arXiv subjects

Bo Lin

Publications and source records attributed to Bo Lin.

At least 73 records · Page 4Linked to original sources

arXiv2022

Programming with rules and everything else, seamlessly

Logic rules are powerful for expressing complex reasoning and analysis problems. At the same time, they are inconvenient or impossible to use for many other aspects of applications. Integrating rules in a language with sets and functions, and furthermore with updates to objects, has been a subject of significant study. What's lacking is a language that integrates all constructs seamlessly. This paper presents a language, Alda, that supports all of rules, sets, functions, updates, and objects as seamlessly integrated built-ins, including concurrent and distributed processes. The key idea is to support predicates as set-valued variables that can be used and updated in any scope, and support queries and inference with both explicit and automatic calls to an inference function. We develop a complete formal semantics for Alda. We design a compilation framework that ensures the declarative semantics of rules, while also being able to exploit available optimizations. We describe a prototype implementation that builds on a powerful extension of Python and employs an efficient logic rule engine. We develop a range of benchmarks and present results of experiments to demonstrate Alda's power for programming and generally good performance.

cs.PL↗

arXiv2022

Tropical Geometric Variation of Phylogenetic Tree Shapes

We study the behavior of phylogenetic tree shapes in the tropical geometric interpretation of tree space. Tree shapes are formally referred to as tree topologies; a tree topology can also be thought of as a tree combinatorial type, which is given by the tree's branching configuration and leaf labeling. We use the tropical line segment as a framework to define notions of variance as well as invariance of tree topologies: we provide a combinatorial search theorem that describes all tree topologies occurring along a tropical line segment, as well as a setting under which tree topologies do not change along a tropical line segment. Our study is motivated by comparison to the moduli space endowed with a geodesic metric proposed by Billera, Holmes, and Vogtmann (referred to as BHV space); we consider the tropical geometric setting as an alternative framework to BHV space for sets of phylogenetic trees. We give an algorithm to compute tropical line segments which is lower in computational complexity than the fastest method currently available for BHV geodesics and show that its trajectory behaves more subtly: while the BHV geodesic traverses the origin for vastly different tree topologies, the tropical line segment bypasses it.

math.CO↗

arXiv2021

Yielding and jerky plasticity of tilt grain boundaries in high-temperature graphene

Graphene is well known for its extraordinary mechanical properties combining brittleness and ductility. While most mechanical studies of graphene focused on the strength and brittle fracture behavior, its ductility, plastic deformation, and the possible brittle-to-ductile transition, which are important for high-temperature mechanical performance and applications, still remain much less understood. Here the mechanical response and deformation dynamics of graphene grain boundaries are investigated through a phase field crystal modeling, showing the pivotal effects of temperature and local dislocation structure. Our results indicate that even at relatively high temperature (around 3350 K), the system is still governed by a brittle fracture and cracking dynamics as found in previous low-temperature experimental and atomistic studies. We also identify another type of failure dynamics with low-angle grain boundary disintegration. When temperature increases a transition to plastic deformation is predicted. The appearance of plastic flow at ultrahigh temperature, particularly the phenomenon of jerky plasticity, is attributed to the stick and climb-glide motion of dislocations around the grain boundary. The corresponding mechanism is intrinsic to two-dimensional systems, and governed by the competition between the driving force of accumulated local stress and the defect pinning effect, without the traditional pathways of dislocation generation needed in three-dimensional materials.

cond-mat.mtrl-sci↗

arXiv2021

Adaptive Strategies to Fast Multipole Method in Photoionization Calculations

Recently, a new framework to compute the photoionization rate in streamer discharges accurately and efficiently using the integral form and the fast multipole method (FMM) was presented. This paper further improves the efficiency of this framework with adaptive strategies. The adaptive strategies are based on the magnitude of radiation and the electric field during the streamer propagation, and are applied to the selection of the source and target points. The accuracy and efficiency of this adaptive FMM are studied quantitatively for different domain sizes, pressures and adaptive criteria, in comparison with some existing efficient approaches to compute the photoionization. It is shown that appropriate adaptive strategies reduce the calculation time of the FMM greatly, and maintain the high accuracy that the numerical error is still much smaller than other models based on partial differential equations. The performance of the proposed adaptive method is also studied for a three-dimensional positive streamer interacting problem with a plasma cloud.

physics.plasm-ph↗

arXiv2021

Beep: Fine-grained Fix Localization by Learning to Predict Buggy Code Elements

Software Fault Localization refers to the activity of finding code elements (e.g., statements) that are related to a software failure. The state-of-the-art fault localization techniques, however, produce coarse-grained results that can deter manual debugging or mislead automated repair tools. In this work, we focus specifically on the fine-grained identification of code elements (i.e., tokens) that must be changed to fix a buggy program: we refer to it as fix localization. This paper introduces a neural network architecture (named Beep) that builds on AST paths to predict the buggy code element as well as the change action that must be applied to repair a program. Leveraging massive data of bugs and patches within the CoCoNut dataset, we trained a model that was (1) effective in localizing the buggy tokens with the Mean First Rank significantly higher than a statistics based baseline and a machine learning-based baseline, and (2) effective in predicting the repair operators (with the associated buggy code elements) with a Recall@1= 30-45% and the Mean First Rank=7-12 (evaluated by CoCoNut, ManySStuBs4J, and Defects4J datasets). To showcase how fine-grained fix localization can help program repair, we employ it in two repair pipelines where we use either a code completion engine to predict the correct token or a set of heuristics to search for the suitable donor code. A key strength of accurate fix localization for program repair is that it reduces the chance of patch overfitting, a challenge in generate-and-validate automated program repair: both two repair pipelines achieve a correctness ratio of 100%, i.e., all generated patches are found to be correct. Moreover, accurate fix localization helps enhance the efficiency of program repair.

cs.SE↗

arXiv2021

Computing the Invariant Distribution of Randomly Perturbed Dynamical Systems Using Deep Learning

The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution based on the Fokker-Planck equation, such as finite difference or finite element methods, are limited to low-dimensional systems due to the curse of dimensionality. In this work, we propose a deep learning based method to compute the generalized potential, i.e. the negative logarithm of the invariant distribution multiplied by the noise. The idea of the method is to learn a decomposition of the force field, as specified by the Fokker-Planck equation, from the trajectory data. The potential component of the decomposition gives the generalized potential. The method can deal with high-dimensional systems, possibly with partially known dynamics. Using the generalized potential also allows us to deal with systems at low temperatures, where the invariant distribution becomes singular around the metastable states. These advantages make it an efficient method to analyze invariant distributions for practical dynamical systems. The effectiveness of the proposed method is demonstrated by numerical examples.

physics.comp-ph↗

arXiv2021

Deep Reinforcement Learning for Electric Vehicle Routing Problem with Time Windows

The past decade has seen a rapid penetration of electric vehicles (EV) in the market, more and more logistics and transportation companies start to deploy EVs for service provision. In order to model the operations of a commercial EV fleet, we utilize the EV routing problem with time windows (EVRPTW). In this research, we propose an end-to-end deep reinforcement learning framework to solve the EVRPTW. In particular, we develop an attention model incorporating the pointer network and a graph embedding technique to parameterize a stochastic policy for solving the EVRPTW. The model is then trained using policy gradient with rollout baseline. Our numerical studies show that the proposed model is able to efficiently solve EVRPTW instances of large sizes that are not solvable with any existing approaches.

cs.LG↗

arXiv2021

An entropic method for discrete systems with Gibbs entropy

We consider general systems of ordinary differential equations with monotonic Gibbs entropy, and introduce an entropic scheme that simply imposes an entropy fix after every time step of any existing time integrator. It is proved that in the general case, our entropy fix has only infinitesimal influence on the numerical order of the original scheme, and in many circumstances, it can be shown that the scheme does not affect the numerical order. Numerical experiments on the linear Fokker-Planck equation and nonlinear Boltzmann equation are carried out to support our numerical analysis.

math.NA↗

arXiv2021

Electric Vehicle Routing and Charging/Discharging under Time-Variant Electricity Prices

The integration of electric vehicles (EVs) with the energy grid has become an important area of research due to the increasing EV penetration in today's transportation systems. Under appropriate management of EV charging and discharging, the grid can currently satisfy the energy requirements of a considerable number of EVs. Furthermore, EVs can help enhance the reliability and stability of the energy grid through ancillary services such as energy storage. This paper proposes the EV routing problem with time windows under time-variant electricity prices (EVRPTW-TP) which optimizes the routing of an EV fleet that are delivering products to customers, jointly with the scheduling of the charging and discharging of the EVs from/to the grid. The proposed model is a multiperiod vehicle routing problem where EVs can stop at charging stations to either recharge their batteries or inject stored energy to the grid. Given the energy costs that vary based on time-of-use, the charging and discharging schedules of the EVs are optimized to benefit from the capability of storing energy by shifting energy demands from peak hours to off-peak hours when the energy price is lower. The vehicles can recover the energy costs and potentially realize profits by injecting energy back to the grid at high price periods. EVRPTW-TP is formulated as an optimization problem. A Lagrangian relaxation approach and a hybrid variable neighborhood search/tabu search heuristic are proposed to obtain high quality lower bounds and feasible solutions, respectively. Numerical experiments on instances from the literature are provided. The proposed heuristic is also evaluated on a case study of an EV fleet providing grocery delivery at the region of Kitchener-Waterloo in Ontario, Canada. Insights on the impacts of energy pricing, service time slots, range reduction in winter as well as fleet size are presented.

math.OC↗

arXiv2021

Tropical Optimal Transport and Wasserstein Distances

We study the problem of optimal transport in tropical geometry and define the Wasserstein-$p$ distances in the continuous metric measure space setting of the tropical projective torus. We specify the tropical metric -- a combinatorial metric that has been used to study of the tropical geometric space of phylogenetic trees -- as the ground metric and study the cases of $p=1,2$ in detail. The case of $p=1$ gives an efficient computation of the infinitely-many geodesics on the tropical projective torus, while the case of $p=2$ gives a form for Fréchet means and a general inner product structure. Our results also provide theoretical foundations for geometric insight a statistical framework in a tropical geometric setting. We construct explicit algorithms for the computation of the tropical Wasserstein-1 and 2 distances and prove their convergence. Our results provide the first study of the Wasserstein distances and optimal transport in tropical geometry. Several numerical examples are provided.

math.OC↗

arXiv2021

Reconstruction of Backbone Curves for Snake Robots

Snake robots composed of alternating single-axis pitch and yaw joints have many internal degrees of freedom, which make them capable of versatile three-dimensional locomotion. In motion planning process, snake robot motions are often designed kinematically by a chronological sequence of continuous backbone curves that capture desired macroscopic shapes of the robot. However, as the geometric arrangement of single-axis rotary joints creates constraints on the rotations in the robot, it is challenging for the robot to reconstruct an arbitrary 3D curve. When the robot configuration does not accurately achieve the desired shapes defined by these backbone curves, the robot can have unexpected contacts with the environment, such that the robot does not achieve the desired motion. In this work, we propose a method for snake robots to reconstruct desired backbone curves by posing an optimization problem that exploits the robot's geometric structure. We verified that our method enables fast and accurate curve-configuration conversions through its applications to commonly used 3D gaits. We also demonstrated via robot experiments that 1) our method results in smooth locomotion on the robot; 2) our method allows the robot to approach the numerically predicted locomotive performance of a sequence of continuous backbone curve.

cs.RO↗

arXiv2021

Deep Learning based Antenna Selection and CSI Extrapolation in Massive MIMO Systems

A critical bottleneck of massive multiple-input multiple-output (MIMO) system is the huge training overhead caused by downlink transmission, like channel estimation, downlink beamforming and covariance observation. In this paper, we propose to use the channel state information (CSI) of a small number of antennas to extrapolate the CSI of the other antennas and reduce the training overhead. Specifically, we design a deep neural network that we call an antenna domain extrapolation network (ADEN) that can exploit the correlation function among antennas. We then propose a deep learning (DL) based antenna selection network (ASN) that can select a limited antennas for optimizing the extrapolation, which is conventionally a type of combinatorial optimization and is difficult to solve. We trickly designed a constrained degradation algorithm to generate a differentiable approximation of the discrete antenna selection vector such that the back-propagation of the neural network can be guaranteed. Numerical results show that the proposed ADEN outperforms the traditional fully connected one, and the antenna selection scheme learned by ASN is much better than the trivially used uniform selection.

eess.SP↗

arXiv2020

A Data Driven Method for Computing Quasipotentials

The quasipotential is a natural generalization of the concept of energy functions to non-equilibrium systems. In the analysis of rare events in stochastic dynamics, it plays a central role in characterizing the statistics of transition events and the likely transition paths. However, computing the quasipotential is challenging, especially in high dimensional dynamical systems where a global landscape is sought. Traditional methods based on the dynamic programming principle or path space minimization tend to suffer from the curse of dimensionality. In this paper, we propose a simple and efficient machine learning method to resolve this problem. The key idea is to learn an orthogonal decomposition of the vector field that drives the dynamics, from which one can identify the quasipotential. We demonstrate on various example systems that our method can effectively compute quasipotential landscapes without requiring spatial discretization or solving path-space optimization problems. Moreover, the method is purely data driven in the sense that only observed trajectories of the dynamics are required for the computation of the quasipotential. These properties make it a promising method to enable the general application of quasipotential analysis to dynamical systems away from equilibrium.

math.DS↗

arXiv2020

Accurate and efficient calculation of photoionization in streamer discharges using fast multipole method

This paper focuses on the three-dimensional simulation of the photoionization in streamer discharges, and provides a general framework to efficiently and accurately calculate the photoionization model using the integral form. The simulation is based on the kernel-independent fast multipole method. The accuracy of this method is studied quantitatively for different domains and various pressures in comparison with other existing models based on partial differential equations (PDEs). The comparison indicates the numerical error of the fast multipole method is much smaller than those of other PDE-based methods, with the reference solution given by direct numerical integration. Such accuracy can be achieved with affordable computational cost, and its performance in both efficiency and accuracy is quite stable for different domains and pressures. Meanwhile, the simulation accelerated by the fast multipole method exhibits good scalability using up to 1280 cores, which shows its capability of three-dimensional simulations using parallel (distributed) computing. The difference of the proposed method and other efficient approximations are also studied in a three-dimensional dynamic problem where two streamers interact.

physics.comp-ph↗

arXiv2020

Bounding The Number of Linear Regions in Local Area for Neural Networks with ReLU Activations

The number of linear regions is one of the distinct properties of the neural networks using piecewise linear activation functions such as ReLU, comparing with those conventional ones using other activation functions. Previous studies showed this property reflected the expressivity of a neural network family ([14]); as a result, it can be used to characterize how the structural complexity of a neural network model affects the function it aims to compute. Nonetheless, it is challenging to directly compute the number of linear regions; therefore, many researchers focus on estimating the bounds (in particular the upper bound) of the number of linear regions for deep neural networks using ReLU. These methods, however, attempted to estimate the upper bound in the entire input space. The theoretical methods are still lacking to estimate the number of linear regions within a specific area of the input space, e.g., a sphere centered at a training data point such as an adversarial example or a backdoor trigger. In this paper, we present the first method to estimate the upper bound of the number of linear regions in any sphere in the input space of a given ReLU neural network. We implemented the method, and computed the bounds in deep neural networks using the piece-wise linear active function. Our experiments showed that, while training a neural network, the boundaries of the linear regions tend to move away from the training data points. In addition, we observe that the spheres centered at the training data points tend to contain more linear regions than any arbitrary points in the input space. To the best of our knowledge, this is the first study of bounding linear regions around a specific data point. We consider our work as a first step toward the investigation of the structural complexity of deep neural networks in a specific input area.

cs.LG↗

arXiv2019

Linear and Rational Factorization of Tropical Polynomials

Already for bivariate tropical polynomials, factorization is an NP-Complete problem. In this paper, we give an efficient algorithm for factorization and rational factorization of a rich class of tropical polynomials in $n$ variables. Special families of these polynomials have appeared in economics, discrete convex analysis, and combinatorics. Our theorems rely on an intrinsic characterization of regular mixed subdivisions of integral polytopes, and lead to many open problems of interest in discrete geometry.

math.CO↗

arXiv2019

An efficient and accurate MPI based parallel simulator for streamer discharges in three dimensions

In this paper, we propose an efficient and accurate message-passing interface (MPI)-based parallel simulator for streamer discharges in three dimensions using the fluid model. First, we propose a new second-order semi-implicit scheme for the temporal discretization of the model that relaxes the dielectric relaxation time restriction. Moreover, it requires solving the Poisson-type equation only once at each time step, while the classical second-order explicit scheme typically needs to do twice. Second, we introduce a geometric multigrid preconditioned FGMRES solver that dramatically improves the efficiency of solving the Poisson-type equation with either constant or variable coefficients. We show numerically that no more than 4 iterations are required for the Poisson solver to converge to a relative residual of $10^{-8}$ during streamer simulations; the FGMRES solver is much faster than R&B SOR and other Krylov subspace solvers. Last but not least, all the methods are implemented using MPI. The parallel efficiency of the code and the fast algorithmic performances are demonstrated by a series of numerical experiments using up to 2560 cores on the Tianhe2-JK clusters. For applications, we study a double-headed streamer discharge as well as the interaction between two streamers, using up to 10.7 billion mesh cells.

physics.comp-ph↗

arXiv2019

High-level Cryptographic Abstractions

The interfaces exposed by commonly used cryptographic libraries are clumsy, complicated, and assume an understanding of cryptographic algorithms. The challenge is to design high-level abstractions that require minimum knowledge and effort to use while also allowing maximum control when needed. This paper proposes such high-level abstractions consisting of simple cryptographic primitives and full declarative configuration. These abstractions can be implemented on top of any cryptographic library in any language. We have implemented these abstractions in Python, and used them to write a wide variety of well-known security protocols, including Signal, Kerberos, and TLS. We show that programs using our abstractions are much smaller and easier to write than using low-level libraries, where size of security protocols implemented is reduced by about a third on average. We show our implementation incurs a small overhead, less than 5 microseconds for shared key operations and less than 341 microseconds (< 1%) for public key operations. We also show our abstractions are safe against main types of cryptographic misuse reported in the literature.

cs.CR↗