Diffractive gluon jet production at hadron colliders in the two-gluon exchange model

Following our recent paper on the calculations of diffractive quark jet production at hadron colliders, we present here the calculations of gluon jet production at hadron colliders in the two-gluon exchange parameterization of the Pomeron model. We use the helicity amplitude method to calculate the cross section formula. We find that for the gluon jet production the diffractive process is related to the differential off-diagonal gluon distribution function in the proton. We estimate the production rate for this process at the Fermilab Tevatron by approximating the off-diagonal gluon distribution function by the usual diagonal gluon distribution.Comment: 17 pages, 6 PS figures, Revte

Feature Incay for Representation Regularization

Softmax loss is widely used in deep neural networks for multi-class classification, where each class is represented by a weight vector, a sample is represented as a feature vector, and the feature vector has the largest projection on the weight vector of the correct category when the model correctly classifies a sample. To ensure generalization, weight decay that shrinks the weight norm is often used as regularizer. Different from traditional learning algorithms where features are fixed and only weights are tunable, features are also tunable as representation learning in deep learning. Thus, we propose feature incay to also regularize representation learning, which favors feature vectors with large norm when the samples can be correctly classified. With the feature incay, feature vectors are further pushed away from the origin along the direction of their corresponding weight vectors, which achieves better inter-class separability. In addition, the proposed feature incay encourages intra-class compactness along the directions of weight vectors by increasing the small feature norm faster than the large ones. Empirical results on MNIST, CIFAR10 and CIFAR100 demonstrate feature incay can improve the generalization ability

Collaborative Learning with Limited Interaction: Tight Bounds for Distributed Exploration in Multi-Armed Bandits

Best arm identification (or, pure exploration) in multi-armed bandits is a fundamental problem in machine learning. In this paper we study the distributed version of this problem where we have multiple agents, and they want to learn the best arm collaboratively. We want to quantify the power of collaboration under limited interaction (or, communication steps), as interaction is expensive in many settings. We measure the running time of a distributed algorithm as the speedup over the best centralized algorithm where there is only one agent. We give almost tight round-speedup tradeoffs for this problem, along which we develop several new techniques for proving lower bounds on the number of communication steps under time or confidence constraints.Comment: 33 page

Some New Symplectic Multiple Timestepping Methods for Multiscale Molecular Dynamics Models

We derived a number of numerical methods to treat biomolecular systems with multiple time scales. Based on the splitting of the operators associated with the slow-varying and fast-varying forces, new multiple time-stepping (MTS) methods are obtained by eliminating the dominant terms in the error. These new methods can be viewed as a generalization of the impulse method. In the implementation of these methods, the long-range forces only need to be computed on the slow time scale, which reduces the computational cost considerably. Preliminary analysis for the energy conservation property is provided

Supervised Nonnegative Matrix Factorization to Predict ICU Mortality Risk

ICU mortality risk prediction is a tough yet important task. On one hand, due to the complex temporal data collected, it is difficult to identify the effective features and interpret them easily; on the other hand, good prediction can help clinicians take timely actions to prevent the mortality. These correspond to the interpretability and accuracy problems. Most existing methods lack of the interpretability, but recently Subgraph Augmented Nonnegative Matrix Factorization (SANMF) has been successfully applied to time series data to provide a path to interpret the features well. Therefore, we adopted this approach as the backbone to analyze the patient data. One limitation of the raw SANMF method is its poor prediction ability due to its unsupervised nature. To deal with this problem, we proposed a supervised SANMF algorithm by integrating the logistic regression loss function into the NMF framework and solved it with an alternating optimization procedure. We used the simulation data to verify the effectiveness of this method, and then we applied it to ICU mortality risk prediction and demonstrated its superiority over other conventional supervised NMF methods.Comment: 7 Pages, 2 figure

Invariant foliations for stochastic dynamical systems with multiplicative stable Levy noise

This work deals with the dynamics of a class of stochastic dynamical systems with a multiplicative non-Gaussian Levy noise. We first establish the existence of stable and unstable foliations for this system via the Lyapunov-Perron method. Then we examine the geometric structure of the invariant foliations, and their relation with invariant manifolds. Finally, we illustrate our results in an example

Dark matter and LHC phenomenology of a scale invariant scotogenic model

We study the phenomenology of a model that addresses the neutrino mass, dark matter, and generation of the electroweak scale in a single framework. Electroweak symmetry breaking is realized via the Coleman-Weinberg mechanism in a classically scale invariant theory, while the neutrino mass is generated radiatively through interactions with dark matter in a typically scotogenic manner. The model introduces a scalar triplet and singlet and a vector-like fermion doublet that carry an odd parity of $Z_2$, and an even parity scalar singlet that helps preserve classical scale invariance. We sample over the parameter space by taking into account various experimental constraints from the dark matter relic density and direct detection, direct scalar searches, neutrino mass, and charged lepton flavor violating decays. We then examine by detailed simulations possible signatures at the LHC to find some benchmark points of the free parameters. We find that the future high-luminosity LHC will have a significant potential in detecting new physics signals in the dilepton channel.Comment: 22 pages, 7 figures, 3 tables; v2: 24 pages, 8 figures, 4 tables, same as the published versio

Ricci-flat graphs with girth four

Lin-Lu-Yau introduced an interesting notion of Ricci curvature for graphs and obtained a complete characterization for all Ricci-flat graphs with girth at least five [1]. In this paper, we propose a concrete approach to construct an infinite family of distinct Ricci-flat graphs of girth four with edge-disjoint 4-cycles and completely characterize all Ricci-flat graphs of girth four with vertex-disjoint 4-cycles

Characterization of the Most Probable Transition Paths of Stochastic Dynamical Systems with Stable L\'{e}vy Noise

This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric $\alpha$-stable L\'{e}vy motion ($0<\alpha<1$) or Brownian motion. For stochastic dynamical systems with Brownian motion, minimizing an action functional is a general method to determine the most probable transition path. We have developed a method based on path integrals to obtain the most probable transition path of stochastic dynamical systems with symmetric $\alpha$-stable L\'{e}vy motion or Brownian motion, and the most probable path can be characterized by a deterministic dynamical system

Thresholding Bandit with Optimal Aggregate Regret

We consider the thresholding bandit problem, whose goal is to find arms of mean rewards above a given threshold $\theta$, with a fixed budget of $T$ trials. We introduce LSA, a new, simple and anytime algorithm that aims to minimize the aggregate regret (or the expected number of mis-classified arms). We prove that our algorithm is instance-wise asymptotically optimal. We also provide comprehensive empirical results to demonstrate the algorithm's superior performance over existing algorithms under a variety of different scenarios