Misfit landforms imposed by ill-conditioned inverse parametric problems

In the paper, we put forward a new topological taxonomy which allows to distinguish and separate multiple solutions to the ill-conditioned parametric inverse problems appearing in engineering, geophysics, medicine, etc. This taxonomy distinguishes the areas of insensitivity to parameters, called landforms of the misfit landscape, be it around minima (lowlands), maxima (uplands), or stationary points (shelves). We proved their important separability and completeness conditions. In particular, lowlands, uplands and shelves are pairwise disjoint and there are no other subsets of the positive measure in the admissible domain on which misfit function takes a constant value. The topological taxonomy is related to the second, 'local' one, which characterizes the types of ill-conditioning of the particular solutions. We hope that the proposed results will be helpful for a better and more precise formulation of the ill-conditioned inverse problems and for selecting and profiling complex optimization strategies used to solve these problems

Metoda rejestracji i wizualizacji ruchu urządzenia mobilnego

The article presents the possibility to use mobile devices for recording and visualizing motion. Research focuses on Android devices. The study was written application for mobile devices that allows reading data from the magnetic sensor and acceleration sensor in three axes X, Y and Z. The tests were made on two devices with similar characteristics. Selected results are presented in the tables.Artykuł przedstawia mozliwość wykorzystania urządzen mobilnych do rejestracji i wizualizacji ruchu. Przeprowadzone badania dotyczą urządzeń z systemem Android. Na potrzeby badań została napisana aplikacja, która umożliwa odczyt danych z sensora przyśpieszenia oraz magnetometru w trzech osiach X, Y i Z. Badania zostały dokonane na dwóch urzadzeniach o podobnych parametrach. Wybrane wyniki zostały przedstawione w postaci tabel

On the Computational Cost and Complexity of Stochastic Inverse Solvers

The goal of this paper is to provide a starting point for investigations into a mainly underdeveloped area of research regarding the computational cost analysis of complex stochastic strategies for solving parametric inverse problems. This area has two main components: solving global optimization problems and solving forward problems (to evaluate the misfit function that we try to minimize). For the first component, we pay particular attention to genetic algorithms with heuristics and to multi-deme algorithms that can be modeled as ergodic Markov chains. We recall a simple method for evaluating the first hitting time for the single-deme algorithm and we extend it to the case of HGS, a multi-deme hierarchic strategy. We focus on the case in which at least the demes in the leaves are well tuned. Finally, we also express the problems of finding local and global optima in terms of a classic complexity theory. We formulate the natural result that finding a local optimum of a function is an NP-complete task, and we argue that finding a global optimum is a much harder, DP-complete, task. Furthermore, we argue that finding all global optima is, possibly, even harder (#P-hard) task. Regarding the second component of solving parametric inverse problems (i.e., regarding the forward problem solvers), we discuss the computational cost of hp-adaptive Finite Element solvers and their rates of convergence with respect to the increasing number of degrees of freedom. The presented results provide a useful taxonomy of problems and methods of studying the computational cost and complexity of various strategies for solving inverse parametric problems. Yet, we stress that our goal was not to deliver detailed evaluations for particular algorithms applied to particular inverse problems, but rather to try to identify possible ways of obtaining such results

A multi objective memetic inverse solver reinforced by local optimization methods

We propose a new memetic strategy that can solve the multi-physics, complex inverse problems, formulated as the multi-objective optimization ones, in which objectives are misfits between the measured and simulated states of various governing processes. The multi-deme structure of the strategy allows for both, intensive, relatively cheap exploration with a moderate accuracy and more accurate search many regions of Pareto set in parallel. The special type of selection operator prefers the coherent alternative solutions, eliminating artifacts appearing in the particular processes. The additional accuracy increment is obtained by the parallel convex searches applied to the local scalarizations of the misfit vector. The strategy is dedicated for solving ill-conditioned problems, for which inverting the single physical process can lead to the ambiguous results. The skill of the selection in artifact elimination is shown on the benchmark problem, while the whole strategy was applied for identification of oil deposits, where the misfits are related to various frequencies of the magnetic and electric waves of the magnetotelluric measurements. 2016 Elsevier B.V

An agent-based model of hierarchic genetic search

AbstractAn effective exploration of the large search space by single population genetic-based metaheuristics may be a very time consuming and complex process, especially in the case of dynamic changes in the system states. Speeding up the search process by the metaheuristic parallelisation must have a significant negative impact on the search accuracy.There is still a lack of complete formal models for parallel genetic and evolutionary techniques, which might support the parameter setting and improve the whole (often very complex) structure management.In this paper, we define a mathematical model of Hierarchical Genetic Search (HGS) based on the genetic multi-agent system paradigm. The model has a decentralised population management mechanism and the relationship among the parallel genetic processes has a multi-level tree structure. Each process in this tree is Markov-type and the conditions of the commutation of the Markovian kernels in HGS branches are formulated

Performance analysis of the TensorFlow library with different optimisation algorithms

This paper presents the results of performance analysis of the Tensorflow library used in machine learning and deep neural networks. The analysis focuses on comparing the parameters obtained when training the neural network model for optimization algorithms: Adam, Nadam, AdaMax, AdaDelta, AdaGrad. Special attention has been paid to the differences between the training efficiency on tasks using microprocessor and graphics card. For the study, neural network models were created in order to recognise Polish handwritten characters. The results obtained showed that the most efficient algorithm is AdaMax, while the computer component used during the research only affects the training time of the neural network model used

BADANIE WPŁYWU STEROWANIA GRĄ PLATFORMOWĄ NA EFEKTYWNOŚĆ ROZGRYWKI

The aim of this research is to check which of two devices the keyboard or the controller – has a positive effect on a player's game-play in a platform game. Four parameters are defined: death count, error count, game time, learning time. A custom game is designed and implemented specifically for the research. The conducted experiment is divided into thirty-minute sessions, during which one player participates in the game after getting acquainted with the game’s mechanics. After completing the game, he/she fills out a survey in which he/she can express his/her level of satisfaction while using the assigned device. Each player has only one attempt. 16 players agree to participate. They are divided into two groups of 8 people each. Participants in the first group use the keyboard while those in the second group use the controller. In order to determine final results for the tested devices, the AHP method is used. The importance values for all pairs of measured parameters are determined in order to calculate their priorities. The priorities allow for distinguishing important from less important parameters. For this purpose, a survey of experienced players is conducted. They help to identify parameter importance. After trials and analysis of responses from the game-play satisfaction and parameter importance surveys, it turns out that players using the keyboard achieve better results, and the keyboard is more satisfying to use.Celem badań było sprawdzenie, które z dwóch urządzeń służących do sterowania postacią w zręcznościowej grze platformowej, klawiatura czy kontroler, wpływa pozytywnie na wyniki rozgrywki gracza. W tym celu zdefiniowane zostały cztery parametry: liczba śmierci, liczba błędów, czas gry, czas nauki. Badania polegały na ukończeniu gry zaprojektowanej i zaprogramowanej specjalnie na potrzeby badań. Badania zostały podzielone na trzydziestominutowe sesje, podczas których jeden gracz brał udział w rozgrywce po wcześniejszym zapoznaniu się z mechanikami gry. Po ukończeniu gry wypełniał ankietę, w której mógł wyrazić swój poziom satysfakcji z korzystania z przypisanego mu urządzenia. Na każdego gracza przypadała jedna próba wykorzystująca klawiaturę lub kontroler. Do badań zgłosiło się 16 osób, które zostały podzielone na dwie grupy badawcze po 8 osób. Uczestnicy z pierwszej grupy korzystali z klawiatury podczas badań, a osoby z drugiej – z kontrolera. Aby wyznaczyć wyniki końcowe dla badanych urządzeń, dzięki którym można było je ze sobą porównać, zastosowana została metoda AHP. Na potrzeby tej metody należało określić przewagi pomiędzy wszystkimi mierzonymi parametrami, aby obliczyć ich wagi. Wagi te przyczynić się miały do wyróżnienia parametrów ważnych od mniej ważnych. W tym celu utworzona została ankieta skierowana do doświadczonych graczy, którzy pomogli w określeniu tych przewag. Po przeprowadzeniu badań i analizie odpowiedzi z ankiet dotyczących satysfakcji z rozgrywki oraz przewag parametrów, okazało się, że gracze korzystający z klawiatury otrzymali lepsze wyniki, a klawiatura była bardziej satysfakcjonująca w użyciu

Existence of solutions for wave-type hemivariational inequalities with noncoercive viscosity damping

AbstractIn this paper we prove the existence of solutions for a hyperbolic hemivariational inequality of the form u″+Au′+Bu+∂j(u)∋f, where B is a linear elliptic operator and A is linear and nonnegative (not necessarily coercive)