background: rna plays key role in many aspects of biological processes and its tertiary structure is critical for its biological function. rna secondary structure represents various significant portions of rna tertiary structure. since the biological function of rna is concluded indirectly from its primary structure, it would be important to analyze the relations between the rna sequences and t...

For simplicity, we adopt the following convention: x, x0, y, y0, r are real numbers, z, z0 are elements of R2, Z is a subset of R2, f , f1, f2 are partial functions from R2 to R, R is a rest, and L is a linear function. Next we state two propositions: (1) domproj(1, 2) = R2 and rng proj(1, 2) = R and for all elements x, y of R holds (proj(1, 2))(〈x, y〉) = x. (2) domproj(2, 2) = R2 and rng proj(...

Minimal perfect hash functions provide space-efficient and collision-free hashing on static sets. Existing algorithms and implementations that build such functions have practical limitations on the number of input elements they can process, due to high construction time, RAM or external memory usage. We revisit a simple algorithm and show that it is highly competitive with the state of the art,...

For simplicity, we adopt the following convention: D is a set, x, x0, y, y0, z, z0, r, s, t are real numbers, p, a, u, u0 are elements of R3, f , f1, f2, f3, g are partial functions from R3 to R, R is a rest, and L is a linear function. We now state three propositions: (1) dom proj(1, 3) = R3 and rng proj(1, 3) = R and for all elements x, y, z of R holds (proj(1, 3))(〈x, y, z〉) = x. (2) dom pro...

A new algorithm for generating order preserving minimal perfect hash functions is presented. The algorithm is probabilistic, involving generation of random graphs. It uses expected linear time and requires a linear number words to represent the hash function, and thus is optimal up to constant factors. It runs very fast in practice.

We investigate notions of randomness in the space C(2N) of continuous functions on 2N. A probability measure is given and a version of the Martin-Löf Test for randomness is defined. Random ∆2 continuous functions exist, but no computable function can be random and no random function can map a computable real to a computable real. The image of a random continuous function is always a perfect set...

We investigate notions of randomness in the space C(2N) of continuous functions on 2N. A probability measure is given and a version of the Martin-Löf Test for randomness is defined. Random ∆2 continuous functions exist, but no computable function can be random and no random function can map a computable real to a computable real. The image of a random continuous function is always a perfect set...

We consider the classical rumor spreading problem, where a piece of information must be disseminated from a single node to all n nodes of a given network. We devise two simple push-based protocols, in which nodes choose the neighbor they send the information to in each round using pairwise independent hash functions, or a pseudo-random generator, respectively. For several wellstudied topologies...

We consider a sequence of independent and identicaly distributed (iid) random variables with absolutely continuous distribution function F(x) and probability density function (pdf) f(x). Let Rnl be the largest observation after observing nth record and R(ns) be the smallest observation after observing the nth record. Then we say Wnr = Rnl− R(ns), n > 1, as the nth record range. We will c...