This paper introduces a new method for proving global stability of fluid flows through the construction of Lyapunov functionals. For finite dimensional approximations of fluid systems, we show how one can exploit recently developed optimization methods based on sum-of-squares decomposition to construct a polynomial Lyapunov function. We then show how these methods can be extended to infinite di...

The clique vector c(G) of a graph G is the sequence (c1, c2, . . . , cd) in N, where ci is the number of cliques in G with i vertices and d is the largest cardinality of a clique in G. In this note, we use tools from commutative algebra to characterize all possible clique vectors of k-connected chordal graphs.

For every pattern P , consisting of a finite set of points in the plane, S′ P (n) is defined as the largest number of similar copies of P among sets of n points in the plane without 3 points on a line. A general construction, based on iterated Minkovski sums, is used to obtain new lower bounds for S′ P (n) when P is an arbitrary pattern. Improved bounds are obtained when P is a triangle or a re...

Let G be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained: except for sources and sinks, the sum of flows into a node equals the sum of flows going out of a node. Given a noisy measurement of the flow on each edge, the problem we address, which we call the MOST PROBABLE FLOW ESTIMATION problem (MPFE), is to estimate the most p...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

In this paper a Lefschetz formula is proved for the geodesic flow of a compact locally symmetric space. The flow is described in terms of actions of split tori of various dimensions and the geometric side of the Lefschetz formula is a sum over closed geodesics which correspond to a given torus. The cohomological side is given in terms of Lie algebra cohomology.

An unoriented flow in a graph, is an assignment of real numbers to the edges, such that the sum of the values of all edges incident with each vertex is zero. This is equivalent to a flow in a bidirected graph all of whose edges are extraverted. A nowhere-zero unoriented k-flow is an unoriented flow with values from the set {±1, . . . ,±(k − 1)}. It has been conjectured that if a graph has a now...

We present a typed intermediate language λ for optimizing compilers for function-oriented and polymorphically typed programming languages (e.g., ML). The language λ is a typed lambda calculus with product, sum, intersection, and union types as well as function types annotated with flow labels. A novel formulation of intersection and union types supports encoding flow information in the typed pr...

We introduce and study a new data sketch for processing massive datasets. It addresses two common problems: 1) computing a sum given arbitrary filter conditions and 2) identifying the frequent items or heavy hitters in a data set. For the former, the sketch provides unbiased estimates with state of the art accuracy. It handles the challenging scenario when the data is disaggregated. In this cas...