Self-avoiding walks and polygons on the triangular lattice

We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40 we also calculate series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and the mean-square distance of a monomer from the end points. For self-avoiding polygons to length 58 we calculate series for the mean-square radius of gyration and the first 10 moments of the area. Analysis of the series yields accurate estimates for the connective constant of triangular self-avoiding walks, $\mu=4.150797226(26)$, and confirms to a high degree of accuracy several theoretical predictions for universal critical exponents and amplitude combinations.Comment: 24 pages, 6 figure

Enumeration of self-avoiding walks on the square lattice

We describe a new algorithm for the enumeration of self-avoiding walks on the square lattice. Using up to 128 processors on a HP Alpha server cluster we have enumerated the number of self-avoiding walks on the square lattice to length 71. Series for the metric properties of mean-square end-to-end distance, mean-square radius of gyration and mean-square distance of monomers from the end points have been derived to length 59. Analysis of the resulting series yields accurate estimates of the critical exponents $\gamma$ and $\nu$ confirming predictions of their exact values. Likewise we obtain accurate amplitude estimates yielding precise values for certain universal amplitude combinations. Finally we report on an analysis giving compelling evidence that the leading non-analytic correction-to-scaling exponent $\Delta_1=3/2$.Comment: 24 pages, 6 figure

Scaling function and universal amplitude combinations for self-avoiding polygons

We analyze new data for self-avoiding polygons, on the square and triangular lattices, enumerated by both perimeter and area, providing evidence that the scaling function is the logarithm of an Airy function. The results imply universal amplitude combinations for all area moments and suggest that rooted self-avoiding polygons may satisfy a $q$-algebraic functional equation.Comment: 9 page

Scaling prediction for self-avoiding polygons revisited

We analyse new exact enumeration data for self-avoiding polygons, counted by perimeter and area on the square, triangular and hexagonal lattices. In extending earlier analyses, we focus on the perimeter moments in the vicinity of the bicritical point. We also consider the shape of the critical curve near the bicritical point, which describes the crossover to the branched polymer phase. Our recently conjectured expression for the scaling function of rooted self-avoiding polygons is further supported. For (unrooted) self-avoiding polygons, the analysis reveals the presence of an additional additive term with a new universal amplitude. We conjecture the exact value of this amplitude.Comment: 17 pages, 3 figure

Phase behaviour of a model of colloidal particles with a fluctuating internal state

Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal particles, with a simple phenomenological model to account for these degrees of freedom, is studied. It is found that the interaction between the particles is not pairwise additive. It is even possible that the interaction between a triplet of particles is attractive while the pair interaction is repulsive. When this is so the liquid phase is either stable only in a small region of the phase diagram or absent altogether.Comment: 12 pages including 4 figure

Sequence Variation and Expression of the Gimap Gene Family in the BB Rat

Positional cloning of lymphopenia (lyp) in the BB rat revealed a frameshift mutation in Gimap5, a member of at least seven related GTPase Immune Associated Protein genes located on rat chromosome 4q24. Our aim was to clone and sequence the cDNA of the BB diabetes prone (DP) and diabetes resistant (DR) alleles of all seven Gimap genes in the congenic DR.lyp rat line with 2 Mb of BB DP DNA introgressed onto the DR genetic background. All (100%) DR.lyp/lyp rats are lymphopenic and develop type 1 diabetes (T1D) by 84 days of age while DR.+/+ rats remain T1D and lyp resistant. Among the seven Gimap genes, the Gimap5 frameshift mutation, a mutant allele that produces no protein, had the greatest impact on lymphopenia in the DR.lyp/lyp rat. Gimap4 and Gimap1 each had one amino acid substitution of unlikely significance for lymphopenia. Quantitative RT-PCR analysis showed a reduction in expression of all seven Gimap genes in DR.lyp/lyp spleen and mesenteric lymph nodes when compared to DR.+/+. Only four; Gimap1, Gimap4, Gimap5, and Gimap9 were reduced in thymus. Our data substantiates the Gimap5 frameshift mutation as the primary defect with only limited contributions to lymphopenia from the remaining Gimap genes

Comments on the continuing widespread and unnecessary use of a defective emission equation in field emission related literature

Field electron emission (FE) has relevance in many different technological contexts. However, many related technological papers use a physically defective elementary FE equation for local emission current density (LECD). This equation takes the tunneling barrier as exactly triangular, as in the original FE theory of 90 years ago. More than 60 years ago, it was shown that the so-called Schottky-Nordheim (SN) barrier, which includes an image-potential-energy term (that models exchange-and-correlation effects) is better physics. For a metal-like emitter with work-function 4.5 eV, the SN-barrier-related Murphy-Good FE equation predicts LECD values that are higher than the elementary equation values by a large factor, often between around 250 and around 500. By failing to mention/apply this 60-year-old established science, or to inform readers of the large errors associated with the elementary equation, many papers (aided by defective reviewing) spread a new kind of "pathological science", and create a modern research-integrity problem. The present paper aims to enhance author and reviewer awareness by summarizing relevant aspects of FE theory, by explicitly identifying the misjudgment in the original 1928 Fowler-Nordheim paper, by explicitly calculating the size of the resulting error, and by showing in detail why most FE theoreticians regard the 1950s modifications as better physics. Suggestions are made, about nomenclature and about citation practice, that may help to diminish misunderstandings.Comment: Submitted for publication; in v2 a correction to historical information (with no numerical consequences) has been made in Appendix

Motor Preparatory Activity in Posterior Parietal Cortex is Modulated by Subjective Absolute Value

For optimal response selection, the consequences associated with behavioral success or failure must be appraised. To determine how monetary consequences influence the neural representations of motor preparation, human brain activity was scanned with fMRI while subjects performed a complex spatial visuomotor task. At the beginning of each trial, reward context cues indicated the potential gain and loss imposed for correct or incorrect trial completion. FMRI-activity in canonical reward structures reflected the expected value related to the context. In contrast, motor preparatory activity in posterior parietal and premotor cortex peaked in high “absolute value” (high gain or loss) conditions: being highest for large gains in subjects who believed they performed well while being highest for large losses in those who believed they performed poorly. These results suggest that the neural activity preceding goal-directed actions incorporates the absolute value of that action, predicated upon subjective, rather than objective, estimates of one's performance

Ernst Freund as Precursor of the Rational Study of Corporate Law

Gindis, David, Ernst Freund as Precursor of the Rational Study of Corporate Law (October 27, 2017). Journal of Institutional Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2905547, doi: https://dx.doi.org/10.2139/ssrn.2905547The rise of large business corporations in the late 19th century compelled many American observers to admit that the nature of the corporation had yet to be understood. Published in this context, Ernst Freund's little-known The Legal Nature of Corporations (1897) was an original attempt to come to terms with a new legal and economic reality. But it can also be described, to paraphrase Oliver Wendell Holmes, as the earliest example of the rational study of corporate law. The paper shows that Freund had the intuitions of an institutional economist, and engaged in what today would be called comparative institutional analysis. Remarkably, his argument that the corporate form secures property against insider defection and against outsiders anticipated recent work on entity shielding and capital lock-in, and can be read as an early contribution to what today would be called the theory of the firm.Peer reviewe

Islands of linkage in an ocean of pervasive recombination reveals two-speed evolution of human cytomegalovirus genomes

Human cytomegalovirus (HCMV) infects most of the population worldwide, persisting throughout the host's life in a latent state with periodic episodes of reactivation. While typically asymptomatic, HCMV can cause fatal disease among congenitally infected infants and immunocompromised patients. These clinical issues are compounded by the emergence of antiviral resistance and the absence of an effective vaccine, the development of which is likely complicated by the numerous immune evasins encoded by HCMV to counter the host's adaptive immune responses, a feature that facilitates frequent super-infections. Understanding the evolutionary dynamics of HCMV is essential for the development of effective new drugs and vaccines. By comparing viral genomes from uncultivated or low-passaged clinical samples of diverse origins, we observe evidence of frequent homologous recombination events, both recent and ancient, and no structure of HCMV genetic diversity at the whole-genome scale. Analysis of individual gene-scale loci reveals a striking dichotomy: while most of the genome is highly conserved, recombines essentially freely and has evolved under purifying selection, 21 genes display extreme diversity, structured into distinct genotypes that do not recombine with each other. Most of these hyper-variable genes encode glycoproteins involved in cell entry or escape of host immunity. Evidence that half of them have diverged through episodes of intense positive selection suggests that rapid evolution of hyper-variable loci is likely driven by interactions with host immunity. It appears that this process is enabled by recombination unlinking hyper-variable loci from strongly constrained neighboring sites. It is conceivable that viral mechanisms facilitating super-infection have evolved to promote recombination between diverged genotypes, allowing the virus to continuously diversify at key loci to escape immune detection, while maintaining a genome optimally adapted to its asymptomatic infectious lifecycle