosmology and introduction of inflation in it is carried out. We study the properties of standard cosmological model developed in the framework of relativistic cosmology and the geometric structure of spacetime connected coherently with it. We examine the geometric properties of space and spacetime ingrained into the standard model of cosmology. The big bang model of the beginning of the universe is based on the standard model which succumbed to failure in explaining the flatness and the large-scale homogeneity of the universe as demonstrated by observational evidence. These cosmological problems were resolved by introducing a brief acceleratedly expanding phase in the very early universe known as inflation. Cosmic inflation by setting the initial conditions of the standard big bang model resolves these problems of the theory. We discuss how the inflationary paradigm solves these problems by proposing the fast expansion period in the early universe.

Hamiltonians describing the relativistic quantum dynamics of a particle with an arbitrary spin are shown to exhibit a supersymmetric structure when the even and odd elements of the Hamiltonian commute. For such supersymmetric Hamiltonians an exact Foldy-Wouthuysen transformation exits which brings it into a block-diagonal form separating the positive and negative energy subspaces. Here the supercharges transform between energy eigenstates of positive and negative energy. The relativistic dynamics of a charged particle in a magnetic field is considered for the case of a scalar (spin-zero) boson obeying the Klein-Gordan equation, a Dirac (spin one-half) fermion and a vector (spin-one) boson characterised by the Proca equation.

This article explores the enduring mysteries of consciousness and the afterlife, two enigmatic topics that have fascinated humanity for ages. Despite extensive scientific efforts, the existence of an afterlife remains unproven, and understanding consciousness remains a significant challenge. The research introduces innovative hypotheses through simple thought experiments with empirical evidence and robust theoretical foundations. It delves into the complexities of consciousness, its relationship with the brain, and the need for interdisciplinary approaches encompassing physics, psychology, and philosophy. Boldly contemplating the probability of a continuous consciousness after death, the study argues that existing evidence strongly supports this idea. Beyond theoretical implications, it envisions practical outcomes, suggesting that insights into these mysteries could enhance human well-being and contribute to a more harmonious world. In summary, this article embarks on a quest to shed light on age-old questions about consciousness and the afterlife. Through fresh methodologies, it aims to provide new perspectives that could reshape our understanding of existence and inspire intellectuals to positive individual and societal advancements including psychological well-being and intelligence.

Healthcare leaders are faced with many financial challenges in the contemporary environment, leading to many bankruptcies in recent years. What is not well understood are the specific conditions that lead to organizational economic failure. Ideally, hospital leaders could examine the literature for guidance to predict bankruptcy before it occurs. However, existing regression methods have proven inadequate, especially when the finance variables follow a nonnormal frequency pattern. Furthermore, the regression approach encounters difficulties due to multicollinearity and nonnormality issues. Therefore, an alternate stochastic approach for predicting the probability of hospital bankruptcy is warranted. This new method includes computing and interpreting the correlations between the hospital’s revenue and expenses for bivariate lognormal data, calculating the risk of bankruptcy due to the mismatch between revenues and expenses, determining the likelihood of a hospital’s expense exceeding the state’s median expense level, and evaluating a hospital’s financial memory level. Ultimately in our research, we demonstrate a novel approach to anticipate hospital bankruptcy, which can be particularly useful for health policy analysts and hospital leaders in making informed financial decisions and proactively managing risks to ensure the sustainability and stability of their institutions.

In public health literature the risk of death or disease associated with a dietary, environmental of behavioral factor is most commonly denoted by odds ratio (OR), hazard ratio (HR) or risk ratio (RR). The ratio indices have several desirable statistical properties. However, the most important question is whether there are some evolved innate norms of perception of risk that people use and what they are. We conducted a simple one question survey of 98 individuals with different age, sex, educational and professional backgrounds. The respondents were asked to judge the relative perceived risk of four different hypothetical habits for which data on the percentage of people affected by the disease with and without the habit was given. They were asked to rank the risks for the four habits. Results showed that the habits that had the highest difference between probability of acquiring the disease were ranked high on risk perception. The probability ratios did not affect risk perception significantly. Further age, sex, profession or formal training in statistics did not affect the response significantly. Even individuals that were formally trained to use OR and HR as risk indicators, preferred using probability differences over ratios for judging their own risk in the perceived context. This preliminary inquiry into intuitive statistical perception suggests that designing statistical indices based on people’s innate perception may be a better strategy than trying to train people to understand the indices designed by expert statisticians.

First, we examine how spin is treated in special relativity and the necessity of introducing spin supplementary conditions (SSC) and how they are related to the choice of a center-of-mass of a spinning particle. Next, we discuss quantum electrodynamics and the Foldy-Wouthuysen transformation which we note is a position operator identical to the Pryce-Newton-Wigner position operator. The classical version of the operators are shown to be essential for the treatment of classical relativistic particles in general relativity, of special interest being the case of binary systems (black holes/neutron stars) which emit gravitational radiation.

Identifying the SARS-CoV-2 virus has been a unique challenge for the scientific community. In this paper, we discuss a practical solution to help guide clinicians with interpretation of the probability that a positive, or negative, COVID-19 test result indicates an infected person, based on their clinical estimate of pre-test probability of infection.The authors conducted a small survey on LinkedIn to confirm that hypothesis that that the clinical pre-test probability of COVID-19 increases relative to local prevalence of disease plus patient age, known contact, and severity of symptoms. We examined results of PPA (Positive Percent Agreement, sensitivity) and NPA (Negative Percent Agreement, specificity) from 73 individual laboratory experiments for molecular tests for SARS-CoV-2 as reported to the FIND database ¹, and for selected methods in FDA EUA submissions^2,3. Authors calculated likelihood ratios to convert pre-test to post-test probability of disease and designed an online calculator to create graphics and text to report results. Despite best efforts, false positive and false negative Covid-19 test results are unavoidable^4,5. A positive or negative test result from one laboratory has a different probability for the presence of disease than the same result from another laboratory. Likelihood ratios and confidence intervals can convert the physician or other healthcare professional’s clinical estimate of pre-test probability to post-test probability of disease. Ranges of probabilities differ depending on proven method PPA and NPA in each laboratory. We recommend that laboratories verify PPA and NPA and utilize a the “Clinician’s Probability Calculator” to verify acceptable test performance and create reports to help guide clinicians with estimation of post-test probability of COVID-19.

We propose a description of the electromagnetic field in the form of a four-component complex spinor, from which a vector of electromagnetic potential with two degrees of freedom, calibrated by two conditions - zero length and zero component along the y-axis - is obtained by using Pauli matrices. A similar approach is applied to the field of a fermion, in particular, the electron. It is known that the quantum field of the electron and the electron itself is a four-component complex spinor, so, existing in the Minkowski vector space, we cannot observe it directly. But with the help of Pauli matrices a vector is formed from the electron spinor, which is known to us as an electric current vector, and this current vector describes exactly a single particle. As a vector, it is available to us for observation in our vector space. Similarly, the electromagnetic field and its photon particle is also a four-component spinor, from which the universal formula using Pauli matrices produces a vector, it is known to us as the electromagnetic potential vector, and it too describes even a single photon. All the differences in the properties of the current vector and the electromagnetic potential vector, and hence the electron and the electromagnetic field, are due only to a slight difference in the structures of their four-component spinors and inextricable linked to them momentum spinors and coordinate spinors. Expressions for the electric and magnetic fields of a photon during its interaction with an electron.Thus, a unified way to describe bosons and fermions in spinor space is proposed. Each spinor using the same formula corresponds to a vector, in the case of a fermion it is a current vector, in the case of a boson it is a vector, for example, of the electromagnetic potential. Each spinor of a field is matched with a spinor of coordinates and a spinor of momentum, which are transformed by the same Lorentz transformations and which have the same structure as their corresponding field spinor, that is, the momentum and coordinates of boson have a bosonic spinor structure, while momentum and coordinates of fermion are a spinor with a fermionic structure. Field, coordinates and momentum vectors of boson automatically have a zero length, while in the case of fermion they all have a nonzero length, so the fermion, in contrast to the boson, has a nonzero mass, nonzero charge and moves with a sub light speed.While quantum mechanics treats probability as a real number, quantum field theory deals with probability as a four-dimensional real vector. The place of the probability amplitude, which in quantum mechanics is a complex number, in quantum field theory is taken by a complex spinor.In the same way as in quantum mechanics the processes of propagation and interaction are described at the level of complex probability amplitudes, and the final result is translated into a real probability value, so in quantum field theory all processes should be described in terms of complex spinor space, and the result is translated into the form of a real vector in Minkowski space.The presented approach, at its proper development, makes it possible to carry out calculations of the interaction of particles in two-dimensional spinor space, and to interpret in terms of the Minkowski vector space only the final results.

Distributions with bounded support show considerable sparsity over those with unbounded support, despite the fact that there are a number of real-world contexts where observations take values from a bounded range (proportions, percentages, and fractions are typical examples). For proportion modelling, a flexible family of two-parameter distribution functions associated with the exponential distribution is proposed here. Mathematical and statistical properties of the novel distribution are examined, including quantiles, mode, moments, hazard rate function, and its characterization. The parameter estimation procedure using the maximum likelihood method was carried out, and applications to environmental and engineering data were also considered. To this end, various statistical tests are used, along with some other information criterion indicators to determine how well the model fits the data. The proposed model is found to be the most efficient plan in most cases for the datasets considered.

The article aims to present an alternative perspective on the relativistic expression of energy. This perspective is based on the virtual use of a Dempster mass spectrometer. In this spectrometer, it is possible to simulate Alfred Bucherer's experiment and conclude, using Lienard's relativistic equation, that the classical expression of energy predicted by Special Relativity is a more complete expression than the one presented by high school and college physics textbooks.

The theory of one-photon ionization and two-photon above-threshold ionization is formulated for applications to heavy atoms in attosecond science using the Dirac-Fock formalism. A direct comparison of the Wigner-Smith-Eisenbud delays for photoionization is made with delays from the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) method. Photoionization by an attosecond pulse train, consisting of monochromatic fields in the extreme ultraviolet range, is computed with many-body effects at the level of the Relativistic Random Phase Approximation (RRPA). Subsequent absorption and emission processes of infrared laser photons in RABBIT are evaluated using static ionic potentials as well as asymptotic properties of relativistic Coulomb functions. As expected, light elements, such as Argon, show negligible relativistic effects, while heavier elements, such a Krypton and Xenon, exhibit delays that depend on the fine-structure of the ionic target. The relativistic effects are notable close to ionization thresholds and Cooper minima with differences in fine-structure delays predicted to be as large as tens of attoseconds. The separability of relativistic RABBIT delays into a Wigner-Smith-Eisenbud delay and a universal continuum--continuum delay is studied with reasonable separability found for photoelectrons emitted along the laser polarization axis in agreement with prior non-relativistic results.

One of creators of quantum mechanics P. Jordan in his work on quantum biology claimed that life's missing laws were the rules of chance and probability of the quantum world. The article presents author’s results of studying frequencies (or probabilities) of nucleotides on so-called epi-chains of long DNA sequences of various eukaryotic and prokaryotic genomes. DNA epi-chains are algorithmically constructed subsequencies of DNA nucleotide sequences. According to the algorithm of construction of any epi-chain of the order n, the epi-chain is such nucleotide subsequence, in which the numerations of adjacent nucleotides differ by natural number n (n = 1, 2, 3, 4,…). Correspondingly each epi-chain of order n ≥ 2 contains n times less nucleotides than the original DNA sequence. The presented results unexpectedly discover that in long single-stranded and double-stranded DNA of any tested genome its DNA epi-chains of different orders n (values n are not too large) have practically identical frequencies (or probabilities) of each kind of nucleotides. These data allow considering DNA as a regular rich set of epi-chains, which can play a certain role in genetic and epigenetic phenomena as the author belives. Appropriate rules of nucleotide frequencies on epi-chains of long DNA sequences are formulated for further their tests on a wider set of genomes. These results testify on existence of long-range coherence in long DNA and remind the Fröhlich's theory of long-range coherence in biological systems. The phenomenological data are discussed from different standpoints: the DNA double helices and helical antennas with circular polarizations of electromagnetic waves; relations with the Fröhlich's theory; numerical analysis of DNA epi-chains under binary representations of nucleotides. Results are useful for developing quantum and algebraic biology.

We give two examples of the appearance of heavy-tailed distributions in applications to social sciences. Among these distributions are the laws of Pareto, Lotka, and some new ones. The examples are illustrated by constructing suitable toy models.

This article presents six probability distributions from the Gamma family with three parameters, for the flood frequency analysis in hydrology. The choice of the Gamma family of statistical dis-tributions was driven by its frequent use in hydrology. In the Faculty of Hydrotechnics, the im-provement of the estimation of maximum flows and including the methodological bases for the realization of a regionalization study with the linear moments method with the corrected pa-rameters was researched, being an element of novelty. The linear moments method is better than MOM because it avoids the choice of skewness depending on the origin of the flows, practiced in Romania. The L-moments method conforms to the current trend for estimating the parameters of statistical distributions. Observed data from hydrometric stations are of relatively short length, so the statistical parameters that characterize them are of a sample that requires correction. The correction of the statistical parameters is proposed, using the method of least squares based on the inverse functions of the statistical distributions expressed with the frequency factor for L-moments. All the necessary elements for their use are presented like, quantile functions, the exact and ap-proximate relations for estimating parameters and frequency factors. A flood frequency analysis case study was carried out for the Ialomita river, to verify the proposed methodology. The per-formance of this distributions is evaluated using Kiling-Gupta and Nash-Sutcliff coefficients.

Estimating the parameters of statistical distributions generally involves solving a system of nonlinear equations or a nonlinear equation, being a technical difficulty in their usual application in hydrology. This article presents improved approximations and, in some cases, new approximations for the estimation with the method of ordinary moments and the method of linear moments, which are useful for the direct calculation of the parameters, because the errors in the approximate estimation are similar to the use of iterative numerical methods. Thirteen statistical distributions of two and three parameters frequently used in hydrology are presented, for which parameter estimation was laborious. Thus, the approximate estimation of the parameters by the two methods is simple but also precise and easily applicable by hydrology researchers. The approximate forms characterized by very small errors are the result of the research conducted within the Faculty of Hydrotechnics to update the romanian normative standards in the hydrotechnical field.

Probability is an open question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the domain of probability extends to the complex space, including the generation of complex trajectories, the definition of the complex probability, the relation of the complex probability to the real quantum probability, and so on. The complex treatment proposed here applies the optimal quantum guidance law to derive the stochastic differential (SD) equation governing the particle’s random motions in the complex plane. The ensemble of the complex quantum random trajectories (CQRTs) solved from the complex SD equation is used to construct the probability distribution ρc(t,x,y) of the particle’s position over the complex plane z=x+iy. The correctness of the obtained complex probability is confirmed by the solution of the complex Fokker-Planck equation. The significant contribution of the complex probability is that it can be used to reconstruct both quantum probability and classical probability, and to clarify their relationship. Although quantum probability and classical probability are both defined on the real axis, they are obtained by projecting complex probability onto the real axis in different ways. This difference explains why the quantum probability cannot exactly converge to the classical probability when the quantum number is large.

To generate a probability density function (PDF) for fitting probability distributions of real data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be adopted as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of trained deep learning model can be used to estimate the PDF. To evaluate the proposed method, numerical experiments with single and mixed distributions are performed. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method.

This study, serving as Part-2 of the research titled "Comparative Analysis of Length Deformation in Classical and Relativistic Mechanics," investigates the behaviour of matter within gravitationally bound systems. Through meticulous examination of projected length alterations, the research highlights differences between classical and relativistic mechanics frameworks, emphasizing the necessity of considering relativistic effects beyond velocity alone. Additionally, the study underscores the crucial role of gravitational effects on the effective mass of moving objects, which emerges as a critical factor in predicting length deformation across scientific disciplines. The incomplete treatment of relativistic effects within Relativistic Mechanics, including acceleration and material stiffness, emphasizes the importance of comprehensively understanding gravitational influences on effective mass. This is evident in gravitational equations, where the gravitational force depends not only on the object's mass but also on its effective mass, influenced by kinetic energy. Thus, incorporating the gravitational effect on effective mass enhances the understanding of length deformation phenomena within gravitationally bound systems, enriching scientific discourse.

In this paper, we investigate the behaviour of a relativistic quantum oscillator under the effects of Lorentz symmetry violation determined by a tensor (KF)µναβ out of the Standard Model Extension. We analyze the quantum system under a Coulomb-type radial electric field and a uniform magnetic induced by Lorentz symmetry breaking effects under a Cornell-type potential, and obtain the bound states solution by solving the Klein-Gordon oscillator. We see a quantum effect due to the dependence of the angular frequency of the oscillator on the quantum numbers of the system, and the energy eigenvalues and the wave-function of the oscillator field get modified by the Lorentz symmetry breaking parameters as well as due to the presence of Cornell-type potential.

The purpose of this paper is to show a new approach to unify the theory of general relativity and quantum physics. For this, we rely on thermodynamics, fluid mechanics and the theory of information. We will then see that the Shannon entropy, Boltzmann and Von Neumann can be the source of gravity, which would be a form emerging. For this, we will study at first what is lacking for the unification of general relativity and physics. Secondly, we will explain the concept of entropic gravity by introducing calculations Erik Verlinde. Then we will explain the concept of entropy Boltzmann, Shannon, Von Neumann and the links between them. Then, we will modify Einstein's equations by transforming the tensor of perfect fluid in terms of entropy. Finally, we will link our theory with experience already carried out as part of a link between gravity and quantum theory.

Research for a theory of quantum gravity has recently led to the use of presheaf topos. Quantum uncertainty is linked to the truth values of intuitionistic logic. This paper proposes transposing this model into a classic probability context, that of conditional mathematical expectations. A simulation of Brownian motion is offered for illustrative purposes.

In this paper, we work with a diffusion-perturbed risk model comprising a surplus generating process and an investment return process. The investment return process is of standard Black-Scholes type, that is, it comprises a single risk-free asset that earns interest at a constant rate and a single risky asset whose price process is modelled by a geometric Brownian motion. Additionally, the company is allowed to purchase noncheap proportional reinsurance priced via the expected value principle. Using the Hamilton-Jacobi-Bellman approach, we derive a second-order Volterra integrodifferential equation which we transform into a linear Volterra integral equation of the second kind. We proceed to solve this integral equation numerically using the block-by-block method for the optimal reinsurance retention level that minimizes the ultimate ruin probability. The numerical results based on light- and heavy-tailed distributions show that proportional reinsurance and investments play a vital role in enhancing the survival of insurance companies. But the ruin probability exhibits sensitivity to the volatility of the stock price.

The relativistic Doppler effect comes from the fact that observers in different inertial reference frames experience space and time differently, while the speed of light remains always the same. Consequently, a wave packet of light exhibits different frequencies, wavelengths, and amplitudes. In this paper, we present a local approach to the relativistic Doppler effect based on relativity, spatial and time translational symmetries, and energy conservation. Afterward, we investigate the implications of the relativistic Doppler effect for the quantum state transformations of wave packets of light and show that a local photon is a local photon at the same point in the spacetime diagram in all inertial frames.

To embrace the special theory of relativity with classical thermodynamics correct Lorentz transformations of thermodynamic state functions are formulated. All of these Lorentz transformations of state functions equally support the time dilation phenomenon which is experimentally verified fact. Relativistic Boltzmann constant proves entropy to be the Lorentz variant. Twin paradox thought experiments for heat engines prove heat flux to be Lorentz variant. Lorentz transformation of entropy and heat flux proves temperature Lorentz invariant. All thermodynamic state functions are proved to be Lorentz variant which is shown in accord with Lorentz transformation of thermodynamic work.

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails less than 50%. Theoretical models for a static case and for five dynamic cases, without and with rebounds, show that there is a small probability that the coin does not fall on its head or tail, depending on initial toss conditions, the coin geometry and conditions of the coin and landing surfaces. For the dynamic model with rebounds, it is found that the probability that a 50 Eurocent coin thrown from a normal height with common initial velocity conditions and appropriate surface conditions will end up on its edge is in the order of one against several thousand.

This paper aims to describe the geometrical structure and explicit expressions of family of finitely parametrized probability densities over smooth manifold $M$. The geometry of family of probability densities on $M$ are inherited from probability densities on Euclidean spaces $\left\{U_\alpha \right\}$ via bundle morphisms, induced by an orientation-preserving diffeomorphisms $\rho_\alpha:U_\alpha \rightarrow M$. Current literature inherits densities on $M$ from tangent spaces via Riemannian exponential map $\exp: T_x M \rightarrow M$; densities on $M$ are defined locally on region where the exponential map is a diffeomorphism. We generalize this approach with an arbitrary orientation-preserving bundle morphism; we show that the dualistic geometry of family of densities on $U_\alpha$ can be inherited to family of densities on $M$. Furthermore, we provide explicit expressions for parametrized probability densities on $\rho_\alpha(U_\alpha) \subset M$. Finally, using the component densities on $\rho_\alpha(U_\alpha)$, we construct parametrized mixture densities on totally bounded subsets of $M$. We provide a description of inherited mixture product dualistic geometry of the family of mixture densities.

We show the tensor properties of joint probabilities on a Riemannian parametric manifold. Initially we develop a binary data matrix for parameter measurements of a large number of particles confining in a closed system in order to retrieve the joint probability densities of related parameters. By introducing a new generalized inner product as a multilinear operation on dual basis of parametric space, we extract the set of joint probabilities and prove them to meet contravariant tensor properties in a general Riemannian parametric space. We show these contravariant tensors reduce to classical ordinary partial derivatives definition in ordinary Euclidean parametric space. Finally we prove by a theorem that symmetrized iterative contravariant derivative of cumulative probability function on Riemannian manifold gives the set of joint probabilities in those manifold. We bring some examples for compatibility with physical tensors.

We start with the discussion on misapplication of classical probability theory by Feynman in his analysis of the two slit experiment (by following the critical argumentation of Koopman, Ballentine, and the author of this paper). The seed of Feynman's conclusion on the impossibility to apply the classical probabilistic description for the two slit experiment is treatment of conditional probabilities corresponding to different experimental contexts as unconditional ones. Then we move to the Bell type inequalities. Bell applied classical probability theory in the same manner as Feynman and, as can be expected, he also obtained the impossibility statement. In contrast to Feynman, he formulated his no-go statement not in the probabilistic terms, but by appealing to nonlocality. This note can be considered as a part of the author's attempts for getting rid off nonlocality from quantum physics.

In this paper, a relativistic scalar particle under Lorentz symmetry breaking effects in the presence of a scalar potential is investigated. We introduce the scalar potential by modifying the mass via transformation M → M+S(r) in the wave equation and analyze the behaviour of a scalar particle. We see that the analytical solution to the KleinGordon equation can be achieved, and the energy eigenvalues and the wave function depends on the Lorentz symmetry breaking parameters as well as potential

In this work, we derive the spectral efficiency, secrecy outage probability, and bit error rate of a communication system assisted by a large intelligent surface (LIS). We consider a single-antenna user and an array of antennas at the transmitter side and the possibility of a direct link between transmitter and receiver. Additionally, there is a single-antenna eavesdropper with a direct link to the transmitter, which is modeled as a Nakagami-m distributed fading coefficient. The channels from transmitter to the LIS and from the LIS to the user may or may not have the line-of-sight (LoS) and are modeled by the Nakagami- m distribution. Moreover, we assume that the LIS elements perform non-ideal phase cancellation leading to a residual phase error that assumes a Von Mises distribution. We show that the resulting channel can be accurately approximated by a Gamma distribution whose parameters are analytically estimated using the moments of the equivalent signal-to-noise ratio. We also provide an upper bound for the error probability for M-QAM modulations. With the derived formulas, we analyze the effect of the strength of the LoS link by varying the Nakagami parameter, m.

We develop an action principle to construct the field equations for dissipative/resistive general relativistic two-temperature plasmas, including a neutrally charged component. The total action is a combination of four pieces: an action for a multi-fluid/plasma system with dissipation/resistivity and entrainment; the Maxwell action for the electromagnetic field; the Coulomb action with a minimal coupling of the four-potential to the charged fluxes; and the Einstein-Hilbert action for gravity (with the metric being minimally coupled to the other action pieces). We use a pull-back formalism from spacetime to abstract matter spaces to build unconstrained variations for the neutral, positively, and negatively charged fluid species and for three associated entropy flows. The full suite of field equations is recast in the so-called ``$3 + 1$'' form (suitable for numerical simulations), where spacetime is broken up into a foliation of spacelike hypersurfaces and a prescribed ``flow-of-time''. A previously constructed phenomenological model for the resistivity is updated to include the modified heat flow and the presence of a neutrally charged species. We impose baryon number and charge conservation as well as the Second Law of Thermodynamics in order to constrain the number of free parameters in the resistivity. Finally, we take the Newtonian limit of the ``$3 + 1$'' form of the field equations which can be compared to existing non-relativistic formulations. Applications include main sequence stars, neutron star interiors, accretion disks, and the early universe.

Superscaling in electron scattering from nuclei is re-examined paying special attention to the definition of the averaged single-nucleon responses. The validity of the extrapolation of nucleon responses in the Fermi gas has been examined, which previously lacked a theoretical foundation. To address this issue, we introduce new averaged responses with a momentum distribution smeared around the Fermi surface, allowing for momenta above the Fermi momentum. This approach solves the problem of negativity in the extrapolation away from the scaling region and, at the same time, validates its use in the scaling analysis. This work has important implications for the interpretation of scaling data and contributes to the development of a more complete understanding of the scaling approach.

A cloud of relativistic material particles is considered, for which the distortions of length and time caused by the presence of the Lorentz factor an order of magnitude greater than curvature of space-time by gravity. The gravitational mass of the cloud is found in the region where its size is insignificant. It is established that the coefficient of dependence of the cloud mass on the total rest mass of its particles includes a complete elliptic integral of the 2nd kind.

The nonlocality of entangled quantum mechanical systems is incompatible with the standard interpretation of special relativity as a single 4D Minkowskian metric spacetime. The difficulty is that the definition of a spacetime interval between any pair of events precludes any form of nonlocal interaction, even the relatively benign non-signaling correlations. By an application of the relativity principle, and the use of the space ←→ time symmetry of the Lorentz boost I propose here a reinterpretation of special relativistic spacetime. This new ontology consists of a set of coexisting 3+1D spaces (‘framespaces’), each containing unique content in the form of a complex density. These spaces are related by the Lorentz boost, and coupled pairwise in a manner dictated by the Lorentz transformation. The inter-space coupling acting on the spacetime content gives rise to a nonlocal wave phenomenon, which is identified as quantum wave mechanics. The interspace coupling strength is then inversely proportional to Planck’s constant. The coexistence of multiple spaces is interpreted as momentum superposition, implying that momentum is the fundamental physical basis of quantum superposition. This new spacetime interpretation of quantum mechanics has many consequences, including explanations of quantum non-locality, the spacetime role of Planck’s constant, quantum measurement as a symmetry-breaking process and the redundancy of description of gauge theory.

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially we develop a binary data matrix to record variables' values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle oriented coordinate and generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar field in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of cumulative probability function defined on Riemannian manifold also gives the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and gives the formal definition of joint probabilities by partial derivatives of cumulative distribution function. The equivalence between symmetrized covariant derivative and generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

The evolution of even and odd Schrödinger cat states of the inverted oscillator is obtained in the center-of-mass tomographic probability description of the two-mode oscillator.The notion of entangled probability distribution is reviewed. Evolution equations describing the time-dependence of probability distributions identified with quantum system states are discussed.The connection with the Schrödinger equation and the von Neumann equation is clarified.

This article analyzes 6 probability distributions from the Generalized Pareto family, with 3, 4 and 5 parameters, with main purpose to identify other distributions from this family with applicability in flood frequency analysis compared to the distribution already used in the literature from this family such as Generalized Pareto Type II and Wakeby. This analysis is part of a larger and more complex research carried out in the Faculty of Hydrotechnics regarding the elaboration of a norm for flood frequency analysis using the linear moments method. In Romania, the standard method of parameter estimation is the method of ordinary moments, thus the transition from this method to the method of linear moments is desired. All the necessary elements for the distributions use are presented like, the probability density functions, the complementary cumulative distribution functions, the quantile functions, the exact and approximate relations for estimating parameters, for both methods of parameters estimation. All these elements are necessary for a proper transition between the two methods, especially since the use of the method of ordinary moments is done by choosing the skewness of the observed data depending on the origin of the maximum flows. A flood frequency analysis case study, using annual maximum and annual exceedance series, was carried out for the Prigor river, to numerically present the analyzed distributions. The performance of this distributions is evaluated using relative mean error, relative absolute error and linear moments diagram.

Most existing flexible count regression models allow only approximate inference. This work proposes a new framework to provide an exact and flexible alternative for modeling and simulating count data with various types of dispersion (equi-, under- and overdispersion). The new method, referred as “balanced discretization”, consists in discretizing continuous probability distributions while preserving expectations. It is easy to generate pseudo random variates from the resulting balanced discrete distribution since it has a simple stochastic representation in terms of the continuous distribution. For illustrative purposes, we have developed the family of balanced discrete gamma distributions which can model equi-, under- and overdispersed count data. This family of count distributions is appropriate for building flexible count regressionmodels because the expectation of the distribution has a simple expression in terms of the parameters of the distribution. Using the Jensen–Shannon divergence measure, we have shown that under equidispersion restriction, the family of balanced discrete gamma distributions is similar to the Poisson distribution. Based on this, we conjecture that while covering all types of dispersion, a count regression model based on the balanced discrete gamma distribution will allow recovering a near Poisson distribution model fit when the data is Poisson distributed.

In this article we explore the limiting behavior of the universal prior distribution obtained when applied over multiple meta-level hierarchy of programs and output data of a computational automata model. We were motivated to alleviate the effect of Solomonoff's assumption that all computable functions or hypotheses of the same length are equally likely, by weighing each program in turn by the algorithmic probability of their description number encoding. In the limiting case, the set of all possible program strings of a fixed-length converges to a distribution of self-replicating quines and quine-relays - having the structure of a constructor. We discuss how experimental algorithmic information theory provides insights towards understanding the fundamental metrics proposed in this work and reflect on the significance of these result in digital physics and the constructor theory of life.

We delve into nonrelativistic quantum electrodynamics within a background magnetic field, ensuring gauge invariance via a vector potential. Our exploration extends to the Lagrangian, which incorporates electron self-interactions and electromagnetic field interactions. Through the path integral formalism, we elucidate the effective action, with a specific focus on the photon propagator and screening effects. Examining density and current components reveals Laurent expansions in the hydrodynamic limit. The equations of motion in real space are derived, leading to discussions on phenomena such as Poiseuille-like flow and the Navier-Stokes equation. To ground our theoretical framework at practical contexts, we consider applications such as the fluid dynamics at binary star systems. Depending on the velocity of the expelled fluid, our analysis allows for both nonrelativistic and relativistic treatments, providing a versatile tool for understanding the intricacies of fluid behavior at astrophysical scenarios. Additionally, we recognize that at the presence of a magnetic field, magnetohydrodynamics becomes crucial. While our current focus is at nonrelativistic quantum electrodynamics, the insights gained here contribute to a broader understanding, offering a comprehensive foundation for quantum electrodynamics analysis at diverse physical systems.

The current letter complements my info-geometric discoveries, especially those provided from two papers of mine. Fundamentally, the statistical relativization of the Generalized Brownian Motion Manifold. Following this innovative and unprecedented track of research will open a plethora of numerous info-geometric investigations to many unexplored related phenomena in the hope to uncover more new interpretations for the Generalized Brownian Motion Manifold from an info-geometric perspective.

The G2 gas cloud motion data and the scarcity of observations on the event horizon-scale distances have challenged the comprehensiveness of the central supermassive black hole model. In addition, the Planck Legacy 2018 release has preferred a positively curved early Universe with a confidence level higher than 99%. This study investigates the impact of the background curvature and its evolution over the conformal time on the formation and morphological evolution of central compact objects and the consequent effect on their host galaxies. The formation of a galaxy from the collapse of a supermassive gas cloud in the early Universe is modeled based on interaction field equations as a 4D relativistic cloud-world that flows and spins through a 4D conformal bulk of a primordial positive curvature considering the preference of the Planck release. Owing to the curved background, this scenario of galaxy formation reveals that the core of the galaxy undergoes a forced vortex formation with a central event horizon leading to opposite vortices (traversable wormholes) that spatially shrink while evolving in the conformal time. It indicates that the galaxy and its core are formed in the same process whereas the surrounding gas clouds form the spiral arms due to the frame-dragging induced by the fast-rotating core. It demonstrates that the accretion flow onto the central supermassive compact object only occurs at the central event horizon of the two opposite vortices while their other ends eject the relativistic jets. This can elucidate the relativistic jet formation and explain the G2 gas cloud motion if its orbit is around one of the vortices but at a distance from the central event horizon. The gravitational potential of the early curved bulk could contribute to galaxy formation while the present spatial flatness deprives the potential of bulk which could lead to galaxy quenching. The formation of a galaxy and its core simultaneously could explain the growth of the supermassive compact galaxy core to a mass of ~10⁹ M_⊙ at just 6% of the current Universe age.

Neuronal timing is critical for many brain functions such as perception and learning. At the level of the chemical synapse, the synaptic delay is determined by the presynaptic release probability (Pr) and the waveform of the presynaptic action potential (AP). Depolarization-induced analogue-digital facilitation (d-ADF) is a form of context-dependent synaptic facilitation that is induced by constant depolarization of the presynaptic neuron and is mediated by voltage inactivation of presynaptic Kv1 channels. Whether synaptic delay is modulated during d-ADF remains unclear. We show here that despite Pr is elevated during d-ADF at L5-L5 synapses, the synaptic delay is surprisingly unchanged, suggesting that both Pr- and AP-dependent changes in synaptic delay compensate for each other. We conclude that in contrast with other short- or long-term modulation of presynaptic release, timing is not affected during d-ADF because of the opposite interaction of Pr- and AP-dependent modulations of synaptic delay.

Understanding swash zone dynamics is of crucial importance for coastal management as the swash motion, consisting of the uprush of the wave on the beach face and the subsequent downrush, is responsible for driving changes the beach morphology trough sediment exchanges between the sub-aerial and sub-aqueous beach. Improved understanding of the probabilistic characteristics of these motions has the potential to allow coastal engineers to develop improved sediment transport models which, in turn, can be further developed into coastal management tools. In this paper, novel descriptors of swash motions are obtained by combining field data and statistical modelling. Our results indicate that the probability distribution function (PDF) of shoreline height (p(ζ)) and trough-to-peak swash heights (p(ρ)) measured at a high energy, sandy beach were both inherently multimodal. Based on the observed multimodality of these PDFs, Gaussian Mixtures are shown to be the best method to statistically model them. Further, our results show that both offshore and surf zone dynamics are responsible for driving swash zone dynamics, which indicates unsaturated swash. The novel methods and results developed in this paper, both data collection and analysis, could aid coastal managers to develop improved swash zone models in the future.

We study the problem of a spherically-symmetric distribution of a perfect relativistic fluid accreting onto a (potentially spinning) black hole within a fully discrete spacetime setting. This problem has previously been studied extensively in the context of continuum spacetimes, beginning with the purely analytic work of Bondi in the spherically-symmetric Newtonian case, Michel in the spherically-symmetric general relativistic case, and Petrich, Shapiro and Teukolsky in the axially-symmetric general relativistic case relevant for spinning black holes. However, the purpose of the present work is to determine the effect of discretization of the underlying spacetime upon the mass/energy and momentum accretion rates, the overall morphology and characteristics of the accretion flow, and the drag force exerted on the black hole in the case of non-zero spin. In order to achieve this, we first develop a novel formulation of the equations of general relativistic hydrodynamics that is more directly amenable to rigorous analysis within a discrete spacetime setting, and we then proceed to implement this formulation into the \textsc{Gravitas} computational general relativity framework. Through a combination of mathematical analysis and explicit numerical simulation in \textsc{Gravitas}, we discover that the mass/energy and momentum accretion rates both decrease monotonically as functions of the underlying spacetime discretization scale, with this effect becoming more pronounced for higher values of the black hole spin parameter, higher fluid temperatures, and stiffer equation of state parameters. We also find that the exerted drag force is highly sensitive to the value of the underlying discretization scale in the case of spinning black hole spacetimes, with certain instabilities becoming significantly more pronounced at certain critical values of the discretization parameter. We discuss some potentially observable consequences of these results, as well as some directions for future theoretical investigation.

On a rotating disk, two particles bounce at the vertices of a regular polygon in opposite directions. On the return to the entry point, a clock measures the time difference, called Sagnac effect. Due to Coriolis effects, the counterclockwise and clockwise paths are different. The particular case of the slow disk where the two trajectories are very close and almost polygonal is studied. The existence of a transition between a classical and a relativistic regime is proved. An experimental verification is proposed. Although the two Sagnac effects seem analogous, in detail their behavior is quite different.

This paper attempts to describe the large-scale (solar system-like, astronomical-scale) systems of the known world using the physical models and mathematical tools of relativistic quantum mechanics. The value of H_x can be introduced and approximated as an analogue of the constant ℏ. Based on the quantum mechanical approach, the proper time scale of the solar system can be determined.

The transport and entanglement of photons is becoming prominent in optics applied to information and quantum computing, where the angular momentum of light stands out in the exchange and inversion of quantized states, with prospects for several technological applications, such as the transport and storage of quantum information. In order to contribute to the understanding of quantized states in photon-matter interaction, we describe a quantized state equation in multidimensional Hilbert space for the diagnosis of OAM states, where probabilities arise in a relativistic setting. It was found that the classical-relativistic variability of the probabilities constitutes a resultant capable of describing the quantized states of light, where the state variable is the variation of the angular momentum of the photon, capable of estimating the orbital angular momentum inversion points at angular incidence. It was found that the chances of finding the quantized states of light at angular incidence can be treated by purely relativistic probabilities, explaining that when both states have equal chances of being found and the angular momentum variation is zero, the source-observer synchronizations occur at the step of increasing relativistic regime of the photon dynamics. We found that the relativistic effect from the perspective of the source referential is able to alter the chances of an event occurring, dilating and contracting the probabilities of finding a quantized state of light at angular incidence.

Using a simple model for internal heat evolution and mass-internal heat relations found for rocky exo planetary objects in the inner solar system we have inferred the phases of volcanism at earth ( EA) or host star ages (SA) in 52 potentially habitable rocky exo planets. We have also calculated the internal tidal heat contributions and magnetic moments of these exo planets. Based on these results we have inferred the probability of existence of life favouring geophysical conditions in the above exo planets at EA and SA. In M star associated exo planets, occurrences of super flares and long night periods may pose problems for the development of advanced life

An exhaustive list of thirteen instances of reports confirming experimentally the relativistic Doppler relation, are examined. For those involving longitudinal Doppler, the non-relativistic relation is seen to be confirmed, within the reported experimental accuracies, to the same degree as the standard relativistic relation. Higher values of the speed of the emitter would be required to examine further the claimed confirmations. For those reports involving saturation spectroscopy, there is much confusion over the appropriate Doppler relation to be used, together with some serious analytical flaws. For the two cases that involve transverse Doppler, there are seen to be either serious faults in the theoretical part, or intrusion from the first order effect. Therefore, the reported conclusions - that the results for the experiments confirm the relativistic SR relation - cannot be justified by any of the experimental works.

Formulating a relativistic equation for particles with arbitrary spin remains an open challenge in theoretical physics. In this study, the main algebraic approaches used to generalize the Dirac and Kemmer–Duffin equations for particles of arbitrary spin are investigated. It is proved that an irreducible relativistic equation formulated using spin matrices satisfying the commutation relations of the de Sitter group leads to inconsistent results, mainly as a consequence of violation of unitarity and the appearance of a mass spectrum that does not reflect the physical reality of elementary particles. However, the introduction of subsidiary conditions resolves the problem of unitarity and restores the physical meaning of the mass spectrum. The equations obtained by these approaches are solved and the physical nature of the solutions is discussed.

This study investigates the impact of temperature-induced quantum proton tunneling probability on DNA amplification during polymerase chain reactions (PCR). Using a simulation model based on a Gaussian wavefunction and finite-difference time-domain method, quantum tunneling of protons across square potential barriers is examined. The results unveil consistent probability distributions for quantum tunneling across various PCR temperatures, with distinct oscillation patterns emerging post-barrier crossing. Acknowledging limitations in initial conditions due to temperature-dependent proton energy, the study highlights the need for refined models and experimental validation. These findings accentuate the potential interplay between quantum mechanics and biological systems, prompting further research to understand quantum tunnelling’s comprehensive effect on genetic variations and molecular processes.

The interaction between oceanographic, meteorological, and hydrological factors can result in an extreme flooding scenario in the low-lying coastal area, called compound flooding (CF) events. For instance, rainfall and storm surge (or high river discharge) can be driven by the same meteorological, tropical or extra-tropical cyclones, resulting in a CF phenomenon. The trivariate distributional framework can significantly explain compound events' statistical behaviour reducing the associated high-impact flood risk. Resolving heterogenous dependency of the multidimensional CF events by incorporating traditional 3-D symmetric or fully nested Archimedean copula is quite complex. The main challenge is to preserve all lower-level dependencies. An approach based on decomposing the full multivariate density into simple local building blocks via conditional independence called vine or pair-copulas is a much more comprehensive way of approximating the trivariate flood dependence structure. In this study, a parametric vine copula of a drawable (D-vine) structure is introduced in the trivariate modelling of flooding events with 46 years of observations of the west Coast of Canada. This trivariate framework searches dependency by combining the joint impact of annual maximum 24-hr rainfall and the highest storm surge and river discharge observed within the time ±1 day of the highest rainfall event. The D-vine structures are constructed in three alternative ways by permutation of the conditioning variables. The most appropriate D-vine structure is selected using the fitness test statistics and estimating trivariate joint and conditional joint return periods. The investigation confirms that the D-vine copula can effectively define the compound phenomenon's dependency. The failure probability (FP) method is also adopted in assessing the trivariate hydrologic risk. It is observed that hydrologic events defined in the trivariate case produce higher FP than in the bivariate (or univariate) case. It is also concluded that hydrologic risk increases (i) with an increase in the service design life of the hydraulic facilities and (ii) with a decrease in return periods.

Both macro and microprojectiles (e.g., interplanetary, interstellar and even intergalactic material) are seen as important vehicles for the exchange of potential (bio)material within our solar system as well as between stellar systems in our Galaxy. Accordingly, this requires estimates of the impact probabilities for different source populations of projectiles, including for intergalactic meteor particles which have received relatively little attention since considered as rare events (discrete occurrences that are statistically improbable due to their very infrequent appearance). We employ the simple but comprehensive model of intergalactic microprojectile capture by the gravity of exoplanets which enables us to estimate the map of collisional probabilities for an available sample of exoplanets in habitable zones around host stars. The model includes a dynamical description of the capture adopted from Mautner model of interstellar exchange of microparticles and changed for our purposes. We use statistical and information metrics to calculate probability map of intergalactic meteorite particle capture. Moreover, by calculating the entropy index map we estimate the concentration of these rare events. We further adopted a model from immigration theory, to show that the time dependent distribution of single molecule immigration of material indicates high survivability of the immigrated material taking into account birth and death processes on our planet. At present immigration of material can not be observationally constrained but it seems reasonable to think that it will be possible in the near future, and to use it along other proposed parameters for life sustainability on some planet.

This paper introduces an approach that chooses the fault detection by calculating probabilities using probability mass function (pmf) and cumulative distribution function (CDF). This work used a method for multiple stuck-at faults by producing a new test pattern in combinational circuits. We assumed that existence of all multiple faults is only because of one single component that is faulty. A complete test set can be created by all possible single stuck-at faults in a combinational circuit using some combination of gates. The test set generation fault detection method is applied on two different 3-bit input variable and 4-bit input variable circuits. The probability of error occurrence is calculated at both 3-bit and 4-bit input variable circuits. The resulting feature is used to obtain maximum error occurrence probability to detect faults by the logic used that the complexity of the circuit is inversely proportional to the fault occurrence probability. Then again, undetectability is directly proportional to the complexity of the circuit. Therefore, finest feasible circuit should have large input variable components with less complexity to reduce the fault occurrence probability.

Cartels cause tremendous damage to the market economy and disadvantage consumers by causing higher prices and lower quality; moreover, they are difficult to detect. We need to prevent them by scientific analysis, which includes the determination of an indicator to explain antitrust enforcement. Particularly, the probability of cartel penalization is a useful indicator for the evaluation of the competition enforcement. This study is to estimate the probability of cartel penalization by using a Bayesian approach. In the empirical study, the probability of cartel penalization is estimated by Bayesian approach from cartel data of Department of Justice in United States from 1970 to 2009. The probability of cartel penalization is seen to be sensitive to change of competition law and the results shows the usefulness of higher interpretation than other research. The result of the policy simulation shows how effective the leniency program is. From this estimation, antitrust enforcement is evaluated, and thereby, can be improved.

The probability distribution of the interevent time between two successive earthquakes has been subject of numerous studies due to its key role in seismic hazard assessment. In recent decades, many distributions have been considered and there has been a long debate about the possible universality of the shape of this distribution when the interevent times are suitably rescaled. In this work we aim to find out if there is a link between the different phases of a seismic cycle and the variations in the distribution that best fits the interevent times. To do this, we consider the seismic activity related to the Mw 6.1 L’Aquila earthquake that occurred on April 6, 2009 in central Italy by analyzing the sequence of events recorded from April 2005 to July 2009, and then the seismic activity linked to the sequence of the Amatrice-Norcia earthquakes of Mw 6 and 6.5 respectively and recorded in the period from January 2009 to June 2018. We take into account some of the most studied distributions in the literature: q-exponential, q-generalized gamma, gamma and exponential distributions and, according to the Bayesian paradigm, we compare the value of their posterior marginal likelihood in shifting time windows with a fixed number of data. The results suggest that the distribution providing the best performance changes over time and its variations may be associated with different phases of the seismic crisis.

6G is already being planned and will employ much higher frequencies, leading to a revolutionary era in communication between people as well as things. It is well known that weather, especially rain, can cause increased attenuation of signal transmission for higher frequencies. The standard methods for evaluating the effect of rain on symbol error rate are based on long-term averaging. These methods are an inaccurate, which results with an inefficient system design. This is critical regarding bandwidth scarcity and energy consumption and requires a more significant margin of effort to cope with the imprecision. Recently we have developed a new and more precise method for calculating communication system performance in case of rain, using the probability density function of rain rate. For high rain rate (above 10mm/hr), for a typical set of parameters, our method shows the symbol error rate in this range to be higher by orders of magnitude than that found by ITU standard methods. Our model also indicates that sensing and measuring the rain rate probability is important in order to provide the required bit error rate to the users. To the best knowledge of the authors, this novel analysis is unique. It can constitute a more effi-cient performance metric for the new era of 6G communication and prevent disruption due to incorrect system design. Keywords: atmospheric propagation, communication system performance, attenuation, com-munication

The Process Algebra model has been shown to provide an alternative mathematical framework for non-relativistic quantum mechanics (NRQM). It reproduces the wave functions of non-relativistic quantum mechanics to a high degree of accuracy. It posits a fundamental level of finite, discrete events upon which the usual entities of NRQM supervene. It has been suggested that the Process Algebra model provides a true completion of NRQM, free of divergences and paradoxes, with causally local information propagation, contextuality and realism. Arguments in support of these claims have been mathematical. Missing has been an ontology of this fundamental level from which the formalism naturally emerges. In this paper it is argued that information and information flow provides this ontology. Higher level constructs such as energy, momentum, mass, spacetime, are all emergent from this fundamental level.

This paper investigates the problem of a relativistic Dirac half-integer spin free particle tunneling through a rectangular quantum-mechanical barrier. If the energy difference between the barrier and the particle is positive, and the barrier width is large enough, there is proof that the tunneling may be superluminal. For first spinor components of particle and antiparticle states, the tunneling is always superluminal regardless the barrier width. Conversely, the second spinor components of particle and antiparticle states may be either subluminal or superluminal depending on the barrier width. These results derive from studying the tunneling time in terms of phase time. For the first spinor components of particle and antiparticle states, it is always negative while for the second spinor components of particle and antiparticle states, it is always positive, whatever the height and width of the barrier. In total, the tunneling time always remains positive for particle states while it becomes negative for antiparticle ones. Furthermore, the phase time tends to zero, increasing the potential barrier both for particle and antiparticle states. This agrees with the interpretation of quantum tunneling that the Heisenberg uncertainty principle provides. This study’s results are innovative with respect to those available in the literature. Moreover, they show that the superluminal behaviour of particles occurs in those processes with high-energy confinement.