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Pair Correlations and Random Walks on the Integers

REFERENCES [KN] KUIPERS, L.—NIEDERREITER, H.: Uniform Distribution of Sequences . Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. [NP] NAIR, R.—POLLICOTT, M.: On pair correlations of sequences in higher dimensions , Israel J. Math. 157 (2007), no. 1, 219–238. [Sp] SPITZER, F. L.: Principles of Random Walks . Second ed. Graduate Texts in Mathematics, Vol. 34. Springer-Verlag, New York-Heidelberg, 1976. [St] STONE, C. T.: On local and ratio limit theorems , in: Proc. of the Fifth

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From dynamics to links: a sparse reconstruction of the topology of a neural network

: Experimental evidence and modeling of a slow k+-dependent mechanism, Journal of Neuroscience , vol. 21, no. 3, pp. 759–770, 2001. 19. T. Nieus, E. Sola, J. Mapelli, E. Saftenku, P. Rossi, and D. E., Ltp regulates burst initiation and frequency at mossy fiber-granule cell synapses of rat cerebellum: experimental observations and theoretical predictions., J Neurophysiol , vol. 95, pp. 686–699, Feb 2006. 20. M. Garofalo, T. Nieus, P. Massobrio, and M. S., Evaluation of the performance of information theory-based methods and cross-correlation to estimate the

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A simplex method for the calibration of a MEG device

Abstract

MagnetoEncephaloGraphy (MEG) devices are helmet–shaped arrays of sensors that measure the tiny magnetic fields produced by neural currents. As they operate at low temperature, they are typically immersed in liquid helium. However, during the cooling process the sensor position and shape can change, with respect to nominal values, due to thermal stress. This implies that an accurate sensor calibration is required before a MEG device is utilized in either neuroscientific research or clinical workflow. Here we describe a calibration scheme developed for the optimal use of a MEG system recently realized at the “Istituto di Cibernetica e Biofisica” of the Italian CNR. To achieve the calibration goal a dedicated magnetic source is used (calibration device) and the geometric parameters of the sensors are determined through an optimisation procedure, based on the Nelder-Mead algorithm, which maximises the correlation coefficient between the predicted and the recorded magnetic field. Then the sensitivity of the sensors is analytically estimated. The developed calibration procedure is validated with synthetic data mimicking a real scenario.

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Dynamics of a bubble rising in gravitational field

, Generalized correlation for bubble motion, AIChE J. , vol. 47, no. 1, pp. 39–44, 2001. 13. J. M. Gordillo, B. Lalanne, F. Risso, D. Legendre, and S. Tanguy, Unsteady rising of clean bubble in low viscosity liquid, Bubble Science, Engineering and Technology , vol. 4, no. 1, pp. 4–11, 2012. 14. G. S. Tuteja, D. Khattar, B. B. Chakraborty, and S. Bansal, Study of an expanding, spherical gas bubble in a liquid under gravity when the centre moves in a vertical plane, Int. J. Contemp. Math. Sciences , vol. 5, no. 22, pp. 1065––1075, 2010. 15. G. K. Batchelor

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The chord length distribution function of a non-convex hexagon

/baeselrea.pdf 3. Salvino Ciccariello: The isotropic correlation function of plane figures: the triangle case, Journal of Physics: Conference Series 24 (2010) 012014, XIV International Conference on Small-Angle Scattering (SAS09), 1-10. http://iopscience.iop.org/article/10.1088/1742-6596/247/1/012014/pdf 4. Vincenzo Conserva, Andrei Duma: Schnitte eine regulären Hexagons im Bufion- und Laplace-Gitter, Fernuniversität Hagen: Seminarberichte aus der Fakultät für Mathematik und Informatik, 78 (2007), 29-36. 5. Andrei Duma, Sebastiano Rizzo: Chord

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On the Pseudorandomness of the Liouville Function of Polynomials over a Finite Field

REFERENCES [1] BRANDSTÄTTER, N.—WINTERHOF, A.: Linear complexity profile of binary sequences with small correlation measure , Period. Math. Hungar. 52 (2006), no. 2, 1–8. [2] CARLITZ, L.: The arithmetic of polynomials in a Galois field , Amer. J.Math. 54 (1932), no. 1, 39-50. [3] CARMON, D.—RUDNICK, Z.: The autocorrelation of the Möbius function and Chowla’s conjecture for the rational function field , Q. J. Math. 65 (2014), no. 1, 53–61. [4] CASSAIGNE J.—FERENCZI, S.—MAUDUIT, C.—RIVAT, J.—SÁRKÖZY, A.: On finite pseudorandom

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Questions Around the Thue-Morse Sequence

Abstract

We intend to unroll the surprizing properties of the Thue-Morse sequence with a harmonic analysis point of view, and mention in passing some related open questions.

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A Note on the Continued Fraction of Minkowski

Abstract

Denote by Θ12, · · · the sequence of approximation coefficients of Minkowski’s diagonal continued fraction expansion of a real irrational number x. For almost all x this is a uniformly distributed sequence in the interval [0, 1/2 ]. The average distance between two consecutive terms of this sequence and their correlation coefficient are explicitly calculated and it is shown why these two values are close to 1/6 and 0, respectively, the corresponding values for a random sequence in [0, 1/2].

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Discrepancy Results for The Van Der Corput Sequence

.—PILLICHSHAMMER, F.: Sums of distances to the nearest integer and the discrepancy of digital nets , Acta Arith. 106 (2003), no. 4, 379–408. [16] LEHMER, D. H.: On Stern’s Diatomic Series , Amer. Math. Monthly 36 (1929), no. 2, 59–67. [17] LIND, D. A.: An extension of Stern’s diatomic series , Duke Math. J. 36 (1969), 55–60. [18] MORGENBESSER, J. F.—SPIEGELHOFER, L.: A reverse order property of correlation measures of the sum-of-digits function , Integers, 12 (2012), Paper No. A47. [19] F. PILLICHSHAMMER, F.: On the discrepancy of (0, 1

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Pierre Liardet (1943–2014)

for binary strings with low aperiodic auto-correlations , Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 2936, Springer-Berlin, 2004, pp. 39–50. [L41] B arat , G.—L iardet , P.: Dynamical systems originated in the Ostrowski alpha-expansion , Ann. Univ. Sci. Budapest. Sect. Comput. 24 (2004), 133–184. [L42] G rabner , P. J.—L iardet , P.—T ichy , R. F.: Spectral disjointness of dynamical systems related to some arithmetic functions , Publ. Math. Debrecen 66

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