1,658 research outputs found
Theory of polyelectrolytes in solvents
Using a continuum description, we account for fluctuations in the ionic
solvent surrounding a Gaussian, charged chain and derive an effective
short-ranged potential between the charges on the chain. This potential is
repulsive at short separations and attractive at longer distances. The chemical
potential can be derived from this potential. When the chemical potential is
positive, it leads to a melt-like state. For a vanishingly low concentration of
segments, this state exhibits scaling behavior for long chains. The Flory
exponent characterizing the radius of gyration for long chains is calculated to
be approximately 0.63, close to the classical value obtained for second order
phase transitions. For short chains, the radius of gyration varies linearly
with , the chain length, and is sensitive to the parameters in the
interaction potential. The linear dependence on the chain length indicates
a stiff behavior. The chemical potential associated with this interaction
changes sign, when the screening length in the ionic solvent exceeds a critical
value. This leads to condensation when the chemical potential is negative. In
this state, it is shown using the mean-field approximation that spherical and
toroidal condensed shapes can be obtained. The thickness of the toroidal
polyelectrolyte is studied as a function of the parameters of the model, such
as the ionic screening length. The predictions of this theory should be
amenable to experimental verification
Onset of self-assembly
We have developed a theory of polymer entanglement using an extended
Cahn-Hilliard functional, with two extra terms. One is a nonlocal attractive
term, operating over mesoscales, which is interpreted as giving rise to
entanglement, and the other a local repulsive term indicative of excluded
volume interactions. This functional can be derived using notions from gauge
theory. We go beyond the Gaussian approximation, to the one-loop level, to show
that the system exhibits a crossover to a state of entanglement as the average
chain length between points of entanglement decreases. This crossover is marked
by critical slowing down, as the effective diffusion constant goes to zero. We
have also computed the tensile modulus of the system, and we find a
corresponding crossover to a regime of high modulus. The single parameter in
our theory is obtained by fitting to available experimental data on polystyrene
melts of various chain lengths. Extrapolation of this fit yields a model for
the cross-over to entanglement. The need for additional experiments detailing
the cross-over to the entangled state is pointed out.Comment: Accepted for publication by Phys. Rev. E. Replaces previous version.
Includes comparison with experimental dat
Bosonization Redux
Paper has been withdrawn for major repairs.Comment: Paper has been withdrawn for major repair
Electrodynamics of a non-relativistic, non-equilibrium plasma
A non-equilibrium plasma was studied using classical electrodynamic field
theory. Non-linear interaction terms contribute to a finite lifetime for the
dressed electrodynamic field. The lifetime exhibits a dependence, where is the number density, is
the electron temperature, is the ion temperature, and is the
temperature of the radiation field. The resulting width of the plasmon
resonance is shown to decrease as equilibrium is approached. Dynamic screening
leads to opaqueness of the plasma for low energy electromagnetic radiation.
This leads to a quadratic correction to the quartic Stefan-Boltzmann law. We
also briefly discuss the effect of dynamic screening on fusion rates. Solitonic
solutions to our non-linear wave equation allow localization of positive
charges, which may enhance fusion rates
An Additive Model View to Sparse Gaussian Process Classifier Design
We consider the problem of designing a sparse Gaussian process classifier
(SGPC) that generalizes well. Viewing SGPC design as constructing an additive
model like in boosting, we present an efficient and effective SGPC design
method to perform a stage-wise optimization of a predictive loss function. We
introduce new methods for two key components viz., site parameter estimation
and basis vector selection in any SGPC design. The proposed adaptive sampling
based basis vector selection method aids in achieving improved generalization
performance at a reduced computational cost. This method can also be used in
conjunction with any other site parameter estimation methods. It has similar
computational and storage complexities as the well-known information vector
machine and is suitable for large datasets. The hyperparameters can be
determined by optimizing a predictive loss function. The experimental results
show better generalization performance of the proposed basis vector selection
method on several benchmark datasets, particularly for relatively smaller basis
vector set sizes or on difficult datasets.Comment: 14 pages, 3 figure
Layer-wise training of deep networks using kernel similarity
Deep learning has shown promising results in many machine learning
applications. The hierarchical feature representation built by deep networks
enable compact and precise encoding of the data. A kernel analysis of the
trained deep networks demonstrated that with deeper layers, more simple and
more accurate data representations are obtained. In this paper, we propose an
approach for layer-wise training of a deep network for the supervised
classification task. A transformation matrix of each layer is obtained by
solving an optimization aimed at a better representation where a subsequent
layer builds its representation on the top of the features produced by a
previous layer. We compared the performance of our approach with a DNN trained
using back-propagation which has same architecture as ours. Experimental
results on the real image datasets demonstrate efficacy of our approach. We
also performed kernel analysis of layer representations to validate the claim
of better feature encoding
Deep Reinforcement Learning for Programming Language Correction
Novice programmers often struggle with the formal syntax of programming
languages. To assist them, we design a novel programming language correction
framework amenable to reinforcement learning. The framework allows an agent to
mimic human actions for text navigation and editing. We demonstrate that the
agent can be trained through self-exploration directly from the raw input, that
is, program text itself, without any knowledge of the formal syntax of the
programming language. We leverage expert demonstrations for one tenth of the
training data to accelerate training. The proposed technique is evaluated on
6975 erroneous C programs with typographic errors, written by students during
an introductory programming course. Our technique fixes 14% more programs and
29% more compiler error messages relative to those fixed by a state-of-the-art
tool, DeepFix, which uses a fully supervised neural machine translation
approach
Improving Generalization Performance by Switching from Adam to SGD
Despite superior training outcomes, adaptive optimization methods such as
Adam, Adagrad or RMSprop have been found to generalize poorly compared to
Stochastic gradient descent (SGD). These methods tend to perform well in the
initial portion of training but are outperformed by SGD at later stages of
training. We investigate a hybrid strategy that begins training with an
adaptive method and switches to SGD when appropriate. Concretely, we propose
SWATS, a simple strategy which switches from Adam to SGD when a triggering
condition is satisfied. The condition we propose relates to the projection of
Adam steps on the gradient subspace. By design, the monitoring process for this
condition adds very little overhead and does not increase the number of
hyperparameters in the optimizer. We report experiments on several standard
benchmarks such as: ResNet, SENet, DenseNet and PyramidNet for the CIFAR-10 and
CIFAR-100 data sets, ResNet on the tiny-ImageNet data set and language modeling
with recurrent networks on the PTB and WT2 data sets. The results show that our
strategy is capable of closing the generalization gap between SGD and Adam on a
majority of the tasks
Large Margin Semi-supervised Structured Output Learning
In structured output learning, obtaining labelled data for real-world
applications is usually costly, while unlabelled examples are available in
abundance. Semi-supervised structured classification has been developed to
handle large amounts of unlabelled structured data. In this work, we consider
semi-supervised structural SVMs with domain constraints. The optimization
problem, which in general is not convex, contains the loss terms associated
with the labelled and unlabelled examples along with the domain constraints. We
propose a simple optimization approach, which alternates between solving a
supervised learning problem and a constraint matching problem. Solving the
constraint matching problem is difficult for structured prediction, and we
propose an efficient and effective hill-climbing method to solve it. The
alternating optimization is carried out within a deterministic annealing
framework, which helps in effective constraint matching, and avoiding local
minima which are not very useful. The algorithm is simple to implement and
achieves comparable generalization performance on benchmark datasets.Comment: 9 page
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