On a q-difference Painlev\'e III equation: I. Derivation, symmetry and Riccati type solutions

A q-difference analogue of the Painlev\'e III equation is considered. Its derivations, affine Weyl group symmetry, and two kinds of special function type solutions are discussed.Comment: arxiv version is already officia

New report on the invasive Bondar's Nesting Whitefly (Paraleyrodes bondari Peracchi) on oil palm in India

This communication is the new report of the neotropical invasive Bondar's Nesting Whitefly (BNW) , Paraleyrodes bondari Peracchi (Hemiptera: Aleyrodidae)incidence in oil palm in India. A typical feature of BNW infestation is the presence of woolly wax nests on the abaxial surface of oil palm leaflets. The nesting whitefly population was observed to increase phenomenally on oil palm and within a year ie., from 2021 to 2022, a 100 per cent palm infestation was observed. During this period the intensity per palm increased by 24.49 per cent and per leaf increased by 63.28 per cent. Analysis of the partial mitochondrial cytochrome oxidase subunit 1 (CO1) sequences from adult specimens indicated 100% nucleotide identity with Bondar's Nesting Whitefly from coconut

On a q-difference Painlev\'e III equation: II. Rational solutions

Rational solutions for a $q$-difference analogue of the Painlev\'e III equation are considered. A Determinant formula of Jacobi-Trudi type for the solutions is constructed.Comment: Archive version is already official. Published by JNMP at http://www.sm.luth.se/math/JNMP

Discrete Painlevé equations from Y-systems

We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free T-systems) were described in the work of Fordy and Marsh, who completely classified all such quivers in the case of period 1, and characterized them in terms of the skew-symmetric exchange matrix B that defines the quiver. A broader notion of periodicity in general cluster algebras was introduced by Nakanishi, who also described the corresponding Y-systems, and T-systems with coefficients. A result of Fomin and Zelevinsky says that the coefficient-free T-system provides a solution of the Y-system. In this paper, we show that in general there is a discrepancy between these two systems, in the sense that the solution of the former does not correspond to the general solution of the latter. This discrepancy is removed by introducing additional non-autonomous coefficients into the T-system. In particular, we focus on the period 1 case and show that, when the exchange matrix B is degenerate, discrete Painlev\'e equations can arise from this construction

The Maupertuis principle and canonical transformations of the extended phase space

We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals of motion, Lax equations, separated variables and action-angles variables. In this review we will discuss namely these induced transformations instead of the various parametric form of the geometric objects

The effect of surveillance and appreciative inquiry on puerperal infections : a longitudinal cohort study in India

Peer reviewedPublisher PD

Genetic variation among species, races, forms and inbred lines of lac insects belonging to the genus Kerria (Homoptera, Tachardiidae)

The lac insects (Homoptera: Tachardiidae), belonging to the genus Kerria, are commercially exploited for the production of lac. Kerria lacca is the most commonly used species in India. RAPD markers were used for assessing genetic variation in forty-eight lines of Kerria, especially among geographic races, infrasubspecific forms, cultivated lines, inbred lines, etc., of K. lacca. In the 48 lines studied, the 26 RAPD primers generated 173 loci, showing 97.7% polymorphism. By using neighbor-joining, the dendrogram generated from the similarity matrix resolved the lines into basically two clusters and outgroups. The major cluster, comprising 32 lines, included mainly cultivated lines of the rangeeni form, geographic races and inbred lines of K. lacca. The second cluster consisted of eight lines of K. lacca, seven of the kusmi form and one of the rangeeni from the southern state of Karnataka. The remaining eight lines formed a series of outgroups, this including a group of three yellow mutant lines of K. lacca and other species of the Kerria studied, among others. Color mutants always showed distinctive banding patterns compared to their wild-type counterparts from the same population. This study also adds support to the current status of kusmi and rangeeni, as infraspecific forms of K. lacca

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

Some integrable maps and their Hirota bilinear forms

We introduce a two-parameter family of birational maps, which reduces to a family previously found by Demskoi, Tran, van der Kamp and Quispel (DTKQ) when one of the parameters is set to zero. The study of the singularity confinement pattern for these maps leads to the introduction of a tau function satisfying a homogeneous recurrence which has the Laurent property, and the tropical (or ultradiscrete) analogue of this homogeneous recurrence confirms the quadratic degree growth found empirically by Demskoi et al. We prove that the tau function also satisfies two different bilinear equations, each of which is a reduction of the Hirota-Miwa equation (also known as the discrete KP equation, or the octahedron recurrence). Furthermore, these bilinear equations are related to reductions of particular two-dimensional integrable lattice equations, of discrete KdV or discrete Toda type. These connections, as well as the cluster algebra structure of the bilinear equations, allow a direct construction of Poisson brackets, Lax pairs and first integrals for the birational maps. As a consequence of the latter results, we show how each member of the family can be lifted to a system that is integrable in the Liouville sense, clarifying observations made previously in the original DTKQ case

Phylogenetic tree information aids supervised learning for predicting protein-protein interaction based on distance matrices

BACKGROUND: Protein-protein interactions are critical for cellular functions. Recently developed computational approaches for predicting protein-protein interactions utilize co-evolutionary information of the interacting partners, e.g., correlations between distance matrices, where each matrix stores the pairwise distances between a protein and its orthologs from a group of reference genomes. RESULTS: We proposed a novel, simple method to account for some of the intra-matrix correlations in improving the prediction accuracy. Specifically, the phylogenetic species tree of the reference genomes is used as a guide tree for hierarchical clustering of the orthologous proteins. The distances between these clusters, derived from the original pairwise distance matrix using the Neighbor Joining algorithm, form intermediate distance matrices, which are then transformed and concatenated into a super phylogenetic vector. A support vector machine is trained and tested on pairs of proteins, represented as super phylogenetic vectors, whose interactions are known. The performance, measured as ROC score in cross validation experiments, shows significant improvement of our method (ROC score 0.8446) over that of using Pearson correlations (0.6587). CONCLUSION: We have shown that the phylogenetic tree can be used as a guide to extract intra-matrix correlations in the distance matrices of orthologous proteins, where these correlations are represented as intermediate distance matrices of the ancestral orthologous proteins. Both the unsupervised and supervised learning paradigms benefit from the explicit inclusion of these intermediate distance matrices, and particularly so in the latter case, which offers a better balance between sensitivity and specificity in the prediction of protein-protein interactions