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

Conditional independence and natural conditional functions

AbstractThe concept of conditional independence (CI) within the framework of natural conditional functions (NCFs) is studied. An NCF is a function asribing natural numbers to possible states of the world; it is the central concept of Spohn's theory of deterministic epistemology. Basic properties of CI within this framework are recalled, and further results analogous to the results concerning probabilistic CI are proved. Firstly, the intersection of two CI-models is shown to be a CI-model. Using this, it is proved that CI-models for NCFs have no finite complete axiomatic characterization (by means of a simple deductive system describing relationships among CI-statements). The last part is devoted to the marginal problem for NCFs. It is shown that (pairwise) consonancy is equivalent to consistency iff the running intersection property holds

Innovation of Uniform Marker Fields for Allowing Better Scale Freedom

Tato práce se zabývá inovací Uniformního Pole Markerů, které pokrývá rozsáhlou oblast a~skládá se ze vzájemně překrývajících se dílčích markerů. Cílem je umožnit detekci z~mnoha různých vzdáleností kamery od pole markerů a~zvýšit tím svobodu pohybu kamery. Práce byla řešena experimentálně a~bylo vytvořeno několik návrhů, které byly podrobeny testům detekčních vlastností. Je představen nový způsob, jak konstruovat pole markerů s~dobrými detekčními vlastnostmi. Pro tento způsob konstrukce je navržen a~implementován algoritmus pro syntézu pole markerů a jsou navrženy změny detekčního algoritmu Uniformních Polí Markerů, které je potřeba provést pro detekci nově navržených polí markerů.This work introduces innovations to the Uniform Marker Fields which cover a~large-scale planar area and are composed of mutually overlapping partial markers. The goal of this work is to enable marker field detection from various camera distances, thus increasing the camera movement freedom. Several marker field designs were experimentally created and their detection properties were tested. A new solution to marker field design is introduced. For this solution a~synthesis algorithm of the marker field is described and implemented. Changes to an existing Uniform Marker Field detection algorithm are proposed, so that the detection algorithm can be used with the marker fields introduced in this work.

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.

Contribution of František Matúš to the research on conditional independence

summary:An overview is given of results achieved by F. Matúš on probabilistic conditional independence (CI). First, his axiomatic characterizations of stochastic functional dependence and unconditional independence are recalled. Then his elegant proof of discrete probabilistic representability of a matroid based on its linear representability over a finite field is recalled. It is explained that this result was a basis of his methodology for constructing a probabilistic representation of a given abstract CI structure. His embedding of matroids into (augmented) abstract CI structures is recalled and his contribution to the theory of semigraphoids is mentioned as well. Finally, his results on the characterization of probabilistic CI structures induced by four discrete random variables and by four regular Gaussian random variables are recalled. Partial probabilistic representability by binary random variables is also mentioned

Efficient algorithms for conditional independence inference

The topic of the paper is computer testing of (probabilistic) conditional independence (CI) implications by an algebraic method of structural imsets. The basic idea is to transform (sets of) CI statements into certain integral vectors and to verify by a computer the corresponding algebraic relation between the vectors, called the independence implication. We interpret the previous methods for computer testing of this implication from the point of view of polyhedral geometry. However, the main contribution of the paper is a new method, based on linear programming (LP). The new method overcomes the limitation of former methods to the number of involved variables. We recall/describe the theoretical basis for all four methods involved in our computational experiments, whose aim was to compare the efficiency of the algorithms. The experiments show that the LP method is clearly the fastest one. As an example of possible application of such algorithms we show that testing inclusion of Bayesian network structures or whether a CI statement is encoded in an acyclic directed graph can be done by the algebraic method