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Stephen S. -T. Yau

Publications and source records attributed to Stephen S. -T. Yau.

34 records · Page 2Linked to original sources
arXiv2019

Microwave Integrated Circuits Design with Relational Induction Neural Network

The automation design of microwave integrated circuits (MWIC) has long been viewed as a fundamental challenge for artificial intelligence owing to its larger solution space and structural complexity than Go. Here, we developed a novel artificial agent, termed Relational Induction Neural Network, that can lead to an automotive design of MWIC and avoid brute-force computing to examine every possible solution, which is a significant breakthrough in the field of electronics. Through the experiments on microwave transmission line circuit, filter circuit and antenna circuit design tasks, strongly competitive results are obtained respectively. Compared with the traditional reinforcement learning method, the learning curve shows that the proposed architecture is able to quickly converge to the pre-designed MWIC model and the convergence rate is up to four orders of magnitude. This is the first study which has been shown that an agent through training or learning to automatically induct the relationship between MWIC's structures without incorporating any of the additional prior knowledge. Notably, the relationship can be explained in terms of the MWIC theory and electromagnetic field distribution. Our work bridges the divide between artificial intelligence and MWIC and can extend to mechanical wave, mechanics and other related fields.

eess.SP↗
arXiv2018

Whole genome single nucleotide polymorphism genotyping of Staphylococcus aureus

Next-generation sequencing technology enables routine detection of bacterial pathogens for clinical diagnostics and genetic research. Whole genome sequencing has been of importance in the epidemiologic analysis of bacterial pathogens. However, few whole genome sequencing-based genotyping pipelines are available for practical applications. Here, we present the whole genome sequencing-based single nucleotide polymorphism (SNP) genotyping method and apply to the evolutionary analysis of methicillin-resistant Staphylococcus aureus. The SNP genotyping method calls genome variants using next-generation sequencing reads of whole genomes and calculates the pair-wise Jaccard distances of the genome variants. The method may reveal the high-resolution whole genome SNP profiles and the structural variants of different isolates of methicillin-resistant S. aureus (MRSA) and methicillin-susceptible S. aureus (MSSA) strains. The phylogenetic analysis of whole genomes and particular regions may monitor and track the evolution and the transmission dynamic of bacterial pathogens. The computer programs of the whole genome sequencing-based SNP genotyping method are available to the public at https://github.com/cyinbox/NGS.

q-bio.GN↗
arXiv2018

Complete Weight Distribution and MacWilliams Identities for Asymmetric Quantum Codes

In 1997, Shor and Laflamme defined the weight enumerators for quantum error-correcting codes and derived a MacWilliams identity. We extend their work by introducing our double weight enumerators and complete weight enumerators. The MacWilliams identities for these enumerators can be obtained similarly. With the help of MacWilliams identities, we obtain various bounds for asymmetric quantum codes.

cs.IT↗
arXiv2016

4d N=2 SCFT from Complete Intersection Singularity

Detailed studies of four dimensional N=2 superconformal field theories (SCFT) defined by isolated complete intersection singularities are performed: we compute the Coulomb branch spectrum, Seiberg-Witten solutions and central charges. Most of our theories have exactly marginal deformations and we identify the weakly coupled gauge theory descriptions for many of them, which involve (affine) D and E shaped quiver gauge theories and theories formed from Argyres-Douglas matters. These investigations provide strong evidence for the singularity approach in classifying 4d N=2 SCFTs.

hep-th↗
arXiv2016

4d N=2 SCFT and singularity theory Part II: Complete intersection

We classify three dimensional isolated weighted homogeneous rational complete intersection singularities, which define many new four dimensional N=2 superconformal field theories. We also determine the mini-versal deformation of these singularities, and therefore solve the Coulomb branch spectrum and Seiberg-Witten solution.

hep-th↗
arXiv2014

Time-dependent Hermite-Galerkin spectral method and its applications

A time-dependent Hermite-Galerkin spectral method (THGSM) is investigated in this paper for the nonlinear convection-diffusion equations in the unbounded domains. The time-dependent scaling factor and translating factor are introduced in the definition of the generalized Hermite functions (GHF). As a consequence, the THGSM based on these GHF has many advantages, not only in theorethical proofs, but also in numerical implementations. The stability and spectral convergence of our proposed method have been established in this paper. The Korteweg-de Vries-Burgers (KdVB) equation and its special cases, including the heat equation and the Burgers' equation, as the examples, have been numerically solved by our method. The numerical results are presented, and it surpasses the existing methods in accuracy. Our theoretical proof of the spectral convergence has been supported by the numerical results.

math.NA↗
arXiv2014

On Classification of Toric Surface Codes of Low Dimension

This work is a natural continuation of our previous work \cite{yz}. In this paper, we give a complete classification of toric surface codes of dimension less than or equal to 6, except a special pair, $C_{P_6^{(4)}}$ and $C_{P_6^{(5)}}$ over $\mathbb{F}_8$. Also, we give an example, $C_{P_6^{(5)}}$ and $C_{P_6^{(6)}}$ over $\mathbb{F}_7$, to illustrate that two monomially equivalent toric codes can be constructed from two lattice non-equivalent polygons.

cs.IT↗
arXiv2014

On the quenching behavior of the MEMS with fringing field

The singular parabolic problem $u_t-\triangle u=λ{\frac{1+δ|\nabla u|^2}{(1-u)^2}}$ on a bounded domain $Ω$ of $\mathbb{R}^n$ with Dirichlet boundary condition, models the Microelectromechanical systems (MEMS) device with fringing field. In this paper, we focus on the quenching behavior of the solution to this equation. We first show that there exists a critical value $λ_δ^*>0$ such that if $0<λ<λ_δ^*$, all solutions exist globally; while for $λ>λ_δ^*$, all the solution will quench in finite time. The estimate of the quenching time in terms of large voltage $λ$ is investigated. Furthermore, the quenching set is a compact subset of $Ω$, provided $Ω$ is a convex bounded domain in $\mathbb{R}^n$. In particular, if the domain $Ω$ is radially symmetric, then the origin is the only quenching point. We not only derive the one-side estimate of the quenching rate, but also further study the refined asymptotic behavior of the finite quenching solution.

math.AP↗
arXiv2014

Hermite spectral method to 1D forward Kolmogorov equation and its application to nonlinear filtering problems

In this paper, we investigate the Hermite spectral method (HSM) to numerically solve the forward Kolmogorov equation (FKE). A useful guideline of choosing the scaling factor of the generalized Hermite functions is given in this paper. It greatly improves the resolution of HSM. The convergence rate of HSM to FKE is analyzed in the suitable function space and has been verified by the numerical simulation. As an important application and our primary motivation to study the HSM to FKE, we work on the implementation of the nonlinear filtering (NLF) problem with a real-time algorithm developed in [17]. The HSM to FKE is served as the off-line computation in this algorithm. The translating factor of the generalized Hermite functions and the moving-window technique are introduced to deal with the drifting of the posterior conditional density function of the states in the on-line experiments. Two numerical experiments of NLF problems are carried out to illustrate the feasibility of our algorithm. Moreover, our algorithm surpasses the particle filter as a real-time solver to NLF.

math.OC↗
arXiv2014

Complete Real Time Solution of the General Nonlinear Filtering Problem without Memory

It is well known that the nonlinear filtering problem has important applications in both military and civil industries. The central problem of nonlinear filtering is to solve the Duncan-Mortensen-Zakai (DMZ) equation in real time and in a memoryless manner. In this paper, we shall extend the algorithm developed previously by S.-T. Yau and the second author to the most general setting of nonlinear filterings, where the explicit time-dependence is in the drift term, observation term, and the variance of the noises could be a matrix of functions of both time and the states. To preserve the off-line virture of the algorithm, necessary modifications are illustrated clearly. Moreover, it is shown rigorously that the approximated solution obtained by the algorithm converges to the real solution in the $L^1$ sense. And the precise error has been estimated. Finally, the numerical simulation support the feasibility and efficiency of our algorithm.

math.OC↗
arXiv2014

Hermite spectral method with hyperbolic cross approximations to high-dimensional parabolic PDEs

It is well-known that sparse grid algorithm has been widely accepted as an efficient tool to overcome the "curse of dimensionality" in some degree. In this note, we first give the error estimate of hyperbolic cross (HC) approximations with generalized Hermite functions. The exponential convergence in both regular and optimized hyperbolic cross approximations has been shown. Moreover, the error estimate of Hermite spectral method to high-dimensional linear parabolic PDEs with HC approximations has been investigated in the properly weighted Korobov spaces. The numerical result verifies the exponential convergence of this approach.

math.NA↗
arXiv2013

Denoising the 3-Base Periodicity Walks of DNA Sequences in Gene Finding

A nonlinear Tracking-Differentiator is one-input-two-output system that can generate smooth approximation of measured signals and get the derivatives of the signals. The nonlinear tracking-Differentiator is explored to denoise and generate the derivatives of the walks of the 3-periodicity of DNA sequences. An improved algorithm for gene finding is presented using the nonlinear Tracking-Differentiator. The gene finding algorithm employs the 3-base periodicity of coding region. The 3-base periodicity DNA walks are denoised and tracked using the nonlinear Tracking-Differentiator. Case studies demonstrate that the nonlinear Tracking-Differentiator is an effective method to improve the accuracy of the gene finding algorithm.

cs.CE↗
arXiv2003

Classification of 3-dimensional isolated rational hypersurface singularities with C*-action

In the paper "Algebraic classification of rational CR structures on topological 5-sphere with transversal holomorphic S^1-action in C^4" (Yau and Yu, Math. Nachrichten 246-247(2002), 207-233), we give algebraic classification of rational CR structures on the topological 5-sphere with transversal holomorphic S^1-action in C^4. Here, algebraic classification of compact strongly pseudoconvex CR manifolds X means classification up to algebraic equivalence, i.e. roughly up to isomorphism of the normalization of the complex analytic variety V which has X as boundary. The problem is intimately related to the study of 3-dimensional isolated rational weighted homogeneous hypersurface singularities with link homeomorphic to S^5. For this, we need the classification of 3-dimensional isolated rational hypersurface singularities with a C*-action. This list is only available at the homepage of one of us. Since there is a desire for a complete list of this classification (cf. Theorem 3.3), we decide to publish it for the convenience of readers.

math.AG↗
arXiv1998

Counterexample to boundary regularity of a strongly pseudoconvex CR submanifold: An addendum to the paper of Harvey-Lawson

The purpose of this paper is to give a counterexample of Theorem 10.4 in [Ann. of Math. 102 (1975), 223-290]. In the Harvey-Lawson paper, a global result is claimed, but only a local result is proven. This theorem has had a big impact on CR geometry for almost a quarter of a century because one can use the theory of isolated singularities to study the theory of CR manifolds and vice versa.

math.CV↗
arXiv1993

Topological invariance of intersection lattices of arrangements in CP^2

Let $\scr A^*=\{l_1,l_2,\cdots,l_n\}$ be a line arrangement in $\Bbb{CP}^2$, i.e., a collection of distinct lines in $\Bbb{CP}^2$. Let $L(\scr A^*)$ be the set of all intersections of elements of $A^*$ partially ordered by $X\leq Y\Leftrightarrow Y\subseteq X$. Let $M(\scr A^*)$ be $\Bbb{CP}^2-\bigcup\scr A^*$ where $\bigcup\scr A^*= \bigcup\{l_i\colon\ 1\leq i\leq n\}$. The central problem of the theory of arrangement of lines in $\Bbb{CP}^2$ is the relationship between $M(\scr A^*)$ and $L(\scr A^*)$.

math.GT↗