This paper is in English. It does not have a specific annotation because it was not presupposed by the book format
We propose a new algorithm for consensus clustering, FCA-Consensus, based on Formal Concept Analysis. As the input, the algorithm takes T partitions of a certain set of objects obtained by k-means algorithm after T runs from different initialisations. The resulting consensus partition is extracted from an antichain of the concept lattice built on a formal context objects×classes, where the classes are the set of all cluster labels from each initial k-means partition. We compare the results of the proposed algorithm in terms of ARI measure with the state-of-the-art algorithms on synthetic datasets. Under certain conditions, the best ARI values are demonstrated by FCA-Consensus.
On the eve of the great troubles: Th e letter sent to the king Henry the Second by the bishop of Nevers
One of the important sources, introducing in many aspects the Civil wars of the 16th century, is the treatise written at the beginning of 1559 and stored in the Paris library of Sainte Genevieve, the “Letter, sent to king Henry the second by Bishop of Nevers. A message from may, 1559”. Its author, with very high probability, was Jacques the Bishop of Nevers Spifame and the text was written in spring of 1559 after his escape from France.
This article is to analyze this little-known source-text. In an address to the monarch the author announces his intention to give advice, how to distinguish the false Church from the true, to explain why and how exactly to cut back on numerous Church benefi ces for the common good, and fi nally to show the path to the cessation of troubles. Despite the subsequent and scandalous fame of Jacques Spifame, the letter was not widely known and was not published. Th is is not surprising, because it very quickly became irrelevant due to the death of the addressee, the French king Henry II.
Attribution of new fragments to Alcmaeon of Croton found in the Turba philosophorum and Aristotle's biological works.
The article presents a brief sketch of the history of the Russian Prokuratura from the point of view of its role in protecting human rights.
A.Herzen as a scholar of contemporary history: Polish aspects. Herzen considered the Polish national movement as the main ally of Russian revolutionaries in their struggle against autocracy and highly appreciated the Poles' sacrifice. However the moderate nature of Polish social doctrine and demands to restore the former eastern border of the Polish-Lithuanian Commonwealth caused Herzen's critical evaluations. The Polish partners of Herzen were not ready to share all of his ideas. Differences of the programs complicated Russian-Polish revolutionary cooperation. Analyzing the Russian-Polish relations of the last three decades, Herzen proposed his own vision of the Russian Empire's contemporary history.
The idea of the high significance of Platonic studies for our comprehension many phenomena in politics, ideology and philosophy of the twentieth century and of our days is all played out. The social project of Plato was considered to be the paradigmatic model for totalitarian regimes of Nazi Germany and Bolshevik Russia or—recently—the only basis for the solution of all contemporary global problems. In this paper some of the main aspects of the analysis of “the social nature of Platonism” by the Russian philosopher and historian of philosophy Aleksey F. Losev (1893–1988) were discussed — predominately as this analysis is given in the outline of the same name, Social Nature of Platonism, included in The Outlines of Antique Symbolism and Mythology (1930).
The paper examines the history of dissemination in 14th-17th centuries in different european countries (especially in Eastern Europe), of one curious text, known as the "Privilege of Alexander the Great for the Slavs." Particular attention was given to the specifically Russian version of this text appeared in the latter half of the XVI century.
The early decades of the nineteenth century were a period of “proactive” improvement and “balance of the imperial situation,”1 both in the content of administrative projects and in their implementation in practices of territorial administration in the Russian Empire. However, Alexander I’s attempt at reforming local administration in 1816–25 remains understudied. The emperor, known for his cautiousness and indecision, endorsed the ideas of Aleksandr Dmitrievich Balashov2 and Viktor Pavlovich Kochubei,3 who called for introduction of viceroyalties (namestnichestvo) as administrative units in the empire. It is still unknown whether Nikolai Nikolaevich Novosil’cev or A.D. Balashov was the true author of the project,4, but without the political will of the monarch, implementation would have been impossible. The empire was to be structured in accordance with a document titled “The List of Governorates and Their Distribution across Viceregal Regions” (Spisok gubernii s raspredeleniem po namestnicheskim okrugam). Amended in 1823–24, it was included in the Book of Civil Statutes (Kniga shtatov po grazhdanskoi chasti)5 and preserved in the archives of the secret “Committee on December 6, 1826.” At the end of the nineteenth century, this list of governor-generalships—as found in the committee papers—was published in the Sbornik Rossiiskogo Imperatorskogo Obshchestva, with further amendments simply ignored.6 This version of the text is most referenced by scholars.
The paper considers Egyptian and Classical connotations for the epithet of Alexander the Great "the new Sesonchosis" in a passage of the Alexander Romance describing his advent to Egypt
The chapter juxtaposes Veselovsky’s theory of the persistence of forms with the set of critical practices known as New Historicism, and shows that both approaches exclude the possibility of new forms arising. The chapter suggests that both the oblivion of an old form and the rise of the new result from a fundamental shift in perception that occurs within the order of verbal creativity and does not lend itself to a historical-deterministic explanation.
In this chapter we are going to examine the logical connections between various descriptions of the Scientific Revolution proposed by Alexandre Koyré. We are going to propose an attentive and detailed reading of texts written by Koyré in different periods of his life in order to identify various aspects of his interpretation of the revolution in thought that occurred in early modern Europe. His most famous description of the Scientific Revolution (the dual characterization) indicates two aspects of the process that led to the emergence of classical physics: “destruction of the Cosmos” and “geometrization of space”. However, Koyré frequently used other expressions for characterization of the period, such as “mathematization of Nature”, or transition “from the world of more-or-less to the universe of precision” and “from the closed world to the open universe”. We could expect that Koyré would try to reduce his initial dual characterization to one single formula. I argue here that, on the contrary, the duality of description had a special meaning which permits us to keep in focus the complexity of the intellectual change that occurred during 17th century, when new science was rising from a new conception of reality, and a new world-view was emerging from the new science
The following topics about subgroups of the Cremona groups are discussed: (1) maximal tori; (2) conjugacy and classification of diagonalizable subgroups of codimensions 0 and 1; (3) conjugacy of finite abelian subgroups; (4) algebraicity of normalizers of diagonalizable subgroups; (5) torsion primes.
Due to the complexity and large dimensions of the task of digital system design debugging decomposition by method of modeling as a whole, algebraic models of decomposition methods are proposed, namely, methods of vertical and horizontal structure decomposition, functional decomposition, decomposition based on error types. An algebraic model of the digital systems software is presented. The software is considered as a semi group of operators.
In big data problems the data usually are collected on many sites, have a huge volume, and new pieces of data are constantly generated. It is often impossible to collect all the data needed for a research project on one computer, and even impractical, since one computer would not be able to process it in a reasonable time. An appropriate data analysis algorithm should, working in parallel on many computers, extract from each set of raw data some intermediate compact “information”, gradually combine and update it, and finally, use the accumulated information to produce the result. When new data appears, it must extract information from them, add it to the accumulated one, and eventually update the result. We consider several examples of a suitable transformation of processing algorithms, discuss specific features of the emerging information spaces and, in particular, their algebraic properties. We also show that the information space often can be equipped with an order relation that reflects the "quality" of the information.
Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities in the data. However this idea can not be used in practice as is because Kolmogorov complexity is not computable.
In recent years resource-bounded algorithmic statistics were created [7, 8]. In this paper we prove a polynomial-time version of the following result of ‘classic’ algorithmic statistics.
Assume that some data were obtained as a result of some unknown experiment. What kind of data should we expect in similar situation (repeating the same experiment)? It turns out that the answer to this question can be formulated in terms of algorithmic statistics . We prove a polynomial-time version of this result under a reasonable complexity theoretic assumption. The same assumption was used by Antunes and Fortnow .
Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of a "good model" is introduced, a natural question arises: it is possible that for some piece of data there is no good model? If yes, how often these bad ("non-stochastic") data appear "in real life"? Another, more technical motivation comes from algorithmic information theory. In this theory a notion of complexity of a finite object (=amount of information in this object) is introduced; it assigns to every object some number, called its algorithmic complexity (or Kolmogorov complexity). Algorithmic statistic provides a more fine-grained classification: for each finite object some curve is defined that characterizes its behavior. It turns out that several different definitions give (approximately) the same curve. In this survey we try to provide an exposition of the main results in the field (including full proofs for the most important ones), as well as some historical comments. We assume that the reader is familiar with the main notions of algorithmic information (Kolmogorov complexity) theory.