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On Lq convergence of the Hamiltonian Monte Carlo

Ghosh Soumyadip, Lu Yingdong, Nowicki Tomasz

Journal of Applied Analysis

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2023

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Vol. 29, nr 1

161--169

EN

We establish Lq convergence for Hamiltonian Monte Carlo (HMC) algorithms. More specifically, under mild conditions for the associated Hamiltonian motion, we show that the outputs of the algorithms converge (strongly for 2 ≤ q < ∞ and weakly for 1 < q < 2) to the desired target distribution. In addition, we establish a general convergence rate for an Lq convergence given a convergence rate at a specific q∗, and apply this result to conclude geometric convergence in the Euclidean space for HMC with uniformly strongly logarithmic concave target and auxiliary distributions.We also present the results of experiments to illustrate convergence in Lq.

2

Analiza porównawcza wydajności czasowej zapytań bazodanowych w języku C#

Nowicki Tomasz, Tomczak Sebastian, Kozieł Grzegorz

Journal of Computer Sciences Institute

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2022

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Vol. 22

8--12

PL

Na świecie istnieje duża liczba aplikacji komputerowych wykorzystujących bazy danych celem utrwalania, przetwarzania i wykorzystania danych, co przekłada się na wiele różnych sposobów obsługi tychże baz. Trudno jest więc wybrać rozwiązanie spełniające potrzeby użytkownika. W niniejszym artykule porówanano pod kątem wydajności trzy rozwiązania dla języka C#: szkielet aplikacji Entity Framework Core, zapytania SQL przesyłane w postaci jednego łańcucha znaków, oraz sparametryzowane zapytania Prepared Statement. Uzyskane w toku badań wyniki pozwoliły określić, że najszybszym rozwiązaniem jest wykorzystanie niesparametryzowanego zapytania SQL. Wykorzystanie Entity Framework Core jest najwolniejszym z trzech badanych rozwiązań.

EN

There are many computer applications in the world that use databases to store, process, and use data. That translates into many different ways of handling these databases. It is therefore difficult to choose a solution that meets the needs of the user. This article compares three C# solutions in terms of time efficiency: the Entity Framework Core application framework, pure SQL queries, and parameterized Prepared Statement queries. The results obtained in the course of the research has shown that the fastest solution is the use of non-parameterised SQL queries. The use of Entity Framework Core is the slowest of the three tested solutions.

3

Productivity of a low-budget computer cluster applied to overcome the n-body problem

Nowicki Tomasz, Gregosiewicz Adam, Łagodowski Zbigniew

Applied Computer Science

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2021

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Vol. 17, no 4

100--109

EN

The classical n-body problem in physics addresses the prediction of individual motions of a group of celestial bodies under gravitational forces and has been studied since Isaac Newton formulated his laws. Nowadays the n-body problem has been recognized in many more fields of science and engineering. Each problem of mutual interaction between objects forming a dynamic group is called as the n-body problem. The cost of the direct algorithm for the problem is O(n2) and is not acceptable from the practical point of view. For this reason cheaper algorithms have been developed successfully reducing the cost to O(nln(n)) or even O(n). Because further improvement of the algorithms is unlikely to happen it is the hardware solutions which can still accelerate the calculations. The obvious answer here is a computer cluster that can preform the calculations in parallel. This paper focuses on the performance of a low-budget computer cluster created on ad hoc basis applied to n-body problem calculation. In order to maintain engineering valuable results a real technical issue was selected to study. It was Discrete Vortex Method that is used for simulating air flows. The pre-sented research included writing original computer code, building a computer cluster, preforming simulations and comparing the results.

4

The Method of Decomposition of Architectural Objects for the preparation of 3D Virtual Models and Replication

Montusiewicz Jerzy, Barszcz Marcin, Dziedzic Krzysztof, Nowicki Tomasz

Advances in Science and Technology. Research Journal

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2021

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Vol. 15, no 2

247--257

EN

3D printing of historic architectural objects reduces the entire digital model by up to 200 times. With this scaling of the digital 3D model, many important architectural and decorative details are lost, and some elements lose their stiffness. Printed 3D models are now used to create specialised museum exhibitions that allow visitors to get to know them kinesthetically. This ability to touch objects applies not only to visually impaired people, but to all interested visitors. The paper describes the preparation of a digital 3D model (D3DM) dedicated to 3D printing by decomposing the real model into sub-models and using different scaling values for individual elements. The practical part presents three-dimensional modelling of historic architectural objects of Lublin and their replicas made on 3D printers in the Fused Filament Fabrication (FFF) technology. Virtual models designed in this way retain important details of objects and are also scalable as a whole, which allows for obtaining printed objects of various dimensions.

5

Błądzenie Monte Carlo według przepisu Hamiltona

Ghosh Soumyadip, Lu Yingdong, Nowicki Tomasz

Wiadomości Matematyczne

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2020

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T. 56, Nr 2

227--239

6

The insulin activity model based on insulin profiles

Nowicki Tomasz

Journal of Computer Sciences Institute

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2019

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Vol. 13

272--278

EN

The purpose of the research was to propound an insulin activity model in a human body after a subcutaneous injection. A deterministic model in the form of a mathematical function was formulated. The research was based on pharmaceutic publicly available drug information published by the manufactures. The paper presents in detail the model. The obtained results can be used in computer simulations of diabetes mellitus therapy. They suggest that activity models may be assigned to types of insulin instead of separate products.

PL

Celem badań było opracowanie modelu aktywności insuliny w organizmie człowieka po wstrzyknięciu podskórnym. Sformułowano model deterministyczny w postaci funkcji matematycznej. Badanie oparto na publicznie dostępnych informacjach farmaceutycznych opublikowanych przez producentów. Artykuł szczegółowo przedstawia model. Uzyskane wyniki mogą być wykorzystane w komputerowych symulacjach terapii cukrzycy. Sugerują one również, że modele aktywności mogą dotyczyć grup insulin zamiast konkretnych preparatów.

7

Dating of the Holstejnskä Cave deposits and their role in the reconstruction of semiblind Holśtejn Valley Cenozoic history (Czech Republic)

Kadlec Jaroslav, Hercman Helena, Nowicki Tomasz, Głazek Jerzy, Vit Jan, Śroubek Pavel, Diehl Jimmy F., Granger Darryl

Geologos

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2000

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Vol. 5

57--64

EN

Large sections in cave deposits are exposed in the Holśtejnska Cave in the Moravian Karst (Czech Republic). The study of the genesis and age of these cave deposits poses a clue to the reconstruction of this cave system and of local paleohydrographic history. The time of deposition was determined by U-series dating of speleothems, 10Be and 26Al dating of quartz pebbles, radiocarbon dating of charcoal, measurement of paleomagnetic record in both clastic sediments and speleothems and by archeological evidence.

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Rozwój systemu jaskiniowego Szczeliny Chochołowskiej (Tatry Zachodnie) w świetle wyników datowania nacieków metodą uranowo-torową

Hercman Helena, Nowicki Tomasz, Lauritzen Stein-Erik

Studia Geologica Polonica

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1998

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Vol. 113

85--103

PL

Datowanie 31 próbek nacieków z jaskini Szczelina Chochołowska metodą uranowo-torową umożliwiło rekonstrukcję warunków klimatycznych w okresie ostatnich 350 tysięcy lat w rejonie Doliny Chochołowskiej oraz etapów rozwoju jaskini. Wydzielono 7 generacji nacieków, które wskazują na okresy ciepłego, wilgotnego klimatu, oddzielone okresami pogorszenia warunków klimatycznych. Wyniki datowania nacieków w powiązaniu z obserwacjami z jaskini umożliwiły stwierdzenie 2 etapów rozwoju Szczeliny Chochołowskiej. Pierwszy etap tworzenia jaskini zakończył się około 350 tysięcy lat temu, a ponowne uaktywnienie krążenia wód i przemodelowanie części jaskini autorzy wiążą z rozwojem lodowca w okresie młodszego plejstocenu.

EN

31 speleothem samples collected in Szczelina Chochołowska Cave (Western Tatra Mts., Poland) were dated using (Figs 1 & 2) 230Th/234U method (Ivanovich & Harmon, 1992). Dates spanning from 2 ka to ca 350 ka (a-particle counting, Tab. 1, Fig. 3) have been identified. On the basis of these dating results it was possible to estimate the climatic changes in Tatra Mts over the last 350 ka. Seven periods of speleothem crystallisation were recognised from the data (Fig. 4). These record periods of warm, humid conditions separated by cold, dry ones marked by breaks in speleothem deposition. The development of the Szczelina Chochołowska Cave is show schematically in Fig. 5. Some 350 ka ago the valley floor was ca 35-45 m above its present level. The passages between cave entrances III and II were dry and speleothem crystallisation was able to start. The second stage of cave activity followed with water flow between III and I entrances and Rura passage development. The water flow through Rura was extorted by big rock fall in Ślepa Komora ca 115-95 ka ago. Later, glacier development in Chochołowska Valley probably created a hydrological barrier in the valley and the water used the older cave passages as a simpler way of circulation.