Dirac-like approach for consistent discretizations of classical constrained theories

We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the constraint surface and the Poisson or Dirac bracket structure. The conditions for the preservation of the constraints are more stringent than in the continuous case and as a consequence some of the continuum constraints become second class upon discretization and need to be solved by fixing their associated Lagrange multipliers. The gauge invariance of the discrete theory is encoded in a set of arbitrary functions that appear in the generating function of the evolution equations. The resulting scheme is general enough to accommodate the treatment of field theories on the lattice. This paper attempts to clarify and put on sounder footing a discretization technique that has already been used to treat a variety of systems, including Yang--Mills theories, BF-theory and general relativity on the lattice.Comment: 11 pages, RevTe

A finite spin-foam-based theory of three and four dimensional quantum gravity

Starting from Ooguri's construction for $BF$ theory in three (and four) dimensions, we show how to construct a well defined theory with an infinite number of degrees of freedom. The spin network states that are kept invariant by the evolution operators of the theory are exact solutions of the Hamiltonian constraint of quantum gravity proposed by Thiemann. The resulting theory is the first example of a well defined, finite, consistent, spin-foam based theory in a situation with an infinite number of degrees of freedom. Since it solves the quantum constraints of general relativity it is also a candidate for a theory of quantum gravity. It is likely, however, that the solutions constructed correspond to a spurious sector of solutions of the constraints. The richness of the resulting theory makes it an interesting example to be analyzed by forthcoming techniques that construct the semi-classical limit of spin network quantum gravity

The large cosmological constant approximation to classical and quantum gravity: model examples

We have recently introduced an approach for studying perturbatively classical and quantum canonical general relativity. The perturbative technique appears to preserve many of the attractive features of the non-perturbative quantization approach based on Ashtekar's new variables and spin networks. With this approach one can find perturbatively classical observables (quantities that have vanishing Poisson brackets with the constraints) and quantum states (states that are annihilated by the quantum constraints). The relative ease with which the technique appears to deal with these traditionally hard problems opens several questions about how relevant the results produced can possibly be. Among the questions is the issue of how useful are results for large values of the cosmological constant and how the approach can deal with several pathologies that are expected to be present in the canonical approach to quantum gravity. With the aim of clarifying these points, and to make our construction as explicit as possible, we study its application in several simple models. We consider Bianchi cosmologies, the asymmetric top, the coupled harmonic oscillators with constant energy density and a simple quantum mechanical system with two Hamiltonian constraints. We find that the technique satisfactorily deals with the pathologies of these models and offers promise for finding (at least some) results even for small values of the cosmological constant. Finally, we briefly sketch how the method would operate in the full four dimensional quantum general relativity case.Comment: 21 pages, RevTex, 2 figures with epsfi

Insulin promotes vascular smooth muscle cell proliferation and apoptosis via differential regulation of tumor necrosis factor‐related apoptosis‐inducing ligand

Background: Insulin regulates glucose homeostasis but can also promote vascular smooth muscle (VSMC) proliferation, important in atherogenesis. Recently, we showed that tumor necrosis factor‐related apoptosis‐inducing ligand (TRAIL) stimulates intimal thickening via accelerated growth of VSMCs. The aim of the present study was to determine whether insulin‐induced effects on VSMCs occur via TRAIL. Methods: Expression of TRAIL and TRAIL receptor in response to insulin and glucose was determined by polymerase chain reaction. Transcriptional activity was assessed using wild‐type and site‐specific mutations of the TRAIL promoter. Chromatin immunoprecipitation studies were performed. VSMC proliferation and apoptosis was measured. Results: Insulin and glucose exposure to VSMC for 24 h stimulated TRAIL mRNA expression. This was also evident at the transcriptional level. Both insulin‐ and glucose‐inducible TRAIL transcriptional activity was blocked by dominant‐negative specificity protein‐1 (Sp1) overexpression. There are five functional Sp1‐binding elements (Sp1‐1, Sp1‐2, Sp‐5/6 and Sp1‐7) on the TRAIL promoter. Insulin required the Sp1‐1 and Sp1‐2 sites, but glucose needed all Sp1‐binding sites to induce transcription. Furthermore, insulin (but not glucose) was able to promote VSMC proliferation over time, associated with increased decoy receptor‐2 (DcR2) expression. In contrast, chronic 5‐day exposure of VSMC to 1 µg/mL insulin repressed TRAIL and DcR2 expression, and reduced Sp1 enrichment on the TRAIL promoter. This was associated with increased cell death. Conclusions: The findings of the present study provide a new mechanistic insight into how TRAIL is regulated by insulin. This may have significant implications at different stages of diabetes‐associated cardiovascular disease. Thus, TRAIL may offer a novel therapeutic solution to combat insulin‐induced vascular pathologies

Lattice knot theory and quantum gravity in the loop representation

We present an implementation of the loop representation of quantum gravity on a square lattice. Instead of starting from a classical lattice theory, quantizing and introducing loops, we proceed backwards, setting up constraints in the lattice loop representation and showing that they have appropriate (singular) continuum limits and algebras. The diffeomorphism constraint reproduces the classical algebra in the continuum and has as solutions lattice analogues of usual knot invariants. We discuss some of the invariants stemming from Chern--Simons theory in the lattice context, including the issue of framing. We also present a regularization of the Hamiltonian constraint. We show that two knot invariants from Chern--Simons theory are annihilated by the Hamiltonian constraint through the use of their skein relations, including intersections. We also discuss the issue of intersections with kinks. This paper is the first step towards setting up the loop representation in a rigorous, computable setting.Comment: 23 pages, RevTeX, 14 figures included with psfi

Superheating fields of superconductors: Asymptotic analysis and numerical results

The superheated Meissner state in type-I superconductors is studied both analytically and numerically within the framework of Ginzburg-Landau theory. Using the method of matched asymptotic expansions we have developed a systematic expansion for the solutions of the Ginzburg-Landau equations in the limit of small $\kappa$, and have determined the maximum superheating field $H_{\rm sh}$ for the existence of the metastable, superheated Meissner state as an expansion in powers of $\kappa^{1/2}$. Our numerical solutions of these equations agree quite well with the asymptotic solutions for $\kappa<0.5$. The same asymptotic methods are also used to study the stability of the solutions, as well as a modified version of the Ginzburg-Landau equations which incorporates nonlocal electrodynamics. Finally, we compare our numerical results for the superheating field for large-$\kappa$ against recent asymptotic results for large-$\kappa$, and again find a close agreement. Our results demonstrate the efficacy of the method of matched asymptotic expansions for dealing with problems in inhomogeneous superconductivity involving boundary layers.Comment: 14 pages, 8 uuencoded figures, Revtex 3.

The Extended Loop Group: An Infinite Dimensional Manifold Associated with the Loop Space

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic properties of this new mathematical structure are analized in detail. Applications of the formalism to field theory, quantum gravity and knot theory are considered.Comment: The resubmited paper contains the title and abstract, that were omitted in the previous version. 42 pages, report IFFI/93.0

Interacting Particles and Strings in Path and Surface Representations

Non-relativistic charged particles and strings coupled with abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. We consider three models: the string in self-interaction through a Kalb-Ramond field in four dimensions, the topological interaction of two particles due to a BF term in 2+1 dimensions, and the string-particle interaction mediated by a BF term in 3+1 dimensions. In the first case one finds that a consistent "surface-representation" can be built provided that the coupling constant is quantized. The geometrical setting that arises corresponds to a generalized version of the Faraday's lines picture: quantum states are labeled by the shape of the string, from which emanate "Faraday`s surfaces". In the other models, the topological interaction can also be described by geometrical means. It is shown that the open-path (or open-surface) dependence carried by the wave functional in these models can be eliminated through an unitary transformation, except by a remaining dependence on the boundary of the path (or surface). These feature is closely related to the presence of anomalous statistics in the 2+1 model, and to a generalized "anyonic behavior" of the string in the other case.Comment: RevTeX 4, 28 page

Clinical profiles and quality of care of subjects with type 2 diabetes according to their cardiovascular risk: an observational, retrospective study

Background: The European Society of Cardiology (ESC) recently defined cardiovascular risk classes for subjects with diabetes. Aim of this study was to explore the distribution of subjects with type 2 diabetes (T2D) by cardiovascular risk groups according to the ESC classification and to describe the quality indicators of care, with particular regard to cardiovascular risk factors. Methods: The study is based on data extracted from electronic medical records of patients treated at the 258 Italian diabetes centers participating in the AMD Annals initiative. Patients with T2D were stratified by cardiovascular risk. General descriptive indicators, measures of intermediate outcomes, intensity/appropriateness of pharmacological treatment for diabetes and cardiovascular risk factors, presence of other complications and overall quality of care were evaluated. Results: Overall, 473,740 subjects with type 2 diabetes (78.5% at very high cardiovascular risk, 20.9% at high risk and 0.6% at moderate risk) were evaluated. Among people with T2D at very high risk: 26.4% had retinopathy, 39.5% had albuminuria, 18.7% had a previous major cardiovascular event, 39.0% had organ damage, 89.1% had three or more risk factors. The use of DPP4-i markedly increased as cardiovascular risk increased. The prescription of secretagogues also increased and that of GLP1-RAs tended to increase. The use of SGLT2-i was still limited, and only slightly higher in subjects with very high cardiovascular risk. The overall quality of care, as summarized by the Q score, tended to be lower as the level of cardiovascular risk increased. Conclusions: A large proportion of subjects with T2D is at high or very high risk. Glucose-lowering drug therapies seem not to be adequately used with respect to their potential advantages in terms of cardiovascular risk reduction. Several actions are necessary to improve the quality of care

Prediction of responsiveness of gait variables to rehabilitation training in Parkinson's disease

Background: Gait disorders represent one of the most disabling features of Parkinson's disease, which may benefit from rehabilitation. No consistent evidence exists about which gait biomechanical factors can be modified by rehabilitation and which clinical characteristic can predict rehabilitation-induced improvements. Objectives: The aims of the study were as follows: (i) to recognize the gait parameters modifiable by a short-term rehabilitation program; (ii) to evaluate the gait parameters that can normalize after rehabilitation; and (iii) to identify clinical variables predicting improvements in gait function after rehabilitation. Methods: Thirty-six patients affected by idiopathic Parkinson's disease in Hoehn-Yahr stage 1-3 and 22 healthy controls were included in the study. Both clinical and instrumental (gait analysis) evaluations were performed before and after a 10-weeks rehabilitation treatment. Time-distance parameters, lower limb joint, and trunk kinematics were measured. Results: At baseline evaluation with matched speed, almost all gait parameters were significantly different between patients and healthy controls. After the 10-weeks rehabilitation, most gait parameters improved, and spatial asymmetry and trunk rotation normalized. Multiple linear regression of gender combined with Unified Parkinson's Disease Rating Scale-III predicted both ΔSpeed and ΔStep length of both sides; gender combined with Unified Parkinson's Disease Rating Scale-II predicted ΔCadence; age combined with Hoehn-Yahr score and disease duration predicted 1trunk rotation range of motion. Conclusions: Impaired gait parameters are susceptible to improvement by rehabilitation, and younger men with Parkinson's disease who are less severely affected and at early disease stage are more susceptible to improvements in gait function after a 10-weeks rehabilitation program