One class of wild but brick-tame matrix problems

We present a class of wild matrix problems (representations of boxes), which are "brick-tame," i.e. only have one-parameter families of \emph{bricks} (representations with trivial endomorphism algebra). This class includes several boxes that arise in study of simple vector bundles on degenerations of elliptic curves, as well as those arising from the coadjoint action of some linear groups.Comment: 19 page

Simple vector bundles on plane degenerations of an elliptic curve

In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classification by describing the simple vector bundles on all reduced plane cubic curves. Our main result states that a simple vector bundle on such a curve is completely determined by its rank, multidegree and determinant. Our approach, based on the representation theory of boxes, also yields an explicit description of the corresponding universal families of simple vector bundles

International Experience of Development of Bank Deposit Insurance System

У статті розглянуто особливості становлення та розвитку систем страхування банківських вкладів у зарубіжних країнах, виявлено класифікаційні ознаки поділу таких систем на моделі: американську та німецьку. Встановлено, що американська модель передбачає створення спеціального державного фінансового органу або органу, підконтрольного державі, участь комерційних банків та інших кредитних установ у системі страхування вкладів, а також спільне фінансування такої системи за рахунок державних коштів і внесків комерційних банків. При німецькій моделі системою страхування банківських вкладів керують асоціації кредитних організацій. Збір коштів здійснюється за рахунок внесків комерційних банків та інших кредитних організацій. Участь держави зведено до мінімуму. У статті виявлено причини створення систем страхування банківських вкладів та вплив, які ці системи здійснюють на банківську систему країни і цілому.The article deals with the peculiarities of formation and development of bank deposit insurance systems in foreign countries, identifies the classification features of the division of such systems into models: American and German. It has been found out that the US model provides for the creation of a special state financial authority or state-controlled body, the participation of commercial banks and other credit institutions in the deposit insurance system, as well as the joint financing of such system at the expense of public funds and contributions of commercial banks. Under the German model, the deposit insurance scheme is managed by associations of credit institutions. Funds are raised through investments from commercial banks and other credit institutions. State involvement is minimized. The article describes the reasons for the creation of bank deposit insurance systems and the impact which these systems produce on the banking system of the country as a whole

Vector bundles and torsion free sheaves on degenerations of elliptic curves

In this paper we give a survey about the classification of vector bundles and torsion free sheaves on degenerations of elliptic curves. Coherent sheaves on singular curves of arithmetic genus one can be studied using the technique of matrix problems or via Fourier-Mukai transforms, both methods are discussed here. Moreover, we include new proofs of some classical results about vector bundles on elliptic curves.Comment: 39 pages, 5 figure

Zhangfei suppresses the growth of Medulloblastoma cells and commits them to programmed cell death

Medulloblastoma cells do not contain detectable amounts of the bZIP protein Zhangfei. However, previous work has shown that expression of this protein in cells of the ONS-76 line, derived from a human medulloblastoma, causes the cells to stop growing and develop processes that resemble neuritis (a characteristic of differentiated neurons). Zhangfei-expressing cells eventually die. My objective was to determine the molecular mechanisms by which Zhangfei influences ONS-76 cells. My strategy was to infect ONS-76 cells with adenovirus vectors expressing either Zhangfei or the control E. coli protein â-galactosidase (LacZ) and then to compare the following parameters in Zhangfei and LacZ-expressing cells: a) markers of apoptosis, autophagy and macropinocytosis (the three main pathways of cell death); b) transcripts for genes involved in neurogenesis and apoptosis; c) phosphorylation of peptide targets of selected cellular protein kinases; and d) active transcription factors. Zhangfei-expressing cells appeared to succumb to apoptosis as determined by the expression of phosphatidylserine on the cell surface and intensity of nuclear staining with the DNA dye Hoechst. Increased staining for autophagic vesicles and upregulated expression of autophagy response genes in these cells indicated that they were undergoing autophagy, possibly associated with apoptosis. My analysis of steady-state transcripts for genes involved in apoptosis and neurogenesis and functional protein kinases in Zhangfei-expressing cells indicated that the mitogen-activated protein kinase (MAPK) pathway was active in these cells. In addition, I found that the transcription factor Brn3a as well as factors implicated in differentiation were also active. These observations led me to hypothesize that Zhangfei enhances the expression of Brn3a, a known inducer of TrkA, the high-affinity receptor for nerve growth factor (NGF). TrkA then binds in an autocrine manner to NGF, triggering the MAPK pathway and leading to differentiation of ONS-76 cells into neuron and glia-like cells, eventually bringing about cell death by apoptosis and autophagy. I tested this hypothesis by showing that Zhangfei could enhance transcription from the isolated Brn3a promoter, that ONS-76 cells produce NGF as detected in a bioassay, and that antibodies against NGF and inhibitors of TrkA and selected components of the MAPK pathway could partially restore the growth of Zhangfei-expressing ONS-76 cells. My work supports previous work highlighting the importance of NGF-TrkA signaling in the outcome of medulloblastomas and shows how Zhangfei is able to trigger this pathway

The complexity of global cardinality constraints

In a constraint satisfaction problem (CSP) the goal is to find an assignment of a given set of variables subject to specified constraints. A global cardinality constraint is an additional requirement that prescribes how many variables must be assigned a certain value. We study the complexity of the problem CCSP(G), the constraint satisfaction problem with global cardinality constraints that allows only relations from the set G. The main result of this paper characterizes sets G that give rise to problems solvable in polynomial time, and states that the remaining such problems are NP-complete

Simple vector bundles on plane degenerations of an elliptic curve

In 1957 Atiyah classifed simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classifcation by describing the simple vector bundles on all reduced plane cubic curves. Our main result states that a simple vector bundle on such a curve is completely determined by its rank, multidegree and determinant. Our approach, based on the representation theory of boxes, also yields an explicit description of the corresponding universal families of simple vector bundles