Virtually Abelian Quantum Walks

We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus on the easiest case of virtually Abelian groups, and introduce a technique to reduce the quantum walk to an equivalent one on an Abelian group with coin system having larger dimension. We apply the technique in the case of two quantum walks on virtually Abelian groups with planar Cayley graphs, finding the exact solution.Comment: 10 pages, 3 figure

Recognizing and Drawing IC-planar Graphs

IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$ vertices, we present an $O(n)$-time algorithm that computes a straight-line drawing of $G$ in quadratic area, and an $O(n^3)$-time algorithm that computes a straight-line drawing of $G$ with right-angle crossings in exponential area. Both these area requirements are worst-case optimal. We also show that it is NP-complete to test IC-planarity both in the general case and in the case in which a rotation system is fixed for the input graph. Furthermore, we describe a polynomial-time algorithm to test whether a set of matching edges can be added to a triangulated planar graph such that the resulting graph is IC-planar

Vitamin D Deficiency in Autism Spectrum Disorder: A Cross-Sectional Study

Vitamin D plays a role in central nervous system (CNS) development. Recent literature focused on Vitamin D status in children and adolescents with autism spectrum disorder (ASD), but with inconsistent results. Our case-control study is aimed at evaluating serum 25-hydroxyl-Vitamin D (25(OH)D) concentration in children with ASD (ASD group, n=54) compared to children affected by other neurological and psychiatric disorders (non-ASD group, n=36). All patients were admitted at the Complex Operative Unit of Child Neuropsychiatry, Polyclinic of Bari, Italy. 25(OH)D was quantified by chemiluminescence immunoassay and level defined as: Deficiency (<20 ng/mL); insufficiency (20-30); normality (30-100); toxicity (>100). Statistical analysis was performed using SPSS20 (significance<0.05). The ASD group showed 25(OH)D a mean level significantly lower than control (p=0.014). Multivariable logistic regression analysis showed an association between ASD and Vitamin D deficiency (p=0.006). The nature of such association is unclear. Vitamin D deficiency may probably act as a risk factor for the development of ASD. Further studies are needed to unravel the role of Vitamin D in ASD etiology and investigate its therapeutic potential

On the relevance of center vortices to QCD

In a numerical experiment, we remove center vortices from an ensemble of lattice SU(2) gauge configurations. This removal adds short-range disorder. Nevertheless, we observe long-range order in the modified ensemble: confinement is lost and chiral symmetry is restored (together with trivial topology), proving that center vortices are responsible for both phenomena. As for the Abelian monopoles, they survive but their percolation properties are lost.Comment: 4 pages, 5 figures; discussion expanded, text compressed... to appear in Phys. Rev. Let

Interaction of Wilson loops in confining vacuum

Nonperturbative and perturbative interaction mechanisms of Wilson loops in gluodynamics are studied within the background field formalism. The first one operates when distance between minimal surfaces of the loops is small and may be important for sea quark effects and strong decay processes. The second mechanism -- perturbative interaction in nonperturbative confining background is found to be physically dominant for all loop configurations characteristic of scattering process. It reduces to perturbative gluon exchanges at small distances, while at larger distances it corresponds to the t-channel exchange of (reggeized) glueball states. Comparison to other approaches is made and possible physical applications are discussed.Comment: LaTeX, 25 pages, 5 EPS-figure

Global Aspects of Abelian and Center Projections in SU(2) Gauge Theory

We show that the global aspects of Abelian and center projection of a SU(2) gauge theory on an arbitrary manifold are naturally described in terms of smooth Deligne cohomology. This is achieved through the introduction of a novel type of differential topological structure, called Cho structure. Half integral monopole charges appear naturally in this framework.Comment: 43 pages, no figures, requires AMS font files AMSSYM.DEF and amssym.tex. Completely rewritten, corrected and streamlined versio

Confinement and Chiral Symmetry Breaking via Domain-Like Structures in the QCD Vacuum

A qualitative mechanism for the emergence of domain structured background gluon fields due to singularities in gauge field configurations is considered, and a model displaying a type of mean field approximation to the QCD partition function based on this mechanism is formulated. Estimation of the vacuum parameters (gluon condensate, topological susceptibility, string constant and quark condensate) indicates that domain-like structures lead to an area law for the Wilson loop, nonzero topological susceptibility and spontaneous breakdown of chiral symmetry. Gluon and ghost propagators in the presence of domains are calculated explicitly and their analytical properties are discussed. The Fourier transforms of the propagators are entire functions and thus describe confined dynamical fields.Comment: RevTeX, 48 pages (32 pages + Appendices A-E), new references added [1,2,4,5] and minor formulae corrected for typographical error

Clinical, epidemiological, and therapeutic hallmarks of pyoderma gangrenosum: a case series of 35 patients

BackgroundOver the past few decades, advances in medical research and diagnostic tools have shed light on some aspects of pyoderma gangrenosum (PG). Nevertheless, the multifactorial etiology, pathogenesis, and optimal management strategies for PG need to be further investigated. To address these knowledge gaps and contribute to a better understanding of this complex dermatological disorder, we collected epidemiological, clinical, and therapeutic aspects of a case series of PG patients occurring in our department over the past 10 years.BackgroundOver the past few decades, advances in medical research and diagnostic tools have shed light on some aspects of pyoderma gangrenosum (PG). Nevertheless, the multifactorial etiology, pathogenesis, and optimal management strategies for PG need to be further investigated. To address these knowledge gaps and contribute to a better understanding of this complex dermatological disorder, we collected epidemiological, clinical, and therapeutic aspects of a case series of PG patients occurring in our department over the past 10 years.MethodsWe performed a single-centered, retrospective, observational study analyzing all cases with a diagnosis of PG observed at the Dermatology clinic of the Fondazione Policlinico A. Gemelli IRCCS Catholic University from January 1, 2013, to January 1, 2023. For each case, we retrieved demographic data, the presence of other skin and systemic conditions, and the histopathological and clinical characteristics of PG, such as clinical variant, number of lesions, disease localization, previous therapy, response to treatment, and occurrence of relapse.ResultsWe included 35 patients, 22 females and 13 males with a mean age of 40.0 years. Twenty patients (57.1%) had multiple localizations of disease, and the most commonly involved site was the lower limbs (85.7%). The lesions were mainly associated with inflammatory bowel diseases (51.4%) and hidradenitis suppurativa (37.1%). Clinical resolution with complete re-epithelialization was achieved in 25 patients (71.4%) with an average time of 20.8 months. On average, patients who underwent therapy with biological drugs had better outcomes.ConclusionsPG is a severe, rare, and pleomorphic disease associated with a broad spectrum of conditions. Corticosteroids remain the primary first-line approach for severe forms, but using biological immunosuppressants is promising

Evidence of asymmetries in the Aldebaran photosphere from multiwavelength lunar occultations

We have recorded three lunar occultations of Aldebaran (α Tau) at different telescopes and using various band-passes, from the ultraviolet to the far red. The data have been analysed using both model-dependent and model-independent methods. The derived uniform-disc angular diameter values have been converted to limb-darkened values using model atmosphere relations and are found in broad agreement among themselves and with previous literature values. The limb-darkened diameter is about 20.3 mas on average. However, we have found indications that the photospheric brightness profile of Aldebaran may have not been symmetric, a finding already reported by other authors for this and for similar late-type stars. At the sampling scale of our brightness profile, between 1 and 2 mas, the uniform and limb-darkened disc models may not be a good description for Aldebaran. The asymmetries appear to differ with wavelength and over the 137-d time span of our measurements. Surface spots appear as a likely explanation for the differences between observations and the models

Matter degrees of freedom and string breaking in Abelian projected quenched SU(2) QCD

In the Abelian projection the Yang--Mills theory contains Abelian gauge fields (diagonal degrees of freedom) and the Abelian matter fields (off-diagonal degrees) described by a complicated action. The matter fields are essential for the breaking of the adjoint string. We obtain numerically the effective action of the Abelian gauge and the Abelian matter fields in quenched SU(2) QCD and show that the Abelian matter fields provide an essential contribution to the total action even in the infrared region. We also observe the breaking of an Abelian analog of the adjoint string using Abelian operators. We show that the adjoint string tension is dominated by the Abelian and the monopole contributions similarly to the case of the fundamental particles. We conclude that the adjoint string breaking can successfully be described in the Abelian projection formalism.Comment: 16 pages, 10 figures, 2 table