We consider the mean uniform (mixed) norms for a sequence of Gaussian random functions. For a wide class of Gaussian processes and fields the (2 log n)1/2-asymptotic for mixed norms is found whenever the volume of the index set is of order n and tends to infinity, for example, n-length time interval for random processes. Some numerical examples demonstrate the rate of convergence for the obtain...

In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which asserts uniform convergence of the empirical Cumulative Distribution Function (CDF) to the CDF of the underlying distribution. Our variant allows for tighter convergence bounds for extreme values of the CDF. We apply our bound in the context of revenue learning, which is a well-studied problem in economics and algo...

In this position paper, the roles of sampling rate, i.e. alternatively, sampling time, have been investigated in the receiver design of a concentration-encoded molecular communication (CEMC) system. While several signal detection algorithms so far in CEMC are based on uniform sampling of concentration intensity at the RN, this paper presents four new sampling rate selection schemes based on bot...

A new wavelet-based L∞ -constrained embedded image coding technique is proposed in this paper. For any desired distortion bound, the embedded bit stream can be truncated at a corresponding bit-rate, for which the required upper bound on the individual elements of the reconstruction error signal is guaranteed. A lifting-based wavelet transform is employed and exact relations are established betw...

  In this paper, we present some important dynamical concepts on uniform space such as the minimal systems, shadowing, and strong shadowing. We explain definitions theorems definition expansive, weak generator, proof of for them. prove that if  be a homeomorphism compact  then  has shadowing only has so also show  and two homeomorphisms spaces ,  is conjugacy from ...

The classical setting of evolutionary game theory, the replicator equation, assumes uniform interaction rates. The rate at which individuals meet and interact is independent of their strategies. Here we extend this framework by allowing the interaction rates to depend on the strategies. This extension leads to non-linear fitness functions. We show that a strict Nash equilibrium remains uninvada...

We consider the problem of uniform generation of random integers in the range 1; n] given only a binary source of randomness. Standard models of randomized algorithms (e.g. probabilistic Turing machines) assume the availability of a random binary source that can generate independent random bits in unit time with uniform probability. This makes the task trivial if n is a power of 2. However, exa...

This paper investigates the effect of input optical pulse energy on the total gain of the semiconductor optical amplifier (SOA) injected with a non-uniform bias current. For ultra-high data rate applications it is essential that the SOA has a fast gain recovery response, thus resulting in maximum SOA gain and reduced gain standard deviation. SOA with higher gain standard deviation will reduce t...