Abstract We theoretically analyze the typical learning performance of ℓ 1 -regularized linear regression ( -LinR) for Ising model selection using replica method from statistical mechanics. For random regular graphs in paramagnetic phase, an accurate estimate sample complexity -LinR is obtained. Remarkably, despite misspecification, consistent with same order as logistic -LogR), i.e. <?CDATA $M=...

We study the random sampling of band-limited functions of several variables. If a band-limited function with bandwidth has its essential support on a cube of volume R, then O(Rd logR) random samples suffice to approximate the function up to a given error with high probability.

The Ramsey multiplicity R(G) of a graph G is the minimum number of monochromatic copies of G in any two-colouring of the edges of Kr(G), where r(G) denotes the Ramsey number of G. Here we prove that odd cycles have super-exponentially large Ramsey multiplicity: If Cn is an odd cycle of length n, then logR(Cn) = Θ(n logn).

El Estado de Guanajuato es el principal productor trigo (Triticum aestivum L.) la región Bajío que segunda zona productora este cereal en México. En ciclo otoño-invierno (OI)1998-99 se sembraron 98 072 ha trigo, con una producción 510 894 t, logr´ó gran medida satisfacer demanda regional. Sin embargo, siembran predominantemente variedades gluten débil y poco fuerte (3900 1999-00), cuya por indu...

the Valiron deficiency of the value a for f(z). (We assume familiarity with the standard notations and basic results of meromorphic function theory, as described for instance in [2].) Some fifty years ago, Valiron [5, 6] constructed examples of integral functions f(z) of order 1 for which A (a , / ) = 1 for an uncountable set of fl-values. On the other hand, he also showed [4] that an integral ...

There has been little research on machine learning for email prioritization customer service excellence. To fill this gap, we propose and assess the efficacy of various techniques classifying emails into three degrees priority: high, low, neutral, based emotions inherent in content. It is predicted that after are classified those categories, recipients will be able to respond more efficiently p...

logR. We regularize the stochastic differential equations by associating with them approximating ordinary differential equations obtained by discretization of the increments of the Wiener process on small intervals. By showing that the flow associated with a regularized equation converges uniformly to the solution of the stochastic differential equation, we simultaneously establish the existenc...

We prove the following: suppose that J{z) is transcendental and meromorphic of finite order in the plane, and that the linear differential polynomial F(z) is defined by and is non-constant, where ak_j(z), ...,ao(z) are rational functions vanishing at infinity. Then N(r,l/(fFF')) = implies that N(r,f) = O(logr). A corresponding result is proved for the case where F =f' + af, where a is a constan...