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Hui Xu

Publications and source records attributed to Hui Xu.

At least 145 records · Page 8Linked to original sources
arXiv2019

Dynamics of scalar fields in an expanding/contracting cosmos at finite temperature

This paper extends the study of the quantum dissipative effects of a cosmological scalar field by taking into account the cosmic expansion and contraction. Cheung, Drewes, Kang and Kim calculated the effective action and quantum dissipative effects of a cosmological scalar field. The analytic expressions for the effective potential and damping coefficient were presented using a simple scalar model with quartic interaction. Their work was done using Minkowski-space propagators in loop diagrams. In this work we incorporate the Hubble expansion and contraction of the comic background, and focus on the thermal dynamics of a scalar field in a regime where the effective potential changes slowly. We let the Hubble parameter, $H$, attain a small but non-zero value and carry out calculations to first order in $H$. If we set $H=0$ all results match those obtained previously in flat spacetime [1]. Interestingly we have to integrate over the resonances, which in turn leads to an amplification of the effects of a non-zero $H$. This is an intriguing phenomenon which cannot be uncovered in flat spacetime. The implications on particle creations in the early universe will be studied in a forthcoming work.

hep-th↗
arXiv2019

Commuting circle diffeomorphisms with their derivatives having mixed moduli of continuity

Let $d\geq 2$ be an integer and let $ω_1,\cdots ,ω_d$ be moduli of continuity in a specified class which contains the moduli of Hölder continuity. Let $f_k$, $k\in\{1,\cdots,d\}$, be $C^{1+ω_k}$ orientation preserving diffeomorphisms of the circle and $f_1,\cdots, f_d$ commute with each other. We prove that if the rotation numbers of $f_k$'s are independent over the rationals and $ω_1(t)\cdotsω_d(t)=tω(t)$ with $\lim_{t\rightarrow 0^+}ω(t)=0$, then $f_1,\cdots,f_d$ are simultaneously (topologically) conjugate to rigid rotations.

math.DS↗
arXiv2018

Firing rate and spatial correlation in a stochastic neural field model

This paper studies a stochastic neural field model that is extended from our previous paper [14]. The neural field model consists of many heterogeneous local populations of neurons. Rigorous results on the stochastic stability are proved, which further imply the well-definedness of quantities including mean firing rate and spike count correlation. Then we devote to address two main topics: the comparison with mean-field approximations and the spatial correlation of spike count. We showed that partial synchronization of spiking activities is a main cause for discrepancies of mean-field approximations. Furthermore, the spike count correlation between local populations are studied. We find that the spike count correlation decays quickly with the distance between corresponding local populations. Some mathematical justifications of the mechanism of this phenomenon is also provided.

math.PR↗
arXiv2018

DeepObfuscation: Securing the Structure of Convolutional Neural Networks via Knowledge Distillation

This paper investigates the piracy problem of deep learning models. Designing and training a well-performing model is generally expensive. However, when releasing them, attackers may reverse engineer the models and pirate their design. This paper, therefore, proposes deep learning obfuscation, aiming at obstructing attackers from pirating a deep learning model. In particular, we focus on obfuscating convolutional neural networks (CNN), a widely employed type of deep learning architectures for image recognition. Our approach obfuscates a CNN model eventually by simulating its feature extractor with a shallow and sequential convolutional block. To this end, we employ a recursive simulation method and a joint training method to train the simulation network. The joint training method leverages both the intermediate knowledge generated by a feature extractor and data labels to train a simulation network. In this way, we can obtain an obfuscated model without accuracy loss. We have verified the feasibility of our approach with three prevalent CNNs, i.e., GoogLeNet, ResNet, and DenseNet. Although these networks are very deep with tens or hundreds of layers, we can simulate them in a shallow network including only five or seven convolutional layers. The obfuscated models are even more efficient than the original models. Our obfuscation approach is very effective to protect the critical structure of a deep learning model from being exposed to attackers. Moreover, it can also thwart attackers from pirating the model with transfer learning or incremental learning techniques because the shallow simulation network bears poor learning ability. To our best knowledge, this paper serves as a first attempt to obfuscate deep learning models, which may shed light on more future studies.

cs.CR↗
arXiv2018

On Benchmarking the Capability of Symbolic Execution Tools with Logic Bombs

Symbolic execution now becomes an indispensable technique for software testing and program analysis. There are several symbolic execution tools available off-the-shelf, and we need a practical benchmark approach to learn their capabilities. Therefore, this paper introduces a novel approach to benchmark symbolic execution tools in a fine-grained and efficient manner. In particular, our approach evaluates the performance of such tools against the known challenges faced by general symbolic execution techniques, such as floating-point numbers and symbolic memories. To this end, we first survey related papers and systematize the challenges of symbolic execution. We extract 12 distinct challenges from the literature and categorize them into two categories: symbolic-reasoning challenges and path-explosion challenges. Then, we develop a dataset of logic bombs and a framework to benchmark symbolic execution tools automatically. For each challenge, our dataset contains several logic bombs, each of which is guarded by a specific challenging problem. If a symbolic execution tool can find test cases to trigger logic bombs, it indicates that the tool can handle the corresponding problems. We have conducted real-world experiments with three popular symbolic execution tools: KLEE, Angr, and Triton. Experimental results show that our approach can reveal their capabilities and limitations in handling particular issues accurately and efficiently. The benchmark process generally takes only dozens of minutes to evaluate a tool. We release our dataset on GitHub as open source, with an aim to better facilitate the community to conduct future work on benchmarking symbolic execution tools.

cs.SE↗
arXiv2018

On-Shell Gauge Invariant Three-Point Amplitudes

Assuming locality, Lorentz invariance and parity conservation we obtain a set of differential equations governing the 3-point interactions of massless bosons, which in turn determines the polynomial ring of these amplitudes. We derive all possible 3-point interactions for tensor fields with polarisations that have total symmetry and mixed symmetry under permutations of Lorentz indices. Constraints on the existence of gauge-invariant cubic vertices for totally symmetric fields are obtained in general spacetime dimensions and are compared with existing results obtained in the covariant and light-cone approaches. Expressing our results in spinor helicity formalism we reproduce the perhaps mysterious mismatch between the covariant approach and the light cone approach in 4 dimensions. Our analysis also shows that there exists a mismatch, in the 3-point gauge invariant amplitudes corresponding to cubic self-interactions, between a scalar field $ϕ$ and an antisymmetric rank-2 tensor field $A_{μν}$. Despite the well-known fact that in 4 dimensions rank-2 anti-symmetric fields are dual to scalar fields in free theories, such duality does not extend to interacting theories.

hep-th↗
arXiv2018

Spectral/hp element methods: recent developments, applications, and perspectives

The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate C0-continuous expansions. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.

physics.flu-dyn↗
arXiv2018

Impact of Land Use on the DOM Composition in Different Seasons in a Subtropical River Flowing through the Region Undergoing Rapid Urbanization

The dissolved organic matter (DOM) composition in river ecosystems could reflect the human impacts on the river ecosystem, and plays an important role in the carbon cycling process. We collected water and phytoplankton samples at 107 sites in the Dongjiang River in two seasons to assess the impact of the sub-catchments land use structure on the DOM composition. The results showed that (1) the forested sub-catchments had higher humic-like C1 (16.45%) and C2 (25.04%) and lower protein-like C3 (22.57%) and C4 (35.95%) than urbanized and mixed forest-agriculture sub-catchments, while the urbanized sub-catchments showed an inverse trend (4.54%, 15.51%, 33.97% and 45.98%, respectively). (2) The significant variation in the proportion of C1 and C4 between the dry and rainy seasons was recorded in both the forested and the mixed forest-agriculture sub-catchments (p<0.01), but only C4 showed an obvious seasonal variation in the urbanized sub-catchments (p<0.01). While the DOM composition was mainly related to the proportion of urbanized land and forested land year-round (p<0.01), it had stronger correlation with forested land in the dry season and urbanized land in the rainy season. (3) No significant correlation between the DOM composition and the agricultural land proportion was found in either season (p>0.05). Our findings indicated that the DOM composition was strongly dependent on the land use structure of the sub-catchments and varied seasonally, but the seasonal variation pattern could be disturbed by human activities in the extensively urbanized catchments. Notably, the higher C4 proportion compared with those in temperate rivers implied a larger amount of CO2 released from the subtropical rivers into the atmosphere when considering bioavailability.

q-bio.PE↗
arXiv2017

Early monsoon drought and mid-summer vapor pressure deficit induce growth cessation of lower margin Picea crassifolia

Extreme climatic events have been shown to be strong drivers of tree growth, forest dynamics, and range contraction. Here we study the climatic drivers of Picea crassifolia Kom., an endemic to northwest China where climate has significantly warmed. Picea crassifolia was sampled from its lower distributional margin to its upper distributional margin on the Helan Mountains to test the hypothesis that 1) growth at the upper limit is limited by cool temperatures and 2) is limited by drought at its lower limit. We found that trees at the lower distributional margin have experienced a higher rate of stem-growth cessation events since 2001 compared to trees at other elevations. While all populations have a similar climatic sensitivity, stem-growth cessation events in trees at lower distributional margin appear to be driven by low precipitation in June as the monsoon begins to deliver moisture to the region. Evidence indicates that mid-summer (July) vapor pressure deficit (VPD) exacerbates the frequency of these events. These data and our analysis makes it evident that an increase in severity and frequency of drought early in the monsoon season could increase the frequency and severity of stem-growth cessation in Picea crassifolia trees at lower elevations. Increases in VPD and warming would likely exacerbate the growth stress of this species on Helan Mountain. Hypothetically, if the combinations of low moisture and increased VPD stress becomes more common, the mortality rate of lower distributional margin trees could increase, especially of those that are already experiencing events of temporary growth cessation.

q-bio.QM↗
arXiv2017

Numerical simulation of polynomial-speed convergence phenomenon

We provide a hybrid method that captures the polynomial speed of convergence and polynomial speed of mixing for Markov processes. The hybrid method that we introduce is based on the coupling technique and renewal theory. We propose to replace some estimates in classical results about the ergodicity of Markov processes by numerical simulations when the corresponding analytical proof is difficult. After that, all remaining conclusions can be derived from rigorous analysis. Then we apply our results to two 1D microscopic heat conduction models. The mixing rate of these two models are expected to be polynomial but very difficult to prove. In both examples, our numerical results match the expected polynomial mixing rate well.

math.NA↗
arXiv2017

On Secure and Usable Program Obfuscation: A Survey

Program obfuscation is a widely employed approach for software intellectual property protection. However, general obfuscation methods (e.g., lexical obfuscation, control obfuscation) implemented in mainstream obfuscation tools are heuristic and have little security guarantee. Recently in 2013, Garg et al. have achieved a breakthrough in secure program obfuscation with a graded encoding mechanism and they have shown that it can fulfill a compelling security property, i.e., indistinguishability. Nevertheless, the mechanism incurs too much overhead for practical usage. Besides, it focuses on obfuscating computation models (e.g., circuits) rather than real codes. In this paper, we aim to explore secure and usable obfuscation approaches from the literature. Our main finding is that currently we still have no such approaches made secure and usable. The main reason is we do not have adequate evaluation metrics concerning both security and performance. On one hand, existing code-oriented obfuscation approaches generally evaluate the increased obscurity rather than security guarantee. On the other hand, the performance requirement for model-oriented obfuscation approaches is too weak to develop practical program obfuscation solutions.

cs.CR↗
arXiv2017

A necessary and sufficient condition for the subexponentiality of product distribution

Let X and Y be two independent and nonnegative random variables with corresponding distributions F and G. Denote by H the distribution of the product XY , called the product convolution of F and G. Cline and Samorodnitsky (1994) proposed sufficient conditions for H to be subexponential, given the subexponentiality of F. Relying on a related result of Tang (2008) on the long-tail of product convolution, we obtain a necessary and sufficient condition for the subexponentiality of H, given that of F. We also study the reverse problem and obtain sufficient conditions for the subexponentiality of F given that of H. Finally, we apply the obtained results to the asymptotic study of the ruin probability in a discrete-time insurance risk model with stochastic returns.

math.PR↗
arXiv2017

Some positive conclusions related to the Embrechts-Goldie' conjecture

In this paper, we give some conditions, under which, if an infinitely divisible distribution supported on $[0,\infty)$ belongs to the intersection of exponential distribution class $\mathcal{L}(γ)$ for some $γ\ge0$ and generalised subexponential distribution class $\mathcal{OS}$, then its L$\rm\acute{e}$vy spectral distribution or convolution of the distribution with itself also belongs to the same one. To this end, we discuss the closure under the compound convolution roots for the class. In addition, we do some in-depth discussion about the above-mentioned conditions, and provide some types of distributions satisfying them. Further, we obtain some local versions of the above-mentioned results by the Esscher transform of distributions. Therefore, some positive conclusions related to the Embrechts-Goldie conjecture are obtained. Prior to this, all corresponding results are negative

math.PR↗
arXiv2017

The uniform local asymptotics of the total net loss process in a new time-dependent bidimensional renewal model

In this paper, we consider a bidimensional renewal risk model with constant force of interest, in which the claim size vector with certain local subexponential marginal distribution and its inter-arrival time are subject to a new time-dependence structure. We obtain the uniform local asymptotics of the total net loss process in the model. Moreover, some specific examples of the joint distribution satisfying the conditions of the dependence structure are given. Finally, in order to illustrate a condition of the above result, a local subexponential distribution is find for the first time that, its local distribution is not almost decreased.

math.PR↗
arXiv2017

The finite-time ruin probability of the nonhomogeneous Poisson risk model with conditionally independent subexponential claims

This paper obtains an asymptotic formula for the finite-time ruin probability of the compound nonhomogeneous Poisson risk model with a constant interest force, in which the claims are conditionally independent random variables with a common subexponential distribution. The paper also obtains some asymptotic relations of randomly weighted sums $\sum_{i=1}^n θ_iX_i$, in which the weights $θ_i$ $i=1,2,\cdots, n$ are positive random variables which are bounded above and the primary random variables $X_i$, $i=1,2,\cdots,n$ are conditionally independent and follow subexponential distributions.

math.PR↗
arXiv2017

Generation of higher-order rogue waves from multi-breathers by double degeneracy in an optical fibre

In this paper, we construct a special kind of breather solution of the nonlinear Schrödinger (NLS) equation, the so-called breather-positon ({\it b-positon} for short), which can be obtained by taking the limit $λ_{j}$ $\rightarrow$ $λ_{1}$ of the Lax pair eigenvalues in the order-$n$ periodic solution which is generated by the $n$-fold Darboux transformation from a special "seed" solution--plane wave. Further, an order-$n$ {\it b-positon} gives an order-$n$ rogue wave under a limit $λ_1\rightarrow λ_0$. Here $λ_0$ is a special eigenvalue in a breather of the NLS equation such that its period goes to infinity. Several analytical plots of order-2 breather confirm visually this double degeneration. The last limit in this double degeneration can be realized approximately in an optical fiber governed by the NLS equation, in which an injected initial ideal pulse is created by a frequency comb system and a programable optical filter (wave shaper) according to the profile of an analytical form of the {\it b-positon} at a certain position $z_0$. We also suggest a new way to observe higher-order rogue waves generation in an optical fiber, namely, measure the patterns at the central region of the higher-order {\it b-positon} generated by above ideal initial pulses when $λ_1$ is very close to the $λ_0$. The excellent agreement between the numerical solutions generated from initial ideal inputs with a low signal noise ratio and analytical solutions of order-2 {\it b-positon}, supports strongly this way in a realistic optical fiber system. Our results also show the validity of the generating mechanism of a higher-order rogue waves from a multi-breathers through the double degeneration.

nlin.SI↗