We consider the problem of detecting a random walk on a graph, based on observations of the graph nodes. When visited by the walk, each node of the graph observes a signal of elevated mean, which we assume can be different across different nodes. Outside of the path of the walk, and also in its absence, nodes measure only noise. Assuming the Neyman-Pearson setting, our goal then is to character...

We give an efficient structural decomposition theorem for formulas that depends on their negation complexity and demonstrate its power with the following applications. We prove that every formula that contains t negation gates can be shrunk using a random restriction to a formula of size O(t) with the shrinkage exponent of monotone formulas. As a result, the shrinkage exponent of formulas that ...

We study a class of $K$ -encoder hypothesis testing against conditional independence problems. Under the criterion that stipulates minimization Type II error subject to (constant) upper bound notation="LaTeX">$\epsilon $ on I error, w...

The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first introduced, and next a regularization scheme is presented. It is shown that the renormalization of an action functional in the generating functional leads to an a...

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper combustion experiments. Using paper sheets of different width lambda L0, we found that the turbulent flame fronts display anomalous...

The aim was to investigate the correlation between compression exponent, compression threshold, and cochlear gain for normal-hearing subjects as inferred from temporal masking curves (TMCs) and distortion-product otoacoustic emission (DPOAEs) input-output (I/O) curves. Care was given to reduce the influence of DPOAE fine structure on the DPOAE I/O curves. A high correlation between compression ...

In some applications, a short private exponent d is chosen to improve the decryption or signing process for RSA public key cryptosystem. However, in a typical RSA, if the private exponent d is selected first, the public exponent e should be of the same order of magnitude as φ(N). Sun et al. devised three RSA variants using unbalanced prime factors p and q to lower the computational cost. Unfort...

It is of course well recognized that the length of time required by a germicide to kill a given number of bacteria varies with the concentration of the substance. The relation between concentration and time can usually be expressed by the formula Ct k, often written in logarithmic form log t = log kn log c for convenience The obvious value of the concentration exponent n is that it gives direct...

| In this paper dynamic exponent-based electronics is introduced as a good candidate for overcoming some of the limitations of classic linear-based electronics. However, the use of the exponential relation as a primitive for the synthesis of electronic circuits implies that we have to deal with analysis and synthesis of dynamic nonlinear circuits. The linear time-varying approximation appears t...

Equivocation rate has been widely used as an information-theoretic measure of security after Shannon[12]. It simplifies problems by removing the effect of atypical behavior from the system. In [11], however, Merhav and Arikan considered the alternative of using guessing exponent to analyze the Shannon’s cipher system. Because guessing exponent captures the atypical behavior, the strongest expre...