arXiv subjects

Ke Wu

Publications and source records attributed to Ke Wu.

At least 127 records · Page 7Linked to original sources

arXiv2020

Correlators in the supereigenvalue model in the Ramond sector

We investigate the supereigenvalue model in the Ramond sector. We prove that its partition function can be obtained by acting on elementary functions with exponents of the given operators. The Virasoro constraints for this supereigenvalue model are presented. The remarkable property of these bosonic constraint operators is that they obey the Witt algebra and null 3-algebra. The compact expression of correlators can be derived from these Virasoro constraints.

hep-th↗

arXiv2019

Exact correlators in the Gaussian Hermitian matrix model

We present the $W_{1+\infty}$ constraints for the Gaussian Hermitian matrix model, where the constructed constraint operators yield the $W_{1+\infty}$ $n$-algebra. For the Virasoro constraints, we note that the constraint operators give the null 3-algebra. With the help of our Virasoro constraints, we derive a new effective formula for correlators in the Gaussian Hermitian matrix model.

hep-th↗

arXiv2019

Block Edit Errors with Transpositions: Deterministic Document Exchange Protocols and Almost Optimal Binary Codes

Document exchange and error correcting codes are two fundamental problems regarding communications. In the first problem, Alice and Bob each holds a string, and the goal is for Alice to send a short sketch to Bob, so that Bob can recover Alice's string. In the second problem, Alice sends a message with some redundant information to Bob through a channel that can add adversarial errors, and the goal is for Bob to correctly recover the message despite the errors. In a recent work \cite{CJLW18}, the authors constructed explicit deterministic document exchange protocols and binary error correcting codes for edit errors with almost optimal parameters.\ Unfortunately, the constructions in \cite{CJLW18} do not work for other common errors such as block transpositions. In this paper, we generalize the constructions in \cite{CJLW18} to handle a much larger class of errors. These include bursts of insertions and deletions, as well as block transpositions. Specifically, we consider document exchange and error correcting codes where the total number of block insertions, block deletions, and block transpositions is at most $k \leq αn/\log n$ for some constant $0<α<1$. In addition, the total number of bits inserted and deleted by the first two kinds of operations is at most $t \leq βn$ for some constant $0<β<1$, where $n$ is the length of Alice's string or message. We construct explicit, deterministic document exchange protocols with sketch size $ O( (k \log n +t) \log^2 \frac{n}{k\log n + t} )$ and explicit binary error correcting code with $O(k \log n \log \log \log n+t)$ redundant bits.

cs.DS↗

arXiv2019

$W_{1+\infty}$ constraints for the hermitian one-matrix model

We construct the multi-variable realizations of the $W_{1+\infty}$ algebra such that they lead to the $W_{1+\infty}$ $n$-algebra. Based on our realizations of the $W_{1+\infty}$ algebra, we derive the $W_{1+\infty}$ constraints for the hermitian one-matrix model. The constraint operators yield not only the $W_{1+\infty}$ algebra but also the closed $W_{1+\infty}$ $n$-algebra.

hep-th↗

arXiv2019

Presentation Proposal: Towards Efficient Data-flow Test Data Generation Using KLEE

Dataflow coverage, one of the white-box testing criteria, focuses on the relations between variable definitions and their uses.Several empirical studies have proved data-flow testing is more effective than control-flow testing. However, data-flow testing still cannot find its adoption in practice, due to the lack of effective tool support. To this end, we propose a guided symbolic execution approach to efficiently search for program paths to satisfy data-flow coverage criteria. We implemented this approach on KLEE and evaluated with 30 program subjects which are constructed by the subjects used in previous data-flow testing literature, SIR, SV-COMP benchmarks. Moreover, we are planning to integrate the data-flow testing technique into the new proposed symbolic execution engine, SmartUnit, which is a cloud-based unit testing service for industrial software, supporting coverage-based testing. It has successfully helped several well-known corporations and institutions in China to adopt coverage-based testing in practice, totally tested more than one million lines of real code from industry.

cs.SE↗

arXiv2019

On $W_{1+\infty}$ $n$-algebra

We present the nontrivial $W_{1+\infty}$ $n$-algebra and analyze its remarkable properties. We investigate the $W_{1+\infty}$ $n$-algebra in the Landau problem and discuss the realization of the classical $w_{\infty}$ 3-algebra. Furthermore, we discuss the case of the many-body system in the lowest Landau level and derive the constraints for correlation functions of the vertex operators.

hep-th↗

arXiv2018

Deterministic Document Exchange Protocols, and Almost Optimal Binary Codes for Edit Errors

We study two basic problems regarding edit error, i.e. document exchange and error correcting codes for edit errors (insdel codes). For message length $n$ and edit error upper bound $k$, it is known that in both problems the optimal sketch size or the optimal number of redundant bits is $Θ(k \log \frac{n}{k})$. However, known constructions are far from achieving these bounds. We significantly improve previous results on both problems. For document exchange, we give an efficient deterministic protocol with sketch size $O(k\log^2 \frac{n}{k})$. This significantly improves the previous best known deterministic protocol, which has sketch size $O(k^2 + k \log^2 n)$ (Belazzougui15). For binary insdel codes, we obtain the following results: 1. An explicit binary insdel code which encodes an $n$-bit message $x$ against $k$ errors with redundancy $O(k \log^2 \frac{n}{k})$. In particular this implies an explicit family of binary insdel codes that can correct $\varepsilon$ fraction of insertions and deletions with rate $1-O(\varepsilon \log^2 (\frac{1}{\varepsilon}))=1-\widetilde{O}(\varepsilon)$. 2. An explicit binary insdel code which encodes an $n$-bit message $x$ against $k$ errors with redundancy $O(k \log n)$. This is the first explicit construction of binary insdel codes that has optimal redundancy for a wide range of error parameters $k$, and this brings our understanding of binary insdel codes much closer to that of standard binary error correcting codes. In obtaining our results we introduce the notion of \emph{$\varepsilon$-self matching hash functions} and \emph{$\varepsilon$-synchronization hash functions}. We believe our techniques can have further applications in the literature.

cs.DS↗

arXiv2018

SmartUnit: Empirical Evaluations for Automated Unit Testing of Embedded Software in Industry

In this paper, we aim at the automated unit coverage-based testing for embedded software. To achieve the goal, by analyzing the industrial requirements and our previous work on automated unit testing tool CAUT, we rebuild a new tool, SmartUnit, to solve the engineering requirements that take place in our partner companies. SmartUnit is a dynamic symbolic execution implementation, which supports statement, branch, boundary value and MC/DC coverage. SmartUnit has been used to test more than one million lines of code in real projects. For confidentiality motives, we select three in-house real projects for the empirical evaluations. We also carry out our evaluations on two open source database projects, SQLite and PostgreSQL, to test the scalability of our tool since the scale of the embedded software project is mostly not large, 5K-50K lines of code on average. From our experimental results, in general, more than 90% of functions in commercial embedded software achieve 100% statement, branch, MC/DC coverage, more than 80% of functions in SQLite achieve 100% MC/DC coverage, and more than 60% of functions in PostgreSQL achieve 100% MC/DC coverage. Moreover, SmartUnit is able to find the runtime exceptions at the unit testing level. We also have reported exceptions like array index out of bounds and divided-by-zero in SQLite. Furthermore, we analyze the reasons of low coverage in automated unit testing in our setting and give a survey on the situation of manual unit testing with respect to automated unit testing in industry.

cs.SE↗

arXiv2018

Classification of cryptocurrency coins and tokens by the dynamics of their market capitalisations

We empirically verify that the market capitalisations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values, with the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simple proportional growth with birth & death model previously employed to describe the size distribution of firms, cities, webpages, etc. We empirically validate the model and its main predictions, in terms of proportional growth (Gibrat's law) of the coins and tokens. Estimating the main parameters of the model, the theoretical predictions for the power-law exponents of coin and token distributions are in remarkable agreement with the empirical estimations, given the simplicity of the model. Our results clearly characterize coins as being "entrenched incumbents" and tokens as an "explosive immature ecosystem", largely due to massive and exuberant Initial Coin Offering activity in the token space. The theory predicts that the exponent for tokens should converge to 1 in the future, reflecting a more reasonable rate of new entrants associated with genuine technological innovations.

physics.soc-ph↗

arXiv2018

Synchronization Strings: Efficient and Fast Deterministic Constructions over Small Alphabets

Synchronization strings are recently introduced by Haeupler and Shahrasbi (STOC 2017) in the study of codes for correcting insertion and deletion errors (insdel codes). They showed that for any parameter $\varepsilon>0$, synchronization strings of arbitrary length exist over an alphabet whose size depends only on $\varepsilon$. Specifically, they obtained an alphabet size of $O(\varepsilon^{-4})$, which left an open question on where the minimal size of such alphabets lies between $Ω(\varepsilon^{-1})$ and $O(\varepsilon^{-4})$. In this work, we partially bridge this gap by providing an improved lower bound of $Ω(\varepsilon^{-3/2})$, and an improved upper bound of $O(\varepsilon^{-2})$. We also provide fast explicit constructions of synchronization strings over small alphabets. Further, along the lines of previous work on similar combinatorial objects, we study the extremal question of the smallest possible alphabet size over which synchronization strings can exist for some constant $\varepsilon < 1$. We show that one can construct $\varepsilon$-synchronization strings over alphabets of size four while no such string exists over binary alphabets. This reduces the extremal question to whether synchronization strings exist over ternary alphabets.

cs.IT↗

arXiv2018

Algebraic formulas for the structure constants in symmetric functions

Littlewood-Richardson rule gives the decomposition formula for the multiplication of two Schur functions, while the decomposition formula for the multiplication of two Hall-Littlewood functions or two universal characters is also given by the combinatorial method. In this paper, using the vertex operator realizations of these symmetric functions, we construct the algebraic forms of these decomposition formulas.

math-ph↗

arXiv2017

Synchronization Strings: Efficient and Fast Deterministic Constructions over Small Alphabets

Synchronization strings are recently introduced by Haeupler and Shahrasbi [HS17a] in the study of codes for correcting insertion and deletion errors (insdel codes). A synchronization string is an encoding of the indices of the symbols in a string, and together with an appropriate decoding algorithm it can transform insertion and deletion errors into standard symbol erasures and corruptions. This reduces the problem of constructing insdel codes to the problem of constructing standard error correcting codes, which is much better understood. Besides this, synchronization strings are also useful in other applications such as synchronization sequences and interactive coding schemes. Amazingly, [HS17a] showed that for any error parameter $\varepsilon>0$, synchronization strings of arbitrary length exist over an alphabet whose size depends only on $\varepsilon$. Specifically, they obtained an alphabet size of $O(\varepsilon^{-4})$, as well as a randomized construction that runs in expected time $O(n^5)$. However, it remains an interesting question to find deterministic and more efficient constructions. In this paper, we improve the construction in [HS17a] in three aspects: we achieve a smaller alphabet size, a deterministic construction, and a faster algorithm. Along the way we introduce a new combinatorial object, and establish a new connection between synchronization strings and insdel codes --- such codes can be used in a simple way to construct synchronization strings. This new connection complements the connection found in [HS17a], and may be of independent interest. In an independent work [HS17c], Haeupler and Shahrasbi also give deterministic constructions of synchronization strings over arbitrary length (or even infinite length). Their constructions can achieve linear construction time, but have alphabet size $\varepsilon^{-O(1)}$, which may be larger than ours.

cs.IT↗

arXiv2017

3-Algebraic structures of the quantum Calogero-Moser model

We investigate the quantum Calogero-Moser model and reveal its hidden symmetries, i.e., the $W_{1+\infty}$ and Virasoro-Witt 3-algebras. In the large $N$ limit, we note that these two infinite dimensional 3-algebras reduce to the $w_{\infty}$ and special Virasoro-Witt 3-algebras which satisfy the fundamental identity condition, respectively.

hep-th↗

arXiv2016

Minimally Supervised Written-to-Spoken Text Normalization

In speech-applications such as text-to-speech (TTS) or automatic speech recognition (ASR), \emph{text normalization} refers to the task of converting from a \emph{written} representation into a representation of how the text is to be \emph{spoken}. In all real-world speech applications, the text normalization engine is developed---in large part---by hand. For example, a hand-built grammar may be used to enumerate the possible ways of saying a given token in a given language, and a statistical model used to select the most appropriate pronunciation in context. In this study we examine the tradeoffs associated with using more or less language-specific domain knowledge in a text normalization engine. In the most data-rich scenario, we have access to a carefully constructed hand-built normalization grammar that for any given token will produce a set of all possible verbalizations for that token. We also assume a corpus of aligned written-spoken utterances, from which we can train a ranking model that selects the appropriate verbalization for the given context. As a substitute for the carefully constructed grammar, we also consider a scenario with a language-universal normalization \emph{covering grammar}, where the developer merely needs to provide a set of lexical items particular to the language. As a substitute for the aligned corpus, we also consider a scenario where one only has the spoken side, and the corresponding written side is "hallucinated" by composing the spoken side with the inverted normalization grammar. We investigate the accuracy of a text normalization engine under each of these scenarios. We report the results of experiments on English and Russian.

cs.CL↗

arXiv2016

Node-By-Node Greedy Deep Learning for Interpretable Features

Multilayer networks have seen a resurgence under the umbrella of deep learning. Current deep learning algorithms train the layers of the network sequentially, improving algorithmic performance as well as providing some regularization. We present a new training algorithm for deep networks which trains \emph{each node in the network} sequentially. Our algorithm is orders of magnitude faster, creates more interpretable internal representations at the node level, while not sacrificing on the ultimate out-of-sample performance.

cs.LG↗

arXiv2015

On q-deformed infinite-dimensional n-algebra

The $q$-deformation of the infinite-dimensional $n$-algebra is investigated. Based on the structure of the $q$-deformed Virasoro-Witt algebra, we derive a nontrivial $q$-deformed Virasoro-Witt $n$-algebra which is nothing but a sh-$n$-Lie algebra. Furthermore in terms of the pseud-differential operators on the quantum plane, we construct the (co)sine $n$-algebra and the $q$-deformed $SDiff(T^2)$ $n$-algebra. We prove that they are the sh-$n$-Lie algebras for the case of even $n$. An explicit physical realization of the (co)sine $n$-algebra is given.

hep-th↗

arXiv2014

On $W_{1+\infty}$ 3-algebra and integrable system

We construct the $W_{1+\infty}$ 3-algebra and investigate the relation between this infinite-dimensional 3-algebra and the integrable systems. Since the $W_{1+\infty}$ 3-algebra with a fixed generator $W^0_0$ in the operator Nambu 3-bracket recovers the $W_{1+\infty}$ algebra, it is natural to derive the KP hierarchy from the Nambu-Poisson evolution equation. For the general case of the $W_{1+\infty}$ 3-algebra, we directly derive the KP and KdV equations from the Nambu-Poisson evolution equation with the different Hamiltonian pairs. We also discuss the connection between the $W_{1+\infty}$ 3-algebra and the dispersionless KdV equations. Due to the Nambu-Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of $W_{1+\infty}$ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized) nonlinear Schrödinger equation and give an application in optical soliton.

nlin.SI↗

arXiv2013

A diagrammatic categorification of the fermion algebra

In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional fermion algebra, and we investigate the properties of this category. The categorical analogues of the Fock states are some kind of 1-morphisms in our category, and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states. All the results in our categorical framework coincide exactly with those in normal quantum mechanics.

math-ph↗