arXiv subjects

Jian Song

Publications and source records attributed to Jian Song.

At least 127 records · Page 7Linked to original sources

arXiv2022

Age of Information Optimization in Multi-Channel Network with Sided Information

We consider a discrete-time multi-channel network where the destination collects time-sensitive packets from multiple sources with sided channel information. The popular metric, Age of Information (AoI), is applied to measure the data freshness at the destination. Due to the interference constraint, only disjoint source-channel pairs can be chosen for transmission in each time slot, and the decision maker should choose the optimal scheduling pairs to minimize the average AoI at the destination. To learn the optimal channel selection, we apply the linear contextual bandit (LCB) framework by utilizing the sided information provided by pilots. Concretely, we establish the relationship between AoI regret and sub-optimal channel selection times and propose both age-independent and age-dependent algorithms. The former method is proven to achieve the sub-linear AoI regret but is outperformed by the latter algorithm both in the linear and non-linear contextual model in simulation.

cs.IT↗

arXiv2022

Enhanced Tracking and Beamforming Codebook Design for Wideband Terahertz Massive MIMO System

True-time-delay (TTD) lines are recently applied inside Terahertz (THz) hybrid-precoding transceiver to acquire high beamforming gain against beam squint effect. However, beam tracking turns into a challenging puzzle where enormous potential beam directions bring about unacceptable overhead consumption. Frequency-scanning-based beam tracking is initially explored but still imperfect in previous studies. In this paper, based on TTD-aided hybrid precoding structure, we give an enhanced frequency-scanning-based tracking scheme. Multiple beams are generated and utilized simultaneously via several subcarriers for tracking at one timeslot. The squint beams' angular coverage at all subcarriers can be flexibly controlled by two different subcarrier-angular mapping policies, named forward-pairing and backward-pairing. Then multiple physical directions can be simultaneously searched in one timeslot for lower overhead consumption. Besides, closed-form searching radius bound, parameter configuration and interferences are theoretically analyzed. Furthermore, we provide the coupled codebook design for TTDs and phase shifters (PSs), with joint consideration of both beamforming and tracking. Analytical and numerical results demonstrate the superiority of the new frequency-scanning-based tracking scheme and beamforming codebook.

cs.IT↗

arXiv2022

Transition behavior of the seizure dynamics modulated by the astrocyte inositol triphosphate noise

Epilepsy is a neurological disorder with recurrent seizures of complexity and randomness. Until now, the mechanism of epileptic randomness has not been fully elucidated. Inspired by the recent finding that astrocyte GTPase-activating protein (G-protein)-coupled receptors could be involved in stochastic epileptic seizures, we proposed a neuron-astrocyte network model, incorporating the noise of the astrocytic second messager, inositol triphosphate (IP3) which is modulated by the G-protein)-coupled receptor activation. Based on this model, we have statistically analysed the transitions of epileptic seizures by performing tens of simulation trials. Our simulation results show that the increase of the IP3 noise intensity induces the depolarization-block epileptic seizures together with an increase in neuronal firing frequency. Meanwhile, a bistable state of neuronal firing emerges under certain noise intensity, during which the neuronal firing pattern switches between regular sparse spiking and epileptic seizure states. This random presence of epileptic seizures is absent when the noise intensity continues to increase, accompanying with an increase in the epileptic depolarization block duration. The simulation results also shed light on the fact that calcium signals in astrocytes play significant roles in the pattern formations of the epileptic seizure. Our results provide a potential pathway for understanding the epileptic randomness.

q-bio.NC↗

arXiv2022

A Fast Butterfly-compressed Hadamard-Babich Integrator for High-Frequency Helmholtz Equations in Inhomogeneous Media with Arbitrary Sources

We present a butterfly-compressed representation of the Hadamard-Babich (HB) ansatz for the Green's function of the high-frequency Helmholtz equation in smooth inhomogeneous media. For a computational domain discretized with $N_v$ discretization cells, the proposed algorithm first solves and tabulates the phase and HB coefficients via eikonal and transport equations with observation points and point sources located at the Chebyshev nodes using a set of much coarser computation grids, and then butterfly compresses the resulting HB interactions from all $N_v$ cell centers to each other. The overall CPU time and memory requirement scale as $O(N_v\log^2N_v)$ for any bounded 2D domains with arbitrary excitation sources. A direct extension of this scheme to bounded 3D domains yields an $O(N_v^{4/3})$ CPU complexity, which can be further reduced to quasi-linear complexities with proposed remedies. The scheme can also efficiently handle scattering problems involving inclusions in inhomogeneous media. Although the current construction of our HB integrator does not accommodate caustics, the resulting HB integrator itself can be applied to certain sources, such as concave-shaped sources, to produce caustic effects. Compared to finite-difference frequency-domain (FDFD) methods, the proposed HB integrator is free of numerical dispersion and requires fewer discretization points per wavelength. As a result, it can solve wave-propagation problems well beyond the capability of existing solvers. Remarkably, the proposed scheme can accurately model wave propagation in 2D domains with 640 wavelengths per direction and in 3D domains with 54 wavelengths per direction on a state-the-art supercomputer at Lawrence Berkeley National Laboratory.

physics.comp-ph↗

arXiv2022

Local noncollapsing for complex Monge-Ampère equations

We prove a local volume noncollapsing estimate for Kähler metrics induced from a family of complex Monge-Ampère equations, assuming a local Ricci curvature lower bound. This local volume estimate can be applied to establish various diameter and gradient estimate.

math.DG↗

arXiv2022

Diameter estimates in Kähler geometry

Diameter estimates for Kähler metrics are established which require only an entropy bound and no lower bound on the Ricci curvature. The proof builds on recent PDE techniques for $L^\infty$ estimates for the Monge-Ampère equation, with a key improvement allowing degeneracies of the volume form of codimension strictly greater than one. As a consequence, diameter bounds are obtained for long-time solutions of the Kähler-Ricci flow and finite-time solutions when the limiting class is big, as well as for special fibrations of Calabi-Yau manifolds.

math.DG↗

arXiv2022

Time- vs. frequency- domain inverse elastic scattering: Theory and experiment

This study formally adapts the time-domain linear sampling method (TLSM) for ultrasonic imaging of stationary and evolving fractures in safety-critical components. The TLSM indicator is then applied to the laboratory test data of [22, 18] and the obtained reconstructions are compared to their frequency-domain counterparts. The results highlight the unique capability of the time-domain imaging functional for high-fidelity tracking of evolving damage, and its relative robustness to sparse and reduced aperture data at moderate noise levels. A comparative analysis of the TLSM images against the multifrequency LSM maps of [22] further reveals that thanks to the full-waveform inversion in time and space, the TLSM generates images of remarkably higher quality with the same dataset.

math.NA↗

arXiv2022

Graph Contrastive Learning for Anomaly Detection

Graph-based anomaly detection has been widely used for detecting malicious activities in real-world applications. Existing attempts to address this problem have thus far focused on structural feature engineering or learning in the binary classification regime. In this work, we propose to leverage graph contrastive coding and present the supervised GraphCAD model for contrasting abnormal nodes with normal ones in terms of their distances to the global context (e.g., the average of all nodes). To handle scenarios with scarce labels, we further enable GraphCAD as a self-supervised framework by designing a graph corrupting strategy for generating synthetic node labels. To achieve the contrastive objective, we design a graph neural network encoder that can infer and further remove suspicious links during message passing, as well as learn the global context of the input graph. We conduct extensive experiments on four public datasets, demonstrating that 1) GraphCAD significantly and consistently outperforms various advanced baselines and 2) its self-supervised version without fine-tuning can achieve comparable performance with its fully supervised version.

cs.LG↗

arXiv2022

Single-scatter channel impulse response model of non-line-of-sight ultraviolet communications

Previous studies on the temporal characteristics of single-scatter transmission in non-line-of-sight (NLOS) ultraviolet communications (UVC) were based on the prolate-spheroidal coordinate system. In this work, a novel single-scatter channel impulse response (CIR) model is proposed in the spherical coordinate system, which is more natural and comprehensible than the prolate-spheroidal coordinate system in practical applications. Additionally, the results of the widely accepted Monte-Carlo (MC)-based channel model of NLOS UVC are provided to verify the proposed single-scatter CIR model. Results indicate that the computational time costed by the proposed single-scatter CIR model is decreased to less than 0.7% of the MC-based one with comparable accuracy in assessing the temporal characteristics of NLOS UVC channels.

eess.SP↗

arXiv2022

GSmooth: Certified Robustness against Semantic Transformations via Generalized Randomized Smoothing

Certified defenses such as randomized smoothing have shown promise towards building reliable machine learning systems against $\ell_p$-norm bounded attacks. However, existing methods are insufficient or unable to provably defend against semantic transformations, especially those without closed-form expressions (such as defocus blur and pixelate), which are more common in practice and often unrestricted. To fill up this gap, we propose generalized randomized smoothing (GSmooth), a unified theoretical framework for certifying robustness against general semantic transformations via a novel dimension augmentation strategy. Under the GSmooth framework, we present a scalable algorithm that uses a surrogate image-to-image network to approximate the complex transformation. The surrogate model provides a powerful tool for studying the properties of semantic transformations and certifying robustness. Experimental results on several datasets demonstrate the effectiveness of our approach for robustness certification against multiple kinds of semantic transformations and corruptions, which is not achievable by the alternative baselines.

cs.LG↗

arXiv2022

Intelligent Reflecting Surface for MIMO VLC: Joint Design of Surface Configuration and Transceiver Signal Processing

With the capability of reconfiguring the wireless electromagnetic environment, intelligent reflecting surface (IRS) is a new paradigm for designing future wireless communication systems. In this paper, we consider optical IRS for improving the performance of visible light communication (VLC) under a multiple-input and multiple-output (MIMO) setting. Specifically, we focus on the downlink communication of an indoor MIMO VLC system and aim to minimize the mean square error (MSE) of demodulated signals at the receiver. To this end, the MIMO channel gain of the IRS-aided VLC is first derived under the point source assumption, based on which the MSE minimization problem is then formulated subject to the emission power constraints. Next, we propose an alternating optimization algorithm, which decomposes the original problem into three subproblems, to iteratively optimize the IRS configuration, the precoding and detection matrices for minimizing the MSE. Moreover, theoretical analysis on the performance of the proposed algorithm in high and low signal-to-noise rate (SNR) regimes is provided, revealing that the joint optimization process can be simplified in such special cases, and the algorithm's convergence property and computational complexity are also discussed. Finally, numerical results show that IRS-aided schemes significantly reduce the MSE as compared to their counterparts without IRS, and the proposed algorithm outperforms other baseline schemes.

cs.IT↗

arXiv2022

Moments and asymptotics for a class of SPDEs with space-time white noise

In this article, we consider the nonlinear stochastic partial differential equation of fractional order in both space and time variables with constant initial condition: \begin{equation*} \left(\partial^β_t+\dfracν{2}\left(-Δ\right)^{α/ 2}\right) u(t, x)= ~ I_{t}^γ\left[λu(t, x) \dot{W}(t, x)\right] \quad t>0,~ x\in\mathbb R^d, \end{equation*} where $\dot{W}$ is space-time white noise, $α>0$, $β\in(0,2]$, $γ\ge 0$, $λ\neq0$ and $ν>0$. The existence and uniqueness of solution in the Itô-Skorohod sense is obtained under Dalang's condition. We obtain explicit formulas for both the second moment and the second moment Lyapunov exponent. We derive the $p$-th moment upper bounds and find the matching lower bounds. Our results solve a large class of conjectures regarding the order of the $p$-th moment Lyapunov exponents. In particular, by letting $β=2$, $α=2$, $γ=0$, and $d=1$, we confirm the following standing conjecture for the stochastic wave equation: \begin{align*} t^{-1}\log\mathbb E[u(t,x)^p] \asymp p^{3/2}, \quad \text{for $p\ge 2$ as $t\to \infty$.} \end{align*} The method for the lower bounds is inspired by a recent work by Hu and Wang [HW21], where the authors focus on the space-time colored Gaussian noise.

math.PR↗

arXiv2022

Hyperbolic Anderson model 2: Strichartz estimates and Stratonovich setting

We study a wave equation in dimension $d\in \{1,2\}$ with a multiplicative space-time Gaussian noise. The existence and uniqueness of the Stratonovich solution is obtained under some conditions imposed on the Gaussian noise. The strategy is to develop some Strichartz type estimates for the wave kernel in weighted Besov spaces, by which we can prove the wellposedness of an associated Young-type equation. Those Strichartz bounds are of independent interest.

math.PR↗

arXiv2022

On mean-field control problems for backward doubly stochastic systems

This article is concerned with stochastic control problems for backward doubly stochastic differential equations of mean-field type, where the coefficient functions depend on the joint distribution of the state process and the control process. We obtain the stochastic maximum principle which serves as a necessary condition for an optimal control, and we also prove its sufficiency under proper conditions. As a byproduct, we prove the well-posedness for a type of mean-field fully coupled forward-backward doubly stochastic differential equation arising naturally from the control problem, which is of interest in its own right. Some examples are provided to illustrate the applications of our results to control problems in the types of scalar interaction and first order interaction.

math.PR↗

arXiv2022

A New Correlation Inequality for Ising Models with External Fields

We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. We show that the influence of boundary conditions on any given spin is maximised when the external field is identically $0$. One corollary is that spin-spin correlations are maximised when the external field vanishes and the boundary condition is free, which proves a conjecture of Shlosman. In particular, the random field Ising model on ${\mathbb Z}^d$, $d\geq 3$, exhibits exponential decay of correlations in the entire high temperature regime of the pure Ising model. Another corollary is that the pure Ising model in $d\geq 3$ satisfies the conjectured strong spatial mixing property in the entire high temperature regime.

math.PR↗

arXiv2022

Hitting probabilities of Gaussian random fields and collision of eigenvalues of random matrices

Let $X= \{X(t), t \in \mathbb R^N\}$ be a centered Gaussian random field with values in $\mathbb R^d$ satisfying certain conditions and let $F \subset \mathbb R^d$ be a Borel set. In our main theorem, we provide a sufficient condition for $F$ to be polar for $X$, i.e. $\mathbb P \big( X(t) \in F \hbox{ for some } t \in \mathbb R^N \big) = 0$, which improves significantly the main result in Dalang et al [7], where the case of $F$ being a singleton was considered. We provide a variety of examples of Gaussian random field for which our result is applicable. Moreover, by using our main theorem, we solve a problem on the existence of collisions of the eigenvalues of random matrices with Gaussian random field entries that was left open in Jaramillo and Nualart [14] and Song et al [21].

math.PR↗

arXiv2022

Sending Timely Status Updates through Channel with Random Delay via Online Learning

In this work, we study a status update system with a source node sending timely information to the destination through a channel with random delay. We measure the timeliness of the information stored at the receiver via the Age of Information (AoI), the time elapsed since the freshest sample stored at the receiver is generated. The goal is to design a sampling strategy that minimizes the total cost of the expected time average AoI and sampling cost in the absence of transmission delay statistics. We reformulate the total cost minimization problem as the optimization of a renewal-reward process, and propose an online sampling strategy based on the Robbins-Monro algorithm. Denote $K$ to be the number of samples we have taken. We show that, when the transmission delay is bounded, the expected time average total cost obtained by the proposed online algorithm converges to the minimum cost when $K$ goes to infinity, and the optimality gap decays with rate $\mathcal{O}\left(\ln K/K\right)$. Simulation results validate the performance of our proposed algorithm.

cs.IT↗

arXiv2022

Optimization on Multi-User Physical Layer Security of Intelligent Reflecting Surface-Aided VLC

This letter investigates physical layer security in intelligent reflecting surface (IRS)-aided visible light communication (VLC). Under the point source assumption, we first elaborate the system model in the scenario with multiple legitimate users and one eavesdropper, where the secrecy rate maximization problem is transformed into an assignment problem by objective function approximation. Then, an iterative Kuhn-Munkres algorithm is proposed to optimize the transformed problem, and its computational complexity is in the second-order form of the numbers of IRS units and transmitters. Moreover, numerical simulations are carried out to verify the approximation performance and the VLC secrecy rate improvement by IRS.

cs.IT↗