arXiv subjects

J. M. Deutsch

Publications and source records attributed to J. M. Deutsch.

49 records · Page 3Linked to original sources

arXiv2001

Algorithm for Finding Optimal Gene Sets in Microarray Prediction

Motivation: Microarray data has been recently been shown to be efficacious in distinguishing closely related cell types that often appear in the diagnosis of cancer. It is useful to determine the minimum number of genes needed to do such a diagnosis both for clinical use and to determine the importance of specific genes for cancer. Here a replication algorithm is used for this purpose. It evolves an ensemble of predictors, all using different combinations of genes to generate a set of optimal predictors. Results: We apply this method to the leukemia data of the Whitehead/MIT group that attempts to differentially diagnose two kinds of leukemia, and also to data of Khan et. al. to distinguish four different kinds of childhood cancers. In the latter case we were able to reduce the number of genes needed from 96 down to 15, while at the same time being able to perfectly classify all of their test data. Availability: http://stravinsky.ucsc.edu/josh/gesses/ Contact: josh@physics.ucsc.edu

physics.bio-ph↗

arXiv1998

Equilibrium size of large ring molecules

The equilibrium properties of isolated ring molecules were investigated using an off-lattice model with no excluded volume but with dynamics that preserve the topological class. Using an efficient set of long range moves, chains of more than 2000 monomers were studied. Despite the lack of any excluded volume interaction, the radius of gyration scaled like that of a self avoiding walk, as had been previously conjectured. However this scaling was only seen for chains greater than 500 monomers.

cond-mat.soft↗

arXiv1996

Macromolecular separation through a porous surface

A new technique for the separation of macromolecules is proposed and investigated. A thin mesh with pores comparable to the radius of gyration of a free chain is used to filter chains according to their length. Without a field it has previously been shown that the permeability decays as a power law with chain length. However by applying particular configurations of pulsed fields, it is possible to have a permeability that decays as an exponential. This faster decay gives much higher resolution of separation. We also propose a modified screen containing an array of holes with barb-like protrusions running parallel to the surface. When static friction is present between the macromolecule and the protrusion, some of the chains get trapped for long durations of time. By using this and a periodic modulation of an applied electric field, high resolution can be attained.

cond-mat.soft↗

arXiv1996

Long Range Moves for High Density Polymer Simulations

Monte Carlo simulations of proteins are hindered by the system's high density which often makes local moves ineffective. Here we devise and test a set of long range moves that work well even when all sites of a lattice simulation are filled. We demonstrate that for a 27-mer cube, the ground state of random heteropolymers can quickly be reached. We discuss results for 48-mer systems where the ground state is known exactly. For ten sequences that were examined, the introduction of long range moves speeds up the search for the ground state by about one order of magnitude. The method is compared to a fast folding chain growth algorithm that had previously been used with much success. The new algorithm here appears to be more efficient. The point is illustrated by the folding of an 80-mer four-helix bundle considered previously.

cond-mat.soft↗

arXiv1996

Design of Force Fields from Data at Finite Temperature

We investigate the problem of how to obtain the force field between atoms of an experimentally determined structure. We show how this problem can be efficiently solved, even at finite temperature, where the position of the atoms differs substantially from the ground state. We apply our method to systems modeling proteins and demonstrate that the correct potentials can be recovered even in the presence of thermal noise.

cond-mat↗

arXiv1995

A New Algorithm for Protein Design

We apply a new approach to the reverse protein folding problem. Our method uses a minimization function in the design process which is different from the energy function used for folding. For a lattice model, we show that this new approach produces sequences that are likely to fold into desired structures. Our method is a significant improvement over previous attempts which used the energy function for designing sequences.

cond-mat↗

arXiv1995

Design of Copolymeric Materials

We devise a method for designing materials that will have some desired structural characteristics. We apply it to multiblock copolymers that have two different types of monomers, A and B. We show how to determine what sequence of A's and B's should be synthesised in order to give a particular structure and morphology. %For example in a melt of such %polymers, one may wish to engineer a body-centered %cubic structure. Using this method in conjunction with the theory of microphase separation developed by Leibler, we show it is possible to efficiently search for a desired morphology. The method is quite general and can be extended to design isolated heteropolymers, such as proteins, with desired structural characteristics. We show that by making certain approximations to the exact algorithm, a method recently proposed by Shakhnovich and Gutin is obtained. The problems with this method are discussed and we propose an improved approximate algorithm that is computationally efficient.

cond-mat↗

arXiv1995

Dynamics of a Polymer in the Presence of Permeable Membranes

We study the diffusion of a linear polymer in the presence of permeable membranes without excluded volume interactions, using scaling theory and Monte Carlo simulations. We find that the average time it takes for a chain with polymerization index~$N$ to cross a single isolated membrane varies with~$N$ as~% $N^{5/2}$, giving its permeability proportional to~$N^2$. When the membranes are stacked with uniform spacing~$d$ in the unit of the monomer size, the dynamics of a polymer is shown to have three different regimes. In the limit of small~\mbox{$d \ll N^{1/2}$}, the chain diffuses through reptation and \mbox{$D\sim N^{-2}$}. When $d$ is comparable to~$N^{1/2}$ the diffusion coefficients parallel and perpendicular to the membranes become different from each other. While the diffusion becomes Rouse-like, i.e.~\mbox{$D\sim N^{-1}$}, in the parallel direction, the motion in the perpendicular direction is still hindered by the two-dimensional networks. The diffusion eventually becomes isotropic and Rouse-like for large~\mbox{$d \gg N$}.

cond-mat↗

arXiv1994

Simulation of forces on polymers due to slippage

We consider the force on the end of a polymer chain being pulled through a network at velocity $v$, using computer simulations. We develop algorithms for measuring the force on the end of the chain using lattice models of polymers. Our algorithm attaches a spring to the end being pulled and uses its average extension to calculate the force. General problems associated with the use of lattice models in obtaining forces are discussed. Variants of this method are used to obtain upper and lower bounds to the force. The results obtained are in agreement with recent analytical predictions and experiments.

cond-mat↗

arXiv1994

Transforming Signs to Phase Distributions in Quantum Simulations

A method is developed which speeds up averaging in quantum simulations where minus signs cause difficulties. A Langevin equation method in conjunction with a replication algorithm is used enabling one to average over a continuously varying complex number. Instead of ensemble averaging this number directly, the phase of the complex number is followed over time. The method is illustrated in some simple cases where the answers obtained can be compared to exact results, and also compared to conventional averaging procedures which converge orders of magnitude slower than this method. Limitations of this method are also described.

comp-gas↗

arXiv1994

Dynamics of a Grafted Chain into a Rubber Network: A Monte Carlo Study (minor grammatical changes)

The dynamics of a single chain tethered to an interface and in contact with a cross-linked network is examined numerically. When the network is put in contact with the tethered chain, the chain moves with dynamics that are highly constrained due to entanglements. When the surface is repulsive, the chain runs straight along the surface and then forms a plume in the network that starts at a distance of order $\sim\!N^{1/2}$ from the graft point. For short times, the chain length in the gel increases algebraically as a function of time, in most cases as $\sim\!t^{1/2}$. The plume configuration is highly metastable and on a much longer time scale the point of entry into the network decreases to zero. This is similar to the relaxation of the arm of a star polymer in a cross-linked network. The above findings are in agreement with the analytical predictions of O'Connor and McLeish. The effects of a chemical disparity between the grafted chain, the network, and the substrate are investigated. Topological constraints are placed in the interface to determine their effects on the dynamics. Chains tethered at both ends are also studied and show a transition in behavior as a function of the thickness of the interface. Above a critical thickness chain does not penetrate.

cond-mat↗

arXiv1993

Probability distributions for multicomponent systems with multiplicative noise

Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that under some symmetry conditions, the probability distribution of a single component has power law tails, with the exponent independent of the strength of additive noise, but dependent on the strength of the multiplicative noise. The classification of these systems into two regimes appears to be possible in the same manner as with just one degree of freedom. A physical system, that of a turbulent fluid undergoing a chemical reaction is predicted to show a transition from exponential to power law tails, as the reaction rate is increased. A variety of systems are studied numerically. A replication algorithm is used to obtain the Lyapunov exponents for high moments, which would be inaccessible by more conventional approaches.

chao-dyn↗

arXiv1993

Probability distributions for one component equations with multiplicative noise

Systems described by equations involving both multiplicative and additive noise are common in nature. Examples include convection of a passive scalar field, polymersin turbulent flow, and noise in dye lasers. In this paper the one component version of this problem is studied. The steady state probability distribution is classified into two different types of behavior. One class has power law tails and the other is of the form of an exponential to a power law. The value of the power law exponent is determined analytically for models having colored gaussian noise. It is found to only depend on the power spectrum of the noise at zero frequency. When non-gaussian noise is considered it is shown that stretched exponential tails are possible. An intuitive understanding of the results is found and makes use of the Lyapunov exponents for these systems.

chao-dyn↗