Closed loop deep brain stimulation: an evolving technology

Deep brain stimulation is an effective and safe medical treatment for a variety of neurological and psychiatric disorders including Parkinson's disease, essential tremor, dystonia, and treatment resistant obsessive compulsive disorder. A closed loop deep brain stimulation (CLDBS) system automatically adjusts stimulation parameters by the brain response in real time. The CLDBS continues to evolve due to the advancement in the brain stimulation technologies. This paper provides a study on the existing systems developed for CLDBS. It highlights the issues associated with CLDBS systems including feedback signal recording and processing, stimulation parameters setting, control algorithm, wireless telemetry, size, and power consumption. The benefits and limitations of the existing CLDBS systems are also presented. Whilst robust clinical proof of the benefits of the technology remains to be achieved, it has the potential to offer several advantages over open loop DBS. The CLDBS can improve efficiency and efficacy of therapy, eliminate lengthy start-up period for programming and adjustment, provide a personalized treatment, and make parameters setting automatic and adaptive.

RFID tag ownership transfer protocol for a closed loop system

In the RFID system a tag is attached to an object which might own by a number of people during its life cycle. As a result, the RFID system requires to transfer ownership of the tag. The ownership transfer has to protect privacy of current and new owner. There are number of ownership transfer protocol proposed to achieve secure ownership transfer. However, most of them are impractical or insecure to implement on current passive RFID tags. We are presenting an ownership transfer protocol using timer based shared secret for closed loop RFID systems. The protocol will ensure security and privacy of involved parties in the idle circumstances. Our comparison shows that the proposed protocol is more secure and practical than existing similar ones.

On the Markovian efficiency of Bertrand and Cournot equilibria

We characterize and compare closed-loop (feedback) price and quantity strategies within a full-fledged dynamic model of oligopolistic competition in which production requires exploitation of a renewable productive asset. Unlike previous papers on the strategic exploitation of productive assets, we allow for imperfect product substitutability, which enables us to deal with price competition. We show that the traditional result that the Bertrand equilibrium is more efficient than the Cournot equilibrium does not necessarily hold in a Markovian environment, either in the short-run or at the stationary equilibrium, or using the discounted sum of welfare as a criterion for relative efficiency.

Scenarios for an RFID tag ownership transfer protocol for a closed loop system

In RFID system a tag is attached to an object which might own by a number of owners during its life time. This requires the RFID system to transfer ownership of the tag to its new owner. The ownership transfer has to protect privacy of current and new owner. Many ownership tag ownership transfer exists in the literature, however, most of them are impractical or insecure to implement on current passive RFID tags. We are proposing a timer based ownership transfer protocol for closed loop RFID systems. The proposal in this paper includes two implement scenario to cover diverse tags type. The protocol will ensure security and privacy of involved parties in the idle circumstances. Our comparison shows that the proposed protocol is more secure and practical than existing similar ones.

Nash equilibrium under knightian uncertainty: breaking down backward induction (extensively revised version)

We define Nash equilibrium for two-person normal form games in the presence of uncertainty, in the sense of Knight(1921). We use the fonna1iution of uncertainty due to Schmeidler and Gilboa. We show tbat there exist Nash equilibria for any degree of uncertainty, as measured by the uncertainty aversion (Dow anel Wer1ang(l992a». We show by example tbat prudent behaviour (maxmin) can be obtained as an outcome even when it is not rationaliuble in the usual sense. Next, we break down backward industion in the twice repeated prisoner's dilemma. We link these results with those on cooperation in the finitely repeated prisoner's dilemma obtained by Kreps-Milgrom-Roberts-Wdson(1982), and withthe 1iterature on epistemological conditions underlying Nash equilibrium. The knowledge notion implicit in this mode1 of equilibrium does not display logical omniscience.

Nash equilibrium under knightian uncertainty: breaking-down backward induction

We present two alternative definitions of Nash equilibrium for two person games in the presence af uncertainty, in the sense of Knight. We use the formalization of uncertainty due to Schmeidler and Gilboa. We show that, with one of the definitions, prudent behaviour (maxmin) can be obtained as an outcome even when it is not rationalizable in the usual sense. Most striking is that with the Same definition we break down backward induction in the twice repeated prisoner's dilemma. We also link these results with the Kreps-Milgrom-Roberts-Wilson explanation of cooperation in the finitely repeated prisoner's dilemma.

A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.

A notion of subgame perfect Nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game.

A notion of subgame perfect nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game .

Existence of nash equilibrium in competitive nonlinear pricing games with adverse selection

We show that for a large class of competitive nonlinear pricing games with adverse selection, the property of better-reply security is naturally satisfied - thus, resolving via a result due to Reny (1999) the issue of existence of Nash equilibrium for a large class of competitive nonlinear pricing games.

Closed loop stability of measure-driven impulsive control systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A comparative evaluation of open loop and closed loop drug administration strategies in the treatment of AIDS.

In recent years, many researchers in the field of biomedical sciences have made successful use of mathematical models to study, in a quantitative way, a multitude of phenomena such as those found in disease dynamics, control of physiological systems, optimization of drug therapy, economics of the preventive medicine and many other applications. The availability of good dynamic models have been providing means for simulation and design of novel control strategies in the context of biological events. This work concerns a particular model related to HIV infection dynamics which is used to allow a comparative evaluation of schemes for treatment of AIDS patients. The mathematical model adopted in this work was proposed by Nowak & Bangham, 1996 and describes the dynamics of viral concentration in terms of interaction with CD4 cells and the cytotoxic T lymphocytes, which are responsible for the defense of the organism. Two conceptually distinct techniques for drug therapy are analyzed: Open Loop Treatment, where a priori fixed dosage is prescribed and Closed Loop Treatment, where the doses are adjusted according to results obtained by laboratory analysis. Simulation results show that the Closed Loop Scheme can achieve improved quality of the treatment in terms of reduction in the viral load and quantity of administered drugs, but with the inconvenience related to the necessity of frequent and periodic laboratory analysis.