arXiv subjects

Wei Dai

Publications and source records attributed to Wei Dai.

At least 235 records · Page 13Linked to original sources

arXiv2020

EVA: An Encrypted Vector Arithmetic Language and Compiler for Efficient Homomorphic Computation

Fully-Homomorphic Encryption (FHE) offers powerful capabilities by enabling secure offloading of both storage and computation, and recent innovations in schemes and implementations have made it all the more attractive. At the same time, FHE is notoriously hard to use with a very constrained programming model, a very unusual performance profile, and many cryptographic constraints. Existing compilers for FHE either target simpler but less efficient FHE schemes or only support specific domains where they can rely on expert-provided high-level runtimes to hide complications. This paper presents a new FHE language called Encrypted Vector Arithmetic (EVA), which includes an optimizing compiler that generates correct and secure FHE programs, while hiding all the complexities of the target FHE scheme. Bolstered by our optimizing compiler, programmers can develop efficient general-purpose FHE applications directly in EVA. For example, we have developed image processing applications using EVA, with a very few lines of code. EVA is designed to also work as an intermediate representation that can be a target for compiling higher-level domain-specific languages. To demonstrate this, we have re-targeted CHET, an existing domain-specific compiler for neural network inference, onto EVA. Due to the novel optimizations in EVA, its programs are on average 5.3x faster than those generated by CHET. We believe that EVA would enable a wider adoption of FHE by making it easier to develop FHE applications and domain-specific FHE compilers.

cs.CR↗

arXiv2020

Transverse Momentum Balance and Angular Distribution of $b\bar{b}$ Dijets in Pb+Pb collisions

The productions of inclusive b-jet and $b\bar{b}$ dijets in Pb+Pb collisions have been investigated by considering the heavy quark and the light quark in-medium evolution simultaneously. The initial hard processes of inclusive b-jet and $b\bar{b}$ dijets productions are described by a next-to-leading order (NLO) plus parton shower Monte Carlo (MC) event generator SHERPA which can be well-matched with the experimental data in p+p collisions. The framework combines the Langevin transport model to describe the evolution of the bottom quark also its collisional energy loss and the higher-twist description to consider the radiative energy loss of both the bottom and light quarks. We compare the theoretical simulation of inclusive jet and inclusive b-jet $R_{\rm AA}$ in Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV with the experimental data, and then present the theoretical simulation of the momentum balance of the $b\bar{b}$ dijet in Pb+Pb collisions at $5.02$ TeV with the recent CMS data for the first time. A similar trend as that in inclusive dijets has been observed in $b\bar{b}$ dijets, the production distribution is shifted to smaller $x_J$ due to the jet quenching effect. At last, the prediction of the normalized azimuthal angle distribution of the $b\bar{b}$ dijet in Pb+Pb collisions at $5.02$ TeV has been reported. The medium induced energy loss effect of the $b\bar{b}$ dijets will overall suppress its production, but the same side ($Δϕ\to 0$ region) suffers more energy loss than away side ($Δϕ\to π$ region), therefore lead to the suppression on the same side and the enhancement on the away side in the normalized azimuthal angle distribution in A+A collisions.

nucl-th↗

arXiv2020

Sharp reversed Hardy-Littlewood-Sobolev inequality with extended kernel

In this paper, we prove the following reversed Hardy-Littlewood-Sobolev inequality with extended kernel \begin{equation*} \int_{\mathbb{R}_+^n}\int_{\partial\mathbb{R}^n_+} \frac{x_n^β}{|x-y|^{n-α}}f(y)g(x) dydx\geq C_{n,α,β,p}\|f\|_{L^{p}(\partial\mathbb{R}_+^n)} \|g\|_{L^{q'}(\mathbb{R}_+^n)} \end{equation*} for any nonnegative functions $f\in L^{p}(\partial\mathbb{R}_+^n)$ and $g\in L^{q'}(\mathbb{R}_+^n)$, where $n\geq2$, $p,\ q'\in (0,1)$, $α>n$, $0\leqβ<\frac{α-n}{n-1}$, $p>\frac{n-1}{α-1-(n-1)β}$ such that $\frac{n-1}{n}\frac{1}{p}+\frac{1}{q'}-\frac{α+β-1}{n}=1$. We prove the existence of extremal functions for the above inequality. Moreover, in the conformal invariant case, we classify all the extremal functions and hence derive the best constant via a variant method of moving spheres, which can be carried out \emph{without lifting the regularity of Lebesgue measurable solutions}. Finally, we derive the sufficient and necessary conditions for existence of positive solutions to the Euler-Lagrange equations by using Pohozaev identities. Our results are inspired by Hang, Wang and Yan \cite{HWY}, Dou, Guo and Zhu \cite{DGZ} for $α<n$ and $β=1$, and Gluck \cite{Gl} for $α<n$ and $β\geq0$.

math.AP↗

arXiv2020

Selective Confidence Intervals for Martingale Regression Model

In this paper we consider the problem of constructing confidence intervals for coefficients of martingale regression models (in particular, time series models) after variable selection. Although constructing confidence intervals are common practice in statistical analysis, it is challenging in our framework due to the data-dependence of the selected model and the correlation among the variables being selected and not selected. We first introduce estimators for the selected coefficients and show that it is consistent under martingale regression model, in which the observations can be dependent and the errors can be heteroskedastic. Then we use the estimators together with a resampling approach to construct confidence intervals. Our simulation results show that our approach outperforms other existing approaches in various data structures.

math.ST↗

arXiv2020

Self-similar solutions of energy-supercritical focusing wave equations in all dimensions

In this paper, we prove the existence of a countable family of regular spherically symmetric self-similar solutions to focusing energy super-critical semi-linear wave equations \begin{equation*} \partial_{tt}u-Δu=|u|^{p-1}u \qquad \text{in} \,\, \mathbb{R}^{N}, \end{equation*} where $N\geq 3$, $1+\frac{4}{N-2}<p$, and, if $N\geq 4$, $p \leq 1+\frac{4}{N-3}$. This was previously known only in the case $N=3$, for integer $p$ (see Bizoń, Maison and Wasserman \cite{BMW}). We also study the asymptotics of these solutions.

math.AP↗

arXiv2020

Direct methods for pseudo-relativistic Schrödinger operators

In this paper, we establish various maximal principles and develop the direct moving planes and sliding methods for equations involving the physically interesting (nonlocal) pseudo-relativistic Schrödinger operators $(-Δ+m^{2})^{s}$ with $s\in(0,1)$ and mass $m>0$. As a consequence, we also derive multiple applications of these direct methods. For instance, we prove monotonicity, symmetry and uniqueness results for solutions to various equations involving the operators $(-Δ+m^{2})^{s}$ in bounded domains, epigraph or $\mathbb{R}^{N}$, including pseudo-relativistic Schrödinger equations, 3D boson star equations and the equations with De Giorgi type nonlinearities.

math.AP↗

arXiv2020

Demonstration of Controlled-Phase Gates between Two Error-Correctable Photonic Qubits

To realize fault-tolerant quantum computing, it is necessary to store quantum information in logical qubits with error correction functions, realized by distributing a logical state among multiple physical qubits or by encoding it in the Hilbert space of a high-dimensional system. Quantum gate operations between these error-correctable logical qubits, which are essential for implementation of any practical quantum computational task, have not been experimentally demonstrated yet. Here we demonstrate a geometric method for realizing controlled-phase gates between two logical qubits encoded in photonic fields stored in cavities. The gates are realized by dispersively coupling an ancillary superconducting qubit to these cavities and driving it to make a cyclic evolution depending on the joint photonic state of the cavities, which produces a conditional geometric phase. We first realize phase gates for photonic qubits with the logical basis states encoded in two quasiorthogonal coherent states, which have important implications for continuous-variable-based quantum computation. Then we use this geometric method to implement a controlled-phase gate between two binomially encoded logical qubits, which have an error-correctable function.

quant-ph↗

arXiv2020

Dictionary Learning with BLOTLESS Update

Algorithms for learning a dictionary to sparsely represent a given dataset typically alternate between sparse coding and dictionary update stages. Methods for dictionary update aim to minimise expansion error by updating dictionary vectors and expansion coefficients given patterns of non-zero coefficients obtained in the sparse coding stage. We propose a block total least squares (BLOTLESS) algorithm for dictionary update. BLOTLESS updates a block of dictionary elements and the corresponding sparse coefficients simultaneously. In the error free case, three necessary conditions for exact recovery are identified. Lower bounds on the number of training data are established so that the necessary conditions hold with high probability. Numerical simulations show that the bounds approximate well the number of training data needed for exact dictionary recovery. Numerical experiments further demonstrate several benefits of dictionary learning with BLOTLESS update compared with state-of-the-art algorithms especially when the amount of training data is small.

eess.SP↗

arXiv2020

Radial distribution of charm quarks in jets in high-energy heavy-ion collisions

Heavy flavor physics in high-energy heavy-ion collisions is a promising and active area to study the mass dependence of the "jet quenching" effects both at the RHIC and the LHC. In this talk, we present the first theoretical study on the $D^0$ meson radial distributions relative to the jet axis both in p+p and Pb+Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV, where a nice agreement of our results with experimental data is observed. The in-medium parton propagations are described by a Monte Carlo transport model which uses the next-to-leading order (NLO) plus parton shower (PS) event generator SHERPA as input and includes elastic (collisional) and inelastic (radiative) in-medium interaction of heavy flavor jet. We find that, at low $D^0$ meson $p_T$, the radial distribution significantly shifts to larger radius indicating a strong diffusion effect, and the diffusion effects decrease quickly with $p_T$ ,which is consistent with the recent CMS measurements. We demonstrate that the angular deviation of charm quarks is sensitive to $D_s$ but not $\hat{q}$, which may provide new constrains on the collisional and radiative heavy quark energy loss.

nucl-th↗

arXiv2020

HEAX: An Architecture for Computing on Encrypted Data

With the rapid increase in cloud computing, concerns surrounding data privacy, security, and confidentiality also have been increased significantly. Not only cloud providers are susceptible to internal and external hacks, but also in some scenarios, data owners cannot outsource the computation due to privacy laws such as GDPR, HIPAA, or CCPA. Fully Homomorphic Encryption (FHE) is a groundbreaking invention in cryptography that, unlike traditional cryptosystems, enables computation on encrypted data without ever decrypting it. However, the most critical obstacle in deploying FHE at large-scale is the enormous computation overhead. In this paper, we present HEAX, a novel hardware architecture for FHE that achieves unprecedented performance improvement. HEAX leverages multiple levels of parallelism, ranging from ciphertext-level to fine-grained modular arithmetic level. Our first contribution is a new highly-parallelizable architecture for number-theoretic transform (NTT) which can be of independent interest as NTT is frequently used in many lattice-based cryptography systems. Building on top of NTT engine, we design a novel architecture for computation on homomorphically encrypted data. We also introduce several techniques to enable an end-to-end, fully pipelined design as well as reducing on-chip memory consumption. Our implementation on reconfigurable hardware demonstrates 164-268x performance improvement for a wide range of FHE parameters.

cs.CR↗

arXiv2019

Benchmarking Contemporary Deep Learning Hardware and Frameworks:A Survey of Qualitative Metrics

This paper surveys benchmarking principles, machine learning devices including GPUs, FPGAs, and ASICs, and deep learning software frameworks. It also reviews these technologies with respect to benchmarking from the perspectives of a 6-metric approach to frameworks and an 11-metric approach to hardware platforms. Because MLPerf is a benchmark organization working with industry and academia, and offering deep learning benchmarks that evaluate training and inference on deep learning hardware devices, the survey also mentions MLPerf benchmark results, benchmark metrics, datasets, deep learning frameworks and algorithms. We summarize seven benchmarking principles, differential characteristics of mainstream AI devices, and qualitative comparison of deep learning hardware and frameworks.

cs.DC↗

arXiv2019

Super-resolved Localisation without Identifying LoS/NLoS Paths

This paper focuses on the problem of localising a transmitting mobile station (MS) using multiple cooperative base stations (BSs). There are two technical difficulties: one is the data association between intermediate parameters and scatters; the other is to identify Line-of-Sight (LoS) and Non-Line-of-Sight (NLoS) paths. Our main contribution is a unified approach bypassing both data association and LoS/NLoS path identification. This is achieved by introducing virtual scatters and then a direct localisation formulation. Modern super-resolution technique is then adapted to cast the localisation problem as convex programming and solve it. Our approach addresses long-standing issues not completely solved in the literature, guarantees a global convergence, achieves good localisation accuracy and demonstrates its robustness to noise in our numerical tests.

eess.SP↗

arXiv2019

Dictionary Learning Using Rank-One Projection (ROP)

Dictionary learning aims to find a dictionary that can sparsely represent the training data. Methods in the literature typically formulate the dictionary learning problem as an optimisation with respect to two variables, i.e., dictionary and sparse coefficients, and solve it by alternating between two stages: sparse coding and dictionary update. The key contribution of this work is a Rank-One Projection (ROP) formulation where dictionary learning is cast as an optimisation with respect to a single variable which is a set of rank one matrices. The resulting algorithm is hence single staged. An alternating direction method of multipliers (ADMM) is derived to solve the optimisation problem and guarantees a global convergence despite non-convexity of the optimisation formulation. Also ROP reduces the number of tuning parameters required in other benchmark algorithms. Numerical tests demonstrate that ROP outperforms other benchmarks for both synthetic and real data especially when the sample number is small.

eess.SP↗

arXiv2019

Diffusion of charm quarks in jets in high-energy heavy-ion collisions

The radial distribution of $D^0$ mesons in jets probes the diffusion of charm quark relative to the jet axis and provides a new perspective to study the interaction mechanisms between heavy quarks and the medium in the nucleus-nucleus collisions. The in-medium parton propagations are described by a Monte Carlo transport model which uses the next-to-leading order (NLO) plus parton shower (PS) event generator SHERPA as input and includes elastic (collisional) and inelastic (radiative) interaction for heavy quarks as well as light partons. At low $D^0$ meson $p_T$, the radial distribution significantly shifts to larger radius indicating a strong diffusion effect which is consistent with the recent experimental data. We demonstrate that the angular deviation of charm quarks declines with $p_T$ and is very sensitive to the collisional more than radiative interaction at $p_T<5$~GeV. As predictions, we present the $D^0$ meson radial distribution in jets in p+p and $0-10\%$ Au+Au collisions at $\sqrt{s_{NN}}=200$~GeV at the RHIC, and also estimate the nuclear modification factor of charm jet in central Au+Au collisions at 200~GeV at the RHIC and central Pb+Pb collisions at $5.02$~TeV at the LHC.

nucl-th↗

arXiv2019

Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians

In this paper, we are concerned with equations \eqref{PDE} involving higher-order fractional Laplacians. By introducing a new approach, we prove the super poly-harmonic properties for nonnegative solutions to \eqref{PDE} (Theorem \ref{Thm0}). Our theorem seems to be the first result on this problem. As a consequence, we derive many important applications of the super poly-harmonic properties. For instance, we establish Liouville theorems, integral representation formula and classification results for nonnegative solutions to fractional higher-order equations \eqref{PDE} with general nonlinearities $f(x,u,Du,\cdots)$ including conformally invariant and odd order cases. In particular, our results completely improve the classification results for third order equations in Dai and Qin \cite{DQ1} by removing the assumptions on integrability. We also derive a characterization for $α$-harmonic functions via averages in the appendix.

math.AP↗

arXiv2019

Classification of nonnegative solutions to static Schrödinger-Hartree-Maxwell type equations

In this paper, we are mainly concerned with the physically interesting static Schrödinger-Hartree-Maxwell type equations \begin{equation*} (-Δ)^{s}u(x)=\left(\frac{1}{|x|^σ}\ast |u|^{p}\right)u^{q}(x) \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n} \end{equation*} involving higher-order or higher-order fractional Laplacians, where $n\geq1$, $0<s:=m+\fracα{2}<\frac{n}{2}$, $m\geq0$ is an integer, $0<α\leq2$, $0<σ<n$, $0<p\leq\frac{2n-σ}{n-2s}$ and $0<q\leq\frac{n+2s-σ}{n-2s}$. We first prove the super poly-harmonic properties of nonnegative classical solutions to the above PDEs, then show the equivalence between the PDEs and the following integral equations \begin{equation*} u(x)=\int_{\mathbb{R}^n}\frac{R_{2s,n}}{|x-y|^{n-2s}}\left(\int_{\mathbb{R}^{n}}\frac{1}{|y-z|^σ}u^p(z)dz\right)u^{q}(y)dy. \end{equation*} Finally, we classify all nonnegative solutions to the integral equations via the method of moving spheres in integral form. As a consequence, we obtain the classification results of nonnegative classical solutions for the PDEs. Our results completely improved the classification results in \cite{CD,DFQ,DL,DQ,Liu}. In critical and super-critical order cases (i.e., $\frac{n}{2}\leq s:=m+\fracα{2}<+\infty$), we also derive Liouville type theorem.

math.AP↗

arXiv2019

Charge-Based Prison Term Prediction with Deep Gating Network

Judgment prediction for legal cases has attracted much research efforts for its practice use, of which the ultimate goal is prison term prediction. While existing work merely predicts the total prison term, in reality a defendant is often charged with multiple crimes. In this paper, we argue that charge-based prison term prediction (CPTP) not only better fits realistic needs, but also makes the total prison term prediction more accurate and interpretable. We collect the first large-scale structured data for CPTP and evaluate several competitive baselines. Based on the observation that fine-grained feature selection is the key to achieving good performance, we propose the Deep Gating Network (DGN) for charge-specific feature selection and aggregation. Experiments show that DGN achieves the state-of-the-art performance.

cs.CL↗

arXiv2019

NLO Productions of $ω$ and $K^0_{\rm S}$ with a Global Extraction of the Jet Transport Parameter in Heavy Ion collisions

In this work, we pave the way to calculate the productions of $ω$ and $K^0_{\rm S}$ mesons at large $p_T$ in p+p and A+A collisions at the RHIC and the LHC. The $ω$ meson fragmentation functions (FFs) in vacuum at next-to-leading order (NLO) are obtained by evolving NLO DGLAP evolution equations with rescaled $ω$ FFs at initial scale $Q_0^2=1.5$ GeV$^2$ from a broken SU(3) model, and the $K^0_{\rm S}$ FFs in vacuum are taken from AKK08 parametrization directly. Within the framework of the NLO pQCD improved parton model, we make good descriptions of the experimental data on $ω$ and $K^0_{\rm S}$ in p+p both at the RHIC and the LHC. With the higher-twist approach to take into account the jet quenching effect by medium modified FFs, the nuclear modification factors for $ω$ meson and $K^0_{\rm S}$ meson at the RHIC and the LHC are presented with different sets of jet transport coefficient $\hat{q}_0$. Then we make a global extraction of $\hat{q}_0$ at the RHIC and the LHC by confronting our model calculations with all available data on 6 identified mesons: $π^0$, $η$, $ρ^0$, $ϕ$, $ω$, and $K^0_{\rm S}$. The minimum value of the total $χ^2/d.o.f$ for productions of these mesons gives the best value of $\hat{q}_0=0.5\rm GeV^2/fm$ for Au+Au collisions with $\sqrt{s_{\rm NN}}=200$ GeV at the RHIC, and $\hat{q}_0=1.2\rm GeV^2/fm$ for Pb+Pb collisions with $\sqrt{s_{\rm NN}}=2.76$ TeV at the LHC respectively, with the QGP spacetime evolution given by an event-by-event viscous hydrodynamics model IEBE-VISHNU. With these global extracted values of $\hat{q}_0$, the nuclear modification factors of $π^0$, $η$, $ρ^0$, $ϕ$, $ω$, and $K^0_{\rm S}$ in A+A collisions are presented, and predictions of yield ratios such as $ω/π^0$ and $K^0_{\rm S}/π^0$ at large $p_T$ in heavy-ion collisions at the RHIC and the LHC are provided.

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