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Melanophoroma is a neoplasm of reptilian pigment cells, considered uncommon and part of a group of neoplasms called chromatophoromas. The objective of this work was to describe a case of melanophoroma in a free‐living Lichtenstein's green racer snake (Philodryas olfersii), presenting with an ulcerative nodular neoformation in the integument of the head region. In the neurologic evaluation, a proprioceptive deficit was observed. Ultrasound, X‐ray, and mass cytology examinations were performed. Radiographic and ultrasound findings of the tumor indicated infiltrative behavior, and cytology indicated a presumptive diagnosis of a melanocytic neoplasm. Based on the results of the examinations and the patient's clinical condition, euthanasia was chosen. At necropsy, there was a nodule measuring 4.5 × 2.5 × 2.0 cm, with a blackish‐colored cut surface, mottled by gray areas, which infiltrated soft tissue and bone, and extended dorsally from the mouth to the cervical musculature. On microscopy, a non‐delimited, non‐encapsulated, and invasive neoplastic proliferation was observed, with moderate cellularity, which was predominantly composed of fusiform cells with distinct borders and foci of epithelioid cells. The cells had ample cytoplasm, which had a brown to black (melanocytic) granular pigment compatible with a melanophoroma. To the best of the authors' knowledge, this is a unique description of a melanophoroma in P. olfersii. [ABSTRACT FROM AUTHOR]

We consider a game-theoretical problem called selfish 2-dimensional bin packing game, a generalization of the 1-dimensional case already treated in the literature. In this game, the items to be packed are rectangles, and the bins are unit squares. The game starts with a set of items arbitrarily packed in bins. The cost of an item is defined as the ratio between its area and the total occupied area of the respective bin. Each item is a selfish player that wants to minimize its cost. A migration of an item to another bin is allowed only when its cost is decreased. We show that this game always converges to a Nash equilibrium (a stable packing where no single item can decrease its cost by migrating to another bin). We show that the pure price of anarchy of this game is unbounded, so we address the particular case where all items are squares. We show that the pure price of anarchy of the selfish square packing game is at least 2. 3 6 3 4 and at most 2. 6 8 7 5. We also present analogous results for the strong Nash equilibrium (a stable packing where no nonempty set of items can simultaneously migrate to another common bin and decrease the cost of each item in the set). We show that the strong price of anarchy when all items are squares is at least 2. 0 7 4 7 and at most 2. 3 6 0 5. [ABSTRACT FROM AUTHOR]

Abstract: Minimum bisection denotes the NP‐hard problem to partition the vertex set of a graph into two sets of equal sizes while minimizing the width of the bisection, which is defined as the number of edges between these two sets. It is intuitively clear that graphs with a somewhat linear structure are easy to bisect, and therefore our aim is to relate the minimum bisection width of a bounded‐degree graph G to a parameter that measures the similarity between G and a path. First, for trees, we use the diameter and show that the minimum bisection width of every tree T on n vertices satisfies  MinBis ( T ) ≤ 8 n Δ ( T ) / diam ( T ). Second, we generalize this to arbitrary graphs with a given tree decomposition  ( T , X ) and give an upper bound on the minimum bisection width that depends on how close  ( T , X ) is to a path decomposition. Moreover, we show that a bisection satisfying our general bound can be computed in time proportional to the encoding length of the tree decomposition when the latter is provided as input. [ABSTRACT FROM AUTHOR]

In the k-center problem, given a metric space V and a positive integer k, one wants to select k elements (centers) of V and an assignment from V to centers, minimizing the maximum distance between an element of V and its assigned center. One of the most general variants is the capacitatedα-fault-tolerant k-center, where centers have a limit on the number of assigned elements, and, if any α centers fail, there is a reassignment from V to non-faulty centers. In this paper, we present a new approach to tackle fault tolerance, by selecting and pre-opening a set of backup centers, then solving the obtained residual instance. For the {0,L}-capacitated case, we give approximations with factor 6 for the basic problem, and 7 for the so called conservative variant, when only clients whose centers failed may be reassigned. Our algorithms improve on the best previously known factors of 9 and 17, respectively. Moreover, we consider the case with general capacities. Assuming α is constant, our method leads to the first approximations for this case. We also derive approximations for the capacitated fault-tolerant k-supplier problem. [ABSTRACT FROM AUTHOR]

Let lpt( G ) be the minimum cardinality of a set of vertices that intersects all longest paths in a connected graph G . We show that, if G is a chordal graph, then lpt ( G ) ≤ max ⁡ { 1 , ω ( G ) − 2 } , where ω ( G ) is the size of a largest clique in G ; that lpt ( G ) ≤ tw ( G ) , where tw ( G ) is the treewidth of G ; and that lpt ( G ) = 1 if G is a bipartite permutation graph or a full substar graph. [ABSTRACT FROM AUTHOR]

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We consider questions related to the existence of spanning trees in connected graphs with the property that, after the removal of any path in the tree, the graph remains connected. We show that, for planar graphs, the existence of trees with this property is closely related to the Hamiltonicity of the graph. For graphs with a 1- or 2-vertex cut, the Hamiltonicity also plays a central role. We also deal with spanning trees satisfying this property restricted to paths arising from fundamental cycles. The cycle space of a graph can be generated by the fundamental cycles of every spanning tree, and Tutte showed that, for a 3-connected graph, it can be generated by nonseparating cycles. We are also interested in the existence of a fundamental basis consisting of nonseparating cycles. [ABSTRACT FROM AUTHOR]

The problem of clustering a set of points moving on the line consists of the following: given positive integers n and k , and the initial position and velocity of n points, find an optimal k -clustering of the points. We consider two classical quality measures for the clustering: minimizing the sum of the clusters diameters and minimizing the maximum diameter of a cluster. For the former, we present a polynomial-time algorithm under some assumptions and, for the latter, a (2.71 + ε )-approximation. [ABSTRACT FROM AUTHOR]

Minimum k -Section denotes the NP-hard problem to partition the vertex set of a graph into k sets of size as equal as possible while minimizing the cut width, which is the number of edges between these sets. When k is an input parameter and n denotes the number of vertices, it is NP-hard to approximate the width of a minimum k -section within a factor of n c for any c < 1 , even when restricted to trees with constant diameter. Here, we show that every tree T allows a k -section of width at most ( k − 1 ) ( 2 + 16 n / diam ( T ) ) Δ ( T ) . This implies a polynomial time constant factor approximation for the Minimum k -Section Problem when restricted to trees with linear diameter and constant maximum degree. [ABSTRACT FROM AUTHOR]

The determination of the (in-)stability of the long-lived consensus problem is a fundamental open problem in distributed systems. We concentrate on the memoryless binary case with geodesic paths. For this case, we offer a conjecture on the instability, measured by the parameter inst , exhibit two classes of colourings which attain the conjectured bound, and improve the known lower bounds for all colourings. We also introduce a related parameter, winst , which measures the stability only for certain geodesics, and for which we also prove lower bounds. [ABSTRACT FROM AUTHOR]

Minimum Bisection denotes the NP-hard problem to partition the vertex set of a graph into two sets of equal sizes while minimizing the number of edges between these two sets. We consider this problem in bounded degree graphs with a given tree decomposition ( T , X ) and prove an upper bound for their minimum bisection width in terms of the structure and width of ( T , X ) . When ( T , X ) is provided as input, a bisection satisfying our bound can be computed in time proportional to the encoding length of ( T , X ) . Furthermore, our result can be generalized to k -section, which is known to be APX-hard even when restricted to trees with bounded degree. [ABSTRACT FROM AUTHOR]

Abstract: In 1966, Gallai asked whether every connected graph has a vertex that is common to all longest paths. The answer to this question is negative. We prove that the answer is positive for outerplanar graphs and 2-trees. Another related question was raised by Zamfirescu in the 1980s: Do any three longest paths in a connected graph have a vertex in common? The answer to this question is unknown. We prove that for connected graphs in which all nontrivial blocks are Hamiltonian the answer is affirmative. Finally, we state a conjecture and explain how it relates to the three longest paths question. [Copyright &y& Elsevier]

Abstract: In 1966, Gallai asked whether every connected graph has a vertex that is common to all its longest paths. The answer to this question is negative. We prove that the answer is positive for outerplanar graphs. Another related question was raised in 1995 at the British Combinatorial Conference: Do any three longest paths in a connected graph have a vertex in common? We prove that, in a connected graph in which all non-trivial blocks are Hamiltonian, any three of its longest paths have a common vertex. Both of these results strengthen a recent result by Axenovich. [Copyright &y& Elsevier]

Abstract: The determination of the stability of the long-lived consensus problem is a fundamental open problem in distributed systems. We concentrate on the memoryless binary case with geodesic paths. We offer a conjecture on the stability in this case, exhibit two classes of colourings which attain this conjectured bound, and improve the known lower bounds for all colourings. We also introduce a related parameter, which measures the stability only for certain geodesics, and for which we also prove lower bounds. [Copyright &y& Elsevier]

Abstract: In this extended abstract, we outline a concurrent implementation of a data structure called skip graphs. This data structure, proposed by Aspnes and Shah, has similar functionality to binary search trees, and has also special features that make it suitable for P2P distributed environments. In our implementation, we used non-blockirig locking primitives to synchronize the operations whenever necessary. The resulting implementation performed well in practice, according to our experiments. [Copyright &y& Elsevier]

Abstract: Let be a mixed graph with vertex set , edge set and arc set . A cycle cover of is a family of cycles of such that each edge/arc of belongs to at least one cycle in . The weight of is . The minimum cycle cover problem is the following: given a strongly connected mixed graph without bridges, find a cycle cover of with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph , find a minimum length closed walk using all edges and arcs of . These problems are NP-hard. We show that they can be solved in polynomial time if has bounded tree-width. [Copyright &y& Elsevier]

A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for MaximumWeight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to ½. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case. [ABSTRACT FROM AUTHOR]

Tuza (1981) conjectured that the size τ (G) of a minimum set of edges that intersects every triangle of a graph G is at most twice the size ν (G) of a maximum set of edge-disjoint triangles of G. In this paper we present three results regarding Tuza's Conjecture. We verify it for graphs with treewidth at most 6; we show that τ (G) ≤ 3 2 ν (G) for every planar triangulation G different from K 4 ; and that τ (G) ≤ 9 5 ν (G) + 1 5 if G is a maximal graph with treewidth 3. Our first result strengthens a result of Tuza, implying that τ (G) ≤ 2 ν (G) for every K 8 -free chordal graph G. [ABSTRACT FROM AUTHOR]

Let lpt (G) be the minimum cardinality of a transversal of longest paths in G , that is, a set of vertices that intersects all longest paths in a graph G. There are several results in the literature bounding the value of lpt (G) in general or in specific classes of graphs. For instance, lpt (G) = 1 if G is a connected partial 2-tree, and a connected partial 3-tree G is known with lpt (G) = 2. We prove that lpt (G) ≤ 3 for every connected partial 3-tree G ; that lpt (G) ≤ 2 for every planar 3-tree G ; and that lpt (G) = 1 if G is a connected bipartite permutation graph or a connected full substar graph. Our first two results can be adapted for broader classes, improving slightly some known general results: we prove that lpt (G) ≤ k for every connected partial k -tree G and that lpt (G) ≤ max { 1 , ω (G) − 2 } for every connected chordal graph G , where ω (G) is the cardinality of a maximum clique in G. [ABSTRACT FROM AUTHOR]

The objective of this study was to assess the placental vasculature and microcotyledons in pregnant mares with chronic laminitis. Twenty-six pregnant mares were enrolled in the study, 13 had chronic laminitis (Laminitis Group) and 13 were healthy mares (Healthy Group). Arterial systolic pressure and heart rate were measured in the last 30 days of gestation. After foaling, the fetal membranes were grossly evaluated and samples were harvested for histopathologic examination. All mares had digitalized images taken from chorioallantois for histomorphometry analyses (software-NIH ImageJ). Images were assessed for: (i) arterioles from the allantoic region: total and lumen vascular diameter and vascular wall thickness; (ii) microcotiledonary and capillary area/field. Mares in the Laminitis Group showed hypertension, shorter gestational length, lower placental weight and lower birthweight (p < 0.05) foal in comparison with mares in the Healthy Group. Laminitis mares had a reduction of vascular lumen diameters in the uterine body and pregnant horn (p < 0.05), vascular wall thickening in the pregnant horn (p < 0.05) and smaller capillary area/field in the microcotyledons of uterine body and pregnant horn (p < 0.05). In conclusion, pregnant mares with chronic laminitis presented signs of hypertension syndrome, and vascular abnormalitities in placental vessels such as reduction in the vascular lumen and capillary area in the microcotyledones, and thickening of the vascular wall. Foals born from mares with chronic laminitis showed lower birth weight and shorter gestation lengths. [ABSTRACT FROM AUTHOR]

In 1966 Gallai asked whether all longest paths in a connected graph have nonempty intersection. This is not true in general and various counterexamples have been found. However, the answer to Gallai’s question is positive for several well-known classes of graphs, as for instance connected outerplanar graphs, connected split graphs, and 2-trees. A graph is series–parallel if it does not contain K 4 as a minor. Series–parallel graphs are also known as partial 2-trees, which are arbitrary subgraphs of 2-trees. We present two independent proofs that every connected series–parallel graph has a vertex that is common to all of its longest paths. Since 2-trees are maximal series–parallel graphs, and outerplanar graphs are also series–parallel, our result captures these two classes in one proof and strengthens them to a larger class of graphs. We also describe how one such vertex can be found in linear time. [ABSTRACT FROM AUTHOR]

Abstract: We study the following problem. Given two sequences and over a finite alphabet, find a repetition-free longest common subsequence of and . We show several algorithmic results, a computational complexity result, and we describe a preliminary experimental study based on the proposed algorithms. We also show that this problem is APX-hard. [Copyright &y& Elsevier]

Abstract: In this study, we evaluate the clinical, histopathological and ultra structural aspects of the infection by field strain (MEL+) and mutated strain (MEL−) of Sporothrix schenckii. The development of sporotrichosis at the inoculation sites was similar for both groups of animals after the second week of the experimental period. Statistical differences appeared only at weeks 3 and 5. The pigmented isolate had greater tissue invasive capacity, promoting the formation of multifocal granulomas, whereas the albino isolate induced an enhanced inflammatory response, restraining the agent to the core of the granulomas. [Copyright &y& Elsevier]