A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency omega. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.

A semi-analytical theory of coastal upwelling and jet

The general forms of the conservation of momentum, temperature and potential vorticity of coastal ocean are obtained in the x-z plane for the nonlinear ocean circulation of Boussinesq fluid, and a elliptic type partial differential equations of second order are derived. Solution of the partial differential equations are obtained under the conditions that the fluid moves along the topography. The numerical results show that there exist both upwelling and downwelling along coastline that mainly depends on the large scale ocean condition. Numerically results of the upwelling (downwelling), coastal jet and temperature front zone are favorable to the observations.

Variation characteristics and ecological risk of heavy metals in the south Yellow Sea surface sediments

Eight cruises were conducted on the south Yellow Sea (SYS) from 1998 to 2005. Variations and the potential ecological risk of heavy metals were studied using the survey data collected during October 2003. The metal content (except for As) was high in the central area where the fine grain size sediments were dominant, and low inshore area where more coarse sediments were present. This suggested that grain size was important in determining distributions of heavy metals. In some local areas, other influencing factors, such as organic content, sedimentation rate, burial efficiency and metal's existing form were discussed. The annual averages of metals showed a stable trend with appreciable fluctuations in 8 years. Using potential ecological risk index (E (RI)) to evaluate the integrated pollution effect of heavy metals, 38.7% of the investigated area was in a moderate degree of contamination, while 77.8% was under moderate ecological risk. However, no distinct correlation was found between E (RI) and plankton biomass. In conclusion, the sediment quality of SYS was good, and the ecological risk was low in general.

Ecological basis of Alpine meadow ecosystem management in Tibet: Haibei Alpine Meadow Ecosystem Research Station

Alpine meadow and shrub are the main pasture types on the Tibetan Plateau, and they cover about 35% of the total land area. In order to understand the structural and functional aspects of the alpine ecosystem and to promote a sustainable animal production system, the Haibei Alpine Meadow Research Station was established in 1976. A series of intensive studies on ecosystem structure and function, including the energy flow and nutrient cycling of the ecosystem, were the main tasks during the first 10 years. Meanwhile, studies with 5 different grazing intensities on both summer and winter pasture have been conducted. In the early years of the 1990s, the research station started to focus its research work on global warming, biodiversity and sustainable animal production systems in pastoral areas. Various methods for improving degraded pasturelands have been developed in the region.

A Theory of Networks for Appxoimation and Learning

Learning an input-output mapping from a set of examples, of the type that many neural networks have been constructed to perform, can be regarded as synthesizing an approximation of a multi-dimensional function, that is solving the problem of hypersurface reconstruction. From this point of view, this form of learning is closely related to classical approximation techniques, such as generalized splines and regularization theory. This paper considers the problems of an exact representation and, in more detail, of the approximation of linear and nolinear mappings in terms of simpler functions of fewer variables. Kolmogorov's theorem concerning the representation of functions of several variables in terms of functions of one variable turns out to be almost irrelevant in the context of networks for learning. We develop a theoretical framework for approximation based on regularization techniques that leads to a class of three-layer networks that we call Generalized Radial Basis Functions (GRBF), since they are mathematically related to the well-known Radial Basis Functions, mainly used for strict interpolation tasks. GRBF networks are not only equivalent to generalized splines, but are also closely related to pattern recognition methods such as Parzen windows and potential functions and to several neural network algorithms, such as Kanerva's associative memory, backpropagation and Kohonen's topology preserving map. They also have an interesting interpretation in terms of prototypes that are synthesized and optimally combined during the learning stage. The paper introduces several extensions and applications of the technique and discusses intriguing analogies with neurobiological data.

Extensions of a Theory of Networks for Approximation and Learning: Outliers and Negative Examples

Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multi-dimensional function. From this point of view, this form of learning is closely related to regularization theory. In this note, we extend the theory by introducing ways of dealing with two aspects of learning: learning in the presence of unreliable examples and learning from positive and negative examples. The first extension corresponds to dealing with outliers among the sparse data. The second one corresponds to exploiting information about points or regions in the range of the function that are forbidden.

A Theory of How the Brain Might Work

I wish to propose a quite speculative new version of the grandmother cell theory to explain how the brain, or parts of it, may work. In particular, I discuss how the visual system may learn to recognize 3D objects. The model would apply directly to the cortical cells involved in visual face recognition. I will also outline the relation of our theory to existing models of the cerebellum and of motor control. Specific biophysical mechanisms can be readily suggested as part of a basic type of neural circuitry that can learn to approximate multidimensional input-output mappings from sets of examples and that is expected to be replicated in different regions of the brain and across modalities. The main points of the theory are: -the brain uses modules for multivariate function approximation as basic components of several of its information processing subsystems. -these modules are realized as HyperBF networks (Poggio and Girosi, 1990a,b). -HyperBF networks can be implemented in terms of biologically plausible mechanisms and circuitry. The theory predicts a specific type of population coding that represents an extension of schemes such as look-up tables. I will conclude with some speculations about the trade-off between memory and computation and the evolution of intelligence.

Motivated Action Theory: A Formal Theory of Causal Reasoning

When we reason about change over time, causation provides an implicit preference: we prefer sequences of situations in which one situation leads causally to the next, rather than sequences in which one situation follows another at random and without causal connections. In this paper, we explore the problem of temporal reasoning --- reasoning about change over time --- and the crucial role that causation plays in our intuitions. We examine previous approaches to temporal reasoning, and their shortcomings, in light of this analysis. We propose a new system for causal reasoning, motivated action theory, which builds upon causation as a crucial preference creterion. Motivated action theory solves the traditional problems of both forward and backward reasoning, and additionally provides a basis for a new theory of explanation.

Toward a Theory of Representation Design

This research is concerned with designing representations for analytical reasoning problems (of the sort found on the GRE and LSAT). These problems test the ability to draw logical conclusions. A computer program was developed that takes as input a straightforward predicate calculus translation of a problem, requests additional information if necessary, decides what to represent and how, designs representations capturing the constraints of the problem, and creates and executes a LISP program that uses those representations to produce a solution. Even though these problems are typically difficult for theorem provers to solve, the LISP program that uses the designed representations is very efficient.

Theory of Handwriting

Handwriting production is viewed as a constrained modulation of an underlying oscillatory process. Coupled oscillations in horizontal and vertical directions produce letter forms, and when superimposed on a rightward constant velocity horizontal sweep result in spatially separated letters. Modulation of the vertical oscillation is responsible for control of letter height, either through altering the frequency or altering the acceleration amplitude. Modulation of the horizontal oscillation is responsible for control of corner shape through altering phase or amplitude. The vertical velocity zero crossing in the velocity space diagram is important from the standpoint of control. Changing the horizontal velocity value at this zero crossing controls corner shape, and such changes can be effected through modifying the horizontal oscillation amplitude and phase. Changing the slope at this zero crossing controls writing slant; this slope depends on the horizontal and vertical velocity zero amplitudes and on the relative phase difference. Letter height modulation is also best applied at the vertical velocity zero crossing to preserve an even baseline. The corner shape and slant constraints completely determine the amplitude and phase relations between the two oscillations. Under these constraints interletter separation is not an independent parameter. This theory applies generally to a number of acceleration oscillation patterns such as sinusoidal, rectangular and trapezoidal oscillations. The oscillation theory also provides an explanation for how handwriting might degenerate with speed. An implementation of the theory in the context of the spring muscle model is developed. Here sinusoidal oscillations arise from a purely mechanical sources; orthogonal antagonistic spring pairs generate particular cycloids depending on the initial conditions. Modulating between cycloids can be achieved by changing the spring zero settings at the appropriate times. Frequency can be modulated either by shifting between coactivation and alternating activation of the antagonistic springs or by presuming variable spring constant springs. An acceleration and position measuring apparatus was developed for measurements of human handwriting. Measurements of human writing are consistent with the oscillation theory. It is shown that the minimum energy movement for the spring muscle is bang-coast-bang. For certain parameter values a singular arc solution can be shown to be minimizing. Experimental measurements however indicate that handwriting is not a minimum energy movement.