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Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…
Accurately predicting the geographic ranges of species is crucial for assisting conservation efforts. Traditionally, range maps were manually created by experts. However, species distribution models (SDMs) and, more recently, deep…
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the…
Graphs drawn in the plane are ubiquitous, arising from data sets through a variety of methods ranging from GIS analysis to image classification to shape analysis. A fundamental problem in this type of data is comparison: given a set of such…
We describe Gauss-type maps as geometric realizations of certain codes in the monoid of nonnegative matrices in the extended modular group. Each such code, together with an appropriate choice of unimodular intervals in P^1R, determines a…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…
A common approach to implementing similarity search applications is the usage of distance functions, where small distances indicate high similarity. In the case of metric distance functions, metric index structures can be used to accelerate…
The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…
The aim of this paper is to investigate an attempt to build a binary classification algorithm using principles of geometry such as vectors, planes, and vector algebra. The basic idea behind the proposed algorithm is that a hyperplane can be…
Binary codes are constructed from incidence matrices of hypergraphs. A combinatroial description is given for the minimum distances of such codes via a combinatorial tool called ``eonv". This combinatorial approach provides a faster…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
Linear complementary dual (LCD) maximum distance separable (MDS) codes are constructed to given specifications. For given $n$ and $r<n$, with $n$ or $r$ (or both) odd, MDS LCD $(n,r)$ codes are constructed over finite fields whose…
Decision Boundary Maps (DBMs) are an effective tool for visualising machine learning classification boundaries. Yet, DBM quality strongly depends on the dimensionality reduction (DR) technique and high dimensional space used for the data…
Iterative majorize-minimize (MM) (also called optimization transfer) algorithms solve challenging numerical optimization problems by solving a series of "easier" optimization problems that are constructed to guarantee monotonic descent of…
Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given…
Most existing motion planning algorithms assume that a map (of some quality) is fully determined prior to generating a motion plan. In many emerging applications of robotics, e.g., fast-moving agile aerial robots with constrained embedded…
A dynamical map is a map which takes one density operator to another. Such a map can be written in an operator-sum representation (OSR) using a spectral decomposition. The method of the construction applies to more general maps which need…
Motivated by recent interest in permutation arrays, we introduce and investigate the more general concept of frequency permutation arrays (FPAs). An FPA of length n=m lambda and distance d is a set T of multipermutations on a multiset of m…
We derive three-dimensional integrable mappings which have two invariants.
The various algorithms used to extrapolate particle trajectories from measurements are often very time-consuming with computational complexities which are typically quadratic. In this article, we propose a new algorithm called GEM with a…