the complexity of finding minimum length generator sequences abstract the computational complexity of the following problem is investigated given a permutation group specified as a set of generators and a single target permutation which is a member of the group what is the shortest expression for the target permutation in terms of the generators the general problem is demonstrated to be psppace complete and indeed is shown to remain so even when the generator set is restricted to contain only two permutations the restriction on generator set cardinality is the best possible as the problem becomes soluble in polynomial time if the generator set cantains only one permutation an interesting feature of this problem is that it does not fall under the headings of two person games or formal languages which cover the great majority of known pspace complete problems some restricted versions of the problem in which the generator set is fixed rather than being part of the problem instance are also investigated and shown to be computationally tractable one result of this kind is that determining the most compact expression of a permutation in terms of cyclicly adjacent transpositions can be achieved in polynomial time thus from an initial arrangement of distinct objects on a circle one can quickly compute the smallest number of interchanges of adjacent objects required to realise any other arrangement surprisingly this problem appears substantially more difficult to solve than the related one for which a solution has been known for some time in which the objects are arranged on a line segment

formality criteria for algebras over operads abstract we study some formality criteria for differential graded algebras over differential graded operads this unifies and generalizes other known approaches like the ones contained in 9 and 14 in particular we construct general operadic kaledin classes and show that they provide obstructions to formality moreover we show that an algebra a is formal if and only if its operadic cohomology spectral sequence degenerates at e 2

effects of publications in proceedings on the measure of the core size of coauthors abstract coauthors ca of a lead investigator li can receive a rank r according to their importance in having published joint publications with the li it is commonly accepted without any proof that publications in peer review journals and for example conference proceedings do not have the same value in a cv and the same applies to papers contributing to encyclopedia and book chapters it is examined here whether the relationship between the number j of publications of some scientist with her his coauthors ranked according to their decreasing importance i e j 1 r as found by ausloos 2013 1 still holds if the overall publication list is broken into such specific types of publications several authors with different careers but mainly having worked in the field of statistical mechanics are studied here to sort out answers to the questions the exponent turns out to be weakly scientist dependent only if the maximum value of j and r is large and is 1 then the m a core value i e the core number of cas for proceedings only is about half of the total one i e when all publications are counted contributions to the numerical values from both encyclopedia and book chapters are marginal the role of a time span on m a is also examined in two cases in relation to career activity considerations it can be considered that the findings serve as a contrasting point of view on how to quantify an individual publication career as recently done by petersen et al 2010 2012 2011 2 3 4 here emphasizing the collaboration size and evolution rather than a citation count moreover specifying the type of publication through the various m a s one can distinguish different behavior patterns of a scientific publication with cas

sequential vs parallel complexity in simple gene assembly we investigate some differences between the general intramolecular model for gene assembly and its restricted simple model although both models satisfactorily sort all current experimental data we show that the general model offers assembly strategies for a given string that vary in both assembly length and the operations used while the simple model will always use the same number of each type of operation to sort a gene when simple operations are applied in parallel this is given a new twist we prove that for any n 1 there exists a string having maximally parallel assemblies of any length between n and 2n

formality of dg algebras after kaledin abstract we provide proper foundations and proofs for the main results of kaledin 2007 ka the results include a flat base change for formality and behavior of formality in flat families of a and dg algebras

sorting permutations and binary strings by length weighted rearrangements abstract comparative genomics is a line of study which aims at determining dis similarities between genomes one way of doing this is to infer the large scale mutations also called genome rearrangements that are responsible for transforming one genome into another under the parsimony principle numerous efforts have been made over the past years regarding the traditional approach in which all genome rearrangements have the same unit cost however since long rearrangements are more likely to disturb the organism some works considered the length weighted approach in which the cost of each rearrangement is a function of its length the problem is thus modeled as follows given two genomes g 1 and g 2 and a set of allowed genome rearrangements each with a given cost determine their distance i e the total cost of a minimum cost sequence of rearrangements from that transforms g 1 into g 2 in this paper we study length weighted reversals and transpositions mainly considering their prefix variants in which the leftmost part of the genome must always be included we present approximation algorithms and bounds on the distances and diameters i e maximum possible distance over any two genomes of same length for eight problems when genomes are represented as permutations and another eight problems when genomes are represented as binary strings in each case considering two different cost functions

sorting by reversals and the theory of 4 regular graphs abstract we show that the theory of sorting by reversals fits into the well established theory of circuit partitions of 4 regular multigraphs which also involves the combinatorial structures of circle graphs and delta matroids in this way we expose strong connections between the two theories that have not been fully appreciated before we also discuss a generalization of sorting by reversals involving the double cut and join dcj operation finally we also show that the theory of sorting by reversals is closely related to that of gene assembly in ciliates

quick greedy computation for minimum common string partition in the minimum common string partition problem one is given two strings s and t with the same character statistics and one seeks for the smallest partition of s into substrings so that t can also be partitioned into the same substring multiset the problem is fundamental in several variants of edit distance with block operations e g signed reversal distance with duplicates and edit distance with moves the minimum common string partition problem is known to be np complete and the best approximation algorithm known has an approximation factor of o lognlog n since the minimum common string partition problem is of utmost practical importance one seeks a heuristic that will 1 usually have a low approximation factor and 2 will run fast a simple greedy algorithm is known which iteratively choose non overlapping longest common substrings of the input strings this algorithm has been well studied from an approximation point of view and it has been shown to have a bad worst case approximation factor however all the bad approximation factors presented so far stem from complicated recursive construction in practice the greedy algorithm seems to have small approximation factors however the best current implementation of greedy runs in quadratic time we propose a novel method to implement greedy in linear time

a 2 approximation algorithm for genome rearrangements by reversals and transpositions recently a new approach to analyze genomes evolving which is based on comparision of gene orders versus traditional comparision of dna sequences was proposed sankoff et al 1992 the approach is based on the global rearrangements e g inversions and transpositions of fragments analysis of genomes evolving by inversions and transpositions leads to a combinatorial problem of sorting by reversals and transpositions i e sorting of a permutation using reversals and transpositions of arbitrary fragments we study sorting of signed permutations by reversals and transpositions a problem which adequately models genome rearrangements as the genes in dna are oriented we establish a lower bound and give a 2 approximation algorithm for the problem

relative singularity categories i auslander resolutions abstract let r be an isolated gorenstein singularity with a non commutative resolution a end r r m in this paper we show that the relative singularity category r a of a has a number of pleasant properties such as being hom finite moreover it determines the classical singularity category d s g r of buchweitz and orlov as a certain canonical quotient category if r has finite cm type which includes for example kleinian singularities then we show the much more surprising result that d s g r determines r aus r where aus r is the corresponding auslander algebra the proofs of these results use dg algebras a koszul duality and the new concept of dg auslander algebras which may be of independent interest

genome rearrangements and sorting by reversals sequence comparison in molecular biology is in the beginning of a major paradigm shift a shift from gene comparison based on local mutations i e insertions deletions and substitutions of nucleotides to chromosome comparison based on global rearrangements i e inversions and transpositions of fragments the classical methods of sequence comparison do not work for global rearrangements and little is known in computer science about the edit distance between sequences if global rearrangements are allowed in the simplest form the problem of gene rearrangements corresponds to sorting by reversals i e sorting of an array using reversals of arbitrary fragments recently kececioglu and sankoff gave the first approximation algorithm for sorting by reversals with guaranteed error bound 2 and identified open problems related to chromosome rearrangements one of these problems is gollan s conjecture on the reversal diameter of the symmetric group this paper proves the conjecture further the problem of expected reversal distance between two random permutations is investigated the reversal distance between two random permutations is shown to be very close to the reversal diameter thereby indicating that reversal distance provides a good separation between related and nonrelated sequences in molecular evolution studies the gene rearrangement problem forces us to consider reversals of signed permutations as the genes in dna could be positively or negatively oriented an approximation algorithm for signed permutation is presented which provides a performance guarantee of 3 over 2 finally using the signed permutations approach an approximation algorithm for sorting by reversals is described which achieves a performance guarantee of 7 over 4

algebras and modules in monoidal model categories in recent years the theory of structured ring spectra formerly known as a infty and e infty ring spectra has been simplified by the discovery of categories of spectra with strictly associative and commutative smash products now a ring spectrum can simply be defined as a monoid with respect to the smash product in one of these new categories of spectra in this paper we provide a general method for constructing model category structures for categories of ring algebra and module spectra this provides the necessary input for obtaining model categories of symmetric ring spectra functors with smash product gamma rings and diagram ring spectra algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra 1991 mathematics subject classification primary 55u35 secondary 18d10

a simpler and faster 1 5 approximation algorithm for sorting by transpositions an important problem in genome rearrangements is sorting permutations by transpositions the complexity of the problem is still open and two rather complicated 1 5 approximation algorithms for sorting linear permutations are known bafna and pevzner 98 and christie 99 the fastest known algorithm is the quadratic algorithm of bafna and pevzner in this paper we observe that the problem of sorting circular permutations by transpositions is equivalent to the problem of sorting linear permutations by transpositions hence all algorithms for sorting linear permutations by transpositions can be used to sort circular permutations our main result is a new o n3 2 log n 1 5 approximation algorithm which is considerably simpler than the previous ones and whose analysis is significantly less involved

successor rules for flipping pancakes and burnt pancakes a stack of n pancakes can be rearranged in all n ways by a sequence of n 1 flips and a stack of n burnt pancakes can be rearranged in all 2 n n ways by a sequence of 2 n n 1 flips in both cases a computer program can efficiently generate suitable solutions we approach these tasks instead from a human perspective how can we determine the next flip directly from the current stack how can we flip the minimum or maximum number of burnt pancakes overall what if we are only allowed to flip the top n 2 n 1 or n burnt pancakes we answer the first question with simple successor rules that take worst case o n time and amortized o 1 time then we answer the second question exactly for minimization and provide conjectures for maximization for the third question we prove that solutions almost certainly exist for pancakes and burnt pancakes using only these three flips more broadly we discuss how efficiency and optimality can shape iterative solutions to hamilton cycle problems in highly symmetric graphs

discussion on the meeting on statistical modelling and analysis of genetic data david j balding imperial college school of medicine london i extendmy apologies to the authors that an unavoidable commitment arising unexpectedly in the 18 hours before the meeting robbed me of my final preparation so that my comments at the meeting were poorly presented i shall try to do a better job in this written version and to leave enough space i shall omit my introductory comments about the role of statisticians in bioinformatics

singularities of moduli spaces of sheaves on k3 surfaces and nakajima quiver varieties abstract the aim of this paper is to study the singularities of certain moduli spaces of sheaves on k3 surfaces by means of nakajima quiver varieties the singularities in question arise from the choice of a non generic polarization with respect to which we consider stability and admit natural symplectic resolutions corresponding to choices of general polarizations for sheaves that are pure of dimension one we show that these moduli spaces are locally around a singular point isomorphic to a quiver variety and that via this isomorphism the natural symplectic resolutions correspond to variations of git quotients of the quiver variety

on some formality criteria for dg lie algebras abstract we give some formality criteria for a differential graded lie algebra to be formal for instance we show that a dg lie algebra l is formal if and only if the natural spectral sequence computing the chevalley eilenberg cohomology h ce l l degenerates at e 2

transforming cabbage into turnip polynomial algorithm for sorting signed permutations by reversals genomes frequently evolve by reversals r i j that transform a gene order 1 i i 1 j 1 j n into 1 i j 1 i 1 j n reversal distance between permutations and sis the minimum number of reversals to transform into a analysis of genome rearrangements in molecular biology started in the late 1930 s when dobzhansky and sturtevant published a milestone paper presenting a rearrangement scenario with 17 inversions between the species of drosophilia analysis of genomes evolving by inversions leads to a combinatorial problem of sorting by reversals studied in detail recently we study sorting of signed permutations by reversals a problem that adequately models rearrangements in a small genomes like chloroplast or mitochondrial dna the previously suggested approximation algorithms for sorting signed permutations by reversals compute the reversal distance between permutations with an astonishing accuracy for both simulated and biological data we prove a duality theorem explaining this intriguing performance and show that there exists a hidden parameter that allows one to compute the reversal distance between signed permutations in polynomial time

dg quotients of dg categories abstract keller introduced a notion of quotient of a differential graded category modulo a full differential graded subcategory which agrees with verdier s notion of quotient of a triangulated category modulo a triangulated subcategory this work is an attempt to further develop his theory

an efficient algorithm for one sided block ordering problem under block interchange distance abstract in this work we study the one sided block ordering problem under block interchange distance given two signed permutations and of size n where represents a partially assembled genome consisting of several blocks i e contigs and represents a completely assembled genome the one sided block ordering problem under block interchange distance is to order i e assemble the blocks of such that the block interchange distance between the assembly of and is minimized the one sided block ordering problem is useful in genome resequencing because its algorithms can be used to assemble the contigs of partially assembled resequencing genomes based on their completely assembled genomes by using permutation groups in algebra we design an efficient algorithm to solve the one sided block ordering problem under block interchange distance in o n log n time moreover we show that the assembly of can be done in o n time and its block interchange distance from can also be calculated in advance in o n time

a faster and simpler algorithm for sorting signed permutations by reversals we give a quadratic time algorithm for finding the minimum number of reversals needed to sort a signed permutation our algorithm is faster than the previous algorithm of hannenhalli and pevzner and its faster implementation by berman and hannenhalli the algorithm is conceptually simple and does not require special data structures our study also considerably simplifies the combinatorial structures used by the analysis

on the complexity of unsigned translocation distance translocation is one of the basic operations for genome rearrangement translocation distance is the minimum number of translocations required to transform one genome into the other in this paper we show that computing the translocation distance for unsigned genomes is np hard moreover we show that approximating the translocation distance for unsigned genomes within ratio 1 00017 is np hard

the evolution of the random reversal graph genomes are typically represented as signed permutations where each integer corresponds to a single gene and its sign indicates the orientation of the gene in this paper we study genome rearrangements via reversals sankoff and blanchette 1999 20 flipping entire segments of genes and changing their orientations this abstraction leads to the notion of the reversal graph in which two signed permutations are neighbors if they differ by one reversal we identify the evolution of multiple genomes within the random reversal graph i e the probability space consisting of subgraphs over signed permutations obtained by selecting edges reversals with independent probability n which is an important framework for the analysis of genome rearrangements in the sense of relating the reversal rate n with the global evolution of genomes our main result shows that the structure of the random reversal graph changes dramatically at n 1 n 1 2 for n 1 n 1 2 the random graph consists of components of size at most o n ln n a s and for 1 n 1 2 there emerges a unique largest component of size 2 n n a s where is the survival probability of a certain branching process this giant component is furthermore dense in the reversal graph

polynomial time sortable stacks of burnt pancakes pancake flipping a famous open problem in computer science can be formalised as the problem of sorting a permutation of positive integers using as few prefix reversals as possible in that context a prefix reversal of length k reverses the order of the first k elements of the permutation the burnt variant of pancake flipping involves permutations of signed integers and reversals in that case not only reverse the order of elements but also invert their signs although three decades have now passed since the first works on these problems neither their computational complexity nor the maximal number of prefix reversals needed to sort a permutation is yet known in this work we prove a new lower bound for sorting burnt pancakes and show that an important class of permutations known as simple permutations can be optimally sorted in polynomial time