Edge states and zero modes in quadratic fermionic models on a 1-D lattice

In una formulazione rigorosa della teoria quantistica, la definizione della varietà Riemanniana spaziale su cui il sistema è vincolato gioca un ruolo fondamentale. La presenza di un bordo sottolinea l'aspetto quantistico del sistema: l'imposizione di condizioni al contorno determina la discretizzazione degli autovalori del Laplaciano, come accade con condizioni note quali quelle periodiche, di Neumann o di Dirichlet. Tuttavia, non sono le uniche possibili. Qualsiasi condizione al bordo che garantisca l'autoaggiunzione dell' operatore Hamiltoniano è ammissibile. Tutte le possibili boundary conditions possono essere catalogate a partire dalla richiesta di conservazione del flusso al bordo della varietà. Alcune possibili condizioni al contorno, permettono l'esistenza di stati legati al bordo, cioè autostati dell' Hamiltoniana con autovalori negativi, detti edge states. Lo scopo di questa tesi è quello di investigare gli effetti di bordo in sistemi unidimensionali implementati su un reticolo discreto, nella prospettiva di capire come simulare proprietà di edge in un reticolo ottico. Il primo caso considerato è un sistema di elettroni liberi. La presenza di edge states è completamente determinata dai parametri di bordo del Laplaciano discreto. Al massimo due edge states emergono, e possono essere legati all' estremità destra o sinistra della catena a seconda delle condizioni al contorno. Anche il modo in cui decadono dal bordo al bulk e completamente determinato dalla scelta delle condizioni. Ammettendo un' interazione quadratica tra siti primi vicini, un secondo tipo di stati emerge in relazione sia alle condizioni al contorno che ai parametri del bulk. Questi stati sono chiamati zero modes, in quanto esiste la possibilità che siano degeneri con lo stato fondamentale. Per implementare le più generali condizioni al contorno, specialmente nel caso interagente, è necessario utilizzare un metodo generale per la diagonalizzazione, che estende la tecnica di Lieb-Shultz-Mattis per Hamiltoniane quadratiche a matrici complesse.

Le funzioni armoniche e le formule di media

In questa tesi studiamo le proprietà fondamentali delle funzioni armoniche. Ricaviamo le formule di media mostrando alcune proprietà importanti, quali la disuguaglianza di Harnack, il teorema di Liouville, il principio del massimo debole e forte. Infine, illustriamo un criterio di risolubilità per il problema di Dirichlet per il Laplaciano in un arbitrario dominio limitato di R^n tramite un metodo noto come metodo di Perron per le funzioni subarmoniche.

Stime Integrali su Gruppi di Tipo H e Principio Forte di Continuazione Unica

Lo scopo di questa tesi è dimostrare il Principio Forte di Continuazione Unica per opportune soluzioni di un'equazione di tipo Schrödinger Du=Vu, ove D è il sub-Laplaciano canonico di un gruppo di tipo H e V è un potenziale opportuno. Nel primo capitolo abbiamo esposto risultati già noti in letteratura sui gruppi di tipo H: partendo dalla definizione di tali gruppi, abbiamo fornito un'utile caratterizzazione in termini "elementari" che permette di esplicitare la soluzione fondamentale dei relativi sub-Laplaciani canonici. Nel secondo capitolo abbiamo mostrato una formula di rappresentazione per funzioni lisce sui gruppi di tipo H, abbiamo dimostrato una forma forte del Principio di Indeterminazione di Heisenberg (sempre nel caso di gruppi di tipo H) e abbiamo fornito una formula per la variazione prima dell'integrale di Dirichlet associato a Du=Vu. Nel terzo capitolo, infine, abbiamo analizzato le proprietà di crescita di funzioni di frequenza, utili a dimostrare le stime integrali che implicano in modo piuttosto immediato il Principio Forte di Continuazione Unica, principale oggetto del nostro studio.

Formula integrale di Poisson

Il tema centrale di questa tesi è lo studio del problema di Dirichlet per il Laplaciano in R^2 usando le serie di Fourier. Il problema di Dirichlet per il Laplaciano consiste nel determinare una funzione f armonica e regolare in un dominio limitato D quando sono noti i valori che f assume sul suo bordo. Ammette una sola soluzione, ma non esistono criteri generali per ricavarla. In questa tesi si mostra come la formula integrale di Poisson, sotto determinate condizioni, risolva il problema di Dirichlet in R^2 e in R^n.

Renal insufficiency is independently associated with a distal distribution pattern of symptomatic lower-limb atherosclerosis

Objectives The purpose of this study was to assess the impact of renal insufficiency (RI) on the distribution pattern of peripheral arterial disease (PAD). We hypothesised that RI is associated with a distally accentuated involvement of the peripheral arterial tree. Design This is a retrospective analysis. Materials and Methods Analysis was based on a consecutive series of 2709 patients with chronic PAD of atherosclerotic origin undergoing primary endovascular treatment of lower-extremity arteries. Atherosclerotic pattern was grouped into femoropopliteal (n = 2085) and infragenicular (n = 892) disease according to target lesions treated while using iliac disease (n = 1133) as reference. Univariable and multivariable multinomial regression analyses were performed to assess relation with RI. Results are shown as relative risk ratio (RRRs) with 95% confidence intervals (95% CIs). A p < 0.05 was considered statistically significant. RI was defined as glomerular filtration rate (GFR) < 60 ml min−1 1.73 m−2. Results Presence of RI was an independent risk factor for a centrifugal lesion pattern (RRR 1.48, 95% CI: 1.17–1.86, p = 0.001). Moreover, a decrease in GFR by 10 ml min−1 1.73 m−2 was associated with an RRR of 1.08 for below-the-knee arterial disease (95% CI: 1.03–1.13, p = 0.003). Conclusion Presence and severity of RI are independent predictors of a distal obstructive pattern in patients with symptomatic PAD.

Reporting of research quality characteristics of studies published in 6 major clinical dental specialty journals

The objective of this article was to record reporting characteristics related to study quality of research published in major specialty dental journals with the highest impact factor (Journal of Endodontics, Journal of Oral and Maxillofacial Surgery, American Journal of Orthodontics and Dentofacial Orthopedics; Pediatric Dentistry, Journal of Clinical Periodontology, and International Journal of Prosthetic Dentistry). The included articles were classified into the following 3 broad subject categories: (1) cross-sectional (snap-shot), (2) observational, and (3) interventional. Multinomial logistic regression was conducted for effect estimation using the journal as the response and randomization, sample calculation, confounding discussed, multivariate analysis, effect measurement, and confidence intervals as the explanatory variables. The results showed that cross-sectional studies were the dominant design (55%), whereas observational investigations accounted for 13%, and interventions/clinical trials for 32%. Reporting on quality characteristics was low for all variables: random allocation (15%), sample size calculation (7%), confounding issues/possible confounders (38%), effect measurements (16%), and multivariate analysis (21%). Eighty-four percent of the published articles reported a statistically significant main finding and only 13% presented confidence intervals. The Journal of Clinical Periodontology showed the highest probability of including quality characteristics in reporting results among all dental journals.

America's Shifting Color Line? Reexamining Determinants of Latino Racial Self-Identification

Objectives. Latinos are the nation's largest minority group and will double in size by 2050. Their size coupled with the fact that Latinos do not constitute a separate race raises questions about Latinos' incorporation into the U. S. racial hierarchy. This article explores patterns of Latino racial identity formation, examining the determinants of racial identity. Methods. Using the 2006 Latino National Survey, I estimate multinomial logit and ordered probit models of identification choices. Results. Latino racial identity is strongly associated with several factors, including socioeconomic status, measures of perceived discrimination and commonality, and measures of acculturation/assimilation. Most Latinos have a broader, more complex understanding of race. Furthermore, some Latinos do believe that they occupy a unique position in the racial hierarchy. Conclusions. The results suggest that the color line W. E. DuBois argued has long divided our nation may eventually shift.

Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word “strongly” is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H∞(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Rates Of Obesity And Incidence Of Diabetes In Hispanics In The United States: An Examination Of The Epidemiological Paradox

Using pooled data from the 2008-2011 National Health Interview Survey and employing multinomial and binomial logistic regression methods, this research examines disparities in rates of obesity and incidence of diabetes between individual Hispanic subgroups in comparison to non-Hispanic whites and blacks. Immigration status(including nativity, duration in the United States, and citizenship status) is hypothesized to play a central role in rates and obesity and incidence of diabetes. Unlike Cuban-Americans, Mexican-Americans, Puerto Ricans, and other Hispanics were more likely to be overweight as well as obese when compared to non-Hispanic whites. Mexican-Americans had the only significance in prevalence of type 2 diabetes in comparison to non-Hispanic whites. Both of these health outcomes are strongly associated with the various immigration variables.

Isospectrality and Heat Content

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schrodinger operators acting in L-2[0,1] with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.

Association of cardiovascular risk factors with pattern of lower limb atherosclerosis in 2659 patients undergoing angioplasty

OBJECTIVES: Aim of this study is to correlate distribution pattern of lower limb atherosclerosis with cardiovascular risk factor profile of patients with peripheral arterial occlusive disease (PAD). PATIENTS AND METHODS: Analysis is based on a consecutive series of 2659 patients (1583 men, 1076 women, 70+/-11 years) with chronic PAD of atherosclerotic origin undergoing primary endovascular treatment of lower extremity arteries. Pattern of atherosclerosis was grouped into iliac (n=1166), femoropopliteal (n=2151) and infrageniculate (n=888) disease defined according to target lesions treated. A multivariable multinomial logistic regression analysis was performed to assess relation with age, gender and classical cardiovascular risk factors (diabetes mellitus, arterial hypertension, hypercholesterolemia, cigarette smoking) using femoropopliteal disease as reference. RESULTS: Iliac disease was associated with younger age (RRR 0.95 per year of age, 95%-CI 0.94-0.96, p<0.001), male gender (RRR 1.32, 95%-CI 1.09-1.59, p=0.004) and cigarette smoking (RRR 2.02, 95%-CI 1.68-2.42, p<0.001). Infrageniculate disease was associated with higher age (RRR 1.02, 95%-CI 1.01-1.02, p<0.001), male gender (RRR 1.23, 95%-CI 1.06-1.41, p=0.005) and diabetes mellitus (RRR 1.68, 95%-CI 1.47-1.92, p<0.001). Hypercholesterolemia was less prevalent in patients with lesions below the knee (RRR 0.82, 95%-CI 0.71-0.94, p=0.006), whereas no distinct pattern was apparent related to arterial hypertension. CONCLUSION: Clinical phenotype of peripheral atherosclerosis varies with prevalence of cardiovascular risk factors suggesting differences in mechanisms involved in iliac as compared with infrageniculate lesions. Identification of molecular mechanism might have influence on future therapeutic strategies in PAD patients.

Posterior Simulation in the Generalized Linear Model with Semiparmetric Random Effects

Generalized linear mixed models with semiparametric random effects are useful in a wide variety of Bayesian applications. When the random effects arise from a mixture of Dirichlet process (MDP) model, normal base measures and Gibbs sampling procedures based on the Pólya urn scheme are often used to simulate posterior draws. These algorithms are applicable in the conjugate case when (for a normal base measure) the likelihood is normal. In the non-conjugate case, the algorithms proposed by MacEachern and Müller (1998) and Neal (2000) are often applied to generate posterior samples. Some common problems associated with simulation algorithms for non-conjugate MDP models include convergence and mixing difficulties. This paper proposes an algorithm based on the Pólya urn scheme that extends the Gibbs sampling algorithms to non-conjugate models with normal base measures and exponential family likelihoods. The algorithm proceeds by making Laplace approximations to the likelihood function, thereby reducing the procedure to that of conjugate normal MDP models. To ensure the validity of the stationary distribution in the non-conjugate case, the proposals are accepted or rejected by a Metropolis-Hastings step. In the special case where the data are normally distributed, the algorithm is identical to the Gibbs sampler.

Discordant responses to potent antiretroviral treatment in previously naive HIV-1-infected adults initiating treatment in resource-constrained countries: the antiretroviral therapy in low-income countries (ART-LINC) collaboration

OBJECTIVES: To assess the frequency of and risk factors for discordant responses at 6 months on highly active antiretroviral therapy (HAART) in previously treatment-naive HIV patients from resource-limited countries. METHODS: The Antiretroviral Therapy in Low-Income Countries Collaboration is a network of clinics providing care and treatment to HIV-infected patients in Africa, Latin America, and Asia. Patients who initiated therapy between 1996 and 2004, were aged 16 years or older, and had a baseline CD4 cell count were included in this analysis. Responses were defined based on plasma viral load (PVL) and CD4 cell count at 6 months as complete virologic and immunologic (VR(+)IR(+)), virologic only (VR(+)IR(-)), immunologic only (VR(-)IR(+)), and nonresponse (VR(-)IR(-)). Multinomial logistic regression was used to assess the association between therapy responses and clinical and demographic variables. RESULTS: Of the 3111 patients eligible for analysis, 1914 had available information at 6 months of therapy: 1074 (56.1%) were VR(+)IR(+), 364 (19.0%) were VR(+)IR(-), 283 (14.8%) were (VR(-)IR(+)), and 193 (10.1%) were VR(-)IR(-). OF THE 3111 patients eligible for analysis, 1914 had available information at 6 months of therapy: 1074 (56.1%) were VRIR, 364 (19.0%) were VRIR, 283 (14.8%) were (VRIR), and 193 (10.1%) were VRIR. Compared with complete responders, virologic-only responders were older, had a higher baseline CD4 cell count, had a lower baseline PVL, and were more likely to have received a nonstandard HAART regimen; immunologic-only responders were younger, had a lower baseline CD4 cell count, had a higher baseline PVL, and were more likely to have received a protease inhibitor-based regimen. CONCLUSIONS: The frequency of and risk factors for discordant responses were comparable to those observed in developed countries. Longer follow-up is needed to assess the long-term impact of discordant responses on mortality in these resource-limited settings.

Incorporating Latent Variables into Discrete Choice Models - A Simultaneous Estimation Approach Using SEM Software

Integrated choice and latent variable (ICLV) models represent a promising new class of models which merge classic choice models with the structural equation approach (SEM) for latent variables. Despite their conceptual appeal, applications of ICLV models in marketing remain rare. We extend previous ICLV applications by first estimating a multinomial choice model and, second, by estimating hierarchical relations between latent variables. An empirical study on travel mode choice clearly demonstrates the value of ICLV models to enhance the understanding of choice processes. In addition to the usually studied directly observable variables such as travel time, we show how abstract motivations such as power and hedonism as well as attitudes such as a desire for flexibility impact on travel mode choice. Furthermore, we show that it is possible to estimate such a complex ICLV model with the widely available structural equation modeling package Mplus. This finding is likely to encourage more widespread application of this appealing model class in the marketing field.