Euclidean matchings and minimality of hyperplane arrangements

We construct a new class of maximal acyclic matchings on the Salvetti complex of a locally finite hyperplane arrangement. Using discrete Morse theory, we then obtain an explicit proof of the minimality of the complement. Our construction provides interesting insights also in the well-studied case of finite arrangements, and gives a nice geometric description of the Betti numbers of the complement. In particular, we solve a conjecture of Drton and Klivans on the characteristic polynomial of finite reflection arrangements. The minimal complex is compatible with restrictions, and this allows us to prove the isomorphism of Brieskorn’s Lemma by a simple bijection of the critical cells. Finally, in the case of line arrangements, we describe the algebraic Morse complex which computes the homology with coefficients in an abelian local system

The essence of psychologic and pedagogical diagnostics

Уточняется понятие «психолого-педагогическая диагностика», рассматриваются функции, принципы, этапы психолого-педагогической диагностикиIn the article the idea of «psychologic and pedagogical diagnostics» is precised, also there are facilities, values, and phases of psychologic and pedagogical diagnostic

Novel Platforms for the Development of a Universal influenza vaccine

Despite advancements in immunotherapeutic approaches, influenza continues to cause severe illness, particularly among immunocompromised individuals, young children, and elderly adults. Vaccination is the most effective way to reduce rates of morbidity and mortality caused by influenza viruses. Frequent genetic shift and drift among influenzavirus strains with the resultant disparity between circulating and vaccine virus strains limits the effectiveness of the available conventional influenza vaccines. One approach to overcome this limitation is to develop a universal influenza vaccine that could provide protection against all subtypes of influenza viruses. Moreover, the development of a novel or improved universal influenza vaccines may be greatly facilitated by new technologies including virus-like particles, T-cell-inducing peptides and recombinant proteins, synthetic viruses, broadly neutralizing antibodies, and nucleic acid-based vaccines. This review discusses recent scientific advances in the development of next-generation universal influenza vaccines.Funding Agencies|GlaxoSmithKline Biologicals SA; Marie-Curie IEF grant SAMUFLU FP7-PEOPLE-IEF [626283]; Marie-Curie ITN grant HOMIN FP7-PEOPLE-ITN [626283]</p

Primary Human Natural Killer Cells Retain Proinflammatory IgG1 at the Cell Surface and Express CD16a Glycoforms with Donor-dependent Variability

Post-translational modification confers diverse functional properties to immune system proteins. The composition of serum proteins such as immunoglobulin G (IgG) strongly associates with disease including forms lacking a fucose modification of the crystallizable fragment (Fc) asparagine(N)-linked glycan that show increased effector function, however, virtually nothing is known about the composition of cell surface receptors or their bound ligands in situ due to low abundance in the circulating blood. We isolated primary NK cells from apheresis filters following plasma or platelet donation to characterize the compositional variability of Fc g receptor IIIa / CD16a and its bound ligand, IgG1. CD16a N162-glycans showed the largest differences between donors; one donor displayed only oligomannose-type N-glycans at N162 that correlate with high affinity IgG1 Fc binding while the other donors displayed a high degree of compositional variability at this site. Hybrid-type N-glycans with intermediate processing dominated at N45 and highly modified, complex-type N-glycans decorated N38 and N74 from all donors. Analysis of the IgG1 ligand bound to NK cell CD16a revealed a sharp decrease in antibody fucosylation (43.2 ±11.0%) versus serum from the same donors (89.7 ±3.9%). Thus, NK cells express CD16a with unique modification patterns and preferentially bind IgG1 without the Fc fucose modification at the cell surface

Does dietary calcium interact with dietary fiber against colorectal cancer? : a case-control study in Central Europe

BACKGROUND: An unfavorable trend of increasing rates of colorectal cancer has been observed across modern societies. In general, dietary factors are understood to be responsible for up to 70% of the disease’s incidence, though there are still many inconsistencies regarding the impact of specific dietary items. Among the dietary minerals, calcium intake may play a crucial role in the prevention. The purpose of this study was to assess the effect of intake of higher levels of dietary calcium on the risk of developing of colorectal cancer, and to evaluate dose dependent effect and to investigate possible effect modification. METHODS: A hospital based case–control study of 1556 patients (703 histologically confirmed colon and rectal incident cases and 853 hospital-based controls) was performed between 2000–2012 in Krakow, Poland. The 148-item semi-quantitative Food Frequency Questionnaire to assess dietary habits and level of nutrients intake was used. Data regarding possible covariates was also collected. RESULTS: After adjustment for age, gender, education, consumption of fruits, raw and cooked vegetables, fish, and alcohol, as well as for intake of fiber, vitamin C, dietary iron, lifetime recreational physical activity, BMI, smoking status, and taking mineral supplements, an increase in the consumption of calcium was associated with the decrease of colon cancer risk (OR = 0.93, 95% CI: 0.89-0.98 for every 100 mg Ca/day increase). Subjects consumed >1000 mg/day showed 46% decrease of colon cancer risk (OR = 0.54, 95% CI: 0.35-0.83). The effect of dietary calcium was modified by dietary fiber (p for interaction =0.015). Finally, consistent decrease of colon cancer risk was observed across increasing levels of dietary calcium and fiber intake. These relationships were not proved for rectal cancer. CONCLUSIONS: The study confirmed the effect of high doses of dietary calcium against the risk of colon cancer development. This relationship was observed across different levels of dietary fiber, and the beneficial effect of dietary calcium depended on the level of dietary fiber suggesting modification effect of calcium and fiber. Further efforts are needed to confirm this association, and also across higher levels of dietary fiber intake

IgG and Fcγ Receptors in Intestinal Immunity and Inflammation.

Fcγ receptors (FcγR) are cell surface glycoproteins that mediate cellular effector functions of immunoglobulin G (IgG) antibodies. Genetic variation in FcγR genes can influence susceptibility to a variety of antibody-mediated autoimmune and inflammatory disorders, including systemic lupus erythematosus (SLE) and rheumatoid arthritis (RA). More recently, however, genetic studies have implicated altered FcγR signaling in the pathogenesis of inflammatory bowel disease (IBD), a condition classically associated with dysregulated innate and T cell immunity. Specifically, a variant of the activating receptor, FcγRIIA, with low affinity for IgG, confers protection against the development of ulcerative colitis, a subset of IBD, leading to a re-evaluation of the role of IgG and FcγRs in gastrointestinal tract immunity, an organ system traditionally associated with IgA. In this review, we summarize our current understanding of IgG and FcγR function at this unique host-environment interface, from the pathogenesis of colitis and defense against enteropathogens, its contribution to maternal-fetal cross-talk and susceptibility to cancer. Finally, we discuss the therapeutic implications of this information, both in terms of how FcγR signaling pathways may be targeted for the treatment of IBD and how FcγR engagement may influence the efficacy of therapeutic monoclonal antibodies in IBD

Vereinfachungsstrategien und Extremalbeispiele von Simplizialkomplexen

Since the beginning of Topology, one of the most used approaches to study a geometric object has been to triangulate it. Many invariants to distinguish between different objects have been introduced over the years, the two most important surely being homology and the fundamental group. However, the direct computation of the fundamental group is infeasible and even homology computations could become computationally very expensive for triangulations with a large number of faces without proper preprocessing. This is why methods to reduce the number of faces of a complex, without changing its homology and homotopy type, are particularly of interest. In this thesis, we will focus on these simplification strategies and on explicit extremal examples. The first problem tackled is that of sphere recognition. It is known that 3-sphere recognition lies in NP and in co-NP, and that d-sphere recognition is undecidable for d > 4. However, the sphere recognition problem does not go away simply because it is algorithmically intractable. To the contrary, it appears naturally in the context of manifold recognition so there is a clear need to find good heuristics to process the examples. Here, we describe an heuristic procedure and its implementation in polymake that is able to recognize quite easily sphericity of even fairly large simplicial complexes. At the same time we show experimentally where the horizons for our heuristic lies, in particular for discrete Morse computations, which has implications for homology computations. Discrete Morse theory generalizes the concept of collapsibility, but even for a simple object like a single simplex one could get stuck during a random collapsing process before reaching a vertex. We show that for a simplex on n vertices, n > 7, there is a collapsing sequence that gets stuck on a d-dimensional simplicial complex on n vertices, for all d not in {1, n - 3, n - 2, n - 1}. Equivalently, and in the language of high-dimensional generalizations of trees, we construct hypertrees that are anticollapsible, but not collapsible. As for a second heuristic for space recognition, we worked on an algorithmic implementation of simple-homotopy theory, introduced by Whitehead in 1939, where not only collapsing moves but also anticollapsing ones are allowed. This provides an alternative to discrete Morse theory for getting rid of local obstructions. We implement a specific simple-homotopy theory heuristic using the mathematical software polymake. This implementation has the double advantage that we remain in the realm of simplicial complexes throughout the reduction; and at the same time, theoretically, we keep the possibility to reduce any contractible complex to a single point. The heuristic algorithm can be used, in particular, to study simply-connected complexes, or, more generally, complexes whose fundamental group has no Whitehead torsion. We shall see that in several contractible examples the heuristic works very well. The heuristic is also of interest when applied to manifolds or complexes of arbitrary topology. Among the many test examples, we describe an explicit 15-vertex triangulation of the Abalone, and more generally, (14k+1)-vertex triangulations of Bing's houses with k rooms. One of the classes of examples on which we run the heuristic are the 3-dimensional lens spaces, which are known to have torsion in their first homology. Using this examples (minus a facet), we managed to find 2-dimensional simplicial complexes with torsion and few vertices. Studying them we constructed sequences of complexes with huge torsion on few vertices. In particular, using Hadamard matrices we were able to give a quadratic time construction of a series of 2-dimensional simplicial complexes on 5n-1 vertices and torsion of size 2^{n \log(n)}. Our explicit series of 2-dimensional simplicial complexes improves a previous construction by Speyer, narrowing the gap to the highest possible asymptotic torsion growth proved by Kalai via a probabilistic argument.Seit den Anfängen der Topologie besteht einer der am häufigsten verwendeten Ansätze zur Untersuchung eines geometrischen Objekts darin, es zu triangulieren. Im Laufe der Jahre wurden viele Invarianten zur Unterscheidung zwischen verschiedenen Objekten eingeführt, die beiden wichtigsten dabei sind sicherlich die Homologie und die Fundamentalgruppe. Die direkte Berechnung der Fundamentalgruppe ist jedoch algorithmisch nicht durchführbar, und selbst Homologieberechnungen können bei Triangulationen mit einer großen Anzahl von Seiten ohne geeignete Vorverarbeitung sehr rechenintensiv werden. Aus diesem Grund sind Methoden zur Reduzierung der Anzahl der Seiten eines Komplexes, ohne dessen Homologie und Homotopietyp zu verändern, von besonderem Interesse. In dieser Arbeit werden wir uns auf diese Vereinfachungsstrategien und auf explizite Extremalbeispiele konzentrieren. Das erste Problem, das wir angehen, ist das der Sphärenerkennung. Es ist bekannt, dass die 3-Sphärenerkennung in NP und in co-NP liegt, und dass die d-Sphärenerkennung für d > 4 unentscheidbar ist. Das Problem der Sphärenerkennung verschwindet jedoch nicht einfach, nur weil es algorithmisch unlösbar ist. Im Gegenteil, es taucht ganz natürlich im Zusammenhang mit der Erkennung von Mannigfaltigkeiten auf, so dass ein klarer Bedarf besteht, gute Heuristiken zur Verarbeitung der Beispiele zu finden. Hier beschreiben wir ein heuristisches Verfahren und seine Implementierung in polymake, das in der Lage ist, die Sphärizität selbst großer Komplexe recht einfach zu erkennen. Gleichzeitig zeigen wir experimentell, wo die Grenzen für unsere Heuristik liegen, insbesondere für diskrete Morseberechnungen, was Auswirkungen auf Homologieberechnungen hat. Die diskrete Morse-Theorie verallgemeinert das Konzept der Kollabierbarkeit, aber selbst für ein einfaches Objekt, wie z.B. für ein einzelnes Simplex, kann man während eines zufälligen Kollaps-Prozesses steckenbleiben, bevor man eine finale Ecke erreicht. Wir zeigen, dass es für ein Simplex auf n Ecken, n > 7, eine kollabierende Sequenz gibt, die auf einem d-dimensionalen simpliziellen Komplex auf n Ecken stecken bleibt, für alle d nicht in {1, n - 3, n - 2, n - 1}. Äquivalent dazu, und in der Sprache der hochdimensionalen Verallgemeinerungen von Bäumen ausgedrückt, konstruieren wir Hypertrees, die antikollabierbar, aber nicht kollabierbar sind. Was eine zweite Heuristik zur topologische Typerkennung betrifft, so haben wir an einer algorithmischen Implementierung der 1939 von Whitehead eingeführten Simple-Homotopy-Theory gearbeitet, bei der nicht nur kollabierende, sondern auch antikollabierende Züge erlaubt sind. Dies bietet eine Alternative zur diskreten Morse-Theorie, um lokale Hindernisse zu beseitigen. Konkret haben wir eine spezialle Fassung der einfachen Homotopietheorie unter Verwendung der mathematischen Software polymake implementiert. Diese Implementierung hat den doppelten Vorteil, dass wir während der gesamten Reduktion im Bereich der simplizialen Komplexe bleiben; und gleichzeitig behalten wir theoretisch die Möglichkeit, jeden zusammenziehbaren Komplex auf einen einzigen Punkt zu reduzieren. Der heuristische Algorithmus kann insbesondere dazu verwendet werden, einfach zusammenhängende Komplexe zu untersuchen, oder, allgemeiner, Komplexe, deren Fundamentalgruppe keine Whitehead-Torsion haben. Wir werden sehen, dass die Heuristik in einen Vielzahl von kontrahierbaren Beispielen sehr gut funktioniert. Die Heuristik ist auch von Interesse, wenn sie auf Mannigfaltigkeiten oder Komplexe beliebiger Topologie angewendet wird. Unter den vielen Testbeispielen beschreiben wir eine explizite 15-Vertex-Triangulation der Abalone und, allgemeiner, (14k+1)-Vertex-Triangulationen von Bing-Häusern mit k Zimmern. Eine der Klassen von Beispielen, auf die wir die Heuristik anwenden, sind die 3-dimensionalen Linsenräume, von denen bekannt ist, dass sie Torsion in ihrer ersten Homologie haben. Unter Verwendung von Triangulierungen von Linsenräumen (minus eine Facette) ist es uns gellungen, 2-dimensionale simplizialen Komplexe mit Torsion und wenigen Ecken zu finden. Denen Untersuchung erlaubte es uns, Serien von Komplexen mit großer Torsion und einer kleinen Eckenanzahl zu konstruieren. Insbesondere konnten wir unter Verwendung von Hadamard-Matrizen eine Serie 2-dimensionale simplizialen Komplexe mit 5n-1 Ecken und einer Torsion der Größe 2^{n \log(n)} in quadratischer Zeit konstruieren. Unsere explizite Serie 2-dimensionaler simplizialer Komplexe verbessert eine frühere Konstruktion von Speyer, indem sie die Lücke zum höchstmöglichen asymptotischen Torsionswachstum verkleinert, das von Kalai über ein probabilistisches Argument nachgewiesen wurde

Hyperplane Arrangment and Discrete Morse Theory

The aim of this thesis is to study the complement of a hyperplane arrangement using the techniques of Discrete Morse theory. A hyperplane arrangement is simply a set A={H_1,H_2,...} of hyperplanes in a vector space. This object has been widely studied especially to find correlations between its topological properties and the combinatorics of the intersections of the hyperplanes. One of the most studied topological objects is the complement, i.e. the vector space minus the hyperplanes and its homology and homotopy groups. One of the question that we are going to answer is if this complement is a minimal space, meaning that it is homotopy equivalent to a CW-complex with as many i-cells as the i-th Betti number. We will see that the answer is positive in various settings. Having a minimal complex, if it is given explicitly, can also help in studying various properties of the complement, we will focus in particular on abelian local homology. Local homology is an important tool for the study of hyperplane arrangements because it gives us informations on a special fibration on the complement, called Milnor fibration as well as informations about the characteristic varieties. Even if there is plenty of research on the subject there is still a lot unknown about local homology even for the most famous arrangements, like the Braid ones. In the first chapter we talk about Discrete Morse theory, first introduced by Forman. The aim is to reduce a CW-complex or in general various type of topological and combinatorial object to smaller ones, called Morse complex with a series of elementary collapsments such that the properties of the complex are still the same. We will study explore the correlation of this theory with shellability and focus on different aspect, all of which will became useful in the following chapters. In the second chapter, we first give a brief introduction to the theory of hyperplane arrangement, presenting some of the most important known results, concerning in particular their combinatorial properties and homology groups. In the special case of complexified real arrangement we introduce the Salvetti complex, a $CW-$complex homotopy equivalent to the complementary of the arrangement. We then review three different articles that with similar techniques have reduced this complex to a minimal one (with as many cells as the Betti numbers). The following chapter introduce the concept of local homology and its correlations with Discrete Morse theory, in particular how we could compute the local homology of the Morse complex. We focus then our attention to a special kind of hyperplane arrangement, called the Braid arrangement and we explicitly write a program in Sage to compute the boundary in local homology. In the last chapter we try to give our small contribute to the subject. It is a joint work with Giovanni Paolini in which in a similar way to what has been done by Delucchi in the case of oriented matroids, we reduce the Salvetti complex in the case of affine, locally finite hyperplane arrangment to a minimal Morse complex giving a special characterization to the critical cells

Un inedito saggio di Irving Lavin sui monumenti equestri e alcune riflessioni sull’ultimo segmento di attività dello studioso

This is a proposed translation to Italian of the inedited essay by Irving Lavin (1927- 2019), dedicated to the birth of the equestrian monuments of the humanistic age. The short essay by the American art historian is introduced by a study in which the genesis of St. Louis’ highly important contributions is examined, which is inscribed within a silloge, result of a thoughtful sedimentation in which Lavin was immersed during the last decades of his life, and dedicated to the theme of art of commemoration. Starting from an exam of the main characteristics of Lavin’s critical methodology, this contribution explores the dense plot, made of cultural references, and complex strategies of analyses through which the short essay evolves. Thus it emerges that the formal and iconographic exam is breaching towards the discovery of connections, with literary testimonies and contemporary philosophies, enlightening the choices made in the elaboration of the same figurative scripts. However, the relations with the literary culture do not assume a mechanical dependency from it; similarly, while unraveling a vast knowledge, the American art historian finds the articulate relationships between works and social groups: nevertheless, the analysis is always stopped to prevent any deterministic subordination of the formal to the latter. On the other hand, such exam is generally tenaciously repeating the centrality of figurative text, of which Lavin is the committed spokesman throughout his illuminating scientific career. Indeed, the same figurative text is an assertive and synthetic representation of ideological demands in accordance with the idea, largely defended by the scholar, of the “modern” artist’s conscience, which is fully conscious of its own intellectual resources.</jats:p