Online learning, in contrast to batch learning, occurs in a sequence of rounds. At the beginning of a round, an example is presented to the learning algorithm, the learning algorithm uses its current hypothesis to label the example, and then the learning algorithm is presented with the correct label and the hypothesis is updated. It is a different learning paradigm than batch learning where we ...

Let $A$ be a nite dimensional $k-$algebra and $R$ be a locally bounded category such that $R rightarrow R/G = A$ is a Galois covering dened by the action of a torsion-free group of automorphisms of $R$. Following [30], we provide criteria on the convex subcategories of a strongly simply connected category R in order to be a cycle- nite category and describe the module category of $A$. We p...

We study the minimization of a convex function f(X) over the set of n × n positive semi-definite matrices, but when the problem is recast as minU g(U) := f(UU >), with U ∈ Rn×r and r ≤ n. We study the performance of gradient descent on g—which we refer to as Factored Gradient Descent (Fgd)—under standard assumptions on the original function f . We provide a rule for selecting the step size and,...

For the proof of Theorem 1, we first prove the following Lemma. Lemma 1. Assume that φ * i (z) is γ-strongly convex function (where γ can be zero). Then for any t > 0 and s ∈ [0, 1], we have

Abstract Sharp bounds are given for the second Hankel determinant of logarithmic coefficients strongly starlike and convex functions.

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

The analysis of flow in water-distribution networks with several pumps by the Content Model may be turned into a non-convex optimization uncertain problem with multiple solutions. Newton-based methods such as GGA are not able to capture a global optimum in these situations. On the other hand, evolutionary methods designed to use the population of individuals may find a global solution even for ...