Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the M...

Let n, p be two strictly positive integers, and let f1(x), . . . , fp(x) ∈ K[x] := K[x1, . . . , xn] be p polynomials of n variables with coefficients in a fieldK of characteristic zero. Denote by An = K[x1, . . . , xn]〈∂x1 , . . . , ∂xn〉 the Weyl algebra with n variables and let s1, . . . , sp be new variables. Denote by L = K[x][f−1 1 , . . . , f−1 p , s1, . . . , sp] · f the free module gene...

Reconstruction of an evolutionary history for a set of organisms is an important research subject in computational biology. One approach motivated by graph theory constructs a relationship graph based on pairwise evolutionary closeness. The approach builds a tree representation equivalent to this graph such that leaves of the tree, corresponding to the organisms, are within a specified distance...

In order to represent, compute and reason with advanced data types one must go beyond the traditional treatment of data types as being inductive types and, instead, consider them as inductive families. Strictly positive types (SPTs) form a grammar for defining inductive types and, consequently, a fundamental question in the the theory of inductive families is what constitutes a corresponding gr...

This paper characterizes a subclass of subsequential string-to-string functions called Output Strictly Local (OSL) and presents a learning algorithm which provably learns any OSL function in polynomial time and data. This algorithm is more efficient than other existing ones capable of learning this class. The OSL class is motivated by the study of the nature of string-to-string transformations,...

We present a strictly lexical parsing model where all the parameters are based on the words. This model does not rely on part-of-speech tags or grammatical categories. It maximizes the conditional probability of the parse tree given the sentence. This is in contrast with most previous models that compute the joint probability of the parse tree and the sentence. Although the maximization of join...

Given a knot K in a closed orientable manifold M we define the growth rate of the tunnel number of K to be grt(K) = lim supn→∞ t(nK)−nt(K) n−1 . As our main result we prove that the Heegaard genus of M is strictly less than the Heegaard genus of the knot exterior if and only if the growth rate is less than 1. In particular this shows that a non-trivial knot in S is never asymptotically super ad...

3.1 Setup The stochastic multi-armed bandit is a classical model for decision making and is defined as follows: There are K arms(different actions). Iteratively, a decision maker chooses an arm k ∈ {1, . . . ,K}, yielding a sequence XK,1, . . . ,XK,t, . . ., which are i.i.d random variables with mean μk. Define μ∗ = maxj μj or ∗ ∈ argmax. A policy π is a sequence {πt}t≥1, which indicates which ...

We study the topology of the space ∂K of complete convex hypersurfaces of R which are homeomorphic to Rn−1. In particular, using Minkowski sums, we construct a deformation retraction of ∂K onto the Grassmannian space of hyperplanes. So every hypersurface in ∂K may be flattened in a canonical way. Further, the total curvature of each hypersurface evolves continuously and monotonically under this...

Let G be a non-empty closed (resp. bounded closed) boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X. Let K(X) denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance. Moreover, let KG(X) denote the closure of the set {A ∈ K(X) : A∩G = ∅}. We prove that the set of all A ∈ KG(X) (resp. A ∈ K(X)), such that the minimizat...