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In this paper we consider the time dependent Peierls-Nabarro model in dimension one. This model is a semi-linear integro-differential equation associated to the half Laplacian. This model describes the evolution of phase transitions…
Converting input symbols to output audio in TTS requires modelling the durations of speech sounds. Leading non-autoregressive (NAR) TTS models treat duration modelling as a regression problem. The same utterance is then spoken with…
Speech production is a dynamic procedure, which involved multi human organs including the tongue, jaw and lips. Modeling the dynamics of the vocal tract deformation is a fundamental problem to understand the speech, which is the most common…
The standard Large Deviation Theory (LDT) is mathematically illustrated by the Boltzmann-Gibbs factor which describes the thermal equilibrium of short-range-interacting many-body Hamiltonian systems, the velocity distribution of which is…
In this paper, we introduce FITS, a lightweight yet powerful model for time series analysis. Unlike existing models that directly process raw time-domain data, FITS operates on the principle that time series can be manipulated through…
As speakers turn their thoughts into sentences, they maintain a balance between the complexity of words and syntax. However, it is unclear whether this syntax-lexicon tradeoff is unique to the spoken language production that is under the…
Time dependent entropy of constant force motion is investigated. Their joint entropy so called Leipnik's entropy is obtained. The main purpose of this work is to calculate Leipnik's entropy by using time dependent wave function which is…
The Levy-flight dynamics can stem from simple random walks in a system whose operational time (number of steps n) typically grows superlinearly with physical time t. Thus, this processes is a kind of continuous-time random walks (CTRW),…
The human society is a very complex system; still, there are several non-trivial, general features. One type of them is the presence of power-law distributed quantities in temporal statistics. In this Letter, we focus on the origin of…
Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the…
Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes…
We present a new neural text to speech (TTS) method that is able to transform text to speech in voices that are sampled in the wild. Unlike other systems, our solution is able to deal with unconstrained voice samples and without requiring…
This brief note complements some results regarding a recently developed technique for the stability analysis of linear time-invariant, time delay systems using the matrix Lambert W function. By means of a numeric example, it is shown that…
The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has…
Text-to-speech (TTS) synthesis is the process of producing synthesized speech from text or phoneme input. Traditional TTS models contain multiple processing steps and require external aligners, which provide attention alignments of…
Stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear…
To characterize the regularity of distribution-path dependent SDEs in the initial distribution which varies in the class of probability measures on the path space, we introduce the intrinsic and Lions derivatives for probability measures on…
The human vocal folds are known to interact with the vocal tract acoustics during voiced speech production; namely a nonlinear source-filter coupling has been observed both by using models and in \emph{in vivo} phonation. These phenomena…
For most stochastic dynamical systems, variables which are tightly regulated tend to respond slowly to external changes. This idea is often discussed for applicable systems, within a linear response regime, through the Fluctuation…
How to distinguish and quantify deterministic and random influences on the statistics of turbulence data in meteorology cases is discussed from first principles. Liquid water path (LWP) changes in clouds, as retrieved from radio signals,…