Non-parametric Estimation of Stochastic Differential Equations with Sparse Gaussian Processes

The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a non-parametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudo-samples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behaviour of complex systems

Evidence of two effects in the size segregation process in a dry granular media

submitted to Physical Review E (february 2004)In a half-filled rotating drum, the size segregation of particles of equal density builds a ring pattern of the large particles, whose location continuously varies from the periphery to the center depending on the size ratio between particles [Thomas, Phys. Rev. E 62, 1 (2000) 961-974]. For small size ratios (typically15): large beads are close to the bottom in a reversing position. The existence of circles with an intermediate radius shows that the segregation at an intermediate level within a flow is possible. In this paper, we experimentally study the segregation of particles of different densities and sizes in a half-filled rotating drum and other devices (chute flow, pile). In the drum, the location of the segregated ring continuously varies from the periphery to the center and is very sensitive to both the size (from 1 to 33) and density (from 0.36 to 4.8) ratios. The densest large beads segregate on a circle close to the center, the lightest large beads on a circle close to the periphery. Consequently, we found that for any tracer, its excess of mass, due to only a size excess, a density excess, or both, leads to a deep inside segregation of the tracer. There is a push-away process that makes heavy beads of any type go downwards, while the excess of size is already known to push large beads towards the surface, by a dynamical sieving process. Each segregation at an intermediate ring corresponds to a balance between these mass and geometrical effects. The segregation level in the flow is determined by the ratio of the intensities of both effects

Granular Flows in a Rotating Drum: the Scaling Law between Velocity and Thickness of the Flow

The flow of dry granular material in a half-filled rotating drum is studied. The thickness of the flowing zone is measured for several rotation speeds, drum sizes and beads sizes (size ratio between drum and beads ranging from 47 to 7400). Varying the rotation speed, a scaling law linking mean velocity vs thickness of the flow, $v\sim h^m$, is deduced for each couple (beads, drum). The obtained exponent $m$ is not always equal to 1, value previously reported in a drum, but varies with the geometry of the system. For small size ratios, exponents higher than 1 are obtained due to a saturation of the flowing zone thickness. The exponent of the power law decreases with the size ratio, leading to exponents lower than 1 for high size ratios. These exponents imply that the velocity gradient of a dry granular flow in a rotating drum is not constant. More fundamentally, these results show that the flow of a granular material in a rotating drum is very sensible to the geometry, and that the deduction of the ``rheology'' of a granular medium flowing in such a geometry is not obvious

Microcredit: MSMEs and Sustainable Development

Microcredit and microfinance are distinct concepts. Doing microcredit part of microfinance. The concept of microcredit is due to Grameen Bank’s founder Muhammad Yunus and started in Bangladesh in 1976. Microcredit is a financial instrument that provides small loans to low-income people without access to formal financing. Moreover, it has been evolving intending to contribute to poverty alleviation, support entrepreneurship, and empowerment of women, combating economic and social exclusion globally. It has an impact in terms of microbusinesses financing and thus on funding MSMEs, which will impact the growth of economies. The evolution of the concept has enabled microcredit to contribute to improving global sustainability levels

On the Rational Type 0f Moment Angle Complexes

In this note it is shown that the moment angle complexes Z(K;(D^2,,S^1)) which are rationally elliptic are a product of odd spheres and a diskComment: This version avoids the use of an incorrect result from the literature in the proof of Theorem 1.3. There is some text overlap with arXiv:1410.645

Faint laser quantum key distribution: Eavesdropping exploiting multiphoton pulses

The technological possibilities of a realistic eavesdropper are discussed. Two eavesdropping strategies taking profit of multiphoton pulses in faint laser QKD are presented. We conclude that, as long as storage of Qubits is technically impossible, faint laser QKD is not limited by this security issue, but mostly by the detector noise.Comment: 7 pages, 6 figure

Early stages of LDL oxidation: apolipoprotein B structural changes monitored by infrared spectroscopy.

Changes in the conformation of apoliprotein B-100 in the early stages of copper-mediated low density lipoprotein oxidation have been monitored by infrared spectroscopy. During the lag phase no variation in structure is observed, indicating that copper binding to the protein does not significantly affect its structure. In the propagation phase, while hydroperoxides are formed but the protein is not modified, no changes in secondary structure are observed, but the thermal profile of the band corresponding to alpha-helix is displaced in frequency, indicating changes in tertiary structure associated with this conformation but not with beta-sheet components. When aldehyde formation starts, a decrease of approximately 3% in the area of bands corresponding to alpha-helix and beta-sheet is produced, concomitantly with an increase in beta-turns and unordered structure. The two bands corresponding to beta-turns vary as well under these conditions, indicating changes in these structures. Also at this stage the thermal profile shows variations in frequency for the bands corresponding to both alpha-helix and beta-sheet.The results are consistent with the hypothesis that as soon as the polyunsaturated fatty acids from the particle core are modified, this change is reflected at the surface, in the alpha-helical components contacting the monolayer.Fil: Chehin, Rosana Nieves. Consejo Superior de Investigaciones Científicas; España. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto Superior de Investigaciones Biológicas. Universidad Nacional de Tucumán. Instituto Superior de Investigaciones Biológicas; Argentina. Universidad del País Vasco; EspañaFil: Rengel, David. Consejo Superior de Investigaciones Científicas; España. Universidad del País Vasco; EspañaFil: Milicua, José Carlos G.. Universidad del País Vasco; España. Consejo Superior de Investigaciones Científicas; EspañaFil: Goñi, Félix M.. Universidad del País Vasco; España. Consejo Superior de Investigaciones Científicas; EspañaFil: Arrondo JL. Consejo Superior de Investigaciones Científicas; España. Universidad del País Vasco; EspañaFil: Pifat, Greta. Rudjer Bošković Institute; Croaci

Graph products of spheres, associative graded algebras and Hilbert series

Given a finite, simple, vertex-weighted graph, we construct a graded associative (non-commutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to edges. We show that the Hilbert series of this algebra is the inverse of the clique polynomial of the graph. Using this result it easy to recognize if the ideal is inert, from which strong results on the algebra follow. Non-commutative Grobner bases play an important role in our proof. There is an interesting application to toric topology. This algebra arises naturally from a partial product of spheres, which is a special case of a generalized moment-angle complex. We apply our result to the loop-space homology of this space.Comment: 19 pages, v3: elaborated on connections to related work, added more citations, to appear in Mathematische Zeitschrif