Definability equals recognizability for graphs of bounded treewidth

We prove a conjecture of Courcelle, which states that a graph property is definable in MSO with modular counting predicates on graphs of constant treewidth if, and only if it is recognizable in the following sense: constant-width tree decompositions of graphs satisfying the property can be recognized by tree automata. While the forward implication is a classic fact known as Courcelle's theorem, the converse direction remained openComment: 21 pages, an extended abstract will appear in the proceedings of LICS 201

Polynomial Time Algorithms in Invariant Theory for Torus Actions

An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, namely, orbit equality, orbit closure intersection, and orbit closure containment. These capture and relate to a variety of problems within mathematics, physics and computer science, optimization and statistics. These orbit problems extend the more basic null cone problem, whose algorithmic complexity has seen significant progress in recent years. In this paper, we initiate a study of these problems by focusing on the actions of commutative groups (namely, tori). We explain how this setting is motivated from questions in algebraic complexity, and is still rich enough to capture interesting combinatorial algorithmic problems. While the structural theory of commutative actions is well understood, no general efficient algorithms were known for the aforementioned problems. Our main results are polynomial time algorithms for all three problems. We also show how to efficiently find separating invariants for orbits, and how to compute systems of generating rational invariants for these actions (in contrast, for polynomial invariants the latter is known to be hard). Our techniques are based on a combination of fundamental results in invariant theory, linear programming, and algorithmic lattice theory

Determining the toxicity of the biomass of Cladophora sp.

Finding new or alternative feeds, feed additives, and raw materials safe for health and the environment is significant in intensifying livestock production. At the same time, the fodder base obtained from aquatic ecosystems – algae – deserves special attention. The advantage of using algae as fodder is using small areas for their cultivation and a high reproduction rate. In addition, algae are grown where other plants cannot grow, and the productivity of algae is several times higher than that of higher plants. Algae can produce beneficial compounds and biomass, which are also used to increase the nutritional value of food products. Biomass obtained from algae is a source of necessary vitamins, minerals, proteins, polyunsaturated fatty acids, antioxidants, and other necessary nutrients. The composition of algae depends on the environment from which this biomass is collected, the conditions of algae cultivation, the season, the species of algae, and many other factors. In addition, it should be noted that some algae, out of the total amount, are toxic when consumed. That is why it is essential to research their toxicity. The article presents the results of studying the toxicity of the biomass of Cladophora sp. on the body of guppy fish. When studying the effect of biomass Cladophora sp. on the body of guppy fish, it was established that its use for 96 hours in doses of 5, 10, 25, 50, and 100 mg/l did not cause their death, and its LC50 is higher than 100 mg/l. In addition, no changes were detected in the behavior of the fish; they were active, mobile, and actively responding to external stimuli. The fish of the experimental groups were not distinguished from those of the control group

Evaluating Matrix Circuits

The circuit evaluation problem (also known as the compressed word problem) for finitely generated linear groups is studied. The best upper bound for this problem is $\mathsf{coRP}$, which is shown by a reduction to polynomial identity testing. Conversely, the compressed word problem for the linear group $\mathsf{SL}_3(\mathbb{Z})$ is equivalent to polynomial identity testing. In the paper, it is shown that the compressed word problem for every finitely generated nilpotent group is in $\mathsf{DET} \subseteq \mathsf{NC}^2$. Within the larger class of polycyclic groups we find examples where the compressed word problem is at least as hard as polynomial identity testing for skew arithmetic circuits

ВИЗНАЧЕННЯ ТОКСИЧНОСТІ НОВОГО ДЕЗІНФІКУЮЧОГО ЗАСОБУ ТДС

The article presents the parameters of acute toxicity and side effects of new acid–detergent disinfectant TDS, which is used to sanitize dairy liquid. It was established that the figures DL50 native solution (concentrate) disinfectant is more than 2500 mg/kg. According to its toxic properties owned disinfectant according to GHS (globally harmonized system of classification and hazard labeling of chemicals) to the V class of toxicity – low toxic substance has weak skin–irritating properties and strong locally irritating action.The working preparation solution (0,5 % concentration) for its toxic properties not classified by GHS, because DL50  is larger that 10,000 mg / kg. Working solution has no skin–irritant properties, and locally irritant effect is 24–48 hours.В статье приведены параметры острой токсичности и побочного действия нового кислотного моюще–дезинфицирующего средства ТДС, который применяется для санитарной обработки молочной посуды. Установлено, что показатели DL50 нативного раствора (концентрата) дезинфектанта — больше 2500 мг/кг. По своим токсичным свойствам дезинфектант принадлежит, согласно СГС (согласованная на глобальном уровне система классификации опасности и маркировки химической продукции), к V классу токсичности – малотоксичные вещества, обладает слабыми кожно–раздражающими свойствами и сильным местно–раздражающим действием. Рабочий раствор препарата (0,5 % концентрации) по своим токсичным свойствам не квалифицируется по СГС, поскольку его DL50 является больше 10000 мг/кг. Рабочий раствор не обладает кожно–раздражающими свойствами, а местно–раздражающее действие проявляется в течение 24–48 часов.У статті наведено параметри гострої токсичності та побічної дії нового кислотного мийно–дезінфікуючого засобу ТДС, що застосовується для санітарної обробки молочного посуду. Встановлено, що показник DL50 нативного  (розчину концентрату) дезінфектанту є більшим як 2500 мг/кг. За своїми токсичними властивостями дезінфектант належить, згідно з УГС (узгоджена на глобальному рівні система класифікації небезпеки та маркування хімічної продукції ), до V класу токсичності – малотоксичні речовини, володіє слабкими шкірно–подразнюючими властивостями та сильною місцево–падразнюючою дією.Робочий розчин препарату у 0,5 % концентрації за своїми токсичними властивостями не кваліфікується за УГС, оскільки DL50  його є більшим, ніж 10000 мг/кг. Робочий розчин не володіє шкірно–подразнюючими властивостями, а місцево–подразнююча дія проявляється протягом 24–48 годин

Robust Simulations and Significant Separations

We define and study a new notion of "robust simulations" between complexity classes which is intermediate between the traditional notions of infinitely-often and almost-everywhere, as well as a corresponding notion of "significant separations". A language L has a robust simulation in a complexity class C if there is a language in C which agrees with L on arbitrarily large polynomial stretches of input lengths. There is a significant separation of L from C if there is no robust simulation of L in C. The new notion of simulation is a cleaner and more natural notion of simulation than the infinitely-often notion. We show that various implications in complexity theory such as the collapse of PH if NP = P and the Karp-Lipton theorem have analogues for robust simulations. We then use these results to prove that most known separations in complexity theory, such as hierarchy theorems, fixed polynomial circuit lower bounds, time-space tradeoffs, and the theorems of Allender and Williams, can be strengthened to significant separations, though in each case, an almost everywhere separation is unknown. Proving our results requires several new ideas, including a completely different proof of the hierarchy theorem for non-deterministic polynomial time than the ones previously known

Переносимость и эффективность химиотерапии у больных туберкулезом легких с множественной лекарственной устойчивостью с включением бедаквилина

The objective: to evaluate safety and efficacy of bedaquiline in the treatment of patients with multiple drug resistant tuberculosis (MDR-TB).Subjects and Methods. Clinical data of 523 patients above 18 years old registered for MDR TB treatment as per regimen 4 were retrospectively analyzed. HIV-negative patients were selected and divided into two groups by the use of bedaquiline in the chemotherapy regimen.Results. In MDR TB treatment regimen containing bedaquiline, adverse reactions were observed in 95.7% of cases, the majority of them (65.2%) were of mild or moderate degree of severity. In 30.4% of such cases, bedaquiline was temporarily discontinued (mostly due to hepatotoxic reactions). No cardiotoxicity was observed as a response to bedaquiline, the median corrected QT interval made 413 ms, the maximum value was 438 ms. Adding bedaquiline to the regimen resulted in faster (in the first 3 months of treatment) and more frequent (in 94.7%) sputum conversion by culture (in the regimens with no bedaquiline, it was achieved in 63.8% of cases, p = 0.019). Treatment with regimens containing bedaquiline was effective in 82.61% of patients, while regimens with no bedaquiline were effective in 65.2% of cases, p = 0.085.Цель исследования: определить безопасность и эффективность применения бедаквилина при лечении больных туберкулезом с множественной лекарственной устойчивостью (МЛУ-ТБ).Материалы и методы. Проведен ретроспективный анализ клинических данных 523 больных старше 18 лет, которые были зарегистрированы для лечения МЛУ-ТБ по четвертому режиму. Были отобраны ВИЧ-негативные пациенты и разделены на две группы в зависимости от применения бедаквилина в схеме химиотерапии.Результаты. Бедаквилинсодержащие схемы лечения больных МЛУ-ТБ имели частоту неблагоприятных побочных реакций в 95,7% случаев, в основном (65,2%) легкой или умеренной степени тяжести. В 30,4% случаев из них (чаще за счет развития гепатотоксических реакций) бедаквилин временно отменялся. Кардиотоксичности в ответ на прием бедаквилина не выявлено, медиана корригированного интервала QT составила 413 мс, максимальное значение ‒ 438 мс. При использовании в схемах бедаквилина быстрее (в первые 3 мес. лечения) и чаще (в 94,7%) фиксировалось прекращение бактериовыделения методом посева (в схемах без него в 63,8% случаев, p = 0,019). Эффективность лечения схемами с применением бедаквилина достигнута у 82,61% больных, схемами без бедаквилина – в 65,2% случаев, p = 0,085

Some Results on Average-Case Hardness Within the Polynomial Hierarchy

Abstract. We prove several results about the average-case complexity of problems in the Polynomial Hierarchy (PH). We give a connection among average-case, worst-case, and non-uniform complexity of optimization problems. Specifically, we show that if P NP is hard in the worst-case then it is either hard on the average (in the sense of Levin) or it is non-uniformly hard (i.e. it does not have small circuits). Recently, Gutfreund, Shaltiel and Ta-Shma (IEEE Conference on Computational Complexity, 2005) showed an interesting worst-case to averagecase connection for languages in NP, under a notion of average-case hardness defined using uniform adversaries. We show that extending their connection to hardness against quasi-polynomial time would imply that NEXP doesn’t have polynomial-size circuits. Finally we prove an unconditional average-case hardness result. We show that for each k, there is an explicit language in P Σ2 which is hard on average for circuits of size n k.