Gauge Theory for Finite-Dimensional Dynamical Systems

Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This theory has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems with implications to numerical integration of differential equations. We distinguish between rescriptive and descriptive gauge symmetry. Rescriptive gauge symmetry is, in essence, re-scaling of the independent variable, while descriptive gauge symmetry is a Yang-Mills-like transformation of the velocity vector field, adapted to finite-dimensional systems. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently "disordered" flow into a regular dynamical process, and that there exists a remarkable connection between gauge transformations and reduction theory of ordinary differential equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse engineering and scientific fields, including quantum mechanics, chemistry, rigid-body dynamics and information theory

Effect of antiferromagnetic exchange interactions on the Glauber dynamics of one-dimensional Ising models

We study the effect of antiferromagnetic interactions on the single spin-flip Glauber dynamics of two different one-dimensional (1D) Ising models with spin $\pm 1$. The first model is an Ising chain with antiferromagnetic exchange interaction limited to nearest neighbors and subject to an oscillating magnetic field. The system of master equations describing the time evolution of sublattice magnetizations can easily be solved within a linear field approximation and a long time limit. Resonant behavior of the magnetization as a function of temperature (stochastic resonance) is found, at low frequency, only when spins on opposite sublattices are uncompensated owing to different gyromagnetic factors (i.e., in the presence of a ferrimagnetic short range order). The second model is the axial next-nearest neighbor Ising (ANNNI) chain, where an antiferromagnetic exchange between next-nearest neighbors (nnn) is assumed to compete with a nearest-neighbor (nn) exchange interaction of either sign. The long time response of the model to a weak, oscillating magnetic field is investigated in the framework of a decoupling approximation for three-spin correlation functions, which is required to close the system of master equations. The calculation, within such an approximate theoretical scheme, of the dynamic critical exponent z, defined as ${1/\tau} \approx ({1/ {\xi}})^z$ (where \tau is the longest relaxation time and \xi is the correlation length of the chain), suggests that the T=0 single spin-flip Glauber dynamics of the ANNNI chain is in a different universality class than that of the unfrustrated Ising chain.Comment: 5 figures. Phys. Rev. B (accepted July 12, 2007

Prevalence of Toxocara canis eggs in dog faeces from public places of Florence, Italy

AbstractTo determine whether canine faecal contamination may represent a source of environmental contamination with Toxocara canis eggs within the urban area of Florence, a total number of 754 dog faeces were collected in 7 public places and examined by routine floatation technique during one-year period. The total prevalence of intestinal nematode eggs was 8.6 %. Trichuris vulpis (4.6 %) eggs were the most prevalent followed by T. canis (3.6 %) and Ancylostomidae (1.7 %) eggs. Mixed infections included T. canis/T. vulpis (0.7 %), Ancylostomidae/T. canis (0.4 %), and Ancylosto-midae/T. vulpis (0.3 %). Total prevalence of intestinal nematode eggs was significantly higher in spring than in winter (OR = 2.06). Our results indicate a low prevalence of T. canis eggs suggesting that dog faeces left on soil are unlikely to cause high environmental contamination with T. canis eggs in the town of Florence

Histamine in diabetes: is it time to reconsider?

The first studies of histamine and diabetes date back to the 1950s. Since that time the involvement of histamine in diabetes was related to its well known vasoactive properties and permeability leakage effects. In particular, the first evidence for a correlation between histamine and diabetes arose in 1989 when an increase in plasma and leucocyte histamine content was observed. Limited independent evidence followed in the subsequent two decades, focusing on both histamine glyceamic control and macro- and microvascular complications of diabetes. However, recent observations have sparked the question whether it is time to reconsider the functional contribution of histamine in diabetes. We reveal an interesting upsurge in the field which provides scope for new insights into the role of histamine in diabetes

Static density response of one-dimensional soft bosons across the clustering transition

One-dimensional bosons interacting via a soft-shoulder potential are investigated at zero temperature. The flatness of the potential at short distances introduces a typical length, such that, at relatively high densities and sufficiently strong interactions, clusters are formed, even in the presence of a completely repulsive potential. We evaluate the static density response function of this system across the transition from the liquid to the cluster liquid phases. Such quantity reveals the density modulations induced by a weak periodic external potential, and is maximal at the clustering wavevector. It is known that this response function is proportional to the static structure factor in the classical regime at high temperature, while for this zero-temperature quantum systems, we extract it from the dynamical structure factor evaluated with quantum Monte Carlo methods.Comment: 7 pages, 3 figures. Proceedings of the "Recent Progress in Many-Body Theories" international conference, Pohang, South Korea, 201

Homocysteine levels and cardiovascular disease in migraine with aura

Clinical studies suggest that hyperhomocysteinemia could be considered an independent risk factor for premature cerebral, peripheral and vascular diseases. A number of authors found an epidemiological correlation between increased risk of cerebrovascular disease and migraine with aura. In this study, 34 patients suffering from migraine with aura and 36 healthy controls were evaluated with respect to total plasma homocysteine levels, measured with FPIA immunoassay in the fasting state and after methionine load. Moreover, vitamin B12, folate and other classic biochemical indicators of atherosclerosis disease were evaluated. In this study, homocysteine levels, both at basal and after load, and other cardiovascular risk factors such as vitamin B12 and apo-LpA were within the normal range. Other multicentric randomised trials are needed to carry on and confirm these data

Human-robot coexistence and interaction in open industrial cells

Recent research results on human\u2013robot interaction and collaborative robotics are leaving behind the traditional paradigm of robots living in a separated space inside safety cages, allowing humans and robot to work together for completing an increasing number of complex industrial tasks. In this context, safety of the human operator is a main concern. In this paper, we present a framework for ensuring human safety in a robotic cell that allows human\u2013robot coexistence and dependable interaction. The framework is based on a layered control architecture that exploits an effective algorithm for online monitoring of relative human\u2013robot distance using depth sensors. This method allows to modify in real time the robot behavior depending on the user position, without limiting the operative robot workspace in a too conservative way. In order to guarantee redundancy and diversity at the safety level, additional certified laser scanners monitor human\u2013robot proximity in the cell and safe communication protocols and logical units are used for the smooth integration with an industrial software for safe low-level robot control. The implemented concept includes a smart human-machine interface to support in-process collaborative activities and for a contactless interaction with gesture recognition of operator commands. Coexistence and interaction are illustrated and tested in an industrial cell, in which a robot moves a tool that measures the quality of a polished metallic part while the operator performs a close evaluation of the same workpiece