Geometric aspects of 2-walk-regular graphs

A $t$-walk-regular graph is a graph for which the number of walks of given length between two vertices depends only on the distance between these two vertices, as long as this distance is at most $t$. Such graphs generalize distance-regular graphs and $t$-arc-transitive graphs. In this paper, we will focus on 1- and in particular 2-walk-regular graphs, and study analogues of certain results that are important for distance regular graphs. We will generalize Delsarte's clique bound to 1-walk-regular graphs, Godsil's multiplicity bound and Terwilliger's analysis of the local structure to 2-walk-regular graphs. We will show that 2-walk-regular graphs have a much richer combinatorial structure than 1-walk-regular graphs, for example by proving that there are finitely many non-geometric 2-walk-regular graphs with given smallest eigenvalue and given diameter (a geometric graph is the point graph of a special partial linear space); a result that is analogous to a result on distance-regular graphs. Such a result does not hold for 1-walk-regular graphs, as our construction methods will show

Multimodal agent interfaces and system architectures for health and fitness companions

Multimodal conversational spoken dialogues using physical and virtual agents provide a potential interface to motivate and support users in the domain of health and fitness. In this paper we present how such multimodal conversational Companions can be implemented to support their owners in various pervasive and mobile settings. In particular, we focus on different forms of multimodality and system architectures for such interfaces

Some families of orthogonal polynomials of a discrete variable and their applications to graphs and codes

We present some related families of orthogonal polynomials of a discrete variable and survey some of their applications in the study of (distance-regular) graphs and (completely regular) codes. One of the main peculiarities of such orthogonal systems is their non-standard normalization condition, requiring that the square norm of each polynomial must equal its value at a given point of the mesh. For instance, when they are de¯ned from the spectrum of a graph, one of these families is the system of the pre- distance polinomials which, in the case of distance-regular graphs, turns out to be the sequence of distance polinomials. The applications range from (quasi-spectral) char- acterizations of distance-regular graphs, walk-regular graphs, local distance-regularity and completely regular codes, to some results on representation theory

Combinatorial vs. algebraic characterizations of pseudo-distance-regularity around a set

Given a simple connected graph $\Gamma$ and a subset of its vertices $C$, the pseudo-distance-regularity around $C$ generalizes, for not necessarily regular graphs, the notion of completely regular code. Up to now, most of the characterizations of pseudo-distance-regularity has been derived from a combinatorial definition. In this paper we propose an algebraic (Terwilliger-like) approach to this notion, showing its equivalence with the combinatorial one. This allows us to give new proofs of known results, and also to obtain new characterizations which do not depend on the so-called $C$-spectrum of $\Gamma$, but only on the positive eigenvector of its adjacency matrix. In the way, we also obtain some results relating the local spectra of a vertex set and its antipodal. As a consequence of our study, we obtain a new characterization of a completely regular code $C$, in terms of the number of walks in $\Gamma$ with an endvertex in $C$

Edge distance-regular graphs

* distance-regularity; * local spectra; * predistance polynomials; * the spectral excess theorem; * generalized odd graphsEdge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edge-distance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.Peer ReviewedPostprint (published version

Edge-distance-regular graphs

Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a graph Γ with adjacency matrix A is edge-distance-regular when it is distance-regular around each of its edges and with the same intersection numbers for any edge taken as a root. In this paper we study this concept, give some of its properties, such as the regularity of Γ, and derive some characterizations. In particular, it is shown that a graph is edge-distance-regular if and only if its k-incidence matrix is a polynomial of degree k in A multiplied by the (standard) incidence matrix. Also, the analogue of the spectral excess theorem for distance-regular graphs is proved, so giving a quasi-spectral characterization of edgedistance-regularity. Finally, it is shown that every nonbipartite graph which is both distance-regular and edge-distance-regular is a generalized odd graph.Preprin

Contract Aware Components, 10 years after

The notion of contract aware components has been published roughly ten years ago and is now becoming mainstream in several fields where the usage of software components is seen as critical. The goal of this paper is to survey domains such as Embedded Systems or Service Oriented Architecture where the notion of contract aware components has been influential. For each of these domains we briefly describe what has been done with this idea and we discuss the remaining challenges.Comment: In Proceedings WCSI 2010, arXiv:1010.233

A Transcriptomic Approach to Search for Novel Phenotypic Regulators in McArdle Disease

McArdle disease is caused by lack of glycogen phosphorylase (GP) activity in skeletal muscle. Patients experience exercise intolerance, presenting as early fatigue and contractures. In this study, we investigated the effects produced by a lack of GP on several genes and proteins of skeletal muscle in McArdle patients. Muscle tissue of 35 patients and 7 healthy controls were used to identify abnormalities in the patients' transcriptomic profile using low-density arrays. Gene expression was analyzed for the influence of variables such as sex and clinical severity. Differences in protein expression were studied by immunoblotting and 2D electrophoresis analysis, and protein complexes were examined by two-dimensional, blue native gel electrophoresis (BN-PAGE). A number of genes including those encoding acetyl-coA carboxylase beta, m-cadherin, calpain III, creatine kinase, glycogen synthase (GS), and sarcoplasmic reticulum calcium ATPase 1 (SERCA1), were found to be downregulated in patients. Specifically, compared to controls, GS and SERCA1 proteins were reduced by 50% and 75% respectively; also, unphosphorylated GS and SERCA1 were highly downregulated. On BN-PAGE analysis, GP was present with GS in two muscle protein complexes. Our findings revealed some issues that could be important in understanding the physiological consequences of McArdle disease: (i) SERCA1 downregulation in patients could result in impaired calcium transport in type II (fast-twitch) muscle fibers, leading to early fatigability during exercise tasks involving type II fibers (which mostly use glycolytic metabolism), i.e. isometric exercise, lifting weights or intense dynamic exercise (stair climbing, bicycling, walking at a very brisk pace), (ii) GP and GS were found together in two protein complexes, which suggests a new regulatory mechanism in the activity of these glycogen enzymes

Tectono-thermal history of an exhumed thrust-sheet-top basin : an example from the south Pyrenean thrust belt

This paper presents a new balanced structural cross-section of the Jaca thrust-sheet-top basin of the southern Pyrenees combined with paleo-thermometry and apatite fission track (AFT) thermochronology data. The cross-section, based on field data and interpretation of industrial seismic reflection profiles, allows refinement of previous interpretations of the south-directed thrust system, involving the identification of new thrust faults, and of the kinematic relationships between basement and cover thrusts from the middle Eocene to the early Miocene. AFT analysis shows a southward decrease in the level of fission track resetting, from totally reset Paleozoic rocks and lower Eocene turbidites (indicative of heating to Tmax>~120°C), to partially reset middle Eocene turbidites and no/very weak resetting in the upper Eocene-lower Oligocene molasse (Tmax<~60°C). AFT results indicate a late Oligocene-early Miocene cooling event throughout the Axial Zone and Jaca Basin. Paleo-maximum temperatures determined by vitrinite reflectance measurements and Raman spectroscopy of carbonaceous material reach up to ~240°C at the base of the turbidite succession. Inverse modelling of AFT and vitrinite reflectance data with the QTQt software for key samples show compatibility between vitrinite-derived Tmax and the AFT reset level for most of the samples. However, they also suggest that the highest temperatures determined in the lowermost turbidites correspond to a thermal anomaly rather than burial heating, possibly due to fluid circulation during thrust activity. From these results, we propose a new sequential restoration of the south Pyrenean thrust system propagation and related basin evolution