Maximum st-flow in directed planar graphs via shortest paths

Minimum cuts have been closely related to shortest paths in planar graphs via planar duality - so long as the graphs are undirected. Even maximum flows are closely related to shortest paths for the same reason - so long as the source and the sink are on a common face. In this paper, we give a correspondence between maximum flows and shortest paths via duality in directed planar graphs with no constraints on the source and sink. We believe this a promising avenue for developing algorithms that are more practical than the current asymptotically best algorithms for maximum st-flow.Comment: 20 pages, 4 figures. Short version to be published in proceedings of IWOCA'1

Planar Induced Subgraphs of Sparse Graphs

We show that every graph has an induced pseudoforest of at least $n-m/4.5$ vertices, an induced partial 2-tree of at least $n-m/5$ vertices, and an induced planar subgraph of at least $n-m/5.2174$ vertices. These results are constructive, implying linear-time algorithms to find the respective induced subgraphs. We also show that the size of the largest $K_h$-minor-free graph in a given graph can sometimes be at most $n-m/6+o(m)$.Comment: Accepted by Graph Drawing 2014. To appear in Journal of Graph Algorithms and Application

The Effect of Planarization on Width

We study the effects of planarization (the construction of a planar diagram $D$ from a non-planar graph $G$ by replacing each crossing by a new vertex) on graph width parameters. We show that for treewidth, pathwidth, branchwidth, clique-width, and tree-depth there exists a family of $n$-vertex graphs with bounded parameter value, all of whose planarizations have parameter value $\Omega(n)$. However, for bandwidth, cutwidth, and carving width, every graph with bounded parameter value has a planarization of linear size whose parameter value remains bounded. The same is true for the treewidth, pathwidth, and branchwidth of graphs of bounded degree.Comment: 15 pages, 6 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Colored Non-Crossing Euclidean Steiner Forest

Given a set of $k$-colored points in the plane, we consider the problem of finding $k$ trees such that each tree connects all points of one color class, no two trees cross, and the total edge length of the trees is minimized. For $k=1$, this is the well-known Euclidean Steiner tree problem. For general $k$, a $k\rho$-approximation algorithm is known, where $\rho \le 1.21$ is the Steiner ratio. We present a PTAS for $k=2$, a $(5/3+\varepsilon)$-approximation algorithm for $k=3$, and two approximation algorithms for general~$k$, with ratios $O(\sqrt n \log k)$ and $k+\varepsilon$

Geometric Multicut: Shortest Fences for Separating Groups of Objects in the Plane

We study the following separation problem: Given a collection of pairwise disjoint coloured objects in the plane with k different colours, compute a shortest “fence” F, i.e., a union of curves of minimum total length, that separates every pair of objects of different colours. Two objects are separated if F contains a simple closed curve that has one object in the interior and the other in the exterior. We refer to the problem as GEOMETRIC k-CUT, as it is a geometric analog to the well-studied multicut problem on graphs. We first give an O(n4log3n)-time algorithm that computes an optimal fence for the case where the input consists of polygons of two colours with n corners in total. We then show that the problem is NP-hard for the case of three colours. Finally, we give a randomised 4/3⋅1.2965-approximation algorithm for polygons and any number of colours

A Poisson model for earthquake frequency uncertainties in seismic hazard analysis

Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete and of unequal variance. In general, the observed number in any given magnitude range is described by a binomial distribution which, given a large total number of events of all magnitudes, approximates to a Poisson distribution for a sufficiently small probability associated with that range. In this paper, we examine four earthquake catalogues: New Zealand (Institute of Geological and Nuclear Sciences), Southern California (Southern California Earthquake Center), the Preliminary Determination of Epicentres and the Harvard Centroid Moment Tensor (both held by the United States Geological Survey). Using independent Poisson distributions to model the observations, we demonstrate a simple way of estimating the uncertainty on the total number of events occurring in a fixed time period.Comment: 9 pages, 3 figures; accepted by GRL after minor addition

Two-week isocaloric time-restricted feeding decreases liver inflammation without significant weight loss in obese mice with non-alcoholic fatty liver disease

Prolonged, isocaloric, time-restricted feeding (TRF) protocols can promote weight loss, improve metabolic dysregulation, and mitigate non-alcoholic fatty liver disease (NAFLD). In addition, 3-day, severe caloric restriction can improve liver metabolism and glucose homeostasis prior to significant weight loss. Thus, we hypothesized that short-term, isocaloric TRF would improve NAFLD and characteristics of metabolic syndrome in diet-induced obese male mice. After 26 weeks of ad libitum access to western diet, mice either continued feeding ad libitum or were provided with access to the same quantity of western diet for 8 h daily, over the course of two weeks. Remarkably, this short-term TRF protocol modestly decreased liver tissue inflammation in the absence of changes in body weight or epidydimal fat mass. There were no changes in hepatic lipid accumulation or other characteristics of NAFLD. We observed no changes in liver lipid metabolism-related gene expression, despite increased plasma free fatty acids and decreased plasma triglycerides in the TRF group. However, liver Grp78 and Txnip expression were decreased with TRF suggesting hepatic endoplasmic reticulum (ER) stress and activation of inflammatory pathways may have been diminished. We conclude that two-week, isocaloric TRF can potentially decrease liver inflammation, without significant weight loss or reductions in hepatic steatosis, in obese mice with NAFLD

Naringenin Prevents Dyslipidemia, Apolipoprotein B Overproduction, and Hyperinsulinemia in LDL Receptor–Null Mice With Diet-Induced Insulin Resistance

OBJECTIVE: The global epidemic of metabolic syndrome and its complications demands rapid evaluation of new and accessible interventions. Insulin resistance is the central biochemical disturbance in the metabolic syndrome. The citrus-derived flavonoid, naringenin, has lipid-lowering properties and inhibits VLDL secretion from cultured hepatocytes in a manner resembling insulin. We evaluated whether naringenin regulates lipoprotein production and insulin sensitivity in the context of insulin resistance in vivo. RESEARCH DESIGN AND METHODS: LDL receptor-null (Ldlr(-/-)) mice fed a high-fat (Western) diet (42% calories from fat and 0.05% cholesterol) become dyslipidemic, insulin and glucose intolerant, and obese. Four groups of mice (standard diet, Western, and Western plus 1% or 3% wt/wt naringenin) were fed ad libitum for 4 weeks. VLDL production and parameters of insulin and glucose tolerance were determined. RESULTS: We report that naringenin treatment of Ldlr(-/-) mice fed a Western diet corrected VLDL overproduction, ameliorated hepatic steatosis, and attenuated dyslipidemia without affecting caloric intake or fat absorption. Naringenin 1) increased hepatic fatty acid oxidation through a peroxisome proliferator-activated receptor (PPAR) gamma coactivator 1alpha/PPARalpha-mediated transcription program; 2) prevented sterol regulatory element-binding protein 1c-mediated lipogenesis in both liver and muscle by reducing fasting hyperinsulinemia; 3) decreased hepatic cholesterol and cholesterol ester synthesis; 4) reduced both VLDL-derived and endogenously synthesized fatty acids, preventing muscle triglyceride accumulation; and 5) improved overall insulin sensitivity and glucose tolerance. CONCLUSIONS: Thus, naringenin, through its correction of many of the metabolic disturbances linked to insulin resistance, represents a promising therapeutic approach for metabolic syndrome

Note on analysis of quartz grain dimensions in foliated greywackes

Quarzkorn-Abmessungen aus Grauwacken wurden auf ein internes Referenzsystem (reference aspect ratio, RAR) bezogen und mit Hilfe der linearen Regressionsanalyse der reduzierten Hauptachse (reduced major axis, RMA) ausgewertet. Das verwendete statistische Verfahren unterscheidet im Gegensatz zur Methode der kleinsten Quadrate nicht zwischen abhängigen und unabhängigen Variablen. Die Anwendung der RMX-Methode in Verbindung mit den RAR-Meßwerten kann sehr hilfreich für Vergleiche innerhalb geschieferter Grauwacken sein, bei denen unterschiedliche Prozesse in Korngrößenbereich wirksam waren wie etwa Drucklösung und Festkörper-Rotation. Die RAR/RMA-Analyse erfaßt Kornregelungen und ist daher auch einsetzbar für die Klassifikation von Schieferungen. Darüber hinaus wird die Anwendung der RAR/RMA-Analyse für die Bestimmung der Deformation diskutiert. Robin strain-Werte werden mit arithmetischen und harmonischen Mittelwerten der RAR-Analyse verglichen. Es zeigt sich, daß das arithmetische Mittel des RAR ein vernünftiges Maß für die longitudinale Deformation darstellt. Quartz grain dimensions, measured parallel to an internal reference system (reference aspect ratio, RAR), were analyzed using the »reduced major axis« (RMA) linear regression analysis. In contrast to least-squares analysis, this statistical technique does not distinguish between dependent and independent variables. Application of the RMA analysis in conjunction with RAR values can be most useful for comparisons between foliated greywackes in which different grain scale processes, such as pressure solution and rigid-body rotation, were active. The RAR/RMA analysis reflects grain alignment and is therefore also useful for cleavage classification. In addition to the above, the application of RAR/RMA analysis for the determination of strain is discussed. Robin strains are compared with the arithmetic and harmonic means from RAR's and it is concluded that the arithmetic mean RAR produces a reasonable estimate of longitudinal strain in these rocks. Les dimensions des grains de quartz, mesurés parallèlement à un système de référence interne (»reference aspect ratio«: RAR) ont été traitées par la méthode de la régression linéaire (»reduced major axis«: RMA). Contrairement à la méthode des moindres carrés, cette technique statistique ne fait pas de distinction entre les variables dépendantes et indépendantes. L'application de ce type de méthode s'avère très utile à la comparaison de grauwackes schisteuses dans lesquelles les dimensions des grains peuvent être la conséquence de processus différents, tels que la dissolution (pressure solution) et la rotation. L'analyse RAR/RMA traduit l'alignement des grains et peut, de ce fait, être utilisée aussi à l'appréciation du type de schistosité. D'autre part, l'auteur discute l'application de l'analyse RAR/RMA à la détermination de la déformation finie. Si on compare les déformations »Robin« aux moyennes arithmétique et harmonique des RAR, on peut conclure que les moyennes RAR arithmétiques fournissent une estimation raisonnable de la déformation longitudinale. Помимо интернациона льной системы RAR, разме ры зерен кварца анализи ровали с помощью регр ессивного анализа «Изменение о сновных осей» — RMA. В отличие от анализа ме тодом наименьшего кв адратов, при названном статис тическом методе разл ичия между зависимыми и не зависимыми переменн ыми не учитываются. Компл ексное применение RAR иPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47848/1/531_2005_Article_BF01821068.pd