A note on AdS cosmology and gauge theory correlator

Using AdS/CFT prescription, we compute two point Yang-Mills correlator on a constant time slice for the Kasner background. Pushing the surface close to the initial singularity, we find, in some cases, the correlator does not develop pole. This is consistent with the observations made in a recent work. We further numerically calculate similar correlator where the bulk is a Kasner AdS soliton. We find that the qualitative behaviour of the correlator remains unchanged.Comment: 17 pages, 2 figures, journal versio

Separability of State Trajectories and its Applications to Security of Cyber-Physical Systems

This article studies a fundamental problem of security of cyber-physical systems (CPSs). We focus on a class of attacks where some of the actuators could be malicious while all the sensors are considered to be honest. We introduce a novel idea of separability of state trajectories that are generated by the honest and corrupt actuators, and establish its connection to the security of CPSs in the context of detecting the presence of malicious actuators (if any,) in the system. As a defense strategy to guard the CPS against malicious attacks, we focus on the mechanism of perturbing the pre-determined control action by injecting a certain class of random process by the honest actuators called private excitation, which is assumed to have a known distribution. As primary contributions we give sufficient conditions for the existence and non-existence of a separator for linear time-invariant stochastic systems, under the assumption that the policies are randomized-Markovian and randomized history dependent. Several technical aspects of the established results are discussed extensively.Comment: 26 page

A discrete-time Pontryagin maximum principle under rate constraints

Limited bandwidth and limited saturation in actuators are practical concerns in control systems. Mathematically, these limitations manifest as constraints being imposed on the control actions, their rates of change, and more generally, the global behavior of their paths. While the problem of actuator saturation has been studied extensively, little attention has been devoted to the problem of actuators having limited bandwidth. While attempts have been made in the direction of incorporating frequency constraints on state-action trajectories before, rate constraints on the control at the design stage have not been studied extensively in the discrete-time regime. This article contributes toward filling this lacuna. In particular, we establish a new discrete-time Pontryagin maximum principle with rate constraints being imposed on the control trajectories, and derive first-order necessary conditions for optimality. A brief discussion on the existence of optimal control is included, and numerical examples are provided to illustrate the results

Nephrocutaneous fistula due to textiloma with in the pelvicalyceal system

Textiloma or gossypiboma is an embarrassing surgical scenario. Nephrocutaneous fistula is itself a rare complication after renal surgeries, but due to textiloma, it is rarest of the rare. In this case, 30-year-old lady presented with the complaints of chronic seropurulent discharge from a wound on her right lumbar region. On exploration it was found to be a retained surgical sponge in pelvicalyceal system, which was there for last seven years

Is Diabetes Pre-coded in the Brain? Role of Hypothalamus, Addiction Network and Social Cognition

The hypothalamus, the master regulator of circadian rhythm, in association with peripheral clocks, play crucial roles in glucose metabolism. Impairment in cerebral sensing, uptake and processing of glucose has been suggested in various animal and human diabetic models. Diabetes Mellitus has been largely superseded by the discovery of insulin and insulin resistance. Expanding horizons of knowledge of the roles of the hypothalamus in glucose metabolism and the overlapping neural pathways of sugar addictionwith other classically described substance and behavioral addictions networks have again thrown some light on the cerebral theory of DM pathogenesis

Towards continuous-time MPC: a novel trajectory optimization algorithm

This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying optimal control problem (OCP) are a linear time-invariant system, quadratic instantaneous and terminal cost functions, and convex path constraints. The thrust of the method involves finitely parameterizing the admissible space of control trajectories and solving the OCP satisfying the given constraints at every time instant in a tractable manner without explicit time-discretization. The ensuing OCP turns out to be a convex semi-infinite program (SIP), and some recently developed results are employed to obtain an optimal solution to this convex SIP. Numerical illustrations on some benchmark models are included to show the efficacy of the algorithm.Comment: Accepted in IEEE Conference on Decision and Control (CDC), 202

Method and electronic device for global optimization to exact solutions of convex semi-infinite problems

Embodiments herein provide a method for determining approximation of Semi-Infinite optimization problem (SIP) to identify outcome of the SIP using a sampler device. Inputs are received from user and defining infinite number of constraints of the SIP making the SIP intractable. A global maximization problem is determined by reformulating the finite dimensional approximation of SIP into a finite dimension problem with finite constraints. An optimal value of the finite dimensional approximation of SIP is obtained based on the global maximization problem using a global optimization technique. A plurality of outcomes of the finite dimensional approximation of SIP is exacted based on the optimal value of the finite dimensional approximation. One of the major advantages of this approach is that it admits a plug-and-play module, where one can use any global optimization method to obtain the optimal value

Method and electronic device for global optimization to exact solutions of convex semi-infinite problems

Embodiments herein provide a method for determining approximation of Semi-Infinite optimization problem (SIP) to identify outcome of the SIP using a sampler device. Inputs are received from user and defining infinite number of constraints of the SIP making the SIP intractable. A global maximization problem is determined by reformulating the finite dimensional approximation of SIP into a finite dimension problem with finite constraints. An optimal value of the finite dimensional approximation of SIP is obtained based on the global maximization problem using a global optimization technique. A plurality of outcomes of the finite dimensional approximation of SIP is exacted based on the optimal value of the finite dimensional approximation. One of the major advantages of this approach is that it admits a plug-and-play module, where one can use any global optimization method to obtain the optimal value