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Given two square matrices A, B of the same size, the two matrices AB and BA may have different ranks. A non-zero square matrix A is called a rankcommutator of a family L of n × n matrices if rank(AL) = rank(LA) holds for every L in L. Let L* denote the family of all rank-commutators of L. In this paper, we investigate the members of L* for the following families L of n×n matrices: all non-zero symmetric matrices; all diagonal matrices; all diagonalizable matrices. In the process, some new notions in linear algebra are created, such as "rank-symmetric matrices" and "determinant equivalent matrices", which might be useful for other study on ranks. A few problems for further study are posed at the end of the paper. [ABSTRACT FROM AUTHOR]

Text Let m be an integer with m ≥ 2 . For A ⊆ Z m and n ∈ Z m , let R 1 ( A , n ) , R 2 ( A , n ) , R 3 ( A , n ) denote the number of solutions of the equation a + a ′ = n with ordered pairs ( a , a ′ ) ∈ A × A , unordered pairs ( a , a ′ ) ∈ A × A ( a ≠ a ′ ) and unordered pairs ( a , a ′ ) ∈ A × A , respectively. In this paper, for i ∈ { 1 , 2 , 3 } , we determine all sets A , B ⊆ Z m such that R i ( A , n ) = R i ( B , n ) for all n ∈ Z m when the cardinality of the symmetric difference of A and B is small or large. These extend some previous results. We also pose some problems for further research. Video For a video summary of this paper, please visit https://youtu.be/stBa9Uy5U0I . [ABSTRACT FROM AUTHOR]

Text Let K be a complete, algebraically closed, non-Archimedean valued field, and let ϕ ∈ K ( z ) with deg ⁡ ( ϕ ) ≥ 2 . In this paper we consider the family of functions ord Res ϕ n ( x ) , which measure the resultant of ϕ n at points x in P K 1 , the Berkovich projective line, and show that they converge locally uniformly to the diagonal values of the Arakelov–Green's function g μ ϕ ( x , x ) attached to the canonical measure of ϕ . Following this, we are able to prove an equidistribution result for Rumely's crucial measures ν ϕ n , each of which is a probability measure supported at finitely many points whose weights are determined by dynamical properties of ϕ . Video For a video summary of this paper, please visit https://youtu.be/YCCZD1iwe00 . [ABSTRACT FROM AUTHOR]

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code. [ABSTRACT FROM AUTHOR]

This paper develops an improved tri-coloured rooted-tree theory for the order conditions for ERKN methods solving general multi-frequency and multidimensional second-order oscillatory systems. The bottleneck of the original tricoloured rooted-tree theory is the existence of numerous redundant trees. In light of the fact that the sum of the products of the symmetries and the elementary differentials is meaningful, this paper naturally introduces the so-called extended elementary differential mappings. Then, the new improved tri-coloured rooted tree theory is established based on a subset of the original tri-coloured rooted-tree set. This new theory makes all redundant trees disappear, and thus, the order conditions of ERKN methods for general multi-frequency and multidimensional second-order oscillatory systems are reduced greatly. Furthermore, with this new theory, we present some new ERKN methods of order up to four. Numerical experiments are implemented and the results show that ERKN methods can be competitive with other existing methods in the scientific literature, especially when comparatively large stepsizes are used. [ABSTRACT FROM AUTHOR]

In this paper we introduce a generalization of a Brauer graph algebra which we call a Brauer configuration algebra. As with Brauer graphs and Brauer graph algebras, to each Brauer configuration, there is an associated Brauer configuration algebra. We show that Brauer configuration algebras are finite dimensional symmetric algebras. After studying and analysing structural properties of Brauer configurations and Brauer configuration algebras, we show that a Brauer configuration algebra is multiserial; that is, its Jacobson radical is a sum of uniserial modules whose pairwise intersection is either zero or a simple module. The paper ends with a detailed study of the relationship between radical cubed zero Brauer configuration algebras, symmetric matrices with non-negative integer entries, finite graphs and associated symmetric radical cubed zero algebras. [ABSTRACT FROM AUTHOR]

In this paper we complete the determination of the Brauer trees of unipotent blocks (with cyclic defect groups) of finite groups of Lie type. These trees were conjectured by the first author in [19]. As a consequence, the Brauer trees of principal ℓ-blocks of finite groups are known for ℓ > 71. [ABSTRACT FROM AUTHOR]

In this paper, we prove abundance for 3-folds with nontrivial Albanese maps, over an algebraically closed field of characteristic p > 5. [ABSTRACT FROM AUTHOR]

Standards-based grading (SBG) is an assessment/grading system that attaches scores to the mastery level of specific learning objectives. This methodology is gaining momentum in the K-12 environment but has been largely overlooked at the post-secondary level. In this paper, I will discuss the implementation of this practice in a College Algebra course. I will also discuss the motivation in attempting an alternative assessment system, the development and implementation process and describe the resulting system. Comparisons will be made between a College Algebra course utilizing the traditional points-based system and the same course in which SBG was incorporated. These comparisons will include observed student behaviors, student perception, the administrative efforts required of the instructor, and student performance in subsequent courses. [ABSTRACT FROM AUTHOR]

One of the main results stated in Theorem 4.4 of our article, which appears in Trans. Amer. Math. Soc. 372 (2019), no. 10, 7191-7223, is that the structure algebra K[M(X,r)], over a field K, of a finite bijective left non-degenerate solution (X,r) of the Yang-Baxter equation is a module-finite central extension of a commutative affine subalgebra. This is proven by showing that the structure monoid M(X,r) is central-by-finite. This however is not true, even in case (X,r) is a (left and right) non-degenerate involutive solution. The proof contains a subtle mistake. However, it turns out that the monoid M(X,r) is abelian-by-finite and thus the conclusion that K[M(X,r)] is a module-finite normal extension of a commutative affine subalgebra remains valid. In particular, K[M(X,r)] is Noetherian and satisfies a polynomial identity. The aim of this paper is to give a proof of this result. In doing so, we also strengthen Lemma 5.3 (and its consequences, namely Lemma 5.4 and Proposition 5.5) showing that these results on the prime spectrum of the structure monoid hold even if the assumption that the solution (X,r) is square-free is omitted. [ABSTRACT FROM AUTHOR]

In this paper, we characterize quasi-Yetter–Drinfeld modules over a Hopf algebra H , which was introduced in [Y. Bazlov and A. Berenstein, Braided doubles and rational Cherednik algebras, Adv. Math. 220 (2009), 1466–1530]. We first show that the quasi-Drinfeld center of the category of H -modules is equivalent to the category H H 𝒬 𝒴 𝒟 of quasi-Yetter–Drinfeld modules. Next, we prove that H H 𝒬 𝒴 𝒟 is equivalent to the category of generalized Hopf bimodules. Finally, we show that H H 𝒬 𝒴 𝒟 is also equivalent to the category of quasi-coactions over some Majid's braided group if H is quasi-triangular. [ABSTRACT FROM AUTHOR]

In this paper, we give a recursive formula for the interesting PBW basis E A of composition subalgebras ℭ ▵ (n) of Ringel–Hall algebras ℌ ▵ (n) of cyclic quivers after [Generic extensions and canonical bases for cyclic quivers, Canad. J. Math. 59(6) (2007) 1260–1283], and another construction of canonical bases of U v + ( 𝔰 𝔩 ̂ n) from the monomial bases m (A) following [Multiplication formulas and canonical basis for quantum affine, 𝔤 𝔩 n , Canad. J. Math. 70(4) (2018) 773–803]. As an application, we will determine all the canonical basis elements of U v + ( 𝔰 𝔩 ̂ 2) associated with modules of Loewy length ≤ 3. Finally, we will discuss the canonical bases between Ringel–Hall algebras and affine quantum Schur algebras. [ABSTRACT FROM AUTHOR]

MashhadBranch,IslamicAzadUniversityLet L be a Lie algebra crossed module and Actpi(L) be a pointwise inner Actor of L. In this paper, we introduce lower and upper central series of L and show that if Actpi (L/Zj(L) /InnAct (L/Zj(L) is the nilpotent of class k wherein Zj (L) denotes the nth term of the upper central series of L, then Actpi(L)/InnAct(LL) is the nilpotent of the maximum class j + k. Moreover, if dim )Li/(Li ∩ Zj(L))) ≤ (1,1), then Actnilpotentofclasspi(L) / InnAct(L) is the nilpotent of the maximum class i + j - 1. [ABSTRACT FROM AUTHOR]

Let τn be a type of algebras in which all operation symbols have arity n, for a fixed n ≥ 1. For 0 < r ≤ n, this paper introduces a special kind of n-ary terms of type τn called K*(n, r)-full terms. The set of all K*(n, r)-full terms of type τn is closed under the superposition operation Sn; hence forms a clone denoted by cloneK*(n,r)(τn). We prove that cloneK* (n,r)(τn) is a Menger algebra of rank n. We study K*(n, r)-full hypersubstitutions and the related K*(n, r)-full closed identities and K*(n, r)-full closed varieties. A connection between identities in cloneK* (n,r)(τn) and K* (n, r)-full closed identities is established. The results obtained generalize the results of Denecke and Jampachon [K. Denecke and P. Jampachon, Clones of full terms, Algebra and Discrete Math. 4 (2004) 1–11]. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with identity, and I a fixed ideal R of and M be an unitary R-module. In this paper we introduce and study the concept of I-nearly prime submodules as genrealizations of nearly prime and we investigate some properties of this class of submodules. Also, some characterizations of I-nearly prime submodules will be given. [ABSTRACT FROM AUTHOR]

Gangyong Lee, S.Tariq Rizvi, and Cosmin S.Roman studied Rickart modules. The main purpose of this paper is to develop the properties of Rickart modules . We prove that each injective and prime module is a Rickart module. And we give characterizations of some kind of rings in term of Rickart modules. [ABSTRACT FROM AUTHOR]

This is the last in a series of articles where we are concerned with normal elements of noncommutative Iwasawa algebras over SL n ⁢ (ℤ p) {\mathrm{SL}_{n}(\mathbb{Z}_{p})}. Our goal in this portion is to give a positive answer to an open question in [D. Han and F. Wei, Normal elements of noncommutative Iwasawa algebras over SL 3 ⁢ (ℤ p) \mathrm{SL}_{3}(\mathbb{Z}_{p}) , Forum Math. 31 2019, 1, 111–147] and make up for an earlier mistake in [F. Wei and D. Bian, Normal elements of completed group algebras over SL n ⁢ (ℤ p) \mathrm{SL}_{n}(\mathbb{Z}_{p}) , Internat. J. Algebra Comput. 20 2010, 8, 1021–1039] simultaneously. Let n ( n ≥ 2 {n\geq 2}) be a positive integer. Let p ( p > 2 {p>2}) be a prime integer, ℤ p {\mathbb{Z}_{p}} the ring of p-adic integers and 𝔽 p {\mathbb{F}_{p}} the finite filed of p elements. Let G = Γ 1 ⁢ (SL n ⁢ (ℤ p)) {G=\Gamma_{1}(\mathrm{SL}_{n}(\mathbb{Z}_{p}))} be the first congruence subgroup of the special linear group SL n ⁢ (ℤ p) {\mathrm{SL}_{n}(\mathbb{Z}_{p})} and Ω G {\Omega_{G}} the mod-p Iwasawa algebra of G defined over 𝔽 p {\mathbb{F}_{p}}. By a purely computational approach, for each nonzero element W ∈ Ω G {W\in\Omega_{G}} , we prove that W is a normal element if and only if W contains constant terms. In this case, W is a unit. Also, the main result has been already proved under "nice prime" condition by Ardakov, Wei and Zhang [Non-existence of reflexive ideals in Iwasawa algebras of Chevalley type, J. Algebra 320 2008, 1, 259–275; Reflexive ideals in Iwasawa algebras, Adv. Math. 218 2008, 3, 865–901]. This paper currently provides a new proof without the "nice prime" condition. As a consequence of the above-mentioned main result, we observe that the center of Ω G {\Omega_{G}} is trivial. [ABSTRACT FROM AUTHOR]

This paper is devoted to the conception of mathematical objects and methods according to d'Alembert. We first recall his vision of the place of mathematics in the knowledge of nature, then the internal hierarchy of the various fields of this science, based on their degree of abstraction from sensations (§1 and 2). Then we come to the ideas of definitions, primitive ideas , simple ideas , and their generation as well as their generalization (§3 and 4). Then, having looked at what he means by quantities, numbers, quantities, as well as his conception of the objects and rules of algebra as abstract ideas by generalization (§5), we approach the question of the reality of mathematical objects with the example of the irrational (§6). The following paragraphs of the text are devoted to the difficulties encountered in various fields and the way d'Alembert tries to solve them: algebra and negative quantities (§7); principles of geometry (§8); the notion of limit as the basis of infinitesimal calculus (§9). His reflections, even if unfinished, were not without posterity (§10). [ABSTRACT FROM AUTHOR]

This paper continues the study of orthonormal bases (ONB) of L 2 [ 0 , 1 ] introduced in Dutkay et al. (J. Math. Anal. Appl. 409(2):1128–1139, 2014) by means of Cuntz algebra O N representations on L 2 [ 0 , 1 ] . For N = 2 , one obtains the classic Walsh system. We show that the ONB property holds precisely because the O N representations are irreducible. We prove an uncertainty principle related to these bases. As an application to discrete signal processing we find a fast generalized transform and compare this generalized transform with the classic one with respect to compression and sparse signal recovery. [ABSTRACT FROM AUTHOR]

Although the use of technology in the K12 classroom has been shown to have a positive impact, research on the use of open education resources (OER) is relatively limited, especially research focusing on low‐achieving students. The present study examines the relationship between usage of Algebra Nation, a self‐guided system that provided instructional videos and practice problems, and the performance of students who had failed the state‐administered Algebra I end‐of‐course (EOC) assessment the previous year. Indicators of usage of Algebra Nation consisted of logins, video views, and practice questions answered. Path analyses and logistic regressions were used to evaluate relationships between usage indicators and algebra scores, controlling for number of absences, free/reduced lunch eligibility, Hispanic/Latino origin, race, and gender. The results indicate that higher levels of logins, video views, and practice questions answered were related to higher scores when the students re‐took the assessment. Logins and practice questions were also related to increases in odds of passing the Algebra I EOC assessment, but not video views. The results suggest that there may be benefits to technology use in the form of an OER adopted by students and teachers on an informal basis and link self‐regulated learning strategies to student achievement. Lay Description: What is already known about this topic: Algebra courses typically have a high failure rate.Repeating algebra is costly for the education system and for the student.Open education resources could potentially be an effective and cost‐efficient approach to algebra instruction. What this paper adds: This study shows that logins, video views, and practice questions answered in an open education resource were positively related to scores on a state‐administered,high‐stakes algebra assessment.The study indicates that the relationship between a self‐regulated learning strategy (i.e., practice questions answered) and student algebra scores is stronger than that between video views and algebra scores.This study shows that student‐driven ad hoc use of online tutoring programme is associated with higher passing rates on the algebra exam. Implications for practice and/or policy: This study demonstrates that informal use of an open education resource with videos and a practice question system can be effective in increasing student scores on algebra assessments.Future research is needed to connect diverse types of student self‐regulated use of open education resources to academic achievement and on how to design resources that encourage effective self‐regulation. [ABSTRACT FROM AUTHOR]

The European Emission Trading System (EU ETS) is commonly regarded as the key pillar of the European climate policy and as the main unifying tool to create a unique carbon price all over Europe. The UK has always played a crucial role in the EU ETS, being one of the most active national registry and a crucial hub for the exchange of allowances in the market. Brexit, therefore, could deeply modify the number and directions of such exchanges as well as the centrality of the other countries in this system. To investigate these issues, the present paper exploits network analysis tools to compare the structure of the EU ETS market in its first two phases with and without the UK, investigating a few different scenarios that might emerge from a possible reallocation of the transactions that have involved UK partners. We find that without the UK the EU ETS network would become in general much more homogeneous, though results may change focusing on the type of accounts involved in the transactions. [ABSTRACT FROM AUTHOR]

Forgery detection is essential to verify the integrity and authenticity of images. Existing block-based detection techniques detect forgery in the same image, most of which use similar frameworks while differ in the feature extraction schemes. These methods have high accuracy in detecting the forged regions, but the computational load is heavy when facing exhaustive search problems. This paper describes a forgery detection method based on local binary pattern residue classes and color regions. An image is divided into overlapped blocks. Local binary pattern residue classes are computed for each block. The plane formed by a dimensional and b dimensional from Lab color space is divided into 16 regions. Similar blocks are searched in the overlapped blocks with the same local binary pattern residue class and color region, then they are grouped into several suspicious regions. Finally, we analyze the multi-region relation of these suspicious regions and their areas to locate the tampered regions. The small hole is filled through the morphologic operation. The results of experiments demonstrated that our method has good performance in that it improved detection accuracy and reduced execution time under various challenging conditions. As the proposed method reduces the search range for similar blocks, it has a higher speed than exhaustive search and has comparable detection results at the same time. [ABSTRACT FROM AUTHOR]

In this paper, we explore the problem of establishing a network among the stocks of a market at high frequency level and give an application to program trading. Our work uses high frequency data from the National Stock Exchange, India, for the year 2014. To begin, we analyse the spectrum of the correlation matrix to establish the presence of linear relations amongst the stock returns. A comparison of correlations with pairwise mutual information shows the further existence of non-linear relations which are not captured by correlation. We also see that the non-linear relations are more pronounced at the high frequency level in comparison to the daily returns used in earlier work. We provide two applications of this approach. First, we construct minimal spanning trees for the stock network based on mutual information and study their topology. The year 2014 saw the conduct of general elections in India and the data allows us to explore their impact on aspects of the network, such as the scale-free property and sectorial clusters. Second, having established the presence of non-linear relations, we would like to be able to exploit them. Previous authors have suggested that peripheral stocks in the network would make good proxies for the Markowitz portfolio but with a much smaller number of stocks. We show that peripheral stocks selected using mutual information perform significantly better than ones selected using correlation. [ABSTRACT FROM AUTHOR]

Path planning for electric vehicles (EVs) can alleviate the limited cruising range and “range anxiety”. Many existing path optimization models cannot produce satisfactory solutions due to the imposition of too many assumptions and simplifications. The targeted optimal-path problem for electric vehicles (EV-TOP), which is proposed in the paper, aims at identifying the targeted optimal path for EVs under the limited battery level. It minimizes the travel cost, which is composed of the travel time and the total time that is spent at charging stations (CSs). The model is much more realistic due to the prediction and the consideration of the waiting times at CSs and more accurate approximations of the electricity consumption function and the charging function. Charging station information and the road traffic state are utilized to calculate the travel cost. The EV-TOP is decomposed into two subproblems: a constrained optimal path problem in the network (EV1-COP) and a shortest path problem in the meta-network (EV2-SP). To solve the EV1-COP, the Lagrangian relaxation algorithm, the simple efficient approximation (SEA) algorithm, and the Martins (MS) deletion algorithm are used. The EV2-SP is solved using Dijkstra’s algorithm. Thus, a polynomial-time approximation algorithm for the EV-TOP is developed. Finally, two computational studies are presented. The first study assesses the performance of the travel cost method. The second study evaluates the performance of our EV-TOP by comparing it with a well-known method. [ABSTRACT FROM AUTHOR]

The estimation of the correct number of dimensions is a long-standing problem in psychometrics. Several methods have been proposed, such as parallel analysis (PA), Kaiser-Guttman’s eigenvalue-greater-than-one rule, multiple average partial procedure (MAP), the maximum-likelihood approaches that use fit indexes as BIC and EBIC and the less used and studied approach called very simple structure (VSS). In the present paper a new approach to estimate the number of dimensions will be introduced and compared via simulation to the traditional techniques pointed above. The approach proposed in the current paper is called exploratory graph analysis (EGA), since it is based on the graphical lasso with the regularization parameter specified using EBIC. The number of dimensions is verified using the walktrap, a random walk algorithm used to identify communities in networks. In total, 32,000 data sets were simulated to fit known factor structures, with the data sets varying across different criteria: number of factors (2 and 4), number of items (5 and 10), sample size (100, 500, 1000 and 5000) and correlation between factors (orthogonal, .20, .50 and .70), resulting in 64 different conditions. For each condition, 500 data sets were simulated using lavaan. The result shows that the EGA performs comparable to parallel analysis, EBIC, eBIC and to Kaiser-Guttman rule in a number of situations, especially when the number of factors was two. However, EGA was the only technique able to correctly estimate the number of dimensions in the four-factor structure when the correlation between factors were .7, showing an accuracy of 100% for a sample size of 5,000 observations. Finally, the EGA was used to estimate the number of factors in a real dataset, in order to compare its performance with the other six techniques tested in the simulation study. [ABSTRACT FROM AUTHOR]

B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the sampled data. The most challenging task in these cases is in the identification of the number of knots and their respective locations in non-uniform space in the most efficient computational cost. This paper presents a new strategy for fitting any forms of curve by B-spline functions via local algorithm. A new two-step method for fast knot calculation is proposed. In the first step, the data is split using a bisecting method with predetermined allowable error to obtain coarse knots. Secondly, the knots are optimized, for both locations and continuity levels, by employing a non-linear least squares technique. The B-spline function is, therefore, obtained by solving the ordinary least squares problem. The performance of the proposed method is validated by using various numerical experimental data, with and without simulated noise, which were generated by a B-spline function and deterministic parametric functions. This paper also discusses the benchmarking of the proposed method to the existing methods in literature. The proposed method is shown to be able to reconstruct B-spline functions from sampled data within acceptable tolerance. It is also shown that, the proposed method can be applied for fitting any types of curves ranging from smooth ones to discontinuous ones. In addition, the method does not require excessive computational cost, which allows it to be used in automatic reverse engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, complex network theory is used to make time-series analysis of key indicators of governance structure and financing data. We analyze scientific listed companies’ governance data from 2010 to 2014 and divide them into groups in accordance with the similarity they share. Then we select sample companies to analyze their financing data and explore the influence of governance structure on financing decision and the financing preference they display. This paper reviews relevant laws and regulations of financing from the perspective of law and economics, then proposes reasonable suggestions to consummate the law for the purpose of regulating listed companies’ financing. The research provides a reference for making qualitative analysis on companies’ financing. [ABSTRACT FROM AUTHOR]

In this paper, for 𝒞 a strict braided monoidal category with tensor product ⊗, we improve the definition of Hom-associative algebra by removing the multiplicativity condition of the automorphismα. After that we state the close connection between the classical notions of (co)algebra, (co)module and Hopf algebra and the corresponding ones in the Hom-world. As a consequence we can study the questions about the Hom-world by passing to the classical one, and the main contribution of this paper is to illustrate the suitable procedure to move from one side to the other. Finally, we apply our techniques to get in the Hom setting some classical results about cleft and Galois extensions. [ABSTRACT FROM PUBLISHER]

Multi-robot task allocation is one of the main problems to address in order to design a multi-robot system, very especially when robots form coalitions that must carry out tasks before a deadline. A lot of factors affect the performance of these systems and among them, this paper is focused on the physical interference effect, produced when two or more robots want to access the same point simultaneously. To our best knowledge, this paper presents the first formal description of multi-robot task allocation that includes a model of interference. Thanks to this description, the complexity of the allocation problem is analyzed. Moreover, the main contribution of this paper is to provide the conditions under which the optimal solution of the aforementioned allocation problem can be obtained solving an integer linear problem. The optimal results are compared to previous allocation algorithms already proposed by the first two authors of this paper and with a new method proposed in this paper. The results obtained show how the new task allocation algorithms reach up more than an 80% of the median of the optimal solution, outperforming previous auction algorithms with a huge reduction of the execution time. [ABSTRACT FROM AUTHOR]

In this paper, we discuss two quotient BI-algebras induced by fuzzy normal subalgebras and induced by fuzzy congruence relations, which are useful in the study of the structural theory of fuzzy quotient BI-algebras. [ABSTRACT FROM AUTHOR]

Background: CD4 cell counts is widely used as a biomarker for treatment progression when studying the efficacy of drugs to treat HIV-infected patients. In the past, it had been also used in determining eligibility to initiate antiretroviral therapy. The main aim of this was to model the evolution of CD4 counts over time and use this model for an early prediction of subject-specific time to cross a pre-specified CD4 threshold. Methods: Hospital based retrospective cohort study of HIV-infected patients was conducted from January 2009 to December 2014 at University of Gondar hospital, Northwest Ethiopia. Fractional polynomial random effect model is used to model the evolution of CD4 counts over time in response to treatment and to estimate the individual probability to be above a pre-selected CD4 threshold. Human subject research approval for this study was received from University of Gondar Research Ethics Committee and the medical director of the hospital. Results: A total of 1347 patients were included in the analysis presented in this paper. The cohort contributed a total of 236.58 per 100 person-years of follow-up. Later the data were divided into two periods: the first is the estimation period in which the parameters of the model are estimated and the second is the prediction period. Based on the parameters from the estimation period, model based prediction for the time to cross a threshold was estimated. The correlations between observed and predicted values of CD4 levels in the estimation period were 0.977 and 0.982 for Neverapine and Efavirenz containing regimens, respectively; while the correlation between the observed and predicted CD4 counts in the prediction period are 0.742 and 0.805 for NVP and EFV, respectively. Conclusions: The model enables us to estimate a subject-specific expected time to cross a CD4 threshold and to estimate a subject-specific probability to have CD4 count above a pre-specified threshold at each time point. By predicting long-term outcomes of CD4 count of the patients one can advise patient about the potential ART benefits that accrue in the long-term. [ABSTRACT FROM AUTHOR]

Abstract The growth of tropical geometry has generated significant interest in the tropical semiring in the past decade. However, there are other semirings in tropical algebra that provide more information, such as the symmetrized (max ⁡ , +) , Izhakian's extended and Izhakian–Rowen's supertropical semirings. In this paper we identify in which of these upper-bound semirings we can express symmetric polynomials in terms of elementary ones. We show that in the case of idempotent semirings we can do this precisely when the Frobenius property is satisfied, that in the case of supertropical semirings this is always possible, and that in non-trivial symmetrized semirings this is never possible. Our results allow us to determine the tropical algebra semirings where an analogue of the Fundamental Theorem of Symmetric Polynomials holds and to what extent. [ABSTRACT FROM AUTHOR]

In this paper, we apply umbral calculus techniques in order to derive explicit exprissions, some properties, recurrence relations and identities for degenerate poly-Genocchi polynomials. Further-more, we derive several explicit expressions of degenerate poly-Genocchi polynomials as linear combinations of some of the well-known families of special polynomials. [ABSTRACT FROM AUTHOR]

With the emergence and widespread application of cloud computing, the use of cloud platforms to solve the problem of secure multi-party computation has emerged as a new research direction. The traditional computation of a solid geometry is performed through mutual interactions between two parties, which is not suitable in an untrusted cloud computing environment. In this paper, we first design a basic protocol for a secure Euclidean distance calculation that is suitable for cloud platforms and can serve as a building block for other protocols on cloud platforms. Using the solution of the Euclidean distance problem as such a building block, we provide a new method that converts the problems of calculating solid triangular areas and solid tetrahedral volumes into the calculation of distances and determinants in three-dimensional space. Then, we discuss solid point-line distance calculations, which extent the idea of the spatial geometry security problem. We present protocols for the above problems and prove that the proposed protocols can resist conspiracy among users and the untrusted cloud platform so that they can effectively ensure the privacy of the users. We also analyze the performances of these solutions. The analysis results show that our scheme is more versatile. [ABSTRACT FROM AUTHOR]

The reuse of business processes (BPs) requires similarities between them to be suitably identified. Various approaches have been introduced to address this problem, but many of them feature a high computational cost and a low level of automation. This paper presents a clustering algorithm that groups business processes retrieved from a multimodal search system (based on textual and structural information). The algorithm is based on Incremental Covering Arrays (ICAs) with different alphabets to determine the possible number of groups to be created for each row of the ICA. The proposed algorithm also incorporates Balanced Bayesian Information Criterion to determine the optimal number of groups and the best solution for each query. Experimental evaluation shows that the use of ICAs with strength four (4) and different alphabets reduces the number of solutions needed to be evaluated and optimizes the number of clusters. The proposed algorithm outperforms other algorithms in various measures (precision, recall, and F-measure) by between 12% and 88%. Friedman and Wilcoxon non-parametric tests gave a 90–95% significance level to the obtained results. Better options of repository search for BPs help companies to reuse them. By thus reusing BPs, managers and analysts can more easily get to know the evolution and trajectory of the company processes, a situation that could be expected to lead to improved managerial and commercial decision making. [ABSTRACT FROM AUTHOR]

Clustering large and complex data sets whose partitions may adopt arbitrary shapes remains a difficult challenge. Part of this challenge comes from the difficulty in defining a similarity measure between the data points that captures the underlying geometry of those data points. In this paper, we propose an algorithm, DCG++ that generates such a similarity measure that is data-driven and ultrametric. DCG++ uses Markov Chain Random Walks to capture the intrinsic geometry of data, scans possible scales, and combines all this information using a simple procedure that is shown to generate an ultrametric. We validate the effectiveness of this similarity measure within the context of clustering on synthetic data with complex geometry, on a real-world data set containing segmented audio records of frog calls described by mel-frequency cepstral coefficients, as well as on an image segmentation problem. The experimental results show a significant improvement on performance with the DCG-based ultrametric compared to using an empirical distance measure. [ABSTRACT FROM AUTHOR]

Owing to the emergence of the Internet and its rapid growth, people can use mobile devices on many social media platforms (blogs, Facebook forums, etc.), and the platforms provide well-known websites for people to express and share their daily activities and ideas on global issues. Many consumers utilize product review websites before making a purchase. Many well-known websites are searched for relevant product reviews and experiences of product use. We can easily collect large amounts of structured and unstructured product data and further analyze the data to determine the desired product information. For this reason, many researchers are gradually focusing on sentiment analysis or opinion exploration (opinion mining) and use this technique to extract and analyze customer opinions and emotions. This paper proposes a sentimental text mining method based on an additional features method to enhance accuracy and reduce implementation time and uses singular value decomposition and principal component analysis for data dimension reduction. This study has four contributions: (1) the proposed algorithm for preprocessing the data for sentiment classification, (2) the additional features to enhance the accuracy of the sentiment classification, (3) the application of singular value decomposition and principal component analysis for data dimension reduction, and (4) the design of five modules based on different features, with or without stemming, to compare the performance results. The experimental results show that the proposed method has better accuracy than other methods and that the proposed method can decrease the implementation time. [ABSTRACT FROM AUTHOR]

The goal of this paper is to construct an action of the cactus group of a Weyl group W on W that is nicely compatible with Kazhdan--Lusztig cells. The action is realized by the wall-crossing bijections that are combinatorial shadows of wall-crossing functors on the category O. [ABSTRACT FROM AUTHOR]

In this paper, we would like to exploit umbral calculus in order to derive explicit expressions, some properties, recurrence relations and identities for poly-Genocchi polynomials. [ABSTRACT FROM AUTHOR]

The software-defined networking (SDN) paradigm has simplified the management of computer networks by decoupling data and control planes. Moreover, the separation of the data and control planes has transitioned network complexity from traditional devices to controllers; therefore, controllers have become indispensable entities in SDN. Controllers have multiple features and direct the network from a central point and respond to updates to topological changes. However, the supportive capability of these features is strong in one controller but weak in another. Due to several controllers and each controller having a set of features, selecting an optimal SDN controller can be considered to be a multi-criteria decision-making (MCDM) problem. Herein, a two-step approach is proposed for SDN controller selection. First, the controllers are ranked with analytical network process (ANP) according to their qualitative features which influence the performance of these controllers and then a performance comparison is performed to check for the QoS improvement. The controller with a high-weight value from the feature-based comparison is quantitatively analysed by experimental analysis. The main contribution of this paper is checking the applicability of the ANP for controller selection in SDN considering its features and performance analysis in real-world Internet and Brite topologies. The simulation results show that the controller computed through the proposed approach outperforms the controller selected with existing approaches. The selection of an optimum controller with ANP results in a reduction of topology discovery time and delay in the normal and traffic load scenario. Similarly, an increase in throughput with a reasonable utilization of the central processing unit (CPU) is observed for the proposed controller. [ABSTRACT FROM AUTHOR]

Diabetic retinopathy is a complication of diabetes that produces changes in the blood vessel structure in the retina, which can cause severe vision problems and even blindness. In this paper, we demonstrate that by identifying topological features in very high resolution retinal images, we can construct a classifier that discriminates between healthy patients and those with diabetic retinopathy using summary statistics of these features. Topological data analysis identifies the features as connected components and holes in the images and describes the extent to which they persist across the image. These features are encoded in persistence diagrams, summaries of which can be used to discrimate between diabetic and healthy patients. The method has the potential to be an effective automated screening tool, with high sensitivity and specificity. [ABSTRACT FROM AUTHOR]

The Changhee polynomials and numbers are introduced in [3], and some interesting identities and properties of these polynomials are found by many researcher. In this paper, we consider the q-analogue of modified degen-erated Changhee polynomials and derive some new and interesting identities and properties of those polynomials. [ABSTRACT FROM AUTHOR]

Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estimation algorithms based on a combination of either the Laplace approximation method or variational approximation method, and automatic optimization techniques implemented in software. An extensive set of simulation studies is used to assess the performances of different methods, from which it is shown that the variational approximation method used in conjunction with automatic optimization offers a powerful tool for estimation. [ABSTRACT FROM AUTHOR]

This study aimed to analyse microstructure data on the density and orientation of collagen fibrils in whole eye globes and to propose an effective method for the preparation of data for use in numerical simulations of the eye’s biomechanical performance. Wide-angle X-ray scattering was applied to seven healthy ex-vivo human eyes. Each eye was dissected into an anterior and a posterior cup, and radial incisions were used to flatten the tissue before microstructure characterisation. A method was developed to use the microstructure data obtained for the dissected tissue to build realistic 3D maps of fibril density and orientation covering the whole eye globe. At the central cornea, 61.5±2.3% of fibrils were aligned within 45° sectors surrounding the two orthogonal directions. In contrast, more than one-third of the total fibril content was concentrated along the circumferential direction at the limbus (37.0±2.4%) and around the optic nerve head (34.8±2.1%). The insertion locations of the four recti muscles exhibited a preference in the meridional direction near the equator (38.6±3.9%). There was also a significant difference in fibril density between the limbus and other regions (ratio = 1.91±0.45, p <0.01 at the central cornea and ratio = 0.80±0.21, p <0.01 at the posterior pole). Characterisation of collagen fibril density and orientation across the whole ocular surface has been possible but required the use of a technique that involved tissue dissection and hence caused tissue damage. The method presented in this paper aimed to minimise the effect of dissection on the quality of obtained data and was successful in identifying fibril distribution trends that were compatible with earlier studies, which concentrated on localised areas of the ocular globe. [ABSTRACT FROM AUTHOR]

The purpose of Fuzzy Comprehensive CS-SVR Model (FCCS-SVR) is to evaluate and monitor the health status of a radar equipment and then keep its safe operation. Due to reasons such as few samples, slow changes and the nonlinear structure of data of fault monitoring signal, the health status evaluation of a radar system is quite difficult. By establishing the evaluation index system of a radar, the combination of AHP method and Entropy weight method is studied in this paper. In order to evaluate the value of health status, several optimization algorithms including PSO, GA, BA and CS are used for optimizing the parameters of SVR model. Meanwhile, in order to avoid the problem that the system is at the edge of the state, a radar health assessment method based on the combination of Fuzzy Comprehensive Evaluation and Cuckoo Search-Support Vector Regression (CS-SVR), which is named as Fuzzy Comprehensive CS-SVR (FCCS-SVR), is further proposed. The result of case analysis reflects that the state evaluation of the radar system is realized. The system performance analysis shows that the use of FCCS-SVR evaluation method provides a high recognition rate and can accurately assess the health status of the radar system. [ABSTRACT FROM AUTHOR]

Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n ≠ 0. An additive mapping δ from R into M is called an (m, n)-Jordan derivation if (m + n)δ(A2) = 2mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every (m, n)-Jordan derivation with m ≠ n from a C* -algebra into its Banach bimodule is zero. An additive mapping δ from R into M is called a (m, n)-Jordan derivable mapping at W in R if (m + n)δ(AB + BA) = 2mδ(A)B + 2mδ(B)A + 2nAδ(B) + 2nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and U=[AMNB] is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero. [ABSTRACT FROM AUTHOR]

Abstract Let I ⊆ k [ x 1 , ... , x n ] be a squarefree monomial ideal in a polynomial ring. In this paper we study multiplications on the minimal free resolution F of k [ x 1 , ... , x n ] / I. In particular, we characterize the possible vectors of total Betti numbers for such ideals which admit a differential graded algebra (DGA) structure on F. We also show that under these assumptions the maximal shifts of the graded Betti numbers are subadditive. On the other hand, we present an example of a strongly generic monomial ideal which does not admit a DGA structure on its minimal free resolution. In particular, this demonstrates that the Hull resolution and the Lyubeznik resolution do not admit DGA structures in general. Finally, we show that it is enough to modify the last map of F to ensure that it admits the structure of a DG algebra. [ABSTRACT FROM AUTHOR]

There is growing interest in the mathematics of Charles L. Dodgson, alias Lewis Carroll (1832-1898). His contributions to geometry, algebra, logic, voting theory and recreational mathematics have been reviewed in recent literature. Dodgson's work in trigonometry is less known. He wrote his initial work on trigonometry, a pamphlet titled The Formulae of Plane Trigonometry, out of concern for his students to ease their studying burden and to improve their performance on examinations. Notable for its precision and completeness, it has all the tell-tale characteristics we associate with the serious mathematical writings he produced throughout his lifetime. He designed his later trigonometric work as the legatee of Augustus De Morgan's correspondence with would-be circle squarers to appeal to and be understood by these mathematical dilettantes. This paper surveys Dodgson's trigonometric work and what it teaches us about Dodgson's mathematical practices. [ABSTRACT FROM AUTHOR]

In this paper, the interactions of some given chaotic properties between a non-autonomous discrete system (X , f 0 , ∞) and its induced set-valued system (K (X) , f ¯ 0 , ∞) are obtained. It is proved that the specification property, property P, topological mixing, mild mixing, and topological exactness of (X , f 0 , ∞) are equivalent to those of (K (X) , f ¯ 0 , ∞) , respectively. It is shown that Robinson chaos (resp. Kato chaos) between (X , f 0 , ∞) and (K (X) , f ¯ 0 , ∞ ) are equivalent under certain conditions. Furthermore, Li-Yorke chaos and distributional chaos of (X , f 0 , ∞) imply those of (K (X) , f ¯ 0 , ∞) , respectively. Topological equi-conjugacy between two systems is proved to be preserved by their induced set-valued systems. Topological entropy of (X , f 0 , ∞) is guaranteed to be no larger than that of (K (X) , f ¯ 0 , ∞). Two examples are finally provided with computer simulations for illustration. [ABSTRACT FROM AUTHOR]

This paper investigates feedback pinning control of synchronization behaviors aroused by epidemic spread on complex networks. Based on the quenched mean field theory, epidemic control synchronization models with the inhibition of contact behavior are constructed, combined with the epidemic transmission system and the adaptive dynamical network carrying active controllers. By the properties of convex functions and the Gerschgorin theorem, the epidemic threshold of the model is obtained, and the global stability of disease-free equilibrium is analyzed. For individual's infected situation, when an epidemic disease spreads, two types of feedback control strategies depending on the diseases' information are designed: the first one only adds controllers to infected individuals, and the other adds controllers to both infected and susceptible ones. By using the Lyapunov stability theory, under designed controllers, some criteria that guarantee the epidemic controlled synchronization system achieving behavior synchronization are also derived. Several numerical simulations are performed to show the effectiveness of our theoretical results. As far as we know, this is the first work to address the controlled behavioral synchronization induced by epidemic spread under the pinning feedback mechanism. It is hopeful that we may have deeper insights into the essence between the disease's spread and collective behavior under active control in complex dynamical networks. [ABSTRACT FROM AUTHOR]