We demonstrate that, even though the RMT approach relies on the assumption that levels are missing at random, it is possible to determine the fraction of missing levels and assign the appropriate symmetry class by comparison of their fluctuation properties with the RMT predictions.We introduce a general approach for the study of the collective dynamics of noninteracting random walkers on connected networks. We analyze the movement of R independent (Markovian) walkers, each defined by its own transition matrix. By using the eigenvalues and eigenvectors of the R independent transition matrices, we deduce analytical expressions for the collective stationary distribution and the average number of steps needed by the random walkers to start in a particular configuration and reach specific nodes the first time (mean first-passage times), as well as global times that characterize the global activity. Selleck GW788388 We apply these results to the study of mean first-encounter times for local and nonlocal random walk strategies on different types of networks, with both synchronous and asynchronous motion.We study the efficiency of sliding locomotion for three-link bodies with prescribed joint angle motions. The bodies move with no inertia, under dry (Coulomb) friction that is anisotropic (different in the directions normal and tangent to the links) and directional (different in the forward and backward tangent directions). Friction coefficient space can be partitioned into several regions, each with distinct types of efficient kinematics. These include kinematics resembling lateral undulation with very anisotropic friction, small-amplitude reciprocal kinematics, very large-amplitude kinematics near isotropic friction, and kinematics that are very asymmetric about the flat state. In the two-parameter shape space, zero net rotation for elliptical trajectories occurs mainly with bilateral or antipodal symmetry. These symmetric subspaces have about the same peak efficiency as the full space but with much smaller dimension. Adding the second or third harmonics greatly increases the numbers of local optimal for efficiency, but only modestly increases the peak efficiency. Random ensembles with higher harmonics have efficiency distributions that peak near a certain nonzero value and decay rapidly up to the maximum efficiency. A stochastic optimization algorithm is developed to compute optima with higher harmonics. These are simple closed curves, sharpened versions of the elliptical optima in most cases, and achieve much higher efficiencies mainly for small normal friction. With a linear (viscous) resistance law, the optimal trajectories are similar in much of the friction coefficient space, and relative efficiencies are much lower except with very large normal friction.Efficient feature selection from high-dimensional datasets is a very important challenge in many data-driven fields of science and engineering. We introduce a statistical mechanics inspired strategy that addresses the problem of sparse feature selection in the context of binary classification by leveraging a computational scheme known as expectation propagation (EP). The algorithm is used in order to train a continuous-weights perceptron learning a classification rule from a set of (possibly partly mislabeled) examples provided by a teacher perceptron with diluted continuous weights. We test the method in the Bayes optimal setting under a variety of conditions and compare it to other state-of-the-art algorithms based on message passing and on expectation maximization approximate inference schemes. Overall, our simulations show that EP is a robust and competitive algorithm in terms of variable selection properties, estimation accuracy, and computational complexity, especially when the student perceptron is trained from correlated patterns that prevent other iterative methods from converging. Furthermore, our numerical tests demonstrate that the algorithm is capable of learning online the unknown values of prior parameters, such as the dilution level of the weights of the teacher perceptron and the fraction of mislabeled examples, quite accurately. This is achieved by means of a simple maximum likelihood strategy that consists in minimizing the free energy associated with the EP algorithm.The one-dimensional δ-function interacting Bose gas (the Lieb-Liniger model) is an integrable system, which can model experiments with ultra-cold atoms in one-dimensional traps. Even though the model is integrable, integrability breaking effects are always present in the real-world experiments. In this work we consider the integrability breaking due to atomic loss, which is the most relevant effect in the experiments. We set up a framework for the exact computation of the losses of the canonical charges of the model, and compute an exact result for the energy loss due to the local K-body processes, valid for arbitrary K. Our result takes the form of multiple integrals, which are explicitly factorized in the experimentally relevant cases of K=1,2,3. A physiological profiling study was done to evaluate thermal strain as well as fluid and electrolyte balances on heat-acclimatised men performing a 72-km route march in a field setting. 38 male soldiers (age range 18-23 years) participated in the study, as part of a cohort that marched for 72 km, with loads for about 26 hours. Core temperature and heart rate sensors were used for the duration of the march. Fluid and food intake and output were monitored for the duration of the march. Blood samples were taken one day before the march (pre-march), immediately after the march before they had any opportunity to recover (Post 1) and on the 15th day after the march to ascertain recovery (Post 2) to assess fluid and electrolyte profiles. Mean core temperature was within safe limits, ranging from 37.1 to 38.1°C throughout the march. There was an average overall decrease in serum sodium levels, a decline in serum sodium concentration in 28 participants and three instances of hyponatraemia (serum sodium concentration < 135 mmol/L). Our study found low thermal strain among heat-acclimatised individuals during a 72-km route march. However, there was an average overall decrease in serum sodium levels, even when the participants were allowed to drink ad libitum. Challenges of exercise-associated hyponatraemia during prolonged activities remain to be addressed.Our study found low thermal strain among heat-acclimatised individuals during a 72-km route march. However, there was an average overall decrease in serum sodium levels, even when the participants were allowed to drink ad libitum. Challenges of exercise-associated hyponatraemia during prolonged activities remain to be addressed.