Leandro Aurichi, Paulo Magalhães Júnior, Guilherme Eduardo Pinto
We prove that every 2k-edge-connected graph with countably many edge-ends admits a k-arc-connected orientation, extending the previous result by Assem, Koloschin and Pitz that also assumed the hypothesis of the graph being locally finite. We prove that, if every locally finite graph has a well-balanced orientation, so does every graph. Lastly, we explore an alternative to the Nash-Williams Orientation Conjecture via topological paths, and prove that it is true for every finitely separated graph.
A Euclidean oriented matroid program yields a partial ordering of the cocircuits of its cocircuit graph. We show that every linear extension of that ordering yields a topological sweep and induces a recursive atom-ordering (a shelling of the cocircuits) of the tope cell of the feasible region. We extend that sweep and obtain also a vertex-shelling of the whole oriented matroid and finally describe some connections to the notion of stackable zontopal tilings and to a counterexample of a conjecture of A. Mandel.
Igor Araujo, József Balogh, Robert A. Krueger
et al.
In 2003, Bohman, Frieze, and Martin initiated the study of randomly perturbed graphs and digraphs. For digraphs, they showed that for every $α>0$, there exists a constant $C$ such that for every $n$-vertex digraph of minimum semi-degree at least $αn$, if one adds $Cn$ random edges then asymptotically almost surely the resulting digraph contains a consistently oriented Hamilton cycle. We generalize their result, showing that the hypothesis of this theorem actually asymptotically almost surely ensures the existence of every orientation of a cycle of every possible length, simultaneously. Moreover, we prove that we can relax the minimum semi-degree condition to a minimum total degree condition when considering orientations of a cycle that do not contain a large number of vertices of indegree $1$. Our proofs make use of a variant of an absorbing method of Montgomery.
Most of the existing deep learning based methods for vessel segmentation neglect two important aspects of retinal vessels, one is the orientation information of vessels, and the other is the contextual information of the whole fundus region. In this paper, we propose a robust Orientation and Context Entangled Network (denoted as OCE-Net), which has the capability of extracting complex orientation and context information of the blood vessels. To achieve complex orientation aware, a Dynamic Complex Orientation Aware Convolution (DCOA Conv) is proposed to extract complex vessels with multiple orientations for improving the vessel continuity. To simultaneously capture the global context information and emphasize the important local information, a Global and Local Fusion Module (GLFM) is developed to simultaneously model the long-range dependency of vessels and focus sufficient attention on local thin vessels. A novel Orientation and Context Entangled Non-local (OCE-NL) module is proposed to entangle the orientation and context information together. In addition, an Unbalanced Attention Refining Module (UARM) is proposed to deal with the unbalanced pixel numbers of background, thick and thin vessels. Extensive experiments were performed on several commonly used datasets (DRIVE, STARE and CHASEDB1) and some more challenging datasets (AV-WIDE, UoA-DR, RFMiD and UK Biobank). The ablation study shows that the proposed method achieves promising performance on maintaining the continuity of thin vessels and the comparative experiments demonstrate that our OCE-Net can achieve state-of-the-art performance on retinal vessel segmentation.
This paper shows that simplicial oriented geometries can be characterized as groupoids with root systems having certain favorable properties, as conjectured by the first author. The proof first translates Handa's characterization of oriented matroids, as acycloids which remain acycloids under iterated elementary contractions, into the language of groupoids with root systems, then establishes favorable lattice theoretic properties of a generalization of a construction which Brink and Howlett used in their study of normalizers of parabolic subgroups of Coxeter groups and uses Björner-Edelman-Ziegler's lattice theoretic characterization of simplicial oriented geometries amongst oriented geometries.
We show the density theorem for the class of finite oriented trees ordered by the homomorphism order. We also show that every interval of oriented trees, in addition to be dense, is in fact universal. We end by considering the fractal property in the class of all finite digraphs.
This article studies the \emph{$k$-forcing number} for oriented graphs, generalizing both the \emph{zero forcing number} for directed graphs and the $k$-forcing number for simple graphs. In particular, given a simple graph $G$, we introduce the maximum (minimum) oriented $k$-forcing number, denoted $\MOF_k(G)$ ($\mof_k(G)$), which is the largest (smallest) $k$-forcing number among all possible orientations of $G$. These new ideas are compared to known graph invariants and it is shown that, among other things, $\mof(G)$ equals the path covering number of $G$ while $\MOF_k(G)$ is greater than or equal to the independence number of $G$ -- with equality holding if $G$ is a tree or if $k$ is at least the maximum degree of $G$. Along the way, we also show that many recent results about $k$-forcing number can be modified for oriented graphs.
We consider quantum algorithms for the unique sink orientation problem on cubes. This problem is widely considered to be of intermediate computational complexity. This is because there no known polynomial algorithm (classical or quantum) from the problem and yet it arrises as part of a series of problems for which it being intractable would imply complexity theoretic collapses. We give a reduction which proves that if one can efficiently evaluate the kth power of the unique sink orientation outmap, then there exists a polynomial time quantum algorithm for the unique sink orientation problem on cubes.
Irina Znakovskaya, Michael Spanner, Sankar De
et al.
The transition between two distinct mechanisms for the laser-induced field-free orientation of CO molecules is observed via measurements of orientation revival times and subsequent comparison to theoretical calculations. In the first mechanism, which we find responsible for the orientation of CO up to peak intensities of 8 x 10^13 W/cm^2, the molecules are impulsively oriented through the hyperpolarizability interaction. At higher intensities, asymmetric depletion through orientation-selective ionization is the dominant orienting mechanism. In addition to the clear identification of the two regimes of orientation, we propose that careful measurements of the onset of the orientation depletion mechanism as a function of the laser intensity will provide a relatively simple route to calibrate absolute rates of non-perturbative strong-field molecular ionization.
We prove a version of the classical Runge and Mergelyan uniform approximation theorems for non-orientable minimal surfaces in Euclidean 3-space R3. Then, we obtain some geometric applications. Among them, we emphasize the following ones: 1. A Gunning-Narasimhan type theorem for non-orientable conformal surfaces. 2. An existence theorem for non-orientable minimal surfaces in R3, with arbitrary conformal structure, properly projecting into a plane. 3. An existence result for non-orientable minimal surfaces in R3 with arbitrary conformal structure and Gauss map omitting one projective direction.
BACKGROUND CYP2E1 encodes an enzyme which is mainly involved in bioactivation of potential carcinogens such as N-nitrosamines. Polymorphisms in the gene have been reported to be associated with cancer. The aim of this study was to evaluate genotype distributions and allele frequencies of five CYP2E1 polymorphisms in Iran. MATERIALS AND METHOD Two hundred healthy individuals of an Iranian population from the southwest were included in this study. PCR-restriction fragment length polymorphism and Tetra-ARMS PCR methods were applied for CYP2E1 genotyping. RESULTS The allele frequencies for *5B, *6, *7B, *2, and *3 were calculated to be 1.5%, 16%, 28.5%, 0%, and 2.75% respectively. Results of this study showed that no significant differences in genotype and allele frequencies of five single nucleotide polymorphisms with respect to the gender and tribes. The chi-square test showed that the genotype frequencies of CYP2E1*5B were similar to Caucasians, but the distribution of CYP2E1*6 genotypes was similar to Asians. The frequencies of CYP2E1*2 (0%) and CYP2E1*3 (2.75%) alleles were within the range for Caucasians and Orientals. In the case of CYP2E1*7B, the data werelimited. Accordingly, the results were only compared with Europeans and the comparison showed significant differences. CONCLUSIONS In conclusion, ethnic and geographic differences may explain discrepancies in the prevalence of CYP2E1 polymorphisms.
Muhammad Anshari, Mohammad N. Almunawar, Patrick K. C. Low
et al.
Customer Relationship Management (CRM) with the Web technology provides healthcare organizations the ability to broaden services beyond its usual practices, and thus provides a particular advantageous environment to achieve complex e-health goals. This paper discusses and demonstrates how a new approach in CRM based on Web 2.0 namely CRM 2.0 will help customers to have greater control in the sense of controlling the process of interaction (empowerment) between healthcare organizations with its customers, and among customers themselves. A survey was conducted to gather preliminary requirements and expectations on empowerment in Brunei. The survey revealed that there is a high demand for empowering customers in Brunei through the Web. Regardless of the limitations of the survey, the general public has responded with a great support for the capabilities of empowerment listed from the questionnaires. The data were analyzed to provide initial ideas and recommendation to a future direction on research for customers' empowerment in e-health services.
Tropical oriented matroids were defined by Ardila and Develin in 2007. They are a tropical analogue of classical oriented matroids in the sense that they encode the properties of the types of points in an arrangement of tropical hyperplanes -- in much the same way as the covectors of (classical) oriented matroids describe the types in arrangements of linear hyperplanes. Ardila and Develin proved that tropical oriented matroids can be represented as mixed subdivisions of dilated simplices. In this paper we show that this correspondence is a bijection. Moreover, a tropical analogue for the Topological Representation Theorem for (classical) oriented matroids by Folkman and Lawrence is presented.
Group Field Theories (GFT) are quantum field theories over group manifolds; they can be seen as a generalization of matrix models. GFT Feynman graphs are tensor graphs generalizing ribbon graphs (or combinatorial maps); these graphs are dual not only to manifolds. In order to simplify the topological structure of these various singularities, colored GFT was recently introduced and intensively studied since. We propose here a different simplification of GFT, which we call multi-orientable GFT. We study the relation between multi-orientable GFT Feynman graphs and colorable graphs. We prove that tadfaces and some generalized tadpoles are absent. Some Feynman amplitude computations are performed. A few remarks on the renormalizability of both multi-orientable and colorable GFT are made. A generalization from three-dimensional to four-dimensional theories is also proposed.
We introduce the notion of Principal Component Analysis (PCA) of image gradient orientations. As image data is typically noisy, but noise is substantially different from Gaussian, traditional PCA of pixel intensities very often fails to estimate reliably the low-dimensional subspace of a given data population. We show that replacing intensities with gradient orientations and the $\ell_2$ norm with a cosine-based distance measure offers, to some extend, a remedy to this problem. Our scheme requires the eigen-decomposition of a covariance matrix and is as computationally efficient as standard $\ell_2$ PCA. We demonstrate some of its favorable properties on robust subspace estimation.