The massless higher-loop two-point function

We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph $G$ to evaluate to multiple zeta values. The criterion depends only on the topology of $G$, and can be checked algorithmically. As a corollary, we reprove the result, due to Bierenbaum and Weinzierl, that the massless 2-loop 2-point function is expressible in terms of multiple zeta values, and generalize this to the 3, 4, and 5-loop cases. We find that the coefficients in the Taylor expansion of planar graphs in this range evaluate to multiple zeta values, but the non-planar graphs with crossing number 1 may evaluate to multiple sums with $6^\mathrm{th}$ roots of unity. Our method fails for the five loop graphs with crossing number 2 obtained by breaking open the bipartite graph $K_{3,4}$ at one edge

The Prosocial Framework: Theory, Practice and Applications Within Schools

Recent collaborations across psychological and evolutionary science have resulted in the emergence of an intervention programme for increasing the cohesion and effectiveness of human group processes. Prosocial (Atkins et al., 2019) combines Acceptance & Commitment Therapy (ACT; S. Hayes et al., 2012) and Multi-Level Selection Theory (Wilson & Sober, 1994) with Nobel Laureate Elinor Ostrom’s Core Design Principles (CDPs) for effective group-level processes (Ostrom, 2012, 2015). Ostrom’s work was ground-breaking but, being primarily descriptive in nature, did not provide a full account of the processes and procedures required to implement the CDPs. The current paper outlines the theoretical underpinnings of Prosocial and offers guidelines for its application within educational communities, providing specific examples of the wide array of ways in which the approach can be applied by professionals such as educational psychologists (EPs) to bring about positive change at the systemic level

Possible Stratification Mechanism in Granular Mixtures

We propose a mechanism to explain what occurs when a mixture of grains of different sizes and different shapes (i.e. different repose angles) is poured into a quasi-two-dimensional cell. Specifically, we develop a model that displays spontaneous stratification of the large and small grains in alternating layers. We find that the key requirement for stratification is a difference in the repose angles of the two pure species, a prediction confirmed by experimental findings. We also identify a kink mechanism that appears to describe essential aspects of the dynamics of stratification.Comment: 4 pages, 4 figures, http://polymer.bu.edu/~hmakse/Home.htm

Combinatorial Markov chains on linear extensions

We consider generalizations of Schuetzenberger's promotion operator on the set L of linear extensions of a finite poset of size n. This gives rise to a strongly connected graph on L. By assigning weights to the edges of the graph in two different ways, we study two Markov chains, both of which are irreducible. The stationary state of one gives rise to the uniform distribution, whereas the weights of the stationary state of the other has a nice product formula. This generalizes results by Hendricks on the Tsetlin library, which corresponds to the case when the poset is the anti-chain and hence L=S_n is the full symmetric group. We also provide explicit eigenvalues of the transition matrix in general when the poset is a rooted forest. This is shown by proving that the associated monoid is R-trivial and then using Steinberg's extension of Brown's theory for Markov chains on left regular bands to R-trivial monoids.Comment: 35 pages, more examples of promotion, rephrased the main theorems in terms of discrete time Markov chain

System-L amino acid transporters play a key role in pancreatic b-cell signalling and function

The branched-chain amino acids (BCAA) leucine, isoleucine and valine, are essential amino acids that play a critical role in cellular signalling and metabolism. They acutely stimulate insulin secretion and activate the regulatory serine/threonine kinase mammalian target of rapamycin complex 1 (mTORC1), a kinase that promotes increased β-cell mass and function. The effects of BCAA on cellular function are dependent on their active transport into mammalian cells via amino acid transporters and thus the expression and activity of these transporters likely influences β-cell signalling and function. In this report we show that the System-L transporters are required for BCAA uptake into clonal β-cell lines and pancreatic islets and that these are essential for signalling to mTORC1. Further investigation revealed that the System-L transporter LAT1 is abundantly expressed in islets and that knock-down of LAT1 using siRNA inhibits mTORC1 signalling, leucine-stimulated insulin secretion and islet cell proliferation. In summary, we show that the System-L transporter LAT1 is required for regulating β-cell signaling and function in islets and thus may be a novel pharmacological/nutritional target for the treatment and prevention of type-2 diabetes

Binary data corruption due to a Brownian agent

We introduce a model of binary data corruption induced by a Brownian agent (active random walker) on a d-dimensional lattice. A continuum formulation allows the exact calculation of several quantities related to the density of corrupted bits \rho; for example the mean of \rho, and the density-density correlation function. Excellent agreement is found with the results from numerical simulations. We also calculate the probability distribution of \rho in d=1, which is found to be log-normal, indicating that the system is governed by extreme fluctuations.Comment: 39 pages, 10 figures, RevTe

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Spontaneous Stratification in Granular Mixtures

Granular materials size segregate when exposed to external periodic perturbations such as vibrations. Moreover, mixtures of grains of different sizes spontaneously segregate in the absence of external perturbations: when a mixture is simply poured onto a pile, the large grains are more likely to be found near the base, while the small grains are more likely to be near the top. Here, we report a spontaneous phenomenon arising when we pour a mixture between two vertical plates: the mixture spontaneously stratifies into alternating layers of small and large grains whenever the large grains are rougher than the small grains. In contrast, we find only spontaneous segregation when the large grains are more rounded than the small grains. The stratification is related to the occurrence of avalanches; during each avalanche the grains comprising the avalanche spontaneously stratify into a pair of layers through a "kink" mechanism, with the small grains forming a sublayer underneath the layer of large grains.Comment: 4 pages, 6 figures, http://polymer.bu.edu/~hmakse/Home.htm