Stability of the Periodic Toda Lattice in the Soliton Region

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the periodic (and slightly more generally of the quasi-periodic finite-gap) Toda lattice for decaying initial data in the soliton region. In addition, we show how to reduce the problem in the remaining region to the known case without solitons.Comment: 28 page

Relative Oscillation Theory for Sturm-Liouville Operators Extended

We extend relative oscillation theory to the case of Sturm--Liouville operators $H u = r^{-1}(-(pu')'+q u)$ with different $p$'s. We show that the weighted number of zeros of Wronskians of certain solutions equals the value of Krein's spectral shift function inside essential spectral gaps.Comment: 16 page

Unique continuation for discrete nonlinear wave equations

We establish unique continuation for various discrete nonlinear wave equations. For example, we show that if two solutions of the Toda lattice coincide for one lattice point in some arbitrarily small time interval, then they coincide everywhere. Moreover, we establish analogous results for the Toda, Kac-van Moerbeke, and Ablowitz-Ladik hierarchies. Although all these equations are integrable, the proof does not use integrability and can be adapted to other equations as well.Comment: 10 page

Passive Supporters of Terrorism and Phase Transitions

We discuss some social contagion processes to describe the formation and spread of radical opinions. The dynamics of opinion spread involves local threshold processes as well as mean field effects. We calculate and observe phase transitions in the dynamical variables resulting in a rapidly increasing number of passive supporters. This strongly indicates that military solutions are inappropriate.Comment: references added concerning previous work of S. Gala

Genetic Variations in Cytokines and Cytokine Receptors Associated with Psoriasis Found by Genome-Wide Association

Genetic variants have long been suspected to be important in psoriasis. Recent work has suggested that HLA-Cw6 on chromosome 6 is the risk variant in the PSORS1 [MIM 177900] susceptibility locus that confers the greatest risk for early onset of psoriasis. Although numerous minor susceptibility loci have been identified by linkage analysis, few biologically relevant candidates have been discovered within these intervals. Recent large-scale genome-wide association studies have yielded new candidates in genes encoding cytokines with functional relevance to psoriasis. Polymorphisms within the genes encoding the IL-12 p40 subunit, IL12B, and one of the IL-23 receptor subunits, IL23R, have been replicated in US and European populations and overlap with risk of Crohn's disease. Polymorphisms within the gene encoding IL-13, a Th2 cytokine, also confer risk for psoriasis. Variants of the gene IL15 encoding IL-15 have been identified that associate with psoriasis in a Chinese population. These discoveries pose the challenge of elucidating the role of common genetic variants in susceptibility to and manifestations of psoriasis

Percutaneous Absorption Of Dexamethasone Estimated By A Plasma Radioimmunoassay

Percutaneous absorption of dexamethasone and its effect on the pituitary adrenal axis were measured in vivo in normal human subjects after application to skin. Specific plasma dexamethasone and cortisol radioimmunoassays were used. Following application of 1% dexamethasone on 500cm2 of normal skin, the plasma dexamethasone concentration was maximal at 2 hr, and the average absorption was 0.25% over 8hr; significant cortisol suppression occurred at 2, 4, and 8hr. This technique: (1) provides an accurate assessment of the in vivo absorption of dexamethasone applied to human skin, (2) avoids exposure of the subjects to radioactive steroids, (3) permits estimation of the quantity of unmetabolized steroids absorbed, and (4) serves as a possible model for the development of similar assays for other topical steroids

Cutaneous Blood Flow and Percutaneous Absorption: A Quantitative Analysis Using a Laser Doppler Velocimeter and a Blood Flow Meter

Cutaneous blood flow has been directly quantitated in vivo for the first time without animal death utilizing the rat skin sandwich flap. This was accomplished by conducting experiments that made a direct correlation between two instruments: a laser Doppler velocimeter and an electromagnetic blood flow meter. Data demonstrate that the correlation between these two instruments is high and reproducible (r = 0.96) with a small (1.3%) coefficient of variation. Blood flow to skin in the unmanipulated state varies from 0.7 to 1.2 mls/min in an anesthetized rat. Application of the blood flow correlation to the determination of percutaneous absorption of caffeine across human skin and benzoic acid across rat skin demonstrates that assuming cutaneous blood flow is a particular value day to day in any skin type results in an apparent wide range of total compound absorbed across that skin on independent occasions. Utilizing actual blood flow measurements to calculate the amount of chemical absorbed reduces the range of variability in the total amount of chemical absorbed and provides a more accurate knowledge of events occurring during a particular time of the absorption process. Quantitation of cutaneous blood flow will be useful in physiologic and pharmacologic studies where actual cutaneous blood flow is likely to be important to the processes studied, e.g., delivery of drug to skin, metabolism within the skin, and disposition of drug to blood and skin following topical drug application

Clinical Symptoms of Skin, Nails, and Joints Manifest Independently in Patients with Concomitant Psoriasis and Psoriatic Arthritis

This study correlated assessment tools for evaluating the severity of skin, nail, and joint symptoms in patients with psoriasis (Pso) and psoriatic arthritis (PsA). Adults with plaque Pso (with or without PsA) were enrolled from four U.S. institutions. Patients were evaluated using a novel 10-area Linear Psoriasis Area and Severity Index (XL-PASI), Psoriatic Arthritis Assessment (PsAA), Psoriatic Arthritis Screening and Evaluation Questionnaire (PASE), Nail Assessment (NA) and Joint Assessment (JA) tools, Psoriasis Weighted Extent and Severity Index (PWESI), and Lattice Physician Global Assessment (LS-PGA). Correlations between assessment tools and individual items in the assessment tools were performed. Data from 180 patients (55 with PsA) were analyzed. Highest correlations between tools (r = 0.77–0.88) were between the XL-PASI, PWESI and LS-PGA. Individual items in the XL-PASI correlated with items in the PWESI for extent skin symptoms, but not for all body areas. Overall, correlations were seen between hands and feet, between face and scalp, and between buttocks, chest, and back. Only low correlation was seen between items assessing joint symptoms with items assessing skin symptoms. These data support the notion that the complex phenotype of psoriatic disease requires instruments that assess the severity of skin, nails, and joints separately