On the Representability of Line Graphs

A graph G=(V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x,y) is in E for each x not equal to y. The motivation to study representable graphs came from algebra, but this subject is interesting from graph theoretical, computer science, and combinatorics on words points of view. In this paper, we prove that for n greater than 3, the line graph of an n-wheel is non-representable. This not only provides a new construction of non-representable graphs, but also answers an open question on representability of the line graph of the 5-wheel, the minimal non-representable graph. Moreover, we show that for n greater than 4, the line graph of the complete graph is also non-representable. We then use these facts to prove that given a graph G which is not a cycle, a path or a claw graph, the graph obtained by taking the line graph of G k-times is guaranteed to be non-representable for k greater than 3.Comment: 10 pages, 5 figure

Restricted non-separable planar maps and some pattern avoiding permutations

Tutte founded the theory of enumeration of planar maps in a series of papers in the 1960s. Rooted non-separable planar maps are in bijection with West-2-stack-sortable permutations, beta(1,0)-trees introduced by Cori, Jacquard and Schaeffer in 1997, as well as a family of permutations defined by the avoidance of two four letter patterns. In this paper we give upper and lower bounds on the number of multiple-edge-free rooted non-separable planar maps. We also use the bijection between rooted non-separable planar maps and a certain class of permutations, found by Claesson, Kitaev and Steingrimsson in 2009, to show that the number of 2-faces (excluding the root-face) in a map equals the number of occurrences of a certain mesh pattern in the permutations. We further show that this number is also the number of nodes in the corresponding beta(1,0)-tree that are single children with maximum label. Finally, we give asymptotics for some of our enumerative results.Comment: 18 pages, 14 figure

Effects of CSF hormones and ionic composition on salt/water metabolism

This collaborative agreement between Drs. Severs and Keil began in 1981, arising from a continuing interest in the issue of what, exactly, are the consequences of headward fluid shifts during manned spaceflight. Such shifts were recognized early by both U.S. and Soviet Scientists because of signs and symptoms referable to the head. Some of these include disturbed vision, puffiness in the face and periorbital areas, headache, vestibular dysfunction and distended jugular veins. We posited that the fluid shift had an immediate effect on the brain, and a long-term action requiring a neural interpretation of the flight environment. This would re-adjust both efferent neural as well as hormonal mechanisms to sustain cardiovascular and fluid/electrolyte balance consonent with survival in microgravity. Work along these lines is summarized

A Crisis of Democratic Legitimacy? It’s about Legitimation, Stupid! European Policy Brief No. 21, March 2014

Are we witnessing a crisis of democratic legitimacy? While citizens may lose trust in political authorities, democratic principles and ideals continue to exercise considerable appeal. This Policy Brief argues that this paradox must be understood as a crisis of legitimation. Research suggests that legitimacy is inherently subjective and must be constantly re-earned. Low levels of political trust can be explained as the result of the complexity of globalised yet fragmented societies. The present feeling of malaise calls for a redefinition of the relationship between citizens and the authorities by which they are ruled. If popular sovereignty is to mean anything in today’s age, it requires a new legitimising narrative

The Discrete Fundamental Group of the Associahedron, and the Exchange Module

The associahedron is an object that has been well studied and has numerous applications, particularly in the theory of operads, the study of non-crossing partitions, lattice theory and more recently in the study of cluster algebras. We approach the associahedron from the point of view of discrete homotopy theory. We study the abelianization of the discrete fundamental group, and show that it is free abelian of rank $\binom{n+2}{4}$. We also find a combinatorial description for a basis of this rank. We also introduce the exchange module of the type $A_n$ cluster algebra, used to model the relations in the cluster algebra. We use the discrete fundamental group to the study of exchange module, and show that it is also free abelian of rank $\binom{n+2}{3}$.Comment: 16 pages, 4 figure

Gap Junction Channels and Cardiac Impulse Propagation

The role of gap junction channels on cardiac impulse propagation is complex. This review focuses on the differential expression of connexins in the heart and the biophysical properties of gap junction channels under normal and disease conditions. Structural determinants of impulse propagation have been gained from biochemical and immunocytochemical studies performed on tissue extracts and intact cardiac tissue. These have defined the distinctive connexin coexpression patterns and relative levels in different cardiac tissues. Functional determinants of impulse propagation have emerged from electrophysiological experiments carried out on cell pairs. The static properties (channel number and conductance) limit the current flow between adjacent cardiomyocytes and thus set the basic conduction velocity. The dynamic properties (voltage-sensitive gating and kinetics of channels) are responsible for a modulation of the conduction velocity during propagated action potentials. The effect is moderate and depends on the type of Cx and channel. For homomeric-homotypic channels, the influence is small to medium; for homomeric-heterotypic channels, it is medium to strong. Since no data are currently available on heteromeric channels, their influence on impulse propagation is speculative. The modulation by gap junction channels is most prominent in tissues at the boundaries between cardiac tissues such as sinoatrial node-atrial muscle, atrioventricular node-His bundle, His bundle-bundle branch and Purkinje fibers-ventricular muscle. The data predict facilitation of orthodromic propagatio

Influence of V5/6-His Tag on the Properties of Gap Junction Channels Composed of Connexin43, Connexin40 or Connexin45

HeLa cells expressing wild-type connexin43, connexin40 or connexin45 and connexins fused with a V5/6-His tag to the carboxyl terminus (CT) domain (Cx43-tag, Cx40-tag, Cx45-tag) were used to study connexin expression and the electrical properties of gap junction channels. Immunoblots and immunolabeling indicated that tagged connexins are synthesized and targeted to gap junctions in a similar manner to their wild-type counterparts. Voltage-clamp experiments on cell pairs revealed that tagged connexins form functional channels. Comparison of multichannel and single-channel conductances indicates that tagging reduces the number of operational channels, implying interference with hemichannel trafficking, docking and/or channel opening. Tagging provoked connexin-specific effects on multichannel and single-channel properties. The Cx43-tag was most affected and the Cx45-tag, least. The modifications included (1) V j-sensitive gating of I j (V j, gap junction voltage; I j, gap junction current), (2) contribution and (3) kinetics of I j deactivation and (4) single-channel conductance. The first three reflect alterations of fast V j gating. Hence, they may be caused by structural and/or electrical changes on the CT that interact with domains of the amino terminus and cytoplasmic loop. The fourth reflects alterations of the ion-conducting pathway. Conceivably, mutations at sites remote from the channel pore, e.g., 6-His-tagged CT, affect protein conformation and thus modify channel properties indirectly. Hence, V5/6-His tagging of connexins is a useful tool for expression studies in vivo. However, it should not be ignored that it introduces connexin-dependent changes in both expression level and electrophysiological propertie