This book constitutes the proceedings of the 16th International Conference on Formal Concept Analysis, ICFCA 2021, held in Strasbourg, France, in June/July 2021.

The 14 full papers and 5 short papers presented in this volume were carefully reviewed and selected from 32 submissions. The book also contains four invited contributions in full paper length.

The research part of this volume is divided in five different sections. First, "Theory" contains compiled works that discuss advances on theoretical aspects of FCA. Second, the section "Rules" consists of contributions devoted to implications and association rules. The third section "Methods and Applications" is composed of results that are concerned with new algorithms and their applications. "Exploration and Visualization" introduces different approaches to data exploration.

This book constitutes the proceedings of the 20th International Conference on Mathematical Optimization Theory and Operations Research, MOTOR 2021, held in Irkutsk, Russia, in July 2021. 

 

The 29 full papers and 1 short paper presented in this volume were carefully reviewed and selected from 102 submissions. Additionally, 2 full invited papers are presented in the volume. The papers are grouped in the following topical sections: ​combinatorial optimization; mathematical programming; bilevel optimization; scheduling problems; game theory and optimal control; operational research and mathematical economics; data analysis.

The book begins with a discussion of what a performant system is and progresses to measuring performance and setting performance goals. It introduces different classes of queries and optimization techniques suitable to each, such as the use of indexes and specific join algorithms. You will learn to read and understand query execution plans along with techniques for influencing those plans for better performance. The book also covers advanced topics such as the use of functions and procedures, dynamic SQL, and generated queries. All of these techniques are then used together to produce performant applications, avoiding the pitfalls of object-relational mappers.

 

The materials of The International Scientific – Practical Conference is presented below. The Conference reflects the modern state of innovation in education, science, industry and social-economic sphere, from the standpoint of introducing new information technologies. It is interesting for a wide range of researchers, teachers, graduate students and professionals in the field of innovation and information technologies.

This special conference starts the new series, and therefore, it launches a tradition to follow, and an opportunity for a rapid spin up. This ICCQ conference was organized by the HSE and leading IT innovative companies such Huawei and Yandex. The ICCQ 2021 attracted a number of renowned experts including Jens Palsberg, Anders Møller, and David West. The papers were submitted from the world over. The conference attracted speakers and attendees from the USA, Europe, and Asia; therefore, this is truly an international event. Although ICCQ started as a relatively small single-day conference, it immediately gained the IEEE support. The plan for the next years is to embrace the world while keeping high quality standards.

We discuss the applicability of multiphase lattice Boltzmann method for the simulation of the drop oscillation. We demonstrate that the simulation of the single drop excited to the first eigenmode does follow Rayleigh formula. Simulations show no sensitivity to the number of the discrete velocities with D3Q19 and D3Q27 representations of the distribution function in three dimensions. The boundaries do influent the motion of the drop—division of the computational area by the even and the odd number of cells comes out important and leads to symmetry violence. The second part of the chapter describes the oscillations of the ensemble of three drops due to the excitation of the central drop in the first eigenmode. The motion of the backdrops does strongly depend on the viscosity of the fluid. We provide future details of simulations.

The relevance of studying the regulation of protein-ligand interactions is due to the emergence of new views on the role of metabolites and their key importance in vital processes. To study the protein-ligand interaction, the AB0 antigen-antibody blood system and the enzyme-substrate system of dehydrogenases were used as a test system, and ethanol was used as an influencing factor. In experiments performed with A and B blood erythrocyte antigens, natural AB0 system antibodies and monoclonal antibodies under the influence of ethanol performed change of the degree of agglutination and the time to onset of erythrocyte agglutination. It was found that ethanol can regulate the enzyme-substrate interactions of dehydrogenases: lactate dehydrogenase (EC 1.1.1.27), glyceraldehyde phosphate dehydrogenase (EC 1.1.1.12), and α-glycerol phosphate dehydrogenase (EC 1.1.1.8). The increase in the activity of studied enzymes under the influence of ethanol in the whole blood hemolysate was 2.5 - 3 times higher than in the isolated medium (with pure enzyme preparations).

This textbook on political geography is devoted to a discipline concerned with the spatial dimensions of politics. This course is an introduction to the study of political science, international relations and area studies, providing a systemic approach to the spatial dimension of political processes at all levels. It covers their basic elements, including states, supranational unions, geopolitical systems, regions, borders, capitals, dependent, and internationally administered territories. Political geography develops fundamental theoretical approaches that give insight into the peculiarities of foreign and domestic policies. The ability to use spatial analysis techniques allows determining patterns and regularities of political phenomena both at the global and the regional and local levels.

This book focuses on crisis management in software development which includes forecasting, responding and adaptive engineering models, methods, patterns and practices. It helps the stakeholders in understanding and identifying the key technology, business and human factors that may result in a software production crisis. These factors are particularly important for the enterprise-scale applications, typically considered very complex in managerial and technological aspects and therefore, specifically addressed by the discipline of software engineering. Therefore, this book throws light on the crisis responsive, resilient methodologies and practices; therewith, it also focuses on their evolutionary changes and the resulting benefits.

The International conference “Linguistic Forum 2020: Language and Artificial Intelligence” took place in 2020 on November 12-14 in Moscow, Russia. The conference is organized by the Institute of Linguistics, Russian Academy of Sciences. This conference is part of a series of annual forums initiated by the Institute of Linguistics RAS in 2019. The aim of the 2020 forum is to foster dialogue among researchers working at the interface of linguistics and artificial intelligence including those engaged in computational linguistics and natural language processing. Developments in AI have been responsible for recent advances in natural language generation and comprehension; they have also expanded the boundaries of these technologies’ applicability. Neural networks and dense embeddings have replaced models based on feature engineering and traditional discrete categories of linguistic analysis. As a result, the boundary between fundamental and applied linguistic research is being eroded. Empirical linguistics is taking on board these new technologies, in part, to enable better modelling of language and documentation of data. AI is also increasingly becoming a part of the everyday life of language users. Can fundamental linguistics currently offer technologically viable ideas or methods? These and similar conceptual and methodological problems were the focus of the forum.

In this paper, a statistical game was defined and solved. Its solution is: the optimal randomized decision rule, the probability of a correct decision on this rule, and the worst a priori distribution of the test subjects knowledge levels. We have developed a method for assessment the accuracy and reliability of decision making by on test results. The proposed program allows you to assessment the reliability of the solution for a test containing 10 items with different levels of difficulty, and 11 different levels of knowledge level.

TThe present paper proposes a model for evaluating geo-ecological protection technologies based on multi-criteria optimization and weighted convolution criteria, on the basis of which the method of calculation is developed, allowing to determine the PQ factor for different objects according to the selected technologies using the Mathlab environment. The work demonstrated the application of the technique in the case of materials made of ash foam concrete with densities and ash content from the incineration of sewage sludge. The determination of the optimum composition of solopenobeton is relevant for the design of noise shields in railway transport. The proposed simulation algorithm in the Matlab environment makes it possible to use the procedure of processing the raw data, using several options of their input: in the form of tables of the format. csv or manual input.

This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.

The Volume includes a Special Section on "Analytical and Computational Methods in Probability"

The materials of the 5th International conference on stochastic methods are presented including the following directions: probability and statistics (analytic modelling, asymptotic methods and limit theorems, stochastic analysis, Markov processes and martingales, actuarial and financial mathematics, et al.); applications of stochastic methods (queueing theory and stochastic networks, reliability theory and risk analysis, probability in indistry, economics and other areas, computer science and computer networks, machine learning and data analysis, etc.).

We construct a mirabolic analogue of the geometric Satake equivalence. We also prove an equivalence that relates representations of a supergroup to the category of GL(N − 1, C[[t]])-equivariant perverse sheaves on the affine Grassmannian of GLN . We explain how our equivalences fit into a more general framework of conjectures due to Gaiotto and to Ben-Zvi, Sakellaridis and Venkatesh.

MiRNA isoforms (isomiRs) are single stranded small RNAs originating from the same pri-miRNA hairpin as a result of cleavage by Drosha and Dicer enzymes. Variations at the 5ʹ-end of a miRNA alter the seed region of the molecule, thus affecting the targetome of the miRNA. In this manuscript, we analysed the distribution of miRNA cleavage positions across 31 different cancers using miRNA sequencing data of TCGA project. As a result, we found that the processing positions are not tissue specific and that all miRNAs could be correctly classified as ones exhibiting homogeneous or heterogeneous cleavage at one of the four cleavage sites. In 42% of cases (42 out of 100 miRNAs), we observed imprecise 5ʹ-end Dicer cleavage, while this fraction was only 14% for Drosha (14 out of 99). To the contrary, almost all cleavage sites of 3ʹ-ends (either Drosha or Dicer) were heterogeneous. With the use of only four nucleotides surrounding a 5ʹ-end Dicer cleavage position we built a model which allowed us to distinguish between homogeneous and heterogeneous cleavage with the reliable quality (ROC AUC = 0.68). Finally, we showed the possible applications of the study by the analysis of two 5ʹ-end isoforms originating from the same exogeneous shRNA hairpin. It turned out that the less expressed shRNA variant was functionally active, which led to the increased off-targeting. Thus, the obtained results could be applied to the design of shRNAs whose processing will result in a single 5ʹ-variant.

There are two different modal logics: the logic T assuming contingency and the logic K = assuming logical determinism. In the paper, I show that the Aristotelian treatise On Interpretation (Περί ερμηνείας, De Interpretatione) has introduced some modal-logical relationships which correspond to T. In this logic, it is supposed that there are contingent events. The Nāgārjunian treatise Īśvara-kartṛtva-nirākṛtiḥ-viṣṇoḥ-ekakartṛtva-nirākaraṇa has introduced some modal-logical relationships which correspond to K =. In this logic, it is supposed that there is a logical determinism: each event happens necessarily (siddha) or it does not happen necessarily (asiddha). The Nāgārjunian approach was inherited by the Yogācārins who developed, first, the doctrine of causality of all real entities (arthakriyātva) and, second, the doctrine of momentariness of all real entities (kṣaṇikavāda). Both doctrines were a philosophical ground of the Yogācārins for the logical determinism. Hence, Aristotle implicitly used the logic T in his modal reasoning. The Madhyamaka and Yogācāra schools implicitly used the logic K = in their modal reasoning.

The goal of the paper is to develop a new algorithm for predicting whether the company will go bankrupt on the base of unbalanced data. To do it, we propose to consider the classification as a multi-objective optimization problem and construct a prediction model as an ensemble while minimizing the parameters FPR (False Positive Rate) and FNR (False Negative Rate) at the same time. To create the ensemble, the proposed algorithm of a Multi-Objective Classifier Selection (MOCS) selects only classifiers that belong to the Pareto-optimal set in FPR/FNR space; that is, there is no dominance between them, and they satisfy some additional conditions. In the general case, MOCS is determined by three parameters: two threshold values that limit false rates (FNR and FPR), and the crowding distance, which defines the uniqueness of the classifier's results. We tested the proposed algorithm on data collected from 2457 Russian companies, 456 of which went bankrupt, and 5910 Polish companies, 410 of which received bankruptcy status. Datasets contain features such as financial ratios and business environment factors. In the testing, we used more than 70 combinations of under-sampling, over-sampling, and no sampling methods with static and dynamic classification models. Final ensembles include seven classifiers for the Russian dataset and four classifiers for the Polish dataset combined by soft voting rule. In both cases, the proposed algorithm produces a significant improvement of prediction results as in terms of standard metrics (geometric mean, the area under the ROC curve) and in the visual representation in the FNR/FPR space, namely in the shift from a Pareto-optimal set of classifiers.

Recent statistics report that more than 3.7 million new cases of cancer occur in Europe yearly, and the disease accounts for approximately 20% of all deaths. High-throughput screening of cancer cell cultures has dominated the search for novel, effective anticancer therapies in the past decades. Recently, functional assays with patient-derived ex vivo 3D cell culture have gained importance for drug discovery and precision medicine. We recently evaluated the major advancements and needs for the 3D cell culture screening, and concluded that strictly standardized and robust sample preparation is the most desired development. Here we propose an artificial intelligence-guided low-cost 3D cell culture delivery system. It consists of a light microscope, a micromanipulator, a syringe pump, and a controller computer. The system performs morphology-based feature analysis on spheroids and can select uniform sized or shaped spheroids to transfer them between various sample holders. It can select the samples from standard sample holders, including Petri dishes and microwell plates, and then transfer them to a variety of holders up to 384 well plates. The device performs reliable semi- and fully automated spheroid transfer. This results in highly controlled experimental conditions and eliminates non-trivial side effects of sample variability that is a key aspect towards next-generation precision medicine.

Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered. The approach interpreting an arbitrary magnetic field distribution as a superposition of localized perturbations (blobs) is developed. We derive a general relation between stochastic properties of an isolated blob and a stochastically homogenous distribution of magnetic field advected by the same stochastic flow. This relation allows us to investigate the evolution of a localized blob at a late stage when its size exceeds the viscous scale. It is shown that in three-dimensional flows, the average magnetic field of the blob increases exponentially in the inertial range of turbulence, as opposed to the late-batchelor stage when it decreases. Our approach reveals the mechanism of dynamo generation in the inertial range both for blobs and homogenous contributions. It explains the absence of dynamo in the two-dimensional case and its efficiency in three dimensions. We propose a way to observe the mechanism in numerical simulations

We consider a linear-quadratic control problem where a time parameter evolves according to a stochastic time scale. The stochastic time scale is defined via a stochastic process with continuously differentiable paths. We obtain an optimal infinite-time control law under criteria similar to the long-run averages. Some examples of stochastic time scales from various applications have been examined.

We consider the nanoscale electronic phase separation in a wide class of different materials,  mostly in strongly correlated electron systems. The phase separation turns out to be quite ubiquitous manifesting itself in different situations, where the itineracy of charge carriers competes with their tendency toward localization. The latter is often related to some specific type of magnetic ordering, e.g. antiferromagnetic in manganites and low-spin states in cobaltites. The interplay between the localization induced lowering of potential energy and metallicity (which provides the gain in the kinetic energy) favors an inhomogeneous ground state such as nanoscale ferromagnetic droplets in an antiferromagnetic insulating background. The present review article deals with the advances in the subject of electronic phase separation and formation of different types of nanoscale ferromagnetic (FM) metallic droplets (FM polarons or ferrons) in antiferromagnetically ordered (AFM), charge-ordered (CO), or orbitally-ordered (OO) insulating matrices, as well as the colossal magnetoresistance (CMR) effect and tunneling electron transport in the nonmetallic phase-separated state of complex magnetic oxides. It also touches upon the compounds with spin-state transitions, inhomogeneous phase separated state in strongly correlated multiband systems, and electron polaron effect.  A special, attention is paid to the systems with the imperfect Fermi surface nesting such as chromium alloys, iron-based pnictides, and AA stacked graphene bilayers. 

Solid-state reaction of CaHPO4 with CaCO3 in >2:1 ratio at 1350 °C resulted in α-tricalcium phosphate (α-TCP) formation, following sintering at 850 °C produced a homogeneous β-TCP phase which does not contain crystalline impurities.

We consider the damped/driven cubic NLS equation on the torus of a large period L with a small nonlinearity of size λ, a properly scaled random forcing and dissipation. We examine its solutions under the subsequent limit when first λ → 0 and then L → ∞. The first limit, called the limit of discrete turbulence, is known to exist, and in this work we study the second limit L → ∞ for solutions to the equations of discrete turbulence. Namely, we decompose the solutions to formal series in amplitude and study the second order truncation of this series. We prove that the energy spectrum of the truncated solutions becomes close to solutions of a damped/driven nonlinear wave kinetic equation. Kinetic nonlinearity of the latter is similar to that which usually appears in works on wave turbulence, but is different from it (in particular, it is non-autonomous). Apart from tools from analysis and stochastic analysis, our work uses two powerful results from the number theory.

Efficient scalability and process synchronization are critical for achieving high performance in distributed computing environments. Analysis of the scalability is usually done using intensive case studies, which give an answer only for the particular set of model parameters. We found an efficient way to analyze the time evolution in models simulated with the Parallel Discrete Event Simulations (PDES) approach. The essential feature of PDES is the concept of local virtual time (LVT) associated with the evolution of each process of the model. The LVT of processes evaluates in simulations and forms a complicated profile. These profiles remind the profiles of the surface growth in the physical devices. In physics, researchers use the concept of universality, which helps to divide the different regimes of the class’s surface growth—each class is described by some universal laws and does not depend on the details of the model. We demonstrate the applicability of this concept and present a model of LVT profile evolution in Personal Communication Service (PCS) model. The PCS network consists of a square grid of radio ports that serve users in their zone (cell). We build the LVT-PCS model, which describes the evolution of the LVT profile associated with the PCS model. We simulate the PCS model using the ROSS simulator (optimistic PDES) and compare results with those simulated by our LVT-PCS model.We found the profile demonstrates property, which is known in physics as roughening transition. We estimate the values of “critical” exponents for two models, which seem to belong to the same universality class. We believe that the similarity we found can be helpful for the preliminary analysis of the model scalability, process desynchronization, and possible deadlocks.

For the optimal success probability under minimum-error discrimination of N≥2 arbitrary quantum states, we find new general lower and upper bounds and specify the relations between these new general bounds and the general bounds known in the literature. The new upper bound explicitly generalizes to N>2 the form of the Helstrom bound. For N=2, each of our new bounds, lower and upper, reduces to the Helstrom bound.

We study, both theoretically and experimentally, the features on the current-voltage characteristic of a highly transparent Josephson junction caused by transition of the superconducting leads to the normal state. These features appear due to the suppression of the Andreev excess current. We show that by tracing the dependence of the voltages, at which the transition occurs, on the bath temperature one can obtain valuable information about the cooling mechanisms in the junction. We verify theory predictions by fabricating two highly transparent superconductor-graphene-superconductor (SGS) Josephson junctions with suspended and non-suspended graphene as an interlayer between Al leads. Applying the above mentioned technique we show that the cooling power of the suspended junction depends on the bath temperature as ∝T^3 close to the superconducting critical temperature.

In 2021, Dzhunusov and Zaitseva classified two-dimensional normal affine commutative algebraic monoids. In this work, we extend this classification to noncommutative monoid structures on normal affine surfaces. We prove that two-dimensional algebraic monoids are toric. We also show how to find all monoid structures on a normal toric surface. Every such structure is induced by a comultiplication formula involving Demazure roots. We also give descriptions of opposite monoids, quotient monoids, and boundary divisors.

For each integer n>0, we construct a series of irreducible algebraic varieties X, for which the automorphism group Aut(X) contains as a subgroup the automorphism group Aut(F_n) of a free group F_n of rank n. For n > 1, such groups Aut(X) are nonamenable, and for n > 2, they are nonlinear and contain the braid group B_n. Some of these varieties X are affine, and among affine, some are rational and some are not, some are smooth and some are singular. The byproduct is that for n > 2, each Cremona group of rank > 3n-1 contains Aut(F_n) and the braid group B_n.

Starting with exploration of the possibility to present the underlying variety of an affine algebraic group in the form of a product of some algebraic varieties, we then explore the naturally arising problem as to what extent the group variety of an algebraic group determines its group structure.

The dynamics of a multiplex heterogeneous network of oscillators is studied. Two types of similar models based on the Hodgkin-Huxley formalism are used as the basic elements of the networks. The first type model demonstrates bursting oscillations. The second model demonstrates bistability between bursting attractor and stable steady state. Basin of attraction of the stable equilibrium in the model is very small. Bistabilty is a result taking into account an additional ion channel, which has a non-monotonic characteristic and can be interpreted as a channel with a communication defect. Suggested multiplex networks assumed more active communication between models with a defect as a result in such networks it is enough to have one element with a communication defect in the subnetworks in order to stabilize the state of equilibrium in the entire network.

We give several characterizations of relative homological epimorphisms in the setting of locally convex topological algebras, thereby correcting a gap in our earlier paper [Trans. Moscow Math. Soc. 2008, 27-104].

Given a connected reductive algebraic group G and a Borel subgroup B⊆G, we study B-normalized one-parameter additive group actions on affine spherical G-varieties. We establish basic properties of such actions and their weights and discuss many examples exhibiting various features. We propose a construction of such actions that generalizes the well-known construction of normalized one-parameter additive group actions on affine toric varieties. Using this construction, for every affine horospherical G-variety X we obtain a complete description of all G-normalized one-parameter additive group actions on X and show that the open G-orbit in X can be connected with every G-stable prime divisor via a suitable choice of a B-normalized one-parameter additive group action. Finally, when G is of semisimple rank 1, we obtain a complete description of all B-normalized one-parameter additive group actions on affine spherical G-varieties having an open orbit of a maximal torus T⊆B.

As an effort to help contain the COVID-19 pandemic, large numbers of SARS-CoV-2 genomes have been sequenced from all continents. More than one million viral sequences are publicly available as of April 2021. Many studies estimate viral genealogies from these sequences, as these can provide valuable information about the spread of the pandemic across time and space. Additionally such data are a rich source of information about molecular evolutionary processes including natural selection, for example allowing the identification and investigating the spread of new variants conferring transmissibility and immunity evasion advantages to the virus. To validate new methods and to verify results resulting from these vast datasets, one needs an efficient simulator able to simulate the pandemic to approximate world-scale scenarios and generate viral genealogies of millions of samples. Here, we introduce a new fast simulator VGsim which addresses this problem. The simulation process is split into two phases. During the forward run the algorithm generates a chain of events reflecting the dynamics of the pandemic using an hierarchical version of the Gillespie algorithm. During the backward run a coalescent-like approach generates a tree genealogy of samples conditioning on the events chain generated during the forward run. Our software can model complex population structure, epistasis and immunity escape. The code is freely available at https://github.com/Genomics-HSE/VGsim.

The guarantee of an anonymous mechanism is the worst case welfare an agent can secure against unanimously adversarial others. How high can such a guarantee be, and what type of mechanism achieves it? We address the worst case design question in the n-person probabilistic voting/bargaining model with p deterministic outcomes. If n is no less than p the uniform lottery is the only maximal (unimprovable) guarantee; there are many more if p>n, in particular the ones inspired by the random dictator mechanism and by voting by veto. If n=2 the maximal set M(n,p) is a simple polytope where each vertex combines a round of vetoes with one of random dictatorship. For p>n>2, we show that the dual veto and random dictator guarantees, together with the uniform one, are the building blocks of 2 to the power d simplices of dimension d in M(n,p), where d is the quotient of p-1 by n. Their vertices are guarantees easy to interpret and implement. The set M(n,p) may contain other guarantees as well; what we can say in full generality is that it is a finite union of polytopes, all sharing the uniform guarantee.

Convergence of order O(1/ √ n) is obtained for the distance in total variation between the Poisson distribution and the distribution of the number of fixed size cycles in generalized random graphs with random vertex weights. The weights are assumed to be independent identically distributed random variables which have a power-law distribution. The proof is based on the Chen–Stein approach and on the derived properties of the ratio of the sum of squares of random variables and the sum of these variables. These properties can be applied to other asymptotic problems related to generalized random graphs

A general scenario for an N-sequential conclusive state discrimination introduced recently in Loubenets and Namkung [arXiv:2102.04747] can provide a multipartite quantum communication realizable in the presence of a noise. In the present article, we propose a new experimental scheme for the implementation of a sequential conclusive discrimination between binary coherent states via indirect measurements within the Jaynes-Cummings interaction model. We find that if the mean photon number is less than 1.6, then, for our two-sequential state discrimination scheme, the optimal success probability is larger than the one presented in Fields, Varga, and Bergou [2020, IEEE Int. Conf. Quant. Eng. Comp.]. We also show that, if the mean photon number is almost equal to 1.2, then the optimal success probability nearly approaches the Helstrom bound.

We research n-gram dictionaries and estimate its coverage and entropy based on the web corpus of English. We consider a method for estimating the coverage of empirically generated dictionaries and an approach to address the disadvantage of low coverage. Based on the ideas of Kolmogorov’s combinatorial approach, we estimate the n-gram entropy of the English language and use mathematical extrapolation to approximate the marginal entropy. In addition, we approximate the number of all possible legal n-grams in the English language for large order of n-grams.

Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.

We show existence of a natural rational structure on periodic cyclic homology, conjectured by L. Katzarkov, M. Kontsevich, T. Pantev, for several classes of dg-categories, including proper connective C-dg-algebras and dg-categories of local systems. The main ingredient is derived nilpotent invariance of A. Blanc's semi-topological K-theory, which we establish along the way.

Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found to deal well with systems with complex free-energy landscapes. Above all else, it promises to deliver unrivaled parallel scaling qualities, being suitable for parallel machines of the biggest caliber. Here we study population annealing using as the main example the two-dimensional Ising model which allows for particularly clean comparisons due to the available exact results and the wealth of published simulational studies employing other approaches. We analyze in depth the accuracy and precision of the method, highlighting its relation to older techniques such as simulated annealing and thermodynamic integration. We introduce intrinsic approaches for the analysis of statistical and systematic errors and provide a detailed picture of the dependence of such errors on the simulation parameters. The results are benchmarked against canonical and parallel tempering simulations.