Approximating Approximate Pattern Matching

Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the approximate pattern matching problem asks for computation of a particular \emph{distance} function between $P$ and every $m$-substring of $T$. We consider a $(1\pm\varepsilon)$ multiplicative approximation variant of this problem, for $\ell_p$ distance function. In this paper, we describe two $(1+\varepsilon)$-approximate algorithms with a runtime of $\widetilde{O}(\frac{n}{\varepsilon})$ for all (constant) non-negative values of $p$. For constant $p \ge 1$ we show a deterministic $(1+\varepsilon)$-approximation algorithm. Previously, such run time was known only for the case of $\ell_1$ distance, by Gawrychowski and Uzna\'nski [ICALP 2018] and only with a randomized algorithm. For constant $0 \le p \le 1$ we show a randomized algorithm for the $\ell_p$, thereby providing a smooth tradeoff between algorithms of Kopelowitz and Porat [FOCS~2015, SOSA~2018] for Hamming distance (case of $p=0$) and of Gawrychowski and Uzna\'nski for $\ell_1$ distance

Power - plant

Projekt „POWER - PLANT“ se zabývá rehabilitací bývalé Ústřední elektrárny a konverze Dolu Schöeller (Nejedlý I a III) v obci Důl Libušín. Nově bude pro objekt elektrárny navržena technologie s progresivním fluidním kotlem na biomasu, parní turbínou o výkonu 7 MW a absorpční (trigenerační) jednotka produkující teplo, chlad a elektřinu, která navíc bude fungovat jako chladič primárního okruhu elektrárny. Zdrojem vody nejen pro elektrárnu bude bývalá těžební jáma Nejedlý I, která je v současnosti zaplavena pitnou vodou o teplotě cca 12°C. Tento systém využívá s vysokou účinností vložené palivo (biomasu), kterého je ve výsledku potřeba méně. Větší podíl vyrobené elektřiny a část tepla budou distribuovány do veřejné sítě. Na většině území budou navrženy veřejně přístupné skleníky z ocelovo-hliníkové konstrukce vyplněné ETFE fólií tvořící tepelně izolační membránu naplněnou vzduchem. Důvodem je vytvoření podmínek pro pěstování tropických a subtropických rostlin. Skleníky budou napojeny na absorpční jednotku elektrárny (prostřednictvím podzemních meandrů ve kterých bude cirkulovat voda), ventilační šachtu dolu a na důlní vodu - tudíž bude možné řídit podmínky vnitřního prostředí těchto staveb bez vlivu ročního období a hlavně bez nutnosti montáže dalších technologických zařízení. Zároveň bude zajištěna kooperace s absorpční jednotkou na chlazení primárního okruhu - proto odpadá nutnost chladících věží, případně ventilátorů. Součástí projektu bude vybudování detašovaných pracovišť Fakulty strojní ČVUT v Praze - Ústavu progresivních technologií a systémů pro energetiku a Fakulty agrobiologie, potravinových a přírodních zdrojů ČZU v Praze. Důvodem je umožnění studentům a vědcům aktivně a hlavně v praxi se podílet na provozu a především vývoji dané problematiky. Pro veřejnost je v areálu kromě samotných skleníků přístupné také vnitřní a venkovní termální koupání. Součástí vstupního vestibulu je bistro a především přednášková síň. Cílem práce je decentralizovaný botanicko-energetický soubor staveb produkující elektřinu, teplo, chlad a biomasu a vytvářející rekreační, edukační a výzkumné podmínky.The "POWER - PLANT" deals with the rehabilitation of the former Central Power Conversion and Dale Schoeller (Nejedly I and III) in the village Libušín Mine. Will be newly designed for building the power plant technology with progressive fluidized bed boiler to biomass steam turbine with an output of 7 MW and absorption (trigeneration) unit producing heat, cooling and electricity, which also will function as a cooler primary circuits. The source of water for the power plant will not only former mining pit Nejedlý I which is currently flooded drinking water at about 12 ° C. This system uses high efficiency embedded fuel (biomass), which is ultimately required less. A greater proportion of electricity generated and part of the heat will be distributed to the public network. In most areas will be proposed publicly accessible greenhouses of steel-aluminum construction filled ETFE foil forming the heat insulating membrane filled with air. The reason is to create conditions for the cultivation of tropical and subtropical plants. Greenhouses will be connected to the absorption unit power (underground meanders through which water will circulate), the ventilation shaft mine and mine water - therefore it will be possible to manage the conditions of the internal environment of the building without the influence of the season and especially without mounting other technological devices. It will provide for cooperation with the absorption unit for cooling the primary circuit - therefore eliminating the need for cooling towers or fans. The project will build a detached departments of the Faculty of Mechanical Engineering in Prague - Institute of progressive technologies and systems for energy and the Faculty of Agronomy and Natural Resources CULS. The reason is to allow students and scientists actively and in practice mainly participate in the operation and especially the development of the issue. The public in the area besides themselves open to the greenhouses indoor and outdoor thermal swimming. Part of the entrance hall is a bistro and foremost lecture hall. The aim is decentralized botanical-energy complex of buildings that produce electricity, heat, cooling, and biomass, and creating recreational, educational and research conditions.

Learning Relevant Reasoning Patterns with Neuro-Logic Programming

Tato práce demonstruje schopnosti vylepšeného neuro-logického frameworku podchytit různé úlohy umělé inteligence, které jsou založeny na různorodých metodách uvažování. Základadem k tomuto frameworku je stávající engine nazvaný Lifted Relational Neural Networks. V práci popisujeme nejčastější metody strojového uvažování používané ve statistických a symbolických metodách a také jak mohou být jednotlivé vzorce uvažování zakódovány do podoby navrženého neuro-logického programování. Dále se blíže zaměřujeme na schopnosti vyjadřování, které vzniknou kombinací obou přístupů. Na vybraných příkladech z herního prostředí ilustrujeme, jak tento společný neuro-logický přístup rozšiřuje schopnosti již existujísích metod uvažování pracovat nad relačními strukturami při zachování výhod neurálního učení.This thesis demonstrates the capability of an enhanced neuro-logic programming framework to capture diverse artificial intelligence tasks based on different reasoning patterns. The enhanced framework is building on existing engine called Lifted Relational Neural Networks. We describe common reasoning patterns used in statistical and symbolic methods and demonstrate how each particular pattern may be captured from the perspective of the proposed neuro-logic programming framework. We discuss the patterns in context of learning and reasoning and further focus more closely on abilities that arise from combination of both approaches. On selected examples from simple game environments, we illustrate how this joint neuro-logic programming approach broadens the scope of existing reasoning patterns through the ability to represent and reason with relational information while keeping the benefits of neural learning

Distributed graph problems through an automata-theoretic lens

The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or parallel algorithm if and only if it has a small locality. In this work we seek to automate the study of solvability and locality: given the description of a graph problem $\Pi$, we would like to determine if $\Pi$ is solvable and what is the asymptotic locality of $\Pi$ as a function of the size of the graph. Put otherwise, we seek to automatically synthesize efficient distributed and parallel algorithms for solving $\Pi$. We focus on locally checkable graph problems; these are problems in which a solution is globally feasible if it looks feasible in all constant-radius neighborhoods. Prior work on such problems has brought primarily bad news: questions related to locality are undecidable in general, and even if we focus on the case of labeled paths and cycles, determining locality is $\mathsf{PSPACE}$-hard (Balliu et al., PODC 2019). We complement prior negative results with efficient algorithms for the cases of unlabeled paths and cycles and, as an extension, for rooted trees. We introduce a new automata-theoretic perspective for studying locally checkable graph problems. We represent a locally checkable problem $\Pi$ as a nondeterministic finite automaton $\mathcal{M}$ over a unary alphabet. We identify polynomial-time-computable properties of the automaton $\mathcal{M}$ that near-completely capture the solvability and locality of $\Pi$ in cycles and paths, with the exception of one specific case that is \mbox{co-\mathsf{NP}}-complete

Efficient Classification of Locally Checkable Problems in Regular Trees

We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the $[\Theta(\log n), \Theta(n)]$ region, in two settings. We present one algorithm for unrooted regular trees and another algorithm for rooted regular trees. The algorithms take the description of a locally checkable labeling problem as input, and the running time is polynomial in the size of the problem description. The algorithms decide if the problem is solvable in $O(\log n)$ rounds. If not, it is known that the complexity has to be $\Theta(n^{1/k})$ for some $k = 1, 2, \dotsc$, and in this case the algorithms also output the right value of the exponent $k$. In rooted trees in the $O(\log n)$ case we can then further determine the exact complexity class by using algorithms from prior work; for unrooted trees the more fine-grained classification in the $O(\log n)$ region remains an open question

Efficient Classification of Locally Checkable Problems in Regular Trees

We give practical, efficient algorithms that automatically determine the asymptotic distributed round complexity of a given locally checkable graph problem in the [Θ(log n), Θ(n)] region, in two settings. We present one algorithm for unrooted regular trees and another algorithm for rooted regular trees. The algorithms take the description of a locally checkable labeling problem as input, and the running time is polynomial in the size of the problem description. The algorithms decide if the problem is solvable in O(log n) rounds. If not, it is known that the complexity has to be Θ(n^{1/k}) for some k = 1, 2, ..., and in this case the algorithms also output the right value of the exponent k. In rooted trees in the O(log n) case we can then further determine the exact complexity class by using algorithms from prior work; for unrooted trees the more fine-grained classification in the O(log n) region remains an open question

Locally Checkable Problems in Rooted Trees

Consider any locally checkable labeling problem Π in rooted regular trees: there is a finite set of labels Σ, and for each label x ∈ Σ we specify what are permitted label combinations of the children for an internal node of label x (the leaf nodes are unconstrained). This formalism is expressive enough to capture many classic problems studied in distributed computing, including vertex coloring, edge coloring, and maximal independent set. We show that the distributed computational complexity of any such problem Π falls in one of the following classes: it is O(1), Θ(log^* n), Θ(log n), or n^{Θ(1)} rounds in trees with n nodes (and all of these classes are nonempty). We show that the complexity of any given problem is the same in all four standard models of distributed graph algorithms: deterministic LOCAL, randomized LOCAL, deterministic CONGEST, and randomized CONGEST model. In particular, we show that randomness does not help in this setting, and the complexity class Θ(log log n) does not exist (while it does exist in the broader setting of general trees). We also show how to systematically determine the complexity class of any such problem Π, i.e., whether Π takes O(1), Θ(log^* n), Θ(log n), or n^{Θ(1)} rounds. While the algorithm may take exponential time in the size of the description of Π, it is nevertheless practical: we provide a freely available implementation of the classifier algorithm, and it is fast enough to classify many problems of interest

Change in Dimensions and Surface Roughness of 42CrMo4 Steel after Nitridation in Plasma and Gas

The influence of plasma nitriding and gas nitriding processes on the change of surface roughness and dimensional accuracy of 42CrMo4 steel was investigated in this paper. Both processes almost always led to changes in the surface texture. After plasma nitriding, clusters of nitride ions were formed on the surface of steel, while gas nitriding very often led to the new creation of a formation of a “plate-like” surface texture. In both cases of these processes, a compound layer in specific thickness was formed, although the parameters of the processes were chosen with the aim of suppressing it. After the optimizing of nitriding parameters during nitriding processes, it was found that there were no changes in the surface roughness evaluated using the Ra parameter. However, it turned out that when using a multi-parameter evaluation of roughness (the parameters Rz, Rsk and Rku were used), there were presented some changes in roughness due to nitriding processes, which affect the functional behavior of the components. Roughness changes were also detected by evaluating surface roughness profiles, where nitriding led to changes in peak heights and valley depths. Nitriding processes further led to changes in dimensions in the form of an increase of 0.032 mm on average. However, the magnitude of the change has some context on chemical composition of material. A larger increase in dimensions was found with gas nitriding. The change in the degree of IT accuracy is closely related to the change in dimension. For both processes, there was a change of one degree of IT accuracy compared to the ground part (from IT8 to IT9). On the basis of the achieved dimensional accuracy results, a coefficient of change in the degree of accuracy IT was created, which can be used to predict changes in the dimensional accuracy of ground surfaces after nitriding processes in degrees of accuracy IT3–IT10. In this study, a tool for predicting changes in degrees of accuracy of ground parts after nitriding processes is presented

Programming education in Scratch and Snap! environments

Scratch2.0 is educational, iconic, scripting programming environment focused on children in range of age from 8 to 16, and being developed by Lifelong Kindergarten group on Massachusetts technology institute (MIT). By composing graphical components in the form of various puzzle pieces we create scripts which individual maskots are acting on the scene and externalize our story. To this environment also exists alternative Snap! (previously called BYOB as modification of Scratchs' first generation), developed by Jens Mönig in cooperation with Brian Harvey, which is trying to remove deficiencies, barriers and poorer possibilities in programming by which Scratch is suffering. Thesis firstly introducing both environments in their major versions or generations (in order of development: Scratch1, BYOB, Scratch2; and Snap!), secondly comparing all of them based on chosen criterias, and finally describing new programming concepts and from them incoming possibilities and techniques, which can be in Snap! unlike in Scratch - and in some cases even in its predecessor BYOB - applied. Included are not only algorithmic examples, but also projects in Snap and ScratchN developed by author of this bachelors thesis. To understand this bachelor thesis is required to have experience with at least one of the environment Scratch1, Scratch2, or BYOB. This thesis was created by typesetting system TeX with usage of OPmac macros

Approximating approximate pattern matching

Given a text T of length n and a pattern P of length m, the approximate pattern matching problem asks for computation of a particular distance function between P and every m-substring of T. We consider a (1 +/- epsilon) multiplicative approximation variant of this problem, for l_p distance function. In this paper, we describe two (1+epsilon)-approximate algorithms with a runtime of O~(n/epsilon) for all (constant) non-negative values of p. For constant p >= 1 we show a deterministic (1+epsilon)-approximation algorithm. Previously, such run time was known only for the case of l_1 distance, by Gawrychowski and Uznanski [ICALP 2018] and only with a randomized algorithm. For constant 0 <= p <= 1 we show a randomized algorithm for the l_p, thereby providing a smooth tradeoff between algorithms of Kopelowitz and Porat [FOCS 2015, SOSA 2018] for Hamming distance (case of p=0) and of Gawrychowski and Uznanski for l_1 distance.ISSN:1868-896