Unitary cycles on Shimura curves and the Shimura lift I

This paper concerns two families of divisors, which we call the `orthogonal' and `unitary' special cycles, defined on integral models of Shimura curves. The orthogonal family was studied extensively by Kudla-Rapoport-Yang, who showed that they are closely related to the Fourier coefficients of modular forms of weight 3/2, while the `unitary' divisors are analogues of cycles appearing in more recent work of Kudla-Rapoport on unitary Shimura varieties. Our main result shows that these two families are related by (a formal version of) the Shimura lift.Comment: 62 pages. Some material from arXiv:1309.2083v1 has been incorporated here, and the main result has been strengthened. Also minor changes to exposition and organizatio

Improper Intersections of Kudla-Rapoport divisors and Eisenstein series

We consider a certain family of Kudla-Rapoport cycles on an integral model of a Shimura variety attached to a unitary group of signature (1,1), and prove that the arithmetic degrees of these cycles can be identified with the Fourier coefficients of the central derivative of an Eisenstein series of genus 2. The integral model in question parametrizes abelian surfaces equipped with a non-principal polarization and an action of an imaginary quadratic number ring, and in this setting the cycles are degenerate: they may contain components of positive dimension. This result can be viewed as confirmation, in the degenerate setting and for dimension 2, of conjectures of Kudla and Kudla-Rapoport that predict relations between the intersection numbers of special cycles and the Fourier coefficients of automorphic forms

Learning a Fuzzy Hyperplane Fat Margin Classifier with Minimum VC dimension

The Vapnik-Chervonenkis (VC) dimension measures the complexity of a learning machine, and a low VC dimension leads to good generalization. The recently proposed Minimal Complexity Machine (MCM) learns a hyperplane classifier by minimizing an exact bound on the VC dimension. This paper extends the MCM classifier to the fuzzy domain. The use of a fuzzy membership is known to reduce the effect of outliers, and to reduce the effect of noise on learning. Experimental results show, that on a number of benchmark datasets, the the fuzzy MCM classifier outperforms SVMs and the conventional MCM in terms of generalization, and that the fuzzy MCM uses fewer support vectors. On several benchmark datasets, the fuzzy MCM classifier yields excellent test set accuracies while using one-tenth the number of support vectors used by SVMs.Comment: arXiv admin note: text overlap with arXiv:1410.457

A Simple and Effective Approach to the Story Cloze Test

In the Story Cloze Test, a system is presented with a 4-sentence prompt to a story, and must determine which one of two potential endings is the 'right' ending to the story. Previous work has shown that ignoring the training set and training a model on the validation set can achieve high accuracy on this task due to stylistic differences between the story endings in the training set and validation and test sets. Following this approach, we present a simpler fully-neural approach to the Story Cloze Test using skip-thought embeddings of the stories in a feed-forward network that achieves close to state-of-the-art performance on this task without any feature engineering. We also find that considering just the last sentence of the prompt instead of the whole prompt yields higher accuracy with our approach.Comment: 6 page

Deep Residual Network based food recognition for enhanced Augmented Reality application

Deep neural network based learning approaches is widely utilized for image classification or object detection based problems with remarkable outcomes. Realtime Object state estimation of objects can be used to track and estimate the features that the object of the current frame possesses without causing any significant delay and misclassification. A system that can detect the features of such objects in the present state from camera images can be used to enhance the application of Augmented Reality for improving user experience and delivering information in a much perceptual way. The focus behind this paper is to determine the most suitable model to create a low-latency assistance AR to aid users by providing them nutritional information about the food that they consume in order to promote healthier life choices. Hence the dataset has been collected and acquired in such a manner, and we conduct various tests in order to identify the most suitable DNN in terms of performance and complexity and establish a system that renders such information realtime to the user.Comment: Total Pages:7 Total Figures:1

Learning Quantum Graphical Models using Constrained Gradient Descent on the Stiefel Manifold

Quantum graphical models (QGMs) extend the classical framework for reasoning about uncertainty by incorporating the quantum mechanical view of probability. Prior work on QGMs has focused on hidden quantum Markov models (HQMMs), which can be formulated using quantum analogues of the sum rule and Bayes rule used in classical graphical models. Despite the focus on developing the QGM framework, there has been little progress in learning these models from data. The existing state-of-the-art approach randomly initializes parameters and iteratively finds unitary transformations that increase the likelihood of the data. While this algorithm demonstrated theoretical strengths of HQMMs over HMMs, it is slow and can only handle a small number of hidden states. In this paper, we tackle the learning problem by solving a constrained optimization problem on the Stiefel manifold using a well-known retraction-based algorithm. We demonstrate that this approach is not only faster and yields better solutions on several datasets, but also scales to larger models that were prohibitively slow to train via the earlier method

Learning Hidden Quantum Markov Models

Hidden Quantum Markov Models (HQMMs) can be thought of as quantum probabilistic graphical models that can model sequential data. We extend previous work on HQMMs with three contributions: (1) we show how classical hidden Markov models (HMMs) can be simulated on a quantum circuit, (2) we reformulate HQMMs by relaxing the constraints for modeling HMMs on quantum circuits, and (3) we present a learning algorithm to estimate the parameters of an HQMM from data. While our algorithm requires further optimization to handle larger datasets, we are able to evaluate our algorithm using several synthetic datasets. We show that on HQMM generated data, our algorithm learns HQMMs with the same number of hidden states and predictive accuracy as the true HQMMs, while HMMs learned with the Baum-Welch algorithm require more states to match the predictive accuracy

Distribution System Load and Forecast Model

This short document provides experimental evidence for the set of assumptions on the mean load and forecast errors made in \cite{Sevlian2014A_Outage} and \cite{Sevlian2014B_Outage}. We show that the mean load at any given node is distributed normally, where we compute the mean and variance. We then present an aggregation-error curve for a single day ahead forecaster. Residual analysis shows that beyond 500 customers, gaussian residuals is a reasonable model. We then show the forecaster has uncorrelated errors

Wrinkling instability of an inhomogeneously stretched viscous sheet

Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed non-uniform temperature field. We first determine the associated base flow by solving the long-timescale stretching flow of a flat sheet as a function of two dimensionless parameters: the normalized stretching velocity $\alpha$, and a dimensionless width of the heating zone $\beta$. This allows us to determine the conditions for the onset of an out-of-plane wrinkling instability stated in terms of an eigenvalue problem for a linear partial differential equation governing the displacement of the midsurface of the sheet. We show the sheet can become unstable in two regions that are upstream and downstream of the heating zone where the minimum in-plane stress is negative. This yields the shape and growth rates of the most unstable buckling mode in both regions for various values of the stretching velocity and heating zone width. A transition from stationary to oscillatory unstable modes is found in the upstream region with increasing $\beta$ while the downstream region is always stationary. We show that the wrinkling instability can be entirely suppressed when the surface tension is large enough relative to the magnitude of the in-plane stress. Finally, we present an operating diagram that indicates regions of the parameter space that result in a required outlet sheet thickness upon stretching, while simultaneously minimizing or suppressing the out-of-plane buckling; a result that is relevant for the glass redraw method used to create ultrathin glass sheets.Comment: 26 pages, 7 figure

An Alternative C++ based HPC system for Hadoop MapReduce

MapReduce is a technique used to vastly improve distributed processing of data and can massively speed up computation. Hadoop and its MapReduce relies on JVM and Java which is expensive on memory. High Performance Computing based MapReduce framework could be used that can perform more memory-efficiently and faster than the standard MapReduce. This paper explores an entirely C++ based approach to the MapReduce and its feasibility on multiple factors like developer friendliness, deployment interface, efficiency and scalability. This paper also introduces Delayed Reduction and deployment techniques that can speed up MapReduce in a compiled environment.Comment: 8 pages, 13 figures, 4 author