Related papers: Calls, zonoids, peacocks and log-concavity
We extend the notion of John's ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
We establish upper bounds for tails of order statistics of isotropic log-concave vectors and apply them to derive a concentration of l_r norms of such vectors.
We develop a calculus based on zonoids - a special class of convex bodies - for the expectation of functionals related to a random submanifold $Z$ defined as the zero set of a smooth vector valued random field on a Riemannian manifold. We…
We give two different definitions of what it means for a matrix-valued function to be log concave, guided by similar notions in complex differential geometry. After discussing a few simple examples, we proceed to develop some of the basic…
In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral…
An analysis of extensive simulations of interacting self-avoiding polygons on cubic lattice shows that the frequencies of different knots realized in a random, collapsed polymer ring decrease as a negative power of the ranking order, and…
Combinatorial objects called rigged configurations give rise to q-analogues of certain Littlewood-Richardson coefficients. The Kostka-Foulkes polynomials and two-column Macdonald-Kostka polynomials occur as special cases. Conjecturally…
If prices of assets traded in a financial market are determined by non-linear pricing rules, different versions of the Call-Put Parity have been considered. We show that, under monotonicity, parities between call and put options and…
We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations which were not supported by its precursor, categorical…
Using log convergent topoi, %In the derived category of filtered complexes of %sheaves of modules over %an isostructure we define two fundamental filtered complexes $(E_{conv},P)$ and $(C_{conv},P)$ for the log scheme obtained by a smooth…
We propose the use of topographic modulation of surfaces to select and localize particles in nematic colloids. By considering convex and concave deformations of one of the confining surfaces we show that the colloid-flat surface repulsion…
We give counterexamples to Okounkov's log-concavity conjecture for Littlewood-Richardson coefficients.
In this paper, we obtain some new inequalities for functions whose second derivatives' absolute value is s-convex and log-convex. Also, we give some applications for numerical integration.
The intrinsic volumes of a convex cone are geometric functionals that return basic structural information about the cone. Recent research has demonstrated that conic intrinsic volumes are valuable for understanding the behavior of random…
Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of…
In the $1970$s Nicolas proved that the coefficients $p_d(n)$ defined by the generating function \begin{equation*} \sum_{n=0}^{\infty} p_d(n) \, q^n = \prod_{n=1}^{\infty} \left( 1- q^n\right)^{-n^{d-1}} \end{equation*} are log-concave for…
We give characterizations of the skein polynomial for links (as well as Jones and Alexander-Conway polynomials derivable from it), avoiding the usual "smoothing of a crossing" move. As by-products we have characterizations of these…
We extend the classical links between valuations and orderings on fields to Tignol-Wadsworth gauges and positive cones on finite-dimensional simple algebras with involution. We also study the compatibility of gauges and positive cones, and…
We study the tractability of conjunctive query answering for queries with unbounded arity. It is well known that tractability of the problem can be characterised in terms of the queries treewidth under the assumption of bounded arity. We…