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 $N$, the chain length, and is sensitive to the parameters in the interaction potential. The linear dependence on the chain length $N$ 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 $\sim n^{-1} T_{e}^{3/2} T_{i}^{-2}T_{r}^{1/2}$ dependence, where $n$ is the number density, $T_{e}$ is the electron temperature, $T_{i}$ is the ion temperature, and $T_{r}$ 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