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1

Conditional mean embedding and optimal feature selection via positive definite kernels

Jorgensen Palle E.T., Song Myung-Sin, Tian James

Opuscula Mathematica

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2024

|

Vol. 44, no. 1

79--103

EN

Motivated by applications, we consider new operator-theoretic approaches to conditional mean embedding (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and constructive learning algorithms. For initially given non-linear data, we consider optimization-based feature selections. This entails the use of convex sets of kernels in a construction of optimal feature selection via regression algorithms from learning models. Thus, with initial inputs of training data (for a suitable learning algorithm), each choice of a kernel K in turn yields a variety of Hilbert spaces and realizations of features. A novel aspect of our work is the inclusion of a secondary optimization process over a specified convex set of positive definite kernels, resulting in the determination of “optimal” feature representations.

2

Modelling a solution of a homogeneous parabolic equation with random initial condition from Lp(Ω)

Kuchinka Katalin, Slyvka-Tylyshchak Ganna

Przegląd Elektrotechniczny

|

2023

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R. 99, nr 5

77--82

EN

In this paper, a model of solutions to the heat equation with initial conditions from the Orlicz space Lp(Ω) of random variables is built. The constructed model approximates the solution of a homogeneous parabolic equation with given reliability and accuracy in some Orlicz space.

PL

W pracy zbudowano model rozwiązan równania ciepła z warunkami początkowymi z przestrzeni Orlicza Lp(Ω) zmiennych losowych. Skonstruowany model przybliza rozwiązanie jednorodnego równania parabolicznego z zadaną niezawodnoscią i dokładnoscią w pewnej przestrzeni Orlicza.

3

On the Poisson XLindley process

Sakri Amine, Seghier Fatma-Zohra, Vinoth Raman, Zeghdoudi Halim

Mathematica Applicanda

|

2023

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Vol. 51, no. 2

273--289

EN

Due to their advantages, non-homogeneous Poisson processes have so far been used extensively in a variety of practical applications. They do, however, also have important application-related limits. A novel counting process model named the Poisson–XLindley Process was created to get around these restrictions. We shall demonstrate that this new model lacks such constraints. These fundamental stochastic properties of the process are derived. Additionally, the dependence structure is examined along with the new idea of positively dependent increments. Generic versions of several of the features derived in this article will be offered. This is an innovative concept related to counting processes, which allows the probability function to be described explicitly. It is one of its major contributions

PL

Niejednorodne procesy Poissona są szeroko stosowane w modelowaniu chociaż mają istotne ograniczenia jesli chcemy uzyskać wysoką zgodność modelu z zjawiskiem. W celu usunięcia tych problemów wprowadzamy zmodyfikowany opis procesu liczącego, nazwany Procesem Poissona XLindleya. W pracy pokazujemy przełamanie istotnych ograniczeń niejednorodnego procesu Poissona przez nowy model. Wyprowadzono podstawowe właściwości probabilistyczne tego procesu, badana jest równiez struktura zależności przyrostów z wykorzystaniem idei przyrostów dodatnio zależnych. W pracy pokazano ogólną wersję funkcjonałów od tego procesu. Ta innowacyjna koncepcja procesu liczącego, pozwalająca na jawny formuły opisujące rozkłady prawdopodobieństwa, jest jednym z jej głównych walorów pracy.

4

New directions in electric arc furnace modeling

Grabowski Dariusz, Klimas Maciej

Archives of Electrical Engineering

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2023

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Vol. 72, nr 1

157--172

EN

This paper presents new directions in the modeling of electric arc furnaces. This work is devoted to an overview of new approaches based on random differential equations, artificial neural networks, chaos theory, and fractional calculus. The foundation of proposed solutions consists of an instantaneous power balance equation related to the electric arc phenomenon. The emphasis is mostly placed on the conclusions that come from a novel interpretation of the equation coefficients.

5

Spectral response of stationary jack-up platforms loaded by sea waves and wind using perturbation method

Rozmarynowski Bogdan, Jesien Wojciech

Polish Maritime Research

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2021

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nr 4

53--62

EN

The paper addresses non-linear vibrations of offshore jack-up drilling platforms loaded by sea waves and wind in their stationary condition using the perturbation method. Non-linearity of dynamic equations of motion for fixed offshore platforms yields from two factors. The first is load excitation generating non-linear velocity coupling in a dynamic system. This coupling is inherent in the modified Morison equation, involving the excitation function in the form of the sum of the inertial and velocity forces of sea waves, taking into account relative wave–structure kinematics. Moreover, the wind acting on the exciting side causes similar effects. The second source is the subsoil‒structure interaction problem, modelled by a system of springs and dashpots that yields stochastic non-linearity of the dynamic system. The matrix equations of structural motion in FEM terms are set up. The perturbation method is adopted to determine the mechanical response of the system, making it possible to determine response spectra of the first and the second approximations for displacements and internal forces of the platform. The paper is the continuation of research detailed in the paper [1]. It is assumed, that the fluctuation parts of the dynamic loading forces are in line with the direction of sea wave propagation. Sea current and lift forces effects are neglected in this study. A numerical example refers to structural data of the Baltic drilling platform in the stationary configuration, i.e. when three legs support the deck above the seawater level.

6

New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry

Alpay Daniel, Jorgensen Palle E.T.

Opuscula Mathematica

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2021

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Vol. 41, no. 3

283--300

EN

We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples. Our results cover the case of measurable positive definite kernels, and we give applications to both stochastic analysis and metric geometry and provide a number of examples.

7

Optimized Method based on Lattice Sequences for Multidimensional Integrals in Neural Networks

Todorov Venelin, Dimov Ivan, Fidanova Stefka

Annals of Computer Science and Information Systems

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2021

|

Vol. 25

243--246

EN

In this work we investigate advanced stochastic methods for solving a specific multidimensional problem related to neural networks. Monte Carlo and quasi-Monte Carlo techniques have been developed over many years in a range of different fields, but have only recently been applied to the problems in neural networks. As well as providing a consistent framework for statistical pattern recognition, the stochastic approach offers a number of practical advantages including a solution to the problem for higher dimensions. For the first time multidimensional integrals up to 100 dimensions related to this area will be discussed in our numerical study.

8

An Optimized Technique for Wigner Kernel Estimation

Todorov Venelin, Fidanova Stefka, Dimov Ivan, Poryazov Stoyan

Annals of Computer Science and Information Systems

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2021

|

Vol. 25

235--238

EN

We study an optimized Adaptive Monte Carlo algorithm for the Wigner kernel- an important problem in quantum mechanics. We will compare the results with the basic adaptive approach and other stochastic approaches for computing the Wigner kernel represented by difficult multidimensional integrals in dimension d up to 12. The higher cases d > 12 will be considered for the first time. A comprehensive study and an analysis of the computational complexity of the optimized Adaptive MC algorithm under consideration has also been presented.

9

An Optimized Stochastic Techniques related to Option Pricing

Todorov Venelin, Dimov Ivan, Fidanova Stefka, Apostolov Stoyan

Annals of Computer Science and Information Systems

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2021

|

Vol. 25

247--250

EN

Recently stochastic methods have become very important tool for high performance computing of very high dimensional problems in computational finance. The advantages and disadvantages of the different highly efficient stochastic methods for multidimensional integrals related to evaluation of European style options will be analyzed. Multidimensional integrals up to 100 dimensions related to European options will be computed with highly efficient optimized lattice rules.

10

Stochastic multi-depot vehicle routing problem with pickup and delivery: an ILS approach

Rios Brenner H. O., Xavier Eduardo C., Miyazawa Flávio K., Amorim Pedro

Annals of Computer Science and Information Systems

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2020

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Vol. 21

307--315

EN

We present a natural probabilistic variation of the multi-depot vehicle routing problem with pickup and delivery (MDVRPPD). In this paper, we present a variation of this deterministic problem, where each pair of pickup and delivery points are present with some probability, and their realization are only known after the routes are computed. We denote this stochastic version by S-MDVRPPD. One route for each depot must be computed satisfying precedence constraints, where each pickup point must appear before its delivery pair in the route. The objective is to find a solution with minimum expected traveling distance. We present a closed-form expression to compute the expected length of an a priori route under general probabilistic assumptions. To solve the S-MDVRPPD we propose an Iterated Local Search (ILS) that uses the Variable Neighborhood Descent (VND) as local search procedure. The proposed heuristic was compared with a Tabu Search (TS) algorithm based on a previous work. We evaluate the performance of these heuristics on a data set adapted from TSPLIB instances. The results show that the ILS proposed is efficient and effective to solve S-MDVRPPD.

11

A New Optimized Stochastic Approach for Multidimensional Integrals in Machine Learning

Todorov Venelin, Apostolov Stoyan, Dimov Ivan, Fidanova Stefka

Annals of Computer Science and Information Systems

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2020

|

Vol. 21

337--340

EN

Stochastic techniques have been developed over many years in a range of different fields, but have only recently been applied to the problems in machine learning. A fundamental problem in this area is the accurate evaluation of multidimensional integrals. An introduction to the theory of the stochastic optimal generating vectors has been given. A new optimized lattice sequence with a special choice of the optimal generating vector have been applied to compute multidimensional integrals up to 30-dimensions. Clearly, the progress in the area of machine learning is closely related to the progress in reliable algorithms for multidimensional integration.

12

A New Optimized Adaptive Approach for Estimation of the Wigner Kernel

Todorov Venelin, Fidanova Stefka, Dimov Ivan, Poryazov Stoyan

Annals of Computer Science and Information Systems

|

2020

|

Vol. 21

341--344

EN

In this paper we study numerically an optimized Adaptive Monte Carlo algorithm for the Wigner kernel - an important problem in quantum mechanics represented by difficult multidimensional integrals. We will show the advantages of the optimized Adaptive MC algorithm and compare the results with the Adaptive approach from our previous work [4] and other stochastic approaches for computing the Wigner kernel in 3,6,9-dimensional case. The 12-dimensional case will be considered for the first time. A comprehensive study and an analysis of the computational complexity of the optimized Adaptive MC algorithm under consideration has also been presented.

13

Modelling the set of earthworks machinery with the use of computer simulation

Rogala Wojciech, Anysz Hubert

Przegląd Naukowy Inżynieria i Kształtowanie Środowiska

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2019

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Vol. 28, No. 1

161--168

EN

The paper presents the comparison of deterministic and stochastic approach for modeling the set of earthworks machinery. Simulation takes into account the normal distribution of cycle time and efficiency of machines and points out its influence for total construction works time. Results of the simulation indicate the need of identification time and efficiency deviation as a risk factor, which can cause delay whenever earthworks cycle includes the serial work of several machines.

14

To calculation the reliability of the body sheets of the storage capacity

Nizhnik Oleksandr, Makhinko Natalia

Journal of New Technologies in Environmental Science

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2019

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Vol. 3, nr 2

96--101

EN

The article deals with the separate questions of the stochastic calculation of the body sheets of steel cylindrical silo capacities. Particular attention is paid to the quantitative evaluation of statistical parameters of the particulate solid characteristics: unit weight, angle of internal friction, lateral pressure ratio and wall friction coefficient. Their analysis and comparison in various regulative documents is represented. The expression for calculating the random value of the horizontal pressure of the particulate solids is formulated and the curves of density and the distribution function of the given quantity are constructed for the case of considering the correlation dependence of the statistical parameters of the particulate solid characteristics and when these quantities are completely independent. Also it is presented an expression for calculating the random value of the critical factor of the sheets of steel storage capacity with the following statistical of the given quantity with different coefficient values of the steel variation. Conclusions are made accordingly to the influence of the coefficient of variation at the value of probability of the failure-free operation of the body sheets.

15

Analiza i ocena funkcjonalności systemu masowej obsługi na podstawie obsługi celnej pojazdów ciężarowych

Lewiński A., Żurek-Mortka M.

Autobusy : technika, eksploatacja, systemy transportowe

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2018

|

R. 19, nr 6

906--910, CD

PL

Artykuł przedstawia modelowanie procesów obsługi celnej pojazdów ciężarowych za wykorzystaniem procesów Markowa oraz teorii masowej obsługi (teorii kolejek), ukazujące przebieg funkcjonowania systemu obsługi zgłoszeń jako systemu zależnego od zdarzeń losowych. System charakteryzowany jest jako system ze strumieniem Poisson’a zgłoszeń na wejściu, wykładniczym czasem obsługi i wieloma stanowiskami obsługi. Wyniki przedstawiono w postaci wykresów na podstawie danych rzeczywistych otrzymanych z oddziału celnego.

EN

Paper discussed the modeling of customs processes for truck vehicles using the Markov processes and mass service theory (queue theory), showing the operation of the notification handling system as a system dependent on random events. The system is characterized as a system with Poisson input stream, exponential service time and many service stations. The results are presented in the form of graphs based on real data received from the customs office.

16

Zastosowanie procesu Markowa w modelowaniu systemu eksploatacji pojazdów mechanicznych

Brzeziński Marian, Zdunek Paulina

Systemy Logistyczne Wojsk

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2017

|

Vol. 46, no.1

6--17

PL

Jednymi z najczęściej wykorzystywanymi w modelowaniu matematycznym procesami stochastycznymi są procesy Markowa. Stanowią one grupę metod analitycznych opartych na analizie procesów losowych, których podstawą jest określenie prawdopodobieństwa przejścia warunkowego. Zaprezentowany w artykule model jednorodnej odnowy prostej dla pojazdów mechanicznych może stanowić podstawę do efektywnego planowania zadań w systemie eksploatacji w danym przedsiębiorstwie.

EN

One of the most commonly used in mathematical modeling of stochastic processes is the Markov processes. They are a group of analytical methods based on the analysis of random processes based on the determination of the probability of a conditional transition. Presented in the article homogeneous model of simple renewal for motor vehicles can be the basis for effective planning of tasks in the system of operation in a enterprise

17

Valuing managerial flexibility : an application of real-option theory to steel industry investments

Rębiasz B., Gaweł B., Skalna I.

Operations Research and Decisions

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2017

|

Vol. 27, No. 2

91--111

EN

In the steel industry which is subject to significant volatility in its output prices and market demands for different ranges of products the diversification of production can generate important value for switch real options. Therefore, a common practice is to invest in various assets, thus generating the possibility of diversification of production and valuable switch options. The incremental benefit of product switch options in steel plant projects has been assessed. Such options are valued using the Monte Carlo simulation and modeling the prices of and demand for steel products as geometric Brownian motion (GBM). Our results show that this option can generate a significant increase in the net present value (NPV) of metallurgical projects.

18

Comparative examination of pollutant emission from an automotive internal combustion engine with the use of vehicle driving tests

Chłopek Z., Biedrzycki J., Lasocki J., Wójcik P.

Combustion Engines

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2016

|

R. 55, nr 1

56--64

EN

The pollutant emission from automotive internal combustion (IC) engines is highly susceptible to engine operation states determined by vehicle velocity processes. The article presents results of comparative examinations of specific distance pollutant emission characteristics determined from various vehicle driving tests. The specific distance pollutant emission was determined using vehicle type-approval and special tests as well as tests developed at the Automotive Industry Institute (PIMOT), treated as realizations of the stochastic process of vehicle velocity. The research results confirmed high susceptibility of the IC engine pollutant emission to the engine operation states, which endorses the usefulness of treating the conditions of operation of automotive engines as stochastic processes.

PL

Emisja zanieczyszczeń z samochodowych silników spalinowych jest bardzo wrażliwa na stany pracy silników zdeterminowane procesami prędkości samochodów. W niniejszej pracy przedstawiono wyniki badań porównawczych charakterystyk emisji drogowej zanieczyszczeń w różnych testach jezdnych. Do wyznaczania emisji drogowej zanieczyszczeń wykorzystano testy stosowane w procedurach homologacyjnych i testy specjalne oraz opracowane w Przemysłowym Instytucie Motoryzacji, traktowane jako realizacje procesu stochastycznego prędkości samochodu. Wyniki badań potwierdziły znaczną wrażliwość emisji zanieczyszczeń na stany pracy silnika spalinowego, co potwierdza celowość traktowania warunków pracy silników samochodowych jako procesów stochastycznych.

19

Stochastic analysis in the acoustics of damped sounds

Banek T.

Mechanics and Control

|

2014

|

Vol. 33, no. 1

1--4

EN

A stochastic model of sound propagation in damping medium is proposed. It consists of: (1) Ito's stochastic differential equation describing the sound propagation, (2) a potential which models the damping effects. However, due to presence of path integrals this model is elaborate and time consuming, hence inappropriate for numerical simulations and/or model calibrations. To make it simpler we used the classical results of stochastic analysis; Feynman-Kac formula and Girsanov tansformation obtaining easy-to-use computational procedure for practical purposes.

PL

W pracy przedstawiono stochastyczny model propagacji dźwięku w ośrodku tłumiącym. W badaniach, do modelowania propagacji dźwięku, zastosowano stochastyczne równanie różniczkowe Ito. Zjawiska tłumienia zamodełowano z zastosowaniem potencjału V(x). Ze względu na obecność całki po trajektoriach opracowanie modelu jest czasochłonne. W celu uproszczenia modelu i umożliwienia jego zastosowania w symulacjach numerycznych wykorzystano wyniki klasycznej analizy stochastycznej. Zastosowanie wzoru Feynmana--Kaca i transformacji Grisanova umożliwiło opracowanie łatwej w użyciu procedury obliczeniowej do zastosowań praktycznych.

20

Probabilistic Constructions of Computable Objects and a Computable Version of Lovász Local Lemma

Rumyantsev A., Shen A.

Fundamenta Informaticae

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2014

|

Vol. 132, nr 1

1--14

EN

A nonconstructive proof can be used to prove the existence of an object with some properties without providing an explicit example of such an object. A special case is a probabilistic proof where we show that an object with required properties appears with some positive probability in some random process. Can we use such arguments to prove the existence of a computable infinite object? Sometimes yes: following [8], we show how the notion of a layerwise computable mapping can be used to prove a computable version of Lovász local lemma.