Torsion pairs and rigid objects in tubes

We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs, maximal rigid objects and the bijection between them geometrically. We also give a similar geometric description in the case of the linear orientation of a Dynkin quiver of type A.Comment: 25 pages, 13 figures. Paper shortened. Minor errors correcte

Mutation in triangulated categories and rigid Cohen-Macaulay modules

We introduce the notion of mutation of $n$-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.Comment: 52 pages. To appear in Invent. Mat

On Morita and derived equivalences for cohomological Mackey algebras

By results of the second author, a source algebra equivalence between two p-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence between two blocks induces a derived equivalence between the corresponding categories ofcohomological Mackey functors. The main result of this paper proves a partial converse: an equivalence (resp. Rickard equivalence) between the categories of cohomological Mackey functors of two blocks of finite groups induces a permeable Morita (resp. derived) equivalence between the two block algebras

The GL(2, C) McKay correspondence

In this paper we show that for any affine complete rational surface singularity the quiver of the reconstruction algebra can be determined combinatorially from the dual graph of the minimal resolution. As a consequence the derived category of the minimal resolution is equivalent to the derived category of an algebra whose quiver is determined by the dual graph. Also, for any finite subgroup G of GL(2,C)GL(2,C), it means that the endomorphism ring of the special CM CC [[x, y]]G-modules can be used to build the dual graph of the minimal resolution of C2/GC2/G, extending McKay’s observation (McKay, Proc Symp Pure Math, 37:183–186, 1980) for finite subgroups of SL(2,C)SL(2,C) to all finite subgroups of GL(2,C)GL(2,C)

Torsion pairs and simple-minded systems in triangulated categories

Let T be a Hom-finite triangulated Krull-Schmidt category over a field k. Inspired by a definition of Koenig and Liu, we say that a family S of pairwise orthogonal objects in T with trivial endomorphism rings is a simple-minded system if its closure under extensions is all of T. We construct torsion pairs in T associated to any subset X of a simple-minded system S, and use these to define left and right mutations of S relative to X. When T has a Serre functor \nu, and S and X are invariant under \nu[1], we show that these mutations are again simple-minded systems. We are particularly interested in the case where T is the stable module category of a self-injective algebra \Lambda. In this case, our mutation procedure parallels that introduced by Koenig and Yang for simple-minded collections in the derived category of \Lambda. It follows that the mutation of the set of simple \Lambda-modules relative to X yields the images of the simple \Gamma-modules under a stable equivalence between \Gamma\ and \Lambda, where \Gamma\ is the tilting mutation of \Lambda\ relative to X.Comment: Minor corrections. To appear in Applied Categorical Structures. The final publication is available at springerlink.com: http://link.springer.com/article/10.1007%2Fs10485-014-9365-

Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice

Efficient Implementation of Bilinear Pairings on ARM Processors

Abstract. As hardware capabilities increase, low-power devices such as smartphones represent a natural environment for the efficient imple-mentation of cryptographic pairings. Few works in the literature have considered such platforms despite their growing importance in a post-PC world. In this paper, we investigate the efficient computation of the Optimal-Ate pairing over Barreto-Naehrig curves in software at differ-ent security levels on ARM processors. We exploit state-of-the-art tech-niques and propose new optimizations to speed up the computation in the tower field and curve arithmetic. In particular, we extend the concept of lazy reduction to inversion in extension fields, analyze an efficient al-ternative for the sparse multiplication used inside the Miller’s algorithm and reduce further the cost of point/line evaluation formulas in affine and projective homogeneous coordinates. In addition, we study the effi-ciency of using M-type sextic twists in the pairing computation and carry out a detailed comparison between affine and projective coordinate sys-tems. Our implementations on various mass-market smartphones and tablets significantly improve the state-of-the-art of pairing computation on ARM-powered devices, outperforming by at least a factor of 3.7 the best previous results in the literature

Realisation functors in tilting theory

Derived equivalences and t-structures are closely related. We use realisation functors associated to t-structures in triangulated categories to establish a derived Morita theory for abelian categories with a projective generator or an injective cogenerator. For this purpose we develop a theory of (non-compact, or large) tilting and cotilting objects that generalises the preceding notions in the literature. Within the scope of derived Morita theory for rings we show that, under some assumptions, the realisation functor is a derived tensor product. This fact allows us to approach a problem by Rickard on the shape of derived equivalences. Finally, we apply the techniques of this new derived Morita theory to show that a recollement of derived categories is a derived version of a recollement of abelian categories if and only if there are tilting or cotilting t-structures glueing to a tilting or a cotilting t-structure. As a further application, we answer a question by Xi on a standard form for recollements of derived module categories for finite dimensional hereditary algebras

A comprehensive structural, biochemical and biological profiling of the human NUDIX hydrolase family

The NUDIX enzymes are involved in cellular metabolism and homeostasis, as well as mRNA processing. Although highly conserved throughout all organisms, their biological roles and biochemical redundancies remain largely unclear. To address this, we globally resolve their individual properties and inter-relationships. We purify 18 of the human NUDIX proteins and screen 52 substrates, providing a substrate redundancy map. Using crystal structures, we generate sequence alignment analyses revealing four major structural classes. To a certain extent, their substrate preference redundancies correlate with structural classes, thus linking structure and activity relationships. To elucidate interdependence among the NUDIX hydrolases, we pairwise deplete them generating an epistatic interaction map, evaluate cell cycle perturbations upon knockdown in normal and cancer cells, and analyse their protein and mRNA expression in normal and cancer tissues. Using a novel FUSION algorithm, we integrate all data creating a comprehensive NUDIX enzyme profile map, which will prove fundamental to understanding their biological functionality

モモセン コウサイキン ビョウキン(オモ ニXanthomonas arboricola pv. pruni)ノ ヤクザイ カンジュセイ ニ カンスル ケンキュウ

モモせん孔細菌病は重要病害の一つであり,国内ではXanthomonas arboricola pv. pruni, Pseudomonas syringae pv. syringae およびBrenneria nigrifluensの3種が病原細菌として報告されている。一般的に本病の主病原はX. a. pv. pruniであるとされているが,それを詳細に調査した報告は少ない。また,本病の防除は抗生物質剤を中心とした薬剤の散布が主である。抗生物質剤は様々な病害で薬剤耐性菌の発生が報告されており問題となっている。本病においても耐性菌の出現による防除効果の低下が懸念されている。そこで,2008年から2011年の4年間に合計7県151ほ場からモモせん孔細菌病罹病試料を採取し,病原細菌を分離,国内で発生している本病の主病原を再確認したところ,分離した菌株のほとんどがX. a. pv. pruniであったことから本病の主病原はX. a. pv. pruniである可能性が示唆された。さらに,菌株のオキシテトラサイクリン,オキソリニック酸およびストレプトマイシンに対する最小生育阻止濃度(MIC)を調査したところ,オキシテトラサイクリンおよびオキソリニック酸に対するMICは25ppm以下であった。一方,ストレプトマイシンに対してはMICが2000ppm以上を示す菌株が200菌株と全体の43%を占めており,ストレプトマイシンに対して耐性を有するX. a. pv. pruniが比較的高い割合で存在することが示唆された。Although bacterial shot hole disease is one of the most important diseases in peach production and three pathogens have been reported from the disease in Japan, there is little investigation on the dominant pathogen. As the use of bactericidal antibiotics is indispensable to control this disease, emergence of the causal bacteria with resistance to bactericides has been reported and is noticed as a serious problem in peach production. Samples of peach plants with bacterial shot hole disease were collected from 151 fields in 7 prefectures in four years from 2008 to 2011 for isolation and reaffirmation of the main causal bacteria. Most frequently isolated bacteria was identified as Xanthomonas arboricola pv. pruni, recognized as the dominant causal agent of bacterial shot hole disease of peach. The bacterial isolates identified as the dominant pathogen were examined for their minimal inhibitory concentration (MIC) against oxytetracycline, oxolinic acid and streptomycin to evaluate their susceptibility. Although all isolates tested were susceptible to oxytetracycline and oxolinic acid and showed <25ppm (MIC), 200 isolates (43% of tested isolates) showed more than 2000ppm (MIC) to streptomycin and were judged as resistant. The results of the survey showed the considerably higher population of X. a. pv. pruni with resistance to streptomycin in peach fields