Related papers: Designing experiments for estimating an appropriat…
We consider nonconforming methods for symmetric elliptic problems and characterize their quasi-optimality in terms of suitable notions of stability and consistency. The quasi-optimality constant is determined and the possible impact of…
Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link…
We consider the problem of "wall-to-wall optimal transport" in which we attempt to maximize the transport of a passive temperature field between hot and cold plates. Specifically, we optimize the choice of the divergence-free velocity field…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…
Trials enroll a large number of subjects in order to attain power, making them expensive and time-consuming. Sample size calculations are often performed with the assumption of an unadjusted analysis, even if the trial analysis plan…
Given a source of iid samples of edges of an input graph $G$ with $n$ vertices and $m$ edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in $G$? Moreover, is it possible to obtain…
In this paper I discuss the kinds of information that can be extracted by our enemy if our jamming is too precise. I show geometric solutions for reconstructing linear routes given certain information about them, such as the shortest…
We study a well known machine learning model -the perceptron- as a simple model of jamming of hard objects. We exhibit two regimes: 1) a convex optimisation regime where jamming is hypostatic and non-critical. 2) a non convex optimisation…
The problem of optimal data collection to efficiently learn the model parameters of a graphite nitridation experiment is studied in the context of Bayesian analysis using both synthetic and real experimental data. The paper emphasizes that…
This paper is a survey work for a bigger project for designing a Visual SLAM robot to generate 3D dense map of an unknown unstructured environment. A lot of factors have to be considered while designing a SLAM robot. Sensing method of the…
We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the…
Fitting probabilistic models to data is often difficult, due to the general intractability of the partition function and its derivatives. Here we propose a new parameter estimation technique that does not require computing an intractable…
The jamming transition of frictionless athermal particles is a paradigm to understand the mechanics of amorphous materials at the atomic scale. Concepts related to the jamming transition and the mechanical response of jammed packings have…
Given a graph $G$ and a set of terminals $T$, a \emph{distance emulator} of $G$ is another graph $H$ (not necessarily a subgraph of $G$) containing $T$, such that all the pairwise distances in $G$ between vertices of $T$ are preserved in…
In this paper, we focus on sensor placement in linear dynamic estimation, where the objective is to place a small number of sensors in a system of interdependent states so to design an estimator with a desired estimation performance. In…
Solving the chemical master equation exactly is typically not possible, so instead we must rely on simulation based methods. Unfortunately, drawing exact realisations, results in simulating every reaction that occurs. This will preclude the…
The coefficient of determination, known as $R^2$, is commonly used as a goodness-of-fit criterion for fitting linear models. $R^2$ is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case…
Dimension reduction algorithms are a crucial part of many data science pipelines, including data exploration, feature creation and selection, and denoising. Despite their wide utilization, many non-linear dimension reduction algorithms are…
We consider long strips of finite width $L \leq 13$ sites of ferromagnetic Ising spins with random couplings distributed according to the binary distribution: $P(J_{ij})= {1 \over 2} ( \delta (J_{ij} -J_0) + \delta (J_{ij} -rJ_0) ) ,\ 0 < r…