2,885 research outputs found
On universal partial words
A universal word for a finite alphabet and some integer is a
word over such that every word in appears exactly once as a subword
(cyclically or linearly). It is well-known and easy to prove that universal
words exist for any and . In this work we initiate the systematic study
of universal partial words. These are words that in addition to the letters
from may contain an arbitrary number of occurrences of a special `joker'
symbol , which can be substituted by any symbol from . For
example, is a linear partial word for the binary alphabet
and for (e.g., the first three letters of yield the
subwords and ). We present results on the existence and
non-existence of linear and cyclic universal partial words in different
situations (depending on the number of s and their positions),
including various explicit constructions. We also provide numerous examples of
universal partial words that we found with the help of a computer
Enantioselective Total Synthesis of (â)-Myrifabral A and B
A catalytic enantioselective approach to the Myrioneuron alkaloids (â)-myrifabral A and (â)-myrifabral B is described. The synthesis was enabled by a palladium-catalyzed enantioselective allylic alkylation, that generates the C(10) all-carbon quaternary center. A key N-acyl iminium ion cyclization forged the cyclohexane fused tricyclic core, while vinyl boronate cross metathesis and oxidation afforded the lactol ring of (â)-myrifabral A. Adaptation of previously reported conditions allowed for the conversion of (â)-myrifabral A to (â)-myrifabral B
Modeling regionalized volumetric differences in protein-ligand binding cavities
Identifying elements of protein structures that create differences in protein-ligand
binding specificity is an essential method for explaining the molecular mechanisms
underlying preferential binding. In some cases, influential mechanisms can be
visually identified by experts in structural biology, but subtler mechanisms, whose
significance may only be apparent from the analysis of many structures, are harder to
find. To assist this process, we present a geometric algorithm and two statistical
models for identifying significant structural differences in protein-ligand binding
cavities. We demonstrate these methods in an analysis of sequentially nonredundant
structural representatives of the canonical serine proteases and the enolase
superfamily. Here, we observed that statistically significant structural variations
identified experimentally established determinants of specificity. We also observed
that an analysis of individual regions inside cavities can reveal areas where small
differences in shape can correspond to differences in specificity
Hybrid fuzzy and sliding-mode control for motorised tether spin-up when coupled with axial vibration
A hybrid fuzzy sliding mode controller is applied to the control of motorised tether spin-up coupled with an axial oscillation phenomenon. A six degree of freedom dynamic model of a motorised momentum exchange tether is used as a basis for interplanetary payload exchange. The tether comprises a symmetrical double payload configuration, with an outrigger counter inertia and massive central facility. It is shown that including axial elasticity permits an enhanced level of performance prediction accuracy and a useful departure from the usual rigid body representations, particularly for accurate payload positioning at strategic points. A special simulation program has been devised in MATLAB and MATHEMATICA for a given initial condition data case
Word-representability of face subdivisions of triangular grid graphs
A graph G = (V, E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if (x, y) â E. A triangular grid graph is a subgraph of a tiling of the plane with equilateral triangles defined by a finite number of triangles, called cells. A face subdivision of a triangular grid graph is replacing some of its cells by plane copies of the complete graph K4. Inspired by a recent elegant result of Akrobotu et al., who classified wordrepresentable triangulations of grid graphs related to convex polyominoes, we characterize word-representable face subdivisions of triangular grid graphs. A key role in the characterization is played by smart orientations introduced by us in this paper. As a corollary to our main result, we obtain that any face subdivision of boundary triangles in the Sierpi´nski gasket graph is wordrepresentable
Lower bounds, and exact enumeration in particular cases, for the probability of existence of a universal cycle or a universal word for a set of words
A universal cycle, or u-cycle, for a given set of words is a circular word that contains each word from the set exactly once as a contiguous subword. The celebrated de Bruijn sequences are a particular case of such a u-cycle, where a set in question is the set A^n of all words of length n over a k-letter alphabet A. A universal word, or u-word, is a linear, i.e., non-circular, version of thuniversal cycle; u-cycle; universal word; u-word; de Bruijn sequencee notion of a u-cycle, and it is defined similarly. Removing some words in A^n may, or may not, result in a set of words for which u-cycle, or u-word, exists. The goal of this paper is to study the probability of existence of the universal objects in such a situation. We give lower bounds for the probability in general cases, and also derive explicit answers for the case of removing up to two words in A^n, or the case when k = 2 and n ⤠4
pClay: A Precise Parallel Algorithm for Comparing Molecular Surfaces
Comparing binding sites as geometric solids can reveal conserved features of protein structure that bind similar molecular fragments and varying features that select different partners. Due to the subtlety of these features, algorithmic efficiency and geometric precision are essential for comparison accuracy. For these reasons, this paper presents pClay, the first structure comparison algorithm to employ fine-grained parallelism to enhance both throughput and efficiency. We evaluated the parallel performance of pClay on both multicore workstation CPUs and a 61-core Xeon Phi, observing scaleable speedup in many thread configurations. Parallelism unlocked levels of precision that were not practical with existing methods. This precision has important applications, which we demonstrate: A statistical model of steric variations in binding cavities, trained with data at the level of precision typical of existing work, can overlook 46% of authentic steric influences on specificity (p <= .02). The same model, trained with more precise data from pClay, overlooked 0% using the same standard of statistical significance. These results demonstrate how enhanced efficiency and precision can advance the detection of binding mechanisms that influence specificity
Hydrodynamic theory of scrambling in chaotic long-range interacting systems
The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a
mean-field theory of out-of-time-ordered commutators in locally interacting
quantum chaotic systems at high energy density; in the systems with power-law
interactions, the corresponding fractional-derivative FKPP equation provides an
analogous mean-field theory. However, the fractional FKPP description is
potentially subject to strong quantum fluctuation effects, so it is not clear a
priori if it provides a suitable effective description for generic chaotic
systems with power-law interactions. Here we study this problem using a model
of coupled quantum dots with interactions decaying as ,
where each dot hosts degrees of freedom. The large limit corresponds to
the mean-field description, while quantum fluctuations contributing to the OTOC
can be modeled by corrections consisting of a cutoff function and
noise. Within this framework, we show that the parameters of the effective
theory can be chosen to reproduce the butterfly light cone scalings that we
previously found for and generic finite . In order to reproduce these
scalings, the fractional index in the FKPP equation needs to be shifted
from the na\"ive value of to a renormalized value . We provide supporting analytic evidence for the cutoff model and
numerical confirmation for the full fractional FKPP equation with cutoff and
noise.Comment: 17+1 pages, 14 figure
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