Chebyshev type lattice path weight polynomials by a constant term method

We prove a constant term theorem which is useful for finding weight polynomials for Ballot/Motzkin paths in a strip with a fixed number of arbitrary `decorated' weights as well as an arbitrary `background' weight. Our CT theorem, like Viennot's lattice path theorem from which it is derived primarily by a change of variable lemma, is expressed in terms of orthogonal polynomials which in our applications of interest often turn out to be non-classical. Hence we also present an efficient method for finding explicit closed form polynomial expressions for these non-classical orthogonal polynomials. Our method for finding the closed form polynomial expressions relies on simple combinatorial manipulations of Viennot's diagrammatic representation for orthogonal polynomials. In the course of the paper we also provide a new proof of Viennot's original orthogonal polynomial lattice path theorem. The new proof is of interest because it uses diagonalization of the transfer matrix, but gets around difficulties that have arisen in past attempts to use this approach. In particular we show how to sum over a set of implicitly defined zeros of a given orthogonal polynomial, either by using properties of residues or by using partial fractions. We conclude by applying the method to two lattice path problems important in the study of polymer physics as models of steric stabilization and sensitized flocculation.Comment: 27 pages, 14 figure

ABCD of Beta Ensembles and Topological Strings

We study beta-ensembles with Bn, Cn, and Dn eigenvalue measure and their relation with refined topological strings. Our results generalize the familiar connections between local topological strings and matrix models leading to An measure, and illustrate that all those classical eigenvalue ensembles, and their topological string counterparts, are related one to another via various deformations and specializations, quantum shifts and discrete quotients. We review the solution of the Gaussian models via Macdonald identities, and interpret them as conifold theories. The interpolation between the various models is plainly apparent in this case. For general polynomial potential, we calculate the partition function in the multi-cut phase in a perturbative fashion, beyond tree-level in the large-N limit. The relation to refined topological string orientifolds on the corresponding local geometry is discussed along the way.Comment: 33 pages, 1 figur

Digital energy visualizations in the workplace: the e-Genie tool

Building management systems are designed for energy managers; there are few energy-feedback systems designed to engage staff. A tool, known as e-Genie, was created with the purpose of engaging workplace occupants with energy data and supporting them to take action to reduce energy use. Building on research insights within the field, e-Genie’s novel approach encourages users to make plans to meet energy-saving goals, supports discussion and considers social energy behaviours (e.g. discussing energy issues, taking part in campaigns) as well as individual actions. A field-based study of e-Genie indicated that visualizations of energy data were engaging and that the discussion ‘Pinboard’ was particularly popular. Pre- and post-survey (N = 77) evaluation of users indicated that people were significantly more concerned about energy issues and reported engaging more in social energy behaviour after about two weeks of e-Genie being installed. Concurrently, objective measures of electricity use decreased over the same period, and continued decreasing over subsequent weeks. Indications are that occupant-facing energy-feedback visualizations can be successful in reducing energy use in the workplace; furthermore, supporting social energy behaviour in the workplace is likely to be a useful direction for promoting action

A Physicist's Proof of the Lagrange-Good Multivariable Inversion Formula

We provide yet another proof of the classical Lagrange-Good multivariable inversion formula using techniques of quantum field theory.Comment: 9 pages, 3 diagram

Quantum curves for Hitchin fibrations and the Eynard-Orantin theory

We generalize the topological recursion of Eynard-Orantin (2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle $T^*C$ of an arbitrary smooth base curve $C$. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal $\hbar$-deformation family of $D$-modules over an arbitrary projective algebraic curve $C$ of genus greater than $1$, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the $SL(2,\mathbb{C})$-character variety of the fundamental group $\pi_1(C)$. We show that the semi-classical limit through the WKB approximation of these $\hbar$-deformed $D$-modules recovers the initial family of Hitchin spectral curves.Comment: 34 page

Ecosystem carbon 7 dioxide fluxes after disturbance in forests of North America

Disturbances are important for renewal of North American forests. Here we summarize more than 180 site years of eddy covariance measurements of carbon dioxide flux made at forest chronosequences in North America. The disturbances included stand-replacing fire (Alaska, Arizona, Manitoba, and Saskatchewan) and harvest (British Columbia, Florida, New Brunswick, Oregon, Quebec, Saskatchewan, and Wisconsin) events, insect infestations (gypsy moth, forest tent caterpillar, and mountain pine beetle), Hurricane Wilma, and silvicultural thinning (Arizona, California, and New Brunswick). Net ecosystem production (NEP) showed a carbon loss from all ecosystems following a stand-replacing disturbance, becoming a carbon sink by 20 years for all ecosystems and by 10 years for most. Maximum carbon losses following disturbance (g C m−2y−1) ranged from 1270 in Florida to 200 in boreal ecosystems. Similarly, for forests less than 100 years old, maximum uptake (g C m−2y−1) was 1180 in Florida mangroves and 210 in boreal ecosystems. More temperate forests had intermediate fluxes. Boreal ecosystems were relatively time invariant after 20 years, whereas western ecosystems tended to increase in carbon gain over time. This was driven mostly by gross photosynthetic production (GPP) because total ecosystem respiration (ER) and heterotrophic respiration were relatively invariant with age. GPP/ER was as low as 0.2 immediately following stand-replacing disturbance reaching a constant value of 1.2 after 20 years. NEP following insect defoliations and silvicultural thinning showed lesser changes than stand-replacing events, with decreases in the year of disturbance followed by rapid recovery. NEP decreased in a mangrove ecosystem following Hurricane Wilma because of a decrease in GPP and an increase in ER

The Bivariate Rogers-Szeg\"{o} Polynomials

We present an operator approach to deriving Mehler's formula and the Rogers formula for the bivariate Rogers-Szeg\"{o} polynomials $h_n(x,y|q)$. The proof of Mehler's formula can be considered as a new approach to the nonsymmetric Poisson kernel formula for the continuous big $q$-Hermite polynomials $H_n(x;a|q)$ due to Askey, Rahman and Suslov. Mehler's formula for $h_n(x,y|q)$ involves a ${}_3\phi_2$ sum and the Rogers formula involves a ${}_2\phi_1$ sum. The proofs of these results are based on parameter augmentation with respect to the $q$-exponential operator and the homogeneous $q$-shift operator in two variables. By extending recent results on the Rogers-Szeg\"{o} polynomials $h_n(x|q)$ due to Hou, Lascoux and Mu, we obtain another Rogers-type formula for $h_n(x,y|q)$. Finally, we give a change of base formula for $H_n(x;a|q)$ which can be used to evaluate some integrals by using the Askey-Wilson integral.Comment: 16 pages, revised version, to appear in J. Phys. A: Math. Theo

Evanescence in Coined Quantum Walks

In this paper we complete the analysis begun by two of the authors in a previous work on the discrete quantum walk on the line [J. Phys. A 36:8775-8795 (2003) quant-ph/0303105 ]. We obtain uniformly convergent asymptotics for the "exponential decay'' regions at the leading edges of the main peaks in the Schr{\"o}dinger (or wave-mechanics) picture. This calculation required us to generalise the method of stationary phase and we describe this extension in some detail, including self-contained proofs of all the technical lemmas required. We also rigorously establish the exact Feynman equivalence between the path-integral and wave-mechanics representations for this system using some techniques from the theory of special functions. Taken together with the previous work, we can now prove every theorem by both routes.Comment: 32 pages AMS LaTeX, 5 figures in .eps format. Rewritten in response to referee comments, including some additional references. v3: typos fixed in equations (131), (133) and (134). v5: published versio