The Network Visibility Problem

Social media is an attention economy where broadcasters are constantly competing for attention in their followers’ feeds. Broadcasters are likely to elicit greater attention from their followers if their posts remain visible at the top of their followers’ feeds for a longer period of time. However, this depends on the rate at which their followers receive information in their feeds, which in turn depends on the broadcasters they follow. Motivated by this observation and recent calls for fairness of exposure in social networks, in this article, we look at the task of recommending links from the perspective of visibility optimization. Given a set of candidate links provided by a link recommendation algorithm, our goal is to find a subset of those links that would provide the highest visibility to a set of broadcasters. To this end, we first show that this problem reduces to maximizing a nonsubmodular nondecreasing set function under matroid constraints. Then, we show that the set function satisfies a notion of approximate submodularity that allows the standard greedy algorithm to enjoy theoretical guarantees. Experiments on both synthetic and real data gathered from Twitter show that the greedy algorithm is able to consistently outperform several competitive baselines.

Two modifications of extension of piyavskii’s global optimization algorithm to a function continuous on a compact interval and its convergence

В работах R.J. Vanderbei доказано, что непрерывная на выпуклом компактном множестве функция обладает свойством $\varepsilon $-липшицевости, обобщающим классическое понятие липшицевости. На основе этого свойства R.J. Vanderbei предложено одно обобщение метода Пиявского поиска глобального минимума непрерывной на отрезке функции. В данной работе предлагаются одна модификация этого метода для положительной $\varepsilon $-константы и одна модификация для положительной $\varepsilon $-константы и условия останова, не зависящего от выбора $\varepsilon $. Доказана сходимость предлагаемых алгоритмов, приведены результаты численных экспериментов на основе применения разработанной программы. Данные методы могут быть применены для оптимизации любых непрерывных на отрезке функций, например, при решении некоторых обратных задачах баллистики и в экономике в прямых задачах потребительского выбора маршаллианского типа с переменными ценами благ и с непрерывной функцией полезности. R.J. Vanderbei in his works proves that any continuous on a compact set function has the $\varepsilon $-Lipschitz property which extends conventional Lipschitz continuity. Based on this feature Vanderbei proposed one extension of Piyavskii’s global optimization algorithm to the continuous function case. In this paper we propose one modification of the Vanderbei’s algorithm for a positive $\varepsilon $-constant and another modification for a positive $\varepsilon $-constant and $\varepsilon $ value independent termination condition. We prove proposed methods convergence and perform several computational experiments with designed software for known test functions.

Recognition Problems for Connectivity Functions

<p>A connectivity function is a symmetric, submodular set function. Connectivity functions arise naturally from graphs, matroids and other structures. This thesis focuses mainly on recognition problems for connectivity functions, that is when a connectivity function comes from a particular type of structure. In particular we give a method for identifying when a connectivity function comes from a graph, which uses no more than a polynomial number of evaluations of the connectivity function. We also give a proof that no such method can exist for matroids.</p>

Medical Image Segmentation Using a Combination of Lattice Boltzmann Method and Fuzzy Clustering Based on GPU CUDA Parallel Processing

The rapid development of computer technology has had a significant influence on advances in medical science. This development concerns segmenting medical images that can be used to help doctors diagnose patient diseases. The boundary between objects contained in an image is captured using the level set function. The equation of the level set function is solved numerically by combining the Lattice Boltzmann (LBM) method and fuzzy clustering. Parallel processing using a graphical processing unit (GPU) accelerates the execution of the segmentation process. The results showed that image segmentation with a relatively large size could be done quickly. The use of parallel programming with the GPU can accelerate up to 39.22 times compared to the speed of serial programming with the CPU. In addition, the comparisons with other research and benchmark data show consistent results.

Recognition Problems for Connectivity Functions

<p>A connectivity function is a symmetric, submodular set function. Connectivity functions arise naturally from graphs, matroids and other structures. This thesis focuses mainly on recognition problems for connectivity functions, that is when a connectivity function comes from a particular type of structure. In particular we give a method for identifying when a connectivity function comes from a graph, which uses no more than a polynomial number of evaluations of the connectivity function. We also give a proof that no such method can exist for matroids.</p>

A topology optimization algorithm based on topological derivative and level-set function for designing phononic crystals

PurposeThis work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.Design/methodology/approachThe resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.FindingsThe description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.Originality/valueThe original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

Magnetic Resonance Imaging Segmentation via Weighted Level Set Model Based on Local Kernel Metric and Spatial Constraint

Magnetic resonance imaging (MRI) segmentation is a fundamental and significant task since it can guide subsequent clinic diagnosis and treatment. However, images are often corrupted by defects such as low-contrast, noise, intensity inhomogeneity, and so on. Therefore, a weighted level set model (WLSM) is proposed in this study to segment inhomogeneous intensity MRI destroyed by noise and weak boundaries. First, in order to segment the intertwined regions of brain tissue accurately, a weighted neighborhood information measure scheme based on local multi information and kernel function is designed. Then, the membership function of fuzzy c-means clustering is used as the spatial constraint of level set model to overcome the sensitivity of level set to initialization, and the evolution of level set function can be adaptively changed according to different tissue information. Finally, the distance regularization term in level set function is replaced by a double potential function to ensure the stability of the energy function in the evolution process. Both real and synthetic MRI images can show the effectiveness and performance of WLSM. In addition, compared with several state-of-the-art models, segmentation accuracy and Jaccard similarity coefficient obtained by WLSM are increased by 0.0586, 0.0362 and 0.1087, 0.0703, respectively.