We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by parti...

We derive the first closed-form optimal refinancing rule: Refinance when the current mortgage interest rate falls below the original rate by at least [Formula: see text] In this formula W(.) is the Lambert W-function, [Formula: see text]ρ is the real discount rate, λ is the expected real rate of exogenous mortgage repayment, σ is the standard deviation of the mortgage rate, κ/M is the ratio of ...

Books and magazines often contain pages containing audacious mixtures of color images and text Our problem consists in coding the background colors of a such documents without wasting bits on background pixels that will be masked by foreground text This paper presents a numerical method for achieving such a result This wavelet technique described in this paper signi cantly reduces the compresse...

done Table vertical elements Please note that we are unable to display vertical rules within the tables nor are we able to write text vertically within the cells please re-layout your table without these vertical elements. We are unable to correctly display merged cells where the merged cell crosses rows. done References please cite all references in numerical order in the text. Reference 34 is...

We describe in this paper the application of numerical machine learning techniques to the extraction of information from a collection of textual data. More precisely, we consider the modeling of text sequences with Hidden Markov Models (HMMs) and Multi-layer Perceptrons (MLPs) and show how these models can be used to perform specific surface extraction tasks (i.e. tasks which do not need in dep...

We present Text Insights, an application for understanding factors of user engagement in Facebook pages. Providing analytics based on natural language processing, Text Insights is complementary to existing tools offering mainly numerical indicators of user engagement. Our system extracts keyphrases from page content in a linguistically motivated manner. Keyphrases are weighted according to thei...

We present an empirical corpus study of the meaning and usage of time phrases in weather forecasts; this is based on a novel corpus analysis technique where we align phrases from the forecast text with data extracted from a numerical weather simulation. Previous papers have summarised this analysis and discussed the substantial variations we discovered among individual writers, which was perhap...

In the era of the web, a huge amount of information is now flowing over the network. Since the range of web content covers subjective opinion as well as objective information, it is now common for people to gather information about products and services that they want to buy. However since a considerable amount of information exists as text-fragments without having any kind of numerical scales,...

on the electron beam generated by the lensing apparatus described in the main text. All numerical examples are meant to be compared with (and are being based on the same parameters as) the ideal case of Fig. 1(c) in the main text, which considers a focal length f = 200nm, densities no = −ni = 6× 1011 cm−2 corresponding to a Fermi wave length λF ≈ 46nm, and a smoothness `s = 30nm of the pn junct...

Readability is defined as the “comprehensibility of written text” [2,3]. It has been measured by various formulae developed for materials written for native speakers of a language (L1), or materials designed for second and/or foreign language students (L2). According to Brown et al. [4], being used with L1 texts, readability formulae provide a numerical index that estimates the reading difficul...