On Box-Perfect Graphs

Let $G=(V,E)$ be a graph and let $A_G$ be the clique-vertex incidence matrix of $G$. It is well known that $G$ is perfect iff the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$ is totally dual integral (TDI). In 1982, Cameron and Edmonds proposed to call $G$ box-perfect if the system $A_{_G}\mathbf x\le \mathbf 1$, $\mathbf x\ge\mathbf0$ is box-totally dual integral (box-TDI), and posed the problem of characterizing such graphs. In this paper we prove the Cameron-Edmonds conjecture on box-perfectness of parity graphs, and identify several other classes of box-perfect graphs. We also develop a general and powerful method for establishing box-perfectness

Ranking tournaments with no errors II: Minimax relation

A tournament T=(V,A) is called cycle Mengerian (CM) if it satisfies the minimax relation on packing and covering cycles, for every nonnegative integral weight function defined on A. The purpose of this series of two papers is to show that a tournament is CM iff it contains none of four Möbius ladders as a subgraph; such a tournament is referred to as Möbius-free. In the first paper we have given a structural description of all Möbius-free tournaments, and have proved that every CM tournament is Möbius-free. In this second paper we establish the converse by using our structural theorems and linear programming approach

Ranking tournaments with no errors I: Structural description

In this series of two papers we examine the classical problem of ranking a set of players on the basis of a set of pairwise comparisons arising from a sports tournament, with the objective of minimizing the total number of upsets, where an upset occurs if a higher ranked player was actually defeated by a lower ranked player. This problem can be rephrased as the so-called minimum feedback arc set problem on tournaments, which arises in a rich variety of applications and has been a subject of extensive research. In this series we study this NP-hard problem using structure-driven and linear programming approaches. Let T=(V,A) be a tournament with a nonnegative integral weight w(e) on each arc e. A subset F of arcs is called a feedback arc set if T\F contains no cycles (directed). A collection C of cycles (with repetition allowed) is called a cycle packing if each arc e is used at most w(e) times by members of C. We call T cycle Mengerian (CM) if, for every nonnegative integral function w defined on A, the minimum total weight of a feedback arc set is equal to the maximum size of a cycle packing. The purpose of these two papers is to show that a tournament is CM iff it contains none of four Möbius ladders as a subgraph; such a tournament is referred to as Möbius-free. In this first paper we present a structural description of all Möbius-free tournaments, which relies heavily on a chain theorem concerning internally 2-strong tournaments

Genome-Wide identification and expression analysis of metal tolerance protein gene family in Medicago truncatula under a broad range of heavy metal stress

Metal tolerance proteins (MTPs) encompass plant membrane divalent cation transporters to specifically participate in heavy metal stress resistance and mineral acquisition. However, the molecular behaviors and biological functions of this family in Medicago truncatula are scarcely known. A total of 12 potential MTP candidate genes in the M. truncatula genome were successfully identified and analyzed for a phylogenetic relationship, chromosomal distributions, gene structures, docking analysis, gene ontology, and previous gene expression. M. truncatula MTPs (MtMTPs) were further classified into three major cation diffusion facilitator (CDFs) groups: Mn-CDFs, Zn-CDFs, and Fe/Zn-CDFs. The structural analysis of MtMTPs displayed high gene similarity within the same group where all of them have cation_efflux domain or ZT_dimer. Cis-acting element analysis suggested that various abiotic stresses and phytohormones could induce the most MtMTP gene transcripts. Among all MTPs, PF16916 is the specific domain, whereas GLY, ILE, LEU, MET, ALA, SER, THR, VAL, ASN, and PHE amino acids were predicted to be the binding residues in the ligand-binding site of all these proteins. RNA-seq and gene ontology analysis revealed the significant role of MTP genes in the growth and development of M. truncatula. MtMTP genes displayed differential responses in plant leaves, stems, and roots under five divalent heavy metals (Cd2+, Co2+, Mn2+, Zn2+, and Fe2+). Ten, seven, and nine MtMTPs responded to at least one metal ion treatment in the leaves, stems, and roots, respectively. Additionally, MtMTP1.1, MtMTP1.2, and MtMTP4 exhibited the highest expression responses in most heavy metal treatments. Our results presented a standpoint on the evolution of MTPs in M. truncatula. Overall, our study provides a novel insight into the evolution of the MTP gene family in M. truncatula and paves the way for additional functional characterization of this gene family

Role of CD34 in inflammatory bowel disease

Inflammatory bowel disease (IBD) is caused by a variety of pathogenic factors, including chronic recurrent inflammation of the ileum, rectum, and colon. Immune cells and adhesion molecules play an important role in the course of the disease, which is actually an autoimmune disease. During IBD, CD34 is involved in mediating the migration of a variety of immune cells (neutrophils, eosinophils, and mast cells) to the inflammatory site, and its interaction with various adhesion molecules is involved in the occurrence and development of IBD. Although the function of CD34 as a partial cell marker is well known, little is known on its role in IBD. Therefore, this article describes the structure and biological function of CD34, as well as on its potential mechanism in the development of IBD

The Enhancing Effects of the Light Chain on Heavy Chain Secretion in Split Delivery of Factor VIII Gene

Coagulation factor VIII (FVIII) is secreted as a heterodimer consisting of a heavy chain (HC) and a light chain (LC), which can be expressed independently and reassociate with recovery of biological activity. Because of the size limitation of adeno-associated virus (AAV) vectors, a strategy for delivering the HC and LC separately has been developed. However, the FVIII HC is secreted 10–100-fold less efficiently than the LC. In this study, we demonstrated that the F309S mutation and enhanced B-domain glycosylations alone are not sufficient to improve FVIII HC secretion, which suggested a role of the FVIII LC in regulating HC secretion. To characterize this role of the FVIII LC, we compared FVIII HC secretion with and without the LC via post-translational protein trans-splicing. As demonstrated in vitro, ligation of the LC to the HC significantly increased HC secretion. Such HC secretion increases were also confirmed in vivo by hydrodynamic injection of FVIII intein plasmids into hemophilia A mice. Moreover, similar enhancement of HC secretion can also be observed when the LC is supplied in trans, which is probably due to the spontaneous association of the HC and the LC in the secretion pathway. In sum, enhancing the secretion of the FVIII HC polypeptide may require the proper association of the FVIII LC polypeptide in cis or in trans. These results may be helpful in designing new strategies to improve FVIII gene delivery

Ranking tournaments with no errors

As various combinatorial optimization problems can be formulated as integer linear programs, polyhedral and linear programming approaches have turned out to be essential and powerful tools for studying these problems. By applying linear programming theory and polyhedral characterization, often, one can determine the polynomial-time solvability of the optimization problems and obtain elegant combinatorial consequences, e.g., min-max theorems. This thesis is devoted to studying the classical combinatorial optimization problem of ranking a set of players on the basis of a set of pairwise comparisons arising from a sports tournament; the objective is to minimize the total number of upsets, where an {\em upset} occurs if a higher ranked player was actually defeated by a lower ranked player. This problem can be rephrased as the so-called minimum feedback arc set problem on tournaments. Let $T = (V,A)$ be a tournament with a nonnegative integral weight $w(e)$ on each arc $e$. A subset $F$ of arcs is called a {\em feedback arc set} (FAS) if $T\backslash F$ contains no cycles (directed). The {\em minimum-weight FAS problem on tournaments}, denoted by FAST, is to find an FAS in the input tournament $T$ with minimum total weight. In 2006, Alon showed that the unweighted version of the FAST ($\bm{w}$ is the all-one vector) is in fact {\em NP}-hard. In 2007, Mathieu and Schudy devised a polynomial time approximation scheme (PTAS) for the FAST. Given these results, it is natural to ask the following question: When can the FAST be solved exactly in polynomial time? Inspired by the title of Mathieu and Schudy's paper, this is equivalent to asking: Which tournaments can be ranked with no errors? The main concern of this thesis is to resolve this \emph{NP}-hard problem using polyhedral and linear programming approaches. A collection ${\cal C}$ of cycles (with repetition allowed) is called a {\em cycle packing} if each arc $e$ is used at most $w(e)$ times by members of ${\cal C}$. We call a tournament $T=(V,A)$ {\em cycle Mengerian} (CM) if, for any nonnegative integral function $\bm{w}$ defined on $A$, the minimum total weight of a feedback arc set is equal to the maximum size of a cycle packing. The main purpose of this thesis is to present a structural characterization of all CM tournaments, which yields a polynomial-time algorithm for the FAST on such tournaments.published_or_final_versionMathematicsDoctoralDoctor of Philosoph