Perturb-and-MAP [1] is a technique for efficiently drawing approximate samples from discrete probabilistic graphical models. These samples are useful for both characterizing the uncertainty in the model, as well as learning its parameters. In this work, we show that this same technique is effective at learning features from images using graphical models with complex dependencies between variabl...

Given a graph F , a graph G is uniquely F -saturated if F is not a subgraph of G and adding any edge of the complement to G completes exactly one copy of F . In this paper we study uniquely Ct-saturated graphs. We prove the following: (1) a graph is uniquely C5-saturated if and only if it is a friendship graph. (2) There are no uniquely C6-saturated graphs or uniquely C7-saturated graphs. (3) F...

A graph G is uniquely Kr-saturated if it contains no clique with r vertices and if for all edges e in the complement, G + e has a unique clique with r vertices. Previously, few examples of uniquely Kr-saturated graphs were known, and little was known about their properties. We search for these graphs by adapting orbital branching, a technique originally developed for symmetric integer linear pr...

Chronic diseases that result in end-stage organ damage cause inflammation, which can reveal sequestered self-antigens (SAgs) in that organ and trigger autoimmunity. The thymus gland deletes self-reactive T-cells against ubiquitously expressed SAgs, while regulatory mechanisms in the periphery control immune responses to tissue-restricted SAgs. It is now established that T-cells reactive to SAgs...

In this paper, we study matching integral graphs of small order. A graph is called matching integral if the zeros of its matching polynomial are all integers. Matching integral graphs were first studied by Akbari, Khalashi, etc. They characterized all traceable graphs which are matching integral. They studied matching integral regular graphs. Furthermore, it has been shown that there is no matc...

There are several versions of the degree constrained subgraph problem, and we refer to the following: Given an undirected graph G = (V, E) with n vertices, and 2n integers al, . . . . a,,, br , . . . . b,, find a subgraph G’ = (V, E’) of G such that ai < dG’(vi) < bi for 1 < i < n and i E’l is maximized. Here d&vi) denotes the degree of vi restricted to G’. This problem has been solved by Urquh...

Higher-order matching is a special case of unification of simply-typed lambda-terms: in a matching equation, one of the two sides contains no unification variables. Loader has recently shown that higher-order matching up to beta equivalence is undecidable, but decidability of higher-order matching up to beta-eta equivalence is a long-standing open problem. We show that higher-order matching up ...