A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$ -Superlinear Convergence for Stochastic Games on Domains

In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear problem into a sequence of linear Dirichlet problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the \(H^2\)-norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo navigation problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.

     

The Ups and Downs of Percent (and Some Interesting Connections)

Percent is a standardized ratio comparison that is often used to describe relative amounts of increase and decrease. In this paper, the nonsymmetric relationship between percent of increase and percent of decrease is explored in several ways. Beginning with a simple graphical representation of the relationship, the functional relationship is developed, with relative decrease expressed as a function of relative increase. Once expressed in the form f(x) = 100x/(100 + x), an immediate connection is made to two other topics commonly found within the study of rates—the work problem and the harmonic mean. Finally, successive percents of increase or decrease are shown to be everyday applications of the geometric mean. This deeper look at a common mathematical concept has uncovered rich structural relationships between topics that are often isolated in the curriculum.     

WITCH: A Penning Trap Retardation Spectrometer Combination for Precision Studies of the Weak Interaction

We present data from three seasons of experimental field work designed to recreate ancient Andean coastal ceramic firing techniques. Based on the recent discovery of two different archaeological ceramic production sites in the La Leche river valley of northern coastal Peru, the opportunity arose to apply Mössbauer spectroscopy and other analytical methods to reconstruct ancient firing procedures. Two sets of firings took place in 1993 and 1997 in Batán Grande using a partially restored Formative kiln from about 800 BC, local hardwood and cow dung as fuel. A third experiment followed in 2000 after the discovery of a Middle Sicán ceramics workshop in use between ca. AD 950 and 1050 at Huaca Sialupe, where an exact replica of an ancient kiln was built from local clay, and fired with local wood and cow dung. Additionally, inverted urns found at Huaca Sialupe were tested for their potential use as furnaces for metal working. Mössbauer spectroscopy was used to compare the physical and chemical state of specimens produced in the field experiments with ancient ceramics and with specimens produced in controlled laboratory experiments.     

On the choice of active space orbitals in MCSCF calculations

We describe a procedure which may be used to aid selection of the active space in multiconfigurational self-consistent field (MCSCF) calculations for general chemical systems. Starting from a restricted Hartree-Fock calculation, we define a hierarchy of interacting virtual orbitals for every occupied orbital. The most strongly interacting orbitals are then taken to constitute the active space in a configuration interaction (CI) calculation. The natural orbital occupation numbers obtained from the CI calculation are then used to choose the active space to be used in a subsequent MCSCF calculation. We illustrate our method on a number of systems (Li₂, B₂, C₂, carbonyl oxide and the transition state for oxidation of H₂S by dioxirane). In all these cases, ‘intuitive’ active spaces are inadequate, as are active spaces derived from the natural orbitals of unrestricted Hartree-Fock calculations.     

Germacrene A is a product of the aristolochene synthase-mediated conversion of farnesylpyrophosphate to aristolochene

The biosynthesis of several sesquiterpenes has been proposed to proceed via germacrene A. However, to date, the production of germacrene A has not been proven directly for any of the sesquiterpene synthases for which it was postulated as an intermediate. We demonstrate here for the first time that significant amounts of germacrene A (7.5% of the total amount of products) are indeed released from wild-type aristolochene synthase (AS) from Penicillium roqueforti. Germacrene A was identified through direct GC-MS comparison to an authentic sample and through production of beta-elemene in a thermal Cope rearrangement. AS also produced a small amount of valencene through deprotonation of C6 rather than C8 in the final step of the reaction. On the basis of the X-ray structure of AS, Tyr 92 was postulated to be the active-site acid responsible for protonation of germacrene A (Caruthers, J. M.; Kang, I.; Rynkiewicz, M. J.; Cane, D. E.; Christianson, D. W. J. Biol. Chem. 2000, 275, 25533-25539). The CD spectra of a mutant protein, ASY92F, in which Tyr 92 was replaced by Phe, and of AS were very similar. ASY92F was approximately 0.1% as active as nonmutated recombinant AS. The steady-state kinetic parameters were measured as 0.138 min(-1) and 0.189 mM for k(cat) and K(M), respectively. Similar to a mutant protein of 5-epi-aristolochene (Rising, K. A.; Starks, C. M.; Noel, J. P.; Chappell, J. J. Am. Chem. Soc. 2000, 122, 1861-1866), the mutant released significant amounts of germacrene A (approximately 29%). ASY92F also produced various amounts of a further five hydrocarbons of molecular weight 204, valencene, beta-(E)-farnesene, alpha- and beta-selinene, and selina-4,11-diene.     

Comment: 2004's fastest organic and biomolecular chemistry!

In January 2003, the Royal Society of Chemistry launched Organic & Biomolecular Chemistry (OBC)--a journal promising to provide high quality research from all aspects of synthetic, physical and biomolecular organic chemistry. The journal was set to build upon the foundations laid down by its predecessor publications (J. Chem. Soc., Perkin Trans. 1 and J. Chem. Soc., Perkin Trans. 2) as well as complement the subject coverage already published in prestigious general chemistry journals such as Chemical Communications and Chemical Society Reviews. Nearly two years on, just how is the programme developing and what can the community expect to see from the Royal Society of Chemistry (RSC)?     

Facile synthesis of novel functionalized bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) derivatives

An improved and efficient synthetic route to four functionalized bis(ethylenedithio)-tetrathiafulvalene (BEDT-TTF) derivatives 2-5 is reported. Tetrathiolate 1 was readily prepared from 2,2'-bis(1,3,4,6-tetrathiapentalen-5-one) under carefully controlled conditions. Subsequent reaction of 1 with selected primary alkyl halides affords new functionalized BEDT-TTF derivatives in good yields.     

Comment: 2004's fastest organic and biomolecular chemistry!

In January 2004, the Royal Society of Chemistry launched Organic & Biomolecular Chemistry (OBC) - a journal promising to provide high quality research from all aspects of synthetic, physical and biomolecular organic chemistry. The journal was set to build upon the foundations laid down by its predecessor publications (J. Chem. Soc., Perkin Trans. 1 and J. Chem. Soc., Perkin Trans. 2) as well as complement the subject coverage already published in prestigious general chemistry journals such as Chemical Communications and Chemical Society Reviews. Nearly two years on, just how is the programme developing and what can the community expect to see from the Royal Society of Chemistry (RSC)?     

Photofragmentation of dichloromethanol Cl2CHOH along C-O and C-Cl cleavages: a theoretical study

Multireference configuration interaction calculations are carried out for ground and excited states of dichloromethanol, Cl2CHOH, to investigate two important photofragmentation processes relevant to atmospheric chemistry. Five low-lying excited states (1(1)A", 2(1)A', 1(3)A", 2(3)A" and 1(3)A') in the energy range between 6.4 and 7.5 eV are found to be highly repulsive for C-Cl elongation, leading to ClCHOH (X2A) and Cl (X2P). Photodissociation along the C-O bond resulting in CHCl2 (X2A') and OH (X2II) has to overcome a barrier of about 0.5 eV because the low-lying excited states 1(1)A", 1(3)A' and 1(3)A" become repulsive only after the C-O bond is elongated by about 0.3 A.     

A review on initiatives for the management of daily medical emergencies prior to the arrival of emergency medical services

Central European Journal of Operations Research - Emergency services worldwide face increasing cost pressure that potentially limits their existing resources. In many countries, emergency services...