Polynomial Dependence Research Articles

Development and evaluation of the effectiveness of the integration gateway for the interaction of the learning management system with external systems and services of state information systems

The paper presents the results of the development of information technology for the interaction of the learning management system with the state information systems of the Republic of Kazakhstan in the field of higher education. Integration with these systems is based on the integration gateway, which is part of the educational portal of the East Kazakhstan Technical University named after D. Serikbayev. Approaches to organizing data exchange with external information systems were analyzed and described, and mechanisms for integrating the national database of the Republic of Kazakhstan with a unified higher education management system were identified. The created integration gateway within the framework of the educational portal interacts with the information systems using the technology of transferring a representative state, data transfer is carried out in text format. The implemented gateway allows you to receive the necessary data from the database of the educational portal, generate data packets for transmission, connect to an external system and transfer data. To evaluate the efficiency of the gateway, computational experiments were carried out in which data of various volumes were transferred through the created gateway to state information systems and the time of their transmission was recorded. Based on the obtained data, the dependences of the transmission time on the amount of transmitted data for each information system with which interaction is carried out were obtained and their graphical display was built. According to the results of the experiments, it was shown that the transmission time has a polynomial dependence on the amount of data, which makes it possible to interact with the indicated information systems in real time

On Polynomials Counting Essentially Irreducible Maps

We consider maps on genus-$g$ surfaces with $n$ (labeled) faces of prescribed even degrees. It is known since work of Norbury that, if one disallows vertices of degree one, the enumeration of such maps is related to the counting of lattice point in the moduli space of genus-$g$ curves with $n$ labeled points and is given by a symmetric polynomial $N_{g,n}(\ell_1,\ldots,\ell_n)$ in the face degrees $2\ell_1, \ldots, 2\ell_n$. We generalize this by restricting to genus-$g$ maps that are essentially $2b$-irreducible for $b\geq 0$, which loosely speaking means that they are not allowed to possess contractible cycles of length less than $2b$ and each such cycle of length $2b$ is required to bound a face of degree $2b$. The enumeration of such maps is shown to be again given by a symmetric polynomial $\hat{N}_{g,n}^{(b)}(\ell_1,\ldots,\ell_n)$ in the face degrees with a polynomial dependence on $b$. These polynomials satisfy (generalized) string and dilaton equations, which for $g\leq 1$ uniquely determine them. The proofs rely heavily on a substitution approach by Bouttier and Guitter and the enumeration of planar maps on genus-$g$ surfaces.

Two-loop tensor integral coefficients in OpenLoops

We present a new and fully general algorithm for the automated construction of the integrands of two-loop scattering amplitudes. This is achieved through a generalisation of the open-loops method to two loops. The core of the algorithm consists of a numerical recursion, where the various building blocks of two-loop diagrams are connected to each other through process-independent operations that depend only on the Feynman rules of the model at hand. This recursion is implemented in terms of tensor coefficients that encode the polynomial dependence of loop numerators on the two independent loop momenta. The resulting coefficients are ready to be combined with corresponding tensor integrals to form scattering probability densities at two loops. To optimise CPU efficiency we have compared several algorithmic options identifying one that outperforms naive solutions by two orders of magnitude. This new algorithm is implemented in the OpenLoops framework in a fully automated way for two-loop QED and QCD corrections to any Standard Model process. The technical performance is discussed in detail for several 2 → 2 and 2 → 3 processes with up to order 105 two-loop diagrams. We find that the CPU cost scales linearly with the number of two-loop diagrams and is comparable to the cost of corresponding real-virtual ingredients in a NNLO calculation. This new algorithm constitutes a key building block for the construction of an automated generator of scattering amplitudes at two loops.

Bound-constrained global optimization of functions with low effective dimensionality using multiple random embeddings

We consider the bound-constrained global optimization of functions with low effective dimensionality, that are constant along an (unknown) linear subspace and only vary over the effective (complement) subspace. We aim to implicitly explore the intrinsic low dimensionality of the constrained landscape using feasible random embeddings, in order to understand and improve the scalability of algorithms for the global optimization of these special-structure problems. A reduced subproblem formulation is investigated that solves the original problem over a random low-dimensional subspace subject to affine constraints, so as to preserve feasibility with respect to the given domain. Under reasonable assumptions, we show that the probability that the reduced problem is successful in solving the original, full-dimensional problem is positive. Furthermore, in the case when the objective’s effective subspace is aligned with the coordinate axes, we provide an asymptotic bound on this success probability that captures its polynomial dependence on the effective and, surprisingly, ambient dimensions. We then propose X-REGO, a generic algorithmic framework that uses multiple random embeddings, solving the above reduced problem repeatedly, approximately and possibly, adaptively. Using the success probability of the reduced subproblems, we prove that X-REGO converges globally, with probability one, and linearly in the number of embeddings, to an epsilon -neighbourhood of a constrained global minimizer. Our numerical experiments on special structure functions illustrate our theoretical findings and the improved scalability of X-REGO variants when coupled with state-of-the-art global—and even local—optimization solvers for the subproblems.

Gradient-Based Algorithms for Convex Discrete Optimization via Simulation

Solving Convex Discrete Optimization via Simulation via Stochastic Search Algorithms Many decision-making problems in operations research and management science require the optimization of large-scale complex stochastic systems with high-dimensional discrete decision variables. For a number of applications, the objective function exhibits convexity in the discrete decision variables, or the problem can be transformed into a convex one. In “Gradient-Based Algorithms for Convex Discrete Optimization via Simulation,” Zhang, Zheng, and Lavaei propose provably efficient simulation–optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. By utilizing the convex structure, the developed algorithms demonstrate a polynomial dependence on the dimension and scale of the decision space. In addition, information-theoretic lower bounds are derived to show the limit of algorithm design. In the case when possibly biased gradient estimators are available, they propose simulation–optimization algorithms to achieve optimality guarantees with a reduced dependence on the dimension.

Points of bounded height on curves and the dimension growth conjecture over Fq[t]$\mathbb {F}_q[t

In this article, we prove several new uniform upper bounds on the number of points of bounded height on varieties over F q [ t ] $\mathbb {F}_q[t]$ . For projective curves, we prove the analogue of Walsh' result with polynomial dependence on q $q$ and the degree d $d$ of the curve. For affine curves, this yields an improvement to bounds by Sedunova, and Cluckers, Forey and Loeser. In higher dimensions, we prove a version of dimension growth for hypersurfaces of degree d ⩾ 64 $d\geqslant 64$ , building on work by Castryck, Cluckers, Dittmann and Nguyen in characteristic zero. These bounds depend polynomially on q $q$ and d $d$ , and it is this dependence which simplifies the treatment of the dimension growth conjecture.

How to understand the structure of beta functions in six-derivative Quantum Gravity?

We extensively motivate the studies of higher-derivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical structure of the exact on the full quantum level beta functions obtained previously for three couplings in front of generally covariant terms with four derivatives (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet scalar) in minimal six-derivative quantum gravity in d = 4 spacetime dimensions. The fundamental role here is played by the ratio x of the coupling in front of the term with Weyl tensors to the coupling in front of the term with Ricci scalars in the original action. We draw a relation between the polynomial dependence on x and the absence/presence of enhanced conformal symmetry and renormalizability in the models where formally x → +∞ in the case of four- and six-derivative theories respectively.

Influence of the crushed stone content on the deformation modulus of the soil-crushed stone layer

Introduction. The purpose of the article is to study the dependence of the deformation modulus of the soil-crushed stone layer of the road surface from the content of crushed stone in the soil-crushed stone mixture and the soil moisture in it. The goal was achieved by performing stamp tests of the models of a road clothing and a roadbed.Materials and methods. The research was carried out by performing stamp tests of models of the roadbed and single-layer road clothes with a soil-crushed stone surface. Before the stamp tests, laboratory work were carried out to determine the parameters subject to input control for crushed stone and soil. Models of road clothes are built from crushed stone materials and soil in the tray. Tests of the roadbed and road clothes are carried out using a rigid round stamp included in the standard kit.Results. The modules of deformation of the soil of the roadbed and road surfaces with a soil-crushed stone layer are calculated from the polynomial dependence of settlement on pressure, regulated by ПНСТ 311-2018. According to the test results, the modulus of deformation of the soil of the roadbed, and the general modulus of deformation on the surface of the soil-crushed stone layer, with different content of crushed stone by the volume of the mixture, were determined. The lowest value of the deformation modulus corresponds to the minimum content of crushed stone in the mixture, which is 40 % by volume of the mixture. The highest value of the deformation modulus was obtained at the maximum content of crushed stone in the mixture, which is 60 % by volume of the mixture. Using the general modules of deformation of different road surfaces and the modules of deformation of the soil of the roadbed, the calculation of the deformation modulus of the soil-crushed stone layer with different content of crushed stone in it is performed. To take into account the influence of moisture of the cohesive soil used in the mixture, correction coefficients are given, the values of which are established by laboratory tests. These coefficients allow us to calculate the modulus of deformation of the soil-crushed stone layer depending on the content of crushed stone and the moisture of the soil used in it.Discussion and conclusions. As a result of experimental work, the modules of deformation of soil-crushed stone of different compositions were determined, with the help of which the design of road surfaces was carried out with the subsequent construction of experimental sites in each of the three road building climatic zones of the Omsk region.

Limitations of empirical supercell extrapolation for calculations of point defects in bulk, at surfaces, and in two-dimensional materials

The commonly employed supercell approach for defects in crystalline materials may introduce spurious interactions between the defect and its periodic images. A rich literature is available on how the interaction energies can be estimated, reduced, or corrected. A simple and seemingly straightforward approach is to extrapolate from a series of finite supercell sizes to the infinite-size limit, assuming a smooth polynomial dependence of the energy on inverse supercell size. In this work, we demonstrate by means of explict density-functional theory supercell calculations and simplified models that wave-function overlap and electrostatic interactions lead to more complex dependencies on supercell size than commonly assumed. We show that this complexity cannot be captured by the simple extrapolation approaches and that suitable correction schemes should be employed.

Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme

We consider the long-time behavior of an explicit tamed exponential Euler scheme applied to a class of parabolic semilinear stochastic partial differential equations driven by additive noise, under a one-sided Lipschitz continuity condition. The setting encompasses nonlinearities with polynomial growth. First, we prove that moment bounds for the numerical scheme hold, with at most polynomial dependence with respect to the time horizon. Second, we apply this result to obtain error estimates, in the weak sense, in terms of the time-step size and of the time horizon, to quantify the error to approximate averages with respect to the invariant distribution of the continuous-time process. We justify the efficiency of using the explicit tamed exponential Euler scheme to approximate the invariant distribution, since the computational cost does not suffer from the at most polynomial growth of the moment bounds. To the best of our knowledge, this is the first result in the literature concerning the approximation of the invariant distribution for SPDEs with non-globally Lipschitz coefficients using an explicit tamed scheme.

An optimization-based algorithm for simultaneous shaping of poles and zeros for non-collocated vibration suppression

This article presents a control design method for simultaneous shaping of the poles and zeros of linear time-invariant systems, motivated by the application of non-collocated vibration suppression to flexible multi-body systems. An entire suppression of vibrations at a target mass for a given excitation frequencies can be recast into the problem of assigning zeros of the transfer function from the excitation force to the target mass' position. The design requirement of achieving sufficient damping in the closed loop system combined with suppressing vibrations at the target, leads to the minimization of the spectral abscissa function of the closed loop system as a function of the controller parameters, subject to zero location constraints. These constraints exhibit polynomial dependence on the controller parameters. We present two approaches to solve the optimization problem which are both based on constraint elimination followed by application of an algorithm for non-smooth unconstrained optimization. The design approach is applicable to delay-free models as well as time-delay models of retarded and neutral type. Simulations results illustrate its applicability to a spring-mass-damper system.

FEATURES OF CALCULATION OF THE REQUIRED QUANTITY OF GRAIN TERMINAL TRACKS IN SEA PORTS IN MODERN CONDITIONS

Purpose. Ukraine is one of the world's five largest producers of grain crops. Much of the grain is exported. Traditionally, grain cargoes are exported through the western land crossings and seaports of the Black and Azov Seas, with the bulk of grain exports going through the port of Nikolaev and the ports of Greater Odessa. Rail transport provides delivery to exporting ports up to 2/3 of the total volume of grain transshipment in ports. Given the significant number of operations in the general technological process of processing grain wagons in ports, the required capacity of technical equipment of railway transport (number of tracks, locomotives, weighing devices, etc.) plays a significant role in the duration of the transshipment process and total operating costs. In this regard, determining the required number of ways to service the flow of grain for export is an urgent task. Methods. Comprehensive analysis of technical equipment and technology of railway transport of grain terminals in seaports, statistical analysis, graph-analytical modeling. Results. Based on the processing of statistics on the delay of wagons due to commercial marriages with grain cargo in the seaport, the conditional division of detained wagons due to and, consequently, the duration of delay of wagons into long and short. The characteristics of random values of the delay of the car are established and the dependence of the number of detained cars on the value of the total car traffic with grain cargo entering the transshipment is obtained. For short-term delays it is a polynomial dependence of the second degree, for long-term delays it is characterized by exponential dependence. Based on research, an additional track capacity has been established for the sedimentation of detained cars and recommendations have been developed for the number of such tracks and their length. Based on the rationing of the duration of shunting operations with delayed wagons, an additional working fleet of shunting locomotives for servicing delayed wagons was determined and recommendations for the location of wagon scales for commercial weighing of wagons in the process of processing grain wagons in the port. Practical significance. The obtained results can be used to determine the number of tracks and the total capacity of grain terminals in seaports. The duration of additional shunting operations to service the detained cars allows to clarify the calculation of the required locomotive fleet of grain terminals.

Закономірність зміни технологічної точності деревообробних верстатів упродовж міжремонтного періоду роботи

The patterns of changes in the technological accuracy of the machine during the overhaul period in the form of a polynomial dependence have been identified, which makes it possible to determine the time and number of adjustments to the machine to ensure its operating capacity according to the criterion of technological accuracy. On the basis of the statistical modeling method, a simulation model-program "ModDynToch" was developed for identifying changes in the technological accuracy of the machine tool with the determination of the time between failures and the required number of machine adjustments during the overhaul period. Based on the results of modeling changes in the technological accuracy of a number of machines for sawing and milling wood, it was found that in order to ensure a working capacity during the overhaul period, each machine requires three adjustments to be made at a certain interval. Based on the analysis of the results of modeling changes in the technological accuracy of machines for sawing and milling wood, it was found that the shortest period of operation for band saw machines is up to 190 hours, for circular saw machines – up to 480 hours, and for milling machines – up to 840 hours. The results of the statistical modeling of the pattern of changes in the technological accuracy of machines during the overhaul period of operation are correlated with operational data with an accuracy of up to 7%, which confirms the reliability of the modeling results.

Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models

Generally, ``fracton'' topological orders are referred to as gapped phases that support \textit{point-like topological excitations} whose mobility is, to some extent, restricted. In our previous work [Phys. Rev. B 101, 245134 (2020)], a large class of exactly solvable models on hypercubic lattices are constructed. In these models, \textit{spatially extended excitations} possess generalized fracton-like properties: not only mobility but also deformability is restricted. As a series work, in this paper, we proceed further to compute ground state degeneracy (GSD) in both isotropic and anisotropic lattices. We decompose and reconstruct ground states through a consistent collection of subsystem ground state sectors, in which mathematical game ``coloring method'' is applied. Finally, we are able to systematically obtain GSD formulas (expressed as $\log_2 GSD$) which exhibit diverse kinds of polynomial dependence on system sizes. For example, the GSD of the model labeled as $[0,1,2,4]$ in four dimensional isotropic hypercubic lattice shows $ 12L^2-12L+4$ dependence on the linear size $L$ of the lattice. Inspired by existing results [Phys. Rev. X 8, 031051 (2018)], we expect that the polynomial formulas encode geometrical and topological fingerprints of higher-dimensional manifolds beyond toric manifolds used in this work. This is left to future investigation.

Diversity of solutions: An exploration through the lens of fixed-parameter tractability theory

When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good solutions. In this work we initiate a systematic study of diversity from the point of view of fixed-parameter tractability theory. First, we consider an intuitive notion of diversity of a collection of solutions which suits a large variety of combinatorial problems of practical interest. We then present an algorithmic framework which –automatically– converts a tree-decomposition-based dynamic programming algorithm for a given combinatorial problem X into a dynamic programming algorithm for the diverse version of X. Surprisingly, our algorithm has a polynomial dependence on the diversity parameter.

FORECASTING THE EFFECTIVENESS OF THE USE OF MEANS OF LABOR ACCORDING TO TREND MODELS

The main purpose of this article is to forecast the effectiveness of the use of fixed assets to improve the effectiveness of the technical potential of the business entity. The scientific article considers the process of predicting the effectiveness of the means used for labor by extrapolation. The analysis of the level of capital effectiveness of the business entity is carried out and its forecasting based on polynomial dependence is carried out. During the study period, the effectiveness of the means used for labor has an ambiguous trend. The worst situation is observed in 2013 when the level of return on assets is the lowest, but by 2015 its value is gradually increasing, then decreasing, in 2017 increasing, and then decreasing again. The largest increase in return on assets took place in 2019, but in the reporting, year compared to the previous year, its level decreased again. Therefore, it was necessary to identify factors that would improve the effectiveness of labor. Five factors were selected (the share of the active part of fixed assets, the ratio of fixed assets, technical capital, labor intensity, the share of workers in the workforce), which have a significant impact on the level of effectiveness of fixed assets. Since the constructed models are adequate in terms of the coefficient of determination and Fisher's criterion, the forecasting is carried out in terms of trend models. This allowed to determine the influence of the time factor on the change in return on assets and the factors that significantly affect its change. The results of the forecast show a further stable increase in return on assets, both in terms of its actual and estimated value. Thus, the effectiveness of the means used for labor of the production enterprise is realized through the systematic management of the business entity to improve the effectiveness in the production process of its technical potential. Keywords: means of labor, capital effectiveness, forecasting, extrapolation method, effectiveness of means used for labor, trend model.

Diversity of littoral zoobenthos in Lake Arakhley (Transbaikalia) during the arid phase

There is little data available on the zoobenthos of the Baikal region’s eastern periphery water bodies in low-water years. The taxonomic diversity of zoobenthos of the littoral zone of a deep lake (Arakhley, Transbaikalia) was studied in an extremely low-water year, 2017. The zoobenthos of the lake littoral zone was represented by 44 taxa. Chironomids accounted for 41% of the zoobenthos taxonomic diversity, 14% each – gastropods and leeches. The taxonomic diversity of the littoral zoobenthos in different parts of the lake varied from 19 to 24 taxa and averaged 22.3 ± 1.97 taxa. The relationship between taxonomic diversity and depth in Lake Arakhley is described by polynomial dependence. Deviations from the relationship identified at the periphery of vegetation thickets were due to the ecotone effect. Obtained data shows the state of zoobenthos taxonomic diversity under conditions of climate aridization and the reduction of littoral sandy habitats.

Radiative contributions to gravitational scattering

The linear-order effects of radiation-reaction on the classical scattering of two point masses, in General Relativity, are derived by a variation-of-constants method. Explicit expressions for the radiation-reaction contributions to the changes of 4-momentum during scattering are given to linear order in the radiative losses of energy, linear-momentum and angular momentum. The polynomial dependence on the masses of the 4-momentum changes is shown to lead to non-trivial identities relating the various radiative losses. At order $G^3$ our results lead to a streamlined classical derivation of results recently derived within a quantum approach. At order $G^4$ we compute the needed radiative losses to next-to-next-to-leading-order in the post-Newtonian expansion, thereby reaching the absolute fourth and a half post-Newtonian level of accuracy in the 4-momentum changes. We also provide explicit expressions, at the absolute sixth post-Newtonian accuracy, for the radiation-graviton contribution to {\it conservative} $O(G^4)$ scattering. At orders $G^5$ and $G^6$ we derive explicit theoretical expressions for the last two hitherto undetermined parameters describing the fifth-post-Newtonian dynamics. Our results at the fifth-post-Newtonian level confirm results of [Nucl. Phys. B \textbf{965}, 115352 (2021)] but exhibit some disagreements with results of [Phys. Rev. D \textbf{101}, 064033 (2020)].

THE METHOD OF EVALUATING THE OPERATION OF RADIO TECHNICIANS OF SPECIAL PURPOSE IN EXTREME (CRISIS) SITUATIONS

In extreme (crisis) situations, tasks arise, requiring an answer to the question of the effectiveness of decisions made. When using radio technicians of special purpose, the results depend on both the ability of the equipment and its condition and from the service personnel. At the same time, it is necessary to take into account the presence of targeted interfering factors. The paper proposed a method for evaluating the operation of radio equipment for special purpose in extreme (crisis) situations, a distinguishing feature of which is to account for the mutual influence of the components of the system. The evolution of the basic component of operation is proposed to approximate polynomial dependence using a fuzzy logic apparatus when making resulting solutions.

On the Issue of Determining Relative Rail Rolling Contact Fatigue Damageability

Adoption of heavy haul traffic on many railroads, comprising Russian railways, has highlighted the relevance of assessing the effect of increased axial loads on the contact fatigue life of rails.The article describes a set of theoretical studies carried out to create a scientifically substantiated method for predicting the contact fatigue life of rails depending on the values of axial loads. The stress-strain state of the contact area has been determined using the finite element model of wheel rolling on a rail. It has been found that the wheel-rail rolling contact area undergoes complex multiaxial loading with the simultaneous action of normal and shear strains. Based on the analysis of models describing multiaxial fatigue damage, the Brown–Miller model was chosen, which considers the simultaneous action of normal strains at the contact area and of maximum shear strains, which most fully describes the stress-strain state of the wheel-rail rolling contact area. To apply the Brown–Miller model, fatigue stress-strain curves for rail steel have been identified. Based on the analysis of methods for determining the parameters of stress-strain curves carried out by V. A. Troschenko, a modified Roessle– Fatemi hardness method has been applied. Based on the experimentally determined values of hardness on the rolling surface, the parameters of the curves of elastic and plastic fatigue have been revealed by calculation and experiment. To establish the damaging effect of the load from wheel rolling on a rail, the concept of relative damage per rolling cycle had been assumed which is the value inverse to the number of cycles preceding formation of a contact-fatigue crack at a given value of the axial load.Calculations of the relative damage rate of the rolling surface of rails caused by contact fatigue defects were carried out with the Fatigue software package considering mean values of the indicators of the degree of fatigue strength and plasticity of rail steel and the calculated stresses in the wheel-rail contact area, as well as the plasticity correction using Neuber method. The polynomial dependence of relative damageability of the rolling surface of rails is obtained. The established functional dependence of relative damageability of the rolling surface of rails on the values of vertical forces can be used as the basis for the developed methodology for predicting the contact fatigue life of rails.