Related papers: Not even wrong: Reply to Loreau and Hector
A union of an arrangement of affine hyperplanes $H$ in $R^d$ is the real algebraic variety associated to the principal ideal generated by the polynomial $p_{H}$ given as the product of the degree one polynomials which define the hyperplanes…
Machine learning-supported decisions, such as ordering diagnostic tests or determining preventive custody, often require converting probabilistic forecasts into binary classifications. We adopt a consequentialist perspective from decision…
We use two different approaches to derive multipartite Leggett-type inequalities, which are generalizations of the two-qubit Leggett-type inequality obtained in [Nature Phys. \textbf{4}, 681 (2008)]. The first approach is based on the…
Variation and selection are the core principles of Darwinian evolution, yet quantitatively relating the diversity of a population to its capacity to respond to selection is challenging. Here, we examine this problem at a molecular level in…
Multi-centre studies increasingly rely on distributed inference, where sites share only centre-level summaries. Homogeneity of parameters across centres is often violated, motivating methods that both \emph{test} for equality and…
We argue that results produced by a heuristic optimisation algorithm cannot be considered reproducible unless the algorithm fully specifies what should be done with solutions generated outside the domain, even in the case of simple box…
$B\to\phi K^*$ ($\btos$) is three separate decays, one for each polarization of the final-state vector mesons (one longitudinal, two transverse). It is observed that the fraction of transverse decays, $\fT$, and the fraction of longitudinal…
The global in time existence of weak solutions to a cross-diffusion system with fractional diffusion in the whole space is proved. The equations describe the evolution of multi-species populations in the regime of large-distance…
The ubiquity of computation in modern scientific research inflicts new challenges for reproducibility. While most journals now require code and data be made available, the standards for organization, annotation, and validation remain lax,…
This is an essay in what might be called ``mathematical metaphysics.'' There is a fundamental duality that run through mathematics and the natural sciences. The duality starts as the logical level; it is represented by the Boolean logic of…
We derive some consequences of the Liouville theorem for plurisubharmonic functions of L.-F. Tam and the author. The first result provides a nonlinear version of the complex splitting theorem (which splits off a factor of $\mathbb{C}$…
In this paper, a detrimental mathematical mistake is pointed out in the proof of \textit{Theorem 1} presented in the paper\textit{ [Generalization of the gradient method with fractional order gradient direction, J. Franklin Inst., 357…
In this work, we study the dynamics of similarity classes of tetrahedra generated by the longest-edge bisection (LEB) algorithm. Building on the normalization strategy introduced by Perdomo and Plaza for triangles, we construct a canonical…
This thesis is split up into two parts: The first one concerns (pseudo)-holomorphic Hamiltonian systems, while the second part is about K\"ahler structures of complex coadjoint orbits. We begin the first part by investigating basic…
Arnold, Falk, and Winther [Bull. Amer. Math. Soc. 47 (2010), 281--354] showed that mixed variational problems, and their numerical approximation by mixed methods, could be most completely understood using the ideas and tools of Hilbert…
We leverage recent advances in heavy-tail approximations for global hypothesis testing with dependent studies to construct approximate confidence regions without modeling or estimating their dependence structures. A non-rejection region is…
In this work, we outline a mathematical description of biodiversity evolution throughout the Phanerozoic based on a simple coupled system of two differential equations and on the division of genera in two classes - Short-lived and…
Feature Engineering (FE) is pivotal in automated machine learning (AutoML) but remains a bottleneck for traditional methods, which operate within rigid search spaces and lack domain awareness. While Large Language Models (LLMs) offer a…
Much of our understanding of ecological and evolutionary mechanisms derives from analysis of low-dimensional models: with few interacting species, or few axes defining "fitness". It is not always clear to what extent the intuition derived…
The heavy quark effective field theory (HQEFT) provides an effective way to deal with the heavy meson decays. In the paper, we adopt two different correlators to derive the light-cone sum rules of the $B \to \pi$ transition form factors…