Making the Punishment Fit the Crime or Taliban Justice? Optimal Penalties Without Commitment

This paper argues that graduated penalties observed in most legal systems may be an attempt to direct law enforcement e orts towards crimes that are socially more harmful, thereby achieving better deterrence overall. The critical assumptions are-- the state cannot commit to a monitoring strategy, and has mixed motives (objectives other than deterrence). However, graduated penalties arise only in the presence of secondary motives that value punishment in itself, such as retribution or nes collected from violators. Other motives that are unrelated to the size of punishment, such as prevention of criminal attempts, will also lead to distortions, but those cannot be corrected by restructuring penalties. The overall harshness of a criminal justice system and the retributive instincts of its designers may be related in counter intuitive ways, and law enforcement may be improved through strategic delegation.Commitment, crime, deterrence, retribution, graduated penalties.

Schwinger-Dyson approach to Liouville Field Theory

We discuss Liouville field theory in the framework of Schwinger-Dyson approach and derive a functional equation for the three-point structure constant. We argue the existence of a second Schwinger-Dyson equation on the basis of the duality between the screening charge operators and obtain a second functional equation for the structure constant. We discuss the utility of the two functional equations to fix the structure constant uniquely

Price Discrimination As Portfolio Diversification

A seller seeking to sell an indivisible object can post (possibly different) prices to each of n buyers. Buyers' valuations are private information and drawn independently from the same distribution. If the seller can choose who to sell to in the event there are several willing buyers, her optimal strategy is to post different prices to different buyers. For some distributions, price discrimination may be profitable even if excess demand must be resolved through a uniform lottery.

Relative Entropy Relaxations for Signomial Optimization

Signomial programs (SPs) are optimization problems specified in terms of signomials, which are weighted sums of exponentials composed with linear functionals of a decision variable. SPs are non-convex optimization problems in general, and families of NP-hard problems can be reduced to SPs. In this paper we describe a hierarchy of convex relaxations to obtain successively tighter lower bounds of the optimal value of SPs. This sequence of lower bounds is computed by solving increasingly larger-sized relative entropy optimization problems, which are convex programs specified in terms of linear and relative entropy functions. Our approach relies crucially on the observation that the relative entropy function -- by virtue of its joint convexity with respect to both arguments -- provides a convex parametrization of certain sets of globally nonnegative signomials with efficiently computable nonnegativity certificates via the arithmetic-geometric-mean inequality. By appealing to representation theorems from real algebraic geometry, we show that our sequences of lower bounds converge to the global optima for broad classes of SPs. Finally, we also demonstrate the effectiveness of our methods via numerical experiments

Photonic-Loop Modeling Using Ghost Waveguides

In this thesis, we present a new method for the modeling and analyzing photonic-loop structures which is based on a rotated directional coupler and ghost waveguide. This new method is less complicated than available methods. Our method of photonic-loop structure modeling is demonstrated by modeling and analyzing a ring resonator and its parameters. We also model and analyze a multi-ring ring resonator

The Land Acquisition Bill-- A Critique and a Proposal

The new Bill on land acquisition recently tabled in Parliament is well intentioned but seriously flawed. Its principal defect is that it attaches an arbitrary mark-up to the historical market price to determine compensation amounts. This will guarantee neither social justice nor the efficient use of resources. The Bill also places unnecessary and severe conditions on land acquisition, such as restrictions on the use of multi-cropped land and insistence on public purpose, all of which are going to stifle the pace of development without promoting the interests of farmers. We present an alternative approach that will allow farmers to choose compensation in either land or cash, determine their own price instead of leaving it to the government’s discretion, and also reallocate the remaining farmland in the most efficient manner. Our proposed method involves a land auction covering not only the project site but also the surrounding agricultural land.

A partial order approach to decentralized control

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 173-177).In this thesis we consider the problem of decentralized control of linear systems. We employ the theory of partially ordered sets (posets) to model and analyze a class of decentralized control problems. Posets have attractive combinatorial and algebraic properties; the combinatorial structure enables us to model a rich class of communication structures in systems, and the algebraic structure allows us to reparametrize optimal control problems to convex problems. Building on this approach, we develop a state-space solution to the problem of designing H₂-optimal controllers. Our solution is based on the exploitation of a key separability property of the problem that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our state-space characterization of the controller is a pair of transfer functions, that belong to the incidence algebra of the poset, are inverses of each other, and are intimately related to estimation of the state along the different paths in the poset. We then view the control design problem from an architectural viewpoint. We propose a natural architecture for poset-causal controllers. In the process, we establish interesting connections between concepts from order theory such as Mobius inversion and control-theoretic concepts such as state estimation, innovation, and separability principles. Finally, we prove that the H₂-optimal controller in fact posseses the proposed controller structure, thereby proving the optimality of the architecture.by Parikshit Shah.Ph.D

Development of a Dynamic Model and Control System for Load-Following Operation of Supercritical Pulverized Coal Power Plants

Thermal power plants that have been designed to operate at their rated capacity are being forced to cycle their load and operate under low-load condition to meet changing load demands due to the increased penetration of renewables into the electric grid. The rapid load-following operation is leading to challenging control problems. The goal of this research is to develop dynamic model and control system for efficient load-following operation. The focus of this work is on supercritical pulverized coal (SCPC) power plants. The steady-state model is developed using Aspen Plus and Aspen Custom Modeler and then converted to a pressure-driven Aspen Plus Dynamics model, where the regulatory control layer and coordinated control system (CCS) are developed for efficient servo control and disturbance rejection characteristics. A detailed three-region dynamic model of the feed water heater is also developed. The model can estimate the changing size of desuperheating, condensing and subcooling zones during load-following. As key components of CCS, control strategies for the coal flow, air flow, boiler feedwater flowrate and reheat steam temperature are developed. The control strategy for the main steam temperature control is developed with due consideration of the time delay of the SCPC syste