We study persistence of periodic solutions perturbed slowly varying discontinuous differential equations assuming that the unperturbed (frozen) equation has a non singular solution. The results this paper are motivated by result Holmes and Wiggins where authors considered two dimensional Hamiltonian family smooth systems depending on scalar variable which is solution singularly equation.

Sound propagation in uniformly lined straight ducts with uniform mean flow is well established by its analytically exact description in duct modes [1, 2, 3]. In cross-wise nonuniform flow there are still modes, although the (Pridmore-Brown) equation that describes them is in general not solvable in terms of standard functions [4, 5, 6, 7, 8, 9] and has to be solved numerically. These modal solu...

What makes some words easy for infants to recognize, and other words difficult? We addressed this issue in the context of prior results suggesting that infants have difficulty recognizing verbs relative to nouns. In this work, we highlight the role played by the distributional contexts in which nouns and verbs occur. Distributional statistics predict that English nouns should generally be easie...

We provide linear approximations to the marginal distributions for a class of infinite-state continuous-time stationary Markov chains in slowly varying environents. We take an approach motivated by light-traffic approximations to stationary point processes, which permits us to consider general stationary environments. Under mild assumptions we show that Jackson networks with routing not affecte...

We study a linear stochastic approximation algorithm that arises in the context of reinforcement learning. The algorithm employs a decreasing step-size, and is driven by Markov noise with time-varying statistics. We show that under suitable conditions, the algorithm can track the changes in the statistics of the Markov noise, as long as these changes are slower than the rate at which the step-s...

A Popov criterion is derived for systems with slowly timevarying parameters. The parameters and their time derivatives are assumed to take values in convex polytopes.

A double sequence x = {xk,l} of points in R is slowly oscillating if for any given ε > 0, there exist α = α(ε) > 0, δ = δ(ε) > 0, and N = N(ε) such that |xk,l−xs,t| < ε whenever k, l ≥ N(ε) and k ≤ s ≤ (1 + α)k, l ≤ t ≤ (1 + δ)l. We study continuity type properties of factorable double functions defined on a double subset A × A of R into R, and obtain interesting results related to uniform cont...

In this study we investigate temporal slowness as a learning principle for receptive fields using slow feature analysis, a new algorithm to determine functions that extract slowly varying signals from the input data. We find a good qualitative and quantitative match between the set of learned functions trained on image sequences and the population of complex cells in the primary visual cortex (...

We present an ad hoc concept modeling approach using distributional semantic models to identify fine-grained entities and their relations in an online search setting. Concepts are generated from user-defined seed terms, distributional evidence, and a relational model over concept distributions. A dimensional indexing model is used for efficient aggregation of distributional, syntactic, and rela...