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

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

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

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

Structures Related to the Emplacement of Shallow-Level Intrusions

A systematic view of the vast nomenclature used to describe the structures of shallow-level intrusions is presented here. Structures are organised in four main groups, according to logical breaks in the timing of magma emplacement, independent of the scales of features: (1) Intrusion-related structures, formed as the magma is making space and then develops into its intrusion shape; (2) Magmatic flow-related structures, developed as magma moves with suspended crystals that are free to rotate; (3) Solid-state, flow-related structures that formed in portions of the intrusions affected by continuing flow of nearby magma, therefore considered to have a syn-magmatic, non-tectonic origin; (4) Thermal and fragmental structures, related to creation of space and impact on host materials. This scheme appears as a rational organisation, helpful in describing and interpreting the large variety of structures observed in shallow-level intrusions

Balanced Schnyder woods for planar triangulations: an experimental study with applications to graph drawing and graph separators

In this work we consider balanced Schnyder woods for planar graphs, which are Schnyder woods where the number of incoming edges of each color at each vertex is balanced as much as possible. We provide a simple linear-time heuristic leading to obtain well balanced Schnyder woods in practice. As test applications we consider two important algorithmic problems: the computation of Schnyder drawings and of small cycle separators. While not being able to provide theoretical guarantees, our experimental results (on a wide collection of planar graphs) suggest that the use of balanced Schnyder woods leads to an improvement of the quality of the layout of Schnyder drawings, and provides an efficient tool for computing short and balanced cycle separators.Comment: Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019

Decrypting magnetic fabrics (AMS, AARM, AIRM) through the analysis of mineral shape fabrics and distribution anisotropy

The fieldwork was supported by the DIPS project (grant no. 240467) and the MIMES project (grant no. 244155) funded by the Norwegian Research Council awarded to O.G. O.P.'s position was funded from Y-TEC.Anisotropy of magnetic susceptibility (AMS) and anisotropy of magnetic remanence (AARM and AIRM) are efficient and versatile techniques to indirectly determine rock fabrics. Yet, deciphering the source of a magnetic fabric remains a crucial and challenging step, notably in the presence of ferrimagnetic phases. Here we use X-ray micro-computed tomography to directly compare mineral shape-preferred orientation and spatial distribution fabrics to AMS, AARM and AIRM fabrics from five hypabyssal trachyandesite samples. Magnetite grains in the trachyandesite are euhedral with a mean aspect ratio of 1.44 (0.24 s.d., long/short axis), and > 50% of the magnetite grains occur in clusters, and they are therefore prone to interact magnetically. Amphibole grains are prolate with magnetite in breakdown rims. We identified three components of the petrofabric that influence the AMS of the analyzed samples: the magnetite and the amphibole shape fabrics and the magnetite spatial distribution. Depending on their relative strength, orientation and shape, these three components interfere either constructively or destructively to produce the AMS fabric. If the three components are coaxial, the result is a relatively strongly anisotropic AMS fabric (P’ = 1.079). If shape fabrics and/or magnetite distribution are non-coaxial, the resulting AMS is weakly anisotropic (P’ = 1.012). This study thus reports quantitative petrofabric data that show the effect of magnetite distribution anisotropy on magnetic fabrics in igneous rocks, which has so far only been predicted by experimental and theoretical models. Our results have first-order implications for the interpretation of petrofabrics using magnetic methods.Publisher PDFPeer reviewe

Aberrant lipid metabolism disrupts calcium homeostasis causing liver endoplasmic reticulum stress in obesity.

The endoplasmic reticulum (ER) is the main site of protein and lipid synthesis, membrane biogenesis, xenobiotic detoxification and cellular calcium storage, and perturbation of ER homeostasis leads to stress and the activation of the unfolded protein response. Chronic activation of ER stress has been shown to have an important role in the development of insulin resistance and diabetes in obesity. However, the mechanisms that lead to chronic ER stress in a metabolic context in general, and in obesity in particular, are not understood. Here we comparatively examined the proteomic and lipidomic landscape of hepatic ER purified from lean and obese mice to explore the mechanisms of chronic ER stress in obesity. We found suppression of protein but stimulation of lipid synthesis in the obese ER without significant alterations in chaperone content. Alterations in ER fatty acid and lipid composition result in the inhibition of sarco/endoplasmic reticulum calcium ATPase (SERCA) activity and ER stress. Correcting the obesity-induced alteration of ER phospholipid composition or hepatic Serca overexpression in vivo both reduced chronic ER stress and improved glucose homeostasis. Hence, we established that abnormal lipid and calcium metabolism are important contributors to hepatic ER stress in obesity