Transfer of K-types on local theta lifts of characters and unitary lowest weight modules

In this paper we study representations of the indefinite orthogonal group O(n,m) which are local theta lifts of one dimensional characters or unitary lowest weight modules of the double covers of the symplectic groups. We apply the transfer of K-types on these representations of O(n,m), and we study their effects on the dual pair correspondences. These results provide examples that the theta lifting is compatible with the transfer of K-types. Finally we will use these results to study subquotients of some cohomologically induced modules

Dirac cohomology, elliptic representations and endoscopy

The first part (Sections 1-6) of this paper is a survey of some of the recent developments in the theory of Dirac cohomology, especially the relationship of Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology; the second part (Sections 7-12) is devoted to understanding the unitary elliptic representations and endoscopic transfer by using the techniques in Dirac cohomology. A few problems and conjectures are proposed for further investigations.Comment: This paper will appear in `Representations of Reductive Groups, in Honor of 60th Birthday of David Vogan', edited by M. Nervins and P. Trapa, published by Springe

Entanglement in spin-one Heisenberg chains

By using the concept of negativity, we study entanglement in spin-one Heisenberg chains. Both the bilinear chain and the bilinear-biquadratic chain are considered. Due to the SU(2) symmetry, the negativity can be determined by two correlators, which greatly facilitate the study of entanglement properties. Analytical results of negativity are obtained in the bilinear model up to four spins and the two-spin bilinear-biquadratic model, and numerical results of negativity are presented. We determine the threshold temperature before which the thermal state is doomed to be entangled.Comment: 7 pages and 4 figure

System of Complex Brownian Motions Associated with the O'Connell Process

The O'Connell process is a softened version (a geometric lifting with a parameter $a>0$) of the noncolliding Brownian motion such that neighboring particles can change the order of positions in one dimension within the characteristic length $a$. This process is not determinantal. Under a special entrance law, however, Borodin and Corwin gave a Fredholm determinant expression for the expectation of an observable, which is a softening of an indicator of a particle position. We rewrite their integral kernel to a form similar to the correlation kernels of determinantal processes and show, if the number of particles is $N$, the rank of the matrix of the Fredholm determinant is $N$. Then we give a representation for the quantity by using an $N$-particle system of complex Brownian motions (CBMs). The complex function, which gives the determinantal expression to the weight of CBM paths, is not entire, but in the combinatorial limit $a \to 0$ it becomes an entire function providing conformal martingales and the CBM representation for the noncolliding Brownian motion is recovered.Comment: v3: AMS_LaTeX, 25 pages, no figure, minor corrections made for publication in J. Stat. Phy

Statistical Mechanics of Membrane Protein Conformation: A Homopolymer Model

The conformation and the phase diagram of a membrane protein are investigated via grand canonical ensemble approach using a homopolymer model. We discuss the nature and pathway of $\alpha$-helix integration into the membrane that results depending upon membrane permeability and polymer adsorptivity. For a membrane with the permeability larger than a critical value, the integration becomes the second order transition that occurs at the same temperature as that of the adsorption transition. For a nonadsorbing membrane, the integration is of the first order due to the aggregation of $\alpha$-helices.Comment: RevTeX with 5 postscript figure

Exotic Spaces in Quantum Gravity I: Euclidean Quantum Gravity in Seven Dimensions

It is well known that in four or more dimensions, there exist exotic manifolds; manifolds that are homeomorphic but not diffeomorphic to each other. More precisely, exotic manifolds are the same topological manifold but have inequivalent differentiable structures. This situation is in contrast to the uniqueness of the differentiable structure on topological manifolds in one, two and three dimensions. As exotic manifolds are not diffeomorphic, one can argue that quantum amplitudes for gravity formulated as functional integrals should include a sum over not only physically distinct geometries and topologies but also inequivalent differentiable structures. But can the inclusion of exotic manifolds in such sums make a significant contribution to these quantum amplitudes? This paper will demonstrate that it will. Simply connected exotic Einstein manifolds with positive curvature exist in seven dimensions. Their metrics are found numerically; they are shown to have volumes of the same order of magnitude. Their contribution to the semiclassical evaluation of the partition function for Euclidean quantum gravity in seven dimensions is evaluated and found to be nontrivial. Consequently, inequivalent differentiable structures should be included in the formulation of sums over histories for quantum gravity.Comment: AmsTex, 23 pages 5 eps figures; replaced figures with ones which are hopefully viewable in pdf forma

A critical test of the assumption that men prefer conformist women and women prefer nonconformist men.

Five studies tested the common assumption that women prefer nonconformist men as romantic partners, whereas men prefer conformist women. Studies 1 and 2 showed that both men and women preferred nonconformist romantic partners, but women overestimated the extent to which men prefer conformist partners. In Study 3, participants ostensibly in a small-group interaction showed preferences for nonconformist opposite-sex targets, a pattern that was particularly evident when men evaluated women. Dating success was greater the more nonconformist the sample was (Study 4), and perceptions of nonconformity in an ex-partner were associated with greater love and attraction toward that partner (Study 5). On the minority of occasions in which effects were moderated by gender, it was in the reverse direction to the traditional wisdom: Conformity was more associated with dating success among men. The studies contradict the notion that men disproportionately prefer conformist women

Climatic versus biotic constraints on carbon and water fluxes in seasonally drought-affected ponderosa pine ecosystems

We investigated the relative importance of climatic versus biotic controls on gross primary production (GPP) and water vapor fluxes in seasonally drought-affected ponderosa pine forests. The study was conducted in young (YS), mature (MS), and old stands (OS) over 4 years at the AmeriFlux Metolius sites. Model simulations showed that interannual variation of GPP did not follow the same trends as precipitation, and effects of climatic variation were smallest at the OS (50%), and intermediate at the YS (<20%). In the young, developing stand, interannual variation in leaf area has larger effects on fluxes than climate, although leaf area is a function of climate in that climate can interact with age-related shifts in carbon allocation and affect whole-tree hydraulic conductance. Older forests, with well-established root systems, appear to be better buffered from effects of seasonal drought and interannual climatic variation. Interannual variation of net ecosystem exchange (NEE) was also lowest at the OS, where NEE is controlled more by interannual variation of ecosystem respiration, 70% of which is from soil, than by the variation of GPP, whereas variation in GPP is the primary reason for interannual changes in NEE at the YS and MS. Across spatially heterogeneous landscapes with high frequency of younger stands resulting from natural and anthropogenic disturbances, interannual climatic variation and change in leaf area are likely to result in large interannual variation in GPP and NEE

Alterations of Central Liver Metabolism of Pediatric Patients with Non-Alcoholic Fatty Liver Disease

Non-alcoholic fatty liver disease (NAFLD) is the most common chronic liver disease in children and is associated with overweight and insulin resistance (IR). Almost nothing is known about in vivo alterations of liver metabolism in NAFLD, especially in the early stages of non-alcoholic steatohepatitis (NASH). Here, we used a complex mathematical model of liver metabolism to quantify the central hepatic metabolic functions of 71 children with biopsy-proven NAFLD. For each patient, a personalized model variant was generated based on enzyme abundances determined by mass spectroscopy. Our analysis revealed statistically significant alterations in the hepatic carbohydrate, lipid, and ammonia metabolism, which increased with the degree of obesity and severity of NAFLD. Histologic features of NASH and IR displayed opposing associations with changes in carbohydrate and lipid metabolism but synergistically decreased urea synthesis in favor of the increased release of glutamine, a driver of liver fibrosis. Taken together, our study reveals already significant alterations in the NASH liver of pediatric patients, which, however, are differently modulated by the simultaneous presence of IR