On a class of exact solutions to the Fokker-Planck equations

In this paper we study under which circumstances there exists a general change of gross variables that transforms any FokkerPlanck equation into another of the OrnsteinUhlenbeck class that, therefore, has an exact solution. We find that any FokkerPlanck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo and Gompertz models.

Petrou type-D perfect-fluid solutions in generalized Kerr-Schild form.

Generalized KerrSchild space-times for a perfect-fluid source are investigated. New Petrov type D perfect fluid solutions are obtained starting from conformally flat perfect-fluid metrics.

Petrou types D and II perfect-fluid solutions in generalized Kerr-Schild form.

Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized KerrSchild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied. Finally, a detailed analysis of a new class of spherically symmetric static perfect-fluid metrics is given.

Plasma lipoprotein-associated phospholipase A2 activity in Alzheimer's disease, amnestic mild cognitive impairment, and cognitively healthy elderly subjects: a cross-sectional study.

ABSTRACT: INTRODUCTION: Lipoprotein-associated phospholipase A2 (Lp-PLA2) is a circulating enzyme with pro-inflammatory and oxidative activities associated with cardiovascular disease and ischemic stroke. While high plasma Lp-PLA2 activity was reported as a risk factor for dementia in the Rotterdam study, no association between Lp-PLA2 mass and dementia or Alzheimer's disease (AD) was detected in the Framingham study. The objectives of the current study were to explore the relationship of plasma Lp-PLA2 activity with cognitive diagnoses (AD, amnestic mild cognitive impairment (aMCI), and cognitively healthy subjects), cardiovascular markers, cerebrospinal fluid (CSF) markers of AD, and apolipoprotein E (APOE) genotype. METHODS: Subjects with mild AD (n = 78) and aMCI (n = 59) were recruited from the Memory Clinic, University Hospital, Basel, Switzerland; cognitively healthy subjects (n = 66) were recruited from the community. Subjects underwent standardised medical, neurological, neuropsychological, imaging, genetic, blood and CSF evaluation. Differences in Lp-PLA2 activity between the cognitive diagnosis groups were tested with ANOVA and in multiple linear regression models with adjustment for covariates. Associations between Lp-PLA2 and markers of cardiovascular disease and AD were explored with Spearman's correlation coefficients. RESULTS: There was no significant difference in plasma Lp-PLA2 activity between AD (197.1 (standard deviation, SD 38.4) nmol/min/ml) and controls (195.4 (SD 41.9)). Gender, statin use and low-density lipoprotein cholesterol (LDL) were independently associated with Lp-PLA2 activity in multiple regression models. Lp-PLA2 activity was correlated with LDL and inversely correlated with high-density lipoprotein (HDL). AD subjects with APOE-ε4 had higher Lp-PLA2 activity (207.9 (SD 41.2)) than AD subjects lacking APOE-ε4 (181.6 (SD 26.0), P = 0.003) although this was attenuated by adjustment for LDL (P = 0.09). No strong correlations were detected for Lp-PLA2 activity and CSF markers of AD. CONCLUSION: Plasma Lp-PLA2 was not associated with a diagnosis of AD or aMCI in this cross-sectional study. The main clinical correlates of Lp-PLA2 activity in AD, aMCI and cognitively healthy subjects were variables associated with lipid metabolism.

Short-term overexpression of a constitutively active form of AMP-activated protein kinase in the liver leads to mild hypoglycemia and fatty liver.

AMP-activated protein kinase (AMPK) is a major therapeutic target for the treatment of diabetes. We investigated the effect of a short-term overexpression of AMPK specifically in the liver by adenovirus-mediated transfer of a gene encoding a constitutively active form of AMPKalpha2 (AMPKalpha2-CA). Hepatic AMPKalpha2-CA expression significantly decreased blood glucose levels and gluconeogenic gene expression. Hepatic expression of AMPKalpha2-CA in streptozotocin-induced and ob/ob diabetic mice abolished hyperglycemia and decreased gluconeogenic gene expression. In normal mouse liver, AMPKalpha2-CA considerably decreased the refeeding-induced transcriptional activation of genes encoding proteins involved in glycolysis and lipogenesis and their upstream regulators, SREBP-1 (sterol regulatory element-binding protein-1) and ChREBP (carbohydrate response element-binding protein). This resulted in decreases in hepatic glycogen synthesis and circulating lipid levels. Surprisingly, despite the inhibition of hepatic lipogenesis, expression of AMPKalpha2-CA led to fatty liver due to the accumulation of lipids released from adipose tissue. The relative scarcity of glucose due to AMPKalpha2-CA expression led to an increase in hepatic fatty acid oxidation and ketone bodies production as an alternative source of energy for peripheral tissues. Thus, short-term AMPK activation in the liver reduces blood glucose levels and results in a switch from glucose to fatty acid utilization to supply energy needs.

Single-valued solutions for the Böhm-Bawerk horse market game

Single-valued solutions for the case of two-sided market games without product differentiation, also known as Böhm-Bawerk horse market games, are analyzed. The nucleolus is proved to coincide with the tau-value, and is thus the midpoint of the core. Moreover a characterization of this setof games in terms of the assignment matrix is provided.

Time consistent Pareto solutions in common access resource gameswith asymmetric players

In the analysis of equilibrium policies in a di erential game, if agents have different time preference rates, the cooperative (Pareto optimum) solution obtained by applying the Pontryagin's Maximum Principle becomes time inconsistent. In this work we derive a set of dynamic programming equations (in discrete and continuous time) whose solutions are time consistent equilibrium rules for N-player cooperative di erential games in which agents di er in their instantaneous utility functions and also in their discount rates of time preference. The results are applied to the study of a cake-eating problem describing the management of a common property exhaustible natural resource. The extension of the results to a simple common property renewable natural resource model in in nite horizon is also discussed.

Heterogeneous discounting in consumption-investment problems. Time consistent solutions

[cat] En aquest treball s'analitza un model estocàstic en temps continu en el que l'agent decisor descompta les utilitats instantànies i la funció final amb taxes de preferència temporal constants però diferents. En aquest context es poden modelitzar problemes en els quals, quan el temps s'acosta al moment final, la valoració de la funció final incrementa en comparació amb les utilitats instantànies. Aquest tipus d'asimetria no es pot descriure ni amb un descompte estàndard ni amb un variable. Per tal d'obtenir solucions consistents temporalment es deriva l'equació de programació dinàmica estocàstica, les solucions de la qual són equilibris Markovians. Per a aquest tipus de preferències temporals, s'estudia el model clàssic de consum i inversió (Merton, 1971) per a les funcions d'utilitat del tipus CRRA i CARA, comparant els equilibris Markovians amb les solucions inconsistents temporalment. Finalment es discuteix la introducció del temps final aleatori.

Coalitionally monotonic set-solutions for cooperative TU games

A static comparative study on set-solutions for cooperative TU games is carried out. The analysis focuses on studying the compatibility between two classical and reasonable properties introduced by Young (1985) in the context of single valued solutions, namely core-selection and coalitional monotonicity. As the main result, it is showed that coalitional monotonicity is not only incompatible with the core-selection property but also with the bargaining-selection property. This new impossibility result reinforces the tradeoff between these kinds of interesting and intuitive economic properties. Positive results about compatibility between desirable economic properties are given replacing the core selection requirement by the core-extension property.

Aggregate monotonic stable single-valued solutions for cooperative games

[cat] En aquest treball caracteritzem les solucions puntuals de jocs cooperatius d'utilitat transferible que compleixen selecció del core i monotonia agregada. També mostrem que aquestes dues propietats són compatibles amb la individualitat racional, la propietat del jugador fals i la propietat de simetria. Finalment, caracteritzem les solucions puntuals que compleixen les cinc propietats a l'hora.

Social dysfunctioning after mild to moderate first-ever stroke at vocational age.

BACKGROUND: With improvements in stroke treatments, the number of patients with dramatic recovery is increasing. However, many of them are still complaining of difficulties in returning to work and every day activities. The aim was to assess work and social dysfunctioning in patients with minor to moderate stroke and explore its contributing factors. METHODS: Consecutive patients were prospectively included at a median 7 months after a first-ever stroke. Scores on the Work and Social Adjustment Scale (WSAS), a generic self-reported scale for assessing social functioning, were correlated with scores on the National Institutes of Health Stroke Scale (NIHSS), activities of daily living, Hospital Anxiety and Depression scale (HAD) and MMSE, Iowa Scale of Personality Changes and return to work at 1 year. RESULTS: Among the 84 included patients (mean age 43.5 years), 57 (68%; 95% CI 57 to 78%) complained of significant perturbation of functioning attributed to stroke. WSAS was highly significantly related to modified Rankin scale, daily living activities, Iowa Scale of Personality Changes and return to work at 1 year. Using ordinal logistic regression, the contributors to WSAS were initial neurological severity (NIHSS at admission), HAD and MMSE. CONCLUSIONS: The study showed that up to 68% of our patients complained of significant work and social dysfunction due to stroke, despite a good clinical outcome. This self-estimation was correlated to external validation criteria, stressing the high burden of stroke from the patient's viewpoint. Moreover, when compared across diseases, social dysfunctioning after mild stroke was as important as in other major disabling diseases.

Velocity fluctuations of fracturelike disruptions of associating polymer solutions

Velocity has been measured as a function of time for propagating crack tips as water is injected into solutions of end-capped associating polymers in a rectanguar Hele-Shaw cell. Measurements were performed for flows with different values of cell gap, channel width, polymer molecular weight, and polymer concentration. The condition for the onset of fracturelike behavior is well described by a Deborah number which uses the shear-thinning shear rate of the polymer solution as a characteristic frequency for network relaxation. At low molecular weight, the onset of fracturelike pattern evolution is accompanied by an abrupt jump in tip velocity, followed by a lower and approximately constant acceleration. At high molecular weight, the transition to fracturelike behavior involves passing through a regime that may be understood in terms of stick-slip dynamics. The crack-tip wanders from side to side and fluctuates (in both speed and velocity along the channel) with a characteristic frequency which depends linearly on the invading fluid injection rate.

Velocity-jump instabilities in Hele-Shaw flow of associating polymer solutions

We study fracturelike flow instabilities that arise when water is injected into a Hele-Shaw cell filled with aqueous solutions of associating polymers. We explore various polymer architectures, molecular weights, and solution concentrations. Simultaneous measurements of the finger tip velocity and of the pressure at the injection point allow us to describe the dynamics of the finger in terms of the finger mobility, which relates the velocity to the pressure gradient. The flow discontinuities, characterized by jumps in the finger tip velocity, which are observed in experiments with some of the polymer solutions, can be modeled by using a nonmonotonic dependence between a characteristic shear stress and the shear rate at the tip of the finger. A simple model, which is based on a viscosity function containing both a Newtonian and a non-Newtonian component, and which predicts nonmonotonic regions when the non-Newtonian component of the viscosity dominates, is shown to agree with the experimental data.