Discrete time optimal control with frequency constraints for non-smooth systems

We present a Pontryagin maximum principle for discrete time optimal control problems with (a) pointwise constraints on the control actions and the states, (b) frequency constraints on the control and the state trajectories, and (c) nonsmooth dynamical systems. Pointwise constraints on the states and the control actions represent desired and/or physical limitations on the states and the control values; such constraints are important and are widely present in the optimal control literature. Constraints of the type (b), while less standard in the literature, effectively serve the purpose of describing important spectral properties of inertial actuators and systems. The conjunction of constraints of the type (a) and (b) is a relatively new phenomenon in optimal control but are important for the synthesis control trajectories with a high degree of fidelity. The maximum principle established here provides first order necessary conditions for optimality that serve as a starting point for the synthesis of control trajectories corresponding to a large class of constrained motion planning problems that have high accuracy in a computationally tractable fashion. Moreover, the ability to handle a reasonably large class of nonsmooth dynamical systems that arise in practice ensures broad applicability our theory, and we include several illustrations of our results on standard problems

Imitative Follower Deception in Stackelberg Games

Information uncertainty is one of the major challenges facing applications of game theory. In the context of Stackelberg games, various approaches have been proposed to deal with the leader's incomplete knowledge about the follower's payoffs, typically by gathering information from the leader's interaction with the follower. Unfortunately, these approaches rely crucially on the assumption that the follower will not strategically exploit this information asymmetry, i.e., the follower behaves truthfully during the interaction according to their actual payoffs. As we show in this paper, the follower may have strong incentives to deceitfully imitate the behavior of a different follower type and, in doing this, benefit significantly from inducing the leader into choosing a highly suboptimal strategy. This raises a fundamental question: how to design a leader strategy in the presence of a deceitful follower? To answer this question, we put forward a basic model of Stackelberg games with (imitative) follower deception and show that the leader is indeed able to reduce the loss due to follower deception with carefully designed policies. We then provide a systematic study of the problem of computing the optimal leader policy and draw a relatively complete picture of the complexity landscape; essentially matching positive and negative complexity results are provided for natural variants of the model. Our intractability results are in sharp contrast to the situation with no deception, where the leader's optimal strategy can be computed in polynomial time, and thus illustrate the intrinsic difficulty of handling follower deception. Through simulations we also examine the benefit of considering follower deception in randomly generated games

Differential Regulation of Cysteinyl Leukotriene Receptor Signaling by Protein Kinase C in Human Mast Cells

Cysteinyl leukotrienes (cys-LTs) are a group of lipid mediators that are potent bronchoconstrictors, powerful inducers of vascular leakage and potentiators of airway hyperresponsiveness. Cys-LTs play an essential role in asthma and are synthesized as well as activated in mast cells (MCs). Cys-LTs relay their effects mainly through two known GPCRs, CysLT1R and CysLT2R. Although protein kinase C (PKC) isoforms are implicated in the regulation of CysLT1R function, neither the role of PKCs in cys-LT-dependent MC inflammatory signaling nor the involvement of specific isoforms in MC function are known. Here, we show that PKC inhibition augmented LTD4 and LTE4-induced calcium influx through CysLT1R in MCs. In contrast, inhibition of PKCs suppressed c-fos expression as well MIP1β generation by cys-LTs. Interestingly, cys-LTs activated both PKCα and PKCε isoforms in MC. However, knockdown of PKCα augmented cys-LT mediated calcium flux, while knockdown of PKCε attenuated cys-LT induced c-fos expression and MIP1β generation. Taken together, these results demonstrate for the first time that cys-LT signaling downstream of CysLT1R in MCs is differentially regulated by two distinct PKCs which modulate inflammatory signals that have significant pathobiologic implications in allergic reactions and asthma pathology

Computation of Stackelberg Equilibria of Finite Sequential Games

The Stackelberg equilibrium solution concept describes optimal strategies to commit to: Player 1 (termed the leader) publicly commits to a strategy and Player 2 (termed the follower) plays a best response to this strategy (ties are broken in favor of the leader). We study Stackelberg equilibria in finite sequential games (or extensive-form games) and provide new exact algorithms, approximate algorithms, and hardness results for several classes of these sequential games

Conceptualization of Machine Learning in Economic Forecasting

Economic forecasting is a very important aspect that policymakers in the financial and corporate organization rely on because helps them to determine future events that might infringe some hardship on the economy and the citizens at large. However, the principal statistical pointers that are available to the public domain provide numerous reservations and doubts for their economics estimates as it is later released with frequent issues to major revisions and also it shows a great lag in decision making for an incoming event. To this effect, the expansion of the latest forecasting patterns was important to address the gaps. Hence, this paper examines the conceptualization of Machine learning in economic forecasting. To achieve this, the Italian economy was used as the dataset, and machine learning controlled tools were used as the method of analysis. The result obtained from this study shows that machine learning is a better model to use in economic forecasting for quick and reliable data to avert future events

Efficient convolvers using the Polynomial Residue Number System technique

The problem of computing linear convolution is a very important one because with linear convolution we can mechanize digital filtering. The linear convolution of two N-point sequences can be computed by the cyclic convolution of the following 2N-point sequences. The original sequence padded with N zero’s each. The cyclic convolution of two N-point sequences requires multiplications and additions for its computation. A very efficient way of computing cyclic convolution of two sequences is by using the Polynomial Residue Number System (PRNS) technique. Using this technique the cyclic convolution of two N-point sequences can be computed using only N multiplications instead of N2 multiplications. This can be achieved based on some forward and inverse PRNS transformation mappings. These mappings rely on additions, subtractions and many scaling operations (multiplications by constants). The PRNS technique would lose a lot in value if these many scaling operations were difficultly implemented. In this thesis we will show how to calculate cyclic convolution of two sequences using the PRNS technique based on forward and inverse transformation mapping which rely on complement operations (negations), additions and rotation operations. These rotation operations do not require any computational hardware. Therefore the complicated hardware required for the scaling operations has now been substituted by rotators, which do not require any computational hardware