Stability of a two-sublattice spin-glass model

We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from antiferromagnetic to spin glass state. The eigenvalues associated with replica-symmetric perturbations are in general complex. The natural generalization of the usual stability condition is to require the real part of these eigenvalues to be positive. The necessary and sufficient conditions for all the roots of the secular equation to have positive real parts is given by the Hurwitz criterion. The generalized stability condition allows a consistent analysis of the phase diagram within the replica-symmetric approximation.Comment: 21 pages, 5 figure

A solute gradient in the tear meniscus I. A hypothesis to explain Marx's line

Marx's line is a line of mucosal staining behind the mucocutaneous junction. It can be demonstrated throughout life in all normal lids by staining with lissamine green and related dyes. Of all the body orifices, only the mucosae of the eye and mouth are directly exposed to the atmosphere. In this paper, we suggest that for the eye, this exposure leads to the formation of Marx's line. The tear meniscus thins progressively toward its apex, where it is pinned at the mucocutaneous junction of the lid. It also thins toward the black line, which segregates the meniscus from the tear film after the blink. We predict that, because of the geometry of the tear meniscus, evaporation generates a solute gradient across the meniscus profile in the anteroposterior plane, which peaks at the meniscus apices at the end of the interblink. One outcome would be to amplify the level of tear molarity at these sites so that they reach hyperosmolar proportions. Preliminary mathematical modeling suggests that dilution of this effect by advection and diffusion of solute away from the meniscus apex at the mucocutaneous junction will be restricted by spatial constraints, the presence of tear and surface mucins at this site, and limited fluid flow. We conclude that evaporative water loss from the tear meniscus may result in a physiological zone of hyperosmolar and related stresses to the occlusal conjunctiva, directly behind the mucocutaneous junction. We hypothesize that this stimulates a high epithelial cell turnover at this site, incomplete epithelial maturation, and a failure to express key molecules such as MUC 16 and galectin-3, which, with the tight junctions between surface epithelial cells, are necessary to seal the ocular surface and prevent penetration of dyes and other molecules into the epithelium. This is proposed as the basis for Marx's line. In Part II of this paper (also published in this issue of The Ocular Surface), we address additional pathophysiological consequences of this mechanism, affecting lid margins

A solute gradient in the tear meniscus II. implications for lid margin disease, including meibomian gland dysfunction

We have hypothesized previously that evaporation from the tears generates a solute gradient across the tear meniscus, which delivers hyperosmolar stress to the mucocutaneous junction (MCJ) of the lid margin. This is proposed as the basis for Marx's line, a line of staining with topically applied dyes that lies directly behind the MCJ. In this article, we consider the implications of this hypothesis for progressive damage to the lid margin as an age-related phenomenon, its amplification in dry eye states, and its possible role in the etiology of meibomian gland dysfunction (MGD). It is suggested that a hyperosmolar or related stimulus, acting behind the MCJ over a lifetime, promotes the anterior migration of the MCJ, which is a feature of the aging lid margin. This mechanism would be amplified in dry eye states, not only by reason of increased tear molarity at the meniscus apex but also by raising the concentration of inflammatory peptides at this site. This could explain the increased width and irregularity of Marx's line in dry eye. While the presence of stem cells at the lid margin may equip this region to respond to such stress, their depletion could be the basis of irreversible lid margin damage. It is further proposed, given the proximity of the MCJ to the meibomian gland orifices, that the solute gradient mechanism could play a role in the initiation of MGD by delivering hyperosmolar and inflammatory stresses to the terminal ducts and orifices of the glands. By the same token, the presence of a zone of increased epithelial permeability in this region may provide a back door route for the delivery of drugs in the treatment of MGD

A mass and solute balance model for tear volume & osmolarity in the normal and the dry eye

Tear hyperosmolarity is thought to play a key role in the mechanism of dry eye, a common symptomatic condition accompanied by visual disturbance, tear film instability, inflammation and damage to the ocular surface. We have constructed a model for the mass and solute balance of the tears, with parameter estimation based on extensive data from the literature which permits the influence of tear evaporation, lacrimal flux and blink rate on tear osmolarity to be explored. In particular the nature of compensatory events has been estimated in aqueous-deficient (ADDE) and evaporative (EDE) dry eye.\ud \ud The model reproduces observed osmolarities of the tear meniscus for the healthy eye and predicts a higher concentration in the tear film than meniscus in normal and dry eye states. The differential is small in the normal eye, but is significantly increased in dry eye, especially for the simultaneous presence of high meniscus concentration and low meniscus radius. This may influence the interpretation of osmolarity values obtained from meniscus samples since they need not fully reflect potential damage to the ocular surface caused by tear film hyperosmolarity.\ud \ud Interrogation of the model suggests that increases in blink rate may play a limited role in compensating for a rise in tear osmolarity in ADDE but that an increase in lacrimal flux, together with an increase in blink rate, may delay the development of hyperosmolarity in EDE. Nonetheless, it is predicted that tear osmolarity may rise to much higher levels in EDE than ADDE before the onset of tear film breakup, in the absence of events at the ocular surface which would independently compromise tear film stability. Differences in the predicted responses of the pre-ocular tears in ADDE compared to EDE or hybrid disease to defined conditions suggest that no single, empirically-accessible variable can act as a surrogate for tear film concentration and the potential for ocular surface damage. This emphasises the need to measure and integrate multiple diagnostic indicators to determine outcomes and prognosis. Modelling predictions in addition show that further studies concerning the possibility of a high lacrimal flux phenotype in EDE are likely to be profitable

Making confining strings out of mesons

The light mesons such as pi, rho, omega, f0, and a0 are possible candidates of magnetic degrees of freedom, if a magnetic dual picture of QCD exists. We construct a linear sigma model to describe spontaneous breaking of the magnetic gauge group, in which there is a stable vortex configuration of vector and scalar mesons. We numerically examine whether such a string can be interpreted as the confining string. By using meson masses and couplings as inputs, we calculate the tension of the string as well as the strength of the Coulomb force between static quarks. They are found to be consistent with those inferred from the quarkonium spectrum and the Regge trajectories of hadrons. By using the same Lagrangian, the critical temperature of the QCD phase transition is estimated, and a non-trivial flavor dependence is predicted. We also discuss a possible connection between the Seiberg duality and the magnetic model we studied.Comment: 22 pages, 2 figures, 3 tables, typos corrected, references adde

187^{187}Re(\gamm,n) cross section close to and above the neutron threshold

The neutron capture cross section of the unstable nucleus $^{186}$Re is studied by investigating the inverse photodisintegration reaction $^{187}$Re($\gamma$,n). The special interest of the {\it s}-process branching point $^{186}$Re is related to the question of possible {\it s}-process contributions to the abundance of the {\it r}-process chronometer nucleus ^{187}$Re. We use the photoactivation technique to measure photodisintegration rates. Our experimental results are in good agreement with two different statistical model calculations. Although the cross sections predicted by both models for the inverse reaction$^{186}$Re(n,$\gamma$) is too low to remove the overproduction of$^{186}$Os; the two predicted neutron-capture cross sections differ by a factor of 2.4; this calls for future theoretical study.Comment: Phys. Rev. C, in pres

Non-Abelian Vortices of Higher Winding Numbers

We make a detailed study of the moduli space of winding number two (k=2) axially symmetric vortices (or equivalently, of co-axial composite of two fundamental vortices), occurring in U(2) gauge theory with two flavors in the Higgs phase, recently discussed by Hashimoto-Tong (hep-th/0506022) and Auzzi-Shifman-Yung (hep-th/0511150). We find that it is a weighted projective space WCP^2_(2,1,1)=CP^2/Z_2. This manifold contains an A_1-type (Z_2) orbifold singularity even though the full moduli space including the relative position moduli is smooth. The SU(2) transformation properties of such vortices are studied. Our results are then generalized to U(N) gauge theory with N flavors, where the internal moduli space of k=2 axially symmetric vortices is found to be a weighted Grassmannian manifold. It contains singularities along a submanifold.Comment: 32 pages, 1 figure, the final version published in PR

The role of human primary motor cortex in the production of skilled finger sequences

Human primary motor cortex (M1) is essential for producing dexterous hand movements. Although distinct subpopulations of neurons are activated during single-finger movements, it remains unknown whetherM1also represents sequences of multiple finger movements. Using novel multivariate functional magnetic resonance imaging (fMRI) analysis techniques and combining evidence from both 3T and 7T fMRI data, we found that after 5 d of intense practice, premotor and parietal areas encoded the different movement sequences. There was little or no evidence for a sequence representation in M1. Instead, activity patterns in M1 could be fully explained by a linear combination of patterns for the constituent individual finger movements, with the strongest weight on the first finger of the sequence. Using passive replay of sequences, we show that this first-finger effect is due to neuronal processes involved in the active execution, rather than to a hemodynamic nonlinearity. These results suggest thatM1receives increased input from areas with sequence representations at the initiation of a sequence, but thatM1activity itself relates to the execution of component finger presses only. These results improve our understanding of the representation of finger sequences in the human neocortex after short-term training and provide important methodological advances for the study of long-term skill development

Spectral-Function Sum Rules in Supersymmetry Breaking Models

The technique of Weinberg's spectral-function sum rule is a powerful tool for a study of models in which global symmetry is dynamically broken. It enables us to convert information on the short-distance behavior of a theory to relations among physical quantities which appear in the low-energy picture of the theory. We apply such technique to general supersymmetry breaking models to derive new sum rules.Comment: 18 pages, 1 figur