arXiv subjects

Ke Wu

Publications and source records attributed to Ke Wu.

At least 109 records · Page 6Linked to original sources

arXiv2022

Symmetric deformed 2D/3D Hurwitz-Kontsevich model and affine Yangian of gl(1)

Since the ($β$-deformed) Hurwitz Kontsevich model corresponds to the special case of affine Yangian of ${\mathfrak{gl}}(1)$. In this paper, we construct two general cases of the $β$-deformed Hurwitz Kontsevich model. We find that the $W$-operators of these two models can be represented by the generators $e_k,\ f_k,ψ_k$ of the affine Yangian of ${\mathfrak{gl}}(1)$, and the eigenstates (the symmetric functions $Y_λ$ and 3-Jack polynomials) can be obtained from the 3D Young diagram representation of affine Yangian of ${\mathfrak{gl}}(1)$. Then we can see that the $W$-operators and eigenstates are symmetric about the permutations of coordinate axes.

math-ph↗

arXiv2022

Higher form Yang-Mills as higher BFYM theories

The YM theory has been generalized to 2YM and 3YM theories. Similarly, we generalize the BFYM theory to "2BFYM" and "3BFYM" theories. Then, we show that these higher BFYM theories can give the formulations of the corresponding higher form YM theories. Finally, we study the gauge symmetries of these higher BFYM theories.

math-ph↗

arXiv2022

On Ergotropic Gap of Tripartite Separable Systems

Extracting work from quantum system is one of the important areas in quantum thermodynamics. As a significant thermodynamic quantity, the ergotropy gap characterizes the difference between the global and local maximum extractable works. We derive an analytical upper bound of the ergotropic gap with respect to $d\times d\times d$ tripartite separable states. This bound also provides a necessary criterion for the separability of tripartite states. Detailed examples are presented to illustrate the efficiency of this separability criterion.

quant-ph↗

arXiv2022

Filter-Bank-Enabled Leaky-Wave Antenna Array Technique for Full-Band-Locked Radar System in Stitched Frequency-Space Domain

Inspired by the filter-bank (FB) concept that is normally used for multi-rate signal processing, an FB-enabled array technique of leaky-wave antennas (LWAs) is proposed and studied for creating full-band-locked frequency-scanning radar (FSR) systems in a stitched frequency-space domain. This is mainly for addressing the coupling dilemma between the range and angle resolutions, which is historically and naturally inherited from a conventional FSR. First of all, the frequency-modulated continuous-wave system architecture is selected to exemplify and recall the characteristics of a conventional FSR with an emphasis on that resolution coupling. Then, a radar solution featuring a stitched frequency-space domain is introduced for the resolution decoupling, depending on an array of FB-enabled LWA channels. With the radar equation, FB-related conditions for realizing the critical frequency-space stitching are analytically derived and equivalently converted into several design specifications of an array of LWAs, i.e., engineered beam-scanning functions, beam-crossovers, and phase alignments. To facilitate the practical implementation of such an array technique, a detailed and generalized design flow is developed. Finally, for a simple proof of concept, an FB-enabled two-channel LWA array is modeled, fabricated, and measured. Simulated and measured results are in a reasonable agreement, and both demonstrate the desired frequency-space stitching behavior, i.e., enhanced spectrum bandwidth and widened radiation beamwidth. The proposed array solution may be potentially deployed for FSR systems with a full-band-locked beam illumination and a decoupled range-angle resolution, which may present a competitor against the phased array technique.

physics.app-ph↗

arXiv2022

Global Normalization for Streaming Speech Recognition in a Modular Framework

We introduce the Globally Normalized Autoregressive Transducer (GNAT) for addressing the label bias problem in streaming speech recognition. Our solution admits a tractable exact computation of the denominator for the sequence-level normalization. Through theoretical and empirical results, we demonstrate that by switching to a globally normalized model, the word error rate gap between streaming and non-streaming speech-recognition models can be greatly reduced (by more than 50\% on the Librispeech dataset). This model is developed in a modular framework which encompasses all the common neural speech recognition models. The modularity of this framework enables controlled comparison of modelling choices and creation of new models.

cs.LG↗

arXiv2022

3-form Yang-Mills based on 2-crossed modules

In this paper, we study the higher Yang-Mills theory in the framework of higher gauge theory. It was shown that the 2-form electromagnetism can be generalized to the 2-form Yang-Mills theory with the group $U(1)$ replaced by a crossed module of Lie groups. To extend this theory to even higher structure, we develop a 3-form Yang-Mills theory with a 2-crossed module of Lie groups. First, we give an explicit construction of non-degenerate symmetric $G$-invariant forms on the 2-crossed module of Lie algebras. Then, we derive the 3-Bianchi-Identities for 3-curvatures. Finally, we create a 3-form Yang-Mills action and obtain the corresponding field equations.

math-ph↗

arXiv2022

Transformer-based Models of Text Normalization for Speech Applications

Text normalization, or the process of transforming text into a consistent, canonical form, is crucial for speech applications such as text-to-speech synthesis (TTS). In TTS, the system must decide whether to verbalize "1995" as "nineteen ninety five" in "born in 1995" or as "one thousand nine hundred ninety five" in "page 1995". We present an experimental comparison of various Transformer-based sequence-to-sequence (seq2seq) models of text normalization for speech and evaluate them on a variety of datasets of written text aligned to its normalized spoken form. These models include variants of the 2-stage RNN-based tagging/seq2seq architecture introduced by Zhang et al. (2019), where we replace the RNN with a Transformer in one or more stages, as well as vanilla Transformers that output string representations of edit sequences. Of our approaches, using Transformers for sentence context encoding within the 2-stage model proved most effective, with the fine-tuned BERT encoder yielding the best performance.

cs.LG↗

arXiv2021

Generalized higher connections and Yang-Mills

We first extend Generalized Differential Calculus (GDC) to higher structures and create generalized G-invariant bilinear forms. In addition, we also focus on developing generalized 2- and 3-connection theories in the framework of GDC. Then, we derive the higher Bianchi-Identities and study the gauge transformations for those generalized higher connections. Finally, we establish the generalized 2- and 3-form Yang-Mills theories based on GDC and obtain the corresponding fields equations.

hep-th↗

arXiv2021

Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions

We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage. One of the most basic versions of this problem was settled more than 50 years ago by Levenshtein, or one substitution, with nearly optimal redundancy. However, this approach fails to extend to many simple and natural variations of the binary single-edit error setting. In this work, we make progress on the code design problem above in three such variations: We construct linear-time encodable and decodable length-$n$ non-binary codes correcting a single edit error with nearly optimal redundancy $\log n+O(\log\log n)$, providing an alternative simpler proof of a result by Cai, Chee, Gabrys, Kiah, and Nguyen (IEEE Trans. Inf. Theory 2021). This is achieved by employing what we call weighted VT sketches, a notion that may be of independent interest. We construct linear-time encodable and list-decodable binary codes with list-size $2$ for one deletion and one substitution with redundancy $4\log n+O(\log\log n)$. This matches the existential bound up to an $O(\log\log n)$ additive term. We show the existence of a binary code correcting one deletion or one adjacent transposition with nearly optimal redundancy $\log n+O(\log\log n)$.

cs.IT↗

arXiv2021

W-representations of the fermionic matrix and Aristotelian tensor models

We show that the fermionic matrix model can be realized by $W$-representation. We construct the Virasoro constraints with higher algebraic structures, where the constraint operators obey the Witt algebra and null 3-algebra. The remarkable feature is that the character expansion of the partition function can be easily derived from such Virasoro constraints. It is a $τ$-function of the KP hierarchy. We construct the fermionic Aristotelian tensor model and give its $W$-representation. Moreover, we analyze the fermionic red tensor model and present the $W$-representation and character expansion of the partition function.

hep-th↗

arXiv2021

FedJAX: Federated learning simulation with JAX

Federated learning is a machine learning technique that enables training across decentralized data. Recently, federated learning has become an active area of research due to an increased focus on privacy and security. In light of this, a variety of open source federated learning libraries have been developed and released. We introduce FedJAX, a JAX-based open source library for federated learning simulations that emphasizes ease-of-use in research. With its simple primitives for implementing federated learning algorithms, prepackaged datasets, models and algorithms, and fast simulation speed, FedJAX aims to make developing and evaluating federated algorithms faster and easier for researchers. Our benchmark results show that FedJAX can be used to train models with federated averaging on the EMNIST dataset in a few minutes and the Stack Overflow dataset in roughly an hour with standard hyperparameters using TPUs.

cs.LG↗

arXiv2021

Auxetics-Inspired Tunable Metamaterials for Magnetic Resonance Imaging

Auxetics refers to structures or materials with a negative Poisson's ratio, thereby capable of exhibiting counter-intuitive behaviors. Herein, auxetic structures are exploited to design mechanically tunable metamaterials in both planar and hemispherical configurations operating at megahertz (MHz) frequencies, optimized for their application to magnetic resonance imaging (MRI). Specially, the reported tunable metamaterials are composed of arrays of inter-jointed unit cells featuring metallic helices, enabling auxetic patterns with a negative Poisson's ratio. The deployable deformation of the metamaterials yields an added degree of freedom with respect to frequency tunability through the resultant modification of the electromagnetic interactions between unit cells. The metamaterials are fabricated using 3D printing technology and a ~20 MHz frequency shift of the resonance mode is enabled during deformation. Experimental validation is performed in a clinical (3.0 Tesla) MRI, demonstrating that the metamaterials enable a marked boost in radiofrequency (RF) field strength under resonance matched conditions, ultimately yielding a dramatic increase in the signal-to-noise ratio (SNR) (~ 4.5X) of MRI. The tunable metamaterials presented herein offer a novel pathway towards the practical utilization of metamaterials in MRI, as well as a range of other emerging applications.

physics.med-ph↗

arXiv2021

W-representation of Rainbow tensor model

We analyze the rainbow tensor model and present the Virasoro constraints, where the constraint operators obey the Witt algebra and null 3-algebra. We generalize the method of W-representation in matrix model to the rainbow tensor model, where the operators preserving and increasing the grading play a crucial role. It is shown that the rainbow tensor model can be realized by acting on elementary function with exponent of the operator increasing the grading. We derive the compact expression of correlators and apply it to several models, i.e., the red tensor model, Aristotelian tensor model and r=4 rainbow tensor model. Furthermore, we discuss the case of the non-Gaussian red tensor model and present a dual expression for partition function through differentiation.

hep-th↗

arXiv2021

A Practical Coding Scheme for the BSC with Feedback

We provide a practical implementation of the rubber method of Ahlswede et al. for binary alphabets. The idea is to create the "skeleton" sequence therein via an arithmetic decoder designed for a particular $k$-th order Markov chain. For the stochastic binary symmetric channel, we show that the scheme is nearly optimal in a strong sense for certain parameters.

cs.IT↗

arXiv2020

Correlators in the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector

We analyze the Gaussian and chiral supereigenvalue models in the Neveu-Schwarz sector. We show that their partition functions can be expressed as the infinite sums of the homogeneous operators acting on the elementary functions. In spite of the fact that the usual W-representations of these matrix models can not be provided here, we can still derive the compact expressions of the correlators in these two supereigenvalue models. Furthermore, the non-Gaussian (chiral) cases are also discussed.

hep-th↗

arXiv2020

A Theory of Multiple-Source Adaptation with Limited Target Labeled Data

We present a theoretical and algorithmic study of the multiple-source domain adaptation problem in the common scenario where the learner has access only to a limited amount of labeled target data, but where the learner has at disposal a large amount of labeled data from multiple source domains. We show that a new family of algorithms based on model selection ideas benefits from very favorable guarantees in this scenario and discuss some theoretical obstacles affecting some alternative techniques. We also report the results of several experiments with our algorithms that demonstrate their practical effectiveness.

cs.LG↗

arXiv2020

Classification of Blow-ups and Monotonicity Formula for Half Laplacian Nonlinear Heat Equation

We consider the nonlinear half laplacian heat equation $$ u_t+(-Δ)^{\frac{1}{2}} u-|u|^{p-1}u=0,\quad \mathbb{R}^n\times (0, T). $$ We prove that all blows-up are type I, provided that $n \leq 4$ and $ 1<p<p_{*} (n)$ where $ p_{*} (n)$ is an explicit exponent which is below $\frac{n+1}{n-1}$, the critical Sobolev exponent. Central to our proof is a Giga-Kohn type monotonicity formula for half laplacian and a Liouville type theorem for self-similar nonlinear heat equation. This is the first instance of a monotonicity formula at the level of the nonlocal equation, without invoking the extension to the half-space.

math.AP↗

arXiv2020

Generalized logistic growth modeling of the COVID-19 outbreak: comparing the dynamics in the 29 provinces in China and in the rest of the world

Started in Wuhan, China, the COVID-19 has been spreading all over the world. We calibrate the logistic growth model, the generalized logistic growth model, the generalized Richards model and the generalized growth model to the reported number of infected cases for the whole of China, 29 provinces in China, and 33 countries and regions that have been or are undergoing major outbreaks. We dissect the development of the epidemics in China and the impact of the drastic control measures both at the aggregate level and within each province. We quantitatively document four phases of the outbreak in China with a detailed analysis on the heterogeneous situations across provinces. The extreme containment measures implemented by China were very effective with some instructive variations across provinces. Borrowing from the experience of China, we made scenario projections on the development of the outbreak in other countries. We identified that outbreaks in 14 countries (mostly in western Europe) have ended, while resurgences of cases have been identified in several among them. The modeling results clearly show longer after-peak trajectories in western countries, in contrast to most provinces in China where the after-peak trajectory is characterized by a much faster decay. We identified three groups of countries in different level of outbreak progress, and provide informative implications for the current global pandemic.

q-bio.PE↗