Hydrophobic amino acids of the group Leu, Ile, Val, Phe, and Met (LIVFM) are distributed in favored or suppressed patterns within protein sequences. The frequencies of all five-position combinations of [symbol: see text] = LIVFM and [symbol: see text] = non-LIVFM residues were analyzed in 48 proteins of known crystallographic structure. Some motifs were strongly preferred or suppressed; e.g., [...

Identifying strongly connected substructures in large networks provides insight into their coarse-grained organization. Several approaches based on the optimization of a quality function, e.g., the modularity, have been proposed. We present here a multistep extension of the greedy algorithm (MSG) that allows the merging of more than one pair of communities at each iteration step. The essential ...

Identifying strongly connected substructures in large networks provides insight into their coarse-grained organization. Several approaches based on the optimization of a quality function, e.g., the modularity, have been proposed. We present here a multistep extension of the greedy algorithm MSG that allows the merging of more than one pair of communities at each iteration step. The essential id...

We prove that every polycyclic group of nonlinear growth admits a strongly aperiodic SFT and has an undecidable domino problem. This answers a question of [5] and generalizes the result of [2]. Subshifts of finite type (SFT for short) in a group G are colorings of the elements of G subject to local constraints. They have been studied extensively for the free abelian group Z [14] and on the free...

Suppose that f(z) is a transcendental entire function and that the Fatou set F (f) 6= ∅. Set B1(f) := sup U supz∈U log(|z| + 3) infw∈U log(|w|+ 3) and B2(f) := sup U supz∈U log log(|z|+ 30) infw∈U log(|w| + 3) , where the supremum supU is taken over all components of F (f). If B1(f) < ∞ or B2(f) < ∞, then we say F (f) is strongly uniformly bounded or uniformly bounded respectively. In this arti...

are classes of starlike and strongly starlike functions of order β (0 < β ≤ 1), respectively. Note that S∗(β)⊂ S∗ for 0< β< 1 and S∗(1)= S∗ [5]. Kanas [2] introduced the subclass R̄δ(β) of function f ∈ S as the following. Definition 1.1. For δ ≥ 0, β ∈ (0,1], a function f normalized by (1.1) belongs to R̄δ(β) if, for z ∈D−{0} and Dδf(z)≠ 0, the following holds: ∣∣∣arg z ( Dδf(z) )′ Dδf(z) ∣∣∣≤ βπ...

the submodules with the property of the title ( a submodule $n$ of an $r$-module $m$ is called strongly dense in $m$, denoted by $nleq_{sd}m$, if for any index set $i$, $prod _{i}nleq_{d}prod _{i}m$) are introduced and fully investigated. it is shown that for each submodule $n$ of $m$ there exists the smallest subset $d&apos;subseteq m$ such that $n+d&apos;$ is a strongly dense submodule of $m$...

In this paper, we introduce the dual notion of strongly top modules and study some of the basic properties of this class of modules.

We derive transitivity of various degrees of proximinality in Banach spaces. When the transitivity does not carry forward to the bigger space we investigate these properties under some additional assumptions of the intermediate space. For instance, we show that if Z ⊆ Y ⊆ X where Z is a finite co-dimensional subspace of X which is strongly proximinal in Y and Y is an M-ideal in X then Z is stro...