An independent broadcast on a connected graph $G$is a function $f:V(G)to mathbb{N}_0$such that, for every vertex $x$ of $G$, the value $f(x)$ is at most the eccentricity of $x$ in $G$,and $f(x)>0$ implies that $f(y)=0$ for every vertex $y$ of $G$ within distance at most $f(x)$ from $x$.The broadcast independence number $alpha_b(G)$ of $G$is the largest weight $sumlimits_{xin V(G)}f(x)$of an ind...

This paper presents a novel static analysis technique to detect XML query-update independence, in the presence of a schema. Rather than types, our system infers chains of types. Each chain represents a path that can be traversed on a valid document during query/update evaluation. The resulting independence analysis is precise, although it raises a challenging issue: recursive schemas may lead t...

The violation of certain Bell inequalities allows for device-independent information processing secure against nonsignaling eavesdroppers. However, this only holds for the Bell network, in which two or more agents perform local measurements on a single shared source of entanglement. To overcome the practical constraints that entangled systems can only be transmitted over relatively short distan...

A conjecture of Sokal [22] regarding the domain of non-vanishing for independence polynomials of graphs, states that given any natural number ∆ ≥ 3, there exists a neighborhood in C of the interval [0, (∆−1) ∆−1 (∆−2)∆ ) on which the independence polynomial of any graph with maximum degree at most ∆ does not vanish. We show here that Sokal’s Conjecture holds, as well as a multivariate version, ...

Over a finite field Fqm , the evaluation of skew polynomials is intimately related to the evaluation of linearized polynomials. This connection allows one to relate the concept of polynomial independence defined for skew polynomials to the familiar concept of linear independence for vector spaces. This relation allows for the definition of a representable matroid called the Fqm[x;σ]-matroid, wi...

We investigate different notions of linear independence and of matrix rank that are relevant for max-plus or tropical semirings. The factor rank and tropical rank have already received attention, we compare them with the ranks defined in terms of signed tropical determinants or arising from a notion of linear independence introduced by Gondran and Minoux. To do this, we revisit the symmetrizati...

We investigate a class of set constraints that is used for the type analysis of concurrent constraint programs. Its constraints are inclusions between rst-order terms (without set operators) interpreted over non-empty sets of nite trees. We show that this class has the independence property. We give a polynomial algorithm for entailment. The independence property is a fundamental property of co...

We can view a Bayesian network as a compact representation of a joint probability distribution (the computational view). We can also view it as a graphical representation of a set of conditional independence statements (the conditional independence view). As it turns out, the two views are equivalent. (For more details please refer to [1] and [2]). In this class, we will focus exclusively on th...

Conditional random fields (CRFs) have shown significant improvements over existing methods for structured data labeling. However independence assumptions made by CRFs decrease the usability of the models produced. Currently, CRF models accomodate dependence between only adjacent labels. Generalized CRFs proposed in this study relaxes assumptions of CRFs without reducing tractability of inferenc...

We calculate the dimensions of the space of Vassiliev invariants coming from the Homfly polynomial of links, and of the space of Vassiliev invariants coming from the Kauffman polynomial of links. We show that the intersection of these spaces is spanned by the Vassiliev invariants coming from the Jones polynomial and from a polynomial called Υ. We also show that linearly independent Vassiliev in...