arXiv subjects

Zhiyuan Wang

Publications and source records attributed to Zhiyuan Wang.

At least 145 records · Page 8Linked to original sources

arXiv2023

Kac-Schwarz Operators of Type $B$, Quantum Spectral Curves, and Spin Hurwitz Numbers

Given a tau-function $τ(t)$ of the BKP hierarchy satisfying $τ(0)=1$, we discuss the relation between its BKP-affine coordinates on the isotropic Sato Grassmannian and its BKP-wave function. Using this result, we formulate a type of Kac-Schwarz operators for $τ(t)$ in terms of BKP-affine coordinates. As an example, we compute the affine coordinates of the BKP tau-function for spin single Hurwitz numbers with completed cycles, and find a pair of Kac-Schwarz operators $(P,Q)$ satisfying $[P,Q]=1$. By doing this, we obtain the quantum spectral curve for spin single Hurwitz numbers.

math-ph↗

arXiv2023

Wearable Sensor-based Multimodal Physiological Responses of Socially Anxious Individuals across Social Contexts

Correctly identifying an individual's social context from passively worn sensors holds promise for delivering just-in-time adaptive interventions (JITAIs) to treat social anxiety disorder. In this study, we present results using passively collected data from a within-subject experiment that assessed physiological response across different social contexts (i.e, alone vs. with others), social phases (i.e., pre- and post-interaction vs. during an interaction), social interaction sizes (i.e., dyadic vs. group interactions), and levels of social threat (i.e., implicit vs. explicit social evaluation). Participants in the study ($N=46$) reported moderate to severe social anxiety symptoms as assessed by the Social Interaction Anxiety Scale ($\geq$34 out of 80). Univariate paired difference tests, multivariate random forest models, and follow-up cluster analyses were used to explore physiological response patterns across different social and non-social contexts. Our results suggest that social context is more reliably distinguishable than social phase, group size, or level of social threat, but that there is considerable variability in physiological response patterns even among these distinguishable contexts. Implications for real-world context detection and deployment of JITAIs are discussed.

cs.CY↗

arXiv2023

An ultra-stable cryogenic sapphire cavity laser with an instability of $1.9\times10^{-16}$ based on a low vibration level cryostat

Cryogenic ultra-stable lasers have extremely low thermal noise limits and frequency drifts, but they are more seriously affected by vibration noise from cryostats. Main material candidates for cryogenic ultra-stable cavities include silicon and sapphire. Although sapphire has many excellent properties at low temperature, the development of sapphire-based cavities is less advanced than that of silicon-based. Using a homemade cryogenic sapphire cavity, we develop an ultra-stable laser source with a frequency instability of $1.9\times10^{-16}$. This is the best frequency instability level among similar systems using cryogenic sapphire cavities reported so far. Low vibration performance of the cryostat is demonstrated with a two-stage vibration isolation, and the vibration suppression is further improved by different mixing ratio of the gas-liquid helium. With this technique, vibrations at frequencies higher than tens of hertz are greatly suppressed.

physics.ins-det↗

arXiv2022

Adaptive Control of Client Selection and Gradient Compression for Efficient Federated Learning

Federated learning (FL) allows multiple clients cooperatively train models without disclosing local data. However, the existing works fail to address all these practical concerns in FL: limited communication resources, dynamic network conditions and heterogeneous client properties, which slow down the convergence of FL. To tackle the above challenges, we propose a heterogeneity-aware FL framework, called FedCG, with adaptive client selection and gradient compression. Specifically, the parameter server (PS) selects a representative client subset considering statistical heterogeneity and sends the global model to them. After local training, these selected clients upload compressed model updates matching their capabilities to the PS for aggregation, which significantly alleviates the communication load and mitigates the straggler effect. We theoretically analyze the impact of both client selection and gradient compression on convergence performance. Guided by the derived convergence rate, we develop an iteration-based algorithm to jointly optimize client selection and compression ratio decision using submodular maximization and linear programming. Extensive experiments on both real-world prototypes and simulations show that FedCG can provide up to 5.3$\times$ speedup compared to other methods.

cs.DC↗

arXiv2022

AACC: Asymmetric Actor-Critic in Contextual Reinforcement Learning

Reinforcement Learning (RL) techniques have drawn great attention in many challenging tasks, but their performance deteriorates dramatically when applied to real-world problems. Various methods, such as domain randomization, have been proposed to deal with such situations by training agents under different environmental setups, and therefore they can be generalized to different environments during deployment. However, they usually do not incorporate the underlying environmental factor information that the agents interact with properly and thus can be overly conservative when facing changes in the surroundings. In this paper, we first formalize the task of adapting to changing environmental dynamics in RL as a generalization problem using Contextual Markov Decision Processes (CMDPs). We then propose the Asymmetric Actor-Critic in Contextual RL (AACC) as an end-to-end actor-critic method to deal with such generalization tasks. We demonstrate the essential improvements in the performance of AACC over existing baselines experimentally in a range of simulated environments.

cs.LG↗

arXiv2022

BKP Hierarchy, Affine Coordinates, and a Formula for Connected Bosonic $N$-Point Functions

We derive a formula for the connected $n$-point functions of a tau-function of the BKP hierarchy in terms of its affine coordinates. This is a BKP-analogue of a formula for KP tau-functions proved by Zhou in [arXiv:1507.01679]. Moreover, we prove a simple relation between the KP-affine coordinates of a tau-function $τ(\mathbf{t})$ of the KdV hierarchy and the BKP-affine coordinates of $τ(\mathbf{t}/2)$. As applications, we present a new algorithm to compute the free energies of the Witten-Kontsevich tau-function and the Brézin-Gross-Witten tau-function.

nlin.SI↗

arXiv2022

From Personalized Medicine to Population Health: A Survey of mHealth Sensing Techniques

Mobile Sensing Apps have been widely used as a practical approach to collect behavioral and health-related information from individuals and provide timely intervention to promote health and well-beings, such as mental health and chronic cares. As the objectives of mobile sensing could be either \emph{(a) personalized medicine for individuals} or \emph{(b) public health for populations}, in this work we review the design of these mobile sensing apps, and propose to categorize the design of these apps/systems in two paradigms -- \emph{(i) Personal Sensing} and \emph{(ii) Crowd Sensing} paradigms. While both sensing paradigms might incorporate with common ubiquitous sensing technologies, such as wearable sensors, mobility monitoring, mobile data offloading, and/or cloud-based data analytics to collect and process sensing data from individuals, we present a novel taxonomy system with two major components that can specify and classify apps/systems from aspects of the life-cycle of mHealth Sensing: \emph{(1) Sensing Task Creation \& Participation}, \emph{(2) Health Surveillance \& Data Collection}, and \emph{(3) Data Analysis \& Knowledge Discovery}. With respect to different goals of the two paradigms, this work systematically reviews this field, and summarizes the design of typical apps/systems in the view of the configurations and interactions between these two components. In addition to summarization, the proposed taxonomy system also helps figure out the potential directions of mobile sensing for health from both personalized medicines and population health perspectives.

cs.LG↗

arXiv2022

Optical trapping of high-aspect-ratio NaYF hexagonal prisms for kHz-MHz gravitational wave detectors

We present experimental results on optical trapping of Yb-doped $β-$NaYF sub-wavelength-thickness high-aspect-ratio hexagonal prisms with a micron-scale radius. The prisms are trapped in vacuum using an optical standing wave, oriented with the normal vector to their face along the beam propagation direction, and exhibit characteristic modes of three translational and two torsional degrees of freedom. The measured motional spectra are compared with numerical simulations. This plate-like geometry simultaneously enables trapping with low photon-recoil-heating, high mass, and high trap frequency, potentially leading to advances in high frequency gravitational wave searches in the Levitated Sensor Detector (LSD), currently under construction. The material used here has previously been shown to exhibit internal cooling via laser refrigeration when optically trapped and illuminated with light of suitable wavelength. Employing such laser refrigeration methods in the context of our work may enable higher trapping intensity thus and higher trap frequencies for gravitational wave searches approaching the several hundred kHz range.

physics.optics↗

arXiv2022

Graph Neural Networks in IoT: A Survey

The Internet of Things (IoT) boom has revolutionized almost every corner of people's daily lives: healthcare, home, transportation, manufacturing, supply chain, and so on. With the recent development of sensor and communication technologies, IoT devices including smart wearables, cameras, smartwatches, and autonomous vehicles can accurately measure and perceive their surrounding environment. Continuous sensing generates massive amounts of data and presents challenges for machine learning. Deep learning models (e.g., convolution neural networks and recurrent neural networks) have been extensively employed in solving IoT tasks by learning patterns from multi-modal sensory data. Graph Neural Networks (GNNs), an emerging and fast-growing family of neural network models, can capture complex interactions within sensor topology and have been demonstrated to achieve state-of-the-art results in numerous IoT learning tasks. In this survey, we present a comprehensive review of recent advances in the application of GNNs to the IoT field, including a deep dive analysis of GNN design in various IoT sensing environments, an overarching list of public data and source code from the collected publications, and future research directions. To keep track of newly published works, we collect representative papers and their open-source implementations and create a Github repository at https://github.com/GuiminDong/GNN4IoT.

cs.LG↗

arXiv2022

Topological correlations in three dimensional classical Ising models: an exact solution with a continuous phase transition

We study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution of the 2D Ising model and the solution of Kitaev's honeycomb model, leading to a three-parameter phase diagram with a third order phase transition between two distinct phases. Interestingly, the phases of this model are distinguished by topological features: the expectation value of a certain family of loop observables depend only on the topology of the loop (whether the loop is contractible), and are quantized at rational values that differ in the two phases. We show that a related exactly solvable 3D classical statistical model with real coupling constants also shows the topological features of one of these phases. Furthermore, even in the model with complex parameters, the partition function has some physical relevance, as it can be interpreted as the transition amplitude of a quantum dynamical process and may shed light on dynamical quantum phase transitions.

cond-mat.stat-mech↗

arXiv2021

Socially-Optimal Mechanism Design for Incentivized Online Learning

Multi-arm bandit (MAB) is a classic online learning framework that studies the sequential decision-making in an uncertain environment. The MAB framework, however, overlooks the scenario where the decision-maker cannot take actions (e.g., pulling arms) directly. It is a practically important scenario in many applications such as spectrum sharing, crowdsensing, and edge computing. In these applications, the decision-maker would incentivize other selfish agents to carry out desired actions (i.e., pulling arms on the decision-maker's behalf). This paper establishes the incentivized online learning (IOL) framework for this scenario. The key challenge to design the IOL framework lies in the tight coupling of the unknown environment learning and asymmetric information revelation. To address this, we construct a special Lagrangian function based on which we propose a socially-optimal mechanism for the IOL framework. Our mechanism satisfies various desirable properties such as agent fairness, incentive compatibility, and voluntary participation. It achieves the same asymptotic performance as the state-of-art benchmark that requires extra information. Our analysis also unveils the power of crowd in the IOL framework: a larger agent crowd enables our mechanism to approach more closely the theoretical upper bound of social performance. Numerical results demonstrate the advantages of our mechanism in large-scale edge computing.

cs.GT↗

arXiv2021

On affine coordinates of the tau-function for open intersection numbers

In Alexandrov's work \cite{al2, al3} it has been shown that the extended partition function $\exp(F^{o,ext}+F^c)$ introduced by Buryak in \cite{bu, bu2} is a tau-function of the KP hierarchy. In this work, we compute the affine coordinates of this tau-function on the Sato Grassmannian, and rewrite the Virasoro constraints as recursions for the affine coordinates in the fermionic picture. As applications we derive some formulas for the extended partition function and the connected $n$-point functions using methods developed by Zhou in \cite{zhou1} based on the boson-fermion correspondence.

math-ph↗

arXiv2021

Topological 1D Gravity, KP Hierarchy, and Orbifold Euler Characteristics of $\overline{\mathcal M}_{g,n}$

In this work we study the tau-function $Z^{1D}$ of the KP hierarchy specified by the topological 1D gravity. As an application, we present two types of algorithms to compute the orbifold Euler characteristics of $\overline{\mathcal M}_{g,n}$. The first is to use (fat or thin) topological recursion formulas emerging from the Virasoro constraints for $Z^{1D}$; and the second is to use a formula for the connected $n$-point functions of a KP tau-function in terms of its affine coordinates on the Sato Grassmannian. This is a sequel to an earlier work.

math-ph↗

arXiv2021

Orbifold Euler Characteristics of $\overline{\mathcal M}_{g,n}$

We solve the problem of the computation of the orbifold Euler characteristics of $\Mbar_{g,n}$. We take the works of Harer-Zagier \cite{hz} and Bini-Harer \cite{bh} as our starting point, and apply the formalisms developed in \cite{wz} and \cite{zhou1} to this problem. These formalisms are typical examples of mathematical methods inspired by quantum field theories. We also present many closed formulas and some numerical data. In genus zero the results are related to Ramanujan polynomials, and in higher genera we get recursion relations almost identical to the recursion relations for Ramanujan polynomials but with different initial values. We also show that the generating series given by the orbifold Euler characteristics of $\overline{\mathcal M}_{g,n}$ is the logarithm of the KP tau-function of the topological 1D gravity evaluated at the times given by the orbifold Euler characteristics of $\overline{\mathcal M}_{g,n}$. Conversely, the logarithm of this tau-function evaluated at the times given by certain generating series of the orbifold Euler characteristics of $\overline{\mathcal M}_{g,n}$ is a generating series of the orbifold Euler characteristics of $\overline{\mathcal M}_{g,n}$. This is a new example of open-closed duality.

math.AG↗

arXiv2021

A formalism of abstract quantum field theory of summation of fat graphs

In this work we present a formalism of abstract quantum field theory for fat graphs and its realizations. This is a generalization of an earlier work for stable graphs. We define the abstract correlators $\mathcal F_g^μ$, abstract free energy $\mathcal F_g$, abstract partition function $\mathcal Z$, and abstract $n$-point functions $\mathcal W_{g,n}$ to be formal summations of fat graphs, and derive quadratic recursions using edge-contraction/vertex-splitting operators, including the abstract Virasoro constraints, an abstract cut-and-join type representation for $\mathcal Z$, and a quadratic recursion for $\mathcal W_{g,n}$ which resembles the Eynard-Orantin topological recursion. When considering the realization by the Hermitian one-matrix models, we obtain the Virasoro constraints, a cut-and-join representation for the partition function $Z_N^{\text{Herm}}$ which proves that $Z_N^{\text{Herm}}$ is a tau-function of KP hierarchy, a recursion for $n$-point functions which is known to be equivalent to the E-O recursion, and a Schrödinger type-equation which is equivalent to the quantum spectral curve. We conjecture that in general cases the realization of the quadratic recursion for $\mathcal W_{g,n}$ is the E-O recursion, where the spectral curve and Bergmann kernel are constructed from realizations of $\mathcal W_{0,1}$ and $\mathcal W_{0,2}$ respectively using the framework of emergent geometry.

math-ph↗

arXiv2021

Bounding the finite-size error of quantum many-body dynamics simulations

Finite-size error (FSE), the discrepancy between an observable in a finite system and in the thermodynamic limit, is ubiquitous in numerical simulations of quantum many body systems. Although a rough estimate of these errors can be obtained from a sequence of finite-size results, a strict, quantitative bound on the magnitude of FSE is still missing. Here we derive rigorous upper bounds on the FSE of local observables in real time quantum dynamics simulations initialized from a product state. In $d$-dimensional locally interacting systems with a finite local Hilbert space, our bound implies $ |\langle \hat{S}(t)\rangle_L-\langle \hat{S}(t)\rangle_\infty|\leq C(2v t/L)^{cL-μ}$, with $v$, $C$, $c$, $μ$ constants independent of $L$ and $t$, which we compute explicitly. For periodic boundary conditions (PBC), the constant $c$ is twice as large as that for open boundary conditions (OBC), suggesting that PBC have smaller FSE than OBC at early times. The bound can be generalized to a large class of correlated initial states as well. As a byproduct, we prove that the FSE of local observables in ground state simulations decays exponentially with $L$, under a suitable spectral gap condition. Our bounds are practically useful in determining the validity of finite-size results, as we demonstrate in simulations of the one-dimensional (1D) quantum Ising and Fermi-Hubbard models.

quant-ph↗

arXiv2021

Taming Time-Varying Information Asymmetry in Fresh Status Acquisition

Many online platforms are providing valuable real-time contents (e.g., traffic) by continuously acquiring the status of different Points of Interest (PoIs). In status acquisition, it is challenging to determine how frequently a PoI should upload its status to a platform, since they are self-interested with private and possibly time-varying preferences. This paper considers a general multi-period status acquisition system, aiming to maximize the aggregate social welfare and ensure the platform freshness. The freshness is measured by a metric termed age of information. For this goal, we devise a long-term decomposition (LtD) mechanism to resolve the time-varying information asymmetry. The key idea is to construct a virtual social welfare that only depends on the current private information, and then decompose the per-period operation into multiple distributed bidding problems for the PoIs and platforms. The LtD mechanism enables the platforms to achieve a tunable trade-off between payoff maximization and freshness conditions. Moreover, the LtD mechanism retains the same social performance compared to the benchmark with symmetric information and asymptotically ensures the platform freshness conditions. Numerical results based on real-world data show that when the platforms pay more attention to payoff maximization, each PoI still obtains a non-negative payoff in the long-term.

cs.GT↗

arXiv2020

Probing topological spin structures using light-polarization and magnetic microscopy

We present an imaging modality that enables detection of magnetic moments and their resulting stray magnetic fields. We use wide-field magnetic imaging that employs a diamond-based magnetometer and has combined magneto-optic detection (e.g. magneto-optic Kerr effect) capabilities. We employ such an instrument to image magnetic (stripe) domains in multilayered ferromagnetic structures.

cond-mat.mtrl-sci↗