Generalized (m,k)-Zipf law for fractional Brownian motion-like time series with or without effect of an additional linear trend

We have translated fractional Brownian motion (FBM) signals into a text based on two ''letters'', as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the $\zeta '$ exponent relating the word frequency and its rank on a log-log plot. We have studied the variation of the Zipf exponent(s) giving the relationship between the frequency of occurrence of words of length $m<8$ made of such two letters: $\zeta '$ is varying as a power law in terms of $m$. We have also searched how the $\zeta '$ exponent of the Zipf law is influenced by a linear trend and the resulting effect of its slope. We can distinguish finite size effects, and results depending whether the starting FBM is persistent or not, i.e. depending on the FBM Hurst exponent $H$. It seems then numerically proven that the Zipf exponent of a persistent signal is more influenced by the trend than that of an antipersistent signal. It appears that the conjectured law $\zeta ' = |2H-1|$ only holds near $H=0.5$. We have also introduced considerations based on the notion of a {\it time dependent Zipf law} along the signal.Comment: 24 pages, 12 figures; to appear in Int. J. Modern Phys

Model-free Probabilistic Movement Primitives for physical interaction

Physical interaction in robotics is a complex problem that requires not only accurate reproduction of the kinematic trajectories but also of the forces and torques exhibited during the movement. We base our approach on Movement Primitives (MP), as MPs provide a framework for modelling complex movements and introduce useful operations on the movements, such as generalization to novel situations, time scaling, and others. Usually, MPs are trained with imitation learning, where an expert demonstrates the trajectories. However, MPs used in physical interaction either require additional learning approaches, e.g., reinforcement learning, or are based on handcrafted solutions. Our goal is to learn and generate movements for physical interaction that are learned with imitation learning, from a small set of demonstrated trajectories. The Probabilistic Movement Primitives (ProMPs) framework is a recent MP approach that introduces beneficial properties, such as combination and blending of MPs, and represents the correlations present in the movement. The ProMPs provides a variable stiffness controller that reproduces the movement but it requires a dynamics model of the system. Learning such a model is not a trivial task, and, therefore, we introduce the model-free ProMPs, that are learning jointly the movement and the necessary actions from a few demonstrations. We derive a variable stiffness controller analytically. We further extent the ProMPs to include force and torque signals, necessary for physical interaction. We evaluate our approach in simulated and real robot tasks

Robust policy updates for stochastic optimal control

For controlling high-dimensional robots, most stochastic optimal control algorithms use approximations of the system dynamics and of the cost function (e.g., using linearizations and Taylor expansions). These approximations are typically only locally correct, which might cause instabilities in the greedy policy updates, lead to oscillations or the algorithms diverge. To overcome these drawbacks, we add a regularization term to the cost function that punishes large policy update steps in the trajectory optimization procedure. We applied this concept to the Approximate Inference Control method (AICO), where the resulting algorithm guarantees convergence for uninformative initial solutions without complex hand-tuning of learning rates. We evaluated our new algorithm on two simulated robotic platforms. A robot arm with five joints was used for reaching multiple targets while keeping the roll angle constant. On the humanoid robot Nao, we show how complex skills like reaching and balancing can be inferred from desired center of gravity or end effector coordinates

On the entropy production of time series with unidirectional linearity

There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are only uncorrelated but not statistically independent of the future. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry. For various physical systems, it is known that time-inversion asymmetries are linked to the thermodynamic entropy production in non-equilibrium states. Here we show that such a link also exists for the above unidirectional linearity. We study the dynamical evolution of a physical toy system with linear coupling to an infinite environment and show that the linearity of the dynamics is inherited to the forward-time conditional probabilities, but not to the backward-time conditionals. The reason for this asymmetry between past and future is that the environment permanently provides particles that are in a product state before they interact with the system, but show statistical dependencies afterwards. From a coarse-grained perspective, the interaction thus generates entropy. We quantitatively relate the strength of the non-linearity of the backward conditionals to the minimal amount of entropy generation.Comment: 16 page

Some comments on nˉp\bar n p-annihilation branching ratios into ππ\pi \pi-, KˉK\bar K K- and πη\pi \eta-channels

We give some remarks on the $\bar n p$-partial branching ratios in flight at low momenta of antineutron, measured by OBELIX collaboration. The comparison is made to the known branching ratios from the $p \bar p$-atomic states. The branching ratio for the reaction $\bar n p \to \pi^+\pi^0$ is found to be suppressed in comparison to what follows from the $p \bar p$-data. It is also shown, that there is no so called dynamic I=0-amplitude suppression for the process $N\bar N \to K\bar K$.Comment: 8 pages, LaTeX, no figure

Particle-Based Mesoscale Hydrodynamic Techniques

Dissipative particle dynamics (DPD) and multi-particle collision (MPC) dynamics are powerful tools to study mesoscale hydrodynamic phenomena accompanied by thermal fluctuations. To understand the advantages of these types of mesoscale simulation techniques in more detail, we propose new two methods, which are intermediate between DPD and MPC -- DPD with a multibody thermostat (DPD-MT), and MPC-Langevin dynamics (MPC-LD). The key features are applying a Langevin thermostat to the relative velocities of pairs of particles or multi-particle collisions, and whether or not to employ collision cells. The viscosity of MPC-LD is derived analytically, in very good agreement with the results of numerical simulations.Comment: 7 pages, 2 figures, 1 tabl

Quartic double solids with ordinary singularities

We study the mixed Hodge structure on the third homology group of a threefold which is the double cover of projective three-space ramified over a quartic surface with a double conic. We deal with the Torelli problem for such threefolds.Comment: 14 pages, presented at the Conference Arnol'd 7

Halothane hepatitis with renal failure treated with hemodialysis and exchange transfusion

A 38-year-old white female, hepatitis B antigen negative, developed fluminating hepatic failure associated with oliguria and severe azotemia after two halothane anesthesia and without exposure to other hepatotoxic drugs or blood transfusions. She was treated with multiple hemodialysis and exchange blood transfusion. The combined treatment corrected the uremic abnormalities and improved her level of consciousness. The liver and kidney function gradually improved, and she made a complete recovery, the first recorded with hepatic and renal failure under these post-anesthetic conditions. Further evaluation of this combined treatment used for this patient is warranted. © 1974 The Japan Surgical Society