Fractal fluctuations in cardiac time series

Human heart rate, controlled by complex feedback mechanisms, is a vital index of systematic circulation. However, it has been shown that beat-to-beat values of heart rate fluctuate continually over a wide range of time scales. Herein we use the relative dispersion, the ratio of the standard deviation to the mean, to show, by systematically aggregating the data, that the correlation in the beat-to-beat cardiac time series is a modulated inverse power law. This scaling property indicates the existence of long-time memory in the underlying cardiac control process and supports the conclusion that heart rate variability is a temporal fractal. We argue that the cardiac control system has allometric properties that enable it to respond to a dynamical environment through scaling.     

Resolution exchange simulation

We extend replica-exchange simulation in two ways and apply our approaches to biomolecules. The first generalization permits exchange simulation between models of differing resolution--i.e., between detailed and coarse-grained models. Such "resolution exchange" can be applied to molecular systems or spin systems. The second extension is to "pseudoexchange" simulations, which require little CPU usage for most levels of the exchange ladder and also substantially reduce the need for overlap between levels. Pseudoexchanges can be used in either replica or resolution exchange simulations. We perform efficient, converged simulations of a 50-atom peptide to illustrate the new approaches.     

Comparison of free energy methods for molecular systems

We present a detailed comparison of computational efficiency and precision for several free energy difference (DeltaF) methods. The analysis includes both equilibrium and nonequilibrium approaches, and distinguishes between unidirectional and bidirectional methodologies. We are primarily interested in comparing two recently proposed approaches, adaptive integration, and single-ensemble path sampling to more established methodologies. As test cases, we study relative solvation free energies of large changes to the size or charge of a Lennard-Jones particle in explicit water. The results show that, for the systems used in this study, both adaptive integration and path sampling offer unique advantages over the more traditional approaches. Specifically, adaptive integration is found to provide very precise long-simulation DeltaF estimates as compared to other methods used in this report, while also offering rapid estimation of DeltaF. The results demonstrate that the adaptive integration approach is the best overall method for the systems studied here. The single-ensemble path sampling approach is found to be superior to ordinary Jarzynski averaging for the unidirectional, "fast-growth" nonequilibrium case. Closer examination of the path sampling approach on a two-dimensional system suggests it may be the overall method of choice when conformational sampling barriers are high. However, it appears that the free energy landscapes for the systems used in this study have rather modest configurational sampling barriers.     

Optimum excess-loss reinsurance: a dynamic framework

The purpose of this article is to consider a two firms excess-loss reinsurance problem. The first firm is defined as the direct underwriter while the second firm is the reinsurer. As in the classical model of collective risk theory 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. The objective of the underwriter is to maximize the expected present value of the long run terminal wealth (investments plus cash) of the firm by selecting an appropriate excess-loss coverage strategy, while the reinsurer seeks to maximize its total expected discounted profit by selecting an optimal loading factor. Since both firms' policies are interdependent we define an insurance game, solved by employing a Stackelberg solution concept. A diffusion approximation is used in order to obtain tractable results for a general claim size distribution. Finally, an example is presented illustrating computational procedures.     

Diorganotin halide carboxylates,thiocarboxylates and halide haloacetates

Twenty-eight diorganotin halide acetates, thioacetates, haloacetates and carboxylates, eighteen not previously reported, have been synthesized by the reaction between the diorganotin oxides and acid halides, and by transacyloxylation reactions between diorganotin halide acetates and carboxylic acids. Infrared in the 2000—200 cm^-1 range, proton and carbon-13 NMR and tin-119m Mössbauer data are interpreted in terms of acetoxy-bridged, trigonal bipyramidal tin in the solid phase with depolymerization occurring in solution where a dynamic equilibrium between diorganotin dihalide and dicarboxylate species is rapidly established. A new infrared absorption also appears at 100–125 cm^-1 to higher frequency of the v_asym(CO₂) which disappears on heating. A dimeric structure based upon four-membered Sn₂O₂ or Sn₂OX rings in which carboxylate group oxygen atoms bridge tin atoms of a second molecule leaving the CO group free is proposed. The halide thioacetates are associated in the solid state but are monomeric in solution.     

Covering times of random walks on bounded degree trees and other graphs

The motivating problem for this paper is to find the expected covering time of a random walk on a balanced binary tree withn vertices. Previous upper bounds for general graphs ofO(|V| |E|)⁽¹⁾ andO(|V| |E|/d _min)⁽²⁾ imply an upper bound ofO(n ²). We show an upper bound on general graphs ofO( |E| log |V|), which implies an upper bound ofO(n log² n). The previous lower bound was (|V| log |V|) for trees.⁽²⁾ In our main result, we show a lower bound of (|V| (log _{d max} |V|)²) for trees, which yields a lower bound of (n log² n). We also extend our techniques to show an upper bound for general graphs ofO(max{E T_i} log |V|).     

Efficient construction of a small hitting set for combinatorial rectangles in high dimension

We describe a deterministic algorithm which, on input integersd, m and real number (0,1), produces a subset S of [m] ^d ={1,2,3,...,m} ^d that hits every combinatorial rectangle in [m] ^d of volume at least , i.e., every subset of [m] ^d the formR ₁×R ₂×...×R _d of size at least m ^d . The cardinality of S is polynomial inm(logd)/, and the time to construct it is polynomial inmd/. The construction of such sets has applications in derandomization methods based on small sample spaces for general multivalued random variables.A preliminary version of this paper appeared in Proceedings of the 25th Annual ACM Symposium on Theory of Computing, 1993.Research partially done while visiting the International Computer Science Institute. Research supported in part by a grant from the Israel-USA Binational Science Foundation.A large portion of this research was done while still at the International Computer Science Institute in Berkeley, California. Research supported in part by National Science Foundation operating grants CCR-9304722 and NCR-9416101, and United States-Israel Binational Science Foundation grant No. 92-00226.Supported in part by NSF under grants CCR-8911388 and CCR-9215293 and by AFOSR grants AFOSR-89-0512 AFOSR-90-0008, and by DIMACS, which is supported by NSF grant STC-91-19999 and by the New Jersey Commission on Science and Technology. Research partially done while visiting the International Computer Science Institute.Partially supported by NSF NYI Grant No. CCR-9457799. Most of this research was done while the author was at MIT, partially supported by an NSF Postdoctoral Fellowship. Research partially done while visiting the International Computer Science Institute.