A flexible Bayesian approach to estimating size-structured matrix population models

The rates of cell growth, division, and carbon loss of microbial populations are key parameters for understanding how organisms interact with their environment and how they contribute to the carbon cycle. However, the invasive nature of current analytical methods has hindered efforts to reliably quantify these parameters. In recent years, size-structured matrix population models (MPMs) have gained popularity for estimating rate parameters of microbial populations by mechanistically describing changes in microbial cell size distributions over time. And yet, the construction, analysis, and biological interpretation of these models are underdeveloped, as current implementations do not adequately constrain or assess the biological feasibility of parameter values, leading to inference which may provide a good fit to observed size distributions but does not necessarily reflect realistic physiological dynamics. Here we present a flexible Bayesian extension of size-structured MPMs for testing underlying assumptions describing the dynamics of a marine phytoplankton population over the day-night cycle. Our Bayesian framework takes prior scientific knowledge into account and generates biologically interpretable results. Using data from an exponentially growing laboratory culture of the cyanobacterium Prochlorococcus, we herein demonstrate the performance improvements of our approach over current models and isolate previously ignored biological processes, such as respiratory and exudative carbon losses, as critical parameters for the modeling of microbial population dynamics. The results demonstrate that this modeling framework can provide deeper insights into microbial population dynamics provided by flow-cytometry time-series data.

Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis

In the framework of Polynomial Eigenvalue Problems (PEPs), most of the matrix polynomials arising in applications are structured polynomials (namely, (skew-)symmetric, (skew-)Hermitian, (anti-)palindromic, or alternating). The standard way to solve PEPs is by means of linearizations. The most frequently used linearizations belong to general constructions, valid for all matrix polynomials of a fixed degree, known as companion linearizations. It is well known, however, that it is not possible to construct companion linearizations that preserve any of the previous structures for matrix polynomials of even degree. This motivates the search for more general companion forms, in particular companion $\ell$-ifications. In this paper, we present, for the first time, a family of (generalized) companion $\ell$-ifications that preserve any of these structures, for matrix polynomials of degree $k=(2d+1)\ell$. We also show how to construct sparse $\ell$-ifications within this family. Finally, we prove that there are no structured companion quadratifications for quartic matrix polynomials.

What you see is where you go: visibility influences movement decisions of a forest bird navigating a three-dimensional-structured matrix

Animal spatial behaviour is often presumed to reflect responses to visual cues. However, inference of behaviour in relation to the environment is challenged by the lack of objective methods to identify the information that effectively is available to an animal from a given location. In general, animals are assumed to have unconstrained information on the environment within a detection circle of a certain radius (the perceptual range; PR). However, visual cues are only available up to the first physical obstruction within an animal's PR, making information availability a function of an animal's location within the physical environment (the effective visual perceptual range; EVPR). By using LiDAR data and viewshed analysis, we modelled forest birds' EVPRs at each step along a movement path. We found that the EVPR was on average 0.063% that of an unconstrained PR and, by applying a step-selection analysis, that individuals are 1.55 times more likely to move to a tree within their EVPR than to an equivalent tree outside it. This demonstrates that behavioural choices can be substantially impacted by the characteristics of an individual's EVPR and highlights that inferences made from movement data may be improved by accounting for the EVPR.

An adaptation for iterative structured matrix completion

<p style='text-indent:20px;'>The task of predicting missing entries of a matrix, from a subset of known entries, is known as <i>matrix completion</i>. In today's data-driven world, data completion is essential whether it is the main goal or a pre-processing step. Structured matrix completion includes any setting in which data is not missing uniformly at random. In recent work, a modification to the standard nuclear norm minimization (NNM) for matrix completion has been developed to take into account <i>sparsity-based</i> structure in the missing entries. This notion of structure is motivated in many settings including recommender systems, where the probability that an entry is observed depends on the value of the entry. We propose adjusting an Iteratively Reweighted Least Squares (IRLS) algorithm for low-rank matrix completion to take into account sparsity-based structure in the missing entries. We also present an iterative gradient-projection-based implementation of the algorithm that can handle large-scale matrices. Finally, we present a robust array of numerical experiments on matrices of varying sizes, ranks, and level of structure. We show that our proposed method is comparable with the adjusted NNM on small-sized matrices, and often outperforms the IRLS algorithm in structured settings on matrices up to size <inline-formula><tex-math id="M1">\begin{document}$ 1000 \times 1000 $\end{document}</tex-math></inline-formula>.</p>

Projected Wirtinger Gradient Descent for Digital Waves Reconstruction

This work attempts to recover digital signals from a few stochastic samples in time domain. The target signal is the linear combination of one-dimensional complex sine components with R different but continuous frequencies. These frequencies control the continuous values in the domain of normalized frequency [0, 1), contrary to the previous research into compressed sensing. To recover the target signal, the problem was transformed into the completion of a low-rank structured matrix, drawing on the linear property of the Hankel matrix. Based on the completion of the structured matrix, the authors put forward a feasible-point algorithm, analyzed its convergence, and speeded up the convergence with the fast iterative shrinkage-thresholding (FIST) algorithm. The initial algorithm and the speed up strategy were proved effective through repeated numerical simulations. The research results shed new lights on the signal recovery in various fields.