We define and study pseudoholomorphic vector bundles structures, particular cases of which are tangent and normal bundle almost complex structures. As an application we deduce normal forms of 1-jets of almost complex structures along a pseudoholomorphic submanifold. In dimension four we relate these normal forms to the problem of pseudoholomorphic foliation of a neighborhood of a curve and the ...

We introduce the notion of difference equation defined on a structured set. The symmetry group of the structure determines the set of difference operators. All main notions in the theory of difference equations are introduced as invariants of the action of the symmetry group. Linear equations are modules over the skew group algebra, solutions are morphisms relating a given equation to other ...

On page 206 in his lost notebook, Ramanujan recorded the following enigmatic identity for his theta function φ(q): φ(e^{−7π√7}) = 7^{−3/4}φ(e^{−π√7}){1 + ( )^{2/7} + ( )^{2/7} + ( )^{2/7}}. We give the three missing terms. In addition, we calculate the class invariant G_{343} and further special values of φ(e^{−nπ}), for n = 7, 21, 35, and 49.

We combine infectious disease transmission and the non-pharmaceutical (NPI) intervention response to disease incidence into one closed model consisting of two coupled delay differential equations for the incidence rate and the time-dependent reproduction number. The model contains three parameters, the initial reproduction number, the intervention strength, and the response delay. The response is ...

Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closed-form solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster ...

We find a two-component generalization of the integrable case of rdDym equation. The reductions of this system include the general rdDym equation, the Boyer-Finley equation, and the deformed Boyer-Finley equation. Also we find a Bäcklund transformation between our generalization and Bodganov's two-component generalization of the universal hierarchy equatio

Objectives:<br> Postoperative delirium is a common complication after major surgery among the elderly. Despite its potentially serious consequences, the complication often goes undetected and undiagnosed. In order to provide diagnosis support one could potentially exploit the information hidden in free text documents from electronic health records usin ...

<b>Background</b> Validated clinical prediction models to identify children with poor prognosis at the time of juvenile idiopathic arthritis (JIA) diagnosis would be very helpful for tailoring treatments, and avoiding under- or over-treatment. Our objective was to externally validate Nordic clinical prediction models in Canadian patients with JIA. <b>Methods</b> We used data from 513 subjects ...

Temporal persistence in unforced climate variability makes detection of trends in surface temperature difficult. Part of the challenge is methodological since standard techniques assume a separation of time scales between trend and noise. In this work we present a novel Bayesian approach to trend detection under the assumption of long-range dependent natural variability, and we use estimates of ...

The Helmholtz equation has been used for modeling the sound pressure field under a harmonic load. Computing harmonic sound pressure fields by means of solving Helmholtz equation can quickly become unfeasible if one wants to study many different geometries for ranges of frequencies. We propose a machine learning approach, namely a feedforward dense neural network, for computing the average sound ...