Stretched Exponential Relaxation in the Biased Random Voter Model

We study the relaxation properties of the voter model with i.i.d. random bias. We prove under mild condions that the disorder-averaged relaxation of this biased random voter model is faster than a stretched exponential with exponent $d/(d+\alpha)$, where $0<\alpha\le 2$ depends on the transition rates of the non-biased voter model. Under an additional assumption, we show that the above upper bound is optimal. The main ingredient of our proof is a result of Donsker and Varadhan (1979).Comment: 14 pages, AMS-LaTe

Hypocretin-1 receptors regulate the reinforcing and reward-enhancing effects of cocaine: pharmacological and behavioral genetics evidence.

Considerable evidence suggests that transmission at hypocretin-1 (orexin-1) receptors (Hcrt-R1) plays an important role in the reinstatement of extinguished cocaine-seeking behaviors in rodents. However, far less is known about the role for hypocretin transmission in regulating ongoing cocaine-taking behavior. Here, we investigated the effects of the selective Hcrt-R1 antagonist SB-334867 on cocaine intake, as measured by intravenous (IV) cocaine self-administration in rats. The stimulatory effects of cocaine on brain reward systems contribute to the establishment and maintenance of cocaine-taking behaviors. Therefore, we also assessed the effects of SB-334867 on the reward-enhancing properties of cocaine, as measured by cocaine-induced lowering of intracranial self-stimulation (ICSS) thresholds. Finally, to definitively establish a role for Hcrt-R1 in regulating cocaine intake, we assessed IV cocaine self-administration in Hcrt-R1 knockout mice. We found that SB-334867 (1-4 mg/kg) dose-dependently decreased cocaine (0.5 mg/kg/infusion) self-administration in rats but did not alter responding for food rewards under the same schedule of reinforcement. This suggests that SB-334867 decreased cocaine reinforcement without negatively impacting operant performance. SB-334867 (1-4 mg/kg) also dose-dependently attenuated the stimulatory effects of cocaine (10 mg/kg) on brain reward systems, as measured by reversal of cocaine-induced lowering of ICSS thresholds in rats. Finally, we found that Hcrt-R1 knockout mice self-administered far less cocaine than wildtype mice across the entire dose-response function. These data demonstrate that Hcrt-R1 play an important role in regulating the reinforcing and reward-enhancing properties of cocaine and suggest that hypocretin transmission is likely essential for establishing and maintaining the cocaine habit in human addicts

Insulin detemir for the treatment of obese patients with type 2 diabetes

The risk for developing type 2 diabetes (T2DM) is greater among obese individuals. Following onset of the disease, patients with T2DM become more likely to be afflicted with diabetic micro- and macrovascular complications. Decreasing body weight has been shown to lower glycosylated hemoglobin and improve other metabolic parameters in patients with T2DM. Medications used to lower blood glucose may increase body weight in patients with T2DM and this has been repeatedly shown to be the case for conventional, human insulin formulations. Insulin detemir is a neutral, soluble, long-acting insulin analog in which threonine-30 of the insulin B-chain is deleted, and the C-terminal lysine is acetylated with myristic acid, a C14 fatty acid chain. Insulin detemir binds to albumin, a property that enhances its pharmacokinetic/pharmacodynamic profile. Results from clinical trials have demonstrated that treatment with insulin detemir is associated with less weight gain than either insulin glargine or neutral protamine Hagedorn insulin. There are many potential reasons for the lower weight gain observed among patients treated with insulin detemir, including lower risk for hypoglycemia and therefore decreased defensive eating due to concern about this adverse event, along with other effects that may be related to the albumin binding of this insulin that may account for lower within-patient variability and consistent action. These might include faster transport across the blood–brain barrier, induction of satiety signaling in the brain, and preferential inhibition of hepatic glucose production versus peripheral glucose uptake. Experiments in diabetic rats have also indicated that insulin detemir increases adiponectin levels, which is associated with both weight loss and decreased eating

Possible loss and recovery of Gibbsianness during the stochastic evolution of Gibbs measures

We consider Ising-spin systems starting from an initial Gibbs measure $\nu$ and evolving under a spin-flip dynamics towards a reversible Gibbs measure $\mu\not=\nu$. Both $\nu$ and $\mu$ are assumed to have a finite-range interaction. We study the Gibbsian character of the measure $\nu S(t)$ at time $t$ and show the following: (1) For all $\nu$ and $\mu$, $\nu S(t)$ is Gibbs for small $t$. (2) If both $\nu$ and $\mu$ have a high or infinite temperature, then $\nu S(t)$ is Gibbs for all $t>0$. (3) If $\nu$ has a low non-zero temperature and a zero magnetic field and $\mu$ has a high or infinite temperature, then $\nu S(t)$ is Gibbs for small $t$ and non-Gibbs for large $t$. (4) If $\nu$ has a low non-zero temperature and a non-zero magnetic field and $\mu$ has a high or infinite temperature, then $\nu S(t)$ is Gibbs for small $t$, non-Gibbs for intermediate $t$, and Gibbs for large $t$. The regime where $\mu$ has a low or zero temperature and $t$ is not small remains open. This regime presumably allows for many different scenarios

Observations on the Performance of Centrifugal Pumps at Low Reynolds Numbers

From the results presented herein it is clear that the viscous flow in the centrifugal pump impeller is very complicated, but we see that the internal flow itself is not necessarily too inefficient and further that the hydraulic torque does not necessarily increase with lower Reynolds numbers. These results mean that the effect of external disc friction and its interaction in the volute are as important as the impeller design itself for such viscous flows. The present tests suggest that a pump which works well at high Reynolds numbers, as for water application, will not necessarily be the best pump for the low Reynolds number application. These internal flows are certainly very complicated and the authors hope that some of the techniques and suggestions made herein will be used for such work by others in the future

The renormalization transformation for two-type branching models

This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting within colonies. Their large-scale space-time behavior can be studied by means of a renormalization program. This program, which has been carried out successfully in a number of other cases (mostly one-dimensional), is based on the construction and the analysis of a nonlinear renormalization transformation, acting on the diffusion function for the components of the system and connecting the evolution of successive block averages on successive time scales. We identify a general class of diffusion functions on the positive quadrant for which this renormalization transformation is well-defined and, subject to a conjecture on its boundary behavior, can be iterated. Within certain subclasses, we identify the fixed points for the transformation and investigate their domains of attraction. These domains of attraction constitute the universality classes of the system under space-time scaling.Comment: 48 pages, revised version, to appear in Ann. Inst. H. Poincare (B) Probab. Statis

The Potential of Restarts for ProbSAT

This work analyses the potential of restarts for probSAT, a quite successful algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT instances that are close to the phase transition. We estimate an optimal restart time from empirical data, reaching a potential speedup factor of 1.39. Calculating restart times from fitted probability distributions reduces this factor to a maximum of 1.30. A spin-off result is that the Weibull distribution approximates the runtime distribution for over 93% of the used instances well. A machine learning pipeline is presented to compute a restart time for a fixed-cutoff strategy to exploit this potential. The main components of the pipeline are a random forest for determining the distribution type and a neural network for the distribution's parameters. ProbSAT performs statistically significantly better than Luby's restart strategy and the policy without restarts when using the presented approach. The structure is particularly advantageous on hard problems.Comment: Eurocast 201

Laboratory Investigations of the Mechanism of Cavitation

The paper describes some experimental investigations of the formation and collapse of cavitation bubbles. The experiments were carried on in the high-speed water tunnel of the Hydrodynamics Laboratory of the California Institute of Technology under the sponsorship of the Research and Development Division of the Bureau of Ordnance of the U. S. Navy and the Fluid Mechanics Section of the Office of Naval Research. A detailed study of the formation and collapse of the individual bubbles has been carried on by the use of high-speed motion pictures taken at rates up to 20,000 per sec. From these records calculations have been made of rate of formation and collapse of the bubbles. Deductions have been drawn from these results concerning the physical mechanism of the cavitation phenomenon