Home Page for Sergei Skorik: research papers, voice activity detection (VAD), robust speech detector

Most of the sources of the papers below can be obtained in the postscript format from the e-print archive if you perform a search for the author "Skorik". The latest paper is available here in pdf format. To view it, you need Adobe Acrobat Reader v 4.0 or higher, which you can download for free:

Choose one of the topics: Speech recognition or Physics or Mathematics

On a cepstrum-based speech detector robust to white noise
with F.Berthommier: We study effects of additive white noise on the cepstral representation of speech signals. Distribution of each individual cepstrum coefficient of speech is shown to depend strongly on noise and to overlap significantly with the cepstrum distribution of noise. Based on these studies, we suggest a scalar quantity, V, equal to the sum of weighted cepstral coefficients, which is able to classify frames containing speech against noise-like frames. The distributions of V for speech and noise frames are reasonably well separated above SNR = 5 dB, demonstrating the feasibility of robust speech detector based on V.
"Speech and Computers" International Workshop, St-Petersburg, September 2000 pdf
On the optimal HMM command recognizer: A brief report on the research concentrated on improving a HMM-based one-word recognizer. The problem studied is achieving the highest recognition rate for selected commands simultaneously with the highest rejection rate for unexpected out-of-vocabulary sequences. The problem was tackled by studying several different topologies of HMM recognizer and trying on different training techniques.
internal Comverse report (1999)
On the implementation of Bayesian post-processing technique: internal Comverse report (1999)
Exactly unsolved problems of interacting 1D fermions: Applications of the integrable system techniques to the non-equilibrium transport problems are discussed. We describe one-dimensional electrons tunneling through a point-like defect either by the s-d exchange (Kondo) mechanism, or via the resonanse level (Anderson) mechanism. These models are potential candidates to be solved exactly in the presence of arbitrary external bias. We draw attention also to several mesoscopical systems which can be tackled by the massless form-factor approach, as perturbations of integrable models. The basic unperturbed model is the massless sine-Gordon model with the interaction (cosine) term restricted to one point, which is integrable. It is being perturbed by the second interaction term, which destroys integrability. Quasi-exact results can be obtained by making use of the basis of massless quasiparticles of the sine-Gordon model.
Exact non-equilibrium current from the partition function for impurity transport problems: We study the partition functions of quantum impurity problems in the domain of complex applied bias for its relation to the non-equilibrium current suggested by Fendley, Lesage and Saleur (cond-mat/9510055). The problem is reformulated as a certain generalization of the linear response theory that accomodates an additional complex variable. It is shown that the mentioned relation holds in a rather generic case in the linear response limit, or under certain condition out of equilibrium. This condition is trivially satisfied by the quadratic Hamiltonians and is rather restrictive for the interacting models. An example is given when the condition is violated.
Rhys. Rev. B (1998)
Exact current-current Green functions in strongly correlated 1D systems with impurity: We derive an exact expression for the Kubo conductance in the Quantum Hall device with the point-like intra-edge backscattering. This involves the calculation of current-current correlator exactly, which we perform using the form-factor method: the full set of intermediate states is inserted in the correlator, and for each term the closed mathematical expression is obtained. It is shown that by making a special choice of intermediate states in accordance with the hidden symmetries of the model, one achieves fast convergence of the series, thus proving the form-factor approach to be especially powerfull.
contribution to the German-Israel winter school on strongly correlated electron systems, Feb 21-28 1997
TOPICS IN TWO-DIMENSIONAL INTEGRABLE FIELD THEORIES WITH BOUNDARY INTERACTIONS
PhD dissertation: We study the issues related to the integrable field theories with boundary interactions. A close attention is drawn to the sine-Gordon model on the semi-infinite line with an additional term $M_B\sin\beta{\varphi-\varphi_0\over 2}$ at the boundary. In particular, we analyze the classical limit and construct solutions to the classical equations of motion, and then perform semi-classical quantization. The non-relativistic limit is shown to correspond to the Calogero-Moser model with a boundary potential. The exact solution is also given by employing the Bethe ansatz technique, and the classification of boundary bound states is done. We also introduce a general method for obtaining the ground state energy for the models on a finite interval with interactions at the boundary, which is inherited from the Destri-deVega method for periodic systems. We review some applications of integrable models to the condensed matter physics. Namely, the models where massless bulk excitations interact with an impurity are treated by means of the form-factor and massless scattering approach to obtain the exact expressions for the current-current correlators. The latter are related to the directly measurable quantities, such as conductivity in the Luttinger liquid with impurity, or magnetic susceptibility in the Kondo model. The purpose of this dissertation is to present new results in the field of two-dimensional physics, obtained by me and my collaborators in the course of my PhD research. Except for the introduction and a short review on impurity problems in condensed matter physics, the dissertation contains only original material, and led to 8 publications.
Form-factors approach to current correlations in one-dimensional systems with impurities
with F.Lesage and H.Saleur: We show how to compute analytically time and space dependent correlations in one dimensional quantum integrable systems with an impurity. Our approach is based on a description of these systems in terms of massless scattering of quasiparticles. Correlators follow then from matrix elements of local operators between multiparticle states, the ``massless form factors''. Although an infinite sum of these form factors has to be considered in principle, we find that for current, spin, and energy operators, only a few (typically two or three) are necessary to obtain an accuracy of more than $1\%$, for {\bf arbitrary coupling strength}, that is all the way from short to large distances. As examples we compute, at zero temperature, the frequency dependent conductance in a Luttinger liquid with impurity, the spectral function in the double well problem of dissipative quantum mechanics and part of the space dependent succeptibility in the Kondo model .
Nucl. Phys. B474 (1996) 602
Time correlations in 1D quantum impurity problems
with F.Lesage and H.Saleur: We develop in this letter an analytical approach using form-factors to compute time dependent correlations in integrable quantum impurity problems. As an example, we obtain for the first time the frequency dependent conductivity $G(\omega)$ for the tunneling between edges in the $\nu=1/3$ fractional quantum Hall effect, and the spectrum $S(\omega)$ of the spin-spin correlation in the the anisotropic Kondo model and equivalently in the double well system of dissipative quantum mechanics, both at vanishing temperature.
Phys. Rev. Lett. 76 (1996) 3388
Surface excitations and surface energy of the antiferromagnetic XXZ chain by the Bethe ansatz approach
with A.Kapustin: We study boundary bound states using the Bethe ansatz formalism for the open $XXZ$ $(\Delta>1)$ chain in a boundary magnetic field $h$. Boundary bound states are represented by the ``boundary strings'' similar to those described in \cite{SS}. We find that for certain values of $h$ the ground state wave function contains boundary strings, and from this infer the existence of two ``critical'' fields in agreement with \cite{MJ}. An expression for the vacuum surface energy in the thermodynamic limit is derived and found to be an analytic function of $h$. We argue that boundary excitations appear only in pairs with ``bulk'' excitations or with boundary excitations at the other end of the chain. We mainly discuss the case where the magnetic fields at the left and the right boundaries are antiparallel, but we also comment on the case of the parallel fields. In the Ising ($\Delta=\infty$) and isotropic ($\Delta=1$) limits our results agree with those previously known.
J.Phys.A29 (1996) 1629
Boundary energy and boundary states in integrable quantum field theories
with A.LeClair, G.Mussardo and H.Saleur: We study the ground state energy of integrable $1+1$ quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new, ``R-channel TBA'', where the boundary is represented by a boundary state, and the thermodynamics involves evaluating scalar products of boundary states with all the states of the theory. In the non-scalar, sine-Gordon case, this is done by generalizing the method of Destri and De Vega. The two approaches are compared. Miscellaneous other results are obtained, in particular formulas for the overall normalization and scalar products of boundary states, exact partition functions for the critical Ising model in a boundary magnetic field, and also results for the energy, excited states and boundary S-matrix of $O(n)$ and minimal models.
Nucl.Phys.B453 (1995) 581
Boundary bound states and boundary bootstrap in the sine-Gordon model with Dirichlet boundary conditions
with H.Saleur: We present a complete study of boundary bound states and related boundary S-matrices for the sine-Gordon model with Dirichlet boundary conditions. Our approach is based partly on the bootstrap procedure, and partly on the explicit solution of the inhomogeneous XXZ model with boundary magnetic field and of the boundary Thirring model. We identify boundary bound states with new ``boundary strings'' in the Bethe ansatz. The boundary energy is also computed.
J.Phys.A28 (1995) 6605
On the non-relativistic limit of the quantum sine-Gordon model with integrable boundary condition
with A.Kapustin: We show that the the generalized Calogero-Moser model with boundary potential of the P\"oschl-Teller type describes the non-relativistic limit of the quantum sine-Gordon model on a half-line with Dirichlet boundary condition.
Phys.Lett. A196 (1994) 47
The boundary sine-Gordon model: classical and semi-classical analysis
with H.Saleur and N.Warner: We consider the sine-Gordon model on a half-line, with an additional potential term of the form $-M\cos{\beta\over 2}(\varphi-\varphi_0)$ at the boundary. We compute the classical time delay for general values of $M$, $\beta$ and $\varphi_0$ using $\tau$-function methods and show that in the classical limit, the method of images still works, despite the non-linearity of the problem. We also perform a semi-classical analysis, and find agreement with the exact quantum S-matrix conjectured by Ghoshal and Zamolodchikov.
Nucl.Phys.B441 (1995) 421
Solution of the Thirring model with imaginary mass and massless scattering
with H.Saleur: The Thirring model with imaginary mass (or the sine-Gordon model with imaginary coupling) is deeply related to all the flows between minimal conformal theories. We solve this model explicitely using the Bethe ansatz. We find that there are Left and Right moving massless excitations with non trivial LR scattering. We compute the S matrix and recover the result conjectured by Fendley et al.
Phys.Lett. B336 (1994) 205
On the spectra of hyperelliptic potentials
with V.Spiridonov: A simple formula for the spectra of singular hyperelliptic potentials is derived with the help of the dressing method. Relation with the self-similar potentials at roots of unity is discussed.
Phys.Lett. A 190 (1994) 90
Self-Similar potentials and the q-oscillator algebra at roots of unity
with V.Spiridonov: Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schr\"odinger equation provide bases of representations of the $q$-deformed Heisenberg-Weyl algebra. When the parameter $q$ is a root of unity the functional form of the potentials can be found explicitly. The general $q^3=1$ and the particular $q^4=1$ potentials are given by the equianharmonic and (pseudo)lemniscatic Weierstrass functions respectively.
Lett.Math.Phys. 28 (1993) 59