This algorithm is introduced by [Zin]. Assuming {lt(·)}t=1 are differentiable: Starting with some arbitrary x1 ∈ X. For t = 1, ...,T • zt+1← xt − η 5 lt(xt). • xt+1←ΠX(zt+1), where ΠX(·) is the projection function. The performance of OGD is described as follows. Theorem .. If there exists some positive constant G,D such that || 5 lt(x)||2 ≤ G,∀t,x ∈ X (.) ||X ||2;= max x,y∈X ||x − y||2 ≤D...

We propose an algorithm for online convex optimization which examines a clipped long-term constraint of the form T ∑ t=1 [g(xt)]+, encoding the cumulative constraint violation. Previous literature has focused on longterm constraints of the form T ∑ t=1 g(xt), for which strictly feasible solutions can cancel out the effects of violated constraints. In this paper, we generalize the results in [16...

A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locatingdominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number λ(G). An LD-set S of a graph G is global if it is an LD-set of both G and its compleme...

Let G (V, E) be an undirected graph. The random walk on G is a Markov chain on V that, at each time step, moves to a uniformly random neighbor of the current vertex. Ffsor x ∈ V , use dx to denote the degree of vertex x. Then more formally, random walk on G is the following process {Xt}. We start at at some node X0 v0 ∈ V . Then if Xt v, we put Xt+1 w with probability 1/dv for every neighbor w ...

We investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence (delayed random walk). The characteristic feature of such a model is the oscillatory behavior of its correlation function. We investigate a model whose transient and stationary oscillatory behavior is analytically tractable. The correspondence of the model...

Consider a non–linear function G(Xt) where Xt is a stationary Gaussian sequence with long–range dependence. The usual reduction principle states that the partial sums of G(Xt) behave asymptotically like the partial sums of the first term in the expansion of G in Hermite polynomials. In the context of the wavelet estimation of the long–range dependence parameter, one replaces the partial sums of...

We formulate the problem of inference in nonlinear dynamical systems (NLDS) in the Expectation-Propagation framework, and propose two novel inference algorithms based on Laplace approximation and the unscented transform (UT). The algorithms are compared empirically and employed as an improved E-step in a conjugate gradient learning algorithm. We illustrate its use for data mining with two high-...

Robertson and Seymour introduced the concept of the tree-width of a graph. It plays an important role in their results on graph minors culminating in their proof of Wagner’s conjecture. This concept seems to be interesting from the algorithmic point of view as well: many graph problems that are NP-complete in general can be polynomially solvable if graphs are constrained to have bounded tree-wi...

A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number λ(G). An LD-set S of a graph G is global if it is an LD-set of both G and its complem...

In this method for identifying autoantibodies to lactate dehydrogenase (anti-LDs) in serum, we used immobilized Protein G to bind IgG-complexed LD and immobilized jacalin to bind IgA-complexed LD, leaving non-complexed LD in solution. The non-complexed LD and total LD were kinetically measured. We report results as LD bound to immobilized Protein G and LD bound to immobilized jacalin. Using ser...