Topics in algorithmic, enumerative and geometric combinatorics

This thesis presents five papers, studying enumerative and extremal problems on combinatorial structures. The first paper studies Forman's discrete Morse theory in the case where a group acts on the underlying complex. We generalize the notion of a Morse matching, and obtain a theory that can be used to simplify the description of the G-homotopy type of a simplicial complex. As an application, we determine the S_2xS_{n-2}-homotopy type of the complex of non-connected graphs on n nodes. In the introduction, connections are drawn between the first paper and the evasiveness conjecture for monotone graph properties. In the second paper, we investigate Hansen polytopes of split graphs. By applying a partitioning technique, the number of nonempty faces is counted, and in particular we confirm Kalai's 3^d-conjecture for such polytopes. Furthermore, a characterization of exactly which Hansen polytopes are also Hanner polytopes is given. We end by constructing an interesting class of Hansen polytopes having very few faces and yet not being Hanner. The third paper studies the problem of packing a pattern as densely as possible into compositions. We are able to find the packing density for some classes of generalized patterns, including all the three letter patterns. In the fourth paper, we present combinatorial proofs of the enumeration of derangements with descents in prescribed positions. To this end, we consider fixed point lambda-coloured permutations, which are easily enumerated. Several formulae regarding these numbers are given, as well as a generalisation of Euler's difference tables. We also prove that except in a trivial special case, the event that pi has descents in a set S of positions is positively correlated with the event that pi is a derangement, if pi is chosen uniformly in S_n. The fifth paper solves a partially ordered generalization of the famous secretary problem. The elements of a finite nonempty partially ordered set are exposed in uniform random order to a selector who, at any given time, can see the relative order of the exposed elements. The selector's task is to choose online a maximal element. We describe a strategy for the general problem that achieves success probability at least 1/e for an arbitrary partial order, thus proving that the linearly ordered set is at least as difficult as any other instance of the problem. To this end, we define a probability measure on the maximal elements of an arbitrary partially ordered set, that may be interesting in its own right

Three-point correlators for giant magnons

Three-point correlation functions in the strong-coupling regime of the AdS/CFT correspondence can be analyzed within a semiclassical approximation when two of the vertex operators correspond to heavy string states having large quantum numbers while the third vertex corresponds to a light state with fixed charges. We consider the case where the heavy string states are chosen to be giant magnon solitons with either a single or two different angular momenta, for various different choices of light string states.Comment: 15 pages. Latex. v2: Misprints corrected. Published versio

Evidence maps and evidence gaps: evidence review mapping as a method for collating and appraising evidence reviews to inform research and policy

Evidence reviews are a key mechanism for incorporating extensive, complex and specialised evidence into policy and practice, and in guiding future research. However, evidence reviews vary in scope and methodological rigour, creating several risks for decision-makers: decisions may be informed by less reliable reviews; apparently conflicting interpretations of evidence may obfuscate decisions; and low quality reviews may create the perception that a topic has been adequately addressed, deterring new syntheses (cryptic evidence gaps). We present a new approach, evidence review mapping, designed to produce a visual representation and critical assessment of the review landscape for a particular environmental topic or question. By systematically selecting and describing the scope and rigour of each review, this helps guide non-specialists to the most relevant and methodologically reliable reviews. The map can also direct future research through the identification of evidence gaps (whether cryptic or otherwise) and redundancy (multiple reviews on similar questions). We consider evidence review mapping a complementary approach to systematic reviews and systematic maps of primary literature and an important tool for facilitating evidence-based decision-making and research efficiency

Investigation of Mitochondrial Dysfunction by Sequential Microplate-Based Respiration Measurements from Intact and Permeabilized Neurons

Mitochondrial dysfunction is a component of many neurodegenerative conditions. Measurement of oxygen consumption from intact neurons enables evaluation of mitochondrial bioenergetics under conditions that are more physiologically realistic compared to isolated mitochondria. However, mechanistic analysis of mitochondrial function in cells is complicated by changing energy demands and lack of substrate control. Here we describe a technique for sequentially measuring respiration from intact and saponin-permeabilized cortical neurons on single microplates. This technique allows control of substrates to individual electron transport chain complexes following permeabilization, as well as side-by-side comparisons to intact cells. To illustrate the utility of the technique, we demonstrate that inhibition of respiration by the drug KB-R7943 in intact neurons is relieved by delivery of the complex II substrate succinate, but not by complex I substrates, via acute saponin permeabilization. In contrast, methyl succinate, a putative cell permeable complex II substrate, failed to rescue respiration in intact neurons and was a poor complex II substrate in permeabilized cells. Sequential measurements of intact and permeabilized cell respiration should be particularly useful for evaluating indirect mitochondrial toxicity due to drugs or cellular signaling events which cannot be readily studied using isolated mitochondria

Human IgG1 Responses to Surface Localised Schistosoma mansoni Ly6 Family Members Drop following Praziquantel Treatment

The heptalaminate-covered, syncytial tegument is an important anatomical adaptation that enables schistosome parasites to maintain long-term, intravascular residence in definitive hosts. Investigation of the proteins present in this surface layer and the immune responses elicited by them during infection is crucial to our understanding of host/parasite interactions. Recent studies have revealed a number of novel tegumental surface proteins including three (SmCD59a, SmCD59b and Sm29) containing uPAR/Ly6 domains (renamed SmLy6A SmLy6B and SmLy6D in this study). While vaccination with SmLy6A (SmCD59a) and SmLy6D (Sm29) induces protective immunity in experimental models, human immunoglobulin responses to representative SmLy6 family members have yet to be thoroughly explored.Using a PSI-BLAST-based search, we present a comprehensive reanalysis of the Schistosoma mansoni Ly6 family (SmLy6A-K). Our examination extends the number of members to eleven (including three novel proteins) and provides strong evidence that the previously identified vaccine candidate Sm29 (renamed SmLy6D) is a unique double uPAR/Ly6 domain-containing representative. Presence of canonical cysteine residues, signal peptides and GPI-anchor sites strongly suggest that all SmLy6 proteins are cell surface-bound. To provide evidence that SmLy6 members are immunogenic in human populations, we report IgG1 (as well as IgG4 and IgE) responses against two surface-bound representatives (SmLy6A and SmLy6B) within a cohort of S. mansoni-infected Ugandan males before and after praziquantel treatment. While pre-treatment IgG1 prevalence for SmLy6A and SmLy6B differs amongst the studied population (7.4% and 25.3% of the cohort, respectively), these values are both higher than IgG1 prevalence (2.7%) for a sub-surface tegumental antigen, SmTAL1. Further, post-treatment IgG1 levels against surface-associated SmLy6A and SmLy6B significantly drop (p = 0.020 and p < 0.001, respectively) when compared to rising IgG1 levels against sub-surface SmTAL1.Collectively, these results expand the number of SmLy6 proteins found within S. mansoni and specifically demonstrate that surface-associated SmLy6A and SmLy6B elicit immunological responses during infection in endemic communities

Magnetic Domains

Recently a Nahm transform has been discovered for magnetic bags, which are conjectured to arise in the large n limit of magnetic monopoles with charge n. We interpret these ideas using string theory and present some partial proofs of this conjecture. We then extend the notion of bags and their Nahm transform to higher gauge theories and arbitrary domains. Bags in four dimensions conjecturally describe the large n limit of n self-dual strings. We show that the corresponding Basu-Harvey equation is the large n limit of an equation describing n M2-branes, and that it has a natural interpretation in loop space. We also formulate our Nahm equations using strong homotopy Lie algebras.Comment: 42 pages, minor improvements, published versio

Longitudinal Evaluation of an N-Ethyl-N-Nitrosourea-Created Murine Model with Normal Pressure Hydrocephalus

Normal-pressure hydrocephalus (NPH) is a neurodegenerative disorder that usually occurs late in adult life. Clinically, the cardinal features include gait disturbances, urinary incontinence, and cognitive decline.Herein we report the characterization of a novel mouse model of NPH (designated p23-ST1), created by N-ethyl-N-nitrosourea (ENU)-induced mutagenesis. The ventricular size in the brain was measured by 3-dimensional micro-magnetic resonance imaging (3D-MRI) and was found to be enlarged. Intracranial pressure was measured and was found to fall within a normal range. A histological assessment and tracer flow study revealed that the cerebral spinal fluid (CSF) pathway of p23-ST1 mice was normal without obstruction. Motor functions were assessed using a rotarod apparatus and a CatWalk gait automatic analyzer. Mutant mice showed poor rotarod performance and gait disturbances. Cognitive function was evaluated using auditory fear-conditioned responses with the mutant displaying both short- and long-term memory deficits. With an increase in urination frequency and volume, the mutant showed features of incontinence. Nissl substance staining and cell-type-specific markers were used to examine the brain pathology. These studies revealed concurrent glial activation and neuronal loss in the periventricular regions of mutant animals. In particular, chronically activated microglia were found in septal areas at a relatively young age, implying that microglial activation might contribute to the pathogenesis of NPH. These defects were transmitted in an autosomal dominant mode with reduced penetrance. Using a whole-genome scan employing 287 single-nucleotide polymorphic (SNP) markers and further refinement using six additional SNP markers and four microsatellite markers, the causative mutation was mapped to a 5.3-cM region on chromosome 4.Our results collectively demonstrate that the p23-ST1 mouse is a novel mouse model of human NPH. Clinical observations suggest that dysfunctions and alterations in the brains of patients with NPH might occur much earlier than the appearance of clinical signs. p23-ST1 mice provide a unique opportunity to characterize molecular changes and the pathogenic mechanism of NPH

Physical and Functional Interaction of NCX1 and EAAC1 Transporters Leading to Glutamate-Enhanced ATP Production in Brain Mitochondria

Glutamate is emerging as a major factor stimulating energy production in CNS. Brain mitochondria can utilize this neurotransmitter as respiratory substrate and specific transporters are required to mediate the glutamate entry into the mitochondrial matrix. Glutamate transporters of the Excitatory Amino Acid Transporters (EAATs) family have been previously well characterized on the cell surface of neuronal and glial cells, representing the primary players for glutamate uptake in mammalian brain. Here, by using western blot, confocal microscopy and immunoelectron microscopy, we report for the first time that the Excitatory Amino Acid Carrier 1 (EAAC1), an EAATs member, is expressed in neuronal and glial mitochondria where it participates in glutamate-stimulated ATP production, evaluated by a luciferase-luciferin system. Mitochondrial metabolic response is counteracted when different EAATs pharmacological blockers or selective EAAC1 antisense oligonucleotides were used. Since EAATs are Na+-dependent proteins, this raised the possibility that other transporters regulating ion gradients across mitochondrial membrane were required for glutamate response. We describe colocalization, mutual activity dependency, physical interaction between EAAC1 and the sodium/calcium exchanger 1 (NCX1) both in neuronal and glial mitochondria, and that NCX1 is an essential modulator of this glutamate transporter. Only NCX1 activity is crucial for such glutamate-stimulated ATP synthesis, as demonstrated by pharmacological blockade and selective knock-down with antisense oligonucleotides. The EAAC1/NCX1-dependent mitochondrial response to glutamate may be a general and alternative mechanism whereby this neurotransmitter sustains ATP production, since we have documented such metabolic response also in mitochondria isolated from heart. The data reported here disclose a new physiological role for mitochondrial NCX1 as the key player in glutamate-induced energy production