## Scientific Publications

### My articles

- Ia. V. Blagouchine and M.–A. Coppo.
“A note on some zeta-function related constants, Gregory coefficients and Ramanujan summation”.
*Manuscript draft*, 2017.

- Ia. V. Blagouchine.
“A note on some recent results for the Bernoulli numbers of the second kind”.
*Journal of Integer Sequences*, vol. 20, no. 3, Article 17.3.8, pp. 1-7, 2017.

- Ia. V. Blagouchine.
“Three notes on Ser's and Hasse's representations for the zeta-functions”, 2016.

- Ia. V. Blagouchine.
“Addendum to Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results”.
*The Ramanujan Journal (Springer)*, pp. 1-5, in press, DOI 10.1007/s11139-015-9763-z, 2016.

- Ia. V. Blagouchine. “Expansions of generalized Euler's constants into the series of polynomials in π
^{-2}and into the formal enveloping series with rational coefficients only”.*Journal of Number Theory (Elsevier)*, vol. 158 & 173, pp. 365–396 & 631–632, 2016.

- Ia. V. Blagouchine. “Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to π
^{-1}”.*Journal of Mathematical Analysis and Applications (Elsevier)*, vol. 442, no. 2, pp. 404–434, 2016.

- Ia. V. Blagouchine. “A theorem for the closed–form evaluation of the first generalized Stieltjes constant at rational arguments”.
*Journal of Number Theory (Elsevier)*, vol. 148 & vol. 151, pp. 537–592 & 276–277, 2015.

- Ia. V. Blagouchine. “Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results”.
*The Ramanujan Journal (Springer)*, vol. 35, no. 1, pp. 21–110, 2014.

- Ia. V. Blagouchine and E. Moreau.
“Comments on 'Unbiased estimates for moments and cumulants in linear regression'”.
*Journal of Statistical Planning and Inference (Elsevier)*, vol. 142, no. 4, pp. 1027–1030, 2012.

- Ia. V. Blagouchine and E. Moreau.
“Analytic Method for the Computation of the Total Harmonic Distortion by the Cauchy Method of Residues”.
*IEEE Transactions on Communications*, vol. 59, no. 9, pp. 2478–2491, 2011.

- Ia. V. Blagouchine and E. Moreau.
“Unbiased Efficient Estimator of the Fourth–Order Cumulant for Random Zero–Mean non–i.i.d. Signal: Particular Case of MA Stochastic Process”.
*IEEE Transactions on Information Theory*, vol. 56, no. 12, pp. 6450–6458, 2010.

- Ia. V. Blagouchine and E. Moreau.
“Control of a Speech Robot via an Optimum Neural–Network–Based Internal Model with Constraints”.
*IEEE Transactions on Robotics*, vol. 26, no. 1, pp. 142–159, 2010.

- Ia. V. Blagouchine and E. Moreau.
“Unbiased Adaptive Estimations of the Fourth–Order Cumulant for Real Random Zero–Mean Signal”.
*IEEE Transactions on Signal Processing*, vol. 57, no. 9, pp. 3330–3346, 2009.

*If you would like to have journal versions of my papers, you can ask them by writing me a kind e–mail.*

My

**h-index**is equal to

**5**accordingly to "Publish or Perish" and to

**4**accordingly to Scopus and to Mendeley.

### My contributions to the OEIS

#### I authored the following OEIS sequences

A269330, A262235, A262856, A262858, A262382, A262383, A262384, A262385, A262386, A262387, A256127, A256128, A256129, A257837, A257964, A257972, A257812, A257898, A257960, A263192, A263193, A270857, A270859, A268893, A268979, A268980, A268981, A268911, A268895, A268464, A269063, A256190, A256191, A256192, A269545, A257955, A269557, A256165, A256166, A256167, A255888, A256609, A255306, A256610, A256612, A256611, A256066, A256614, A256615, A256616, A269546, A257957, A269558, A269547, A257958, A257959, A269559,...#### and also contributed to

A001620, A058303, A065434, A115252, A195189, A000629, A002206, A002207, A075266, A002657, A002790, A006953, A099769, A088538, A030169, A030171, A155968, A254327, A254331, A254345, A254347, A254348, A251866, A254349, A254350, A255188, A255189, A257963,...### Reviewer of the Following Scientific Journals, Societies and Conferences

- Journal of Number Theory (Elsevier).
- Comptes–Rendus Mathematique (Elsevier).
- Journal of Mathematical Analysis and Applications (Elsevier).
- Computational Statistics & Data Analysis (Elsevier).
- American Mathematical Society (Mathematical Reviews).
- IEEE Transactions on Information Theory (IEEE TIT).
- IEEE Transactions on Signal Processing (IEEE TSP).
- Journal of the Acoustical Society of America (JASA).
- IEEE/ASME International Conference on Advanced Intelligent Mechatronics.
- IEEE Conference: Intelligent Robots and Systems (IROS).
- IEEE Conference: BioRob.

### My Ph.D. Thesis (with *summa cum laude*)

*Title*

Speech modeling and processing. Control of a Speech Robot via an Optimum Neural–Network–Based Internal Model with Constraints.
Statistical tools in speech processing.
*Abstract*

This Ph.D. dissertation deals with speech modeling and processing, which both share the speech quality aspect.
An optimum internal model with constraints is proposed and
discussed for the control of a biomechanical speech robot based on the equilibrium point
hypothesis (EPH, λ–model). It is supposed that the robot internal space is composed of the
motor commands λ of the equilibrium point hypothesis. The main idea of the work is that
the robot movements, and in particular the robot speech production, are carried out in such a
way that, the length of the path traveled in the internal space, is minimized, under acoustical
and mechanical constraints. Mathematical aspect of the problem leads to one of the problems
of variational calculus, the so–called geodesic problem, whose exact analytical solution is quite
complicated. By using some empirical findings, an approximate solution for the proposed optimum
internal model is then developed and implemented. It gives interesting and challenging
results, and shows that the proposed internal model is quite realistic; namely, some similarities
are found between the robot speech and the real one. Next, by aiming to analyze speech signal,
several methods of statistical speech signal processing are developed. They are based on higher–order statistics
(namely, on normalized central moments and on the fourth–order cumulant), as
well as on discrete normalized entropy. In this framework, we also designed an unbiased and
efficient estimator of the fourth–order cumulant in both batch and adaptive versions.
*Keywords*

Robotics, optimal and adaptive control, speech production, speech motor control,
optimum task planning, artificial intelligence, equilibrium point hypothesis (EPH, λ–model),
artificial neural networks (ANN), internal model, mathematical physics, variational calculus,
constrained optimization, geodesic problem, Euler–Lagrange equation, differential equations,
statistical signal processing, estimation, adaptive estimation, bias, MSE, higher–order statistics,
cumulants, moments, entropy.
*Acknowledgment*

Acknowledgment for the help and other things goes to the following persons (see electronic version of the Ph.D. dissertation for details):
Eric Moreau,
Salah Bourennane,
Yannick Deville,
Jean–Christophe Pesquet,
Michel Paindavoine,
Sylvain Maire,
Nicolas Maubec, Béatrice Marulier, Marina Schelkounova (Марина Щелкунова), Noëlle Maitre, Moustafa Belqasmi,
Alexei N. Popov (Алексей Н. Попов), Dimitri Andreevich Lissatchenko (Дмитрий Андреевич Лисаченко),
Sergei Nikolaevich Manida
(Сергей Николаевич Манида),
François Brut,
Nicolas André, Bleicke Holm, Guillaume Gibert, Romain Marret, Jacques Schneider, Bernard Xerri, Jean Barrère, Bruno Borloz,
Christian Tavernier,
Nadège Thirion–Moreau,
Paola Goatin,
Rémi Dubroca, Virginie Attina,
Antoine Serrurier,
Jana Brunner,
Luis Hernández Gómez,
Raphaëlle Lirou,
Caroline
Dufy,
Estelle Lezean,
and especially, to **my grand–farthers**.