Multilevel programming can provide the right mathematical formulations for modeling sequential decision-making problems. In such cases, it is implicit that each level anticipates optimal reaction of subsequent ones. Defender–attacker–defender trilevel programs are a particular case interest encompasses fortification strategy, followed by an attack, and consequent recovery defensive strategy. “M...

In this work, we analyze a sequential game played in graph called the Multilevel Critical Node problem (MCN). A defender and an attacker are players of game. The starts by preventively interdicting vertices (vaccination) from being attacked. Then, infects subset non-vaccinated and, finally, reacts with protection strategy. We provide first computational complexity results associated MCN its sub...

Social networks are flourishing because of fast growing Internet and the World Wide Web, and more research efforts have been put on Social Network Analysis (SNA). A social network can be modeled like a graph, where the nodes represent persons, and an edge between them represent direct relationship between the persons. One of the issues in SNA is to identifying criminals from groups of individua...

We introduce a simple tool that can be used to reduce non-injective instances of the hidden shift problem over arbitrary group to injective instances over the same group. In particular, we show that the average-case non-injective hidden shift problem admit this reduction. We show similar results for (non-injective) hidden shift problem for bent functions. We generalize the notion of influence a...

There are two well known transformations from non-binary constraints to binary constraints applicable to constraint satisfaction problems (CSPs) with finite domains: the dual transformation and the hidden (variable) transformation. We perform a detailed formal comparison of these two transformations. Our comparison focuses on two backtracking algorithms that maintain a local consistency propert...

The Cascade Correlation architecture is unique in its abilities to construct sensibly a network topology during training — taking into account all possible connections. This paper investigates a number of different connection strategies for the hidden nodes that Cascade Correlation inserts into a network, by limiting the connections a hidden node may make.

in the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. in this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. two path inequalities for the node-only interdiction problem are represented. it has been proved that the integrality gap of relaxation of the maximum fl...

Sum product networks (SPNs) are a new class of deep probabilistic models. They can contain multiple hidden layers while keeping their inference and training times tractable. An SPN consists of interleaving layers of sum nodes and product nodes. A sum node can be interpreted as a hidden variable, and a product node can be viewed as a feature capturing rich interactions among an SPN’s inputs. We ...