Optimality Conditions for Semivectorial Bilevel Convex Optimal Control Problems

We present optimality conditions for bilevel optimal control problems where the upper level, to be solved by a leader, is a scalar optimal control problem and the lower level, to be solved by several followers, is a multiobjective convex optimal control problem. Multiobjective optimal control problems arise in many application areas where several conflicting objectives need to be considered. Minimize several objective functionals leads to solutions such that none of the objective functional values can be improved further without deteriorating another. The set of all such solutions is referred to as efficient (also called Pareto optimal, noninferior, or nondominated) set of solutions. The lower level of the semivectorial bilevel optimal control problems can be considered to be associated to a ”grande coalition” of a p-player cooperative differential game, every player having its own objective and control function. We consider situations in which these p-?players react as ”followers” to every decision imposed by a ”leader” (who acts at the so-called upper level). The best reply correspondence of the followers being in general non uniquely determined, the leader cannot predict the followers choice simply on the basis of his rational behavior. So, the choice of the best strategy from the leader point of view depends of how the followers choose a strategy among his best responses. In this paper, we will consider two (extreme) possibilities: (i) the optimistic situation, when for every decison of the leader, the followers will choose a strategy amongst the efficient controls which minimizes the (scalar) objective of the leader; in this case the leader will choose a strategy which minimizes the best he can obtain amongst all the best responses of the followers: (ii) the pessimistic situation, when the followers can choose amongst the efficient controls one which maximizes the (scalar) objective of the leader; in this case the leader will choose a strategy which minimizes the worst he could obtain amongst all the best responses of the followers. This paper continues the research initiated in [17] where existence results for these problems have been obtained.

Hawala: How Extralegal Compliance Helps Bank the Unbanked

Informal value transfer systems (IVTS\u27) predate not only traditional banking systems, but the entire Western European civilization as well. Used as a reliable method to transfer value from one geographic region to another through a close-knit network of trusted individuals, IVTS\u27 serve as an invaluable facilitator for the movement of billions of dollars across international borders without ever leaving a paper trail. The term “hawala”, which is Arabic for “transfer” or “trust”, is an IVTS that serves as a parallel banking system for those wishing to send value (often in the form of currency) overseas. Hawala has historically thrived as a connection to the global economy in parts of the world where sociopolitical unrest may have disrupted day-to-day financial activities and its resilience, among other factors, has propelled it to the preferred method of value movement by its customers (Viles, 2008). With conservative estimates between $100 billion to$300 billion annually, the massive movement of value through hawala on a global scale continues to be unregulated and operates in secrecy through trusted networks that have been in place for centuries. Consumers of hawala range from individuals wanting to send remittances to relatives in a foreign country to terrorists attempting to fund their activities under the radar of government surveillance (Dougherty, 2006). While there are obvious and glaring money laundering risks associated with hawala, do the dangers of regulating such a robust IVTS outweigh the benefits of complying with U.S. laws and regulations

Steady state temperature distribution in a rotating disk

The purpose of this investigation was to obtain an expression for the steady state temperature distribution of a disk of uniform thickness rotating at a constant speed in ambient air while absorbing heat through the periphery at a constant rate. Engineers encounter such problems in connection with brakes of several varieties. The general solution obtained here could be extended to similar physical problems such as grinding wheels, disk clutches, and so on. A differential equation was obtained for the temperature in the disk by the application of Fourier\u27s conduction law and Newton’s convection law. A solution of this equation was obtained in the form of a Bessel function of the first kind and order zero and the constants of integration as determined by the boundary conditions --Introduction, page 1

Towards the Definition, Measurement and Assessment of the Anaesthetic State

The definition of the anaesthetic state is discussed. We see the anaesthetic state as a central nervous system state, which results from the interaction between the effects of anaesthetic dose and the effects of surgical stimulation on that system. However, the effects of surgical stimulation, although they may be described as an ordered sequence of events, cannot be quantified. And the wide variation in anaesthetic requirement means that anaesthetic dose can, at best be, defined with respect to a single point (or points) on a qualitative scale. It is therefore difficult to assess the various techniques proposed as monitors of the anaesthetic state. These techniques are reviewed and it is apparent, that without a clear definition of the anaesthetic state, these techniques cannot be fully assessed. There is therefore a need for an individually valid anaesthetic state ("gold standard") to which other methods can be compared. Clinical signs form the basis for the administration of thousands of successful anaesthetics each day and, despite some inadequacies, are currently the only practical, universally accepted indicators of anaesthetic adequacy. However, their interpretation is both subjective and variable. A reproducible, individualised description of the anaesthetic state, based on clinical signs would allow this and other techniques to be more fully assessed. The objective of the work presented in this thesis was to investigate whether a clinically acceptable anaesthetic state could be produced by a control system designed to maintain the patients systolic arterial pressure (SAP) at a predetermined level by altering the inspired concentration of enflurane or isoflurane. Such a control system, though limited in that it uses only one clinical sign, should help to standardise the management of the anaesthetic state. A proportional - integral control system was set up with an RML 380Z-D computer interfaced to a Critikon Dinamap 1846 and a vaporizer controller. A program, written in BASIC, was designed to maintain the patients SAP at 90% of that predicted from age and sex standardised tables. The controller took data from the Dinamap, which was set to cycle at one minute intervals, and changed the inspired volatile concentration via the vaporizer controller. In a preliminary study some patients were hypotensive, relative to the target SAP, following induction but prior to surgery. These patients therefore received minimal concentrations of volatile anaesthetic initially. Others received a relative overdose of anaesthetic during the procedure. Two additional rules were incorporated in the control algorithm to limit these effects. First, a minimum inspired concentration of 0.6% was delivered for the first 10 minutes and second, if the inspired dose of volatile anaesthetic exceeded a preset limit, the controller instructed the anaesthetist to give a bolus of morphine and reset the integral. This limit was defined as a total inspired concentration of more than 15% over 5 consecutive vaporizer settings with each individual setting exceeding 2.5%. This rule could only be activated once in 15 minutes. The study was carried out on 57 ASA I and II female patients admitted for routine gynaecological surgery. All patients were artificially ventilated and received a standard, nitrous oxide based anaesthetic supplemented with morphine at induction, and enflurane (22 patients) or isoflurane (35 patients). The dosage of volatile anaesthetic and the requirement of additional morphine were determined by the controller. During surgery cardiovascular data and the inspired volatile requirement were recorded every minute and clinical signs "scored". Recovery times were measured and all patients interviewed post-operatively to discover whether they had been aware during anaesthesia. An adequate anaesthetic state was defined by strict criteria based on cardiovascular variables, the goodness of control, recovery time and absence of awareness post-operatively. No patient recalled any intraoperative event. Overall, 53.8% of cases satisfied all criteria. A failure to achieve two or more of these criteria occurred in 7.5% of patients in the groups not requiring additional morphine compared to 83.3% of the patients who did require additional morphine. The use of SAP as the sole variable to control the delivery of anaesthetic agents, can be criticised on several grounds. However, it is one of the few quantifiable indices available and increases in SAP are commonly treated with anaesthetic agents. Further, we carefully excluded those cases in whom SAP is likely to unreliable e.g. hypertensive patients. Although our method of selecting the TSAP is crude, and those patients who required additional morphine may reflect those in whom the TSAP is low, the controller achieved the immediate aim of controlling SAP and also produced a pattern of clinical signs recognisable as general anaesthesia. Pupil diameter was measured in 34 patients. A significant correlation was found between pupil diameter and SAP in 5 cases. There was no difference in the clinical anaesthetic state in those patients in whom a significant correlation was found and those in whom there was no significant correlation. Spectral edge frequency (SEF) was measured in eight of the patients who received isoflurane using a Neurotrac monitor. Due to limitations in data recording we were not able to correlate SEF with SAP. However, SEF was plotted against SAP for seven patients during relatively stable periods of SAP control. A visual relationship was apparent between SAP and SEF in 4 cases. The significance of this finding is unknown. In a further case the EEG became isoelectric at the time a morphine bolus was requested by the computer. The processed EEG may be a better method of assessing a relative anaesthetic overdose than SAP alone during nitrous oxide-morphine-isoflurane anaesthesia. In summary, a computer control system has been developed and tested. The controller achieved the immediate aim of controlling SAP and also produced a pattern of clinical signs recognisable as general anaesthesia

Accelerated Quantum Dynamics

In this dissertation we develop a formalism for the computation of observables due to acceleration-induced particle physics processes. By using the spacetime structure produced by acceleration, we examine the properties of accelerated particle detectors as well as accelerated fields. General expressions for the transition rate, multiplicity, power, spectra, and displacement law of particles undergoing time-dependent acceleration and transitioning into a final state of arbitrary particle number are obtained. The transition rate, power, and spectra are characterized by unique polynomials of multiplicity and thermal distributions of both bosonic and fermionic statistics. The acceleration-dependent multiplicities are computed in terms of the branching fractions of the associated inertial processes. The displacement law of the spectra predicts that the energy of the emitted particles is directly proportional to the accelerated temperature

Overlapping in social studies courses as revealed in textbooks

Thesis (Ed.M.)--Boston University, 1948. This item was digitized by the Internet Archive

Oh Helen!

https://digitalcommons.library.umaine.edu/mmb-vp/2275/thumbnail.jp