Stability for a GNS inequality and the Log-HLS inequality, with application to the critical mass Keller-Segel equation

Starting from the quantitative stability result of Bianchi and Egnell for the 2-Sobolev inequality, we deduce several different stability results for a Gagliardo-Nirenberg-Sobolev inequality in the plane. Then, exploiting the connection between this inequality and a fast diffusion equation, we get a quantitative stability for the Log-HLS inequality. Finally, using all these estimates, we prove a quantitative convergence result for the critical mass Keller-Segel system

Energy Efficiency in MIMO Underlay and Overlay Device-to-Device Communications and Cognitive Radio Systems

This paper addresses the problem of resource allocation for systems in which a primary and a secondary link share the available spectrum by an underlay or overlay approach. After observing that such a scenario models both cognitive radio and D2D communications, we formulate the problem as the maximization of the secondary energy efficiency subject to a minimum rate requirement for the primary user. This leads to challenging non-convex, fractional problems. In the underlay scenario, we obtain the global solution by means of a suitable reformulation. In the overlay scenario, two algorithms are proposed. The first one yields a resource allocation fulfilling the first-order optimality conditions of the resource allocation problem, by solving a sequence of easier fractional problems. The second one enjoys a weaker optimality claim, but an even lower computational complexity. Numerical results demonstrate the merits of the proposed algorithms both in terms of energy-efficient performance and complexity, also showing that the two proposed algorithms for the overlay scenario perform very similarly, despite the different complexity.Comment: to appear in IEEE Transactions on Signal Processin

Resource Allocation for Energy-Efficient 3-Way Relay Channels

Throughput and energy efficiency in 3-way relay channels are studied in this paper. Unlike previous contributions, we consider a circular message exchange. First, an outer bound and achievable sum rate expressions for different relaying protocols are derived for 3-way relay channels. The sum capacity is characterized for certain SNR regimes. Next, leveraging the derived achievable sum rate expressions, cooperative and competitive maximization of the energy efficiency are considered. For the cooperative case, both low-complexity and globally optimal algorithms for joint power allocation at the users and at the relay are designed so as to maximize the system global energy efficiency. For the competitive case, a game theoretic approach is taken, and it is shown that the best response dynamics is guaranteed to converge to a Nash equilibrium. A power consumption model for mmWave board-to-board communications is developed, and numerical results are provided to corroborate and provide insight on the theoretical findings.Comment: Submitted to IEEE Transactions on Wireless Communication

Can Inflation solve the Hierarchy Problem?

Inflation with tunneling from a false to a true vacuum becomes viable in the presence of a scalar field that slows down the initial de Sitter phase. As a by-product this field also sets dynamically the value of the Newton constant observed today. This can be very large if the tunneling rate (which is exponentially sensitive to the barrier) is small enough. Therefore along with Inflation we also provide a natural dynamical explanation for why gravity is so weak today. Moreover we predict a spectrum of gravity waves peaked at around 0.1 mHz, that will be detectable by the planned space inteferometer LISA. Finally we discuss interesting predictions on cosmological scalar and tensor fluctuations in the light the WMAP 3-year data.Comment: 7 pages. Replaced version with comparison with WMAP 3-year dat

Sex and Age-Related Differences in Neuroticism and Allostatic Load Index in Urban Patients with General Anxiety Disorder Treated with Alprazolam

Introduction: Allostatic Load (AL) index proposes indicators for the functioningof the main potentially stress-affected systems. Sex differences instress response and stress-related diseases susceptibility have been describedfor the general population. In this observational study we describe the effectsof sex and age on allostatic load variables, in a cohort of patients with generalanxiety disorders and neuroticism treated with alprazolam during 12 weeks,before and after treatment. Methods: Patients with general (DSM IV) anxietydisorders with >6 in Hamilton scale, Allostatic load (>1 Crimmins and SeemanAL modified criteria) and neuroticism >18 (NEO-FFI inventory), wereincluded. All patients completed psychiatric assessment, allostatic load indexdetermination before (−1 week) and after 12 weeks of treatment with alprazolam(0.25 - 1 mg/t.i.d). Allostatic load parameters comprised cardiovascular,metabolic and inflammatory variables. Univariate analysis (two-wayANOVA), Student?s t-test (related variables) and Pearson correlations weredetermined. Results: Fifty-four patients, 35 females (48.6 ± 11.7 years) and 19males (44.2 ± 12.8 years) with general anxiety disorder were included; 28 patientswith <50 years (60.7% females), and 26 with ≥50 years (69.2% females).Younger patients (<50 years) (two-way ANOVA, p = 0.02) were significantlyassociated with lower allostatic load index after treatment. However, womenshowed higher anxiety levels in both, before (Two-way ANOVA, p = 0.059)and after treatment (two-way ANOVA, p = 0.005), with a significantly betterprofile than men in many individual AL variables, particularly cardiovascular(systolic blood pressure), obesity (body mass index), and lipids (higher HDLlevels). After treatment a higher reduction of fibrinogen levels was found inmen (two-way ANOVA, p = 0.02). Conclusions: In this preliminary analysiswe described sex and age differences in psychiatry aspects and allostatic loadindexes in patients with general anxiety disorders in the short-term treatmentwith alprazolam. These considerations remark the need of pondering sex andage differences during the use of drugs for protracted periods.Fil: D`Alessio, Luciana. Universidad Nacional Arturo Jauretche. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Provincia de Buenos Aires. Ministerio de Salud. Hospital Alta Complejidad en Red El Cruce Dr. Néstor Carlos Kirchner Samic. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Unidad Ejecutora de Estudios en Neurociencias y Sistemas Complejos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Soria, Carlos A.. Henri Laborit Institute Of Biosciences; ArgentinaFil: Remedi, Carolina. Henri Laborit Institute Of Biosciences; Argentina; ArgentinaFil: Roldán, Emilio J. A.. Instituto de Neurobiología IDNEU; Argentin

A Laplacian-based algorithm for non-isothermal atomistic-continuum hybrid simulation of micro and nano-flows

We propose a new hybrid algorithm for incompressible micro and nanoflows that applies to non-isothermal steady-state flows and does not require the calculation of the Irving–Kirkwood stress tensor or heat flux vector. The method is validated by simulating the flow in a channel under the effect of a gravity-like force with bounding walls at two different temperatures and velocities. The model shows very accurate results compared to benchmark full MD simulations. In the temperature results, in particular, the contribution of viscous dissipation is correctly evaluated