Hubbard chain with a Kondo impurity

A Bethe Ansatz solution of a (modified) Hubbard chain with a Kondo impurity of arbitrary spin S at a highly symmetric line of parameter space is proposed and explored. Our results confirm the existence of a strong-coupling (line of) fixed-point(s) with ferromagnetic Kondo coupling as first hypothetized by Furusaki and Nagaosa on the basis of perturbative renormalization group calculations. For on-site Hubbard repulsion and ferromagnetic Kondo exchange, the ground state has spin S-1/2, i.e., is a singlet when S=1/2. The contributions of the impurity to the magnetic susceptibility and low-temperature specific heat are discussed. While the Wilson ratio is unity in the half-filled band, it is found to be a function of density and interaction away from half-filling.Comment: 5 pages, Revte

Effect of the Output of the System in Signal Detection

We analyze the consequences that the choice of the output of the system has in the efficiency of signal detection. It is shown that the signal and the signal-to-noise ratio (SNR), used to characterize the phenomenon of stochastic resonance, strongly depend on the form of the output. In particular, the SNR may be enhanced for an adequate output.Comment: 4 pages, RevTex, 6 PostScript figure

A polarized beam splitter using an anisotropic medium slab

The propagation of electromagnetic waves in the anisotropic medium with a single-sheeted hyperboloid dispersion relation is investigated. It is found that in such an anisotropic medium E- and H-polarized waves have the same dispersion relation, while E- and H-polarized waves exhibit opposite amphoteric refraction characteristics. E- (or H-) polarized waves are positively refracted whereas H- (or E-) polarized waves are negatively refracted at the interface associated with the anisotropic medium. By suitably using the properties of anomalous refraction in the anisotropic medium it is possible to realize a very simple and very efficient beam splitter to route the light. It is shown that the splitting angle and the splitting distance between E- and H- polarized beam is the function of anisotropic parameters, incident angle and slab thickness.Comment: 14 pages, 6 figure

Interparticle interactions:Energy potentials, energy transfer, and nanoscale mechanical motion in response to optical radiation

In the interactions between particles of material with slightly different electronic levels, unusually large shifts in the pair potential can result from photoexcitation, and on subsequent electronic excitation transfer. To elicit these phenomena, it is necessary to understand the fundamental differences between a variety of optical properties deriving from dispersion interactions, and processes such as resonance energy transfer that occur under laser irradiance. This helps dispel some confusion in the recent literature. By developing and interpreting the theory at a deeper level, one can anticipate that in suitable systems, light absorption and energy transfer will be accompanied by significant displacements in interparticle separation, leading to nanoscale mechanical motion

Solving analytic differential equations in polynomial time over unbounded domains

In this paper we consider the computational complexity of solving initial-value problems de ned with analytic ordinary diferential equations (ODEs) over unbounded domains of Rn and Cn, under the Computable Analysis setting. We show that the solution can be computed in polynomial time over its maximal interval of de nition, provided it satis es a very generous bound on its growth, and that the function admits an analytic extension to the complex plane

The general purpose analog computer and computable analysis are two equivalent paradigms of analog computation

In this paper we revisit one of the rst models of analog computation, Shannon's General Purpose Analog Computer (GPAC). The GPAC has often been argued to be weaker than computable analysis. As main contribution, we show that if we change the notion of GPACcomputability in a natural way, we compute exactly all real computable functions (in the sense of computable analysis). Moreover, since GPACs are equivalent to systems of polynomial di erential equations then we show that all real computable functions can be de ned by such models

Generalization of p-regularity notion and tangent cone description in the singular case

The theory of p-regularity has approximately twenty-five years’ history and many results have been obtained up to now. The main result of this theory is description of tangent cone to zero set in singular case. However there are numerous nonlinear objects for which the p-regularity condition fails, especially for p > 2. In this paper we generalize the p-regularity notion as a starting point for more detailed consideration based on different p-factor operators constructions

Robust computations with dynamical systems

In this paper we discuss the computational power of Lipschitz dynamical systems which are robust to in nitesimal perturbations. Whereas the study in [1] was done only for not-so-natural systems from a classical mathematical point of view (discontinuous di erential equation systems, discontinuous piecewise a ne maps, or perturbed Turing machines), we prove that the results presented there can be generalized to Lipschitz and computable dynamical systems. In other words, we prove that the perturbed reachability problem (i.e. the reachability problem for systems which are subjected to in nitesimal perturbations) is co-recursively enumerable for this kind of systems. Using this result we show that if robustness to in nitesimal perturbations is also required, the reachability problem becomes decidable. This result can be interpreted in the following manner: undecidability of veri cation doesn't hold for Lipschitz, computable and robust systems. We also show that the perturbed reachability problem is co-r.e. complete even for C1-systems

Analysis of serum inflammatory mediators identifies unique dynamic networks associated with death and spontaneous survival in pediatric acute liver failure

Background: Tools to predict death or spontaneous survival are necessary to inform liver transplantation (LTx) decisions in pediatric acute liver failure (PALF), but such tools are not available. Recent data suggest that immune/inflammatory dysregulation occurs in the setting of acute liver failure. We hypothesized that specific, dynamic, and measurable patterns of immune/inflammatory dysregulation will correlate with outcomes in PALF. Methods: We assayed 26 inflammatory mediators on stored serum samples obtained from a convenience sample of 49 children in the PALF study group (PALFSG) collected within 7 days after enrollment. Outcomes were assessed within 21 days of enrollment consisting of spontaneous survivors, non-survivors, and LTx recipients. Data were subjected to statistical analysis, patient-specific Principal Component Analysis (PCA), and Dynamic Bayesian Network (DBN) inference. Findings: Raw inflammatory mediator levels assessed over time did not distinguish among PALF outcomes. However, DBN analysis did reveal distinct interferon-gamma-related networks that distinguished spontaneous survivors from those who died. The network identified in LTx patients pre-transplant was more like that seen in spontaneous survivors than in those who died, a finding supported by PCA. Interpretation: The application of DBN analysis of inflammatory mediators in this small patient sample appears to differentiate survivors from non-survivors in PALF. Patterns associated with LTx pre-transplant were more like those seen in spontaneous survivors than in those who died. DBN-based analyses might lead to a better prediction of outcome in PALF, and could also have more general utility in other complex diseases with an inflammatory etiology. Copyright: © 2013 Azhar et al