A Connection Between GRBF and MLP

Both multilayer perceptrons (MLP) and Generalized Radial Basis Functions (GRBF) have good approximation properties, theoretically and experimentally. Are they related? The main point of this paper is to show that for normalized inputs, multilayer perceptron networks are radial function networks (albeit with a non-standard radial function). This provides an interpretation of the weights w as centers t of the radial function network, and therefore as equivalent to templates. This insight may be useful for practical applications, including better initialization procedures for MLP. In the remainder of the paper, we discuss the relation between the radial functions that correspond to the sigmoid for normalized inputs and well-behaved radial basis functions, such as the Gaussian. In particular, we observe that the radial function associated with the sigmoid is an activation function that is good approximation to Gaussian basis functions for a range of values of the bias parameter. The implication is that a MLP network can always simulate a Gaussian GRBF network (with the same number of units but less parameters); the converse is true only for certain values of the bias parameter. Numerical experiments indicate that this constraint is not always satisfied in practice by MLP networks trained with backpropagation. Multiscale GRBF networks, on the other hand, can approximate MLP networks with a similar number of parameters.

Surface Reflectance Estimation and Natural Illumination Statistics

Humans recognize optical reflectance properties of surfaces such as metal, plastic, or paper from a single image without knowledge of illumination. We develop a machine vision system to perform similar recognition tasks automatically. Reflectance estimation under unknown, arbitrary illumination proves highly underconstrained due to the variety of potential illumination distributions and surface reflectance properties. We have found that the spatial structure of real-world illumination possesses some of the statistical regularities observed in the natural image statistics literature. A human or computer vision system may be able to exploit this prior information to determine the most likely surface reflectance given an observed image. We develop an algorithm for reflectance classification under unknown real-world illumination, which learns relationships between surface reflectance and certain features (statistics) computed from a single observed image. We also develop an automatic feature selection method.

Application of metabolomics to plant genotype discrimination using statistics and machine learning

Janet Taylor, Ross D King, Thomas Altmann and Oliver Fiehn (2002). Application of metabolomics to plant genotype discrimination using statistics and machine learning. 1st European Conference on Computational Biology (ECCB). (published as a journal supplement in Bioinformatics 18: S241-S248).

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

A Bayesian Approach for TCP to Distinguish Congestion from Wireless Losses

(This Technical Report revises TR-BUCS-2003-011) The Transmission Control Protocol (TCP) has been the protocol of choice for many Internet applications requiring reliable connections. The design of TCP has been challenged by the extension of connections over wireless links. In this paper, we investigate a Bayesian approach to infer at the source host the reason of a packet loss, whether congestion or wireless transmission error. Our approach is "mostly" end-to-end since it requires only one long-term average quantity (namely, long-term average packet loss probability over the wireless segment) that may be best obtained with help from the network (e.g. wireless access agent).Specifically, we use Maximum Likelihood Ratio tests to evaluate TCP as a classifier of the type of packet loss. We study the effectiveness of short-term classification of packet errors (congestion vs. wireless), given stationary prior error probabilities and distributions of packet delays conditioned on the type of packet loss (measured over a larger time scale). Using our Bayesian-based approach and extensive simulations, we demonstrate that congestion-induced losses and losses due to wireless transmission errors produce sufficiently different statistics upon which an efficient online error classifier can be built. We introduce a simple queueing model to underline the conditional delay distributions arising from different kinds of packet losses over a heterogeneous wired/wireless path. We show how Hidden Markov Models (HMMs) can be used by a TCP connection to infer efficiently conditional delay distributions. We demonstrate how estimation accuracy is influenced by different proportions of congestion versus wireless losses and penalties on incorrect classification.

DIP: Density Inference Protocol for wireless sensor networks and its application to density-unbiased statistics

Wireless sensor networks have recently emerged as enablers of important applications such as environmental, chemical and nuclear sensing systems. Such applications have sophisticated spatial-temporal semantics that set them aside from traditional wireless networks. For example, the computation of temperature averaged over the sensor field must take into account local densities. This is crucial since otherwise the estimated average temperature can be biased by over-sampling areas where a lot more sensors exist. Thus, we envision that a fundamental service that a wireless sensor network should provide is that of estimating local densities. In this paper, we propose a lightweight probabilistic density inference protocol, we call DIP, which allows each sensor node to implicitly estimate its neighborhood size without the explicit exchange of node identifiers as in existing density discovery schemes. The theoretical basis of DIP is a probabilistic analysis which gives the relationship between the number of sensor nodes contending in the neighborhood of a node and the level of contention measured by that node. Extensive simulations confirm the premise of DIP: it can provide statistically reliable and accurate estimates of local density at a very low energy cost and constant running time. We demonstrate how applications could be built on top of our DIP-based service by computing density-unbiased statistics from estimated local densities.

Connection Scheduling in Web Servers

Under high loads, a Web server may be servicing many hundreds of connections concurrently. In traditional Web servers, the question of the order in which concurrent connections are serviced has been left to the operating system. In this paper we ask whether servers might provide better service by using non-traditional service ordering. In particular, for the case when a Web server is serving static files, we examine the costs and benefits of a policy that gives preferential service to short connections. We start by assessing the scheduling behavior of a commonly used server (Apache running on Linux) with respect to connection size and show that it does not appear to provide preferential service to short connections. We then examine the potential performance improvements of a policy that does favor short connections (shortest-connection-first). We show that mean response time can be improved by factors of four or five under shortest-connection-first, as compared to an (Apache-like) size-independent policy. Finally we assess the costs of shortest-connection-first scheduling in terms of unfairness (i.e., the degree to which long connections suffer). We show that under shortest-connection-first scheduling, long connections pay very little penalty. This surprising result can be understood as a consequence of heavy-tailed Web server workloads, in which most connections are small, but most server load is due to the few large connections. We support this explanation using analysis.

An Independent-Connection Model for Traffic Matrices

A common assumption made in traffic matrix (TM) modeling and estimation is independence of a packet's network ingress and egress. We argue that in real IP networks, this assumption should not and does not hold. The fact that most traffic consists of two-way exchanges of packets means that traffic streams flowing in opposite directions at any point in the network are not independent. In this paper we propose a model for traffic matrices based on independence of connections rather than packets. We argue that the independent connection (IC) model is more intuitive, and has a more direct connection to underlying network phenomena than the gravity model. To validate the IC model, we show that it fits real data better than the gravity model and that it works well as a prior in the TM estimation problem. We study the model's parameters empirically and identify useful stability properties. This justifies the use of the simpler versions of the model for TM applications. To illustrate the utility of the model we focus on two such applications: synthetic TM generation and TM estimation. To the best of our knowledge this is the first traffic matrix model that incorporates properties of bidirectional traffic.

Fixational Instability and Natural Image Statistics: Implications for Early Visual Representations

Under natural viewing conditions small movements of the eye, head, and body prevent the maintenance of a steady direction of gaze. It is known that stimuli tend to fade when they a restabilized on the retina for several seconds. However; it is unclear whether the physiological motion of the retinal image serves a visual purpose during the brief periods of natural visual fixation. This study examines the impact of fixational instability on the statistics of the visua1 input to the retina and on the structure of neural activity in the early visual system. We show that fixational instability introduces a component in the retinal input signals that in the presence of natural images, lacks spatial correlations. This component strongly influences neural activity in a model of the LGN. It decorrelates cell responses even if the contrast sensitivity functions of simulated cells arc not perfectly tuned to counterbalance the power-law spectrum of natural images. A decorrelation of neural activity at the early stages of the visual system has been proposed to be beneficial for discarding statistical redundancies in the input signals. The results of this study suggest that fixational instability might contribute to establishing efficient representations of natural stimuli.

The Celtic dragon slayer - a literary analysis of Tochmarc Emire in connection with Tristan et Iseut

As Celtic scholars have long noted, the medieval Irish tale Tochmarc Emire “The Courtship of Emer” is heavily indebted to other medieval Irish texts. In this tale of courtship and otherworldly quests, the Irish hero Cú Chulainn must prove himself worthy of the hand of the noblewoman Emer. Among his overseas adventures, Cú Chulainn rescues a princess from three attackers of the Fomoire. This episode may represent the only medieval Irish example of AT300 “The Dragon Slayer”, a story pattern known from classical models such as the stories of Perseus and Andromeda; and Hercules and Hesione. Moreover, in the company of Cú Chulainn we find a character otherwise unknown to Irish tradition by the name of Drust mac Seirb. This has led scholars to argue that Tochmarc Emire may preserve a Celtic precursor of the Continental Tristan legend, seeing in Drust the Pictish origin of the character Tristan, himself a famous dragon slayer. In this interdisciplinary dissertation, a number of questions are addressed. If the redactor of Tochmarc Emire drew on material from outside Irish tradition, what does this tell us about medieval Irish concepts of literature and genre? Further, what evidence do we have for tracing the origin of the Continental Tristan legend back to Pictland, and what explanation might we offer for a putative Pictish prince featuring in an Irish Dragon Slayer story? Finally, what place does the Dragon Slayer episode occupy within Tochmarc Emire and can we find other narratives, Celtic or classical or other, fitting the pattern of AT300, which may strengthen the link between Tochmarc Emire and Tristan?

Monopoles for gravitation and for higher spin fields

We consider massless higher spin gauge theories with both electric and magnetic sources, with a special emphasis on the spin two case. We write the equations of motion at the linear level (with conserved external sources) and introduce Dirac strings so as to derive the equations from a variational principle. We then derive a quantization condition that generalizes the familiar Dirac quantization condition, and which involves the conserved charges associated with the asymptotic symmetries for higher spins. Next we discuss briefly how the result extends to the nonlinear theory. This is done in the context of gravitation, where the Taub-NUT solution provides the exact solution of the field equations with both types of sources. We rederive, in analogy with electromagnetism, the quantization condition from the quantization of the angular momentum. We also observe that the Taub-NUT metric is asymptotically flat at spatial infinity in the sense of Regge and Teitelboim (including their parity conditions). It follows, in particular, that one can consistently consider in the variational principle configurations with different electric and magnetic masses. © 2006 The American Physical Society.

A note on spin-s duality

Duality is investigated for higher spin (s ≥ 2), free, massless, bosonic gauge fields. We show how the dual formulations can be derived from a common "parent", first-order action. This goes beyond most of the previous treatments where higher-spin duality was investigated at the level of the equations of motion only. In D = 4 spacetime dimensions, the dual theories turn out to be described by the same Pauli-Fierz (s = 2) or Fronsdal (s ≥ 3) action (as it is the case for spin 1). In the particular s = 2 D = 5 case, the Pauli-Fierz action and the Curtright action are shown to be related through duality. A crucial ingredient of the analysis is given by the first-order, gauge-like, reformulation of higher spin theories due to Vasiliev. © SISSA/ISAS 2003.