A replacement model for an additive damage model with restoration

A system existing in a random environment receives shocks at random points of time. Each shock causes a random amount of damage which accumulates over time. A breakdown can occur only upon the occurrence of a shock according to a known failure probability function. Upon failure the system is replaced by a new identical one with a given cost. When the system is replaced before failure, a smaller cost is incurred. Thus, there is an incentive to attempt to replace the system before failure. The damage process is controlled by means of a maintenance policy which causes the accumulated damage to decrease at a known restoration rate. We introduce sufficient conditions under which an optimal replacement policy which minimizes the total expected discounted cost is a control limit policy. The relationship between the undiscounted case and the discounted case is examined. Finally, an example is given illustrating computational procedures.     

Use of Inappropriate and Inaccurate Conceptual Knowledge to Solve an Osmosis Problem

Two outstanding high school science students each generated a correct answer to an osmosis problem. The solution processes are noteworthy because the problem solvers did not blindly use algorithms. They relied, instead, on conceptual knowledge which was inaccurate and inappropriate to the problem. They thought the osmosis problem was about air pressure, and some of their knowledge about air pressure was inaccurate. Thus, even when students rely on conceptual knowledge to solve a problem, correct answers need not indicate adequate understanding. Characteristics of the problem solvers, salient properties of the problem that could contribute to the problem misrepresentation, and spurious correct answers are identified. Finally, some instructional recommendations and research questions are presented.     

Structural information from the Mössbauer quadrupole splitting of tint(IV) chloride complexes

An empirical linear relationship has been found between the Sn-Cl distance in octahedral tin(IV) chloride complexes and the Mössbauer partial quadrupole splitting of the ligands. The correlationd(Sn-Cl)=(–0.044±0.002) (4 PQS)+(2.420±0.003) Å can be used to predict Sn-Cl distances and get information about the tin-ligand bond strength and the sign of the quadrupole splitting. The relationship suggests that bond distances are strongly affected by rehybridization at the tin atom. The cis or trans structure of tin(IV) chloride complexes cannot be assigned on the basis of the resolvable or unresolvable nature of the Mössbauer doublets, which are rationalized by means of the correlation with the Sn-Cl distances.Deceased on December 4, 1987.     

Optimal investment policy of an insurance firm

In this paper we consider an investment problem by an insurance firm. As in the classical model of collective risk, it is assumed that premium payments are received deterministically from policyholders at a constant rate, while the claim process is determined by a compound Poisson process. We introduce a conversion mechanism of funds from cash into investments and vice versa. Contrary to the conventional collective risk model we do not assume a ruin barrier. Instead we introduce conversion costs to account for the problems implicit in reaching the zero boundary. The objective of the firm is to maximize its net profit by selecting an appropriate investment strategy. A diffusion approximation is suggested in order to obtain tractable results for a general claim size distribution.     

Nanothermometry: From Microscopy to Thermal Treatments

Measuring temperature in cells and tissues remotely, with sufficient sensitivity, and in real time presents a new paradigm in engineering, chemistry and biology. Traditional sensors, such as contact thermometers, thermocouples, and electrodes, are too large to measure the temperature with subcellular resolution and are too invasive to measure the temperature in deep tissue. The new challenge requires novel approaches in designing biocompatible temperature sensors—nanothermometers—and innovative techniques for their measurements. In the last two decades, a variety of nanothermometers whose response reflected the thermal environment within a physiological temperature range have been identified as potential sensors. This review covers the principles and aspects of nanothermometer design driven by two emerging areas: single‐cell thermogenesis and image guided thermal treatments. The review highlights the current trends in nanothermometry illustrated with recent representative examples.     

Extending fragment-based free energy calculations with library Monte Carlo simulation: annealing in interaction space

Pre-calculated libraries of molecular fragment configurations have previously been used as a basis for both equilibrium sampling (via library-based Monte Carlo) and for obtaining absolute free energies using a polymer-growth formalism. Here, we combine the two approaches to extend the size of systems for which free energies can be calculated. We study a series of all-atom poly-alanine systems in a simple dielectric solvent and find that precise free energies can be obtained rapidly. For instance, for 12 residues, less than an hour of single-processor time is required. The combined approach is formally equivalent to the annealed importance sampling algorithm; instead of annealing by decreasing temperature, however, interactions among fragments are gradually added as the molecule is grown. We discuss implications for future binding affinity calculations in which a ligand is grown into a binding site.     

Accelerating molecular Monte Carlo simulations using distance and orientation-dependent energy tables: tuning from atomistic accuracy to smoothed "coarse-grained" models

Typically, the most time consuming part of any atomistic molecular simulation is the repeated calculation of distances, energies, and forces between pairs of atoms. However, many molecules contain nearly rigid multi-atom groups such as rings and other conjugated moieties, whose rigidity can be exploited to significantly speed-up computations. The availability of GB-scale random-access memory (RAM) offers the possibility of tabulation (precalculation) of distance- and orientation-dependent interactions among such rigid molecular bodies. Here, we perform an investigation of this energy tabulation approach for a fluid of atomistic-but rigid-benzene molecules at standard temperature and density. In particular, using O(1) GB of RAM, we construct an energy look-up table, which encompasses the full range of allowed relative positions and orientations between a pair of whole molecules. We obtain a hardware-dependent speed-up of a factor of 24-50 as compared to an ordinary ("exact") Monte Carlo simulation and find excellent agreement between energetic and structural properties. Second, we examine the somewhat reduced fidelity of results obtained using energy tables based on much less memory use. Third, the energy table serves as a convenient platform to explore potential energy smoothing techniques, akin to coarse-graining. Simulations with smoothed tables exhibit near atomistic accuracy while increasing diffusivity. The combined speed-up in sampling from tabulation and smoothing exceeds a factor of 100. For future applications, greater speed-ups can be expected for larger rigid groups, such as those found in biomolecules.     

Diorganostyrylzinndiorganophosphine und ihre tricarbonylnickel-komplexe

Diorganostyryltin chlorides R₂StySnCl (R = C₄H₉, p-CH₃C₆H₄, R₂ = (CH₂)₅) react with trimethylsilyl di-t-butylphosphine or trimethylsilyl diphenylphosphine to form trimethylchlorosilane and the corresponding diorganostyryltin-diorganophosphines, which can be separated and characterized by IR, NMR, Mössbauer and mass spectroscopy. With Ni(CO)₄ the tin—phosphorus derivatives give diorganostyryltin diorganophosphinetricarbonylnickel complexes.     

Peptide conformational equilibria computed via a single-stage shifting protocol

We study the conformational equilibria of two peptides using a novel statistical mechanics approach designed for calculating free energy differences between highly dissimilar conformational states. Our results elucidate the contrasting roles of entropy in implicitly solvated leucine dipeptide and decaglycine. The method extends earlier work by Voter and overcomes the notorious "overlap" problem in free energy computations by constructing a mathematically equivalent calculation with high conformational similarity. The approach requires only equilibrium simulations of the two states of interest, without the need for sampling transition states. We discuss possible extensions and optimizations of the approach.