Central Path Research Articles

Design and Application of Intelligent Processing Technology for Animation Images Based on Deep Learning

The origins of anime can be traced all the way back to the Homo sapiens period of human civilization. Nowadays, anime is a record of life as well as a popular kind of entertainment and a source of ideal trust for many individuals. Children and individuals of all classes and ages enjoy anime. In the opinion of most people, anime is not simply a form of amusement and pleasure, but it can also express deeper meanings, transmit other cultures, and inspire individuals to pursue their aspirations. Image stylistic migration based on convolutional neural networks has developed as a central research path in recent years, and attempts on style migration have evolved as well. However, there are few studies on style migration. In this paper, we propose a deep learning-based solution to the problem of anime-style migration. Experiments on a relevant database show that our proposed method is effective and accurate and has commercial and academic significance.

Antimagic orientation of subdivided caterpillars

Let m≥1 be an integer and G be a graph with m edges. We say that G has an antimagic orientation if G has an orientation D and a bijection τ:A(D)→{1,…,m} such that no two vertices in D have the same vertex-sum under τ, where the vertex-sum of a vertex v in D under τ is the sum of labels of all arcs entering v minus the sum of labels of all arcs leaving v. Hefetz et al. (2010) conjectured that every connected graph admits an antimagic orientation. The conjecture was confirmed for certain classes of graphs such as regular graphs, graphs with minimum degree at least 33, bipartite graphs with no vertex of degree zero or two, and trees including caterpillars and complete k-ary trees. We prove that every subdivided caterpillar admits an antimagic orientation, where a subdivided caterpillar is a subdivision of a caterpillar T such that the edges of T that are not on the central path of T are subdivided the same number of times.

Traces on diagram algebras I: Free partition quantum groups, random lattice paths and random walks on trees

We classify extremal traces on the seven direct limit algebras of noncrossing partitions arising from the classification of free partition quantum groups of Banica–Speicher [5] and Weber [42]. For the infinite-dimensional Temperley–Lieb algebra (corresponding to the quantum group O N + $O^+_N$ ) and the Motzkin algebra ( B N + $B^+_N$ ), the classification of extremal traces implies a classification result for well-known types of central random lattice paths. For the 2-Fuss–Catalan algebra ( H N + $H_N^+$ ), we solve the classification problem by computing the minimal or exit boundary (also known as the absolute) for central random walks on the Fibonacci tree, thereby solving a probabilistic problem of independent interest, and to our knowledge the first such result for a nonhomogeneous tree. In the course of this article, we also discuss the branching graphs for all seven examples of free partition quantum groups, compute those that were not already known, and provide new formulae for the dimensions of their irreducible representations.

Machine learning prediction and tau-based screening identifies potential Alzheimer\u2019s disease genes relevant to immunity

With increased research funding for Alzheimer’s disease (AD) and related disorders across the globe, large amounts of data are being generated. Several studies employed machine learning methods to understand the ever-growing omics data to enhance early diagnosis, map complex disease networks, or uncover potential drug targets. We describe results based on a Target Central Resource Database protein knowledge graph and evidence paths transformed into vectors by metapath matching. We extracted features between specific genes and diseases, then trained and optimized our model using XGBoost, termed MPxgb(AD). To determine our MPxgb(AD) prediction performance, we examined the top twenty predicted genes through an experimental screening pipeline. Our analysis identified potential AD risk genes: FRRS1, CTRAM, SCGB3A1, FAM92B/CIBAR2, and TMEFF2. FRRS1 and FAM92B are considered dark genes, while CTRAM, SCGB3A1, and TMEFF2 are connected to TREM2-TYROBP, IL-1β-TNFα, and MTOR-APP AD-risk nodes, suggesting relevance to the pathogenesis of AD.

An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming

An Interior Point Parameterized Central Path Following Algorithm for Linearly Constrained Convex Programming

Research on the Construction Path of Financial Media Center in Higher Vocational Colleges——Take Zibo Vocational Institute as an Example

Research on the Construction Path of Financial Media Center in Higher Vocational Colleges——Take Zibo Vocational Institute as an Example

The path of canine visceral leishmaniasis versus the path of Center for Zoonoses Control: contributions of spatial analysis to health.

Visceral leishmaniasis (VL) is a public health problem in Brazilian municipalities. As much as there is a planning of public policies regards VL in São Paulo State, new cases have been reported and spread. This paper aims to discuss how the Center for Zoonoses Control conducts its actions spatially in endemic city of Presidente Prudente, São Paulo State. Data are from the Municipal Health Department of Presidente Prudente, Adolfo Lutz Institute, and Brazilian Institute of Geography and Statistics. We spatially estimated the dog population per census tract and used geoprocessing tools to perform choropleth maps, spatial trends, and spatial autocorrelation. We found a spatial pattern of higher prevalence in the city's outskirt and a positive statistically significant spatial autocorrelation (I = 0.2, p-value < 0.000) with clusters of high-high relationships in the Northwest part of the city. Moreover, we identified a different direction in the path of the conducted serosurveys versus the canine VL trend, which stresses the fragility of the Center for Zoonoses Control actions to control the disease. The Center for Zoonoses Control always seems to chase the disease. The spatial analysis may be useful for rethinking how the service works and helps in public policies.

A full-modified-Newton step $ O(n) $ infeasible interior-point method for the special weighted linear complementarity problem

&lt;p style='text-indent:20px;'&gt;The weighted complementarity problem (wCP) can be applied to a large variety of equilibrium problems in science, economics and engineering. Since formulating an equilibrium problem as a wCP may lead to highly efficient algorithms for its numerical solution, wCP is a nontrivial generalization of the complementarity problem. In this paper we consider a special weighted linear complementarity problem (wLCP), which is the more general optimization of the Fisher market equilibrium problem. A full-modified-Newton infeasible interior-point method (IIPM) for the special wLCP is proposed. The algorithm reformulates the central path of the perturbed problem as an equivalent system of equations, and uses only full-Newton steps at each iteration, so-called a feasibility step (i.e., a full-modified-Newton step) and several usual centering steps. The polynomial complexity of the algorithm is as good as the best known iteration bound for these types of IIPMs in linear optimization.&lt;/p&gt;

미디어 융합을 배경으로한 틱톡플랫폼 기반의 광둥 문화 단편 영상 해외 소통 전략에 관한 연구

Due to the rapid development of network media and the popularity of mobile social media, the form of fused media development has been vigorously developed. The new “short-time” video format for real-time sharing and seamless docking on short video social platforms meets people’s need for relaxation of “fragmented” time. Based on the characteristics of the TikTok, this article analyzes the overseas communication strategies of Guangdong culture short videos from influencing factors and case studies.<BR> The purpose of this article is to establish an overseas communication strategy based on the ELM.<BR> Therefore, this article can study the factors that affect the effect of overseas communication through SPSS analysis.<BR> First, using the ELM, four model hypotheses are proposed under the center path and the edge path.<BR> Second, through designing questionnaires and data collection, SPSS data analysis shows that the H1, H2, and H3 hypotheses are established, and three main factors affecting overseas communication are explored: high-quality content, user attitudes-participation, and media popularity. H4 hypothesis does not hold, delete the creators.<BR> Third, through case studies, analyze the specific advantages of overseas communication.<BR> Finally, propose some strategies. Based on these research results, we look forward to the combination of Guangdong culture and commercial products to enhance the influence of overseas communication.

A predictor-corrector affine scaling method to train optimized extreme learning machine

Optimized extreme learning machine (OELM) has been shown to achieve high performance on classification problems due to its simple dual form. This paper presents a predictor-corrector affine scaling interior point method to exploit the dual problem of OELM. This method aims to combine a predictor step with a corrector step for determining the descent Newton direction. At each iteration, the predictor step focuses on the complementarity gap reduction and computes an affine scaling direction to estimate the extent of the reduction of complementarity gap, while the corrector step traces the central path towards the optimal solution by high order approximation, and computes the corresponding center direction. Then, the Newton direction is combined by using both two directions, and the iteration sequence of interior feasible points converges to the optimal solution. Extensive experimental evaluations on various benchmark datasets show that the proposed algorithms outperform other interior point-based or active set-based algorithms. Moreover, they are able to converge in fewer iterations, which are independent of kernel type, dataset size and dimensionality.

The Impact of Chinese Seals on the Structure, Design, and Usage of the Īl-Khānids Seals and Coins

Il-Khanid seals and coins are a type of seal featuring figurative patterns typically characterized by the Rectangular style of Kufic script, the absence of figures, extensive use of calligraphy, geometric, and abstract patterns. Although it is based on the Persian seal-carving tradition, the Īl-Khānids seals and coins exhibit various elements from the Chinese seals (印章), and also similar in their style to the Mongolian writing systems. While the Silk Road, the central path for trade and economic purposes, brought together China and Persia, the two nations had strong influences regarding culture, tradition, and religion, and Persian art has applied many Chinese artistic elements, particularly in the art of seal making. Indeed, the historical evidence suggests that the Mongolian Empire employed the Chinese seals (印章) throughout their territory, stretching from China to Persia.&#x0D; The intercultural influences through the Silk Road seem to be well-rooted in Central Asia, and for the first time, Chinese culture is seen abundantly in the Īl-Khānids seal history, as well as the Rectangular style of Kufic script on the seals and coins, influenced by the Uighur script. This paper uses an interdisciplinary approach to analyse the Chinese and the Īl-Khānids seals and coins to survey transmission of the Chinese tradition through Silk Road cultural exchanges. The results show that there exists a strong possibility that the manner in which the writing of Arabic characters in the Rectangular Kufic writing system was inserted at the top to the bottom unexpectedly followed the style of Mongolian words.

The business of postcolonial immigration: marketing of immigration services in Punjab, India

In this paper, I show that immigration consulting agencies in the Doaba region of Punjab, India, mobilise the imaginary of the ‘West’ as a place to be successful and modern in order to sell their services. My focus is on the design of promotional materials created by the agencies that are well integrated into the visual landscape of this region. Thus I analyse this imaginary as presented in banners, posters, and signboards. The visual data is complemented with semi structured interviews conducted with staff and owners at the agencies, ethnographic observations as well as information gleaned from the agencies’ websites. The study is novel in its exploration of the visual environment in pre-migration contexts where international migration is portrayed as a central path to prosperity. It is exploratory in nature and raises many questions for future researchers to pursue.

Scalable multi‐agent formation control under switching leader–follower directed graph

AbstractThis work considers formation control of single integrator agents interconnected under switching leader–follower network, where the size of the formation is scalable via a scaling factor determined by a leader agent. Past works on scalable formation are limited to the case where the communication network is considered to be fixed. This work proposes a new distributed algorithm for scalable formation problem that works under a switching network. The scaling is based on the location of the origin of the formation which can be adjusted by the leader agent. In addition, agents move together along a center path where the offset of the center path can also be adjusted by the leader agent. Numerical examples are shown to illustrate the proposed approach.

Curiosities and counterexamples in smooth convex optimization

Counterexamples to some old-standing optimization problems in the smooth convex coercive setting are provided. We show that block-coordinate, steepest descent with exact search or Bregman descent methods do not generally converge. Other failures of various desirable features are established: directional convergence of Cauchy’s gradient curves, convergence of Newton’s flow, finite length of Tikhonov path, convergence of central paths, or smooth Kurdyka–Łojasiewicz inequality. All examples are planar. These examples are based on general smooth convex interpolation results. Given a decreasing sequence of positively curved \(C^k\) convex compact sets in the plane, we provide a level set interpolation of a \(C^k\) smooth convex function where \(k\ge 2\) is arbitrary. If the intersection is reduced to one point our interpolant has positive definite Hessian, otherwise it is positive definite out of the solution set. Furthermore, given a sequence of decreasing polygons we provide an interpolant agreeing with the vertices and whose gradients coincide with prescribed normals.

Colourful components in k-caterpillars and planar graphs

A connected component of a vertex-coloured graph is said to be colourful if all its vertices have different colours. By extension, a graph is colourful if all its connected components are colourful. Given a vertex-coloured graph G and an integer p, the Colourful Components problem asks whether there exist at most p edges whose removal makes G colourful and the Colourful Partition problem asks whether there exists a partition of G into at most p colourful components. In order to refine our understanding of the complexity of the problems on trees, we study both problems on k-caterpillars, which are trees with a central path P such that every vertex not in P is within distance k from a vertex in P. We prove that Colourful Components and Colourful Partition are NP-complete on 4-caterpillars with maximum degree 3, 3-caterpillars with maximum degree 4 and 2-caterpillars with maximum degree 5. On the other hand, we show that the problems are linear-time solvable on 1-caterpillars. Hence, our results imply two complexity dichotomies on trees: Colourful Components and Colourful Partition are linear-time solvable on trees with maximum degree d if d≤2 (that is, on paths), and NP-complete otherwise; Colourful Components and Colourful Partition are linear-time solvable on k-caterpillars if k≤1, and NP-complete otherwise. We leave three open cases which, if solved, would provide a complexity dichotomy for both problems on k-caterpillars, for every non-negative integer k, with respect to the maximum degree. We also show that Colourful Components is NP-complete on 5-coloured planar graphs with maximum degree 4 and on 12-coloured planar graphs with maximum degree 3. Our results answer two open questions of Bulteau et al. mentioned in Bulteau et al. (2019) [6].

Optimal step length for the Newton method: case of self-concordant functions

The theoretical foundation of path-following methods is the performance analysis of the (damped) Newton step on the class of self-concordant functions. However, the bounds available in the literature and used in the design of path-following methods are not optimal. In this contribution we use methods of optimal control theory to compute the optimal step length of the Newton method on the class of self-concordant functions, as a function of the initial Newton decrement, and the resulting worst-case decrease of the decrement. The exact bounds are expressed in terms of solutions of ordinary differential equations which cannot be integrated explicitly. We provide approximate numerical and analytic expressions which are accurate enough for use in optimization methods. Consequently, the neighbourhood of the central path in which the iterates of path-following methods are required to stay can be enlarged, enabling faster progress along the central path during each iteration and hence fewer iterations to achieve a given accuracy.

Implementation of the Full-Newton Step Algorithm for Weighted Linear Complementarity Problems

Abstract We present a path-following interior-point algorithm for solving the weighted linear complementarity problem from the implementation point of view. We studied two variants, which differ only in the method of updating the parameter which characterizes the central path. The implementation was done in the C++ programming language and the obtained numerical results prove the efficiency of the proposed method.

Predictor-corrector interior-point algorithm for [formula omitted]-linear complementarity problems based on a new type of algebraic equivalent transformation technique

We propose a new predictor-corrector (PC) interior-point algorithm (IPA) for solving linear complementarity problem (LCP) with P*(κ)-matrices. The introduced IPA uses a new type of algebraic equivalent transformation (AET) on the centering equations of the system defining the central path. The new technique was introduced by Darvay and Takács (2018) for linear optimization. The search direction discussed in this paper can be derived from positive-asymptotic kernel function using the function φ(t)=t2 in the new type of AET. We prove that the IPA has O((1+4κ)nlog3nμ04ϵ) iteration complexity, where κ is an upper bound of the handicap of the input matrix. To the best of our knowledge, this is the first PC IPA for P*(κ)-LCPs which is based on this search direction.

From Fork Decoupling to Star-Topology Decoupling

Fork decoupling is a recent approach to exploiting problem structure in state space search. The problem is assumed to take the form of a fork, where a single (large) center component provides preconditions for several (small) leaf components. The leaves are then conditionally independent in the sense that, given a fixed center path p, the compliant leaf moves - those leaf moves enabled by the preconditions supplied along p - can be scheduled independently for each leaf. Fork-decoupled state space search exploits this through conducting a regular search over center paths, augmented with maintenance of the compliant paths for each leaf individually. We herein show that the same ideas apply to much more general star-topology structures, where leaves may supply preconditions for the center, and actions may affect several leaves simultaneously as long as they also affect the center. Our empirical evaluation in planning, super-imposing star topologies by automatically grouping the state variables into suitable components, shows the merits of the approach.

Test Particle Model Predictions of SEP Electron Transport and Precipitation at Mars

AbstractExtreme space weather events can episodically release solar energetic particles (SEPs) that precipitate into planetary atmospheres, leading to aurora and increased ionization. While the induced magnetosphere of Mars does not substantially obstruct SEP protons, the effect on SEP electrons is not known. We use a test particle model modified for relativistic electrons to model transport of 10–200 keV electrons from outside the bow shock and deep in the magnetotail of Mars. We find a substantial influence of curvature and gradient drifts on precipitation, leading to depletions in the bow shock and transport onto closed field lines. The model estimates ∼3% of incident flux precipitates into the Mars atmosphere for a typical SEP event under nominal solar wind conditions, exceeding the estimate from the guiding center path approximation without drift terms. Precipitation is globally patchy. The model estimates 55% of electrons precipitating into cusps along open field lines and 45% precipitating on closed field lines, suggesting drift and nonadiabatic transport mechanisms have a significant influence on precipitation. We also predict that the fraction of precipitating differential flux increases as a function of energy. We discuss how these predictions would be affected by disturbed conditions that tend to accompany the arrival of SEPs and by differing SEP electron spectra hardness and anisotropy. We finally discuss how the simulation predictions compare to observations of diffuse aurora.