相关论文: Log-balanced combinatorial sequences
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
We prove the optimal regularity for some class of vector-valued variational inequalities with gradient constraints. We also give a new proof for the optimal regularity of some scalar variational inequalities with gradient constraints. In…
We develop a combinatorial model of the associated Hermite polynomials and their moments, and prove their orthogonality with a sign-reversing involution. We find combinatorial interpretations of the moments as complete matchings, connected…
Horizontal and vertical generating functions and recursion relations have been investigated by Comtet for triangular double sequences. In this paper we investigate the horizontal and vertical log-concavity of triangular sequences assigned…
We introduce a new class of problems lying halfway between questions about graph capacity and intersection. We say that two binary sequences x and y of the same length have a skewincidence if there is a coordinate i for which x_i=y_{i+1}=1…
We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is…
We derive two-sided bounds for moments of linear combinations of coordinates od unconditional log-concave vectors. We also investigate how well moments of such combinations may be approximated by moments of Gaussian random variables.
A triangle $\{a(n,k)\}_{0\le k\le n}$ of nonnegative numbers is LC-positive if for each $r$, the sequence of polynomials $\sum_{k=r}^{n}a(n,k)q^k$ is $q$-log-concave. It is double LC-positive if both triangles $\{a(n,k)\}$ and…
A $(d-1)$-dimensional simplicial complex is called balanced if its underlying graph admits a proper $d$-coloring. We show that many well-known face enumeration results have natural balanced analogs (or at least conjectural analogs).…
We prove that any subset $A \subseteq [3]^n$ with $3^{-n}|A| \ge (\log\log\log\log n)^{-c}$ contains a combinatorial line of length $3$, i.e., $x, y, z \in A$, not all equal, with $x_i=y_i=z_i$ or $(x_i,y_i,z_i)=(0,1,2)$ for all $i = 1, 2,…
It is known that if A and B are two n-by-n complex matrices and (A,A^T) is simultaneously equivalent to (B,B^T), then A is congruent to B. We extend this statement to multilinear forms.
By well known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we…
A social choice correspondence satisfies balancedness if, for every pair of alternatives, x and y, and every pair of individuals, i and j, whenever a profile has x adjacent to but just above y for individual i while individual j has y…
We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…
Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics. Structural completeness and decidability of…
We introduce the notion of logarithmically concave (or log-concave) sequences in Coding Theory. A sequence $a_0, a_1, \dots, a_n$ of real numbers is called log-concave if $a_i^2 \ge a_{i-1}a_{i+1}$ for all $1 \le i \le n-1$. A natural…
A collection of converse theorems for integral quadratic constraints (IQCs) is established for linear time-invariant systems. It is demonstrated that when a system interconnected in feedback with an arbitrary system satisfying an IQC is…
We study higher order convexity properties of random point sets in the unit square. Given $n$ uniform i.i.d random points, we derive asymptotic estimates for the maximal number of them which are in $k$-monotone position, subject to mild…
A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior…
Cluster synchronisation is a key phenomenon observed in networks of coupled dynamical units. Its presence has been linked to symmetry and, more generally, to equability of the underlying pattern of interactions between dynamical units.…