Equality in Borell-Brascamp-Lieb inequalities on curved spaces

By using optimal mass transportation and a quantitative H\"older inequality, we provide estimates for the Borell-Brascamp-Lieb deficit on complete Riemannian manifolds. Accordingly, equality cases in Borell-Brascamp-Lieb inequalities (including Brunn-Minkowski and Pr\'ekopa-Leindler inequalities) are characterized in terms of the optimal transport map between suitable marginal probability measures. These results provide several qualitative applications both in the flat and non-flat frameworks. In particular, by using Caffarelli's regularity result for the Monge-Amp\`ere equation, we {give a new proof} of Dubuc's characterization of the equality in Borell-Brascamp-Lieb inequalities in the Euclidean setting. When the $n$-dimensional Riemannian manifold has Ricci curvature ${\rm Ric}(M)\geq (n-1)k$ for some $k\in \mathbb R$, it turns out that equality in the Borell-Brascamp-Lieb inequality is expected only when a particular region of the manifold between the marginal supports has constant sectional curvature $k$. A precise characterization is provided for the equality in the Lott-Sturm-Villani-type distorted Brunn-Minkowski inequality on Riemannian manifolds. Related results for (not necessarily reversible) Finsler manifolds are also presented.Comment: 28 pages (with 1 figure); to appear in Advances in Mathematic

Fault tolerance in super-scalar and VLIW processors

In this paper, we present a method for utilizing the spare capacity in super-scalar and very long instruction word (VLIW) processors to tolerate functional unit failures. Unlike previous work that was primarily interested in detection of transient faults, we are concerned with more permanent and/or intermittent faults which necessitate processor reconfiguration. Our method utilizes the VLIW compiler or the superscalar scheduler to insert redundant operations whenever idle functional units exist. The results of these redundant operations are used to detect and diagnose functional unit failures. For super-scalar processors, the scheduler can then utilize this information to ensure that operations are performed only on non-faulty units. In VLIW processors, this is equivalent to recompiling the code to run on the remaining non-faulty functional units. Since in certain applications, recompilation may not be possible, we consider two alternative reconfiguration strategies for VLIW processors. These strategies sacrifice storage space and execution time, respectively, in order to reconfigure without recompiling. We present Markov models that describe the behavior of processors using these different approaches and we evaluate their reliabilities. The results show that, while super-scalar and VLIW with recompilation provide the highest reliability, all proposed strategies significantly increase reliability over that of an unprotected processor

Job Polarization in the U.S.: A Reassessment of the Evidence from the 1980s and 1990s

In this paper, we review the evidence for job polarization in the U.S. and provide a description of the occupational employment changes that characterized the U.S. labor market during the 1970s, 1980s, and 1990s. We begin by replicating the existing job polarization trends, which are produced using a modified occupational coding scheme intended to make occupational categories comparable over time. Using two alternative procedures to obtain consistent occupational codes across decades, we show that the finding that jobs polarized in the 1990s relative to the 1980s no longer holds. Instead, we find that occupational employment shifts were very similar during the two decades. In addition, we demonstrate that the method used to rank occupations according to their skill content has a substantial impact on the employment growth in low-skill job categories. Finally, using an additional occupational crosswalk that allows us to obtain consistent occupational categories from 1970 to 2002, we provide evidence in favor of a long-term trend towards employment growth in high-skill jobs and employment decline in some middle-skill jobs, but no sharp contrast between the 1980s and the 1990s. Our findings suggest that the evolution of the occupational employment structure and the divergent wage growth patterns observed during the 1980s and 1990s do not easily fit within the routinization story as usually told.Job Polarization, Occupational Employment, Employment Growth, Wage Inequality

Geometric inequalities on Heisenberg groups

We establish geometric inequalities in the sub-Riemannian setting of the Heisenberg group $\mathbb H^n$. Our results include a natural sub-Riemannian version of the celebrated curvature-dimension condition of Lott-Villani and Sturm and also a geodesic version of the Borell-Brascamp-Lieb inequality akin to the one obtained by Cordero-Erausquin, McCann and Schmuckenschl\"ager. The latter statement implies sub-Riemannian versions of the geodesic Pr\'ekopa-Leindler and Brunn-Minkowski inequalities. The proofs are based on optimal mass transportation and Riemannian approximation of $\mathbb H^n$ developed by Ambrosio and Rigot. These results refute a general point of view, according to which no geometric inequalities can be derived by optimal mass transportation on singular spaces.Comment: to appear in Calculus of Variations and Partial Differential Equations (42 pages, 1 figure

The isotope effect in the Hubbard model with local phonons

The isotope effect (IE) in the two-dimensional Hubbard model with Holstein phonons is studied using the dynamical cluster approximation with quantum Monte Carlo. At small electron-phonon (EP) coupling the IE is negligible. For larger EP coupling there is a large and positive IE on the superconducting temperature that decreases with increasing doping. A significant IE also appears in the low-energy density of states, kinetic energy and charge excitation spectrum. A negligible IE is found in the pseudogap and antiferromagnetic (AF) properties at small doping whereas the AF susceptibility at intermediate doping increases with decreasing phonon frequency $\omega_0$. This IE stems from increased polaronic effects with decreasing $\omega_0$. A larger IE at smaller doping occurs due to stronger polaronic effects determined by the interplay of the EP interaction with stronger AF correlations. The IE of the Hubbard-Holstein model exhibits many similarities with the IE measured in cuprate superconductors

Some Characteristics of the New Enterprises and the Profile of New Entrepreneurs

The implementation of a scientific management generating performances that can lead the sector of SMEs to the requests of the Lisbon Strategy, cannot be completed without the existence of well-trained entrepreneurs, capable to improve their skills in modern management, thus leading to competitive results in a highly competitive market. The analysis performed by this research allows us to formulate, synthetically, strengths and weaknesses in the entrepreneurial evolution during the 1995-2007period.new enterprise; entrepreneur; new enterprise foundation rate; the entrepreneur’s socio-professional profile; the entrepreneur’s level of education.

Existence of Rank Two Vector Bundles on Higher Dimensional Toric Varieties

In the mid 70's, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on P^n is a direct sum of line bundles. This conjecture remains still open. In this paper, we construct indecomposable rank two vector bundles on a large class of Fano toric varieties. Unfortunately, this class does not contain P^nComment: 8 page

Possible errors in establishing the sample dimensions of survey investigations

Starting from the „rough” use of 1,500-1,800 subject samples in field researches with populations of the dimensions of a medium town, a capital or an entire country, which generates doubts and possible questions related to the representativeness of the investigated samples as well as to the conclusions of these researches, we developed the reconstruction of the necessary interactions in determining the sample volume, and also identified some inadvertencies. Some improvements solutions were also recommended.confidence interval, distribution laws, probable error, representativeness, sample volume.