When does a Bounded Domain Cover a Projective Manifold? (Survey)

* The research has been partially supported by Bulgarian Funding Organizations, sponsoring the Algebra Section of the Mathematics Institute, Bulgarian Academy of Sciences, a Contract between the Humboldt Univestit¨at and the University of Sofia, and Grant MM 412 / 94 from the Bulgarian Board of Education and Technology

Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.

Block, L. (2011). ‘From politics to policing: the rationality gap in EU Council policy- making’

Book review: L Block. (2011). From Politics to Policing: The Rationality Gap in EU Council Policy-Making The Hague: Eleven International Publishing. ISBN: 978-94-9094-737-8, 361 pages.

A pénzügyi eszközök árazásának alaptétele, lokálisan korlátos szemimartingál árfolyamok esetén (The fundamental theorem of asset pricing for locally bounded semimartingales)

A pénzügyi eszközök árazásának alaptétele - kissé pongyolán megfogalmazva - azt állítja, hogy egy értékpapírpiacon akkor nincs arbitrázs, ha létezik egy az eredetivel ekvivalens valószínűségi mérték, amelyre vonatkozóan az értékpapírok árait leíró folyamat egy bizonyos értelemben "martingál". Az első ilyen jellegű állítást M. Harrison és S. R. Pliska bizonyították arra esetre, amikor a valószínűségi mező végesen generált. Azóta a tételnek számos általánosítása született. Ezek közül az egyik legismertebb a Dalang{Morton{ Willinger-tétel, ami már teljesen általános valószínűségi mezőből indul ki, de felteszi, hogy az időparaméter diszkrét, és az időhorizont véges. Időközben a tételnek számos folytonos időparaméterű folyamatokra vonatkozó változata is született. Az alaptételt általános esetben, vagyis amikor valószínűségi mező teljesen általános, és az értékpapírok piaci árait leíró folyamat lokálisan korlátos szemimartingál, Delbaen és W. Schachermayer bizonyították be. A Delbaen{Schachermayer-féle alaptétel a maga nemében egy igen általános áll ítás. A tétel bizonyítása igen hosszadalmas, és a funkcionálanalízis valamint a sztochasztikus folyamatok általános elméletének mély eredményeit használja. Utóbbi tudományterület nagy részét P. A. Meyer és a francia strassbourgi iskola matematikusai dolgozták ki a 60-as évek végétől kezdve. A terület megértését tehát alaposan megnehezíti, hogy a felhasznált matematikai apparátus viszonylag friss, egy része pedig csak francia nyelven érhető el. Meggyőződésünk szerint az eredeti, 1994-es Delbaen és Schachermayer-féle bizonyítás csak kevesek által hozzáférhető. A tételnek tudomásunk szerint azóta sem született tankönyvi feldolgozása, annak ellenére, hogy maga az állítás közgazdász körökben is széles körben ismerté vált, és az eredeti cikket számos szerző idézi. Az itt bemutatott bizonyítás Delbaen és Schachermayer 1992 és 2006 közötti írásain alapul. ______ The Delbaen and Schachermayer's theorem is one of the deepest results of mathematical finance. In this article we tried to rethink and slightly simplify the original proof of the theorem to make understandable for nonspecialists who are familiar with general theory of stochastic processes. We give a detailed proof of the theorem and we give new proofs for some of the used statements.

Language, Logos, and Social Ontology: Naturalist and Post-Naturalist Narratives of Human Rationality and Social Reality

I distinguish two ways that philosophers have approached and explained the reality and status of human social institutions. I call these approaches “naturalist” and “post-naturalist”. Common to both approaches is an understanding that the status of mind and its relation to the world or “nature” has implications on a conception of the status of institutional reality. Naturalists hold that mind is explicable within a scientific frame that conceives of mind as a fundamentally material process. By proxy, social reality is also materially explicable. Post-naturalists critique this view, holding instead that naturalism is parasitic on contemporary science—it therefore is non-compulsory and distorts how we ought to understand mind and social reality. A comparison of naturalism and post-naturalism will comprise the content of the first chapter. The second chapter turns to tracing out the dimensions of a post-naturalist narrative of mind and social reality. Post-naturalists conceive of mind and its activity of thought as sui generis, and it transpires from this that social institutions are better understood as a rational mind’s mode of the expression in the world. Post-naturalism conceives of social reality as a necessary dimension of thought. Thought requires a second person and thereby a tradition or context of norms that come to both structure its expression and become the products of expression. This is in contrast to the idea that social reality is a production of minds, and thereby derivative. Social reality, self-conscious thought, and thought of the second person are therefore three dimensions of a greater unity.

More elementary operators that are spectrally bounded

We discuss some necessary and some sufficient conditions for an elementary operator x↦∑ⁿ_i=1a_ixb_i on a Banach algebra A to be spectrally bounded. In the case of length three, we obtain a complete characterisation when A acts irreducibly on a Banach space of dimension greater than three.

Efficient Learning of Bayesian Networks with Bounded Tree-width

Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods \cite{korhonen2exact, nie2014advances} tackle the problem by using $k$-trees to learn the optimal Bayesian network with tree-width up to $k$. Finding the best $k$-tree, however, is computationally intractable. In this paper, we propose a sampling method to efficiently find representative $k$-trees by introducing an informative score function to characterize the quality of a $k$-tree. To further improve the quality of the $k$-trees, we propose a probabilistic hill climbing approach that locally refines the sampled $k$-trees. The proposed algorithm can efficiently learn a quality Bayesian network with tree-width at most $k$. Experimental results demonstrate that our approach is more computationally efficient than the exact methods with comparable accuracy, and outperforms most existing approximate methods.

Learning Treewidth-Bounded Bayesian Networks with Thousands of Variables

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian network greatly reduces the complexity of inferences. Yet, being a global property of the graph, it considerably increases the difficulty of the learning process. Our novel algorithm accomplishes this task, scaling both to large domains and to large treewidths. Our novel approach consistently outperforms the state of the art on experiments with up to thousands of variables.

Rule-based and Resource-bounded: A New Look at Epistemic Logic

Syntactic logics do not suffer from the problems of logical omniscience but are often thought to lack interesting properties relating to epistemic notions. By focusing on the case of rule-based agents, I develop a framework for modelling resource-bounded agents and show that the resulting models have a number of interesting properties.

Emotional Theory of Rationality

In recent decades, it has been definitely established the existence of a close relationship between the emotional phenomena and rational processes, but we still do not have a unified definition, or effective models to describe any of them well. To advance our understanding of the mechanisms governing the behavior of living beings we must integrate multiple theories, experiments and models from both fields. In this paper we propose a new theoretical framework that allows integrating and understanding, from a functional point of view, the emotion-cognition duality. Our reasoning, based on evolutionary principles, add to the definition and understanding of emotion, justifying its origin, explaining its mission and dynamics, and linking it to higher cognitive processes, mainly with attention, cognition, decision-making and consciousness. According to our theory, emotions are the mechanism for brain function optimization, besides being the contingency and stimuli prioritization system. As a result of this approach, we have developed a dynamic systems-level model capable of providing plausible explanations for some psychological and behavioral phenomena, and establish a new framework for scientific definition of some fundamental psychological terms.

Unpacking insanity defence standards: an experimental study of rationality and control tests in criminal law

The present study investigated the impact of different legal standards on mock juror decisions concerning whether a defendant was guilty or not guilty by reason of insanity. Undergraduate students (N = 477) read a simulated case summary involving a murder case and were asked to make an insanity determination. The cases differed in terms of the condition of the defendant (rationality deficit or control deficit) and the legal standard given to the jurors to make the determination (Model Penal Code, McNaughten or McNaughten plus a separate control determination). The effects of these variables on the insanity determination were investigated. Jurors also completed questionnaires measuring individualism and hierarchy attitudes and perceptions of facts in the case. Results indicate that under current insanity standards jurors do not distinguish between defendants with rationality deficits and defendants with control deficits regardless of whether the legal standard requires them to do so. Even defendants who lacked control were found guilty at equal rates under a legal standard excusing rationality deficits only and a legal standard excluding control and rationality deficits. This was improved by adding a control test as a partial defence, to be determined after a rationality determination. Implications for the insanity defence in the Criminal Justice System are discussed.

A survey of the northern neck of Virginia, being the lands belonging to the Rt. Honourable Thomas Lord Fairfax Baron Cameron, bounded by & within the Bay of Chesapoyocke and between the rivers Rappahannock and Potowmack: With the courses of the rivers Rappahannock and Potowmack, in Virginia, as surveyed according to order in the years 1736 & 1737.

Scale ca. 1:875,000.