A characterization of Schauder frames which are near-Schauder bases

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we give a solution to this problem using the notion of the minimal-associated sequence spaces and the minimal-associated reconstruction operators for Schauder frames. We prove that a Schauder frame is a near-Schauder basis if and only if the kernel of the minimal-associated reconstruction operator contains no copy of $c_0$. In particular, a Schauder frame of a Banach space with no copy of $c_0$ is a near-Schauder basis if and only if the minimal-associated sequence space contains no copy of $c_0$. In these cases, the minimal-associated reconstruction operator has a finite dimensional kernel and the dimension of the kernel is exactly the excess of the near-Schauder basis. Using these results, we make related applications on Besselian frames and near-Riesz bases.Comment: 12 page

Finite quantum tomography via semidefinite programming

Using the the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: qudit tomography, N-qubit tomography, phase tomography and coherent spin state tomography, where that obtained results are in agreement with those of References \cite{schack,Pegg,Barnett,Buzek,Weigert}.Comment: 25 page

Self-similarity and long-time behavior of solutions of the diffusion equation with nonlinear absorption and a boundary source

This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in developing tissues. For the considered class of models, we establish existence of a new type of ultra-singular self-similar solutions. These solutions arise as limits of the solutions of the initial value problem with zero initial data and infinitely strong source at the boundary. We prove existence and uniqueness of such solutions in the suitable weighted energy spaces. Moreover, we prove that the obtained self-similar solutions are the long-time limits of the solutions of the initial value problem with zero initial data and a time-independent boundary source

Binary optical communication in single-mode and entangled quantum noisy channels

We address binary optical communication in single-mode and entangled quantum noisy channels. For single-mode we present a systematic comparison between direct photodetection and homodyne detection in realistic conditions, i.e. taking into account the noise that occurs both during the propagation and the detection of the signals. We then consider entangled channels based on twin-beam state of radiation, and show that with realistic heterodyne detection the error probability at fixed channel energy is reduced in comparison to the single-mode cases for a large range of values of quantum efficiency and noise parameters

Sex Differences in Long-Term Trends of Psychosocial Factors and Gender Effect on Risk of Cardiovascular Diseases: Arterial Hypertension, Myocardial Infarction and Stroke

Introduction: The study aimed to determine gender differences in the prevalence and dynamics of affective states over a long period, i.e., 23 years, and to establish their effect on the risk of cardiovascular diseases (CVD), i.e., arterial hypertension (AH), myocardial infarction (MI), and stroke among the population aged 25–64 in Russia / Siberia. Methods: Between 1994 and 2017, we conducted 4 screening surveys of representative samples (totalling 4,815 people) under the international programs MONICA and HAPIEE in Russia / Siberia. To determine the sex differences in cardiovascular risk from 1994 to 2010, we observed cohorts formed from the screened individuals without CVD and diabetes mellitus (DM). Results: High levels of affective states in the period from 1994 to 2003, especially in women, were replaced by a downward trend in 2013. At the same time, there was a reduction in the gender gap in terms of frequency of depression lower 1%, and men in the younger age groups reported higher levels of personal anxiety (49.3% vs 46.1% in adults aged 35-44y) and vital exhaustion (16.9% vs 15.6%) than women in 2017. We found that men with unfavourable levels of affective states have a 3–5 fold higher risk of hypertension and stroke, while women have a higher risk of myocardial infarction (p for all < 0.05). Hostility in men is associated with a negative risk of myocardial infarction and stroke (HR=0.3 and HR=0.29, respectively; p for all < 0.05). However, this was levelled out by unfavourable social characteristics. Conclusions: The downward trends in prevalence of psychosocial factors were unstable and associated with reduced gender gap for affective states. It had a significant impact on the gender magnitude of cardiovascular risk

The interplay of intrinsic and extrinsic bounded noises in genetic networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a genetic network. The influence of intrinsic and extrinsic noises on genetic networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: $(i)$ the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, $(ii)$ a model of enzymatic futile cycle and $(iii)$ a genetic toggle switch. In $(ii)$ and $(iii)$ we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possibile functional role of bounded noises