A Combinatorial Formula for Principal Minors of a Matrix with Tree-metric Exponents and Its Applications

Let $T$ be a tree with a vertex set $\{ 1,2,\dots, N \}$. Denote by $d_{ij}$ the distance between vertices $i$ and $j$. In this paper, we present an explicit combinatorial formula of principal minors of the matrix $(t^{d_{ij}})$, and its applications to tropical geometry, study of multivariate stable polynomials, and representation of valuated matroids. We also give an analogous formula for a skew-symmetric matrix associated with $T$.Comment: 16 page

A Three-Term Conjugate Gradient Method with Sufficient Descent Property for Unconstrained Optimization

Conjugate gradient methods are widely used for solving large-scale unconstrained optimization problems, because they do not need the storage of matrices. In this paper, we propose a general form of three-term conjugate gradient methods which always generate a sufficient descent direction. We give a sufficient condition for the global convergence of the proposed general method. Moreover, we present a specific three-term conjugate gradient method based on the multi-step quasi-Newton method. Finally, some numerical results of the proposed method are given

静圧気体軸受の理論的研究

京都大学0048新制・課程博士工学博士甲第484号工博第83号新制||工||50(附属図書館)UT51-42-F972京都大学大学院工学研究科機械工学専攻(主査)教授 森 美郎, 教授 佐々木 外喜雄, 教授 佐藤 俊学位規則第5条第1項該当Kyoto UniversityDFA

Inexact proximal DC Newton-type method for nonconvex composite functions

We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possible nonsmooth DC function. The application of proximal DC algorithms to address this problem class is well-known. In this paper, we combine a proximal DC algorithm with an inexact proximal Newton-type method to propose an inexact proximal DC Newton-type method. We demonstrate global convergence properties of the proposed method. In addition, we give a memoryless quasi-Newton matrix for scaled proximal mappings and consider a two-dimensional system of semi-smooth equations that arise in calculating scaled proximal mappings. To efficiently obtain the scaled proximal mappings, we adopt a semi-smooth Newton method to inexactly solve the system. Finally, we present some numerical experiments to investigate the efficiency of the proposed method, showing that the proposed method outperforms existing methods

Copy number loss of (src homology 2 domain containing)-transforming protein 2 (SHC2) gene: discordant loss in monozygotic twins and frequent loss in patients with multiple system atrophy

<p>Abstract</p> <p>Background</p> <p>Multiple system atrophy (MSA) is a sporadic disease. Its pathogenesis may involve multiple genetic and nongenetic factors, but its etiology remains largely unknown. We hypothesized that the genome of a patient with MSA would demonstrate copy number variations (CNVs) in the genes or genomic regions of interest. To identify genomic alterations increasing the risk for MSA, we examined a pair of monozygotic (MZ) twins discordant for the MSA phenotype and 32 patients with MSA.</p> <p>Results</p> <p>By whole-genome CNV analysis using a combination of CNV beadchip and comparative genomic hybridization (CGH)-based CNV microarrays followed by region-targeting, high-density, custom-made oligonucleotide tiling microarray analysis, we identified disease-specific copy number loss of the (Src homology 2 domain containing)-transforming protein 2 (<it>SHC2</it>) gene in the distal 350-kb subtelomeric region of 19p13.3 in the affected MZ twin and 10 of the 31 patients with MSA but not in 2 independent control populations (<it>p </it>= 1.04 × 10^-8, odds ratio = 89.8, Pearson's chi-square test).</p> <p>Conclusions</p> <p>Copy number loss of <it>SHC2 </it>strongly indicates a causal link to MSA. CNV analysis of phenotypically discordant MZ twins is a powerful tool for identifying disease-predisposing loci. Our results would enable the identification of novel diagnostic measure, therapeutic targets and better understanding of the etiology of MSA.</p