Counting matrices over finite fields with support on skew Young diagrams and complements of Rothe diagrams

We consider the problem of finding the number of matrices over a finite field with a certain rank and with support that avoids a subset of the entries. These matrices are a q-analogue of permutations with restricted positions (i.e., rook placements). For general sets of entries these numbers of matrices are not polynomials in q (Stembridge 98); however, when the set of entries is a Young diagram, the numbers, up to a power of q-1, are polynomials with nonnegative coefficients (Haglund 98). In this paper, we give a number of conditions under which these numbers are polynomials in q, or even polynomials with nonnegative integer coefficients. We extend Haglund's result to complements of skew Young diagrams, and we apply this result to the case when the set of entries is the Rothe diagram of a permutation. In particular, we give a necessary and sufficient condition on the permutation for its Rothe diagram to be the complement of a skew Young diagram up to rearrangement of rows and columns. We end by giving conjectures connecting invertible matrices whose support avoids a Rothe diagram and Poincar\'e polynomials of the strong Bruhat order.Comment: 24 pages, 9 figures, 1 tabl

A Two-Tiered Correlation of Dark Matter with Missing Transverse Energy: Reconstructing the Lightest Supersymmetric Particle Mass at the LHC

We suggest that non-trivial correlations between the dark matter particle mass and collider based probes of missing transverse energy H_T^miss may facilitate a two tiered approach to the initial discovery of supersymmetry and the subsequent reconstruction of the LSP mass at the LHC. These correlations are demonstrated via extensive Monte Carlo simulation of seventeen benchmark models, each sampled at five distinct LHC center-of-mass beam energies, spanning the parameter space of No-Scale F-SU(5).This construction is defined in turn by the union of the Flipped SU(5) Grand Unified Theory, two pairs of hypothetical TeV scale vector-like supersymmetric multiplets with origins in F-theory, and the dynamically established boundary conditions of No-Scale Supergravity. In addition, we consider a control sample comprised of a standard minimal Supergravity benchmark point. Led by a striking similarity between the H_T^miss distribution and the familiar power spectrum of a black body radiator at various temperatures, we implement a broad empirical fit of our simulation against a Poisson distribution ansatz. We advance the resulting fit as a theoretical blueprint for deducing the mass of the LSP, utilizing only the missing transverse energy in a statistical sampling of >= 9 jet events. Cumulative uncertainties central to the method subsist at a satisfactory 12-15% level. The fact that supersymmetric particle spectrum of No-Scale F-SU(5) has thrived the withering onslaught of early LHC data that is steadily decimating the Constrained Minimal Supersymmetric Standard Model and minimal Supergravity parameter spaces is a prime motivation for augmenting more conventional LSP search methodologies with the presently proposed alternative.Comment: JHEP version, 17 pages, 9 Figures, 2 Table

Reconciling gene family evolution and species evolution

Species evolution can often be adequately described with a phylogenetic tree. Interestingly, this is the case also for the evolution of homologous genes; a gene in an ancestral species may – through gene duplication, gene loss, lateral gene transfer (LGT), and speciation events – give rise to a gene family distributed across contemporaneous species. However, molecular sequence evolution and genetic recombination make the history – the gene tree – non-trivial to reconstruct from present-day sequences. This history is of biological interest, e.g., for inferring potential functional equivalences of extant gene pairs. In this thesis, we present biologically sound probabilistic models for gene family evolution guided by species evolution – effectively yielding a gene-species tree reconciliation. Using Bayesian Markov-chain Monte Carlo (MCMC) inference techniques, we show that by taking advantage of the information provided by the species tree, our methods achieve more reliable gene tree estimates than traditional species tree-uninformed approaches. Specifically, we describe a comprehensive model that accounts for gene duplication, gene loss, a relaxed molecular clock, and sequence evolution, and we show that the method performs admirably on synthetic and biological data. Further-more, we present two expansions of the inference procedure, enabling it to pro-vide (i) refined gene tree estimates with timed duplications, and (ii) probabilistic orthology estimates – i.e., that the origin of a pair of extant genes is a speciation. Finally, we present a substantial development of the model to account also for LGT. A sophisticated algorithmic framework of dynamic programming and numerical methods for differential equations is used to resolve the computational hurdles that LGT brings about. We apply the method on two bacterial datasets where LGT is believed to be prominent, in order to estimate genome-wide LGT and duplication rates. We further show that traditional methods – in which gene trees are reconstructed and reconciled with the species tree in separate stages – are prone to yield inferior gene tree estimates that will overestimate the number of LGT events.Arters evolution kan i många fall beskrivas med ett träd, vilket redan Darwins anteckningsböcker från HMS Beagle vittnar om. Detta gäller också homologa gener; en gen i en ancestral art kan – genom genduplikationer, genförluster, lateral gentransfer (LGT) och artbildningar – ge upphov till en genfamilj spridd över samtida arter. Att från sekvenser från nu levande arter rekonstruera genfamiljens framväxt – genträdet – är icke-trivialt på grund av genetisk rekombination och sekvensevolution. Genträdet är emellertid av biologiskt intresse, i synnerhet för att det möjliggör antaganden om funktionellt släktskap mellan nutida genpar. Denna avhandling behandlar biologiskt välgrundade sannolikhetsmodeller för genfamiljsevolution. Dessa modeller tar hjälp av artevolutionens starka inverkan på genfamiljens historia, och ger väsentligen upphov till en förlikning av genträd och artträd. Genom Bayesiansk inferens baserad på Markov-chain Monte Carlo (MCMC) visar vi att våra metoder presterar bättre genträdsskattningar än traditionella ansatser som inte tar artträdet i beaktning. Mer specifikt beskriver vi en modell som omfattar genduplikationer, genförluster, en relaxerad molekylär klocka, samt sekvensevolution, och visar att metoden ger högkvalitativa skattningar på både syntetiska och biologiska data. Vidare presenterar vi två utvidgningar av detta ramverk som möjliggör (i) genträdsskattningar med tidpunkter för duplikationer, samt (ii) probabilistiska ortologiskattningar – d.v.s. att två nutida gener härstammar från en artbildning. Slutligen presenterar vi en modell som inkluderar LGT utöver ovan nämnda mekanismer. De beräkningsmässiga svårigheter som LGT ger upphov till löses med ett intrikat ramverk av dynamisk programmering och numeriska metoder för differentialekvationer. Vi tillämpar metoden för att skatta LGT- och duplikationsraten hos två bakteriella dataset där LGT förmodas ha spelat en central roll. Vi visar också att traditionella metoder – där genträd skattas och förlikas med artträdet i separata steg – tenderar att ge sämre genträdsskattningar, och därmed överskatta antalet LGT-händelser.At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 5: Manuscript.</p

Orienteering in the library? : A case study about the possibilities to guide the visitors at Hammarö bibliotek

The aim of this Master’s thesis is to investigate how a public library should sign and organize their resources to make them as accessible as possible to the users of the library. Our theory, Paul Arthur’s and Romedi Passini’s wayfinding theory, is about how people search through information loaded environments. Our empirical material consists mainly of three parts: an inventory of the resources and guiding at Hammarö bibliotek, eight interviews with visitors at Hammarö bibliotek and observations of how visitors use and interact with the library, its resources and guiding. With this material we got an image of the staff’s plans about the organization and guiding in the library, what the visitors thought about the library’s organization and guiding and how they used and interacted with the library. When analysing the empirical material with the wayfinding theory we found out that the library users searched through Hammarö bibliotek like its resources were hierarchically structured. On the whole the public library’s resources were structured hierarchically, but for various reasons the structure were not consistent. Our conclusions were that Hammarö bibliotek should organize their resources more consistent and make the organization mainly known for the users of the library in the entrance. The users also need to be led to the parts of the library that differ from the hierarchic structure. This is possible through a consistent and consequent signage system, which we discuss in this thesis.Uppsatsnivå: