Antimedian graphs

Antimedian graphs are introduced as the graphs in which for every triple of vertices there exists a unique vertex x that maximizes the sum of the distances from x to the vertices of the triple. The Cartesian product of graphs is antimedian if and only if its factors are antimedian. It is proved that multiplying a non-antimedian vertex in an antimedian graph yields a larger antimedian graph. Thin even belts are introduced and proved to be antimedian. A characterization of antimedian trees is given that leads to a linear recognition algorithm.

Almost Self-Centered Median And Chordal Graphs

Almost self-centered graphs were recently introduced as the graphs with exactly two non-central vertices. In this paper we characterize almost selfcentered graphs among median graphs and among chordal graphs. In the first case P4 and the graphs obtained from hypercubes by attaching to them a single leaf are the only such graphs. Among chordal graph the variety of almost self-centered graph is much richer, despite the fact that their diameter is at most 3. We also discuss almost self-centered graphs among partial cubes and among k-chordal graphs, classes of graphs that generalize median and chordal graphs, respectively. Characterizations of almost self-centered graphs among these two classes seem elusive

On strongly regular graphs with m2 = qm3 and m3 = qm2

2010 Mathematics Subject Classification: 05C50.

Approximation Algorithms for Network Design and Orienteering

This thesis presents approximation algorithms for some NP-Hard combinatorial optimization problems on graphs and networks; in particular, we study problems related to Network Design. Under the widely-believed complexity-theoretic assumption that P is not equal to NP, there are no efficient (i.e., polynomial-time) algorithms that solve these problems exactly. Hence, if one desires efficient algorithms for such problems, it is necessary to consider approximate solutions: An approximation algorithm for an NP-Hard problem is a polynomial time algorithm which, for any instance of the problem, finds a solution whose value is guaranteed to be within a multiplicative factor of the value of an optimal solution to that instance. We attempt to design algorithms for which this factor, referred to as the approximation ratio of the algorithm, is as small as possible. The field of Network Design comprises a large class of problems that deal with constructing networks of low cost and/or high capacity, routing data through existing networks, and many related issues. In this thesis, we focus chiefly on designing fault-tolerant networks. Two vertices u,v in a network are said to be k-edge-connected if deleting any set of k − 1 edges leaves u and v connected; similarly, they are k-vertex connected if deleting any set of k − 1 other vertices or edges leaves u and v connected. We focus on building networks that are highly connected, meaning that even if a small number of edges and nodes fail, the remaining nodes will still be able to communicate. A brief description of some of our results is given below. We study the problem of building 2-vertex-connected networks that are large and have low cost. Given an n-node graph with costs on its edges and any integer k, we give an O(log n log k) approximation for the problem of finding a minimum-cost 2-vertex-connected subgraph containing at least k nodes. We also give an algorithm of similar approximation ratio for maximizing the number of nodes in a 2-vertex-connected subgraph subject to a budget constraint on the total cost of its edges. Our algorithms are based on a pruning process that, given a 2-vertex-connected graph, finds a 2-vertex-connected subgraph of any desired size and of density comparable to the input graph, where the density of a graph is the ratio of its cost to the number of vertices it contains. This pruning algorithm is simple and efficient, and is likely to find additional applications. Recent breakthroughs on vertex-connectivity have made use of algorithms for element-connectivity problems. We develop an algorithm that, given a graph with some vertices marked as terminals, significantly simplifies the graph while preserving the pairwise element-connectivity of all terminals; in fact, the resulting graph is bipartite. We believe that our simplification/reduction algorithm will be a useful tool in many settings. We illustrate its applicability by giving algorithms to find many trees that each span a given terminal set, while being disjoint on edges and non-terminal vertices; such problems have applications in VLSI design and other areas. We also use this reduction algorithm to analyze simple algorithms for single-sink network design problems with high vertex-connectivity requirements; we give an O(k log n)-approximation for the problem of k-connecting a given set of terminals to a common sink. We study similar problems in which different types of links, of varying capacities and costs, can be used to connect nodes; assuming there are economies of scale, we give algorithms to construct low-cost networks with sufficient capacity or bandwidth to simultaneously support flow from each terminal to the common sink along many vertex-disjoint paths. We further investigate capacitated network design, where edges may have arbitrary costs and capacities. Given a connectivity requirement R_uv for each pair of vertices u,v, the goal is to find a low-cost network which, for each uv, can support a flow of R_uv units of traffic between u and v. We study several special cases of this problem, giving both algorithmic and hardness results. In addition to Network Design, we consider certain Traveling Salesperson-like problems, where the goal is to find short walks that visit many distinct vertices. We give a (2 + epsilon)-approximation for Orienteering in undirected graphs, achieving the best known approximation ratio, and the first approximation algorithm for Orienteering in directed graphs. We also give improved algorithms for Orienteering with time windows, in which vertices must be visited between specified release times and deadlines, and other related problems. These problems are motivated by applications in the fields of vehicle routing, delivery and transportation of goods, and robot path planning.

Computing median and antimedian sets in median graphs

The median (antimedian) set of a profile π = (u1, . . . , uk) of vertices of a graphG is the set of vertices x that minimize (maximize) the remoteness i d(x,ui ). Two algorithms for median graphs G of complexity O(nidim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles and will be in practice often faster than the other algorithm which in addition computes antimedian sets and remoteness functions and works in all partial cubes

Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes

An antimedian of a pro le = (x1; x2; : : : ; xk) of vertices of a graph G is a vertex maximizing the sum of the distances to the elements of the pro le. The antimedian function is de ned on the set of all pro les on G and has as output the set of antimedians of a pro le. It is a typical location function for nding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes.

Simultaneous Embeddings Of Graphs As Median And Antimedian Subgraphs

The distance DG(v) of a vertex v in an undirected graph G is the sum of the distances between v and all other vertices of G. The set of vertices in G with maximum (minimum) distance is the antimedian (median) set of a graph G. It is proved that for arbitrary graphs G and J and a positive integer r 2, there exists a connected graph H such that G is the antimedian and J the median subgraphs of H, respectively, and that dH(G, J) = r. When both G and J are connected, G and J can in addition be made convex subgraphs of H.

On the generalized obnoxious center problem: antimedian subsets

The set of vertices that maximize (minimize) the remoteness is the antimedian (median) set of the profile. It is proved that for an arbitrary graph G and S V (G) it can be decided in polynomial time whether S is the antimedian set of some profile. Graphs in which every antimedian set is connected are also considered.

Vector and axial-vector correlators in a non-local chiral quark model

The behavior of the non-perturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with non-local quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH and OPAL data on hadronic tau decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic pi(+/-) - pi(0) mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be chi'(0) approximate to (50 MeV)(2). In addition, the fulfillment of the Crewther theorem is demonstrated.

Transposable elements: structure and dynamic of the autonomous retrotransposon R2 in Arthropoda with non-canonical reproduction

Eukaryotic ribosomal DNA constitutes a multi gene family organized in a cluster called nucleolar organizer region (NOR); this region is composed usually by hundreds to thousands of tandemly repeated units. Ribosomal genes, being repeated sequences, evolve following the typical pattern of concerted evolution. The autonomous retroelement R2 inserts in the ribosomal gene 28S, leading to defective 28S rDNA genes. R2 element, being a retrotransposon, performs its activity in the genome multiplying its copy number through a “copy and paste” mechanism called target primed reverse transcription. It consists in the retrotranscription of the element’s mRNA into DNA, then the DNA is integrated in the target site. Since the retrotranscription can be interrupted, but the integration will be carried out anyway, truncated copies of the element will also be present in the genome. The study of these truncated variants is a tool to examine the activity of the element. R2 phylogeny appears, in general, not consistent with that of its hosts, except some cases (e.g. Drosophila spp. and Reticulitermes spp.); moreover R2 is absent in some species (Fugu rubripes, human, mouse, etc.), while other species have more R2 lineages in their genome (the turtle Mauremys reevesii, the Japanese beetle Popilia japonica, etc). R2 elements here presented are isolated in 4 species of notostracan branchiopods and in two species of stick insects, whose reproductive strategies range from strict gonochorism to unisexuality. From sequencing data emerges that in Triops cancriformis (Spanish gonochoric population), in Lepidurus arcticus (two putatively unisexual populations from Iceland) and in Bacillus rossius (gonochoric population from Capalbio) the R2 elements are complete and encode functional proteins, reflecting the general features of this family of transposable elements. On the other hand, R2 from Italian and Austrian populations of T. cancriformis (respectively unisexual and hermaphroditic), Lepidurus lubbocki (two elements within the same Italian population, gonochoric but with unfunctional males) and Bacillus grandii grandii (gonochoric population from Ponte Manghisi) have sequences that encode incomplete or non-functional proteins in which it is possible to recognize only part of the characteristic domains. In Lepidurus couesii (Italian gonochoric populations) different elements were found as in L. lubbocki, and the sequencing is still in progress. Two hypothesis are given to explain the inconsistency of R2/host phylogeny: vertical inheritance of the element followed by extinction/diversification or horizontal transmission. My data support previous study that state the vertical transmission as the most likely explanation; nevertheless horizontal transfer events can’t be excluded. I also studied the element’s activity in Spanish populations of T. cancriformis, in L. lubbocki, in L. arcticus and in gonochoric and parthenogenetic populations of B. rossius. In gonochoric populations of T. cancriformis and B. rossius I found that each individual has its own private set of truncated variants. The situation is the opposite for the remaining hermaphroditic/parthenogenetic species and populations, all individuals sharing – in the so far analyzed samples - the majority of variants. This situation is very interesting, because it isn’t concordant with the Muller’s ratchet theory that hypothesizes the parthenogenetic populations being either devoided of transposable elements or TEs overloaded. My data suggest a possible epigenetic mechanism that can block the retrotransposon activity, and in this way deleterious mutations don’t accumulate.

Non-self-adjoint graphs

On finite metric graphs we consider Laplace operators, subject to various classes of non-self-adjoint boundary conditions imposed at graph vertices. We investigate spectral properties, existence of a Riesz basis of projectors and similarity transforms to self-adjoint Laplacians. Among other things, we describe a simple way to relate the similarity transforms between Laplacians on certain graphs with elementary similarity transforms between matrices defining the boundary conditions.

Egfr Activating Mutations And Their Association With Response To Platinum-doublet Chemotherapy In Brazilian Non-small Cell Lung Cancer Patients.

The aim of the study was to analyze the frequency of epidermal growth factor receptor (EGFR) mutations in Brazilian non-small cell lung cancer patients and to correlate these mutations with response to benefit of platinum-based chemotherapy in non-small cell lung cancer (NSCLC). Our cohort consisted of prospective patients with NSCLCs who received chemotherapy (platinum derivates plus paclitaxel) at the [UNICAMP], Brazil. EGFR exons 18-21 were analyzed in tumor-derived DNA. Fifty patients were included in the study (25 with adenocarcinoma). EGFR mutations were identified in 6/50 (12 %) NSCLCs and in 6/25 (24 %) adenocarcinomas; representing the frequency of EGFR mutations in a mostly self-reported White (82.0 %) southeastern Brazilian population of NSCLCs. Patients with NSCLCs harboring EGFR exon 19 deletions or the exon 21 L858R mutation were found to have a higher chance of response to platinum-paclitaxel (OR 9.67 [95 % CI 1.03-90.41], p = 0.047). We report the frequency of EGFR activating mutations in a typical southeastern Brazilian population with NSCLC, which are similar to that of other countries with Western European ethnicity. EGFR mutations seem to be predictive of a response to platinum-paclitaxel, and additional studies are needed to confirm or refute this relationship.

Fatty Acid Synthase Inhibitors Induce Apoptosis In Non-tumorigenic Melan-a Cells Associated With Inhibition Of Mitochondrial Respiration.

The metabolic enzyme fatty acid synthase (FASN) is responsible for the endogenous synthesis of palmitate, a saturated long-chain fatty acid. In contrast to most normal tissues, a variety of human cancers overexpress FASN. One such cancer is cutaneous melanoma, in which the level of FASN expression is associated with tumor invasion and poor prognosis. We previously reported that two FASN inhibitors, cerulenin and orlistat, induce apoptosis in B16-F10 mouse melanoma cells via the intrinsic apoptosis pathway. Here, we investigated the effects of these inhibitors on non-tumorigenic melan-a cells. Cerulenin and orlistat treatments were found to induce apoptosis and decrease cell proliferation, in addition to inducing the release of mitochondrial cytochrome c and activating caspases-9 and -3. Transfection with FASN siRNA did not result in apoptosis. Mass spectrometry analysis demonstrated that treatment with the FASN inhibitors did not alter either the mitochondrial free fatty acid content or composition. This result suggests that cerulenin- and orlistat-induced apoptosis events are independent of FASN inhibition. Analysis of the energy-linked functions of melan-a mitochondria demonstrated the inhibition of respiration, followed by a significant decrease in mitochondrial membrane potential (ΔΨm) and the stimulation of superoxide anion generation. The inhibition of NADH-linked substrate oxidation was approximately 40% and 61% for cerulenin and orlistat treatments, respectively, and the inhibition of succinate oxidation was approximately 46% and 52%, respectively. In contrast, no significant inhibition occurred when respiration was supported by the complex IV substrate N,N,N',N'-tetramethyl-p-phenylenediamine (TMPD). The protection conferred by the free radical scavenger N-acetyl-cysteine indicates that the FASN inhibitors induced apoptosis through an oxidative stress-associated mechanism. In combination, the present results demonstrate that cerulenin and orlistat induce apoptosis in non-tumorigenic cells via mitochondrial dysfunction, independent of FASN inhibition.

Imported Malaria In A Non-endemic Area: The Experience Of The University Of Campinas Hospital In The Brazilian Southeast.

Although malaria in Brazil almost exclusively occurs within the boundaries of the Amazon Region, some concerns are raised regarding imported malaria to non-endemic areas of the country, notably increased incidence of complications due to delayed diagnoses. However, although imported malaria in Brazil represents a major health problem, only a few studies have addressed this subject. A retrospective case series is presented in which 263 medical charts were analysed to investigate the clinical and epidemiological characterization of malaria cases that were diagnosed and treated at Hospital & Clinics, State University of Campinas between 1998 and 2011. Amongst all medical charts analysed, 224 patients had a parasitological confirmed diagnosis of malaria. Plasmodium vivax and Plasmodium falciparum were responsible for 67% and 30% of the infections, respectively. The majority of patients were male (83%) of a productive age (median, 37 years old). Importantly, severe complications did not differ significantly between P. vivax (14 cases, 9%) and P. falciparum (7 cases, 10%) infections. Severe malaria cases were frequent among imported cases in Brazil outside of the Amazon area. The findings reinforce the idea that P. vivax infections in Brazil are not benign, regardless the endemicity of the area studied. Moreover, as the hospital is located in a privileged site, it could be used for future studies of malaria relapses and primaquine resistance mechanisms. Finally, based on the volume of cases treated and the secondary complications, referral malaria services are needed in the non-endemic areas of Brazil for a rapid and efficient and treatment.

Evaluation Of Fe Uptake And Translocation In Transgenic And Non-transgenic Soybean Plants Using Enriched Stable (57)fe As A Tracer.

A tracer experiment is carried out with transgenic T (variety M 7211 RR) and non-transgenic NT (variety MSOY 8200) soybean plants to evaluate if genetic modification can influence the uptake and translocation of Fe. A chelate of EDTA with enriched stable (57)Fe is applied to the plants cultivated in vermiculite plus substrate and the (57)Fe acts as a tracer. The exposure of plants to enriched (57)Fe causes the dilution of the natural previously existing Fe in the plant compartments and then the changed Fe isotopic ratio ((57)Fe/(56)Fe) is measured using a quadrupole-based inductively coupled plasma mass spectrometer equipped with a dynamic reaction cell (DRC). Mathematical calculations based on the isotope dilution methodology allow distinguishing the natural abundance Fe from the enriched Fe (incorporated during the experiment). The NT soybean plants acquire higher amounts of Fe from natural abundance (originally present in the soil) and from enriched Fe (coming from the (57)Fe-EDTA during the experiment) than T soybean ones, demonstrating that the NT soybean plants probably absorb higher amounts of Fe, independently of the source. The percentage of newly incorporated Fe (coming from the treatment) was approximately 2.0 and 1.1% for NT and T soybean plants, respectively. A higher fraction (90.1%) of enriched Fe is translocated to upper parts, and a slightly lower fraction (3.8%) is accumulated in the stems by NT plants than by T ones (85.1%; 5.1%). Moreover, in both plants, the Fe-EDTA facilitates the transport and translocation of Fe to the leaves. The genetic modification is probably responsible for differences observed between T and NT soybean plants.