The Poincaré function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V. Arnold’s conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and transitively on the base. Then we survey the known counting results for differential invariants and derive new formulae for several other classification problems in ...

Paraconformal or GL(2, ℝ) geometry on an <i>n</i>-dimensional manifold <i>M</i> is defined by a field of rational normal curves of degree <i>n</i> – 1 in the projectivised cotangent bundle <i>ℙT*M</i>. Such geometry is known to arise on solution spaces of ODEs with vanishing Wünschmann (Doubrov–Wilczynski) invariants. In this paper we discuss yet another natural source of <i>GL</i>(2, ℝ) structures, ...

In this paper we study various aspects concerning almost affine codes, a class including, and strictly larger than, that of linear codes. We use the combinatorial tool demi-matroids to show how one can define relative length/dimension and dimension/length profiles of flags (chains) of almost affine codes. In addition we show two specific results. One such result is how one can express the relative ...

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 ...

There is sparse research on quality of life (QoL) as an outcome measure in patients with substance use disorders (SUD), with or without attention deficit hyperactivity disorder (ADHD). We aimed to investigate whether SUD patients with and without ADHD (SUD + ADHD vs. SUD − ADHD) differed in QoL at baseline and at a 12-month follow-up after SUD treatment. The groups were additionally compared with ...

Skin cancer is one of the most common types of cancer. Skin cancers are classified as nonmelanoma and melanoma, with the first type being the most frequent and the second type being the most deadly. The key to effective treatment of skin cancer is early detection. With the recent increase of computational power, the number of algorithms to detect and classify skin lesions has increased. The overall ...

For dengue fever and other seasonal epidemics we show how the stability of the preceding inter-outbreak period can predict subsequent total outbreak magnitude, and that a feasible stability metric can be computed from incidence data alone. As an observable of a dynamical system, incidence data contains information about the underlying mechanisms: climatic drivers, changing serotype pools, the ecology ...

We consider Legendrian contact structures on odd-dimensional complex analytic manifolds. We are particularly interested in integrable structures, which can be encoded by compatible complete systems of second order PDEs on a scalar function of many independent variables and considered up to point transformations. Using the techniques of parabolic differential geometry, we compute the associated ...

Earth’s global surface temperature shows variability on an extended range of temporal scales and satisfies an emergent scaling symmetry. Recent studies indicate that scale invariance is not only a feature of the observed temperature fluctuations, but an inherent property of the temperature response to radiative forcing, and a principle that links the fast and slow climate responses. It provides a ...

Einstein–Weyl structures on a three-dimensional manifold <i>M</i> are given by a system <i>E</i> of PDEs on sections of a bundle over <i>M</i>. This system is invariant under the Lie pseudogroup <i>G</i> of local diffeomorphisms on <i>M</i>. Two Einstein–Weyl structures are locally equivalent if there exists a local diffeomorphism taking one to the other. Our goal is to describe the quotient equation ...