Related papers: Filaments and voids in planar central configuratio…
Context. Filaments are ubiquitous in the Galaxy, and they host star formation. Detecting them in a reliable way is therefore key towards our understanding of the star formation process. Aims. We explore whether supervised machine learning…
Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…
A theory is constructed for dense ionic solutions near charged planar walls that is valid for strong inter-ionic correlations. This theory predicts a fluctuation-induced, first-order transition and spontaneous charge density ordering at the…
A new class of random spatial tessellations is introduced -- the so-called column tessellations of three-dimensional space. The construction is based on a stationary planar tessellation. Each cell of the spatial tessellation is a prism…
An interesting description of a collinear configuration of four particles is found in terms of two spherical coordinates. An algorithm to compute the four coordinates of particles of a collinear Four-Body central configuration is presented…
We identify cosmic voids from galaxy density fields under the theory of void-cluster correspondence. We extend the previous novel void-identification method developed for the matter density field to the galaxy density field for practical…
The large--scale structure (LSS) in the Universe comprises a complicated filamentary network of matter. We study this network using a high--resolution simulation of structure formation of a $\Lambda$ Cold Dark Matter cosmology. We…
Large scale surveys have brought about a revolution in astronomy. To analyse the resulting wealth of data, we need automated tools to identify, classify, and quantify the important underlying structures. We present here a method for…
Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in…
We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of…
The system of a closed vortex filament is an integrable Hamiltonian one, namely, a Hamiltonian system with an infinite sequense of constants of motion in involution. An algebraic framework is given for the aim of describing differential…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
In this paper we study spiderweb central configurations for the $N$-body problem, i.e configurations given by $N=n \times \ell+1$ masses located at the intersection points of $\ell$ concurrent equidistributed half-lines with $n$ circles and…
This paper focuses on studying the configuration spaces of graphs realised in $\mathbb C^2$, such that the configuration space is, after normalisation, one dimensional. If this is the case, then the configuration space is, generically, a…
This research investigates centered co-circular central configurations in the general power-law potential $n$-body problem. Firstly, there are no such configurations when all masses are equal, except for two; secondly, unless all masses are…
In 1970 Zel'dovich published a far-reaching paper presenting a simple equation describing the nonlinear growth of primordial density inhomogeneities. The equation was remarkably successful in explaining the large scale structure in the…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
In this paper we develop symbolic computation algorithms to investigate finiteness of central configurations for the planar $n$-body problem. Our approach is based on Albouy-Kaloshin's work on finiteness of central configurations for the…
This paper examines the existence of centered co-circular central configurations in the general power-law potential n-body problem. We prove the nonexistence of such configurations when the system consists of n-3 equal masses and three…
On the basis of empirical evidence from molecular dynamics simulations, molecular conformational space can be described by means of a partition of central conical regions characterized by the dominance relations between cartesian…