Generalization of Vegetation Indices for Monitoring the Terrestrial Biosphere

<p>Vegetation indices are the most widely used tool in remote sensing and multispectral imaging applications. This paper introduces a nonlinear generalization of the broad family of vegetation indices based on spectral band differences and ratios. The presented indices exploit all higher-order relations of the involved spectral channels, are easy to derive and use, and give some insight on problem complexity. The framework is illustrated to generalize the widely adopted Normalized Difference Vegetation Index (NDVI). Its nonlinear generalization named, kernel NDVI (kNDVI), largely improves performance over NDVI and the recent NIRv in monitoring key vegetation parameters, showing much higher correlation with independent products, such as the MODIS leaf area index (LAI), flux tower gross primary productivity (GPP), and GOME-2 sun-induced fluorescence. The family of indices constitutes a valuable choice for many applications that require spatially explicit and time-resolved analysis of Earth observation data.</p><p><span> Reference: <strong>"<span>A Unified Vegetation Index for Quantifying the Terrestrial Biosphere</span>"</strong>, </span><span>Gustau Camps-Valls, Manuel Campos-Taberner, Álvaro Moreno-Martı́nez, Sophia Walther, Grégory Duveiller, Alessandro Cescatti, Miguel Mahecha, Jordi Muñoz-Marı́, Francisco Javier Garcı́a-Haro, Luis Guanter, John Gamon, Martin Jung, Markus Reichstein, Steven W. Running. </span><em><span><span>Science Advances, in press</span></span><span>, </span> <span>2021</span> </em></p>

Finding Saddle-Node Bifurcations via a Nonlinear Generalized Collatz–Wielandt Formula

The Collatz–Wielandt formula obtained by Lothar Collatz (1942) and Helmut Wielandt (1950) provides a simple variational characterization of the Perron–Frobenius eigenvalue of certain types of matrices. We introduce a nonlinear generalization of the Collatz–Wielandt formula and show that it enables finding the so-called maximal saddle-node bifurcations of systems of nonlinear equations. As a consequence, we obtain an easily verifiable criterion for the detection of such saddle-node bifurcations. We illustrate our approach by examples of finite-difference approximations of nonlinear partial differential equations and a system of power flow.

Nonlinear generalization of the monotone single index model

Single index model is a powerful yet simple model, widely used in statistics, machine learning and other scientific fields. It models the regression function as $g(\left <{a},{x}\right>)$, where $a$ is an unknown index vector and $x$ are the features. This paper deals with a nonlinear generalization of this framework to allow for a regressor that uses multiple index vectors, adapting to local changes in the responses. To do so, we exploit the conditional distribution over function-driven partitions and use linear regression to locally estimate index vectors. We then regress by applying a k-nearest neighbor-type estimator that uses a localized proxy of the geodesic metric. We present theoretical guarantees for estimation of local index vectors and out-of-sample prediction and demonstrate the performance of our method with experiments on synthetic and real-world data sets, comparing it with state-of-the-art methods.

Pilot-Wave Theory for a Relativistic Spin Zero Particle

In the usual approach to the pilot-wave theory for a spin zero particle one starts with the Klein-Gordon equation, which is the relativistic generalization of the Schrodinger equation. This approach encounters several difficulties including superluminal motion and particle trajectories that move backwards in time. In this paper I start with the relativistic classical Hamilton-Jacobi equation and introduce the quantum potential in a way that avoids the above mentioned difficulties. Particle trajectories are timelike or null and are future pointing. The wave equation satisfied by the field is a nonlinear generalization of the Klein-Gordon equation.

The Effect of the Size of the Sample on Results of Indentation Tests

The results of the numerical solution of the problem about interaction between spherical stamp and weakly compressible elastic specimen are investigated. The nonlinear generalization of linear elastic Hencky model is used as a constitutive relation. The results of the indentation problem solution are in good agreement with experimental data. The tests were performed on the kinematical loading fixture. The influence of geometrical parameters of specimen during indentation test on stress strain state and macro response are investigated.

Лазерная нанофлюидика жидких кристаллов

Several scenarios of formation of hydrodynamic flows in nanoscale planar-oriented liquid-crystal (POLC) channels are described by numerical methods within nonlinear generalization of the classical Ericksen–Leslie theory, which allows for consideration of thermomechanical contributions both to the expression for shear stress and the equation of entropy balance. A vortex flow can eventually be formed in a nanoscale POLC channel as a result of the formation of both temperature gradient ∇ T (in the initially uniformly heated POLC channel under focused laser irradiation) and director field gradient $$\nabla {\mathbf{\hat {n}}}$$ (under a static electric field arising in the natural way at the LC phase/solid interface) and due to the interaction between ∇ T and $$\nabla {\mathbf{\hat {n}}}$$ .

Термомеханический режим формирования вихревых течений в гибридно ориентированном нематическом канале

In this paper, we described numerically several scenarios of formation of vortex flows (VF) in microsized hybrid-oriented liquid crystal (HOLC) channels with orientation defects using a nonlinear generalization of the classical Ericksen–Leslie theory that allows taking into account termomechanical contribution, both in the expression for the shear stress and in the entropy balance equation. An analysis of the numerical results showed that there are two or one vortices in the HOLC channel although two vortices directed towards each other are generated at the initial stage of the VT formation Thermomechanically Excited Vortical Flow.

Gradient Dynamics and Entropy Production Maximization

We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs–-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell–Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.