Finite Set Of Parameters Research Articles

ÉVALUATION DE LA VARIABILITÉ DE TENSION DANS LES SYSTÈMES ÉLECTRIQUES

Processes in large energy systems exhibit a high variability due to the stochastic nature of electricity production and use. However, the control of the energy transfer aims to achieve steady state operation, which is mostly described by signals fully identifiable by a finite set of parameters. Part of the control system is the process of information delivered through measurements. In this paper, we analyze the impact of the measurement system deployed for reporting the RMS parameter of the voltage signal on the quality of information in LV distribution networks. The operation of such networks is highly stochastic, and the chosen models based on averaging are not always appropriate; therefore, we propose to apply a statistic metric, i.e., the coefficient of variation of the root mean square deviation CV(RMSD).

Small Stochastic Data Compactification Concept Justified in the Entropy Basis.

Measurement is a typical way of gathering information about an investigated object, generalized by a finite set of characteristic parameters. The result of each iteration of the measurement is an instance of the class of the investigated object in the form of a set of values of characteristic parameters. An ordered set of instances forms a collection whose dimensionality for a real object is a factor that cannot be ignored. Managing the dimensionality of data collections, as well as classification, regression, and clustering, are fundamental problems for machine learning. Compactification is the approximation of the original data collection by an equivalent collection (with a reduced dimension of characteristic parameters) with the control of accompanying information capacity losses. Related to compactification is the data completeness verifying procedure, which is characteristic of the data reliability assessment. If there are stochastic parameters among the initial data collection characteristic parameters, the compactification procedure becomes more complicated. To take this into account, this study proposes a model of a structured collection of stochastic data defined in terms of relative entropy. The compactification of such a data model is formalized by an iterative procedure aimed at maximizing the relative entropy of sequential implementation of direct and reverse projections of data collections, taking into account the estimates of the probability distribution densities of their attributes. The procedure for approximating the relative entropy function of compactification to reduce the computational complexity of the latter is proposed. To qualitatively assess compactification this study undertakes a formal analysis that uses data collection information capacity and the absolute and relative share of information losses due to compaction as its metrics. Taking into account the semantic connection of compactification and completeness, the proposed metric is also relevant for the task of assessing data reliability. Testing the proposed compactification procedure proved both its stability and efficiency in comparison with previously used analogues, such as the principal component analysis method and the random projection method.

An efficient strategy to implement local porosity constraints in the multiscale design of solids with parameterized biomimetic microstructures

In previous works, the authors introduced a multiscale optimization method to maximize the stiffness of elastic solids with biomimetic cancellous microstructures described by a finite set of parameters. Although effective, the procedure is computationally expensive when solving large-scale problems using per-element non-linear constraints to impose local bounds on the solid volume fraction. This work improves the computational performance of the method by exploring two strategies to completely dispense with nonlinear local constraints: to bound the microparameters so the microsctructures are always within the solid fraction of trabecular bone, and to map the microparameters onto an auxiliary set of parameters that are linearly bounded. As a side effect, the design spaces are reduced. Such reductions are assessed in terms of the bulk and shear moduli and elastic symmetries, which are compared to those of natural bone. Performances of the two strategies are assessed by solving a series of benchmark problems and studying the stiffness of a hip prosthesis. The strategy based on the isoparametric mapping achieves the best results, performing up to 2000 times faster while marginally reducing the design space. Thus, the isoparametric mapping approach makes the multiscale design method a suitable tool for solving large-scale problems of practical interest.

Inverse-designed growth-based cellular metamaterials

Advancements in machine learning have sparked significant interest in designing mechanical metamaterials, i.e., materials that derive their properties from their inherent microstructure rather than just their constituent material. We propose a data-driven exploration of the design space of growth-based cellular metamaterials based on star-shaped distances. These two-dimensional metamaterials are based on periodically-repeating unit cells consisting of material and void patterns with non-trivial geometries. Machine learning models exploiting large datasets are then employed to inverse design growth-based metamaterials for tailored anisotropic stiffness. Firstly, a forward model is created to bypass the growth and homogenization process and accurately predict the mechanical properties given a finite set of design parameters. Secondly, an inverse model is used to invert the structure–property maps and enable the accurate prediction of designs for a given anisotropic stiffness query. We successfully demonstrate the frameworks’ generalization capabilities by inverse designing for stiffness properties chosen from outside the domain of the design space.

Inference in a similarity-based spatial autoregressive model

In this article, we develop asymptotic theory for a spatial autoregressive (SAR) model where the network structure is defined according to a similarity-based weight matrix, in line with the similarity theory, which in turn has an axiomatic justification. We prove consistency of the quasi-maximum-likelihood estimator and derive its limit distribution. The contribution of this article is two-fold: on one hand, we incorporate a regression component in the data generating process while allowing the similarity structure to accommodate non-ordered data and by estimating explicitly the weight of the similarity, allowing it to be equal to unity. On the other hand, this work complements the literature on SAR models by adopting a data-driven weight matrix which depends on a finite set of parameters that have to be estimated. The spatial parameter, which corresponds to the weight of the similarity structure, is in turn allowed to take values at the boundary of the standard SAR parameter space. In addition, our setup accommodates strong forms of cross-sectional correlation that are normally ruled out in the standard SAR literature. Our framework is general enough to include as special cases also the random walk with a drift model, the local to unit root model (LUR) with a drift and the model for moderate integration with a drift.

Learning Resilient Radio Resource Management Policies With Graph Neural Networks

We consider the problems of user selection and power control in wireless interference networks, comprising multiple access points (APs) communicating with a group of user equipment devices (UEs) over a shared wireless medium. To achieve a high aggregate rate, while ensuring fairness across all users, we formulate a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">resilient</i> radio resource management (RRM) policy optimization problem with per-user minimum-capacity constraints that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">adapt</i> to the underlying network conditions via learnable slack variables. We reformulate the problem in the Lagrangian dual domain, and show that we can parameterize the RRM policies using a finite set of parameters, which can be trained alongside the slack and dual variables via an unsupervised primal-dual approach thanks to a provably small duality gap. We use a scalable and permutation-equivariant graph neural network (GNN) architecture to parameterize the RRM policies based on a graph topology derived from the instantaneous channel conditions. Through experimental results, we verify that the minimum-capacity constraints adapt to the underlying network configurations and channel conditions. We further demonstrate that, thanks to such adaptation, our proposed method achieves a superior tradeoff between the average rate and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$5^\mathrm{th}$</tex-math></inline-formula> percentile rate—a metric that quantifies the level of fairness in the resource allocation decisions—as compared to baseline algorithms.

Приближенное решение задачи двух тел, возмущённой периодическим ускорением

In this paper, author proposes an approach to approximate orbital dynamics in the model of a perturbed Two--Body problem, which leads to a system of equations with a closed-form solution. The approach is based on representing the components of the disturbing acceleration by Fourier series in eccentric longitude with constant coefficients, writing out the equations of the perturbed two-body problem in terms of modified equinoctial elements, and averaging the right-hand sides of the equations of motion over the mean longitude on one orbit. It is discovered that the influence of disturbing acceleration on the resulting averaged equations can be parameterized by a finite set of scalar parameters, which are the coefficients of the Fourier series. Solutions of the averaged equations are found in a closed form in case of orbits with low eccentricity.

Compactness and connectedness via the class of soft somewhat open sets

&lt;abstract&gt;&lt;p&gt;This paper is devoted to study the concepts of compactness, Lindelöfness and connectedness via the class of soft somewhat open sets which represents one of the generalizations of soft open sets. Beside investigation the main properties of these concepts, it is demonstrated, with the help of examples, that some properties of their counterparts via soft open sets are invalid. Also, the relationships between these concepts and their counterparts defined in classical topology (which is studied herein under the name of parametric topology) are discussed in detail. Moreover, we provide the sufficient conditions that guarantee the equivalence between them. In this regard, it is proved that all introduced types of soft compact and Lindelöf spaces are transmitted to all parametric topologies without imposing any conditions, whereas the converse holds true under the conditions of a full soft topology and a finite (countable) set of parameters. These characterizations represent a unique behavior of these spaces compared to the other types defined by celebrated generalizations of soft open sets. Also, there is no relationship associating soft $ sw $-connectedness with its counterparts via parametric topologies. We successfully describe soft $ sw $-disconnectedness using soft open sets instead of soft $ sw $-open sets and consequently prove that the concepts of soft $ sw $-connected and soft hyperconnected spaces are identical. In conclusion, the obtained results show that the framework given in this manuscript enriches and generalizes the previous works, and has a good application prospect.&lt;/p&gt;&lt;/abstract&gt;

State and Parameter Estimation of Non-Uniform Transmission Line Using Kronecker Product Based Modeling

The distributed parameters of a non-uniform transmission line (NTL) are assumed to depend on a finite set of unknown parameters, for example, their spatial Fourier series coefficients. The line equations are set up taking random voltage and current line loading into account with the random loading being assumed to be white Gaussian noise in the time and spatial variables. Bypassing over to the spatial Fourier series domain, these line stochastic differential equations (SDEs) are expressed as a truncated sequence of coupled stochastic differential equations for the spatial Fourier series components of the line voltage and current. The coefficients that appear in these stochastic differential equations are the spatial Fourier series coefficients of the distributed line parameters and these coefficients in turn are linear functions of the unknown parameters. By separating these complex stochastic differential equations into their real and imaginary part, the line equations become a finite set of SDEs for the extended state defined to be the real and imaginary components of the line voltage and current as well as the parameters on which the distributed parameters depend. The measurement model is assumed to be white Gaussian noise corrupted versions of the line voltage and current sampled at a discrete set of spatial points on the line and this measurement model can be expressed as a linear transformation of the state variables, i.e, of the spatial Fourier series components of the line voltage and current plus a white measurement noise vector. This work uses sparse matrix factorization using Kronecker product to implement the Fourier unitary transform. This work implements perturbation theory for non-uniform transmission line. The extended Kalman filter (EKF) equations are derived for this state and measurement model and our real timeline voltage and current and distributed parameter estimates show excellent agreement with the true values based on MATLAB simulations. The use of sparse matrix factorization using Kronecker product ease the mathematical complexity and provides compact representation.

Linear orders in NIP structures

We show that every unstable NIP theory admits a ⋁-definable linear quasi-order, over a finite set of parameters. In particular, if the theory is ω-categorical, then it interprets an infinite linear order. This partially answers a longstanding open question.

Image Compression Using Fractal Functions

The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving complex problems requires the use of large amounts of spatial data, efficient storage of data on on-board recording media and their transmission via communication channels. This leads to the need to create new effective methods of compression and data transmission of remote sensing of the Earth. The possibility of using fractal functions for image processing, which were transmitted via the satellite radio channel of a spacecraft, is considered. The information obtained by such a system is presented in the form of aerospace images that need to be processed and analyzed in order to obtain information about the objects that are displayed. An algorithm for constructing image encoding–decoding using a class of continuous functions that depend on a finite set of parameters and have fractal properties is investigated. The mathematical model used in fractal image compression is called a system of iterative functions. The encoding process is time consuming because it performs a large number of transformations and mathematical calculations. However, due to this, a high degree of image compression is achieved. This class of functions has an interesting property—knowing the initial sets of numbers, we can easily calculate the value of the function, but when the values of the function are known, it is very difficult to return the initial set of values, because there are a huge number of such combinations. Therefore, in order to de-encode the image, it is necessary to know fractal codes that will help to restore the raster image.

The complexity of reachability in parametric Markov decision processes

This article presents the complexity of reachability decision problems for parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. In particular, we study the complexity of finding values for these parameters such that the induced MDP satisfies some maximal or minimal reachability probability constraints. We discuss different variants depending on the comparison operator in the constraints and the domain of the parameter values. We improve all known lower bounds for this problem, and notably provide ETR-completeness results for distinct variants of this problem.

Two-alternative optimization of moderate batch data processing

We consider optimization of moderate batch data processing in the framework of Bernoulli two-armed bandit problem with indefinite control horizon. We assume that there are two alternative processing methods with different a priori unknown efficiencies which are caused by different reasons including those related to legislation. One has to find the most efficient method and to provide its predominant usage. The arising batches of data with close properties have moderate and possibly uncertain sizes. The problem is considered in minimax setting. According to the main theorem of the game theory minimax risk and minimax strategy are searched for as Bayesian ones corresponding to approximately the worst-case prior distribution concentrated on the finite set of parameters. Numerical experiments show that this approach provides good approximations of minimax strategy and minimax risk.

Pluralisation in Ígálá and English

Languages of the world have certain similar linguistic features in terms of a finite set of fundamental principles which are universal to all languages on one hand, and a finite set of parameters which determine syntactic variability amongst them. In order to substantiate evidence of linguistic universals, there is need for comparative analysis of languages. The thrust of the paper is to expound the diversities and similarities in Ígálá and English linguistic systems in the area of patterns of pluralisation. The paper is hinged on Inferential-realizational theory. The paper observed that the noun class in Ígálá is marked for number through three inflectional markers [ám(á), ìb(ó) and áb(ó)] while the noun class in English is inflected for number by the following exponents: [-s, -es, -ies, -en, -ren, -ves] not losing sight of zero concept. Germane to this work is the fact that Ígálá and English exhibit extended exponence- a linguistic situation where a particular morphosyntactic property could be expressed by more than one morphological marking in the same word depending on the lexeme’s root. Plural markers in Ígálá are prefixes while plural markers in English are suffixes. In conclusion, English and Ígálá are uniform in one specific sense of the capacity to inflect words for grammatical purposes, but have different structures in the process of inflection or associating an inflected word with a specific set of morphosyntactic properties.

Learning to Optimize Computational Resources: Frugal Training with Generalization Guarantees

Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research provides algorithms that return nearly-optimal parameters from within a finite set. These algorithms can be used when the parameter space is infinite by providing as input a random sample of parameters. This data-independent discretization, however, might miss pockets of nearly-optimal parameters: prior research has presented scenarios where the only viable parameters lie within an arbitrarily small region. We provide an algorithm that learns a finite set of promising parameters from within an infinite set. Our algorithm can help compile a configuration portfolio, or it can be used to select the input to a configuration algorithm for finite parameter spaces. Our approach applies to any configuration problem that satisfies a simple yet ubiquitous structure: the algorithm's performance is a piecewise constant function of its parameters. Prior research has exhibited this structure in domains from integer programming to clustering.

Parametric Markov chains: PCTL complexity and fraction-free Gaussian elimination

Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints over a finite set of parameters. Important tasks in the analysis of parametric Markov chains are (1) computing closed-form solutions for reachability probabilities and other quantitative measures and (2) finding symbolic representations of the set of parameter valuations for which a given temporal logical formula holds as well as (3) the decision variant of (2) that asks whether there exists a parameter valuation where a temporal logical formula holds. Our contribution to (1) is to show that existing implementations for computing rational functions for reachability probabilities or expected costs in parametric Markov chains can be improved by using fraction-free Gaussian elimination, a long-known technique for linear equation systems with parametric coefficients. Our contribution to (2) and (3) is a complexity-theoretic discussion of the model-checking problem for parametric Markov chains and probabilistic computation tree logic (PCTL) formulas. We present an exponential-time algorithm for (2) and a PSPACE upper bound for (3). Moreover, we identify fragments of PCTL and subclasses of parametric Markov chains where (1) and (3) are solvable in polynomial time and establish NP-hardness for other PCTL fragments.

Constrained Subspace Method for the Identification of Structured State-Space Models (COSMOS)

In this article, a unified identification framework called constrained subspace method for structured state-space models (COSMOS) is presented, where the structure is defined by a user-specified linear or polynomial parametrization. The new approach operates directly from the input and output data, which differs from the traditional two-step method that first obtains a state-space realization followed by the system-parameter estimation. The new identification framework relies on a subspace inspired linear regression problem which may not yield a consistent estimate in the presence of process noise. To alleviate this problem, the linear regression formulation is imposed by structured and low-rank constraints in terms of a finite set of system Markov parameters and the user specified model parameters. The nonconvex nature of the constrained optimization problem is dealt with by transforming the problem into a difference-of-convex optimization problem, which is then handled by the sequential convex programming strategy. Numerical simulation examples show that the proposed identification method is more robust than the classical prediction-error method initialized by random initial values in converging to local minima, but at the cost of heavier computational burden.

Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods

In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modeled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the stochastic partial differential system and establish its well-posedness. We then discuss the approximation of the parameter-dependent problem by non-intrusive techniques based on Polynomial Chaos decompositions. We specifically focus on sparse spectral projection methods, which essentially amount to performing an ensemble of deterministic model simulations to estimate the expansion coefficients. The deterministic solver is based on a Hybrid High-Order discretization supporting general polyhedral meshes and arbitrary approximation orders. We numerically investigate the convergence of the probability error of the Polynomial Chaos approximation with respect to the level of the sparse grid. Finally, we assess the propagation of the input uncertainty onto the solution considering an injection–extraction problem.

Intelligent OFDM telecommunication system. Part 3. Anti-eavesdropping and anti-jamming properties of system, based on many-parameter wavelet and Golay transforms

In this paper, we aim to investigate the superiority and practicability of many-parameter wavelet and Golay transforms (MPWT and MPGT) from the physical layer security (PHY-LS) perspective. We propose novel Intelligent OFDM-telecommunication system (Intelligent-OFDM-TCS), based on many-parameter transforms (MPTs). New system uses inverse MPT for modulation at the transmitter and direct MPT for demodulation at the receiver. The purpose of employing the MPTs is to improve the PHY-LS of wireless transmissions against to the wide-band anti-jamming communication. Each MPT depends on finite set of independent Jacobi parameters (angles), which could be changed independently one of another. When parameters are changed, multi-parametric transform is changed too taking form of a set known (and unknown) orthogonal (or unitary) wavelet transforms. We implement the following performances as bit error rate (BER), symbol error rate (SER), peak to average power ratio (PAPR), the Shannon-Wyner secrecy capacity (SWSC) for novel Intelligent-MPWT-OFDM-TCS. Previous research has shown that the conventional OFDM TCS based on discrete Fourier transform (DFT) has unsatisfactory characteristics in BER, PARP, SWSC and in anti-eavesdropping communications. We study Intelligent-MPT-OFDM-TCS to find out optimal values of angle parameters of MPT optimized BER, PAPR, SWSC, anti-eavesdropping effects. Simulation results show that the proposed Intelligent OFDM-TCS have better performances than the conventional OFDM system based on DFT against eavesdropping.

Intelligent OFDM telecommunication system. Part 1. Model of complex and quaternion systems

In this paper, we aim to investigate the superiority and practicability of many-parameter transforms (MPTs) from the physical layer security (PHY-LS) perspective. We propose novel Intelligent OFDM-telecommunication systems based on complex and quaternion MPTs. The new systems use inverse MPT (IMPT) for modulation at the transmitter and MPT for demodulation at the receiver. The purpose of employing the MPT is to improve: 1) the PHY-LS of wireless transmissions against to the wide-band anti-jamming and anti-eavesdropping communication; 2) the bit error rate (BER) performance with respect to the conventional OFDM-TCS; 3) the peak to average power ratio (PAPR). Each MPT depends on finite set of independent parameters (angles). When parameters are changed, many-parametric transform is also changed taking form of a set known (and unknown) orthogonal (or unitary) transforms. For this reason, the concrete values of parameters are specific “key” for entry into OFDM-TCS. Vector of parameters belong to multi-dimension torus space. Scanning of this space for find out the “key” (the concrete values of parameters) is hard problem. MPT has the form of the product of the Jacobi rotation matrixes and it describes a fast algorithm for MPT. The main advantage of using MPT in OFDM TCS is that it is a very flexible anti-eavesdropping and anti-jamming Intelligent OFDM TCS. To the best of our knowledge, this is the first work that utilizes the MPT theory to facilitate the PHY-LS through parameterization of unitary transforms.