Marginal distributions in (2N)(\bf 2N)-dimensional phase space and the quantum (N+1)(\bf N+1) marginal theorem

We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e. depending on a (complete) commuting set of $N$ variables, are considered. A diagrammatic or graph theoretic formulation of the problem is developed. We then exactly determine the set of ``admissible'' data, i.e. those types of data for which the problem always admits solutions. This is done in the case where the joint distributions originate from quantum mechanics as well as in the case where this constraint is not imposed. In particular, it is shown that a necessary (but not sufficient) condition for the existence of solutions is $n\leq N+1$. When the data are admissible and the quantum constraint is not imposed, the general solution for the phase space density is determined explicitly. For admissible data of a quantum origin, the general solution is given in certain (but not all) cases. In the remaining cases, only a subset of solutions is obtained.Comment: 29 pages (Work supported by the Indo-French Centre for the Promotion of Advanced Research, Project Nb 1501-02). v2 to add a report-n

The quantum anharmonic oscillator in the Heisenberg picture and multiple scale techniques

Multiple scale techniques are well-known in classical mechanics to give perturbation series free from resonant terms. When applied to the quantum anharmonic oscillator, these techniques lead to interesting features concerning the solution of the Heisenberg equations of motion and the Hamiltonian spectrum.Comment: 18 page

Joint Probabilities Reproducing Three EPR Experiments On Two Qubits

An eight parameter family of the most general nonnegative quadruple probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3 pairs of analyser settings are used. It is a simultaneous representation of 3 Bohr-incompatible experimental configurations valid for arbitrary quantum states.Comment: Typo corrected in abstrac

Altered Prostasin (CAP1/Prss8) Expression Favors Inflammation and Tissue Remodeling in DSS-induced Colitis.

Inflammatory bowel diseases (IBD) including ulcerative colitis and Crohn's disease are diseases with impaired epithelial barrier function. We aimed to investigate whether mutated prostasin and thus, reduced colonic epithelial sodium channel activity predisposes to develop an experimentally dextran sodium sulfate (DSS)-induced colitis. Wildtype, heterozygous (fr/+), and homozygous (fr/fr) prostasin-mutant rats were treated 7 days with DSS followed by 7 days of recovery and analyzed with respect to histology, clinicopathological parameters, inflammatory marker mRNA transcript expression, and sodium transporter protein expression. In this study, a more detailed analysis on rat fr/fr colons revealed reduced numbers of crypt and goblet cells, and local angiodysplasia, as compared with heterozygous (fr/+) and wildtype littermates. Following 2% DSS treatment for 7 days followed by 7 days recovery, fr/fr animals lost body weight, and reached maximal diarrhea score and highest disease activity after only 3 days, and strongly increased cytokine levels. The histology score significantly increased in all groups, but fr/fr colons further displayed pronounced histological alterations with near absence of goblet cells, rearrangement of the lamina propria, and presence of neutrophils, eosinophils, and macrophages. Additionally, fr/fr colons showed ulcerations and edemas that were absent in fr/+ and wildtype littermates. Following recovery, fr/fr rats reached, although significantly delayed, near-normal diarrhea score and disease activity, but exhibited severe architectural remodeling, despite unchanged sodium transporter protein expression. In summary, our results demonstrate a protective role of colonic prostasin expression against experimental colitis, and thus represent a susceptibility gene in the development of inflammatory bowel disease

Exchange operator formalism for N-body spin models with near-neighbors interactions

We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete description of a certain flag of finite-dimensional spaces of spin functions preserved by the Hamiltonian of each model. By explicitly diagonalizing the Hamiltonian in the latter spaces, we compute several infinite families of eigenfunctions of the above models in closed form in terms of generalized Laguerre and Jacobi polynomials.Comment: RevTeX, 31 pages, no figures; important additional conten

Leukoencephalopathy upon disruption of the chloride channel ClC-2

ClC-2 is a broadly expressed plasma membrane chloride channel that is modulated by voltage, cell swelling, and pH. A human mutation leading to a heterozygous loss of ClC-2 has previously been reported to be associated with epilepsy, whereas the disruption of Clcn2 in mice led to testicular and retinal degeneration. We now show that the white matter of the brain and spinal cord of ClC-2 knock-out mice developed widespread vacuolation that progressed with age. Fluid-filled spaces appeared between myelin sheaths of the central but not the peripheral nervous system. Neuronal morphology, in contrast, seemed normal. Except for the previously reported blindness, neurological deficits were mild and included a decreased conduction velocity in neurons of the central auditory pathway. The heterozygous loss of ClC-2 had no detectable functional or morphological consequences. Neither heterozygous nor homozygous ClC-2 knock-out mice had lowered seizure thresholds. Sequencing of a large collection of human DNA and electrophysiological analysis showed that several ClC-2 sequence abnormalities previously found in patients with epilepsy most likely represent innocuous polymorphisms

SLC2A9 (GLUT9) mediates urate reabsorption in the mouse kidney.

Uric acid (UA) is a metabolite of purine degradation and is involved in gout flairs and kidney stones formation. GLUT9 (SLC2A9) was previously shown to be a urate transporter in vitro. In vivo, humans carrying GLUT9 loss-of-function mutations have familial renal hypouricemia type 2, a condition characterized by hypouricemia, UA renal wasting associated with kidney stones, and an increased propensity to acute renal failure during strenuous exercise. Mice carrying a deletion of GLUT9 in the whole body are hyperuricemic and display a severe nephropathy due to intratubular uric acid precipitation. However, the precise role of GLUT9 in the kidney remains poorly characterized. We developed a mouse model in which GLUT9 was deleted specifically along the whole nephron in a tetracycline-inducible manner (subsequently called kidney-inducible KO or kiKO). The urate/creatinine ratio was increased as early as 4 days after induction of the KO and no GLUT9 protein was visible on kidney extracts. kiKO mice are morphologically identical to their wild-type littermates and had no spontaneous kidney stones. Twenty-four-hour urine collection revealed a major increase of urate urinary excretion rate and of the fractional excretion of urate, with no difference in urate concentration in the plasma. Polyuria was observed, but kiKO mice were still able to concentrate urine after water restriction. KiKO mice displayed lower blood pressure accompanied by an increased heart rate. Overall, these results indicate that GLUT9 is a crucial player in renal handling of urate in vivo and a putative target for uricosuric drugs

Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems

The Hall--Post inequalities provide lower bounds on $N$-body energies in terms of $N'$-body energies with $N'<N$. They are rewritten and generalized to be tested with exactly-solvable models of Calogero-Sutherland type in one and higher dimensions. The bound for $N$ spinless fermions in one dimension is better saturated at large coupling than for noninteracting fermions in an oscillatorComment: 7 pages, Latex2e, 2 .eps figure

On quaternary complex Hadamard matrices of small orders

One of the main goals of design theory is to classify, characterize and count various combinatorial objects with some prescribed properties. In most cases, however, one quickly encounters a combinatorial explosion and even if the complete enumeration of the objects is possible, there is no apparent way how to study them in details, store them efficiently, or generate a particular one rapidly. In this paper we propose a novel method to deal with these difficulties, and illustrate it by presenting the classification of quaternary complex Hadamard matrices up to order 8. The obtained matrices are members of only a handful of parametric families, and each inequivalent matrix, up to transposition, can be identified through its fingerprint.Comment: 7 page