Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equations

Parameter inference for ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODE solutions are typically approximated by deterministic algorithms, new research on probabilistic solvers indicates that they produce more reliable parameter estimates by better accounting for numerical errors. However, many ODE systems are highly sensitive to their parameter values. This produces deep local minima in the likelihood function -- a problem which existing probabilistic solvers have yet to resolve. Here, we show that a Bayesian filtering paradigm for probabilistic ODE solution can dramatically reduce sensitivity to parameters by learning from the noisy ODE observations in a data-adaptive manner. Our method is applicable to ODEs with partially unobserved components and with arbitrary non-Gaussian noise. Several examples demonstrate that it is more accurate than existing probabilistic ODE solvers, and even in some cases than the exact ODE likelihood.Comment: 9 pages, 5 figure

An upper bound on the total inelastic cross-section as a function of the total cross-section

Recently Andr\'e Martin has proved a rigorous upper bound on the inelastic cross-section $\sigma_{inel}$ at high energy which is one-fourth of the known Froissart-Martin-Lukaszuk upper bound on $\sigma_{tot}$. Here we obtain an upper bound on $\sigma_{inel}$ in terms of $\sigma_{tot}$ and show that the Martin bound on $\sigma_{inel}$ is improved significantly with this added information.Comment: 4 page

Towards a guided atom interferometer based on a superconducting atom chip

We evaluate the realization of a novel geometry of a guided atom interferometer based on a high temperature superconducting microstructure. The interferometer type structure is obtained with a guiding potential realized by two current carrying superconducting wires in combination with a closed superconducting loop sustaining a persistent current. We present the layout and realization of our superconducting atom chip. By employing simulations we discuss the critical parameters of the interferometer guide in particular near the splitting regions of the matter waves. Based on measurements of the relevant chip properties we discuss the application of a compact and reliable on-chip atom interferometer.Comment: 14 pages, 7 figures, accepted for New Journal of Physic

Stabilization of highly polar BiFeO3_3-like structure: a new interface design route for enhanced ferroelectricity in artificial perovskite superlattices

In ABO3 perovskites, oxygen octahedron rotations are common structural distortions that can promote large ferroelectricity in BiFeO3 with an R3c structure [1], but suppress ferroelectricity in CaTiO3 with a Pbnm symmetry [2]. For many CaTiO3-like perovskites, the BiFeO3 structure is a metastable phase. Here, we report the stabilization of the highly-polar BiFeO3-like phase of CaTiO3 in a BaTiO3/CaTiO3 superlattice grown on a SrTiO3 substrate. The stabilization is realized by a reconstruction of oxygen octahedron rotations at the interface from the pattern of nonpolar bulk CaTiO3 to a different pattern that is characteristic of a BiFeO3 phase. The reconstruction is interpreted through a combination of amplitude-contrast sub 0.1nm high-resolution transmission electron microscopy and first-principles theories of the structure, energetics, and polarization of the superlattice and its constituents. We further predict a number of new artificial ferroelectric materials demonstrating that nonpolar perovskites can be turned into ferroelectrics via this interface mechanism. Therefore, a large number of perovskites with the CaTiO3 structure type, which include many magnetic representatives, are now good candidates as novel highly-polar multiferroic materials [3].Comment: Phys. Rev. X, in productio

Discrete Miranda-Talenti estimates and applications to linear and nonlinear PDEs

In this thesis, we construct simple and convergent finite element methods for linear and nonlinear elliptic differential equations in non-divergence form with discontinuous coefficients. The methods are based on a discrete Miranda-Talenti estimate, which relates the H2 semi-norm of piecewise polynomials with the L2 norm of its Laplacian on convex domains. We develop a stability and convergence theory of the proposed methods, and back up the theory with numerical experiments. Furthermore, we construct a finite element method for the Monge-Ampere problem by using an equivalent Hamilton-Jacobi-Bellman formulation

X-ray absorption of liquid water by advanced ab initio methods

Oxygen K-edge X-ray absorption spectra of liquid water are computed based on the configurations from advanced ab initio molecular dynamics simulations, as well as an electron excitation theory from the GW method. One one hand, the molecular structures of liquid water are accurately predicted by including both van der Waals interactions and hybrid functional (PBE0). On the other hand, the dynamic screening effects on electron excitation are approximately described by the recently developed enhanced static Coulomb hole and screened exchange approximation by Kang and Hybertsen [Phys. Rev. B 82, 195108 (2010)]. The resulting spectra of liquid water are in better quantitative agreement with the experimental spectra due to the softened hydrogen bonds and the slightly broadened spectra originating from the better screening model.Comment: 10 pages, 5 figures, accepted by Phys. Rev.

The maximum disjoint paths problem on multi-relations social networks

Motivated by applications to social network analysis (SNA), we study the problem of finding the maximum number of disjoint uni-color paths in an edge-colored graph. We show the NP-hardness and the approximability of the problem, and both approximation and exact algorithms are proposed. Since short paths are much more significant in SNA, we also study the length-bounded version of the problem, in which the lengths of paths are required to be upper bounded by a fixed integer $l$. It is shown that the problem can be solved in polynomial time for $l=3$ and is NP-hard for $l\geq 4$. We also show that the problem can be approximated with ratio $(l-1)/2+\epsilon$ in polynomial time for any $\epsilon >0$. Particularly, for $l=4$, we develop an efficient 2-approximation algorithm

ZEST: Attention-based Zero-Shot Learning for Unseen IoT Device Classification

Recent research works have proposed machine learning models for classifying IoT devices connected to a network. However, there is still a practical challenge of not having all devices (and hence their traffic) available during the training of a model. This essentially means, during the operational phase, we need to classify new devices not seen in the training phase. To address this challenge, we propose ZEST -- a ZSL (zero-shot learning) framework based on self-attention for classifying both seen and unseen devices. ZEST consists of i) a self-attention based network feature extractor, termed SANE, for extracting latent space representations of IoT traffic, ii) a generative model that trains a decoder using latent features to generate pseudo data, and iii) a supervised model that is trained on the generated pseudo data for classifying devices. We carry out extensive experiments on real IoT traffic data; our experiments demonstrate i) ZEST achieves significant improvement (in terms of accuracy) over the baselines; ii) SANE is able to better extract meaningful representations than LSTM which has been commonly used for modeling network traffic.Comment: 9 pages, 6 figures, 3 table

Reinforcement Learning in Computing and Network Convergence Orchestration

As computing power is becoming the core productivity of the digital economy era, the concept of Computing and Network Convergence (CNC), under which network and computing resources can be dynamically scheduled and allocated according to users' needs, has been proposed and attracted wide attention. Based on the tasks' properties, the network orchestration plane needs to flexibly deploy tasks to appropriate computing nodes and arrange paths to the computing nodes. This is a orchestration problem that involves resource scheduling and path arrangement. Since CNC is relatively new, in this paper, we review some researches and applications on CNC. Then, we design a CNC orchestration method using reinforcement learning (RL), which is the first attempt, that can flexibly allocate and schedule computing resources and network resources. Which aims at high profit and low latency. Meanwhile, we use multi-factors to determine the optimization objective so that the orchestration strategy is optimized in terms of total performance from different aspects, such as cost, profit, latency and system overload in our experiment. The experiments shows that the proposed RL-based method can achieve higher profit and lower latency than the greedy method, random selection and balanced-resource method. We demonstrate RL is suitable for CNC orchestration. This paper enlightens the RL application on CNC orchestration