Optimal control, geometry, and quantum computing

We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.

A state-contingent production approach to principal-agent problems with an application to point-source pollution control

Two basic representations of principal-agent relationships, the 'state-space' and 'parameterized distribution' formulations, have emerged. Although the state-space formulation appears more natural, analytical studies using this formulation have had limited success. This paper develops a state-space formulation of the moral-hazard problem using a general representation of production under uncertainty. A closed-form solution for the agency-cost problem is derived. Comparative-static results are deduced. Next we solve the principal's problem of selecting the optimal output given the agency-cost function. The analysis is applied to the problem of point-source pollution control. (C) 1998 Published by Elsevier Science S.A. All rights reserved.

Perforin and interferon-gamma activities independently control tumor initiation, growth, and metastasis

Perforin (pfp) and interferon-gamma (IFN-gamma) together in C57BL/6 (B6) and BALB/c mouse strains provided optimal protection in 3 separate tumor models controlled by innate immunity. Using experimental (B6, RM-1 prostate carcinoma) and spontaneous (BALB/c, DA3 mammary carcinoma) models of metastatic cancer, mice deficient in both pfp and IFN-gamma were significantly less proficient than pfp- or IFN-gamma -deficient mice in preventing metastasis of tumor cells to the lung. Pfp and IFN-gamma -deficient mice were as susceptible as mice depleted of natural killer (NK) cells in both tumor metastasis models, and IFN-gamma appeared to play an early role in protection from metastasis, Previous experiments in a model of fibrosarcoma induced by the chemical carcinogen methylcholanthrene indicated an important role for NK1.1(+) T cells, Herein, both pfp and IFN-gamma played critical and independent roles in providing the host with protection equivalent to that mediated by NK1.1+ T cells, Further analysis demonstrated that IFN-gamma, but not pfp, controlled the growth rate of sarcomas arising in these mice. Thus, this is the first study to demonstrate that host IFN-gamma, and direct cytotoxicity mediated by cytotoxic lymphocytes expressing pfp independently contribute antitumor effector functions that together control the initiation, growth, and spread of tumors in mice, (C) 2001 by The American Society of Hematology.

The role of vaccines in the control of STDs: HPV vaccines

Prophylactic vaccines for genital human papillomavirus (HPV) infection have been shown to be feasible in animal models, and suitable vaccine material based on virus-like particles can be produced in bulk at reasonable cost. Initiation of phase III clinical trials will follow definition of trial outcome measures through further epidemiological studies, and development-of assays of host protective immunity. Vaccines could in principle eliminate HPV-related disease, as the human race is the only natural host for the relevant papillomaviruses (PVs). Therapeutic vaccines for genital HPV infection are also possible, but have not yet been demonstrated as feasible in practice because the choice of vaccine antigens is difficult, the method of their optimal delivery is uncertain, and the nature of the relevant antiviral immunity is unknown. PV species specificity will require trials to be conducted in man, which will slow definition of an ideal vaccine.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.

The effect of resource aggregation at different scales: Optimal foraging behavior of Cotesia rubecula

Resources can be aggregated both within and between patches. In this article, we examine how aggregation at these different scales influences the behavior and performance of foragers. We developed an optimal foraging model of the foraging behavior of the parasitoid wasp Cotesia rubecula parasitizing the larvae of the cabbage butterfly Pieris rapae. The optimal behavior was found using stochastic dynamic programming. The most interesting and novel result is that the effect of resource aggregation within and between patches depends on the degree of aggregation both within and between patches as well as on the local host density in the occupied patch, but lifetime reproductive success depends only on aggregation within patches. Our findings have profound implications for the way in which we measure heterogeneity at different scales and model the response of organisms to spatial heterogeneity.

Optimal input states and feedback for interferometric phase estimation

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2 for states considered bq previous authors. We prove, that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However. we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above N-2. With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of N-1. For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

A hedging point strategy - balancing effluent quality, economy and robustness in the control of wastewater treatment plants

An operational space map is an efficient tool to compare a large number of operational strategies to find an optimal choice of setpoints based on a multicriterion. Typically, such a multicriterion includes a weighted sum of cost of operation and effluent quality. Due to the relative high cost of aeration such a definition of optimality result in a relatively high fraction of the effluent total nitrogen in the form of ammonium. Such a strategy may however introduce a risk into operation because a low degree of ammonium removal leads to a low amount of nitrifiers. This in turn leads to a reduced ability to reject event disturbances, such as large variations in the ammonium load, drop in temperature, the presence of toxic/inhibitory compounds in the influent etc. Hedging is a risk minimisation tool, with the aim to "reduce one's risk of loss on a bet or speculation by compensating transactions on the other side" (The Concise Oxford Dictionary (1995)). In wastewater treatment plant operation hedging can be applied by choosing a higher level of ammonium removal to increase the amount of nitrifiers. This is a sensible way to introduce disturbance rejection ability into the multi criterion. In practice, this is done by deciding upon an internal effluent ammonium criterion. In some countries such as Germany, a separate criterion already applies to the level of ammonium in the effluent. However, in most countries the effluent criterion applies to total nitrogen only. In these cases, an internal effluent ammonium criterion should be selected in order to secure proper disturbance rejection ability.

Review and future directions in the modelling and control of continuous drum granulation

Many granulation plants operate well below design capacity, suffering from high recycle rates and even periodic instabilities. This behaviour cannot be fully predicted using the present models. The main objective of the paper is to provide an overview of the current status of model development for granulation processes and suggest future directions for research and development. The end-use of the models is focused on the optimal design and control of granulation plants using the improved predictions of process dynamics. The development of novel models involving mechanistically based structural switching methods is proposed in the paper. A number of guidelines are proposed for the selection of control relevant model structures. (C) 2002 Published by Elsevier Science B.V.

Practicality of time-optimal two-qubit Hamiltonian simulation

What is the time-optimal way of using a set of control Hamiltonians to obtain a desired interaction? Vidal, Hammerer, and Cirac [Phys. Rev. Lett. 88, 237902 (2002)] have obtained a set of powerful results characterizing the time-optimal simulation of a two-qubit quantum gate using a fixed interaction Hamiltonian and fast local control over the individual qubits. How practically useful are these results? We prove that there are two-qubit Hamiltonians such that time-optimal simulation requires infinitely many steps of evolution, each infinitesimally small, and thus is physically impractical. A procedure is given to determine which two-qubit Hamiltonians have this property, and we show that almost all Hamiltonians do. Finally, we determine some bounds on the penalty that must be paid in the simulation time if the number of steps is fixed at a finite number, and show that the cost in simulation time is not too great.

The stochastic Gross-Pitaevskii equation: II

We provide a derivation of a more accurate version of the stochastic Gross-Pitaevskii equation, as introduced by Gardiner et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 1555). This derivation does not rely on the concept of local energy and momentum conservation and is based on a quasiclassical Wigner function representation of a 'high temperature' master equation for a Bose gas, which includes only modes below an energy cut-off ER that are sufficiently highly occupied (the condensate band). The modes above this cutoff (the non-condensate band) are treated as being essentially thermalized. The interaction between these two bands, known as growth and scattering processes, provides noise and damping terms in the equation of motion for the condensate band, which we call the stochastic Gross-Pitaevskii equation. This approach is distinguished by the control of the approximations made in its derivation and by the feasibility of its numerical implementation.