Rate of inter-herd transmission of classical swine fever virus by different types of contact during the 1997-8 epidemic in The Netherlands

In this study we quanti®ed the rate at which classical swine fever had been transmitted by several different types of inter-herd contact during the 1997±8 epidemic in The Netherlands. During that epidemic 428 CSFV-infected pig herds were detected, 403 of which were include in this study. The estimated rates of transmission were 0±065 per shipment of live pigs, 0±011 per contact by a pig transportation lorry, 0±0068 per person contact, 0±0007 per dose of semen, 0±0065 per contact with a potentially contaminated pig assembly point, 0±027 per week per infected herd within a radius of 500 metres and 0±0078 per week per infected herd at a distance between 500 and 1000 metres. These transmission rates can be used to optimize the strategy to stop future epidemics of CSF in The Netherlands. In addition, the analysis demonstrated in this paper, can be used to quantify CSFV transmission rates from other epidemics

Smoothed Analysis of Tensor Decompositions

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and tensors analogs of much of the matrix algebra toolkit are unlikely to exist because of hardness results. Efficient decomposition in the overcomplete case (where rank exceeds dimension) is particularly challenging. We introduce a smoothed analysis model for studying these questions and develop an efficient algorithm for tensor decomposition in the highly overcomplete case (rank polynomial in the dimension). In this setting, we show that our algorithm is robust to inverse polynomial error -- a crucial property for applications in learning since we are only allowed a polynomial number of samples. While algorithms are known for exact tensor decomposition in some overcomplete settings, our main contribution is in analyzing their stability in the framework of smoothed analysis. Our main technical contribution is to show that tensor products of perturbed vectors are linearly independent in a robust sense (i.e. the associated matrix has singular values that are at least an inverse polynomial). This key result paves the way for applying tensor methods to learning problems in the smoothed setting. In particular, we use it to obtain results for learning multi-view models and mixtures of axis-aligned Gaussians where there are many more "components" than dimensions. The assumption here is that the model is not adversarially chosen, formalized by a perturbation of model parameters. We believe this an appealing way to analyze realistic instances of learning problems, since this framework allows us to overcome many of the usual limitations of using tensor methods.Comment: 32 pages (including appendix

New nonlinear dielectric materials: Linear electrorheological fluids under the influence of electrostriction

The usual approach to the development of new nonlinear dielectric materials focuses on the search for materials in which the components possess an inherently large nonlinear dielectric response. In contrast, based on thermodynamics, we have presented a first-principles approach to obtain the electrostriction-induced effective third-order nonlinear susceptibility for the electrorheological (ER) fluids in which the components have inherent linear, rather than nonlinear, responses. In detail, this kind of nonlinear susceptibility is in general of about the same order of magnitude as the compressibility of the linear ER fluid at constant pressure. Moreover, our approach has been demonstrated in excellent agreement with a different statistical method. Thus, such linear ER fluids can serve as a new nonlinear dielectric material.Comment: 11 page

Frequency down conversion through Bose condensation of light

We propose an experimental set up allowing to convert an input light of wavelengths about $1-2 \mu m$ into an output light of a lower frequency. The basic principle of operating relies on the nonlinear optical properties exhibited by a microcavity filled with glass. The light inside this material behaves like a 2D interacting Bose gas susceptible to thermalise and create a quasi-condensate. Extension of this setup to a photonic bandgap material (fiber grating) allows the light to behave like a 3D Bose gas leading, after thermalisation, to the formation of a Bose condensate. Theoretical estimations show that a conversion of $1 \mu m$ into $1.5 \mu m$ is achieved with an input pulse of about $1 ns$ with a peak power of $10^3 W$, using a fiber grating containing an integrated cavity of size about $500 \mu m \times 100 \mu m^2$.Comment: 4 pages, 1 figure

Intensity limits for stationary and interacting multi-soliton complexes

We obtain an accurate estimate for the peak intensities of multi-soliton complexes for a Kerr-type nonlinearity in the (1+1) - dimension problem. Using exact analytical solutions of the integrable set of nonlinear Schrodinger equations, we establish a rigorous relationship between the eigenvalues of incoherently-coupled fundamental solitons and the range of admissible intensities. A clear geometrical interpretation of this effect is given.Comment: 3 pages, 3 figure

Self-written waveguides in photopolymerizable resins

We study the optically-induced growth and interaction of self-written waveguides in a photopolymerizable resin. We investigate experimentally how the interaction depends on the mutual coherence and relative power of the input beams, and suggest an improved analytical model that describes the growth of single self-written waveguides and the main features of their interaction in photosensitive materials.Comment: 3 pages, 3 figure

Interaction of vector solitons with a nonlinear interface

We develop the analytical method of field momenta for analyzing the dynamics of optical vector solitons in photorefractive nonlinear media. First, we derive the effective evolution equations for the parameters of multi-component solitons composed of incoherently coupled beams and investigate the soliton internal oscillations associated with the relative motion of the soliton components. Then, we apply this method for analyzing the vector soliton scattering by a nonlinear interface. In particular, we show that a vector soliton can be reflected, transmitted, captured, or split into separate components, depending on the initial energy of its internal degree of freedom. The results are verified by direct numerical simulations of spatial optical solitons in photorefractive nonlinear media