Girsanov functionals and optimal bang-bang laws for final value stochastic control

AbstractGirsanov's theorem is a generalization of the Cameron-Martin formula for the derivative of a measure induced by a translation in Wiener space. It states that for ϕ a nonanticipative Brownian functional with ∫|ϕ|2 ds < ∞ a.s. and dP̃=exp[ζ(ϕ)] dP with Ẽ {1}=1, where ζ(ϕ) = ∫ϕdw-12∫|ϕ|2 ds, the translated functions (Tw)(t) = wt - ∫0tϕds are a Wiener process under P̃. The Girsanov functionals exp [ζ(ϕ)] have been used in stochastic control theory to define measures corresponding to solutions of stochastic DEs with only measurable control laws entering the right-hand sides. The present aim is to show that these same concepts have direct practical application to final value problems with bounded control. This is done here by an example, the noisy integrator: Make E{x21}∣small, subject to dxt = ut dt + dwt, |u|⩽ 1, xt observed. For each control law there is a definite cost v(1−t, x) of starting at x, t and using that law till t = 1, expressible as an integral with respect to (a suitable) P̃. By restricting attention to a dense set of smooth laws, using Itô's lemma, Kac's theorem, and the maximum principle for parabolic equations, it is possible to calculate sgn vx for a critical class of control laws, then to compare control laws, “solve” the Bellman-Hamilton-Jacobi equation, and thus justify selection of the obvious bang-bang law as optimal

The Development of Transport in the Czech Republic

Before 1989, transport in the former Czechoslovakia met its tasks based on the controlling principles of planned economy, focused eastwards and oriented on cooperation between the Eastern Bloc countries within COMECOM. Due to the preference for raw material extraction and heavy industry, the transport sector dealt mainly with transporting commodities of these branches with high demands in volume. The planned economic principles were also reflected by the consistent division of transport work with a preference for stack substrate transport by rail. The change of the political and economic circumstances in November 1989 influenced the life and needs of society substantially. A market economy has come, focused on the market of developed European countries and having an impact on the transport sector as such, individual transport systems, transport preferences and transported commodities [2]. As at 1 January 1993, Czechoslovakia has been divided into two independent countries, i.e. the Czech Republic and Slovakia. Therefore the following data from the Transport Statistics of the Czech Republic [1] are comparable starting from 1994. The authors of the article had data available until 2006

Quantum Circuits for the Unitary Permutation Problem

We consider the Unitary Permutation problem which consists, given $n$ unitary gates $U_1, \ldots, U_n$ and a permutation $\sigma$ of $\{1,\ldots, n\}$, in applying the unitary gates in the order specified by $\sigma$, i.e. in performing $U_{\sigma(n)}\ldots U_{\sigma(1)}$. This problem has been introduced and investigated by Colnaghi et al. where two models of computations are considered. This first is the (standard) model of query complexity: the complexity measure is the number of calls to any of the unitary gates $U_i$ in a quantum circuit which solves the problem. The second model provides quantum switches and treats unitary transformations as inputs of second order. In that case the complexity measure is the number of quantum switches. In their paper, Colnaghi et al. have shown that the problem can be solved within $n^2$ calls in the query model and $\frac{n(n-1)}2$ quantum switches in the new model. We refine these results by proving that $n\log_2(n) +\Theta(n)$ quantum switches are necessary and sufficient to solve this problem, whereas $n^2-2n+4$ calls are sufficient to solve this problem in the standard quantum circuit model. We prove, with an additional assumption on the family of gates used in the circuits, that $n^2-o(n^{7/4+\epsilon})$ queries are required, for any $\epsilon >0$. The upper and lower bounds for the standard quantum circuit model are established by pointing out connections with the permutation as substring problem introduced by Karp.Comment: 8 pages, 5 figure

thermodynamic properties of pb3u11o36

Abstract In order to progress in the development of Lead-cooled Fast Reactors, from the safety point of view it is essential to understand the chemical compatibility between liquid lead and uranium oxide. In the present work, entropy and heat capacity of Pb3U11O36, a possible ternary compound coming from fuel-coolant chemical interaction, were determined for the first time. Entropy at 298.15 K was obtained from low temperature heat capacity measurements using the Physical Property Measurement System (PPMS) in the temperature range 2–300 K, while the high temperature heat capacity has been measured by a drop calorimeter from 373 K to 1200 K. The experimental thermodynamic properties were compared with the values computed by means of DFT-GGA simulations, obtaining a very good agreement

LTL Parameter Synthesis of Parametric Timed Automata

The parameter synthesis problem for parametric timed automata is undecidable in general even for very simple reachability properties. In this paper we introduce restrictions on parameter valuations under which the parameter synthesis problem is decidable for LTL properties. The investigated bounded integer parameter synthesis problem could be solved using an explicit enumeration of all possible parameter valuations. We propose an alternative symbolic zone-based method for this problem which results in a faster computation. Our technique extends the ideas of the automata-based approach to LTL model checking of timed automata. To justify the usefulness of our approach, we provide experimental evaluation and compare our method with explicit enumeration technique.Comment: 23 pages, extended versio

Early Childhood Lower Respiratory Illness and Air Pollution

BackgroundFew studies of air pollutants address morbidity in preschool children. In this study we evaluated bronchitis in children from two Czech districts: Teplice, with high ambient air pollution, and Prachatice, characterized by lower exposures.ObjectivesOur goal was to examine rates of lower respiratory illnesses in preschool children in relation to ambient particles and hydrocarbons.MethodsAir monitoring for particulate matter 2 years of age, for PAHs compared with fine particles. Preschool-age children may be particularly vulnerable to air pollution–induced illnesses