Optimal Control of Nonlocal Thermistor Equations

We are concerned with the optimal control problem of the well known nonlocal thermistor problem, i.e., in studying the heat transfer in the resistor device whose electrical conductivity is strongly dependent on the temperature. Existence of an optimal control is proved. The optimality system consisting of the state system coupled with adjoint equations is derived, together with a characterization of the optimal control. Uniqueness of solution to the optimality system, and therefore the uniqueness of the optimal control, is established. The last part is devoted to numerical simulations.Comment: Submitted 21-March-2012; revised 11-June-2012; accepted 13-June-2012; for publication in the International Journal of Contro

Optimal Control of the Thermistor Problem in Three Spatial Dimensions

This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Pr\"uss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results

Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction

The spectral problem of the Dirac equation in an external quadratic vector potential is considered using the methods of the perturbation theory. The problem is singular and the perturbation series is asymptotic, so that the methods for dealing with divergent series must be used. Among these, the Distributional Borel Sum appears to be the most well suited tool to give answers and to describe the spectral properties of the system. A detailed investigation is made in one and in three space dimensions with a central potential. We present numerical results for the Dirac equation in one space dimension: these are obtained by determining the perturbation expansion and using the Pad\'e approximants for calculating the distributional Borel transform. A complete agreement is found with previous non-perturbative results obtained by the numerical solution of the singular boundary value problem and the determination of the density of the states from the continuous spectrum.Comment: 10 pages, 1 figur

Impact of climate change on crop production in southern Mali and the potential of adaptation strategies. [P95]

Climate variability and change are affecting rural livelihoods in Mali today and present a growing challenge in the region, as in many other parts of the African continent. We used a database of long-term (from 1965 to 2005) weather records and crop yields of a field experiment conducted from 1965 to 1993 at the N'Tarla in southern Mali to quantify possible historical changes of climate and their impact on yields of cotton, sorghum, and groundnut. Series of future climate data coupled with the calibrated crop growth model APSIM were then used to simulate impacts of climate change on crop production and evaluate adaptation options of crop management, such as planting date, fertilization and choice of variety. We found that temperature and the total number of dry days within the growing season had significantly increased over the 1965-2005 period. These climate changes reduced cotton yields, but no significant relationship was found for sorghum or groundnut. Predicted future changes in climate are in line with the historical changes. By mid-century, predicted maize grain yield losses under current farmer's practice are between 51% and 57%. For millet average yield losses are between 7% and 12%. A major challenge of adaptation strategies to climate variability and change is to match the crop growth cycle to the length of the rainy season. If crop management is improved – to avoid delays in planting date, to increase rates of fertilizer use and to use the best performing crop varieties – the loss in crop yield due to climate change can be compensated and even turned into a yield increase compared with current yields. (Texte intégral

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

Genome editing with Cas9 in adult mice corrects a disease mutation and phenotype

We demonstrate CRISPR-Cas9–mediated correction of a Fah mutation in hepatocytes in a mouse model of the human disease hereditary tyrosinemia. Delivery of components of the CRISPR-Cas9 system by hydrodynamic injection resulted in initial expression of the wild-type Fah protein in ~1/250 liver cells. Expansion of Fah-positive hepatocytes rescued the body weight loss phenotype. Our study indicates that CRISPR-Cas9–mediated genome editing is possible in adult animals and has potential for correction of human genetic diseases.National Cancer Institute (U.S.) (Grant 2-PO1-CA42063)National Cancer Institute (U.S.) (Core Grant P30-CA14051)National Institutes of Health (U.S.) (Grant R01-CA133404)David H. Koch Institute for Integrative Cancer Research at MIT (Marie D. and Pierre Casimir-Lambert Fund)National Institutes of Health (U.S.) (Centers for Cancer Nanotechnology Excellence 5-U54-CA151884-04)MIT-Harvard Center of Cancer Nanotechnology ExcellenceNational Institutes of Health (U.S.) (1K99CA169512

Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic

Estimation of the national disease burden of influenza-associated severe acute respiratory illness in Kenya and Guatemala : a novel methodology

Background: Knowing the national disease burden of severe influenza in low-income countries can inform policy decisions around influenza treatment and prevention. We present a novel methodology using locally generated data for estimating this burden. Methods and Findings: This method begins with calculating the hospitalized severe acute respiratory illness (SARI) incidence for children <5 years old and persons ≥5 years old from population-based surveillance in one province. This base rate of SARI is then adjusted for each province based on the prevalence of risk factors and healthcare-seeking behavior. The percentage of SARI with influenza virus detected is determined from provincial-level sentinel surveillance and applied to the adjusted provincial rates of hospitalized SARI. Healthcare-seeking data from healthcare utilization surveys is used to estimate non-hospitalized influenza-associated SARI. Rates of hospitalized and non-hospitalized influenza-associated SARI are applied to census data to calculate the national number of cases. The method was field-tested in Kenya, and validated in Guatemala, using data from August 2009–July 2011. In Kenya (2009 population 38.6 million persons), the annual number of hospitalized influenza-associated SARI cases ranged from 17,129–27,659 for children <5 years old (2.9–4.7 per 1,000 persons) and 6,882–7,836 for persons ≥5 years old (0.21–0.24 per 1,000 persons), depending on year and base rate used. In Guatemala (2011 population 14.7 million persons), the annual number of hospitalized cases of influenza-associated pneumonia ranged from 1,065–2,259 (0.5–1.0 per 1,000 persons) among children <5 years old and 779–2,252 cases (0.1–0.2 per 1,000 persons) for persons ≥5 years old, depending on year and base rate used. In both countries, the number of non-hospitalized influenza-associated cases was several-fold higher than the hospitalized cases. Conclusions: Influenza virus was associated with a substantial amount of severe disease in Kenya and Guatemala. This method can be performed in most low and lower-middle income countries