The free energy principle (FEP) is a mathematical and scientific principle that describes the relationship between the physical behavior of a dynamical system and the interpretation of such behavior as carrying out inference. It blurs the boundary between the ontological mode of the system of interest and the epistemological significance it acquires through its dynamic interaction with the environment. New materialism (or neo-materialism), despite lacking a single definition, refers to a range of emerging perspectives that attempt to dismantle the long-held divisions between ontology, epistemology, and even ethics, with the aim of achieving a comprehensive transformation of naturalized thinking. In this context, new materialism provides powerful tools to reframe some of the conceptual foundations of the FEP. This paper is the first in a series that aims to systematically construct a neo-materialistic perspective for the FEP, exploring its wide-ranging implications. It serves as an introduction to the series, arguing for the justification of deploying new materialism to reframe the FEP and introducing some essential concepts to be utilized in developing a neo-materialistic account of the FEP.

It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Although quantum mechanics correctly predicts what it is possible to observe (the emissions) it ignores the other half of natural phenomena, what cannot be observed (the absorptions), thereby violating the conservation laws. By describing only one-half of radiation processes conceptual difficulties such as wave function collapse, infinite paths, and inscrutable mathematics seem to be insoluble mysteries. The deficiencies are corrected by introducing Hamilton’s principle S = ∫ Ldt and applying the methods of quantum field theory to derive relativistic equations of motion. The calculus of variations is used to show that the wave function represents an incomplete equation of motion because it equals twice the allowable action minimum.

The meaning and evolution of the notion of “temperature” (which is a key concept for the condensed and gaseous matter theories) is addressed from the different points of view. The concept of temperature turns out to be much more fundamental than it is conventionally thought. In particular, the temperature may be introduced for the systems built of “small” number of particles and particles in rest. The Kelvin temperature scale may be introduced into the quantum and relativistic physics due to the fact, that the efficiency of the quantum and relativistic Carnot cycles coincides with that of the classical one. The relation of the temperature to the metrics of the configurational space describing the behavior of system built from non-interacting particles is demonstrated. The Landauer principle asserts that the temperature of the system is the only physical value defining the energy cost of isothermal erasing of the single bit of information. The role of the temperature the cosmic microwave background in the modern cosmology is discussed.

Experimental recordings of the collective activity of interacting spiking neurons exhibit random behavior and memory effects, thus the stochastic process modeling the spiking activity is expected to show some degree of time irreversibility. We use the thermodynamic formalism to build a framework, in the context of spike train statistics, to quantify the degree of irreversibility of any parametric maximum entropy measure under arbitrary constraints, and provide an explicit formula for the information entropy production of the inferred Markov maximum entropy process. We provide examples to illustrate our results and discuss the importance of time irreversibility for modeling the spike train statistics.

Confidence interval of is an interval corresponding to a specified confidence and including the true value. It can be used to describe the precision of a statistical quantity and quantify its uncertainty. Although the principle of maximum entropy (POME) has been used for a variety of applications in hydrology, the confidence intervals of the POME quantile estimators have not been available. In this study, the calculation formulas of asymptotic variances and confidence intervals of quantiles based on POME for Gamma, Pearson type 3 (P3) and Extreme value type 1 (EV1) distributions were derived. Monte Carlo Simulation experiments were performed to evaluate the performance of derived formulas for finite samples. Using four data sets for annual precipitation at the Weihe River basin in China, the derived formulas were applied for calculating the variances and confidence intervals of precipitation quantiles for different return periods and the results were compared with those of the methods of moments (MOM) and of maximum likelihood (ML) method. It is shown that POME yields the smallest standard errors and the narrowest confidence intervals of quantile estimators among the three methods, and can reduce the uncertainty of quantile estimators

We propose a notion of a ternary skew-symmetric covariant tensor of 3rd order, consider it as a 3-dimensional matrix and study a ten-dimensional complex space of these tensors. We split this space into a direct sum of two five-dimensional subspaces and in each subspace there is an irreducible representation of the rotation group SO(3)↪SO(5). We find two independent SO(3)-invariants of ternary skew-symmetric tensors, where one of them is the Hermitian metric and the other is the quadratic form. We find the stabilizer of this quadratic form and its invariant properties. Making use of these invariant properties we define a SO(3)-irreducible geometric structure on a five-dimensional complex Hermitian manifold. We study a connection on a five-dimensional complex Hermitian manifold with a SO(3)-irreducible geometric structure, find its curvature and torsion. The structures proposed in this paper and their study are motivated by a ternary generalization of the Pauli’s principle proposed by R. Kerner.

In this paper, we relate Poisson’s summation formula to Heisenberg’s uncertainty principle. They both express Fourier dualities within the space of tempered distributions and these dualities are furthermore the inverses of one another. While Poisson’s summation formula expresses a duality between discretization and periodization, Heisenberg’s uncertainty principle expresses a duality between regularization and localization. We define regularization and localization on generalized functions and show that the Fourier transform of regular functions are local functions and, vice versa, the Fourier transform of local functions are regular functions.

We take a heterodox approach to the ΛFRW Cosmology starting from the modification of Newtonian gravity by explicitly incorporating Mach's Principle through an additional term a great scale in the gravitation. The results show that at the after of the matter-radiation decoupling, the distribution of matter at scales greater than 10Mpc contributes with an inverse Yukawa-like field, which verifies the observations: resulting null in the inner solar system, weakly attractive in ranges of interstellar comoving distances, very attractive in comoving distance ranges comparable to the clusters of galaxies, and repulsive in cosmic scales. This additional term explains dark energy, removes the incompatibility between the density of matter and the flatness of the universe; and also allows the theoretical deduction of the Hubble-Lemaitre Law. Additionally, Birkhoff Theorem, Virial Theorem, the missing mass of Zwicky, the BAO, gravitational redshift are discussed. It is concluded that the dark energy and the missing mass can be approached with the usual physics if a classical, large-scale modification of the Inverse Square Law.

An overview of the link between nonequilibrium thermodynamics and complexity theory is offered. It is shown how the rate of entropy production can be quantified through the spectrum of the Lyapunov exponents. It was shown how the entropy production per unit of time meets the necessary and sufficient conditions to be a Lyapunov function and constitutes per se an extremal principle. The entropy production fractal dimension conjecture was established. It is shown how the rate of entropy production as a non-extremal criterion represents an alternative way of sensitivity analysis of differential equations. Finally, an extension to biophysical-chemical systems, on the one hand, the use of the dissipation function is shown, as a thermodynamic potential out of equilibrium, in the characterization of biological phase transitions. On the other hand, it was evidenced how the rate of entropy production represents a physical quantity to evaluate the complexity and robustness of cancer.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

The relationship of the animal with its environment has been of longstanding interest in philosophy and science. Here I provide a brief introduction to concepts that place an emphasis on mutualism as the basis of organism - environment interaction, in contrast to the long standing view that the environment exerts an instrumental role in shaping the organism. Two influential theories have been von Uexküll’s theory of umwelt and Gibson’s theory of affordances. The former envisioned the animal as immersed in its surroundings (umwelt) to form a functional unit. In a similar manner, the latter theory describes a unity between 1) environmental information that provides the animal with opportunities for action (affordances) and 2) the ability of the animal to perceive and engage with those affordances. These views have influenced more recent ecological models of the organism as the functional unit of biology and have also influenced models of immune function. In ecological models, agency is seen as the ability of the organism to predict and control its engagement with the environment in order to maintain its integrity. The predominant contemporary model of neural function in which perception and action are understood to operate through Bayes-like active inference complements the concept of agency as proposed by the mutualism models. However, it is suggested that rather than a constant mutualism, encounters between organism and environment range over a dynamic spectrum from dualism to mutualism. It is also suggested that along this spectrum, agency emerges when the balance of instrumentality shifts from the environment to the organism, and that the balance of this relationship can further progress towards a felicitous mutualism. Meaning emerges between environmental information and an agent as opportunity for action. Implications for opportunities to foster agency in animals within our care is noted.

An exact solution is obtained for the kinetic energy in the general case of the spatial motion of solids with arbitrary rotation, which differs from the Koenig formula by three additional terms with centrifugal moments of inertia. The description of motion in the Lagrange form and the superposition principle are used, which provides a geometric summation of the velocities and accelerations of the joint motions in the Lagrange form for any particle at any time. The integrand function in the equation for kinetic energy is represented by the sum of the identical velocity components of the joint plane-parallel motions. The moments of inertia in the Koenig formula do not change during movement and can be calculated from the current or initial state of the body. The centrifugal moments change and turn to 0 when rotating relative to the main central axes only for bodies with equal main moments of inertia, for example, for a ball. In other cases, the difference in the main moments of inertia leads to cyclic changes in the kinetic energy with the possible manifestation of precession and nutation, the amplitude of which depends on the angular velocities of rotation of the body. An example of using equations for a robot with one helical and two rotational kinematic pairs is given.

In the present paper, based on the ideas of Algerian physicist M.E. Hassani, the generalized Hassani spatio-temporal transformations in real Hilbert space are introduced. The original transformations, introduced by M.E. Hassani, are the particular cases of the transformations, introduced in this paper. It is proven that the classes of generalized Hassani transforms do not form a group of operators in the general case. Further, using these generalized Hassani transformations as well as the theory of changeable sets and universal kinematics, the mathematically strict models of Hassani kinematics are constructed and the performance of the relativity principle in these models is discussed.

In this paper, we will revisit the derivation of Heisenberg's uncertainty principle. We will see how the Heisenberg principle collapses at the Planck scale by introducing a minor modification. The beauty of our suggested modification is that it does not change the main equations in quantum mechanics; it only gives them a Planck scale limit where uncertainty collapses. We suspect that Einstein could have been right after all, when he stated, ``God does not throw dice." His now-famous saying was an expression of his skepticism towards the concept that quantum randomness could be the ruling force, even at the deepest levels of reality. Here we will explore the quantum realm with a fresh perspective, by re-deriving the Heisenberg principle in relation to the Planck scale. We will show how this idea also leads to an upper boundary on uncertainty, in addition to the lower boundary. These upper and lower boundaries are identical for the Planck mass particle; in fact, they are zero, and this highlights the truly unique nature of the Planck mass particle. Further, there may be a close connection between light and the Planck mass particle: In our model, the standard relativistic energy momentum relation also seems to apply to light, while in modern physics light generally stands outside the standard relativistic momentum energy relation. We will also suggest a new way to look at elementary particles, where mass and time are closely related, consistent with some of the recent work in experimental physics. Our model leads to a new time operator that does not appear to be in conflict with the Pauli objection. This indicates that both mass and momentum come in quanta, which are perfectly correlated to an internal Compton `clock' frequency in elementary particles.

Central to an understanding of the physical nature of biosystems is an apprehension of their ability to control entropy dynamics in their environment.  To achieve ongoing stability and survival, living systems must adaptively respond to incoming information signals concerning matter and energy perturbations in their biological continuum (biocontinuum).  Entropy dynamics for the living system are then determined by the natural drive for reconciliation of these information divergences in the context of the constraints formed by the geometry of the biocontinuum information space.  The configuration of this information geometry is determined by the inherent biological structure, processes and adaptive controls that are necessary for the stable functioning of the organism.  The trajectory of this adaptive reconciliation process can be described by an information-theoretic formulation of the living system’s procedure for actionable knowledge acquisition that incorporates the axiomatic inference of the Kullback Principle of Minimum Information Discrimination (a derivative of Jaynes’ principle of maximal entropy). Utilizing relative information for entropic inference provides for the incorporation of a background of the adaptive constraints in biosystems within the operations of Fisher biologic replicator dynamics.  This mathematical expression for entropic dynamics within the biocontinuum may then serve as a theoretical framework for the general analysis of biological phenomena.

The paper is concerned with a class of stochastic differential equations in infinite dimensional Hilbert space with random coefficients driven by Teugel's martingales which are more general processes. and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with L\'{e}vy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classicconvex variation method and dual technique.The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum - not taken into account by Fourier theory and let alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: a) compact support with excellent energy output treatment, b) low computational cost, O(N) for signals and O(N2) for images, c) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.

For the better part of a century researchers across disciplines have sought to explain the crystallography of the elemental transition metals: hexagonal close packed, body centered cubic, and face centered cubic in a form similar to that used to rationalize the structure of organic molecules and inorganic complexes. Pauling himself tried with limited success to address the origins of transition metal stability. These early investigators were handicapped, however, by incomplete knowledge regarding the structure of metallic charge density. Here we exploit modern approaches to charge analysis to first comprehensively describe transition metal charge density. Then, we use topological partitioning and quantum mechanically rigorous treatments of kinetic energy to account for the structure of the density as arising from the interactions between metallic tetrahedra. We argue that the crystallography of the early transition metals results from charge transfer from the so called “octahedral” to “tetrahedral holes” while the face centered cubic structure of the late transition metals is a consequence of antibonding interactions that increase octahedral hole kinetic energy.

This paper presents three types of tensor Conjugate-Gradient methods for solving large-scale linear discrete ill-posed problems based on the t-product between third-order tensors. An automatical determination strategy of a suitable regularization parameter is proposed for the tensor conjugate gradient (tCG) method. A truncated version and a preprocessed verion of the tCG method are further presented. The discrepancy principle is employed to determine a suitable regularization parameter. Several numerical examples are given to show the effectiveness of the proposed tCG methods in image and video restoration.

The Developing Countries Vaccine Manufacturing Network coordinated a multi-laboratory study funded by the US National Institute for Innovation in Manufacturing Biopharmaceuticals to assess the performance of the Pertussis Serological Potency Test (PSPT) in the laboratories of seven whole-cell pertussis vaccine (wP) manufacturers and three National Control Laboratories based in Southeast Asian countries. To this end, common protocols for the immunization of mice and serological testing by ELISA were shared with all laboratories. Each laboratory used their own wP vaccines and the reference vaccine routinely used in the regulatory required mouse protection test (MPT) and assayed the products both in the MPT and PSPT. Whereas in all laboratories the PSPT showed decreased serum IgG levels after immunization with sub-potent compared to potent final batches, some issues were encountered during execution of the assay, which prevented drawing of definitive conclusions on assay performance. Nevertheless, the study provided the participants with the opportunity to familiarize themselves with the PSPT protocols and revealed the next steps to be addressed for implementation of the method.

The paper deals with one new property of the linear time-optimal control problems with real eigenvalues of the system, no matter of the number of eigenvalue multiplicity. This property unveils a prospective of synthesizing the time-optimal control without the need of describing the switching hyper-surfaces. The already chrestomathy example of the time-optimal control of a double integrator is resolved by the new technique and compared with the classical synthesis.

We show that, as in the case of the principle of minimum action in classical and quantum mechanics, there exists an even more general principle in the very fundamental structure of quantum space-time: This is the principle of minimal group that allows to consistently and simultaneously obtain a natural description of the spacetime dynamics and the physical states admissible in it. The theoretical construction is based on the physical states that are average values of the generators of the Metaplectic group Mp(n) , the double covering of SL(2C) in a vector representation, with respect to the coherent states carrying the spin weight. Our main results here are: (i) There exists a connection between the dynamics given by the Metaplectic group symmetry generators and the physical states (mappings of the generators through bilinear combinations of the basic states). (ii) The ground states are coherent states of the Perelomov-Klauder type defined by the action of the Metaplectic group which divide the Hilbert space into even and odd states mutually orthogonal. They carry a spin weight 1/4 and 3/4 respectively from which, two other basic states can be formed. (iii) The physical states, mapped bilinearly with the basic 1/4 and 3/4 spin weight states, plus their symmetric and antisymmetric combinations, have spin contents s = 0, 1/2, 1, 3/2 and 2. (iv) The generators realized with the bosonic variables of the harmonic oscillator introduce a natural supersymmetry and a superspace whose line element is the geometrical Lagrangian of our model. (v) From the line element as operator level, a coherent physical state of spin 2 can be obtained and naturally related to the metric tensor. (vi) The metric tensor is naturally discretized by taking the discrete series given by the basic states (coherent states) in the n number representation, reaching the classical (continuous) space-time for n going to infinity. (vii) There emerges a relation between the eigenvalue of our coherent state metric solution and the black hole area (entropy) as A_{bh}/4 l_{p}^{2} = I alpha I relating the phase space of the metric found g_{ab} and the black hole area A_{bh} through the Planck length l_{p}^{2} and the eigenvalue I alpha I of the coherent states. As a consequence of the lowest level of the quantum discrete space-time spectrum, eg the ground state associated to n = 0 and its characteristic length, there exists a minimum entropy related to the black hole history.

In this paper we will find that, according to holographic principle {\cite{Holografico}} and thus considering Universe as the ensemble of $\aleph$ information bits or minimum particles of mass $m_{g}$, the contribution to galactic rotation curves can be due the rest of the visible Universe through a non-local collective gravitational interaction of all particles within the Universe's horizon, as a consequence of which all particles are gravitationally entangled and form a unified statistical ensemble. Therefore, we can to describe this global effect in terms of standard local Newtonian gravity within galaxies for the explanation of flatness galactic rotation curves as a possible alternative to the dark matter or MOND hypothesis. We will find a solution for the baryonic Tully-Fischer relation: $M_{b} = A v_{f}^4 \iff A = \left[a_{0}G \right]^{-1}$ with $a_{0} = \frac{cH_{0}}{2\pi}$, where $H_{0}$ is the Hubble constant at present Time $t_{0}$ and $M_{b}$, $G$ and $c$ are the galaxy baryonic mass, gravitational constant and constant speed of light in vacuum respectively. Also we will find the mass discrepancy-acceleration relation, thus obtaining a possible solution for each of the three laws of rotationally supported galaxies proposed in ({\cite{McGaugh}},{\cite{McGaugh1}}).

According to the current understanding, the recently observed accelerated expansion of the universe is caused by the dark or the vacuum energy. Attempts to calculate the magnitude of this energy using the standard model of particle physics led to values which are 59 – 120 orders of magnitude larger than the experimentally estimated one. Even though the expanding space has positive internal energy, in a flat universe it is completely balanced by the negative energy of gravitational field making the net energy equal to zero. However, the current physical theories may breakdown for times less than or on the order of Planck time and one cannot assume that the above assertion concerning the balance of two energies is valid also in this time scale. In this note it is assumed that this balance of the two energies during the creation of new space as the universe expands takes place only for times larger than the Planck time. If this assumption is correct, the net energy of the newly created space remains positive for times on the order of Planck time and the positive vacuum energy has to be burrowed from empty space before it is being balanced by gravity. This can happen only within the restrictions of the time-energy uncertainty principle. In this note it is shown that such considerations lead to a vacuum energy density of about 0.3 Nanojoules per cubic meter which has to be compared with the measured value of 0.6 Nanojoules per cubic meter.

We show that one of the two important uncertainty principles derived by Maccone and Pati \textit{[Phys. Rev. Lett., 2014]} can be derived for arbitrary maps defined on subsets of $\mathcal{L}^p$ spaces for $1< p<\infty$. Our main tool is the Clarkson inequalities. We also derive a nonlinear uncertainty principle for weak parallelogram spaces and Type-p Banach spaces.

This paper explores the ethical considerations surrounding the research on echinoderms, a group of invertebrates that has recently garnered attention in the scientific community. We emphasize the importance of responsible animal handling and the need for an ethical framework that encompasses echinoderms. The 3R's principle, advocating for the replacement of conscious living vertebrates with non-sentient material in research, is discussed as a guiding tool in current animal research practices. As invertebrates are generally classified as non-sentient animals, the Replacement dimension tends to favor them as prevalent models in experimental research. While we currently lack the means to assess the mental states of invertebrates, there is undeniable evidence of social behavior in many species, suggesting that a lack of interactions with these organisms could potentially adversely affect their well-being. In the last few years, considerable progress has been made in developing an ethical framework that takes invertebrates into account, particularly cephalopods, crustaceans, and echinoderms. In this context, we discuss the development of a broader conceptual framework of 5R’s that includes Responsibility and Respect, which may guide practices ensuring welfare in echinoderms, even in the absence of any particular normative.

The German Constitutional Court’s climate verdict provides a re-interpretation of liberal- democratic core concepts and is highly relevant for liberal constitutional law in general – including EU and international law. The verdict accepts human rights as intertemporal and globally applicable; it applies the precautionary principle to these rights and frees them from the misleading causality debate. However, the court fails to address the most important violations of human rights, and it categorised climate policy as a greater threat to freedom than climate change. And the court does not make it clear that the Paris 1.5-degree limit implies a radically smaller carbon budget. Furthermore, little attention has so far been paid to the fact that the ruling implies an obligation for more EU climate protection, especially since most emissions are regulated supranationally. To be effective, the EU emissions trading system demands a reform, which should go well beyond the existing EU proposals to enable societal transformation to sustainability.

Our knowledge of physics and chemistry is relatively well defined. Results from that knowledge are predictable as, largely, are those of their technical offspring such as electrical, chemical, me-chanical and civil engineering. By contrast biology is relatively unconstrained and unpredictable. A factor common to all areas is the trade-off, which provides a means of defining and quantifying a problem and, ideally, its solution. In order to understand the anatomy of the trade-off and how to handle it, its development (as the dialectic) is tracked from Hegel and Marx to its implementa-tion as dialectical materialism in Russian philosophy and TRIZ, the Theory of Invention. With the ready availability of mathematical techniques, such as multi-objective analysis and the Pareto set, the trade-off is well-adapted to bridging the gaps between the quantified and the unquantifiable, allowing modelling and the transfer of concepts by analogy. It is thus an ideal tool for biomimet-ics. An intracranial endoscope can be derived with little change from the egg-laying tube of a wood wasp. More complex transfers become available as the technique is developed. Most im-portant, as more trade-offs are analyzed, their results are stored to be used again in the solution of problems. There is no other system in biomimetics which can do this.

Most quantum gravity theories endow space-time with a discreet nature by space quantization on the order of Planck length (lp ). This discreetness could be demonstrated by confirmation of Lorentz invariance violations (LIV) manifested at length scales proportional to lp. In this paper, space-time line elements compatible with the uncertainty principle are calculated for a homogeneous, isotropic expanding Universe represented by the Friedmann-Lemaitre-Robertson-Walker solution to General Relativity (FLRW or FRW metric). To achieve this, the covariant geometric uncertainty principle (GeUP) is applied as a constraint over geodesics in FRW geometries. A generic expression for the quadratic proper space-time line element is derived, proportional to Planck length-squared and dependent on two contributions. The first is associated to the energy-time uncertainty, and the second depends on the Hubble function. The results are in agreement with space-time quantization on the expected length orders, according to quantum gravity theories and experimental constraints on LIV.

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches on it, we show that entropy has a universal stochastic definition which is not disorder. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept and promotes entropy as the mother of creativity and evolution. As social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether the maximum entropy, applied to the distribution of wealth quantified by annual income, can give an objective description. Using publicly available income data, we show that the income distribution is consistent with the principle of the maximum entropy. The increase of entropy is associated to increase of society’s wealth yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in development and increase of the entropy of income. Such findings are contrary to the theories of ecological economics and other theories which use the term entropy in a Malthusian perspective.

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible.

We consider boundary value problems for a nonlinear mass transfer model, which generalizes the classical Boussinesq approximation, under inhomogeneous Dirichlet boundary conditions for the velocity and the substance’s concentration. It is assumed that the leading coefficients of viscosity and diffusion and the buoyancy force in the model equations depend on concentration. We develop mathematical apparatus of studying inhomogeneous boundary value problems under consideration. It is based on using of a weak solution of the boundary value problem and construction of liftings of the inhomogeneous boundary data. They remove the inhomogeneity of the data and reduce original problems to equivalent homogeneous boundary value problems. Based on this apparatus we will prove the theorem of the global existence of a weak solution to boundary value problem under study and establish important properties of the solution. In particular, we will prove the validity of the maximum principle for the substance’s concentration. We will also establish sufficient conditions for the problem data, ensuring the local uniqueness of weak solutions.

Efficient train driving plays a vital role in reducing the overall energy consumption in the railway sector. An energy minimising control strategy can be computed using the framework given by optimal control theory, in particular the Pontryagin maximum principle. Our optimisation approach is based on an algorithm presented by Khmelnitsky that considers electric trains equipped with regenerative braking. A derivation of Khmelnitsky’s theory from a more general formulation of the maximum principle is given in this article, and a complete list of switching cases between different driving regimes has been included that is essential for practical application. A number of numerical examples are added to visualise the various switching cases. Energy consumption data from real-life operation of passenger trains are compared to the calculated energy minimum. In the presented study, the optimised strategy was able to save 37 percent of the average energy demand of the train in operation.

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.

In this paper, we suggest an expansion of the Planck distribution function derived from the Boltzmann principle. Thereby, we consider expanding Planck's law with a new distribution function, and discuss fine structure constant. Furthermore, using ideas applied to the expansion of the Planck distribution function, we show that Von Koch's inequality can be derived without using the Riemann Hypothesis, that is, the Riemann Hypothesis is true, and that the abc conjecture is not true. Furthermore, we define a generalization of Entropy and discuss that Entropy is relevant to dynamical systems described by logistic function models, such as the growth of bacteria and populations.

In this article, the Legendre-Gould Hopper polynomials are combined with Sheffer sequences to introduce certain mixed type special polynomials. Generating functions, differential equations and certain other properties of Legendre-Gould Hopper based Sheffer polynomials are derived. Further, operational and integral representations providing connections between these polynomials and known special polynomials are established. Certain identities and results for some members of these new mixed polynomials are also obtained. Finally, the determinantal definitions of Legendre-Gould Hopper based Sheffer polynomials are also given.

Uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys.\ Lett.\ A\textbf{382}, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

Around early Jurassic some small-sized diurnal reptiles increased the endothermic metabolism and extended their activity to dark time, to fill the void nocturnal niche. Their excellent visual capabilities, acuity, spatial resolution and chromatic discrimination were traded-off for increased sensitivity, useful for the nocturnal dim lit, but they turned defenseless against the dangerous daylight. To avoid blindness -and extinction- they rested in lightproof burrows with closed eyes during daytime. For further security, they developed a bi-stable switch separating nocturnal activity and diurnal rest. This was how the mammalian sleep was born. The development of the cortex, with improved audition and olfaction, compensated the visual impairments. The K-Pg event extinguished the dinosaurs softening the evolutionary pressure for maintaining nocturnal life. The variability in mammalian chronotypes and sleeping patterns increased greatly, but most of the newly developed variations lacked adaptive significance and only quiescence remained invariable. Therefore, quiescence must be the single vital trait of sleep.The Wilson’s Principle of Stringency: “Time-energy budgets evolve to fit to the times of greatest stringency”, explains why wildly gluttonous foraging and ceaseless reproductive activity is non-adaptive. Furtherly, the victims of predation aren’t the sleeping animals, but the immature, sick and senescent ones. Therefore, contrary to current opinion, excessive foraging and reproductive activity is non-adaptive and the claimed disadvantages of sleep are uncertain. Oppositely, quiescence, either resulting from sleep or laziness, is adaptive. We conclude that the vital function of sleep consists in enforcing quiescence in both nocturnal and diurnal mammals.

This work has its origin in intuitive physical and statistical considerations. The problem of optimizing an artificial neural network is treated as a physical system, composed of a conservative vector force field. The derived scalar potential is a measure of the potential energy of the network, a function of the distance between predictions and targets. Starting from some analogies with wave mechanics, the description of the sys-tem is justified with an eigenvalue equation that is a variant of the Schr˜odinger equation, in which the potential is defined by the mutual information between inputs and targets. The weights and parameters of the network, as well as those of the state function, are varied so as to minimize energy, using an equivalent of the variational theorem of wave mechanics. The minimum energy thus obtained implies the principle of minimum mutual information (MinMI). We also propose a definition of the potential work produced by the force field to bring a network from an arbitrary probability distribution to the potential-constrained system, which allows to establish a measure of the complexity of the system. At the end of the discussion we expose a recursive procedure that allows to refine the state function and bypass some initial assumptions, as well as a discussion of some topics in quantum mechanics applied to the formalism, such as the uncertainty principle and the temporal evolution of the system. Results demonstrate how the minimization of energy effectively leads to a decrease in the average error between network predictions and targets.

We introduce and investigate a simple and explicitly mechanical model of Maxwell's demon -- a device that interacts with a memory register (a stream of bits), a thermal reservoir (an ideal gas) and a work reservoir (a mass that can be lifted or lowered). Our device is similar to one that we have briefly described elsewhere [1], but it has the additional feature that it can be programmed to recognize a chosen reference sequence, for instance, the binary representation of $\pi$. If the bits in the memory register match those of the reference sequence, then the device extracts heat from the thermal reservoir and converts it into work to lift a small mass. Conversely, the device can operate as a generalized Landauer's eraser (or copier), harnessing the energy of a dropping mass to write the chosen reference sequence onto the memory register, replacing whatever information may previously have been stored there. Our model can be interpreted either as a machine that autonomously performs a conversion between information and energy, or else as a feedback-controlled device that is operated by an external agent. We derive generalized second laws of thermodynamics for both pictures. We illustrate our model with numerical simulations, as well as analytical calculations in a particular, exactly solvable limit.

Currently, there are two approaches to the foundations of thermodynamics. One, associated with the mechanistical Clausius-Boltzmann tradition, is favored by the physics community. The other, associated with the post-mechanical Carnot tradition, is favored by the engineering community. The bold hypothesis is that the conceptual foundation of engineering thermodynamics is the more comprehensive. Therefore, contrary to the dominant consensus, engineering thermodynamics (ET) represents the true foundation of thermodynamics. The foundational issue is crucial to a number of unresolved current and historical issues in thermodynamic theory and practice. ET formally explains the limited successes of the ‘rational mechanical’ approaches as idealizing special cases. Thermodynamic phenomena are uniquely dissymmetric and can never be completely understood in terms of symmetry-based mechanical concepts. Consequently, ET understands thermodynamic phenomena in new way, in terms of the post-mechanical formulation of action. The ET concept of action and the action framework trace back to Maupertuis’s Principle of Least Action, both clarified in the engineering worldview research program of Lazare and Sadi Carnot. Despite the intervening Lagrangian ‘mechanical idealization of action’, the original dualistic, indeterminate engineering understanding of action, somewhat unexpectedly, re-emerged in Planck’s quantum of action. The link between engineering thermodynamics and quantum theory is not spurious and each of our current formulations helps us develop our understanding of the other. Both the ET and quantum theory understandings of thermodynamic phenomena, as essentially dissymmetric (viz. embracing complementary), entail that there must be an irreducible, cumulative historical, qualitatively emergent, aspect of reality.

This paper addresses the issues of how we can quantify structural information for nonparametric distributions and how we can detect its changes. Structural information refers to an index for a global understanding of a data distribution. When we consider the problem of clustering using a parametric model such as a Gaussian mixture model, the number of mixture components (clusters) can be thought of as structural information in the model. However, there does not exist any notion of structural information for nonparametric modeling of data. In this paper we introduce a novel notion of {\em kernel complexity} (KC) as structural information in the nonparametric setting. The key idea of KC is to combine the information bias inspired by the Gini index with the information quantity measured in terms of the normalized maximum likelihood (NML) code length. We empirically show that KC has a property similar to the number of clusters in a parametric model. We further propose a framework for structural change detection with KC in nonparametric distributions. With synthetic and real data sets we empirically demonstrate that our framework enables us to detect structural changes underlying the data and their early warning signals.

A method is proposed for describing the dynamics of systems of interacting particles in terms of an auxiliary field, which in the static mode is equivalent to given interatomic potentials, and in the dynamic mode is a classical relativistic composite field. It is established that for interatomic potentials, the Fourier transform of which is a rational algebraic function of the wave vector, the auxiliary field is a composition of elementary fields that satisfy the Klein-Gordon equation with complex masses. The interaction between particles carried by the auxiliary field is nonlocal both in space variables and in time. The temporal non-locality is due to the dynamic nature of the auxiliary field and can be described in terms of functional-differential equations of retarded type. Due to the finiteness mass of the auxiliary field, the delay in interactions between particles can be arbitrarily large. A qualitative analysis of the dynamics of few-body and many-body systems with retarded interactions has been carried out, and a non-statistical mechanisms for both the thermodynamic behavior of systems and synergistic effects has been established.

Abstract: The internationally accepted goals of eliminating climate gas emissions implies substantial investments in renewable energy (RE) facilities. This will inevitably lead to major impacts on landscapes. Landscape concerns linked to RE facilities are already leading to controversies in many local communities. In this article, we focus on the question of landscape democracy related to the establishment of RE facilities. Based on recommendations from the European Landscape Convention, an analytical framework is presented identifying three main dimensions of landscape democracy, followed by an overview of arrangements, procedures and methods that are or may be used to encourage democracy. The procedures and methods are analysed based on examples from Denmark and Norway. This is followed by an analysis of decision levels with a special focus on the principle of subsidiarity. Finally, recommendations are presented to strengthen landscape democracy in relation to the installation of RE-facilities.

The mechanisms of natural oscillations and resonance are described, considering the peculiarities of the transformation of elastic and kinetic energy in the implementation of the law of conservation of energy in local and integral volumes of the body, using the concept of mechanics based on the concepts of space, time and energy. When describing the motion in the Lagrange form, the elastic deformation energy of the particles is determined by the quadratic invariant of the tensor, whose components are the partial derivatives of Euler variables with respect to Lagrange variables. The increment of the invariant due to elastic deformation is represented as the sum of two scalars, one of which depends on the average value of the relative lengths of the edges of the particles in the form of an infinitesimal parallelepiped, the second is equal to the standard deviation of these lengths from the average value. It is shown that each of the scalars can be represented in the form of two dimensionless kinematic parameters of elastic energy, which participate in different ways in the implementation of the law of conservation of energy. One part of the elastic energy passes into kinetic energy and participates in the implementation of the law of conservation of energy for the body as a whole, considering external forces. The second part is not converted into kinetic energy but changes the deformed state of the particles in accordance with the equations of motion while maintaining the same level of the part of the elastic energy of the particles used for this. The kinematic parameters differ from the volume density of the corresponding types of energy by a factor equal to the elastic modulus, which is directly proportional to the density and heat capacity of the material and inversely proportional to the volume compression coefficient. Transverse, torsional, and longitudinal vibrations are considered free and under resonance conditions. The mechanisms of transformation of forced vibrations into their own after the termination of external influences and resonance at the superposition of free and forced vibrations with the same or similar frequency are considered. The formation of a new free wave at each cycle with an increase in the amplitude, which occurs mainly due to internal energy sources, and not external forces, is justified.

In the century and a half since Maxwell first conjured his “finite being” which Lord Kelvin subsequently dubbed a “daemon”, researchers have explored the connections between non-equilibrium thermodynamics, entropy, and information theory. In recent years various Thermodynamic Uncertainty Relations (TURs) have been derived to inform upon the relationship between the entropy production and the precision possible in thermodynamic machines and processes. In this paper the recently derived TURs are applied to the hypothetical thermodynamic economy as described by Parker [1]. The TURs define the lower bound on the total entropy production of the economy. Changes in this entropy production rate has consequences on the stability of the economic system and plays a central role in the business cycle. This new perspective has important implications for policy makers, researchers, and other economic actors.

Re-interpretation of the Fermat principle governing propagation of light in media within the Ramsey Theory is suggested. Complete bi-colored graphs corresponding to the light propagation in media are considered. The vertices of the graphs correspond to the points of the real physical space, in which light sources or sensors are placed. Red links in the graphs correspond to the actual optical paths, emerging from the Fermat principle. A variety of optical events: refraction, reflection, etc. may be involved in the light propagation. Green links, in turn, denote the trial/virtual optical paths, which actually do not occur. The Ramsey Theorem states that within the graph containing six points, inevitably, actual or virtual optical cycle will be necessarily present. Implementation of the Ramsey Theorem to the light propagation in metamaterials is discussed. The Fermat Principle states that in metamaterials a light ray in going from point S to point P must traverse an optical path length L that is stationary with respect to variations of this path. Thus, bi-colored graphs built of links corresponding to maxima or minima of optical paths become possible. Graphs, comprising six vertices, inevitably will demonstrate optical cycles, built of the mono-colored links corresponding to the maxima or minima of the optical path. The notion of the “inverse graph” is introduced and discussed. The total number of triangles in the “direct” (source) and “inverse” Ramsey optical graphs is the same, Optical interpretation of the infinite Ramsey Theorem is suggested.

This article develops a duality principle and a related convex dual formulation suitable for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a model in non-linear elasticity.

This article develops duality principles and related convex dual formulations suitable for the local optimization of non-convex primal formulations for a large class of models in physics and engineering. The results are based on standard tools of functional analysis, calculus of variations and duality theory. In particular, we develop applications to a Ginzburg-Landau type equation.

Quantum gravity theories rely on a minimal measurable length for their formulations, which clashes with the classical formulation of the uncertainty principle and with Lorentz invariance from general relativity. These incompatibilities led to the development of the generalized uncertainty principle (GUP) from string theories and its various modifications. GUP and covariant formulations of the uncertainty principle are discussed, together with implications for space-time quantization.

In light of the self-simulation hypothesis, a simple form implementation of the principle of efficient language is discussed in a self-referential geometric quasicrystalline state sum model in three dimensions. Emergence is discussed in context of geometric state sum models.

We discuss the fate of the correspondence principle beyond quantum mechanics, specifically in quantum field theory and quantum gravity, in connection with the intrinsic limitations of the human ability to observe the external world. We conclude that the best correspondence principle is made of unitarity, locality, proper renormalizability (a refinement of strict renormalizability), combined with fundamental local symmetries and the requirement of having a finite number of fields. Quantum gravity is identified in an essentially unique way. The gauge interactions are uniquely identified in form. Instead, the matter sector remains basically unrestricted. The major prediction is the violation of causality at small distances.

We explore several ways, in order to include fermionic structures naturally in a physical theory in C⁴. We begin with the standard Dirac formalism and we proceed by using Cartan's property of triality as a second option. Afterwards, we suggest a new approach (in a preliminary basis), by introducing an 1-linear form, as the "square root of the geometry" derived by the usual 2-linear forms (quadratic forms). Keeping this way, we introduce n-linear forms, in order to formulate a new geometric structure, which could be suitable for the formulation of a pure geometric unied theory.

The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance based risk analysis. Considering the Solvency II Standard Formula from the viewpoint of linear geometry, we immediately find that it defines a norm and therefore provides a homogeneous and sub-additive tool for risk aggregation. Hence Euler's Principle for the reallocation of risk capital applies and yields explicit formulas for capital allocation in the framework given by the Solvency II Standard Formula. This gives rise to the definition of diversification functions, which we define as monotone, subadditive, and homogeneous functions on a convex cone. Diversification functions constitute a class of models for the study of the aggregation of risk, and diversification. The aggregation of risk measures using a diversification function preserves the respective properties of these risk measures. Examples of diversification functions are given by seminorms, which are monotone on the convex cone of non-negative vectors. Each L^p norm has this property, and any scalar product given by a non-negative positive semidefinite matrix does as well. In particular, the Standard Formula is a diversification function and hence a risk measure that preserves homogeneity, subadditivity, and convexity.

According to the Cosmological Principle the Universe is isotropic and no preferred direction would be seen by an observer that might be stationary with respect to the expanding cosmic fluid. However, because of observer’s partaking in the solar system peculiar motion, there would appear in some of the observed properties of the Cosmos a dipole anisotropy, which could in turn be exploited to determine the peculiar motion of the solar system. The dipole anisotropy in the Cosmic Microwave Background Radiation (CMBR) has given a peculiar velocity vector 370 km s−1 along l=264∘,b=48∘. However, some other dipoles, for instance, from the number counts, sky brightness or redshift distributions in large samples of distant Active Galactic Nuclei (AGNs), have yielded values of the peculiar velocity many times larger than that from the CMBR, though surprisingly, in all cases the directions agreed with the CMBR dipole. Here we determine our peculiar motion from a sample of 0.28 million AGNs, selected from the Mid Infra Red Active Galactic Nuclei (MIRAGN) sample comprising more than a million sources. From this, we find a peculiar velocity, which is more than four times the CMBR value, although the direction seems to be within ∼2σ of the CMBR dipole. A genuine value of the solar peculiar velocity should be the same irrespective of the data or the technique employed to estimate it. Therefore, such discordant dipole amplitudes, might mean that the explanation for these dipoles, including that of the CMBR, might in fact be something else. But, the observed fact that the direction in all cases, is the same, though obtained from completely independent surveys using different instruments and techniques, by different sets of people employing different computing routines, might nonetheless indicate that these dipoles are not merely due to some systematics, otherwise why would they all be pointing along the same direction. It might instead suggest a preferred direction in the Universe, implying a genuine anisotropy, which would violate the Cosmological Principle, the core of the modern cosmology.

The theory of special relativity has reexamined and reconstructed the concepts of space and time, which are indispensable for describing physical laws, consequently instigating a major revolution in physics in general. Although the correctness of the special theory of relativity has been con-firmed by many observations and experiments, it is unclear why the "principle of relativity" and the "principle of the constant speed of light," which form the basis of the idea, are valid. Moreo-ver, although special relativity has advanced our understanding of time, our understanding of the fundamental question, "What is time?" is still limited. The theory of special relativity regards space as a four-dimensional construct consisting of one-dimensional time and three-dimensional space. This paper proposes an alternative framework, wherein real space is uniform and isotropic four-dimensional space, and elementary particles are waves that propagate through this four-dimensional space at a constant speed. This new perspective provides evidence to support two of Einstein’s key principles—the "principle of relativity" and the "principle of the constant speed of light." Furthermore, this model clarifies what time is and why time flows at a constant rate from the past to the future.

In previous studies we found that generalized functions can be smooth, discrete, periodic or discrete periodic and they can either be local or global and they are regular or generalized functions. We also saw that these properties were related to Poisson’s summation formula on one hand and to Heisenberg’s uncertainty principle on the other. In this paper, we interlink these studies and show that scalars (real or complex numbers) considered as trivial functions are discrete and periodic, local and global as well as regular and generalized, simultaneously. However, this is also a paradox because it means that Dirac’s δ and 1 (its Fourier transform) coincide. They both are unity. We show that δ and 1 coincide in the sense of scalars (real or complex numbers) but they differ in the sense of (generalized) functions. This result can moreover be related to Max Born’s principle of reciprocity. It also answers an open question in present-day quantum mechanics because it means that the Dirac delta squared is simply delta.

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

The design of thin-walled structures is commonly based on the solutions of linear boundary-valued problems, formulated within well-developed theories for elastic plates and shells. However, in modern appliances, especially in MEMS design, it is necessary to take into account non-linear mechanical effects that become decisive for flexible elements. Among substantial non-linear effects, that significantly change the deformation properties of thin plates, are the effects of residual stresses caused by incompatibility of deformations, which inevitably arise during the manufacture of ultra-thin elements. The development of new methods of mathematical modeling of residual stresses and incompatible finite deformations in plates is the subject of the paper. To this end the local unloading hypothesis is used. It makes possible to define smooth fields of local deformations (inverse implant field) for the mathematical formalization of incompatibility. The main outcomes are field equations, natural boundary conditions and conservation laws, derived from least action principle and variational symmetries with account of implant field. The derivations were carried out in the framework of elasticity theory for simple materials and, over and above, within the Cosserat’s theory of a two-dimensional continuum. As illustrative examples the distributions of incompatible deformations in a circular plate are considered.

The objective of this paper is to present a mathematical formalism that states a bridge between Physics and Psychology, concretely between analytical dynamics and personality theory in order to open new insights in this theory. In this formalism energy plays a central role. First, the short-term personality dynamics can be measured by the General Factor of Personality (GFP) response to an arbitrary stimulus. This GFP dynamical response is modelled by a stimulus-response model: an integro-differential equation. The bridge between Physics and Psychology is provided when the stimulus-response model can be formulated as a linear second order differential equation and, subsequently, reformulated as a Newtonian equation. This bridge is strengthened when the Newtonian equation is derived from a minimum action principle, obtaining the current Lagrangian and Hamiltonian functions. However, the Hamiltonian is a non-conserved energy. Then, some changes provide a conserved Hamiltonian function: the Ermakov-Lewis energy. This energy is presented, as well as the GFP dynamical response that can be derived from it. An application case is presented: an experimental design in which 28 individuals consumed 26.51 g of alcohol. This experiment provides an ordinal scale for the Ermakov-Lewis energies that predicts the effect of a single dose of alcohol.

Is it possible to measure the dispersion of ex-ante chances (i.e. chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex-ante chances in various areas with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk to become ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk like the overwhelming majority of the population but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.

The complete-lattice approach to optimization problems with a vector- or even set-valued objective already produced a variety of new concepts and results and was successfully applied in finance, statistics and game theory. For example, the duality issue for multi-criteria and vector optimization problems could be solved using the complete-lattice approach, compare [11]. So far, it has been applied to set-valued dynamic risk measures (in the stochastic case), as discussed in Feinstein, Rudloff etc. (see [11], for example), but it has not been applied to deterministic calculus of variations and optimal control problems. In this paper, the following problem of set-valued optimization is considered: minimize the functional $$ \overline J_t[y]=\int_0^t \overline L(s,y(s),\dot y(s))\ ds + U_0(y(0)) $$ over all admissible arcs $y$, where $\overline L$ is the associated multifunction to a vector-valued Lagrangian $L$, the integral is in the Aumann sense and $U_0$ is the initial cost. A new concept of \emph{value function}, for which a Bellman's optimality principle holds, is introduced. Also the classical result of the Hopf-Lax formula holds for the generalized value function. Finally, a derivative with respect to the time $t$ and a directional derivative with respect to $x$ of the value function are defined, based on ideas close to the concepts in [12]. The value function is proved to be solution of a suitable Hamilton-Jacobi equation.

The success of source protection in ensuring safe drinking water is centered around being able to understand the hazards present in the catchment then plan and implement control measures to manage water quality risk to levels which can be controlled through downstream barriers. The programs in place to manage source protection are complex sociotechnical systems involving policy, standards, regulators, technology, human factors and so on. This study uses System Theoretic Process Analysis (STPA) to analyze the operational hazards of a typical drinking water source protection (DWSP) program and identify control measures to ensure safe operations. To validate the results a questionnaire was developed and distributed to specialists in DWSP in Taiwan, Australia and Greece. Using Principle Components Analysis (PCA) of the questionnaire responses, the study identified four critical success factors (CSFs) for DWSP. The four factors identified are ‘Policy and Government Agency Support of Source Protection’, ‘Catchment Risk Monitoring and Information’, ‘Support of Operational Field Activities’ and ‘Response to Water Quality Threats’. The results of this study provide insight into the approach of grouping of source protection measures to identify a series of targeted CSF for operational source protection programs. Using CSF can aide catchment management agencies in ensuring that the risk level in the catchment is managed effectively and that threats to public health from drinking water are managed appropriately.

In France, the regional airport’s demand for services is facing challenges due to the continuous expansion of the high-speed train, high-speed line, and highway networks. This study focuses on the viability of regional airports in France through technical efficiency using data envelopment, principle component analysis, Malmquist productivity index, and regression analysis using bootstrapping. To face the current competitive environment, the regional airports in France adopted strategies, such as the construction of low-cost carrier (LCC) dedicated terminals (LCCTs) with lower expenses to attract more LCCs, increasing non-aeronautical revenue, and hosting regional hubs of LCCs. This is the first study that analyzes all of the French regional airports. The findings indicate that the existence of LCCTs positively affects technical efficiency on the airport’s performance, and share of LCCs at a regional airport leads to neither the efficiency nor the profit level.

We present a modified version of the Szilard Engine, demonstrating that an explicit measurement procedure is entirely unnecessary for its operation. By considering our modified engine, we are able to provide a new interpretation of Landauer’s original argument for the cost of erasure. From this view, we demonstrate that a reset operation is strictly impossible in a dynamical system with only conservative forces. Then, we prove that to approach a reset yields an unavoidable instability at the reset point. Finally, we present an original proof of Landauer’s principle that is completely independent from the Second Law of Thermodynamics.

Mass plays a strange multiple role in classical physics. This results in a difference between gravity and all other forces - a difference that stood at the beginning of Einstein's development of his general theory of relativity. The equivalence principle (EP) deals with homogenious gravitational fields, which, in fact, don‘t exist in nature. There is only an approximation for this field in Einstein-Lift possible for local situations. Nevertheless this EP can be true, because in classical formal binary logic there can be formulated a true conclusion from a wrong premise or assumption.

Master equations define the dynamics that govern the time evolution of various physical processes on lattices. In the continuum limit, master equations lead to Fokker-Planck partial differential equations that represent the dynamics of physical systems in continuous spaces. Over the last few decades, nonlinear Fokker-Planck equations have become very popular in condensed matter physics and in statistical physics. Numerical solutions of these equations require the use of discretization schemes. However, the discrete evolution equation obtained by the discretization of a Fokker-Planck partial differential equation depends on the specific discretization scheme. In general, the discretized form is different from the master equation that has generated the respective Fokker-Planck equation in the continuum limit. Therefore, the knowledge of the master equation associated with a given Fokker-Planck equation is extremely important for the correct numerical integration of the latter, since it provides a unique, physically motivated discretization scheme. This paper shows that the Kinetic Interaction Principle (KIP) that governs the particle kinetics of many body systems, introduced in [G. Kaniadakis, Physica A 296, 405 (2001)], univocally defines a very simple master equation that in the continuum limit yields the nonlinear Fokker-Planck equation in its most general form.

With reference to our recently proposed Planck Scale White Hole Cosmology (PS-WHC) or Flat Space Cosmology (PS-FSC), we make an attempt to quantify galactic dark matter and flat rotation speeds in terms of galactic visible matter and cosmic mass. Considering recently observed dwarf galaxies having very little dark matter and assuming a time dependent reference mass unit of $M_X\cong \left(\mbox{3.0 to 4.0}\right)\times 10^{38}$ kg, we suggest an empirical relation for galactic dark matter $M_d$ via galactic visible mass $M_v$ as,$M_d \cong \frac{M_v^{3/2}}{M_X^{1/2}}$. This relation helps in fitting flat rotation speeds starting from 8 km/sec (for Segue 2) to 500 km/sec (for UGC12591). Modifying MOND's galactic flat rotation speed relation with Hubble mass $M_0\cong \left(\frac{c^3}{2GH_0}\right)$ of the universe, ratio of galactic flat rotation speed $V_G$ to speed of light $c$ can be shown to be approximately $\frac{V_G}{c} \cong 0.5 \left(\frac{M_v}{M_0}\right)^{1/4}$. Considering the sum of galactic dark matter and visible matter, ratio of galactic flat rotation speed to speed of light can be shown to be approximately $\frac{V_G}{c}\cong 0.25 \left(\frac{M_v+M_d}{M_0}\right)^{1/4}$. With further study, dark matter's nature, effect and distribution can be understood in terms of visible matter's extended gravity and extended theories of gravity can be understood with 'distance cosmic mass' rather than the empirical 'minimum acceleration'.

In this paper, we obtain the existence and uniqueness theorem for solutions of Caputo type fractional stochastic delay differential systems (FSDDSs) with Poisson jumps by utilizing delayed perturbation of Mittag-Leffler function. Moreover, by using Burkholder-Davis-Gundy's inequality, Doob's martingale inequality and Holder inequality, we prove that the solution of the averaged FSDDSs converges to that of the standard FSDDSs in the sense of Lp. Some known results in the literature are extended.

The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of scienThe Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.ce, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.

Perinatal mortality is a major issue in laboratory mouse breeding. We compared a counting method using daily checks (DAILY_CHECK) with a method combining daily checks with detailed video analyses to detect cannibalisms (VIDEO_TRACK) for estimating the number of C57BL/6 pups born, died and weaned in 193 litters from trios with (TRIO-OVERLAP) or without (TRIO-NO_OVERLAP) the presence of another litter. Linear mixed models were used at litter level. To understand if cannibalism was associated with active killing (infanticide), we analysed VIDEO_TRACK recordings of 109 litters from TRIO-OVERLAP, TRIO-NO_OVERLAP or SOLO (single dams). We used Kaplan-Meier method and logistic regression at pup level. For DAILY_CHECK, the mean litter size was 35% smaller than for VIDEO_TRACK (P&lt;0.0001) and the number of dead pups was twice lower (P&lt;0.0001). The risk of pup loss was higher for TRIO-OVERLAP than TRIO-NO_OVERLAP (P&lt;0.0001). A high number of pup losses occurred between birth and the first cage checking. Analyses of VIDEO_TRACK data indicated that pups were clearly dead at the start of most of the cannibalism events and infanticide was rare. As most pups die and disappear before the first cage check, many breeding facilities are likely to be unaware of their real rates of mouse pup mortality.

In this paper, we look at how Artificial Swarm Intelligence can evolve using evolutionary algorithms that try to minimize the sensory surprise of the system. We will show how to apply the free-energy principle, borrowed from statistical physics, to quantitatively describe the optimization method (sensory surprise minimization), which can be used to support lifelong learning. We provide our ideas about how to combine this optimization method with evolutionary algorithms in order to boost the development of specialized Artificial Neural Networks, which define the proprioceptive configuration of particular robotic units that are part of a swarm. We consider how optimization of the free-energy can promote the homeostasis of the swarm system, i.e. ensures that the system remains within its sensory boundaries throughout its active lifetime. We will show how complex distributed cognitive systems can be build in the form of hierarchical modular system, which consists of specialized micro-intelligent agents connected through information channels. We will also consider the co-evolution of various robotic swarm units, which can result in development of proprioception and a comprehensive awareness of the properties of the environment. And finally, we will give a brief outline of how this system can be implemented in practice and of our progress in this area.

We study the effect of the generation of the mechanical transverse wave (MTW)　travelling in the opposite direction (OD) to a moving medium (MM) on the relativistic energy conservation law (RECL). From the viewpoint of the relativity of simultaneity (RS), the time on the coordinate coinciding with the advance end of the wave (AEW) travelling toward the rear of the MM passes faster than that on the coordinate coinciding with the wave source (WS). Then the AEW in the MM travels forward compared to that in the rest frame of reference (RFR) which is stationary relative to the medium when the time on the coordinate coinciding with the WS is same for each inertial frame of reference (IFR). Hence, the coordinate interval (CI) between the AEW and WS in the MM is observed to be larger than that between them in the RFR. We show that this difference holds true for the CI of any portion having transverse velocities mutually converted by the Lorentz transformation (LT). This difference in the CI leads to that in the rest mass (RM). We demonstrate that the RM included in wave motion (WM) in the MM is larger than one included in WM in the RFR when comparing the portions having transverse velocities mutually converted by the LT. This relation holds true for all portions in WM. Therefore, the total coordinate interval of the portion (CIP) and total RM (TRM) included in WM in the MM (WMMM) are large compared to them included in WM in the RFR. Furthermore, we compare the relativistic kinetic energy (RKE) of the MTW travelling in the OD to the MM (ODMM) with that of the MTW propagating in the direction vertical to the moving direction of the medium. We prove that the CIP and RM included in the former MTW are larger than them included in the latter MTW when comparing each portion with the same transverse velocity (TV). Moreover, the total CIP and TRM included in the former MTW are also large compared to them included in the latter MTW. The reason for these is that the latter CIP and RM are equal to them in the RFR when comparing the portions having transverse velocities mutually converted by the LT. On the other hand, the energy supplied to generate each MTW is the same. From these, we demonstrate that the RKE of the MTW travelling in the ODMM can be larger than the total relativistic energy (TRE) of the MTW propagating in the direction vertical to the moving direction of the medium. Consequently, we propose a violation of the RECL and Einstein’s principle of relativity (EPR) because the TRE is not necessarily conserved in the IFR in which the medium is moving.

The present paper reviews evidence for ecological evolution of Montiaceae. Montiaceae (Portulacineae) comprise a family of ca. 275 species and ca. 25 subspecific taxa of flowering plants distributed mainly in extreme western America, with additional endemism elsewhere, including other continents and islands. They have diversified repeatedly across steep ecological gradients. Based on narrative analysis, I argue that phylogenetic transitions from annual to perennial life history have been more frequent than suggested by computational phylogenetic reconstructions. I suggest that a reported phylogenetic correlation between the evolution of life history and temperature niche is coincidental and not causal. I demonstrate how statistical phylogenetic comparative analysis (PhCA) missed evidence for marked moisture niche diversification among Montiaceae. I discount PhCA evidence for the relation between Montiaceae genome duplication and ecological diversification. Based on the present analysis of Montiaceae evolution, I criticize the premise of the prevalent statistical approach to PhCA, which tests Darwinian deterministic hypotheses against stochastic evolutionary null models. I discuss theoretical/empirical evidence that evolution is neither stochastic, nor Darwinistically-determined, but idiosyncratic. Idiosyncraticity describes the outcome of a stochastically perturbed nonlinear chaos-like process. The Principle of Evolutionary Idiosyncraticity (PEI) is based on the evolutionary theory of Natural Drift, which maintains that determinism in evolution is a property of the organism and not, as maintained by the theory of Natural Selection, its traits or its milieu. This determinism is characteristic of chaotic functions, which are absolutely determinate, generate self-similarity, but remain absolutely unpredictable. PEI explains precisely observations that evolution proceeds not linearly, but chaotically, producing both quasi-linear fractal-like patterns and non-linear jumps. PEI has ramifications for all areas of macroevolutionary research. In particular, it demonstrates both the fallacy and futility of the statistical PhCA approach that interprets evolutionary causes in terms of evolutionary correlations. However, statistical methods of PhCA can be applied heuristically and fruitfully to reveal idiosyncraticity and discover evolutionary novelty. This, in turn, is demonstrated by the emergence of statistical anomalies in evolutionary analyses of Montiaceae.

The spatial resolution measurement limitation of the position-momentum uncertainty principle is shown to mathematically originate from the Bekenstein entropy bound and the associated second law of thermodynamics, as a special case in which a statistical thermodynamic distribution of energies is specialized to a fixed, definite probe energy equal to the average energy of that distribution. This is used in combination with the Wein displacement law to predict an ultraviolet cutoff for Planck blackbody radiation at about ⅛ of the Wein peak. A new UV photon counting experiment is proposed to test for this. A physical understanding of these results may be provided by a UV-complete, intelligible theory of general relativistic quantum mechanics in which the observation of a blackbody spectrum is simply a remote observation of Hawking radiation emitted from black hole fluctuations in the gravitational vacuum.

Following Smolin, we proceed to unification of general relativity and quantum theory by operating solely with events, i.e., without appealing to physical systems and space-time. The universe is modelled as a dendrogram (finite tree) expressing the hierarchic relations between events. This is the observational (epistemic) model; the ontic model is based on p-adic numbers (infinite trees). Hence, we use novel mathematics—not only space-time but even real numbers are not in use. Here, the p-adic space (which is zero dimensional) serves as the base for the holographic image of the universe. In this way our theory relates to p-adic physics; in particular, p-adic string theory and complex disordered systems (p-adic representation of Parisi matrix for spin glasses). Our Dendrogramic-Holographic (DH) theory matches perfectly with the Mach’s principle and Brans-Dicke theory. We found surprising informational interrelation between the fundamental constants, h, c, G, and their DH-analogues, h(D), c(D), G(D). DH-theory is part of Wheeler’s project on the information restructuring of physics. It is also a step towards the Unified Field theory. The universal potential V is nonlocal, but this is relational DH-nonlocality. V can be coupled to the Bohm quantum potential by moving to the real representation. This coupling enhanced the role of the Bohm potential.

We explore the possibility to form a physical theory in $C^4$. We argue that the expansion of our usual 4-d real space-time to a 4-d complex space-time, can serve us to describe geometrically electromagnetism and nuclear fields and unify it with gravity, in a different way that Kaluza-Klein theories do. Specifically, the electromagnetic field $A_\mu$, is included in the free geodesic equation of $C^4$. By embedding our usual 4-d real space-time in the symplectic 8-d real space-time (symplectic $R^8$ is algebraically isomorphic to $C^4$), we derive the usual geodesic equation of a charged particle in gravitational field, plus new information which is interpreted. Afterwards, we formulate and explore the extended special relativity and extended general relativity an $C^4$ or$R^8$. After embedding our usual 4-d space-time in $R^8$, two new phenomena rise naturally, that are interpreted as "dark matter" and "dark energy". A new cosmological model is presented, while the geometrical terms associated with "dark matter" and "dark energy" are investigated. Similarities, patterns and differences between "dark matter", "dark energy", ordinary matter and radiation are presented, where "dark energy" is a dynamic entity and "dark matter" reveal itself as a "mediator" betwen ordinary matter and "dark energy". Moreover, "dark matter" is deeply connected with "dark energy". Furthermore, the extended Hamilton-Jacobi equation of the extended space-time, is transformed naturally as an extended Klein-Gordon equation, in order to get in contact with quantum theories. By solving the Klein-Gordon equation analytically, we derive an eigenvalue for Higg's boson mass value at 125,173945 $Gev/c^{2}$. The extended Klein-Gordon equation, also connects Higg's boson (or vacuum) with Cosmology, due to the existence of our second "time" T (cosmological time), which serve us to connect quantum theories with Cosmology. Afterwards, in the general case, we explore the symmetries of the curved Hamilton-Jacobi equation locally, in order to investigate the consequences of a $C^4$ space-time in Standard Model. An extension to Standard Model is revealed, especially in the sector of strong nuclear field. The Stiefel manifold $SU(4)/SU(2)$ seems capable not only to describe the strong nuclear field but give us,as well, enough room to explore in the future, the possibility to explain quark confinment. Our extension, flavors firstly the unification of nuclear fields and afterwards the unification of nuclear fields with electromagnetic field. The desired grand unification, is achieved locally, through the symmetry group $GL(4,C)\simeq SO(4,4)\cap U(4)$ and we present a potential mechanism to reduce the existing particle numbers to just six. Afterwards,23 present the extended Dirac equation in $C^4$ space-time (Majorana-Weyl representation) plus a preliminary attempt to introduce a pure geometric structure for fermions. Finally, we consider a new geometric structure through n-linear forms in order to give geometric explanation for quantisation

The article obtains large deviation asymptotic for sub-critical communication networks modelled as signal-interference-noise-ratio(SINR) random networks. To achieve this, we define the empirical power measure and the empirical connectivity measure, as well as prove joint large deviation principles(LDPs) for the two empirical measures on two different scales. Using the joint LDPs, we prove an Asymptotic equipartition property(AEP) for wireless telecommunication Networks modelled as the subcritical SINR random networks. Further, we prove a Local Large deviation principle(LLDP) for the sub-critical SINR random network. From the LLDPs, we prove the large deviation principle, and a classical McMillan Theorem for the stochastic SINR model processes. Note that, the LDPs for the empirical measures of this stochastic SINR random network model were derived on spaces of measures equipped with the $\tau-$ topology, and the LLDPs were deduced in the space of SINR model process without any topological limitations. We motivate the study by describing a possible anomaly detection test for SINR random networks.

This paper discovers that current canonical variational principle and canonical Noether theorem of (in)finite freedom systems for different physics systems have neglected doublet extreme value processes of the general extreme value functional that both is derived by variational principle and is necessarily be taken in deriving all ( quantum ) physics laws in phase space, but which have not been done for over one century since Noether's showing her distinguished theorem, which lead to the crisis deriving all (quantum) physics laws (necessary) in phase space. We discover there is the hidden logic cycle that people assume canonical equations, and then they finally deduce canonical equations by the equivalent relation in the whole processes in all current references. We correct the current key mistake concepts that when physics systems take the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current references. The real physics should be what after taking the physics systems' variational extreme values, the physics systems' general extremum functional needs to further take the general extremum functional's minimum absolute extremum zero, otherwise, the appearing processes of physics systems still are virtual processes. Conservation current equations and conservation currents, in phase space, of general canonical variational principle and general canonical Noether theorem are, respectively, deduced for the first time. Using the general extremum functionals' doublet extreme value processes, the hidden logic cycle and the crisis in current canonical variational principle and current canonical Noether theorem are solved. Consequently, the new mathematical pictures, classical and quantum new physics in phase space and the new mathematical and physical doublet extremum processes for (in)finite freedom systems are discovered. General canonical variational principle and general canonical Noether theorem naturally are given, which would rewrite all the different sciences in phase space, as key tools of studying and dealing with them.

Humanity faces serious social and environmental problems, including climate change and biodiversity loss. Risks are increasing and conditions deteriorating. Increasingly, scientists, global policy experts, and the general public conclude that incremental approaches are insufficient and transformative change is needed across all sectors of society. However, the meaning of transformation is still unsettled in the literature, as is the proper role of science in fostering it. This paper is the first in a three-part series that adds to the discussion by proposing a novel science-driven research-and-development program aimed at societal transformation. More than a proposal, it offers a perspective and conceptual framework from which societal transformation might be approached and understood. While acknowledging the necessity of reform to existing societal systems (e.g., governance, economic, and financial systems), the focus of the series is on transformation understood as systems change or systems migration—the de novo development of and migration to new societal systems. The series provides definitions, aims, reasoning, worldview, and a theory of change, and discusses fitness metrics and design principles for new systems. This first paper proposes a worldview built using ideas from evolutionary biology, complex systems science, cognitive sciences, and information theory that is intended to serve as the foundation for the R&amp;D program.

Terms related to gradients of scalar fields are introduced as scalar products into the formulation of entropy. A Lagrange density is then formulated by adding constraints based on known conservation laws. Applying the Lagrange formalism to the resulting Lagrange density leads to the Poisson equation of gravitation and also includes terms being related to curvature of space. The formalism further leads to terms possibly explaining nonlinear extensions known from modified Newtonian dynamics approaches. The article concludes with a short discussion of the presented methodology and provides an outlook on other phenomena, which might be tackled using this new approach.

If we assume that: a. The four fundamental forces of nature are independent waves without rest masses, and their speeds are constant in a vacuum, just like light. b. Light or electromagnetic waves and gravity are comparable in structures. Weak and strong interactions are similar in structures. c. Light and weak interaction have the same speed c_L with spin number +1 or –1. d. Gravity and strong interaction have the same speed c_G without spin. e. The primary particles, namely electrons, electron neutrinos, and dark neutrinos in this paper, are made by the above four waves. We can find and describe some fundamental characteristics of the primary particles (e.g., their sizes, energies, and interactions) and introduce new attractive results from them (e.g., the source of the Pauli exclusion principle, the solution to the Einstein-Podolsky-Rosen paradox, and c_G slightly faster than c_L).

The aim of this work is to broaden the theory of computation by making use of fuzzy sets and multisets, which are generalization of ordinary sets. We study fuzzy multiset finite automata (FMFA), which are characterized by the incorporation of vagueness when it comes to the choice of the next state and multiple occurrences of the same input symbol. The resulting automaton is a genaralization of both classical automata and fuzzy automata. We discuss the algebraic characteristics of FMFA sub-automata—separatedness, strongly connectedness, cyclic, directable, and triangular FMFA in terms of equivalence classes induced by an equivalence relation defined on state set of FMFA. Intrestingly, for a given FMFA, a new FMFA can be constructed that is a homomorphic image of the original FMFA. We define different posets structures that can be associated with a given FMFA and show that some of them are upper semilattices and discuss the inter-relationship of a given poset, a finite upper semilattice (FUSL), a FMFA and a posets/FUSL associated with a given FMFA. Finally, we introduce the concept of decomposition of a FMFA in two different ways and characterize the strongly connected, triangular and directable FMFA.

The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible paradigm. However, to date, the essential rationale for and analysis of classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics, and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer's Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed.

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 recent Google’s claim on breakthrough in quantum computing is a gong signal for further analysis of foundational roots of (possible) superiority of some quantum algorithms over the corresponding classical algorithms. This note is a step in this direction. We start with critical analysis of rather common reference to entanglement and quantum nonlocality as the basic sources of quantum superiority. We elevate the role of the Bohr’s principle of complementarity¹ (PCOM) by interpreting the Bell-experiments as statistical tests of this principle. (Our analysis also includes comparison of classical vs genuine quantum entanglements.) After a brief presentation of PCOM and endowing it with the information interpretation, we analyze its computational counterpart. The main implication of PCOM is that by using the quantum representation of probability, one need not compute the joint probability distribution (jpd) for observables involved in the process of computation. Jpd’s calculation is exponentially time consuming. Consequently, classical probabilistic algorithms involving calculation of jpd for n random variables can be over-performed by quantum algorithms (for big values of n). Quantum algorithms are based on quantum probability calculus. It is crucial that the latter modifies the classical formula of total probability (FTP). Probability inference based on the quantum version of FTP leads to constructive interference of probabilities increasing probabilities of some events. We also stress the role the basic feature of the genuine quantum superposition comparing with the classical wave superposition: generation of discrete events in measurements on superposition states. Finally, the problem of superiority of quantum computations is coupled with the quantum measurement problem and linearity of dynamics of the quantum state update.

Using assembly theory, we investigate the assembly pathways of fixed-length binary strings formed by joining the individual bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below and above, and we conjecture about the form of the upper bound. We show that a string having the smallest assembly index can be assembled by an elegant trivial program of length equal to this index, if the length of the string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index that could assemble this string. We conjecture that a black hole surface is defined by a balanced distinct string that satisfies the upper bound of a distinct string assembly index. The results confirm that four Planck areas provide a minimum information capacity that provides a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that the problem of determining the assembly index of a given binary string is NP-complete, while the problem of creating the string so that it would have a predetermined maximum assembly index is NP-hard. Therefore, once the new information is assembled by a dissipative structure or by a human, increasing the information entropy according to the second law of infodynamics, it is subject to the second law of thermodynamics, and nature seeks to optimize its assembly pathway.

The absolute time and relative time are defined in terms of the 4-D Euclidean space. Our universe is the 3-D x₁x₂x₃ quantized photon space which follows the absolute time simultaneity when the universe moves along the absolute time axis of ct. The length expansion of Dx = gDx₀ is derived under the condition of the absolute time (ct) simultaneity. From the similarity between this length expansion of Dx = gDx₀ and the energy increasing of E = gE₀, it is assumed that the energy is proportional to the particle size of Dx. The extension of this assumption to the 4-D Euclidean space gives the new definition that the particle energy (E) is the 4-D volume. Then, the particle mass energy is defined as E= mc² = cDtDV = gE₀. The masses of the elementary particles are originated from the 4-D warped volume of the photon space because the particle is the warped photon space with the velocity of v < c. Therefore, the Higgs boson concept in the standard model (SM) is not needed in the present 3-D quantized space model (TQSM). The scalar boson with the spin of zero, photon with the spin of 1 and graviton with the spin of 2 are the two-boson states. Therefore, the observed Higgs boson is reinterpreted as the two-boson state of the scalar boson with the spin of zero. The cosmic muon observation and twin paradox are explained by using the absolute time and relative time. The relative time is the observed time in the twin paradox and cosmic muon observation. In the twin paradox, a person who travels the long distance is more aged than a person on the earth in terms of the relative time ages because of the space and time conversion effect (STCE effect) of the moving space distance (x). But twins are in the same ages in terms of the absolute time without STCE effect. The fast-moving cosmic muon has the expanded half-life from the time expansion of the relative time. Also, the quantum entanglement and Pauli exclusion principle are explained. The quantum base of the photon space line connects two entangled particles. Two particles and quantum base system is fluctuated along the absolute time axis by the time clicking when one particle is measured. Another particle is instantly selected by the time clicking. This is called as the quantum entanglement. The photons which are the flat photon space with the constant speed of c along the space axis and absolute time axis have the 4-D photon velocity of c_eff = 2^0.5 c. Total 10-D Euclidean space including three 3-D quantized spaces and one absolute time axis is required for the electric charges (EC), lepton charges (CC) and color charges (CC) of the elementary particles. The 3-D photon space is very stiff along the absolute time (ct) axis and very soft along the space axes. The Coulomb force through the photons (2EM waves) of the space fluctuations is much stronger than the Gravitational force through the gravitons (G waves) of the time fluctuations between two electrons.

An event occurring within a stationary environment, in the direction toward which an observer self-rotates, is perceived to precede a simultaneous event, in the direction away from which she moves. When self-rotation results from angular acceleration in the dark, perception of space is also distorted, such that the subjective straight-ahead shifts in the opposite direction to motion and temporal event promotion. A reference frameshift theory, based on the special theory of relativity, is proposed to explain these findings. Here, a hyperbolic tangent transformation of objective angular velocity constrains subjective self-rotation velocity within finite bounds, consistent with it being a limited perceptual resource. Identifying this subjective variable with vestibular nystagmus slow-phase angular velocity, the asymptotic perceived self-rotation velocity is estimated at ~200 °⁄s. When included in the Lorentz transformations of the new formalism, this value predicts experimental simultaneity distortion. Hypothetically, the hyperbolic tangent objective-to-subjective transfer function would maximize the differential entropy of the percept, and thereby also the stimulus/percept mutual information, if angular velocities of body rotation encountered in naturalistic environmental interaction have a logistic probability density distribution of scale 100 °⁄s, a proposed experimental test of the scheme.

A time interval only description necessarily needs its own independent definitions, without one moment time coordinates to it. In this paper derived are time interval only set properties, including commutation relations, addition, multiplication and derivatives. Time interval only set commutation relations, consistent with one moment time set properties, are introduced by defining correspondence relations for these sets. Time development and equilibrium within the time interval description depend on the well-known ‘mean velocity theorem’ and the time interval version of the Legendre transform. In contrast, usually applied is only the traditional vector and one moment time coordinate kinematic approach from Newton’s laws. The main results of this paper are correspondences and time interval only set commutation relations. All other properties are derived from these results, while for the time interval only set, different from the one moment time set the canonical property is not valid. The time interval only description can be applied assuming spherical symmetric star-source radiation propagation, with finite time intervals for realistic measurement events. From time development with (a-)symmetry of time intervals, and from Curie’s principle, change can be described with a set theoretic approach. Time interval only set properties include the time interval only version of Noether charges and structure constants. A time interval only description for wave propagation, including group-velocity, for zero and non-zero mass wave particles, relates to the properties of the time interval only set. A second result in terms of the time interval only description is propagation wave energy equivalence with gravitation energy, derived from time interval only set commutation relations. A time interval approach, however including one moment time description dependence, was introduced in earlier publications of this author. In part 1 investigated are the time interval only set and its properties, a forthcoming part 2 to application of the time interval only description to specific groups of stars as emission sources.

Imaginary dimensions in physics require an imaginary set of base Planck units and some negative parameter $c_n$ corresponding to the speed of light in vacuum $c$. The second, negative fine-structure constant $\alpha_2^{-1} \approx -140.178$ present in Fresnel coefficients for the normal incidence of electromagnetic radiation on monolayer graphene leads to the imaginary Planck units. Furthermore, it sets $c_n \approx -3.06 \times 10^8~\text{[m/s]}$. It follows that electric charges are the same in real and imaginary dimensions. Neutron stars and white dwarfs, objects emitting perfect black-body radiation, need energy exceeding their mass-energy equivalence ratios. Complex energies are defined in terms of real and imaginary Planck units. Their imaginary parts, inaccessible for direct observation, store the excess of these energies. It follows that black holes are fundamentally uncharged, charged micro neutron stars and white dwarfs with masses lower than $5.7275 \times 10^{-10}~[\text{kg}]$ are unphysical, and the radii of white dwarfs' cores are limited to $R_{\text{WD}} < 6.7933~G M_{\text{WD}}/c^2$. It is conjectured that the maximum atomic number $Z=238$. A black-body object is in the equilibrium of complex energies of masses, charges, and wavelengths if its radius $R_\text{eq} \approx 2.7665~G M_{\text{BBO}}/c^2$, which corrects the value of the photon sphere radius $R_{\text{ps}}=3G M/c^2$, taking into account the value(s) of the fine-structure constant(s), which is otherwise neglected in general relativity.

Dirac's Large Number Hypothesis (LNH), proposed in 1937, has captivated the scientific community with its exploration of profound correlations between cosmic and atomic scales. This hypothesis delves into the intricate interplay between the infinitesimally small and the vastly large, offering potential insights into the fundamental nature of the universe. As we continue to uncover the mysteries of the cosmos, the LNH oscillates on the precipice of scientific acceptance—neither fully validated nor entirely dismissed. In this review paper, we embark on a comprehensive journey through Dirac's LNH, shedding light on its theoretical underpinnings, its implications for universe models, and its resonance with the Anthropic Principle. We delve into the possibilities of variable gravitational constants and continuous mass creation, inviting further exploration into the intricacies of our cosmic symphony. By embracing the ongoing quest for understanding, we endeavor to unravel the profound harmonies that connect the infinitesimal with the infinite, contributing to the symphony of knowledge in theoretical physics and cosmology.