992 research outputs found
A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow genetic variation
We study the coupled dynamics of primary and secondary structure formation
(i.e. slow genetic sequence selection and fast folding) in the context of a
solvable microscopic model that includes both short-range steric forces and and
long-range polarity-driven forces. Our solution is based on the diagonalization
of replicated transfer matrices, and leads in the thermodynamic limit to
explicit predictions regarding phase transitions and phase diagrams at genetic
equilibrium. The predicted phenomenology allows for natural physical
interpretations, and finds satisfactory support in numerical simulations.Comment: 51 pages, 13 figures, submitted to J. Phys.
The use of adjectives in English fiction
The article investigates the use of adjectives in the English fiction. It explains the peculiarities of the English adjectives; analyzes the usage of adjectives in the books of English authors.Π‘ΡΠ°ΡΡΡ ΠΈΡΡΠ»Π΅Π΄ΡΠ΅Ρ ΡΠΏΠΎΡΡΠ΅Π±Π»Π΅Π½ΠΈΠ΅ ΠΈΠΌΠ΅Π½ΠΈ ΠΏΡΠΈΠ»Π°Π³Π°ΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ Π² Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠΉ Ρ
ΡΠ΄ΠΎΠΆΠ΅ΡΡΠ²Π΅Π½Π½ΠΎΠΉ Π»ΠΈΡΠ΅ΡΠ°ΡΡΡΠ΅. ΠΠ½Π° ΠΎΠ±ΡΡΡΠ½ΡΠ΅Ρ ΠΎΡΠΎΠ±Π΅Π½Π½ΠΎΡΡΠΈ ΠΏΡΠΈΠ»Π°Π³Π°ΡΠ΅Π»ΡΠ½ΡΡ
Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΎΠ³ΠΎ ΡΠ·ΡΠΊΠ°, Π° ΡΠ°ΠΊΠΆΠ΅ Π°Π½Π°Π»ΠΈΠ·ΠΈΡΡΠ΅Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΡΠΈΠ»Π°Π³Π°ΡΠ΅Π»ΡΠ½ΡΡ
Π² ΠΊΠ½ΠΈΠ³Π°Ρ
Π°Π½Π³Π»ΠΈΠΉΡΠΊΠΈΡ
Π°Π²ΡΠΎΡΠΎΠ²
Exact Markov chain Monte Carlo and Bayesian linear regression
In this work we investigate the use of perfect sampling methods within the context of Bayesian linear regression. We focus on inference problems related to the marginal posterior model probabilities. Model averaged inference for the response and Bayesian variable selection are considered. Perfect sampling is an alternate form of Markov chain Monte Carlo that generates exact sample points from the posterior of interest. This approach removes the need for burn-in assessment faced by traditional MCMC methods. For model averaged inference, we find the monotone Gibbs coupling from the past (CFTP) algorithm is the preferred choice. This requires the predictor matrix be orthogonal, preventing variable selection, but allowing model averaging for prediction of the response. Exploring choices of priors for the parameters in the Bayesian linear model, we investigate sufficiency for monotonicity assuming Gaussian errors. We discover that a number of other sufficient conditions exist, besides an orthogonal predictor matrix, for the construction of a monotone Gibbs Markov chain. Requiring an orthogonal predictor matrix, we investigate new methods of orthogonalizing the original predictor matrix. We find that a new method using the modified Gram-Schmidt orthogonalization procedure performs comparably with existing transformation methods, such as generalized principal components. Accounting for the effect of using an orthogonal predictor matrix, we discover that inference using model averaging for in-sample prediction of the response is comparable between the original and orthogonal predictor matrix. The Gibbs sampler is then investigated for sampling when using the original predictor matrix and the orthogonal predictor matrix. We find that a hybrid method, using a standard Gibbs sampler on the orthogonal space in conjunction with the monotone CFTP Gibbs sampler, provides the fastest computation and convergence to the posterior distribution. We conclude the hybrid approach should be used when the monotone Gibbs CFTP sampler becomes impractical, due to large backwards coupling times. We demonstrate large backwards coupling times occur when the sample size is close to the number of predictors, or when hyper-parameter choices increase model competition. The monotone Gibbs CFTP sampler should be taken advantage of when the backwards coupling time is small. For the problem of variable selection we turn to the exact version of the independent Metropolis-Hastings (IMH) algorithm. We reiterate the notion that the exact IMH sampler is redundant, being a needlessly complicated rejection sampler. We then determine a rejection sampler is feasible for variable selection when the sample size is close to the number of predictors and using Zellnerβs prior with a small value for the hyper-parameter c. Finally, we use the example of simulating from the posterior of c conditional on a model to demonstrate how the use of an exact IMH view-point clarifies how the rejection sampler can be adapted to improve efficiency
Slowly evolving geometry in recurrent neural networks I: extreme dilution regime
We study extremely diluted spin models of neural networks in which the
connectivity evolves in time, although adiabatically slowly compared to the
neurons, according to stochastic equations which on average aim to reduce
frustration. The (fast) neurons and (slow) connectivity variables equilibrate
separately, but at different temperatures. Our model is exactly solvable in
equilibrium. We obtain phase diagrams upon making the condensed ansatz (i.e.
recall of one pattern). These show that, as the connectivity temperature is
lowered, the volume of the retrieval phase diverges and the fraction of
mis-aligned spins is reduced. Still one always retains a region in the
retrieval phase where recall states other than the one corresponding to the
`condensed' pattern are locally stable, so the associative memory character of
our model is preserved.Comment: 18 pages, 6 figure
Diagonalization of replicated transfer matrices for disordered Ising spin systems
We present an alternative procedure for solving the eigenvalue problem of
replicated transfer matrices describing disordered spin systems with (random)
1D nearest neighbor bonds and/or random fields, possibly in combination with
(random) long range bonds. Our method is based on transforming the original
eigenvalue problem for a matrix (where ) into an
eigenvalue problem for integral operators. We first develop our formalism for
the Ising chain with random bonds and fields, where we recover known results.
We then apply our methods to models of spins which interact simultaneously via
a one-dimensional ring and via more complex long-range connectivity structures,
e.g. dimensional neural networks and `small world' magnets.
Numerical simulations confirm our predictions satisfactorily.Comment: 24 pages, LaTex, IOP macro
Arbeidsmarkt: sterke daling gewerkte uren.
Hervorming Sociale Regelgevin
Modelling topical photodynamic therapy treatment including the continuous production of Protoporphyrin IX
C L Campbell acknowledges financial support from an UK EPSRC PhD studentship (EP/K503162/1) and the Alfred Stewart Trust.Most existing theoretical models of photodynamic therapy (PDT) assume a uniform initial distribution of the photosensitive molecule, Protoporphyrin IX (PpIX). This is an adequate assumption when the prodrug is systematically administered; however for topical PDT this is no longer a valid assumption. Topical application and subsequent diffusion of the prodrug results in an inhomogeneous distribution of PpIX, especially after short incubation times, prior to light illumination. In this work a theoretical simulation of PDT where the PpIX distribution depends on the incubation time and the treatment modality is described. Three steps of the PpIX production are considered. The first is the distribution of the topically applied prodrug, the second in the conversion from the prodrug to PpIX and the third is the light distribution which affects the PpIX distribution through photobleaching. The light distribution is modelled using a Monte Carlo radiation transfer model and indicates treatment depths of around 2 mm during daylight PDT and approximately 3 mm during conventional PDT. The results suggest that treatment depths are not only limited by the light penetration but also by the PpIX distributionPostprintPeer reviewe
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