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1
Content available remote Combinatorial Etude
100%
Stoenchev M. , Todorov V.
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2021
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tom Vol. 25
231--234
EN
The purpose of this article is to consider a special class of combinatorial problems, the so called Prouhet-Tarry Escot problem, solution of which is realized by constructing finite sequences of ±1. For example, for fixed p∈N, is well known the existence of np∈N with the property: any set of np consecutive integers can be divided into 2 sets, with equal sums of its p[th] powers. The considered property remains valid also for sets of finite arithmetic progressions of complex numbers.
2
Content available remote An optimization technique for estimating Sobol sensitivity indices
100%
Todorov V. , Georgiev S.
Annals of Computer Science and Information Systems
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2022
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tom Vol. 32
93--96
EN
In this paper we proposed an optimization techniquefor improving the Monte Carlo algorithms based on Halton and Sobol algorithms. The novelty of the proposed approaches is that the optimization of the Halton and Sobol sequences is applied for the first time and essentially improves the results by the original sequences. The results will be of great importance for the environment protection and the trustability of forecasts.
3
Content available remote A stochastic optimization method for European option pricing
100%
Todorov V. , Georgiev S.
Annals of Computer Science and Information Systems
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2022
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tom Vol. 32
97--100
EN
In the contemporary finance the Monte Carlo andquasi-Monte Carlo methods are solid instruments to solve various problems. In the paper the problem of finding the fair value of European style options is considered. Regarding the option pricing problems, Monte Carlo methods are extremely efficient and useful, especially in higher dimensions. In this paper we show simulation optimization methods which essentially improve the accuracy of the standard approaches for European style options.
4
Content available remote Optimized Nano Grid Approach for Small Critical Loads
80%
Todorov D. , Todorov V. , Fidanova S.
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2021
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tom Vol. 26
81--84
EN
This study is focused on the possibility of utilizing solar energy nano grids for feeding small scale critical loads. The reasons conditioning this necessity are reviewed and the strengths of small scale micro grids over the centralized type of powering are stated. On the basis of studies on renewable energy sources, photovoltaic converters are pointed to be most appropriate for small scale generation in urban conditions at specific geographical region. The loads of typical traffic lights show that they are relatively constant, which makes such consumers very suitable for micro or nano grids.
5
Content available remote Optimized stochastic methods for sensitivity analysis for large-scale air pollution model
80%
Todorov V. , Ostromsky T. , Dimov I. , Georgieva R.
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2021
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tom Vol. 26
85--88
EN
Environmental security is rapidly becoming a significant topic of present interest all over the world, and environmental modelling has a very high priority in various scientific fields, respectively. Different optimizations of the Latin Hypercube Sampling algorithm have been used in our sensitivity studies of the model output results for some air pollutants with respect to the emission levels and some chemical reactions rates.
6
Content available remote A New Optimized Stochastic Approach for Multidimensional Integrals in Machine Learning
80%
Todorov V. , Apostolov S. , Dimov I. , Fidanova S.
Annals of Computer Science and Information Systems
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2020
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tom 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.
7
Content available remote Optimized lattice rule and adaptive approach for multidimensional integrals with applications
80%
Todorov V. , Dimov I. , Fidanova S. , Poryazov S.
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2021
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tom Vol. 26
75--80
EN
In this work we make a comparison between optimized lattice and adaptive stochastic approaches for multidimensional integrals with different dimensions. Some of the integrals has applications in environmental safety and control theory.
8
Content available remote Optimized Stochastic Approach for Integral Equations
80%
Todorov V. , Fidanova S. , Dimov I. , Georgieva R.
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2021
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tom Vol. 25
239--242
EN
An optimized Monte Carlo approach (OPTIMIZED MC) for a Fredholm integral equations of the second kind is presented and discussed in the present paper. Numerical examples and results are discussed and MC algorithms with various initial and transition probabilities are compared.
9
Content available remote Optimized Method based on Lattice Sequences for Multidimensional Integrals in Neural Networks
80%
Todorov V. , Dimov I. , Fidanova S.
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2021
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tom 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.
10
Content available remote An Optimized Technique for Wigner Kernel Estimation
80%
Todorov V. , Fidanova S. , Dimov I. , Poryazov S.
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2021
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tom 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.
11
Content available remote An Optimized Stochastic Techniques related to Option Pricing
80%
Todorov V. , Dimov I. , Fidanova S. , Apostolov S.
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2021
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tom 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.
12
Content available remote An optimized Monte Carlo approach for multidimensional integrals related to intelligent systems
61%
Todorov V. , Dimov I. , Fidanova S. , Georgieva R. , Ostromsky T. , Poryazov S.
Annals of Computer Science and Information Systems
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2022
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tom Vol. 32
101--104
EN
We study an optimized Monte Carlo algorithm forsolving multidimensional integrals related to intelligent systems. Recently Shaowei Lin consider the difficult task of evaluating multidimensional integrals with very high dimensions which are important to machine learning for intelligent systems. Lin multidimensional integrals with 3 to 30 dimensions, related to applications in machine learning, will be evaluated with the presented optimized Monte Carlo algorithm and some advantageous of the method will be analyzed.
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