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The k-token graph F k (G) of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It was proved that the algebraic connectivity of F k (G) equals the algebraic connectivity of G with a proof using random walks and interchange of processes on a weighted graph. However, no algebraic or combinatorial proof is known, and it would be a hit in the area. In this paper, we algebraically prove that the algebraic connectivity of F k (G) equals the one of G for new infinite families of graphs, such as trees, some graphs with hanging trees, and graphs with minimum degree large enough. Some examples of these families are the following: the cocktail party graph, the complement graph of a cycle, and the complete multipartite graph. [ABSTRACT FROM AUTHOR]

We describe, in a very explicit way, a method for determining the spectra and bases of all the corresponding eigenspaces of arbitrary lifts of graphs (regular or not). [ABSTRACT FROM AUTHOR]

Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are Cayley graphs of abelian groups. Such groups can be constructed using a generalization to Z n of the concept of congruence in Z . Here we use this approach to present some families of mixed graphs, which, for every fixed value of the degree, have an asymptotically large number of vertices as the diameter increases. In some cases, the results obtained are shown to be optimal. [ABSTRACT FROM AUTHOR]

A correction to the article "Dietary Total Antioxidant Capacity and Mortality in the PREDIMED Study" by P. Henríquez-Sánchez et al. which appeared in the December 8, 2021 issue is presented.

We present a method to derive the complete spectrum of the lift Γ α of a base digraph Γ , with voltage assignment α on a (finite) group G. The method is based on assigning to Γ a quotient-like matrix whose entries are elements of the group algebra C [ G ] , which fully represents Γ α . This allows us to derive the eigenvectors and eigenvalues of the lift in terms of those of the base digraph and the irreducible characters of G. Thus, our main theorem generalizes some previous results of Lovász and Babai concerning the spectra of Cayley digraphs. [ABSTRACT FROM AUTHOR]

This technique, described in 1978 by Gil-Vernet [[1]], is based on an open retroperitoneal approach through a lumbotomy, with nephrectomy of the native kidney and use of the recipient splenic artery, the renal vein, and the urinary pelvis for the arterial, venous, and urinary anastomoses, respectively. Besides, in this particular setting, specific benefits of robotic surgery can improve the recipient renal vein and splenic artery dissection, as well as facilitate the vascular anastomoses. Keywords: Robot-assisted kidney transplantation; Orthotopic kidney transplantation; Kidney transplantation; Minimally invasive surgery; Robotic surgical procedures EN Robot-assisted kidney transplantation Orthotopic kidney transplantation Kidney transplantation Minimally invasive surgery Robotic surgical procedures 2811 2813 3 08/05/21 20210701 NES 210701 Francesc Vigués and A. Breda are on behalf of ERUS RAKT Group. [Extracted from the article]

We introduce the concept of distance mean-regular graph, which can be seen as a generalization of both vertex-transitive and distance-regular graphs. Let $$\Gamma $$ be a graph with vertex set V, diameter D, adjacency matrix $$\varvec{A}$$ , and adjacency algebra $$\mathcal{A}$$ . Then, $$\Gamma $$ is distance mean-regular when, for a given $$u\in V$$ , the averages of the intersection numbers $$p_{ij}^h(u,v)=|\Gamma _i(u)\cap \Gamma _j(v)|$$ (number of vertices at distance i from u and distance j from v) computed over all vertices v at a given distance $$h\in \{0,1,\ldots ,D\}$$ from u, do not depend on u. In this work we study some properties and characterizations of these graphs. For instance, it is shown that a distance mean-regular graph is always distance degree-regular, and we give a condition for the converse to be also true. Some algebraic and spectral properties of distance mean-regular graphs are also investigated. We show that, for distance mean regular-graphs, the role of the distance matrices of distance-regular graphs is played for the so-called distance mean-regular matrices. These matrices are computed from a sequence of orthogonal polynomials evaluated at the adjacency matrix of $$\Gamma $$ and, hence, they generate a subalgebra of $$\mathcal{A}$$ . Some other algebras associated to distance mean-regular graphs are also characterized. [ABSTRACT FROM AUTHOR]

Let $$\Gamma $$ be a distance-regular graph with diameter d and Kneser graph $$K=\Gamma _d$$ , the distance- d graph of $$\Gamma $$ . We say that $$\Gamma $$ is partially antipodal when K has fewer distinct eigenvalues than $$\Gamma $$ . In particular, this is the case of antipodal distance-regular graphs ( K with only two distinct eigenvalues) and the so-called half-antipodal distance-regular graphs ( K with only one negative eigenvalue). We provide a characterization of partially antipodal distance-regular graphs (among regular graphs with $$d+1$$ distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex. This can be seen as a more general version of the so-called spectral excess theorem, which allows us to characterize those distance-regular graphs which are half-antipodal, antipodal, bipartite, or with Kneser graph being strongly regular. [ABSTRACT FROM AUTHOR]

Purpose: The aim of the present study was to assess the association between the dietary total antioxidant capacity, the dietary intake of different antioxidants and mortality in a Mediterranean population at high cardiovascular disease risk. Methods: A total of 7,447 subjects from the PREDIMED study (multicenter, parallel group, randomized controlled clinical trial), were analyzed treating data as an observational cohort. Different antioxidant vitamin intake and total dietary antioxidant capacity were calculated from a validated 137-item food frequency questionnaire at baseline and updated yearly. Deaths were ascertained through contact with families and general practitioners, review of medical records and consultation of the National Death Index. Cox regression models were fitted to assess the relationship between dietary total antioxidant capacity and mortality. Dietary total antioxidant capacity was estimated using ferric-reducing antioxidant power assays. Results: A total of 319 deaths were recorded after a median follow-up of 4.3 years. Subjects belonging to the upper quintile of antioxidant capacity were younger, ex-smokers, with high educational level, and more active and had higher alcohol intake. Multivariable-adjusted models revealed no statistically significant difference between total dietary antioxidant capacity and mortality (Q5 vs. Q1 ref HR 0.85; 95 % CI 0.60-1.20) neither for the intake of all the vitamins studied. Conclusions: No statistically significant association was found between antioxidant capacity and total mortality in elderly subjects at high cardiovascular risk. [ABSTRACT FROM AUTHOR]

Important health benefits have been reported recently to phytate intake. This includes the prevention of pathological calcifications such as renal calculi, dental calculi and cardiovascular calcification, due its action as crystallization inhibitor of calcium salts, and as preventive of cancer. The aim of this study was to establish a relation between the intake of phytate, through consumption of typical components of the Mediterranean diet (including nuts), and its excretion in urine. This study recruited participants from subjects included in a larger trial (PREDIMED) of food habits, that were assigned to one of two diet groups: (1) the Mediterranean diet with low proportion of phytate-rich food group, where participants were asked to maintain their usual diet; and (2) the Mediterranean diet with high proportion of phytate-rich food group, where participants were asked to increase phytate-rich foods in their diet. Phytate intake was assessed on the basis of a food frequency questionnaire. Urinary phytate excretion was determined in 2-h urine samples. The overall phytate consumption of the Mediterranean diet with high proportion of phytate-rich food group (672 ± 50 mg) was significantly higher than the Mediterranean diet with low proportion of phytate-rich food group (422 ± 34 mg), representing a 59% difference. Urinary phytate excretion was also significantly higher (54%) in the Mediterranean diet with high proportion of phytate-rich food group (1,016 ± 70 μg/L) than the Mediterranean diet with low proportion of phytate-rich food group (659 ± 45 μg/L). Mediterranean diets high in whole cereals, legumes and nuts compared to Mediterranean diets low in these phytate-rich foods increase the urinary phytate excretion in humans. [ABSTRACT FROM AUTHOR]

Objective:To evaluate associations between components of the Mediterranean diet and circulating markers of inflammation in a large cohort of asymptomatic subjects at high risk for cardiovascular disease.Subjects/Methods:A total of 339 men and 433 women aged between 55 and 80 years at high cardiovascular risk because of presence of diabetes or at least three classical cardiovascular risk factors, food consumption was determined by a semi-quantitative food frequency questionnaire. Serum concentrations of high-sensitivity C-reactive protein (CRP) were measured by immunonephelometry and those of interleukin-6 (IL-6), intracellular adhesion molecule-1 (ICAM-1) and vascular cell adhesion molecule-1 (VCAM-1) by enzyme-linked immunosorbent assay.Results:After adjusting for age, gender, body mass index, diabetes, smoking, use of statins, non-steroidal antiinflammatory drugs and aspirin, a higher consumption of fruits and cereals was associated with lower concentrations of IL-6 (P for trend 0.005;both). Subjects with the highest consumption of nuts and virgin olive oil showed the lowest concentrations of VCAM-1, ICAM-1, IL-6 and CRP; albeit only for ICAM-1 was this difference statistically significant in the case of nuts (for trend 0.003) and for VCAM-1 in the case of virgin olive oil (P for trend 0.02). Participants with higher adherence to the Mediterranean-type diet did not show significantly lower concentrations of inflammatory markers (P<0.1 for VCAM-1 and ICAM-1).Conclusions:The consumption of some typical Mediterranean foods (fruits, cereals, virgin olive oil and nuts) was associated with lower serum concentrations of inflammatory markers especially those related to endothelial function, in subjects with high cardiovascular risk living in a Mediterranean country.European Journal of Clinical Nutrition (2008) 62, 651–659; doi:10.1038/sj.ejcn.1602762; published online 18 April 2007 [ABSTRACT FROM AUTHOR]