Number of Common Sites Visited by N Random Walkers

We compute analytically the mean number of common sites, W_N(t), visited by N independent random walkers each of length t and all starting at the origin at t=0 in d dimensions. We show that in the (N-d) plane, there are three distinct regimes for the asymptotic large t growth of W_N(t). These three regimes are separated by two critical lines d=2 and d=d_c(N)=2N/(N-1) in the (N-d) plane. For d<2, W_N(t)\sim t^{d/2} for large t (the N dependence is only in the prefactor). For 2<d<d_c(N), W_N(t)\sim t^{\nu} where the exponent \nu= N-d(N-1)/2 varies with N and d. For d>d_c(N), W_N(t) approaches a constant as t\to \infty. Exactly at the critical dimensions there are logaritmic corrections: for d=2, we get W_N(t)\sim t/[\ln t]^N, while for d=d_c(N), W_N(t)\sim \ln t for large t. Our analytical predictions are verified in numerical simulations.Comment: 5 pages, 3 .eps figures include

Kinetics of stochastically-gated diffusion-limited reactions and geometry of random walk trajectories

In this paper we study the kinetics of diffusion-limited, pseudo-first-order A + B -> B reactions in situations in which the particles' intrinsic reactivities vary randomly in time. That is, we suppose that the particles are bearing "gates" which interchange randomly and independently of each other between two states - an active state, when the reaction may take place, and a blocked state, when the reaction is completly inhibited. We consider four different models, such that the A particle can be either mobile or immobile, gated or ungated, as well as ungated or gated B particles can be fixed at random positions or move randomly. All models are formulated on a $d$-dimensional regular lattice and we suppose that the mobile species perform independent, homogeneous, discrete-time lattice random walks. The model involving a single, immobile, ungated target A and a concentration of mobile, gated B particles is solved exactly. For the remaining three models we determine exactly, in form of rigorous lower and upper bounds, the large-N asymptotical behavior of the A particle survival probability. We also realize that for all four models studied here such a probalibity can be interpreted as the moment generating function of some functionals of random walk trajectories, such as, e.g., the number of self-intersections, the number of sites visited exactly a given number of times, "residence time" on a random array of lattice sites and etc. Our results thus apply to the asymptotical behavior of the corresponding generating functions which has not been known as yet.Comment: Latex, 45 pages, 5 ps-figures, submitted to PR

Order statistics of the trapping problem

When a large number N of independent diffusing particles are placed upon a site of a d-dimensional Euclidean lattice randomly occupied by a concentration c of traps, what is the m-th moment of the time t_{j,N} elapsed until the first j are trapped? An exact answer is given in terms of the probability Phi_M(t) that no particle of an initial set of M=N, N-1,..., N-j particles is trapped by time t. The Rosenstock approximation is used to evaluate Phi_M(t), and it is found that for a large range of trap concentracions the m-th moment of t_{j,N} goes as x^{-m} and its variance as x^{-2}, x being ln^{2/d} (1-c) ln N. A rigorous asymptotic expression (dominant and two corrective terms) is given for for the one-dimensional lattice.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

The roots of "Western European societal evolution". A concept of Europe by Jenő Szűcs

Jenő Szűcs wrote his essay entitled Sketch on the three regions of Europe in the early 1980s in Hungary. During these years, a historically well-argued opinion emphasising a substantial difference between Central European and Eastern European societies was warmly received in various circles of the political opposition. In a wider European perspective Szűcs used the old “liberty topos” which claims that the history of Europe is no other than the fulfillment of liberty. In his Sketch, Szűcs does not only concentrate on questions concerning the Middle Ages in Western Europe. Yet it is this stream of thought which brought a new perspective to explaining European history. His picture of the Middle Ages represents well that there is a way to integrate all typical Western motifs of post-war self-definition into a single theory. Mainly, the “liberty motif”, as a sign of “Europeanism” – in the interpretation of Bibó’s concept, Anglo-saxon Marxists and Weber’s social theory –, developed from medieval concepts of state and society and from an analysis of economic and social structures. Szűcs’s historical aspect was a typical intellectual product of the 1980s: this was the time when a few Central European historians started to outline non-Marxist aspects of social theory and categories of modernisation theories, but concealing them with Marxist terminology

Efficacy and Safety of Technosphere Inhaled Insulin Compared With Technosphere Powder Placebo in Insulin-Naive Type 2 Diabetes Suboptimally Controlled With Oral Agents

OBJECTIVE—This double-blind, placebo-controlled, randomized, multicenter, parallel-group study compared the efficacy, safety, and tolerability of Technosphere insulin with Technosphere powder as placebo in insulin-naive type 2 diabetic patients whose diabetes was suboptimally controlled with oral antidiabetic agents

Diffusion with random distribution of static traps

The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability P(c,t) as a function of the trap concentration c and the time t. Theoretical arguments are presented, based on earlier work of Donsker and Varadhan and of Rosenstock, why in two dimensions one expects a data collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both data collapses show a clear crossover from the early-time Rosenstock behavior to Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure

Update and Next Steps for Real-World Translation of Interventions for Type 2 Diabetes Prevention: Reflections From a Diabetes Care Editors’ Expert Forum

The International Diabetes Federation estimates that 415 million adults worldwide now have diabetes and 318 million have impaired glucose tolerance. These numbers are expected to increase to 642 million and 482 million, respectively, by 2040. This burgeoning pandemic places an enormous burden on countries worldwide, particularly resource-poor regions. Numerous landmark trials evaluating both intensive lifestyle modification and pharmacological interventions have persuasively demonstrated that type 2 diabetes can be prevented or its onset can be delayed in high-risk individuals with impaired glucose tolerance. However, key challenges remain, including how to scale up such approaches for widespread translation and implementation, how to select appropriately from various interventions and tailor them for different populations and settings, and how to ensure that preventive interventions yield clinically meaningful, cost-effective outcomes. In June 2015, a Diabetes Care Editors’ Expert Forum convened to discuss these issues. This article, an outgrowth of the forum, begins with a summary of seminal prevention trials, followed by a discussion of considerations for selecting appropriate populations for intervention and the clinical implications of the various diagnostic criteria for prediabetes. The authors outline knowledge gaps in need of elucidation and explore a possible new avenue for securing regulatory approval of a prevention-related indication for metformin, as well as specific considerations for future pharmacological interventions to delay the onset of type 2 diabetes. They conclude with descriptions of some innovative, pragmatic translational initiatives already under way around the world

Determinants of the Use of a Diabetes Risk-Screening Test

A study was designed to investigate why people do or do not make use of a diabetes risk test developed to facilitate the timely diagnosis of diabetes. Data were collected using a web-based questionnaire, which was based on the Health Belief Model, the Theory of Planned Behavior, and the Threatening Medical Situations Inventory. People who had and had not used the risk test were recruited to complete the survey. The sample consisted of 205 respondents: 44% who had used the test and 56% who had not. The hypothesized relationships between the dependent variable (diabetes risk test use) and the determinants used in this study were tested using logistic regression analysis. Only two significant predictors of diabetes risk test use were found: gender and barriers. More women than men use the test. Furthermore, people who experience more barriers will be less inclined to use the test. The contribution of diabetes screening tests fully depends on people’s willingness to use them. To optimize the usage of such test, it is especially important to address the barriers as perceived by the public. Two types of barriers must be addressed: practical barriers (time to take the test, fear of complexity of the test), and consequential barriers (fear of the disease and treatment, uncertainties about where to go in the case of an increased risk of diabetes)

DURAbility of Basal Versus Lispro Mix 75/25 Insulin Efficacy (DURABLE) Trial 24-Week Results: Safety and efficacy of insulin lispro mix 75/25 versus insulin glargine added to oral antihyperglycemic drugs in patients with type 2 diabetes

OBJECTIVE - To compare the ability of two starter insulin regimens to achieve glycemic control in a large, ethnically diverse population with type 2 diabetes. RESEARCH DESIGN AND METHODS - During the initiation phase of the DURABLE trial, patients were randomized to a twice-daily lispro mix 75/25 (LM75/25; 75% lispro protamine suspension, 25% lispro) (n = 1,045) or daily glargine (GL) (n = 1,046) with continuation of prestudy oral antihyperglycemic drugs. RESULTS - Baseline A1C was similar (LM75/25: 9.1 +/- 1.3%; GL: 9.0 +/- 1.2%; P = 0.414). At 24 weeks, LM75/25 patients had tower A1C than GL patients (7.2 +/- 1.1. vs. 7.3 +/- 1.1%, P = 0.005), greater A1C reduction (-1.8 +/- 1.3 vs. -1.7 +/- 1.3%, P = 0.005), and higher percentage reaching A1C target CONCLUSIONS - Compared With GL, LM75/25 resulted in slightly lower A1C at 24 weeks and a moderately higher percentage reaching A1C targe