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Yining Hu

Publications and source records attributed to Yining Hu.

31 records · Page 2Linked to original sources
arXiv2019

On the automaticity of sequences defined by continued fractions

Continued fraction expansions and Hankel determinants of automatic sequences are extensively studied during the last two decades. These studies found applications in number theory in evaluating irrationality exponents. The present paper is motivated by the converse problem: to study continued fractions of which the elements form an automatic sequence. We consider two such continued fractions defined by the Thue-Morse and period-doubling sequences respectively, and prove that they are congruent to algebraic series in $\mathbb{Z}[[x]]$ modulo $4$. Consequently, the sequences of the coefficients of the power series expansions of the two continued fractions modulo $4$ are $2$-automatic. Our approach is to first guess the explicit formulas of certain subsequences of $(P_n(x))$ and $(Q_n(x))$, where $P_n(x)/Q_n(x)$ is the canonical representation of the truncated continued fractions, then prove these formulas by an intricate induction involving eight subsequences while exploiting the relations between these subsequences.

math.CO↗
arXiv2019

Learning Sentence Embeddings for Coherence Modelling and Beyond

We present a novel and effective technique for performing text coherence tasks while facilitating deeper insights into the data. Despite obtaining ever-increasing task performance, modern deep-learning approaches to NLP tasks often only provide users with the final network decision and no additional understanding of the data. In this work, we show that a new type of sentence embedding learned through self-supervision can be applied effectively to text coherence tasks while serving as a window through which deeper understanding of the data can be obtained. To produce these sentence embeddings, we train a recurrent neural network to take individual sentences and predict their location in a document in the form of a distribution over locations. We demonstrate that these embeddings, combined with simple visual heuristics, can be used to achieve performance competitive with state-of-the-art on multiple text coherence tasks, outperforming more complex and specialized approaches. Additionally, we demonstrate that these embeddings can provide insights useful to writers for improving writing quality and informing document structuring, and assisting readers in summarizing and locating information.

cs.CL↗
arXiv2019

Blockchain-based Smart Contracts - Applications and Challenges

A blockchain-based smart contract or a "smart contract" for short, is a computer program intended to digitally facilitate the negotiation or contractual terms directly between users when certain conditions are met. With the advance in blockchain technology, smart contracts are being used to serve a wide range of purposes ranging from self-managed identities on public blockchains to automating business collaboration on permissioned blockchains. In this paper, we present a comprehensive survey of smart contracts with a focus on existing applications and challenges they face.

cs.CY↗
arXiv2018

On the automaticity of the Hankel determinants of a family of automatic sequences

Hankel determinants and automatic sequences are two classical subjects widely studied in Mathematics and Theoretical Computer Science. However, these two topics were considered totally independently, until in 1998, when Allouche, Peyrière, Wen and Wen proved that all the Hankel determinants of the Thue-Morse sequence are nonzero. This property allowed Bugeaud to prove that the irrationality exponents of the Thue-Morse-Mahler numbers are exactly 2. Since then, the Hankel determinants of several other automatic sequences, in particular, the paperfolding sequence, the Stern sequence, the period-doubling sequence, are studied by Coons, Vrbik, Guo, Wu, Wen, Bugeaud, Fu, Han, Fokkink, Kraaikamp, and Shallit. On the other hand, it is known that the Hankel determinants of a rational power series are ultimately zero, and the Hankel determinants of a quadratic power series over finite fields are ultimately periodic. It is therefore natural to ask if we can obtain similar results about the Hankel determinants of algebraic series. In the present paper, we provide a partial answer to this question by establishing the automaticity of the reduced Hankel determinants modulo $2$ of $\pm 1$-automatic sequences with kernel of cardinality at most $2$.

math.CO↗
arXiv2018

A Delay-Tolerant Payment Scheme Based on the Ethereum Blockchain

Banking as an essential service can be hard to access in remote, rural regions where the network connectivity is intermittent. Although micro-banking has been made possible by SMS or USSD messages in some places, their security flaws and session-based nature prevent them from a wider adoption. Global level cryptocurrencies enable low-cost, secure and pervasive money transferring among distributed peers, but are still limited in their ability to reach more people in remote communities. We proposed to take advantage of the delay-tolerant nature of blockchains to deliver banking services to remote communities that only connect to the broader Internet intermittently. Using a base station that offers connectivity within the local area, regular transaction processing is solely handled by blockchain miners. The bank only joins to process currency exchange requests, reward miners and track user balances when the connection is available. By distributing the verification and storage tasks among peers, our system design saves on the overall deployment and operational costs without sacrificing the reliability and trustwor- thiness. Through theoretical and empirical analysis, we provided insights to system design, tested its robustness against network disturbances, and demonstrated the feasibility of implementation on off-the-shelf computers and mobile devices.

cs.CY↗
arXiv2017

BreathRNNet: Breathing Based Authentication on Resource-Constrained IoT Devices using RNNs

Recurrent neural networks (RNNs) have shown promising results in audio and speech processing applications due to their strong capabilities in modelling sequential data. In many applications, RNNs tend to outperform conventional models based on GMM/UBMs and i-vectors. Increasing popularity of IoT devices makes a strong case for implementing RNN based inferences for applications such as acoustics based authentication, voice commands, and edge analytics for smart homes. Nonetheless, the feasibility and performance of RNN based inferences on resources-constrained IoT devices remain largely unexplored. In this paper, we investigate the feasibility of using RNNs for an end-to-end authentication system based on breathing acoustics. We evaluate the performance of RNN models on three types of devices; smartphone, smartwatch, and Raspberry Pi and show that unlike CNN models, RNN models can be easily ported onto resource-constrained devices without a significant loss in accuracy.

cs.CR↗
arXiv2016

Are wearable devices ready for HTTPS? Measuring the cost of secure communication protocols on wearable devices

The majority of available wearable devices require communication with Internet servers for data analysis and storage, and rely on a paired smartphone to enable secure communication. However, wearable devices are mostly equipped with WiFi network interfaces, enabling direct communication with the Internet. Secure communication protocols should then run on these wearables itself, yet it is not clear if they can be efficiently supported. In this paper, we show that wearable devices are ready for direct and secure Internet communication by means of experiments with both controlled and Internet servers. We observe that the overall energy consumption and communication delay can be reduced with direct Internet connection via WiFi from wearables compared to using smartphones as relays via Bluetooth. We also show that the additional HTTPS cost caused by TLS handshake and encryption is closely related to number of parallel connections, and has the same relative impact on wearables and smartphones.

cs.CR↗
arXiv2016

Explicit Implicit Function Theorem for All Fields

We give an explicit implicit function theorem for formal power series that is valid for all fields, which implies in particular Lagrange inversion formula and and Flajolet-Soria coefficient extraction formula known for fields of characteristic 0.

math.AC↗
arXiv2016

Combinatorial proof of the transcendence of $L(1,χ_s)/Π$

We give a combinatorial proof of the transcendence of $L(1,χ_s)/Π$, where $L(1,χ_s)$ (resp. $Π$) is the analogue in characteristic $p$ of the function $L$ of Dirichlet (resp. $π$). This result has been proven by G. Damamme using the criteria of de Mathan. Our proof is based on the Theorem of Christol and another property of $k$-automatic sequences.

math.CO↗
arXiv2016

Subword Complexity and (non)-automaticity of certain completely multiplicative functions

In this article, we prove that for a completely multiplicative function $f$ from $\mathbb{N}^*$ to a field $K$ such that the set $$\{p \;|\; f(p)\neq 1_K \;\mbox{and }p \mbox{ is prime}\}$$ is finite, the asymptotic subword complexity of $f$ is $Θ(n^t)$, where $t$ is the number of primes $p$ that $f(p)\neq 0_K, 1_K$. This proves in particular that sequences like $((-1)^{v_2(n)+v_3(n)})_n$ are not $k$-automatic for $k\geq 2$.

math.CO↗
arXiv2015

Coefficient Extraction Formula and Furstenberg's Theorems

In this article, using a Proposition of Furstenberg, we give a coefficient extraction formula for algebraic series that is valid for all fields, of which the Flajolet-Soria coefficient extraction formula for the complex field is a special case.

math.CO↗