On the equivalence of modes of convergence for log-concave measures

An important theme in recent work in asymptotic geometric analysis is that many classical implications between different types of geometric or functional inequalities can be reversed in the presence of convexity assumptions. In this note, we explore the extent to which different notions of distance between probability measures are comparable for log-concave distributions. Our results imply that weak convergence of isotropic log-concave distributions is equivalent to convergence in total variation, and is further equivalent to convergence in relative entropy when the limit measure is Gaussian.Comment: v3: Minor tweak in exposition. To appear in GAFA seminar note

Remarks on the Central Limit Theorem for Non-Convex Bodies

In this note, we study possible extensions of the Central Limit Theorem for non-convex bodies. First, we prove a Berry-Esseen type theorem for a certain class of unconditional bodies that are not necessarily convex. Then, we consider a widely-known class of non-convex bodies, the so-called p-convex bodies, and construct a counter-example for this class

Hamiltonian submanifolds of regular polytopes

We investigate polyhedral $2k$-manifolds as subcomplexes of the boundary complex of a regular polytope. We call such a subcomplex {\it $k$-Hamiltonian} if it contains the full $k$-skeleton of the polytope. Since the case of the cube is well known and since the case of a simplex was also previously studied (these are so-called {\it super-neighborly triangulations}) we focus on the case of the cross polytope and the sporadic regular 4-polytopes. By our results the existence of 1-Hamiltonian surfaces is now decided for all regular polytopes. Furthermore we investigate 2-Hamiltonian 4-manifolds in the $d$-dimensional cross polytope. These are the "regular cases" satisfying equality in Sparla's inequality. In particular, we present a new example with 16 vertices which is highly symmetric with an automorphism group of order 128. Topologically it is homeomorphic to a connected sum of 7 copies of $S^2 \times S^2$. By this example all regular cases of $n$ vertices with $n < 20$ or, equivalently, all cases of regular $d$-polytopes with $d\leq 9$ are now decided.Comment: 26 pages, 4 figure

Now or never: perceptions of uniqueness induce acceptance of price increases for experiences more than for objects

Seven studies test and support the prediction that consumers are more willing to accept a price increase for an experiential versus a material purchase; an effect explained by the greater uniqueness of experiences. Critically, the uniqueness model advanced here is found to be independent of the happiness consumers derive from the purchase. To gain a deeper understanding of the uniqueness mechanism, this investigation then advances and tests a four-facet framework of uniqueness (unique opportunity, unique purchase, unique identity, and counterconformity). Together, the findings converge on the conclusion that consumers perceive the opportunity to have a particular experience (vs. object) as more unique, and this unique opportunity increases their willingness to accept a price increase. Overall, this work extends the experiential versus material purchases literature into a new domain—that of pricing; identifies the dimension—uniqueness—and its precise facet responsible for the effect—unique opportunity; and demonstrates that this model unfolds in a pattern distinct from the oft researched model centered on consumer happiness. Theoretical and practical implications are discussed.info:eu-repo/semantics/acceptedVersio

Electrostatic modification of infrared response in gated structures based on VO2

We investigate the changes in the infrared response due to charge carriers introduced by electrostatic doping of the correlated insulator vanadium dioxide (VO2) integrated in the architecture of the field effect transistor. Accumulation of holes at the VO2 interface with the gate dielectric leads to an increase in infrared absorption. This phenomenon is observed only in the insulator-to-metal transition regime of VO2 with coexisting metallic and insulating regions. We postulate that doped holes lead to the growth of the metallic islands thereby promoting percolation, an effect that persists upon removal of the applied gate voltage.Comment: 14 pages, including 4 figure

Rapid quantification of naive alloreactive T cells by TNF-alpha production and correlation with allograft rejection in mice

Allograft transplantation requires chronic immunosuppression, but there is no effective strategy to evaluate the long-term maintenance of immunosuppression other than assessment of graft function. The ability to monitor naive alloreactive T cells would provide an alternative guide for drug therapy at early, preclinical stages of graft rejection and for evaluating tolerance-inducing protocols. To detect and quantify naive alloreactive T cells directly ex vivo, we used the unique ability of naive T cells to rapidly produce TNF-alpha but not IFN-gamma. Naive alloreactive T cells were identified by the production of TNF-alpha after a 5-hour in vitro stimulation with alloantigen and were distinguished from effector/memory alloreactive T cells by the inability to produce IFN-gamma. Moreover, naive alloreactive T cells were not detected in mice tolerized against specific alloantigens. The frequency of TNF-alpha-producing cells was predictive for rejection in an in vivo cytotoxicity assay and correlated with skin allograft rejection. Naive alloreactive T cells were also detected in humans, suggesting clinical relevance. We conclude that rapid production of TNF-alpha can be used to quantify naive alloreactive T cells, that it is abrogated after the induction of tolerance, and that it is a potential tool to predict allograft rejection

Collisional kinetics of non-uniform electric field, low-pressure, direct-current discharges in H2_{2}

A model of the collisional kinetics of energetic hydrogen atoms, molecules, and ions in pure H$_2$ discharges is used to predict H$_\alpha$ emission profiles and spatial distributions of emission from the cathode regions of low-pressure, weakly-ionized discharges for comparison with a wide variety of experiments. Positive and negative ion energy distributions are also predicted. The model developed for spatially uniform electric fields and current densities less than $10^{-3}$ A/m$^2$ is extended to non-uniform electric fields, current densities of $10^{3}$ A/m$^2$, and electric field to gas density ratios $E/N = 1.3$ MTd at 0.002 to 5 Torr pressure. (1 Td = $10^{-21}$ V m$^2$ and 1 Torr = 133 Pa) The observed far-wing Doppler broadening and spatial distribution of the H$_\alpha$ emission is consistent with reactions among H$^+$, H$_2^+$, H$_3^+$, and H$^-H$ ions, fast H atoms, and fast H$_2$ molecules, and with reflection, excitation, and attachment to fast H atoms at surfaces. The H$_\alpha$ excitation and H$^-$ formation occur principally by collisions of fast H, fast H$_2$, and H$^+$ with H$_2$. Simplifications include using a one-dimensional geometry, a multi-beam transport model, and the average cathode-fall electric field. The H$_\alpha$ emission is linear with current density over eight orders of magnitude. The calculated ion energy distributions agree satisfactorily with experiment for H$_2^+$ and H$_3^+$, but are only in qualitative agreement for H$^+$ and H$^-$. The experiments successfully modeled range from short-gap, parallel-plane glow discharges to beam-like, electrostatic-confinement discharges.Comment: Submitted to Plasmas Sources Science and Technology 8/18/201

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe