An infinite hierarchy in a class of polynomial-time program schemes

We define a class of program schemes RFDPS constructed around notions of forall-loops, repeat-loops, arrays and if-then-else instructions, and which take finite structures as inputs, and we examine the class of problems, denoted RFDPS also, accepted by such program schemes. The class of program schemes RFDPS is a logic, in Gurevich's sense, in that: every program scheme accepts an isomorphism-closed class of finite structures; we can recursively check whether a given finite structure is accepted by a given program scheme; and we can recursively enumerate the program schemes of RFDPS. We show that the class of problems RFDPS properly contains the class of problems definable in inductive fixed-point logic (for example, the well-known problem Parity is in RFDPS) and that there is a strict, infinite hierarchy of classes of problems within RFDPS (the union of which is RFDPS) parameterized by the depth of nesting of forall-loops in our program schemes. This is the first strict, infinite hierarchy in any polynomial-time logic properly extending inductive fixed-point logic (with the property that the union of the classes in the hierarchy consists of all problems definable in the logic). The fact that there are problems (like Parity) in RFDPS which cannot be defined in many of the more traditional logics of finite model theory (which often have zero-one laws) essentially means that existing tools, techniques and logical hierarchy results are of limited use to us

Genesis of ancestral haplotypes: RNA modifications and reverse transcription–mediated polymorphisms

Understanding the genesis of the block haplotype structure of the genome is a major challenge. With the completion of the sequencing of the Human Genome and the initiation of the HapMap project the concept that the chromosomes of the mammalian genome are a mosaic, or patchwork, of conserved extended block haplotype sequences is now accepted by the mainstream genomics research community. Ancestral Haplotypes (AHs) can be viewed as a recombined string of smaller Polymorphic Frozen Blocks (PFBs). How have such variant extended DNA sequence tracts emerged in evolution? Here the relevant literature on the problem is reviewed from various fields of molecular and cell biology particularly molecular immunology and comparative and functional genomics. Based on our synthesis we then advance a testable molecular and cellular model. A critical part of the analysis concerns the origin of the strand biased mutation signatures in the transcribed regions of the human and higher primate genome, A-to-G versus T-to-C (ratio ~1.5 fold) and C-to-T versus G-to-A (≥1.5 fold). A comparison and evaluation of the current state of the fields of immunoglobulin Somatic Hypermutation (SHM) and Transcription-Coupled DNA Repair focused on how mutations in newly synthesized RNA might be copied back to DNA thus accounting for some of the genome-wide strand biases (e.g., the A-to-G vs T-to-C component of the strand biased spectrum). We hypothesize that the genesis of PFBs and extended AHs occurs during mutagenic episodes in evolution (e.g., retroviral infections) and that many of the critical DNA sequence diversifying events occur first at the RNA level, e.g., recombination between RNA strings resulting in tandem and dispersed RNA duplications (retroduplications), RNA mutations via adenosine-to-inosine pre-mRNA editing events as well as error prone RNA synthesis. These are then copied back into DNA by a cellular reverse transcription process (also likely to be error-prone) that we have called "reverse transcription-mediated long DNA conversion." Finally we suggest that all these activities and others can be envisaged as being brought physically under the umbrella of special sites in the nucleus involved in transcription known as "transcription factories."

Action-gradient-minimizing pseudo-orbits and almost-invariant tori

Transport in near-integrable, but partially chaotic, $1 1/2$ degree-of-freedom Hamiltonian systems is blocked by invariant tori and is reduced at \emph{almost}-invariant tori, both associated with the invariant tori of a neighboring integrable system. "Almost invariant" tori with rational rotation number can be defined using continuous families of periodic \emph{pseudo-orbits} to foliate the surfaces, while irrational-rotation-number tori can be defined by nesting with sequences of such rational tori. Three definitions of "pseudo-orbit," \emph{action-gradient--minimizing} (AGMin), \emph{quadratic-flux-minimizing} (QFMin) and \emph{ghost} orbits, based on variants of Hamilton's Principle, use different strategies to extremize the action as closely as possible. Equivalent Lagrangian (configuration-space action) and Hamiltonian (phase-space action) formulations, and a new approach to visualizing action-minimizing and minimax orbits based on AGMin pseudo-orbits, are presented.Comment: Accepted for publication in a special issue of Communications in Nonlinear Science and Numerical Simulation (CNSNS) entitled "The mathematical structure of fluids and plasmas : a volume dedicated to the 60th birthday of Phil Morrison

Genomic evolution and polymorphism: Segmental duplications and haplotypes at 108 regions on 21 chromosomes

We describe here extensive, previously unknown, genomic polymorphism in 120 regions, covering 19 autosomes and both sex chromosomes. Each contains duplication within multigene clusters. Of these, 108 are extremely polymorphic with multiple haplotypes.We used the genomic matching technique (GMT), previously used to characterise the major histocompatibility complex (MHC) and regulators of complement activation (RCA).This genome-wide extension of this technique enables the examination of many underlying cis, trans and epistatic interactions responsible for phenotypic differences especially in relation to individuality, evolution and disease susceptibility.The extent of the diversity could not have been predicted and suggests a new model of primate evolution based on conservation of polymorphism rather than de novo mutation

Development of planar pixel modules for the ATLAS high luminosity LHC tracker upgrade

The high-luminosity LHC will present significant challenges for tracking systems. ATLAS is preparing to upgrade the entire tracking system, which will include a significantly larger pixel detector. This paper reports on the development of large area planar detectors for the outer pixel layers and the pixel endcaps. Large area sensors have been fabricated and mounted onto 4 FE-I4 readout ASICs, the so-called quad-modules, and their performance evaluated in the laboratory and testbeam. Results from characterisation of sensors prior to assembly, experience with module assembly, including bump-bonding and results from laboratory and testbeam studies are presented

Well-Posed Initial-Boundary Evolution in General Relativity

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code which satisfies convergence tests in the nonlinear regime and is robustly stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational waveform radiated to infinity.Comment: 5 pages, 6 figures; added another convergence plot to Fig. 2 + minor change

Power Counting in the Soft-Collinear Effective Theory

We describe in some detail the derivation of a power counting formula for the soft-collinear effective theory (SCET). This formula constrains which operators are required to correctly describe the infrared at any order in the Lambda_QCD/Q expansion (lambda expansion). The result assigns a unique lambda-dimension to graphs in SCET solely from vertices, is gauge independent, and can be applied independent of the process. For processes with an OPE the lambda-dimension has a correspondence with dynamical twist.Comment: 12 pages, 1 fig, journal versio

E-learning as a tool for knowledge transfer through traditional and independent study at two UK higher educational institutes: a case study

Much has been made of the advances in computer aided learning activities. Websites, virtual campus, the increased use of Web CT and chat rooms and further advances in the use of WebCT are becoming more commonplace in UK universities. This paper looks for ways of changing higher education students’ perception of the usefulness of recommended internet web sites for learning purposes, with the intention of increasing the usage rate of recommended module web-sites. The change could represent an adaptation of the existing, well-known technology to change students’ perception regarding its potentially formative role. Subsequently, the outcomes from this preliminary research could be used in order to enhance the quality of the Internet use for teaching and learning purposes

Edge magnetoplasmons in periodically modulated structures

We present a microscopic treatment of edge magnetoplasmons (EMP's) within the random-phase approximation for strong magnetic fields, low temperatures, and filling factor $\nu =1(2)$, when a weak short-period superlattice potential is imposed along the Hall bar. The modulation potential modifies both the spatial structure and the dispersion relation of the fundamental EMP and leads to the appearance of a novel gapless mode of the fundamental EMP. For sufficiently weak modulation strengths the phase velocity of this novel mode is almost the same as the group velocity of the edge states but it should be quite smaller for stronger modulation. We discuss in detail the spatial structure of the charge density of the renormalized and the novel fundamental EMP's.Comment: 8 pages, 4 figure

Strategic investment explains patterns of cooperation and cheating in a microbe

Contributing to cooperation is typically costly, while its rewards are often available to all members of a social group. So why should individuals be willing to pay these costs, especially if they could cheat by exploiting the investments of others? Kin selection theory broadly predicts that individuals should invest more into cooperation if their relatedness to group members is high (assuming they can discriminate kin from nonkin). To better understand how relatedness affects cooperation, we derived the ‟Collective Investment" game, which provides quantitative predictions for patterns of strategic investment depending on the level of relatedness. We then tested these predictions by experimentally manipulating relatedness (genotype frequencies) in mixed cooperative aggregations of the social amoeba Dictyostelium discoideum, which builds a stalk to facilitate spore dispersal. Measurements of stalk investment by natural strains correspond to the predicted patterns of relatedness-dependent strategic investment, wherein investment by a strain increases with its relatedness to the group. Furthermore, if overall group relatedness is relatively low (i.e., no strain is at high frequency in a group) strains face a scenario akin to the "Prisoner's Dilemma" and suffer from insufficient collective investment. We find that strains employ relatedness-dependent segregation to avoid these pernicious conditions. These findings demonstrate that simple organisms like D. discoideum are not restricted to being ‟cheaters" or ‟cooperators" but instead measure their relatedness to their group and strategically modulate their investment into cooperation accordingly. Consequently, all individuals will sometimes appear to cooperate and sometimes cheat due to the dynamics of strategic investing