Hierarchical Dobinski-type relations via substitution and the moment problem

We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form exp(x (a*)^r a), r=1,2,..., under the composition of their exponential generating functions (egf). They turn out to be of Sheffer-type. We demonstrate that two key properties of these sequences remain preserved under substitutional composition: (a)the property of being the solution of the Stieltjes moment problem; and (b) the representation of these sequences through infinite series (Dobinski-type relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobinski-type formulas and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.Comment: 14 pages, 31 reference

Influence of reaction atmosphere (H2O, N2, H2, CO2, CO) on fluidized-bed fast pyrolysis of biomass using detailed tar vapor chemistry in computational fluid dynamics

Secondary pyrolysis in fluidized bed fast pyrolysis of biomass is the focus of this work. A novel computational fluid dynamics (CFD) model coupled with a comprehensive chemistry scheme (134 species and 4169 reactions, in CHEMKIN format) has been developed to investigate this complex phenomenon. Previous results from a transient three-dimensional model of primary pyrolysis were used for the source terms of primary products in this model. A parametric study of reaction atmospheres (H2O, N2, H2, CO2, CO) has been performed. For the N2 and H2O atmosphere, results of the model compared favorably to experimentally obtained yields after the temperature was adjusted to a value higher than that used in experiments. One notable deviation versus experiments is pyrolytic water yield and yield of higher hydrocarbons. The model suggests a not overly strong impact of the reaction atmosphere. However, both chemical and physical effects were observed. Most notably, effects could be seen on the yield of various compounds, temperature profile throughout the reactor system, residence time, radical concentration, and turbulent intensity. At the investigated temperature (873 K), turbulent intensity appeared to have the strongest influence on liquid yield. With the aid of acceleration techniques, most importantly dimension reduction, chemistry agglomeration, and in-situ tabulation, a converged solution could be obtained within a reasonable time (∼30 h). As such, a new potentially useful method has been suggested for numerical analysis of fast pyrolysis

Generalized Fock spaces and the Stirling numbers

The Bargmann-Fock-Segal space plays an important role in mathematical physics, and has been extended into a number of directions. In the present paper we imbed this space into a Gelfand triple. The spaces forming the Fr\'echet part (i.e. the space of test functions) of the triple are characterized both in a geometric way and in terms of the adjoint of multiplication by the complex variable, using the Stirling numbers of the second kind. The dual of the space of test functions has a topological algebra structure, of the kind introduced and studied by the first named author and G. Salomon.Comment: revised versio

Dobinski-type relations and the Log-normal distribution

We consider sequences of generalized Bell numbers B(n), n=0,1,... for which there exist Dobinski-type summation formulas; that is, where B(n) is represented as an infinite sum over k of terms P(k)^n/D(k). These include the standard Bell numbers and their generalizations appearing in the normal ordering of powers of boson monomials, as well as variants of the "ordered" Bell numbers. For any such B we demonstrate that every positive integral power of B(m(n)), where m(n) is a quadratic function of n with positive integral coefficients, is the n-th moment of a positive function on the positive real axis, given by a weighted infinite sum of log-normal distributions.Comment: 7 pages, 2 Figure

Constructive biases in clinical judgment

With a pair of oppositely valenced stimuli, rating the first one sometimes leads to a more extreme evaluation for the second (e.g., if the second is negatively valenced, rating the first stimulus would lead to a more negative rating for the second; White et al., 2014). We considered an evaluation bias in the case of clinical diagnosis relating to eating disorders. A population sample which included experienced clinical psychologists and psychiatrists, showed partial evidence of an evaluation bias, when judging descriptions of individuals designed to be consistent with eating disorders or not. Quantum probability theory, the probability rules from quantum mechanics without any of the physics, is particularly well-suited to modeling the evaluation bias (and constructive influences generally), because a measurement (or judgement) can change the state of the system. We applied a previous quantum model to the present result, an extension of the model embodying noisy processes, and Hogarth and Einhorn’s (1992) belief adjustment model. We discuss how model fits inform an examination of rationality in the observed behavior

Bell correlations outside physics

Correlations are ubiquitous in nature and their principled study is of paramount importance in scientific development. The seminal contributions from John Bell offer a framework for analyzing the correlations between the components of quantum mechanical systems and have instigated an experimental tradition which has recently culminated with the Nobel Prize in Physics (2022). In physics, Bell’s framework allows the demonstration of the non-classical nature of quantum systems just from the analysis of the observed correlation patterns. Bell’s ideas need not be restricted to physics. Our contribution is to show an example of a Bell approach, based on the insight that correlations can be broken down into a part due to common, ostensibly significant causes, and a part due to noise. We employ data from finance (price changes of securities) as an example to demonstrate our approach, highlighting several general applications: first, we demonstrate a new measure of association, informed by the assumed causal relationship between variables. Second, our framework can lead to streamlined Bell-type tests of widely employed models of association, which are in principle applicable to any discipline. In the area of finance, such models of association are Factor Models and the bivariate Gaussian model. Overall, we show that Bell’s approach and the models we consider are applicable as general statistical techniques, without any domain specificity. We hope that our work will pave the way for extending our general understanding for how the structure of associations can be analyzed

Indicators of resilience in socio-ecological production landscapes (SEPLs)

The following policy report constitutes an important supplement to a set of 20 indicators for resilience in socio-ecological production landscapes (SEPLs) that was developed over the course of joint collaboration between Bioversity International and the United Nations University Institute of Advanced Studies (UNU-IAS). The indicators were disseminated widely in pamphlet form for the first time in March 2012. Subsequently, a need was identified for sharing a more in-depth overview of the considerations that went into creating this list of indicators as well as the outcomes of initial field-testing

Polymorphisms in RAD51, XRCC2 and XRCC3 genes of the homologous recombination repair in colorectal cancer—a case control study

XRCC2 and XRCC3 proteins are structurally and functionally related to RAD51 which play an important role in the homologous recombination, the process frequently involved in cancer transformation. In our previous work we show that the 135G>C polymorphism (rs1801320) of the RAD51 gene can modify the effect of the Thr241Met polymorphism (rs861539) of the XRCC3 gene. We tested the association between the 135G>C polymorphism of the RAD51 gene, the Thr241Met polymorphism of the XRCC3 gene and the Arg188His polymorphism (rs3218536) of the XRCC2 gene and colorectal cancer risk and clinicopathological parameters. Polymorphisms were evaluated by restriction fragment length polymorphism polymerase chain reaction (RFLP-PCR) in 100 patients with invasive adenocarcinoma of the colon and in 100 sex, age and ethnicity matched cancer–free controls. We stratified the patients by genotypes, tumour Duke’s and TNM stage and calculated the linkage of each genotype with each stratum. Carriers of Arg188Arg/Me241tMet, His188His/Thr241Thr and His188His/G135G genotypes had an increased risk of colorectal cancer occurrence (OR 5.70, 95% CI 1.10–29.5; OR 12.4, 95% CI 1.63–94.9; OR 5.88, 95% CI 1.21–28.5, respectively). The C135C genotype decreased the risk of colorectal cancer singly (OR 0.06, 95% CI 0.02–0.22) as well as in combination with other two polymorphisms. TNM and Duke’s staging were not related to any of these polymorphisms. Our results suggest that the 135G>C polymorphism of the RAD51 gene can be an independent marker of colorectal cancer risk. The Thr241Met polymorphism of the XRCC3 gene and the Arg188His polymorphism of the XRCC2 gene can modify the risk of colorectal cancer