The Phase Transition Analysis for the Random Regular Exact 2-(d,k)-SAT Problem

In a regular (d,k)-CNF formula, each clause has length k and each variable appears d times. A regular structure such as this is symmetric, and the satisfiability problem of this symmetric structure is called the (d,k)-SAT problem for short. The regular exact 2-(d,k)-SAT problem is that for a (d,k)-CNF formula F, if there is a truth assignment T, then exactly two literals of each clause in F are true. If the formula F contains only positive or negative literals, then there is a satisfiable assignment T with a size of 2n/k such that F is 2-exactly satisfiable. This paper introduces the (d,k)-SAT instance generation model, constructs the solution space, and employs the method of the first and second moments to present the phase transition point d* of the 2-(d,k)-SAT instance with only positive literals. When d<d*, the 2-(d,k)-SAT instance can be satisfied with high probability. When d>d*, the 2-(d,k)-SAT instance can not be satisfied with high probability. Finally, the verification results demonstrate that the theoretical results are consistent with the experimental results.

On the computational cost of the set cover approach for the optimal camera placement problem and possible set-cover-inspired trade-offs for surveillance infrastructure design

The NP-hard minimum set cover problem (SCP) is a very typical model to use when attempting to formalise optimal camera placement (OCP) applications. In a generic form, the OCP problem relates to the positioning of individual cameras such that the overall network is able to cover a given area while meeting a set of application-specific requirements (image quality, redundancy, ...) and optimising an objective, typically minimum cost or maximum coverage. In this paper, we focus on an application called global or persistent surveillance: camera networks which ensure full coverage of a given area. As preliminary work, an instance generation framework is proposed to create OCP instances from real-world data and solve them using existing literature. The computational cost of both the instance generation process and the solving algorithms however highlights a need for more efficient methods for decision makers to use in real-world settings. In this paper, we therefore propose to review the suitability of the approach, and more specifically to question two key elements: the impact of sampling frequencies and the importance of rigid full-coverage constraints. The results allow us to quickly provide decision makers with an overview of available solutions and trade-offs.

Visual sentiment analysis via deep multiple clustered instance learning

The increasing tendency of people expressing opinions via images online has motivated the development of automatic assessment of sentiment from visual contents. Based on the observation that visual sentiment is conveyed through many visual elements in images, we put forward to tackle visual sentiment analysis under multiple instance learning (MIL) formulation. We propose a deep multiple clustered instance learning formulation, under which a deep multiple clustered instance learning network (DMCILN) is constructed for visual sentiment analysis. Specifically, the input image is converted into a bag of instances through visual instance generation module, which is composed of a pre-trained convolutional neural network (CNN) and two adaptation layers. Then, a fuzzy c-means routing algorithm is introduced for generating clustered instances as semantic mid-level representation to bridge the instance-to-bag gap. To explore the relationships between clustered instances and bags, we construct an attention based MIL pooling layer for representing bag features. A multi-head mechanism is integrated to form MIL ensembles, which enables to weigh the contribution of each clustered instance in different subspaces for generating more robust bag representation. Finally, we conduct extensive experiments on several datasets, and the experimental results verify the feasibility of our proposed approach for visual sentiment analysis.