Two-Dimensional Bosonization from Variable Shifts in the Path Integral

A method to perform bosonization of a fermionic theory in (1+1) dimensions in a path integral framework is developed. The method relies exclusively on the path integral property of allowing variable shifts, and does not depend on the explicit form of Greens functions. Two examples, the Schwinger model and the massless Thirring model, are worked out.Comment: 4 page

Hamiltonicity of 3-arc graphs

An arc of a graph is an oriented edge and a 3-arc is a 4-tuple $(v,u,x,y)$ of vertices such that both $(v,u,x)$ and $(u,x,y)$ are paths of length two. The 3-arc graph of a graph $G$ is defined to have vertices the arcs of $G$ such that two arcs $uv, xy$ are adjacent if and only if $(v,u,x,y)$ is a 3-arc of $G$. In this paper we prove that any connected 3-arc graph is Hamiltonian, and all iterative 3-arc graphs of any connected graph of minimum degree at least three are Hamiltonian. As a consequence we obtain that if a vertex-transitive graph is isomorphic to the 3-arc graph of a connected arc-transitive graph of degree at least three, then it is Hamiltonian. This confirms the well known conjecture, that all vertex-transitive graphs with finitely many exceptions are Hamiltonian, for a large family of vertex-transitive graphs. We also prove that if a graph with at least four vertices is Hamilton-connected, then so are its iterative 3-arc graphs.Comment: in press Graphs and Combinatorics, 201

Straight-line Drawability of a Planar Graph Plus an Edge

We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The characterization enables a linear-time testing algorithm to determine whether an almost-planar graph admits a straight-line drawing, and a linear-time drawing algorithm that constructs such a drawing, if it exists. We also show that some almost-planar graphs require exponential area for a straight-line drawing

Combinatorial Properties of Triangle-Free Rectangle Arrangements and the Squarability Problem

We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of rectangles intersects. First, we investigate combinatorial contact arrangements, i.e., arrangements of interior-disjoint rectangles, with a triangle-free intersection graph. We show that such rectangle arrangements are in bijection with the 4-orientations of an underlying planar multigraph and prove that there is a corresponding geometric rectangle contact arrangement. Moreover, we prove that every triangle-free planar graph is the contact graph of such an arrangement. Secondly, we introduce the question whether a given rectangle arrangement has a combinatorially equivalent square arrangement. In addition to some necessary conditions and counterexamples, we show that rectangle arrangements pierced by a horizontal line are squarable under certain sufficient conditions.Comment: 15 pages, 13 figures, extended version of a paper to appear at the International Symposium on Graph Drawing and Network Visualization (GD) 201

Convexity-Increasing Morphs of Planar Graphs

We study the problem of convexifying drawings of planar graphs. Given any planar straight-line drawing of an internally 3-connected graph, we show how to morph the drawing to one with strictly convex faces while maintaining planarity at all times. Our morph is convexity-increasing, meaning that once an angle is convex, it remains convex. We give an efficient algorithm that constructs such a morph as a composition of a linear number of steps where each step either moves vertices along horizontal lines or moves vertices along vertical lines. Moreover, we show that a linear number of steps is worst-case optimal. To obtain our result, we use a well-known technique by Hong and Nagamochi for finding redrawings with convex faces while preserving y-coordinates. Using a variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and Nagamochi's result which comes with a better running time. This is of independent interest, as Hong and Nagamochi's technique serves as a building block in existing morphing algorithms.Comment: Preliminary version in Proc. WG 201

On vertex coloring without monochromatic triangles

We study a certain relaxation of the classic vertex coloring problem, namely, a coloring of vertices of undirected, simple graphs, such that there are no monochromatic triangles. We give the first classification of the problem in terms of classic and parametrized algorithms. Several computational complexity results are also presented, which improve on the previous results found in the literature. We propose the new structural parameter for undirected, simple graphs -- the triangle-free chromatic number $\chi_3$. We bound $\chi_3$ by other known structural parameters. We also present two classes of graphs with interesting coloring properties, that play pivotal role in proving useful observation about our problem. We give/ask several conjectures/questions throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac

Size effect on magnetism of Fe thin films in Fe/Ir superlattices

In ferromagnetic thin films, the Curie temperature variation with the thickness is always considered as continuous when the thickness is varied from $n$ to $n+1$ atomic planes. We show that it is not the case for Fe in Fe/Ir superlattices. For an integer number of atomic planes, a unique magnetic transition is observed by susceptibility measurements, whereas two magnetic transitions are observed for fractional numbers of planes. This behavior is attributed to successive transitions of areas with $n$ and $n+1$ atomic planes, for which the $T_c$'s are not the same. Indeed, the magnetic correlation length is presumably shorter than the average size of the terraces. Monte carlo simulations are performed to support this explanation.Comment: LaTeX file with Revtex, 5 pages, 5 eps figures, to appear in Phys. Rev. Let

Can GPR4 be a potential therapeutic target for COVID-19?

This study was supported in part by the North Carolina COVID-19 Special State Appropriations. Research in the author's laboratory was also supported by a grant from the National Institutes of Health (R15DK109484, to LY).Coronavirus disease 19 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), first emerged in late 2019 and has since rapidly become a global pandemic. SARS-CoV-2 infection causes damages to the lung and other organs. The clinical manifestations of COVID-19 range widely from asymptomatic infection, mild respiratory illness to severe pneumonia with respiratory failure and death. Autopsy studies demonstrate that diffuse alveolar damage, inflammatory cell infiltration, edema, proteinaceous exudates, and vascular thromboembolism in the lung as well as extrapulmonary injuries in other organs represent key pathological findings. Herein, we hypothesize that GPR4 plays an integral role in COVID-19 pathophysiology and is a potential therapeutic target for the treatment of COVID-19. GPR4 is a pro-inflammatory G protein-coupled receptor (GPCR) highly expressed in vascular endothelial cells and serves as a “gatekeeper� to regulate endothelium-blood cell interaction and leukocyte infiltration. GPR4 also regulates vascular permeability and tissue edema under inflammatory conditions. Therefore, we hypothesize that GPR4 antagonism can potentially be exploited to mitigate the hyper-inflammatory response, vessel hyper-permeability, pulmonary edema, exudate formation, vascular thromboembolism and tissue injury associated with COVID-19.ECU Open Access Publishing Support Fun