The origin of Herz spaces is the study of characterization of functions and multipliers on the classical Hardy spaces ([1, 8]). By virtue of many authors’ works Herz spaces have became one of the remarkable classes of function spaces in harmonic analysis now. One of the important problems on the spaces is boundedness of sublinear operators satisfying proper conditions. Hernández, Li, Lu and Yan...

Sublinear time algorithms represent a new paradigm in computing, where an algorithm must give some sort of an answer after inspecting only a very small portion of the input. We discuss the types of answers that one can hope to achieve in this setting.

Let 0 < a < b < ∞, and for each edge e of Zd let ωe = a or ωe = b, each with probability 1/2, independently. This induces a random metric distω on the vertices of Z d, called first passage percolation. We prove that for d > 1 the distance distω(0, v) from the origin to a vertex v, |v| > 2, has variance bounded by C |v|/ log |v|, where C = C(a, b, d) is a constant which may only depend on a, b a...

The present paper deals with the subject of approximate string matching and demonstrates how Chang and Lawler [CL94] conceived a new sublinear time algorithm out of ideas that had previously been known. The problem is to find all locations in a text of length n over a b-letter alphabet where a pattern of length m occurs with up to k differences (substitutions, insertions, deletions). The algori...

We study the problem of parameterized matching in a stream where we want to output matches between a pattern of length m and the last m symbols of the stream before the next symbol arrives. Parameterized matching is a natural generalisation of exact matching where an arbitrary one-to-one relabelling of pattern symbols is allowed. We show how this problem can be solved in constant time per arriv...

We propose a public-key traitor tracing scheme in which (1) the size of a ciphertext is sublinear in the number of receivers and (2) black-box tracing is efficiently achieved against self-defensive pirate decoders. When assuming that a pirate decoder can take some self-defensive reaction (e.g., erasing all of the internal keys and shutting down) to escape from tracing if it detects tracing, it ...

We will present an algorithm, based on SA-techniques and a sampling procedure, that colors a given random 3-colorable graph with high probability in sublinear time. This result is the rst theoretical justiication of many excellent experimental performance results of Simulated Annealing 10, 17] applied to graph coloring problems.

The problem of order-preserving matching has gained attention lately. The text and the pattern consist of numbers. The task is to find all substrings in the text which have the same relative order as the pattern. The problem has applications in analysis of time series like stock market or weather data. Solutions based on the KMP and BMH algorithms have been presented earlier. We present a new s...

Online learning algorithms are designed to learn even when their input is generated by an adversary. The widely-accepted formal definition of an online algorithm’s ability to learn is the game-theoretic notion of regret. We argue that the standard definition of regret becomes inadequate if the adversary is allowed to adapt to the online algorithm’s actions. We define the alternative notion of p...

Inputs from the two eyes are first combined in simple cells in the primary visual cortex. Consequently, visual cortical neurons need to have the flexibility to encode visual features under both monocular and binocular situations. Here we show that binocular orientation selectivity of mouse simple cells is nearly identical to monocular orientation selectivity in both anaesthetized and awake cond...