The maxima and minima of sL(x)) — n(x), iR(x)) — n(x), and sL2(x)) — n2(x) in various intervals up to x = 8 x 10 are tabulated. Here n(x) and n2(x) are respectively the number of primes and twin primes not exceeding x, L(x) is the logarithmic integral, R(x) is Riemann's approximation to ir(x), and L2(x) is the Hardy-Littlewood approximation to ti"2(;c). The computation of the sum of inverses of...

Let (X, dX) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f : X → T such that for every x ∈ X, ED [ max y∈X\{x} dT ( f (x), f (y)) dX(x, y) ] ≤ C(log n), where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient...

An important problem in medical image analysis is the segmentation of anatomical regions of interest. Once regions of interest are segmented, one can extract shape, appearance, and structural features that can be analyzed for disease diagnosis or treatment evaluation. Diffusion tensor magnetic resonance imaging (DT-MRI) is a relatively new medical imaging modality that captures unique water dif...

The results obtained in §§1-2 are applied in §3 to show that the maximum possible value of dt{B log/'(z) + C log [/(z)/z]} at a point Zo of the unit circle, for the class of functions f(z) =z+ • • • which map |z| <1 conformally onto star-shaped regions, is attained for a function w=f(z) which maps the unit circle onto the w-plane with one or two radial slits. In §§4-5, we decide between these t...

By introducing a ∫ dt g (TrΦ(t)) 2 term into the action of the c = 1 matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral generates multiple spherical “bubbles” which touch one another at single points. At a special value of g, the sum over connected surfaces behaves as ∆ log∆, where ∆ is the cosmological con...

We propose a new interpretation of spiking neurons as Bayesian integrators accumulating evidence over time about events in the external world or the body, and communicating to other neurons their certainties about these events. In this model, spikes signal the occurrence of new information, i.e. what cannot be predicted from the past activity. As a result, firing statistics are close to Poisson...

Driven by many real applications, graph pattern matching has attracted a great deal of attention recently. Consider that a twigpattern matching may result in an extremely large number of matches in a graph; this may not only confuse users by providing too many results but also lead to high computational costs. In this paper, we study the problem of top-k tree pattern matching; that is, given a ...

The emergence of wireless telephone and broadband technologies has drastically altered the traditional household choice set for satisfying their communications needs. In this paper we explore this evolution. To do so, we extend the traditional (node-to-node) demand structure by permitting households to derive utility from communication with others while either the initiator or the recipient of ...

For help in preparation of this article, thanks to Dylan Davies, Schlumberger Cambridge Research, Ahmad Madjidi, Schlumberger GeoQuest, Abu Dhabi, UAE; Nabil Mazzawi, Schlumberger Wireline & Testing, Tripoli, Libya; Perry Nice, Statoil, Stavanger, Norway; Barry Nicholson, Schlumberger Wireline & Testing, Jakarta, Indonesia; Daniel Roche, Elf, Bergen, Norway; Philippe Rutman and Derek Stark, Sch...

The present paper is part I of a series of three closely related papers in which the inverse measure dt of a given measure dt on is introduced In the rst case discussed in detail and are multifractal in the usual sense that is both are linearly self similar and continuous but not di erentiable and both are non zero for every interval of Under these assumptions the H older spectra of dt and dt a...