Quantum fermions from classical bits

A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically on bit configurations. The genuinely probabilistic character of quantum physics is realized by probabilistic initial conditions. In turn, the probabilistic automaton is equivalent to the classical statistical system of a generalized Ising model. For a description of the probabilistic information at any given time quantum concepts as wave functions and non-commuting operators for observables emerge naturally. Quantum mechanics can be understood as a particular case of classical statistics. This offers prospects to realize aspects of quantum computing in the form of probabilistic classical computing. This article is part of the theme issue ‘Quantum technologies in particle physics’.

Rethinking Categories and Dimensions in the DSM

This paper addresses the role of categories and dimensions in the classification of psychopathology. While psychopathology does not sort itself out neatly into natural categories, we do find rough, symptom-based groupings that, through refinement, become diagnostic categories. Given that these categories suffer from comorbidity, uncertain boundaries, and excessive “unspecified disorder” diagnoses, there has been a move toward refining the diagnoses with dimensional measures. The paper traces efforts both to improve the diagnostic categories with validators that allow at least partial validity and to introduce dimensional measures into the diagnostic manual. Drawing from the philosophical pragmatism of Charles Sanders Peirce, William James, and John Dewey, which emphasizes the practical, effect-sensitive consequences of a theory along with an emphasis on empirical evidence and the progressive, probabilistic character of knowledge, the paper argues that these efforts must be guided both by scientific validity and clinical utility.

Generalized allocation scheme with cell occupancies from a fixed finite set

We consider a generalized scheme of allocation of n particles (elements) over unordered cells (components) under the condition that the number of particles in each cell belongs to a fixed finite set A of positive integers. A new asymptotic estimates for the total number In(A) of variants of allocations of n particles are obtained under some conditions on the set A; these estimates have an explicit form (up to equivalence). Some examples of combinatorial-probabilistic character are given to illustrate by particular cases the notions introduced and results obtained. For previously known theorems on the convergence to the normal law of the total number of components and numbers of components with given cardinalities the norming parameters are obtained in the explicit form without using roots of algebraic or transcendent equations.

ASSESSMENT OF RELIABILITY OF THE DRIVER – CAR – ROAD – ENVIRONMENT (DCRЕ) SYSTEM IN MOUNTAIN CONDITIONS

The article provides an assessment of the factors affecting the reliability of the DCRE system in mountain conditions. A more detailed classification of factors affecting the reliability of the DCRE system in mountain conditions is given for such groups of features as design and technological, operational and road-climatic. In addition, the article gives a classification of factors affecting the reliability of the DCRE system in mountain conditions based on controllability. In both classifications, particular importance is given to such factors as altitude, the reliability structure of the elements of the DCRE system, the reliability structure of the elements of the car, the subsystems of the DCRE system, the probabilistic nature of the influence of external influences on the elements of the car, the types and frequency of maneuvers, their dynamism, etc. The specifics of the influence of the main factors determining the reliability and durability of heavy-duty mining car in difficult and extreme conditions of cargo transportation in mountain conditions are analyzed and justified. To assess the influence of the stochastic nature of external influences that determine the dynamics of the interaction of the car with the roadway, depending on the sample size, the nature of the process, the state of the object under study and other factors, the most rational methods based on probability theory are substantiated. Three of them are recommended for an adequate assessment of the impact of external influences on the output indicators of the car, in particular to assess the process of interaction of the car with the roadbed, which has a probabilistic character. Among the recommended estimation methods are included such methods as the method of approximating the external load with a periodic function such as a sinusoid with certain values of the amplitude and period of oscillation, the method of expanding the periodic function in Fourier series and the probabilistic-statistical method, which is based on taking into account the action of many random factors characterized by stable frequency.

Probabilistic approach to near acceptance of expert decisions on examinations of difficult objects

The aim of the article is to ground the probabilistic approach to the acceptance of expert decisions on examinations of difficult objects with the use of the information technologies conducted on the basis of the used methodologies of realization of examinations. Criminalistics identification researches of difficult objects are conducted by comparison of the identification signs got from debatable (investigated) and exemplary (experimental) identifying objects. For comparison at first it is necessary to measure them, and already after it to compare inter se, i.e. to find the measure of closeness between the compared identification signs. And here are two aspects of estimation of authenticity of results of comparison. First from them belongs to determination of probability of complete coincidence of parameters of identification signs of two different objects. In other words, it is the aspect of proof of strict individuality of descriptions of the investigated objects, confessed in the whole world and allowing to use the categorical form of formulation of conclusion of expert. The calculation of probability of coincidence of fingerprint cards of two different personalities belongs exactly to this aspect. The second aspect is related to probabilistic character of processes of both origin of identification signs in difficult objects and their selection, measuring and comparison during realization of criminalistics researches. Exactly he is related to the probabilistic going near the estimation of results of criminalistics researches of difficult objects. It is shown that the result of any examination of difficult object, related to measuring of concrete sizes, is characterized by the presence of random constituent and its result must be presented in a probabilistic form. There are three separate random values determined by probability, characterizing examination and tool intended for identification researches of difficult objects At creation of tool for realization of examinations of difficult objects and its introduction into practice, the curves of values of probability errors of І and ІІ family must be made and its minimum efficiency must be determined. Exactl efficiency of tool must serve as a criterion for its suitability for realization of expert researches.

A probabilistic approach to modeling collisions with thin barriers

In many fracture problems, fragmentation is essentially a probabilistic process, which is determined by the stochastic nature of the distribution of inhomogeneities of the internal structure of material. The probabilistic approach is described, which allows us to model structural heterogeneities of the material in a simple form, practically without any complication of the model and additional experiments. Using experimental data and numerical simulation results, it is shown that the introduction of only one additional parameter (dispersion of the strength properties distribution) into the material model makes it possible to give a probabilistic character to the crack formation process at any scale level, which corresponds to theoretical concepts and experimental data. Distribution of materials strength characteristics (according to the selected distribution law) in the cells of the computational domain is used for initial heterogeneities and materials structure defects modeling. It is shown that the number and size of the “petals” at the penetration of thin barriers depend of the speed of the projectile and the strength characteristics of the barrier.

Nekhoroshev Stability for the Dirichlet Toda Lattice

In this work, we prove a Nekhoroshev-type stability theorem for the Toda lattice with Dirichlet boundary conditions, i.e., with fixed ends. The Toda lattice is a member of the family of Fermi-Pasta-Ulam (FPU) chains, and in view of the unexpected recurrence phenomena numerically observed in these chains, it has been a long-standing research aim to apply the theory of perturbed integrable systems to these chains, in particular to the Toda lattice which has been shown to be a completely integrable system. The Dirichlet Toda lattice can be treated mathematically by using symmetries of the periodic Toda lattice. Precisely, by treating the phase space of the former system as an invariant subset of the latter one, namely as the fixed point set of an important symmetry of the periodic lattice, the results already obtained for the periodic lattice can be used to obtain analogous results for the Dirichlet lattice. In this way, we transfer our stability results for the periodic lattice to the Dirichlet lattice. The Nekhoroshev theorem is a perturbation theory result which does not have the probabilistic character of related theorems, and the lattice with fixed ends is more important for applications than the periodic one.

METHODOLOGICAL PRINCIPLES OF CALENDAR PLANNING BY PROBABILISTIC CHARACTER OF CONSTRUCTION

It is defined that the tasks of reducing the cost of construction products should not be solved by saving the direct costs, but due to objective reduction of costs by rationality of the production work organization. It is established that construction works are fulfield in prone to changes of the environment conditions, so not only these factors should be taken into account in the process of construction, but also those that may only be predicted with a certain probability. It was developed the dependence of the work duration calculation both with the usage of a set of construction machine and without its usage by applying the coefficient of the construction project sensitivity to the factors of a changing environment. The proposed calculation allows to reduce the failure risk of the commissioning project terms and provides an opportunity to accelerate the construction process in the given specific conditions. It was carried out the estimation of the coefficient of sensitivity in different local conditions depending on the influence of various factors: weather conditions; provision of material resources; number and qualifications of workers.