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

CO₂ transport, variability, and budget over the southern California Air Basin using the high-resolution WRF-VPRM Model during the CalNex 2010 campaign

To study regional-scale carbon dioxide (CO2) transport, temporal variability, and budget over the Southern California Air Basin (SoCAB) during the California Research at the Nexus of Air Quality and Climate Change (CalNex) 2010 campaign period, a model that couples the Weather Research and Forecasting (WRF) Model with the Vegetation Photosynthesis and Respiration Model (VPRM) has been used. Our numerical simulations use anthropogenic CO2 emissions of the Hestia Project 2010 fossil-fuel CO2 emissions data products along with optimized VPRM parameters at ‘‘FLUXNET’’ sites, for biospheric CO2 fluxes over SoCAB. The simulated meteorological conditions have been validated with ground and aircraft observations, as well as with background CO2 concentrations from the coastal Palos Verdes site. The model captures the temporal pattern of CO2 concentrations at the ground site at the California Institute of Technology in Pasadena, but it overestimates the magnitude in early daytime. Analysis ofCO2 by wind directions reveals the overestimate is due to advection from the south and southwest, where downtown Los Angeles is located. The model also captures the vertical profile of CO2 concentrations along with the flight tracks. The optimized VPRM parameters have significantly improved simulated net ecosystem exchange at each vegetation-class site and thus the regional CO2 budget. The total biospheric contribution ranges approximately from 224% to 220% (daytime) of the total anthropogenic CO2 emissions during the study period

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

Exclusion statistics,operator algebras and Fock space representations

We study exclusion statistics within the second quantized approach. We consider operator algebras with positive definite Fock space and restrict them in a such a way that certain state vectors in Fock space are forbidden ab initio.We describe three characteristic examples of such exclusion, namely exclusion on the base space which is characterized by states with specific constraint on quantum numbers belonging to base space M (e.g. Calogero-Sutherland type of exclusion statistics), exclusion in the single-oscillator Fock space, where some states in single oscillator Fock space are forbidden (e.g. the Gentile realization of exclusion statistics) and a combination of these two exclusions (e.g. Green's realization of para-Fermi statistics). For these types of exclusions we discuss extended Haldane statistics parameters g, recently introduced by two of us in Mod.Phys.Lett.A 11, 3081 (1996), and associated counting rules. Within these three types of exclusions in Fock space the original Haldane exclusion statistics cannot be realized.Comment: Latex,31 pages,no figures,to appear in J.Phys.A : Math.Ge

Living with interpersonal data: observability and accountability in the age of pervasive ICT

The Internet of Things, alongside existing mobile digital technologies, heralds a world in which pervasive sensing constantly captures data about us. Simultaneous with this technology programme are moves by policymakers to shore up the digital economy through the legislating of new trust-building models of data management. These moves seek to give individuals control and oversight of their personal data. Within shared settings, the consequences of these changes are the large-scale generation of interpersonal data generated by and acting on the group rather than individual. We consider how such systems create new forms of observability and hence accountability among members of the home, and draw on the work of Simmel and Goffman to explore how these demands are managed. Such management mitigates the more extreme possibilities for domestic monitoring posited by these systems, yet without careful design there remains a considerable danger of unanticipated negative consequences

Prenatal origin of childhood AML occurs less frequently than in childhood ALL

Background While there is enough convincing evidence in childhood acute lymphoblastic leukemia (ALL), the data on the pre-natal origin in childhood acute myeloid leukemia (AML) are less comprehensive. Our study aimed to screen Guthrie cards (neonatal blood spots) of non-infant childhood AML and ALL patients for the presence of their respective leukemic markers. Methods We analysed Guthrie cards of 12 ALL patients aged 2–6 years using immunoglobulin (Ig) and T-cell receptor (TCR) gene rearrangements (n = 15) and/or intronic breakpoints of TEL/AML1 fusion gene (n = 3). In AML patients (n = 13, age 1–14 years) PML/RARalpha (n = 4), CBFbeta/MYH11 (n = 3), AML1/ETO (n = 2), MLL/AF6 (n = 1), MLL/AF9 (n = 1) and MLL/AF10 (n = 1) fusion genes and/or internal tandem duplication of FLT3 gene (FLT3/ITD) (n = 2) were used as clonotypic markers. Assay sensitivity determined using serial dilutions of patient DNA into the DNA of a healthy donor allowed us to detect the pre-leukemic clone in Guthrie card providing 1–3 positive cells were present in the neonatal blood spot. Results In 3 patients with ALL (25%) we reproducibly detected their leukemic markers (Ig/TCR n = 2; TEL/AML1 n = 1) in the Guthrie card. We did not find patient-specific molecular markers in any patient with AML. Conclusion In the largest cohort examined so far we used identical approach for the backtracking of non-infant childhood ALL and AML. Our data suggest that either the prenatal origin of AML is less frequent or the load of pre-leukemic cells is significantly lower at birth in AML compared to ALL cases

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

Influence of cranial radiotherapy on outcome in children with acute lymphoblastic leukemia treated with contemporary therapy

Purpose We sought to determine whether cranial radiotherapy (CRT) is necessary to prevent relapse in any subgroup of children with acute lymphoblastic leukemia (ALL). Patients and Methods We obtained aggregate data on relapse and survival outcomes for 16,623 patients age 1 to 18 years old with newly diagnosed ALL treated between 1996 and 2007 by 10 cooperative study groups from around the world. The proportion of patients eligible for prophylactic CRT varied from 0%to 33% by trial and was not related to the proportion eligible for allogeneic stem-cell transplantation in first complete remission. Using a random effects model, with CRT as a dichotomous covariate, we performed a single-arm metaanalysis to compare event-free survival and cumulative incidence of isolated or any CNS relapse and isolated bone marrow relapse in high-risk subgroups of patients who either did or did not receive CRT. Results Although there was significant heterogeneity in all outcome end points according to trial, CRT was associated with a reduced risk of relapse only in the small subgroup of patients with overt CNS disease at diagnosis, who had a significantly lower risk of isolated CNS relapse (4% with CRT v 17% without CRT; P = .02) and a trend toward lower risk of any CNS relapse (7% with CRT v 17% without CRT; P = .09). However, this group had a relatively high rate of events regardless of whether or not they received CRT (32% [95% CI, 26% to 39%] v 34% [95% CI, 19% to 54%]; P = .8). Conclusion CRT does not have an impact on the risk of relapse in children with ALL treated on contemporary protocols

The Impact of Boreal Forest Fire on Climate Warming

We report measurements and analysis of a boreal forest fire, integrating the effects of greenhouse gases, aerosols, black carbon deposition on snow and sea ice, and postfire changes in surface albedo. The net effect of all agents was to increase radiative forcing during the first year (34 ± 31 Watts per square meter of burned area), but to decrease radiative forcing when averaged over an 80-year fire cycle (–2.3 ± 2.2 Watts per square meter) because multidecadal increases in surface albedo had a larger impact than fire-emitted greenhouse gases. This result implies that future increases in boreal fire may not accelerate climate warming