A benchmark of optimally folded protein structures using integer programming and the 3D-HP-SC model

The Protein Structure Prediction (PSP) problem comprises, among other issues, forecasting the three-dimensional native structure of proteins using only their primary structure information. Most computational studies in this area use synthetic data instead of real biological data. However, the closer to the real-world, the more the impact of results and their applicability. This work presents 17 real protein sequences extracted from the Protein Data Bank for a benchmark to the PSP problem using the tri-dimensional Hydrophobic-Polar with Side-Chains model (3D-HP-SC). The native structure of these proteins was found by maximizing the number of hydrophobic contacts between the side-chains of amino acids. The problem was treated as an optimization problem and solved by means of an Integer Programming approach. Although the method optimally solves the problem, the processing time has an exponential trend. Therefore, due to computational limitations, the method is a proof-of-concept and it is not applicable to large sequences. For unknown sequences, an upper bound of the number of hydrophobic contacts (using this model) can be found, due to a linear relationship with the number of hydrophobic residues. The comparison between the predicted and the biological structures showed that the highest similarity between them was found with distance thresholds around 5.2–8.2 Å. Both the dataset and the programs developed will be freely available to foster further research in the area.     

On null sequences for Banach operator ideals,trace duality and approximation properties

Let be a Banach operator ideal and X be a Banach space. We undertake the study of the vector space of ‐null sequences of Carl and Stephani on X , , from a unified point of view after we introduce a norm which makes it a Banach space. To give accurate results we consider local versions of the different types of accessibility of Banach operator ideals. We show that in the most common situations, when is right‐accessible for , behaves much alike . When this is the case we give a geometric tensor product representation of . On the other hand, we show an example where the representation fails. Also, via a trace duality formula, we characterize the dual space of . We apply our results to study some problems related with the ‐approximation property giving a trace condition which is used to solve the remaining case () of a problem posed by Kim (2015). Namely, we prove that if a dual space has the ‐approximation property then the space has the ‐approximation property.     

��ƽ��ND���в��ֺ͵ľ�ȷ������

In this paper, by using central limit theorem of ND sequences and probability inequality, the precise asymptotics for partial sums of nonstationary ND sequences is investigated, and the same results with it under that of NA sequences are obtained.     

Tight Heffter Arrays Exist for all Possible Values

A tight Heffter array is an matrix with nonzero entries from such that (i) the sum of the elements in each row and each column is 0, and (ii) no element from appears twice. We prove that exist if and only if both m and n are at least 3. If H has the property that all entries are integers of magnitude at most , every row and column sum is 0 over the integers, and H also satisfies ), we call H an integer Heffter array. We show integer Heffter arrays exist if and only if . Finally, an integer Heffter array is shiftable if each row and column contains the same number of positive and negative integers. We show that shiftable integer arrays exists exactly when both are even.     

伽罗瓦环上的一类No序列的构造

近年来,伽罗瓦环上的序列理论成为人们研究的热点问题.有限域上的No序列是一类伪随机序列,它在序列密码中占具十分重要的角色.本文利用伽罗瓦环上的置换,构造了伽罗瓦环Z_(p~e)上的一类新的No序列,并且研究了其线性复杂度.研究的结果表明此类No序列具有相当大的线性复杂度.     

Oligo-Quinolylene–Vinylene Foldamers

Quinoline based aromatic amide foldamers are known to adopt stable folded conformations. We have developed a synthetic approach to produce similar oligomers where all amide bonds, or part of them, have been replaced by an isosteric vinylene group. The results of solution and solid state structural studies show that oligomers exclusively containing vinylene linkages are not well folded, and adopt predominantly flat conformations. In contrast, a vinylene segment flanked by helical oligoamides also folds in a helix, albeit with a slightly lower curvature. The presence of vinylene functions also result in an extension of π-conjugation across the oligomer that may change charge transport properties. Altogether, these results pave the way to foldamers in which both structural control and specific electronic properties may be engineered.