Entropy scaling laws for diffusion

Comment to the letter of Samanta et al., Phys. Rev. Lett. 92, 145901 (2004).Comment: 2 pages, 1 figur

The cc-map, Tits Satake subalgebras and the search for N=2\mathcal{N}=2 inflaton potentials

In this paper we address the general problem of including inflationary models exhibiting Starobinsky-like potentials into (symmetric) $\mathcal{N}=2$ supergravities. This is done by gauging suitable abelian isometries of the hypermultiplet sector and then truncating the resulting theory to a single scalar field. By using the characteristic properties of the global symmetry groups of the $\mathcal{N}=2$ supergravities we are able to make a general statement on the possible $\alpha$-attractor models which can obtained upon truncation. We find that in symmetric $\mathcal{N}=2$ models group theoretical constraints restrict the allowed values of the parameter $\alpha$ to be $\alpha=1,\,\frac{2}{3},\, \frac{1}{3}$. This confirms and generalizes results recently obtained in the literature. Our analysis heavily relies on the mathematical structure of symmetric $\mathcal{N}=2$ supergravities, in particular on the so called $c$-map connection between Quaternionic K\"ahler manifolds starting from Special K\"ahler ones. A general statement on the possible consistent truncations of the gauged models, leading to Starobinsky-like potentials, requires the essential help of Tits Satake universality classes. The paper is mathematically self-contained and aims at presenting the involved mathematical structures to a public not only of physicists but also of mathematicians. To this end the main mathematical structures and the general gauging procedure of $\mathcal{N}=2$ supergravities is reviewed in some detail.Comment: 101 pages, LaTeX sourc

The N=2 supersymmetric unconstrained matrix GNLS hierarchies

The generalization of the N=2 supersymmetric chiral matrix (k|n,m)--GNLS hierarchy (Lett. Math. Phys. 45 (1998) 63, solv-int/9711009) to the case when matrix entries are bosonic and fermionic unconstrained N=2 superfields is proposed. This is done by exhibiting the corresponding matrix Lax--pair representation in terms of N=2 unconstrained superfields. It is demonstrated that when matrix entries are chiral and antichiral N=2 superfields, it reproduces the N=2 chiral matrix (k|n,m)-GNLS hierarchy, while in the scalar case, k=1, it is equivalent to the N=2 supersymmetric multicomponent hierarchy (J. Phys. A29 (1996) 1281, hep-th/9510185). The simplest example --the N=2 unconstrained (1|1,0)--GNLS hierarchy-- and its reduction to the N=2 supersymmetric {\alpha}=1 KdV hierarchy are discussed in more detail, and its rich symmetry structure is uncovered.Comment: 11 pages, LaTex, misprints correcte

Quantitative estimates of convergence in nonlinear operator extensions of Korovkin's theorems

This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of continuous real functions. Several examples illustrating the theory are included.Comment: 10 page

Insights into the Fallback Path of Best-Effort Hardware Transactional Memory Systems

DOI 10.1007/978-3-319-43659-3Current industry proposals for Hardware Transactional Memory (HTM) focus on best-effort solutions (BE-HTM) where hardware limits are imposed on transactions. These designs may show a significant performance degradation due to high contention scenarios and different hardware and operating system limitations that abort transactions, e.g. cache overflows, hardware and software exceptions, etc. To deal with these events and to ensure forward progress, BE-HTM systems usually provide a software fallback path to execute a lock-based version of the code. In this paper, we propose a hardware implementation of an irrevocability mechanism as an alternative to the software fallback path to gain insight into the hardware improvements that could enhance the execution of such a fallback. Our mechanism anticipates the abort that causes the transaction serialization, and stalls other transactions in the system so that transactional work loss is mini- mized. In addition, we evaluate the main software fallback path approaches and propose the use of ticket locks that hold precise information of the number of transactions waiting to enter the fallback. Thus, the separation of transactional and fallback execution can be achieved in a precise manner. The evaluation is carried out using the Simics/GEMS simulator and the complete range of STAMP transactional suite benchmarks. We obtain significant performance benefits of around twice the speedup and an abort reduction of 50% over the software fallback path for a number of benchmarks.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech