Anomalous structural and mechanical properties of solids confined in quasi one dimensional strips

We show using computer simulations and mean field theory that a system of particles in two dimensions, when confined laterally by a pair of parallel hard walls within a quasi one dimensional channel, possesses several anomalous structural and mechanical properties not observed in the bulk. Depending on the density $\rho$ and the distance between the walls $L_y$, the system shows structural characteristics analogous to a weakly modulated liquid, a strongly modulated smectic, a triangular solid or a buckled phase. At fixed $\rho$, a change in $L_y$ leads to many reentrant discontinuous transitions involving changes in the number of layers parallel to the confining walls depending crucially on the commensurability of inter-layer spacing with $L_y$. The solid shows resistance to elongation but not to shear. When strained beyond the elastic limit it fails undergoing plastic deformation but surprisingly, as the strain is reversed, the material recovers completely and returns to its original undeformed state. We obtain the phase diagram from mean field theory and finite size simulations and discuss the effect of fluctuations.Comment: 14 pages, 13 figures; revised version, accepted in J. Chem. Phy

A Note on Effective String Theory

Motivated by the possibility of an effective string description for the infrared limit of pure Yang-Mills theory, we present a toy model for an effective theory of random surfaces propagating in a target space of $D>2$. We show that the scaling exponents for the fixed area partition function of the theory are apparently well behaved. We make some observations regarding the usefulness of this toy model.Comment: 17 pages, LATEX, UTTG-21-9

Many-body Dynamics of D0--Branes

We show that the growth of the size with the number of partons holds in a Thomas-Fermi analysis of the threshold bound state of D0--branes. Our results sharpen the evidence that for a fixed value of the eleven dimensional radius the partonic velocities can be made arbitrarily small as one approaches the large N limit.Comment: 9 pages, latex, minor change

Damping Control in Power Systems Under Constrained Communication Bandwidth: A Predictor Corrector Strategy

Damping electromechanical oscillations in power systems using feedback signals from remote sensors is likely to be affected by occasional low bandwidth availability due to increasing use of shared communication in future. In this paper, a predictor corrector (PC) strategy is applied to deal with situations of low-feedback data rate (bandwidth), where conventional feedback (CF) would suffer. Knowledge of nominal system dynamics is used to approximate (predict) the actual system behavior during intervals when data from remote sensors are not available. Recent samples of the states from a reduced observer at the remote location are used to periodically reset (correct) the nominal dynamics. The closed-loop performance deteriorates as the actual operating condition drifts away from the nominal dynamics. Nonetheless, significantly better performance compared to CF is obtained under low-bandwidth situations. The analytical criterion for closed-loop stability of the overall system is validated through a simulation study. It is demonstrated that even for reasonably low data rates the closed-loop stability is usually ensured for a typical power system application confirming the effectiveness of this approach. The deterioration in performance is also quantified in terms of the difference between the nominal and off-nominal dynamics

A semiclassical theory of quantum noise in open chaotic systems

We consider the quantum evolution of classically chaotic systems in contact with surroundings. Based on $\hbar$-scaling of an equation for time evolution of the Wigner's quasi-probability distribution function in presence of dissipation and thermal diffusion we derive a semiclassical equation for quantum fluctuations. This identifies an early regime of evolution dominated by fluctuations in the curvature of the potential due to classical chaos and dissipation. A stochastic treatment of this classical fluctuations leads us to a Fokker-Planck equation which is reminiscent of Kramers' equation for thermally activated processes. This reveals an interplay of three aspects of evolution of quantum noise in weakly dissipative open systems; the reversible Liouville flow, the irreversible chaotic diffusion which is characteristic of the system itself, and irreversible dissipation induced by the external reservoir. It has been demonstrated that in the dissipation-free case a competition between Liouville flow in the contracting direction of phase space and chaotic diffusion sets a critical width in the Wigner function for quantum fluctuations. We also show how the initial quantum noise gets amplified by classical chaos and ultimately equilibrated under the influence of dissipation. We establish that there exists a critical limit to the expansion of phase space. The limit is determined by chaotic diffusion and dissipation. Making use of appropriate quantum-classical correspondence we verify the semiclassical analysis by the fully quantum simulation in a chaotic quartic oscillator.Comment: Plain Latex, 27 pages, 6 ps figure, To appear in Physica

Pre- and Post-alpha Motoneuronal Control of the Soleus H-reflex during Sinusoidal Hip Movements in Human Spinal Cord Injury

The aim of this study was to establish the contribution of hip-mediated sensory feedback to spinal interneuronal circuits during dynamic conditions in people with incomplete spinal cord injury (SCI). Specifically, we investigated the effects of synergistic and antagonistic group I afferents on the soleus H-reflex during imposed sinusoidal hip movements. The soleus H-reflex was conditioned by stimulating the common peroneal nerve (CPN) at short (2, 3, and 4 ms) and long (80, 100, and 120 ms) conditioning test (C-T) intervals to assess the reciprocal and pre-synaptic inhibition of the soleus H-reflex, respectively. The soleus H-reflex was also conditioned by medial gastrocnemius (MG) nerve stimulation at C-T intervals ranging from 4 to 7 ms to assess changes in autogenic Ib inhibition during hip movement. Sinusoidal hip movements were imposed to the right hip joint at 0.2 Hz by the Biodex system while subjects were supine. The effects of sinusoidal hip movement on five leg muscles along with hip, knee, and ankle joint torques were also established during sensorimotor conditioning of the reflex. Phase-dependent modulation of antagonistic and synergistic muscle afferents was present during hip movement, with the reciprocal, pre-synaptic, and Ib inhibition to be significantly reduced during hip extension and reinforced during hip flexion. Reflexive muscle and joint torque responses – induced by the hip movement – were entrained to specific phases of hip movement. This study provides evidence that hip-mediated input acts as a controlling signal of pre- and post-alpha motoneuronal control of the soleus H-reflex. The expression of these spinal interneuronal circuits during imposed sinusoidal hip movements is discussed with respect to motor recovery in humans after SCI

Differentially Private Empirical Risk Minimization

Privacy-preserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacy-preserving approximations of classifiers learned via (regularized) empirical risk minimization (ERM). These algorithms are private under the $\epsilon$-differential privacy definition due to Dwork et al. (2006). First we apply the output perturbation ideas of Dwork et al. (2006), to ERM classification. Then we propose a new method, objective perturbation, for privacy-preserving machine learning algorithm design. This method entails perturbing the objective function before optimizing over classifiers. If the loss and regularizer satisfy certain convexity and differentiability criteria, we prove theoretical results showing that our algorithms preserve privacy, and provide generalization bounds for linear and nonlinear kernels. We further present a privacy-preserving technique for tuning the parameters in general machine learning algorithms, thereby providing end-to-end privacy guarantees for the training process. We apply these results to produce privacy-preserving analogues of regularized logistic regression and support vector machines. We obtain encouraging results from evaluating their performance on real demographic and benchmark data sets. Our results show that both theoretically and empirically, objective perturbation is superior to the previous state-of-the-art, output perturbation, in managing the inherent tradeoff between privacy and learning performance.Comment: 40 pages, 7 figures, accepted to the Journal of Machine Learning Researc