Effects of Complex Parameters on t→ch^0 in Supersymmetric QCD

We investigate the leading SUSY-QCD contributions to the branch ratio (BR) oft→ch~0 within the context of the minimal supersymmetric standard model (MSSM) with complex parameters,assuming more generally that there is a misalignment between the squark and quark that leads to a flavor non-diagonal squark mass matrix.We introduce complex phases only in μ and At,namely φ_μ and φ_(Aq),for simplicity,and study the dependence of the BR of t→ch~0 on these phase parameters.Our calculations show that these CP-violation phases and the flavor mixing parameter λ influence the BR oft→ch~0 considerably,and the effect induced by φ_(At) is much larger than that by φ_μ and φ_(Ac(?)u.For different values of the complex parameters μ and A_t that are set in this paper,the BR of t -+ ch~ is in the range of 10~(-7)～10~(-6),depending mainly on the value of the trilinear coupling A_t.

Group control for procedural rules:parameterized complexity and consecutive domains

We consider GROUP CONTROL BY ADDING INDIVIDUALS(GCAI)in the setting of group identification for two procedural rules-the consensus-start-respecting rule and the liberal-start-respecting rule.It is known that GCAI for both rules are NP-hard,but whether they are fixed-parameter tractable with respect to the number of distinguished individuals remained open.We resolve both open problems in the affirmative.In addition,we strengthen the NP-hardness of GCAI by showing that,with respect to the natural parameter the number of added individuals,GCAI for both rules are W[2]-hard.Notably,the W[2]-hardness for the liberal-startrespecting rule holds even when restricted to a very special case where the qualifications of individuals satisfy the so-called consecutive ones property.However,for the consensus-startrespecting rule,the problem becomes polynomial-time solvable in this special case.We also study a dual restriction where the disqualifications of individuals fulfill the consecutive ones property,and show that under this restriction GCAI for both rules turn out to be polynomial-time solvable.Our reductions for showing W[2]-hardness also imply several algorithmic lowerbounds.

Counting Problems in Parameterized Complexity

Parameterized complexity is a multivariate theory for the analysis of computational problems. It leads to practically efficient algorithms for many NP-hard problems and also provides a much finer complexity classification for other intractable problems. Although the theory is mostly on decision problems, parameterized complexity naturally extends to counting problems as well. The purpose of this article is to survey a few aspects of parameterized counting complexity, with a particular emphasis on some general frameworks in which parameterized complexity proves to be indispensable.

Some Open Problems in Parameterized Complexity Related to the Work of Jianer Chen

This short paper highlights some open problems related to the work of Jianer Chen in the area of parameterized/multivariate algorithmics.

On the parameterized complexity of minimum/maximum degree vertex deletion on several special graphs

In the minimum degree vertex deletion problem,we are given a graph,a distinguished vertex in the graph,and an integer κ,and the question is whether we can delete at most κ vertices from the graph so that the distinguished vertex has the unique minimum degree.The maximum degree vertex deletion problem is defined analogously but here we want the distinguished vertex to have the unique maximum degree.It is known that both problems areΨ-hard and fixed-parameter intractable with respect to some natural parameters.In this paper,we study the(parameterized)complexity of these two problems restricted to split graphs,p-degenerate graphs,and planar graphs.Our study provides a comprehensive complexity landscape of the two problems restricted to these special graphs.

Guest Editorial: Special Issue on Parameterized Complexity

Dedication.This Special Issue on Parameterized Complexity of Tsinghua Science and Technology is a tribute to the influential contributions of Jianer Chen to parameterized complexity algorithmics.It is an occasion to celebrate the many important contributions to this new and prospering branch of theoretical computer science made by Jianer Chen,as he reaches the ripe young age of 60.

Z-scan analysis of high-order nonlinear refraction effect induced by using elliptic Gaussian beam

The irradiance of an elliptic Gaussian beam that is high enough to excite high-order nonlinear refraction effect is used to calculate the normalized on-axis transmittance function in the z-scan technique by introducing complex beam parameters which make the calculation simpler. The transmittance formula is applied to the first-, first two-, and first three-order nonlinearities. Numerical evaluation shows that the symmetry no longer holds when using an elliptic Gaussian beam instead of a circular Gaussian beam. A distortion is observed in the central part of the curve, which decreases as ellipticity increases. Moreover, the variation of the normalized peak-valley difference decreases as ellipticity decreases.

Detection of macular ganglion cell complex loss and correlation with choroidal thickness in chronic and recurrent central serous chorioretinopathy

AIM:To investigate the association of ganglion cell complex thickness(GCCt),global loss volume percentage(GLV%),and focal loss volume percentage(FLV%)with structural and functional findings among patients with chronic central serous chorioretinopathy(CCSC)and recurrent central serous chorioretinopathy(RCSC)by optical coherence tomography(OCT).METHODS:Among 29 patients with monocular affected central serous chorioretinopathy(CSC),15 had CCSC,and 14 had RCSC.The GCCt,FLV%,GLV%,and subfoveal choroidal thickness(SFCT)and sublesional choroidal thickness(SLCT)values were determined using OCT,and the association of these characteristics with neural structure parameters,choroidal morphology,features and functional alterations were estimated for the CCSC and RCSC patients.RESULTS:In CCSC,the affected eyes had significantly lower GCCt values than the fellow eyes in the macular regions(all P<0.05),with the highest GCCt observed in the inferior area.A significant association was found between the GCCt in different regions and the change in best corrected visual acuity(BCVA;r=-0.696;-0.695;-0.694,P<0.05)in CCSC patients.A statistically significant moderate negative correlation indicated that long-term CCSC was associated with greater differences in the GCCt in different regions between affected and fellow eyes(r=-0.562;r=-0.556;r=0.525,P<0.05).Additionally,observation of thickened SFCT was associated with a worse FLV%(r=0.599;r=0.546,P<0.05)in both groups.Similarly,thickened SLCT was associated with FLV%in RCSC patients(r=0.544,P<0.05).CONCLUSION:The distribution and GCCt are associated with the duration and visual outcomes of CCSC,whereas there is no correlation among RCSC patients.FLV%may be instrumental in differentiating the various outer choroidal vessels(pachyvessels)in long-term CSC.These results suggest that neural structure parameters may aid in estimating and predicting the recovery of altered morphology and function in CCSC and RCSC patients.

Call for Papers Special Issue on Parameterized Complexity

Manuscripts are invited for a Special Issue on Parameterized Complexity published by the Tsinghua Science and Technology. The field of parameterized complexity is a vibrant research area and has witnessed a tremendous growth in the last two decades. It has become a central area in theoretical computer science, with applications to bioinformatics, artificial intelligence, and many other areas. The Special Issue invites regular and survey papers pertaining to parameterized complexity, for example, Design and analysis of parameterized and kernelization algorithms, Complexity and lower bounds, Connections between parameterized complexity and approximation. Other topics in parameterized complexity are also welcome. The Special Issue will have a dedication to Professor Janier Chert, Texas A＆M University and Central South University of China, on the occasion of his 60th birthday, in recognition of his valuable contributions to the field of parameterized complexity.

Software Analytics of Open Source Business Software

This paper applies software analytics to open source code. Open-source software gives both individuals and businesses the flexibility to work with different parts of available code to modify it or incorporate it into their own project. The open source software market is growing. Major companies such as AWS, Facebook, Google, IBM, Microsoft, Netflix, SAP, Cisco, Intel, and Tesla have joined the open source software community. In this study, a sample of 40 open source applications was selected. Traditional McCabe software metrics including cyclomatic and essential complexities were examined. An analytical comparison of this set of metrics and derived metrics for high risk software was utilized as a basis for addressing risk management in the adoption and integration decisions of open source software. From this comparison, refinements were added, and contemporary concepts of design and data metrics derived from cyclomatic complexity were integrated into a classification scheme for software quality. It was found that 84% of the sample open source applications were classified as moderate low risk or low risk indicating that open source software exhibits low risk characteristics. The 40 open source applications were the base data for the model resulting in a technique which is applicable to any open source code regardless of functionality, language, or size.

Software Metric Analysis of Open-Source Business Software

Over the past decade, open-source software use has grown. Today, many companies including Google, Microsoft, Meta, RedHat, MongoDB, and Apache are major participants of open-source contributions. With the increased use of open-source software or integration of open-source software into custom-developed software, the quality of this software component increases in importance. This study examined a sample of open-source applications from GitHub. Static software analytics were conducted, and each application was classified for its risk level. In the analyzed applications, it was found that 90% of the applications were classified as low risk or moderate low risk indicating a high level of quality for open-source applications.

HSS METHOD WITH A COMPLEX PARAMETER FOR THE SOLUTION OF COMPLEX LINEAR SYSTEM

In this paper, a complex parameter is employed in the Hermitian and skew-Hermitian splitting （HSS） method （Bai, Golub and Ng： SIAM J. Matrix Anal. Appl., 24（2003）, 603-626） for solving the complex linear system Ax = f. The convergence of the resulting method is proved when the spectrum of the matrix A lie in the right upper （or lower） part of the complex plane. We also derive an upper bound of the spectral radius of the HSS iteration matrix, and a estimated optimal parameter a （denoted by a^st） of this upper bound is presented. Numerical experiments on two modified model problems show that the HSS method with a est has a smaller spectral radius than that with the real parameter which minimizes the corresponding upper hound. In particular, for the ＇dominant＇ imaginary part of the matrix A, this improvement is considerable. We also test the GMRES method preconditioned by the HSS preconditioning matrix with our parameter a est.

Parameter Ecology for Feedback Vertex Set

This paper deals with the FEEDBACK VERTEX SET problem on undirected graphs, which asks for the existence of a vertex set of bounded size that intersects all cycles. Due it is theoretical and practical importance,the problem has been the subject of intensive study. Motivated by the parameter ecology program we attempt to classify the parameterized and kernelization complexity of FEEDBACK VERTEX SET for a wide range of parameters.We survey known results and present several new complexity classifications. For example, we prove that FEEDBACK VERTEX SET is fixed-parameter tractable parameterized by the vertex-deletion distance to a chordal graph. We also prove that the problem admits a polynomial kernel when parameterized by the vertex-deletion distance to a pseudo forest, a graph in which every connected component has at most one cycle. In contrast, we prove that a slightly smaller parameterization does not allow for a polynomial kernel unless NP coNP=poly and the polynomial-time hierarchy collapses.

Parameterized Algorithmics for Computational Social Choice:Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science,and Social Science on the one side, and Mathematics and Computer Science（including Artificial Intelligence and Multiagent Systems） on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context. This work is dedicated to Jianer Chen, one of the strongest problem solvers in the history of parameterized algorithmics,on the occasion of his 60 th birthday.

Approximation Algorithm Based on Chain Implication for Constrained Minimum Vertex Covers in Bipartite Graphs

The constrained minimum vertex cover problem on bipartite graphs （the Min-CVCB problem） is an important NP-complete problem. This paper presents a polynomial time approximation algorithm for the problem based on the technique of chain implication. For any given constant ε〉 0, if an instance of the Min-CVCB problem has a minimum vertex cover of size （ku, kl）, our algorithm constructs a vertex cover of size （ku^＊, kl^＊）, satisfying max{ku^＊/ku, kl^＊/kl} ≤ 1 ＋ ε.

2k-Vertex Kernels for Cluster Deletion and Strong Triadic Closure

Cluster deletion and strong triadic closure are two important NP-complete problems that have received sig-nificant attention due to their applications in various areas,including social networks and data analysis.Although cluster deletion and strong triadic closure are closely linked by induced paths on three vertices,there are subtle differences be-tween them.In some cases,the solutions of strong triadic closure and cluster deletion are quite different.In this paper,we study the parameterized algorithms for these two problems.More specifically,we focus on the kernels of these two prob-lems.Instead of separating the critical clique and its neighbors for analysis,we consider them as a whole,which allows us to more effectively bound the number of related vertices.In addition,in analyzing the kernel of strong triadic closure,we introduce the concept of edge-disjoint induced path on three vertices,which enables us to obtain the lower bound of weak edge number in a more concise way.Our analysis demonstrates that cluster deletion and strong triadic closure both admit 2k-vertex kernels.These results represent improvements over previously best-known kernels for both problems.Further-more,our analysis provides additional insights into the relationship between cluster deletion and strong triadic closure.

Social Choice Meets Graph Drawing: How to Get Subexponential Time Algorithms for Ranking and Drawing Problems

We analyze a common feature of p-Kemeny AGGregation（p-KAGG） and p-One-Sided Crossing Minimization（p-OSCM） to provide new insights and findings of interest to both the graph drawing community and the social choice community. We obtain parameterized subexponential-time algorithms for p-KAGG—a problem in social choice theory—and for p-OSCM—a problem in graph drawing. These algorithms run in time O＊（2O（√k log k））,where k is the parameter, and significantly improve the previous best algorithms with running times O.1.403k/and O.1.4656k/, respectively. We also study natural ＂above-guarantee＂ versions of these problems and show them to be fixed parameter tractable. In fact, we show that the above-guarantee versions of these problems are equivalent to a weighted variant of p-directed feedback arc set. Our results for the above-guarantee version of p-KAGG reveal an interesting contrast. We show that when the number of ＂votes＂ in the input to p-KAGG is odd the above guarantee version can still be solved in time O＊（2O（√k log k））, while if it is even then the problem cannot have a subexponential time algorithm unless the exponential time hypothesis fails（equivalently, unless FPT D M[1]）.