Talk 1: Convolutional neural networks against the curse of dimensionality

Convolutional Neural Networks are a powerful class of non-linear representations that have shown through numerous supervised learning tasks their ability to extract rich information from images, speech and text, with excellent statistical generalization. These are examples of truly high-dimensional signals, in which classical statistical models suffer from the curse of dimensionality, referring to their inability to generalize well unless provided with exponentially large amounts of training data. In this talk we will start by studying statistical models defined from wavelet scattering networks, a class of CNNs where the convolutional filter banks are given by complex, multi-resolution wavelet families. The reasons for such success lie on their ability to preserve discriminative information while being stable with respect to high-dimensional deformations, providing a framework that partially extends to trained CNNs. We will give conditions under which signals can be recovered from their scattering coefficients, and will discuss a family of Gibbs processes defined by CNN sufficient statistics, from which one can sample image and auditory textures. Although the scattering recovery is non-convex and corresponds to a generalized phase recovery problem, gradient descent algorithms show good empirical performance and enjoy weak convergence properties. We will discuss connections with non-linear compressed sensing, applications to texture synthesis, inverse problems such as super-resolution, as well as an application to sentence modeling, where convolutions are generalized using associative trees to generate robust sentence representations

Automorphic Lie Algebras and Cohomology of Root Systems

A cohomology theory of root systems emerges naturally in the context of Automorphic Lie Algebras, where it helps formulating some structure theory questions. In particular, one can find concrete models for an Automorphic Lie Algebra by integrating cocycles. In this paper we define this cohomology and show its connection with the theory of Automorphic Lie Algebras. Furthermore, we discuss its properties: we define the cup product, we show that it can be restricted to symmetric forms, that it is equivariant with respect to the automorphism group of the root system, and finally we show acyclicity at dimension two of the symmetric part, which is exactly what is needed to find concrete models for Automorphic Lie Algebras. Furthermore, we show how the cohomology of root systems finds application beyond the theory of Automorphic Lie Algebras by applying it to the theory of contractions and filtrations of Lie algebras. In particular, we show that contractions associated to Cartan $\mathbb{Z}$-filtrations of simple Lie algebras are classified by $2$-cocycles, due again to the vanishing of the symmetric part of the second cohomology group.Comment: 26 pages, standard LaTeX2

The economics of private equity investment : a symposium sponsored by the Center for the Study of Innovation and Productivity, Federal Reserve Bank of San Francisco, October 19, 2007

Capital market ; Financial markets ; Securities

Faster Calculation of Superquadric Shapes

Nonparametric methods of calculating points on the curve produce the recently introduced superquadric objects at great savings in time

Network power flow analysis for a high penetration of distributed generation

Increasing numbers of very small generators are being connected to electricity distribution systems around the world. Examples include photovoltaics (PV) and gas-fired domestic-scale combined heat and power (micro-CHP) systems, with electrical outputs in the region of 1 to 2 kW. These generators are normally installed within consumers' premises and connected to the domestic electricity supply network (230 V single-phase in Europe, 120 V in North America). There is a growing need to understand and quantify the technical impact that high penetrations of such generators may have on the operation of distribution systems. This paper presents an approach to analyzing this impact together with results indicating that considerable penetrations of micro-generation can be accommodated in a typical distribution system

Modeling of tuning of microresonator filters by perturbational evaluation of cavity mode phase shifts

Microresonator filters, realized by evanescent coupling of circular cavities with two parallel bus waveguides, are promising candidates for applications in dense wavelength division multiplexing. Tunability of these filters is an essential feature for their successful deployment. In this paper we present a framework for modeling of tuning of the microresonators by changes of their cavity core refractive index. Using a reciprocity theorem, a perturbational expression for changes in the cavity propagation constants due to slight modifications of the cavity core refractive index is derived. This expression permits to analytically calculate shifts in spectral response of the 2D resonators. Comparisons of the resultant shifts and spectra with direct simulations based on coupled mode theory show satisfactory agreement

Effects of Soret, Dufour, chemical reaction, thermal radiation and volumentric heat generation/absorption on mixed convection stagnation point flow on an Iso-thermal vertical plate in porous media

A mathematical model is analyzed in order to study the effects of Soret, Dufour, chemical reaction, thermal radiation and volumentric heat generation/absorption on mixed convection stagnation point flow on an Iso-thermal vertical plate in a porous media. The governing partial differential equations are transformed into set of coupled ordinary differential equations, which are solved numerically using Runge-Kutta sixth order method along with shooting technique. The physical interpretation to this expression is assigned through graphs and tables for the wall shear stress , Nusselt number and Sherwood number . Results were compared with the existing literature and showed a perfect agreement. Similarly, results showed that the fields were influenced appreciably by the effects of the governing parameters: Soret number Sr, Dufour number Df, chemical reaction parameter γ, thermal radiation parameter Ra, order of reactions n, thermal Grashof number GT, solutal Grashof number GC, Prandtl number Pr, permeability parameter K, rate of heat generation/absorption parameter S, and magnetic field strength parameter M. It was evident that for some kind of mixtures such as the light and medium molecular weight, the Soret and Dufour’s effects should be considered as well

Increasing security of supply by the use of a local power controller during large system disturbances

This paper describes intelligent ways in which distributed generation and local loads can be controlled during large system disturbances, using Local Power Controllers. When distributed generation is available, and a system disturbance is detected early enough, the generation can be dispatched, and its output power can be matched as closely as possible to local microgrid demand levels. Priority-based load shedding can be implemented to aid this process. In this state, the local microgrid supports the wider network by relieving the wider network of the micro-grid load. Should grid performance degrade further, the local microgrid can separate itself from the network and maintain power to the most important local loads, re-synchronising to the grid only after more normal performance is regained. Such an intelligent system would be a suitable for hospitals, data centres, or any other industrial facility where there are critical loads. The paper demonstrates the actions of such Local Power Controllers using laboratory experiments at the 10kVA scale

Stabilization of grid frequency through dynamic demand control

Frequency stability in electricity networks is essential to the maintenance of supply quality and security. This paper investigates whether a degree of built-in frequency stability could be provided by incorporating dynamic demand control into certain consumer appliances. Such devices would monitor system frequency (a universally available indicator of supply-demand imbalance) and switch the appliance on or off accordingly, striking a compromise between the needs of the appliance and the grid. A simplified computer model of a power grid was created incorporating aggregate generator inertia, governor action and load-frequency dependence plus refrigerators with dynamic demand controllers. Simulation modelling studies were carried out to investigate the system's response to a sudden loss of generation, and to fluctuating wind power. The studies indicated a significant delay in frequency-fall and a reduced dependence on rapidly deployable backup generation

Pattern formation in large domains

Pattern formation is a phenomenon that arises in a wide variety of physical, chemical and biological situations. A great deal of theoretical progress has been made in understanding the universal aspects of pattern formation in terms of amplitudes of the modes that make up the pattern. Much of the theory has sound mathematical justification, but experiments and numerical simulations over the last decade have revealed complex two-dimensional patterns that do not have a satisfactory theoretical explanation. This paper focuses on quasi-patterns, where the appearance of small divisors causes the standard theoretical method to fail, and ends with a discussion of other outstanding problems in the theory of two-dimensional pattern formation in large domains