A new approach to satellite-based estimation of precipitation over snow cover

Current satellite-based remote-sensing approaches are largely incapable of estimating precipitation over snow cover. This note reports a proof-of-concept study of a new satellite-based approach to the estimation of precipitation over snow-covered surfaces. The method is based on the principle that precipitation can be inferred from the changes in the snow water equivalent of the snowpack. Using satellite-based snow water equivalent measurements, we derived daily precipitation amounts for the northern hemisphere for three snow-accumulation seasons, and evaluated these against independent reference datasets. The new precipitation estimates captured realistic-looking storm events over largely un-instrumented regions. However, the data are noisy and, on a seasonal scale, the amount of precipitation is believed to be underestimated. Nevertheless, current uncertainty in snow measurements, albeit large (50–100%), is still lower than direct precipitation measurements over snow (100–140%) and therefore this approach is still useful. The method will become more feasible as the quality of remotely sensed snow measurements improves.     

How We Broke the Union Code (148 Years Too Late)

Abstract

We decrypt a hitherto undeciphered Union message from the United States Civil War. Our means of cryptanalysis of the (Stager) cipher combines an appreciation of the limitations of human-generated randomness and several applications of the principle known as Ockham's Razor. We work without any codebooks and, in the process of our analysis, identify and explain the error that was made in the encryption of this letter from Porter to McClellan (about 148 years ago) that likely led to it being undecipherable—until now.     

Classroom furniture and anthropometric characteristics of Iranian high school students: Proposed dimensions based on anthropometric data

The study evaluated the potential mismatch between classroom furniture dimensions and anthropometric characteristics of 978 Iranian high school students (498 girls, 480 boys), aged 15-18 years. Nine anthropometric measurements (stature, sitting height, sitting shoulder height, popliteal height, hip breadth, elbow-seat height, buttock-popliteal length, buttock-knee length and thigh clearance) and five dimensions from the existing classroom furniture were measured and then compared together (using match criterion equations) to identify any potential mismatch between them. The results indicated a considerable mismatch between body dimensions of the students and the existing classroom furniture, with seat height (60.9%), seat width (54.7%) and desktop height (51.7%) being the furniture dimensions with a higher level of mismatch. The levels of mismatch varied between the high-school grade levels and between genders, indicating their special requirements and possible problems. The proposed dimensions of the classroom furniture more appropriate for the students were given. This additional information on students' anthropometry can be used by local furniture industries as a starting point for designing more appropriate furniture for school children, or used by schools to aid in furniture selection.     

On the existence of virtual exosystems for synchronized linear networks

When dealing with heterogeneous networks, where the agents are governed by non-identical models, interesting questions arise regarding the ability of the network to synchronize to a common non-trivial output trajectory, as well as the nature of such a trajectory. On this topic, Wieland, Allgöwer, and Sepulchre have recently derived results showing that for a class of heterogeneous networks of dynamically controlled linear agents, non-trivial output synchronization implies the existence of an observable virtual exosystem for which the regulator equations are solvable for each agent. Moreover, this virtual exosystem defines the output trajectories on the agreement manifold and is contained within each agent as an internal model. In this paper, we shed further light on this topic by showing that, under a more general set of assumptions, non-trivial output synchronization can occur in the absence of such a virtual exosystem. We propose a modified result for this case that specifies the existence of a possibly unobservable virtual exosystem for which the regulator equations are solvable, and for which the observable part defines the output trajectories on the agreement manifold. We also show that a variation of the virtual exosystem is contained within each agent as an internal model.     

Robust non-fragile LQ controllers: The static state feedback case

This paper describes the synthesis of non-fragile or resilient regulators for linear systems. A general framework for fragility is described using state-space methodologies, and the LQ/H₂ static state-feedback problem is examined in detail. We discuss the multiplicative structured uncertainties case, and propose remedies of the fragility problem using an optimization programming framework via matrix inequalities. A special case that leads to a convex optimization framework via linear matrix inequalities (LMIs) will be considered. The benchmark problem is taken as an example to show how special controller gain variations can affect the performance of the closed-loop system.     

Robustification of input redundant feedback systems using robust actuator weighting in the control allocation problem

In this article, a new methodology for robust actuator weighting in the control allocation (CA) problem of input redundant feedback systems is addressed. The methodology is based on the control structural properties of the plant which were previously used for control configuration selection. Robust performance (RP) measures including H _∞ norm and structured singular value of the closed-loop system are used in this article. The capability of the approach is proven with application to lateral dynamics control of the vehicle over-actuated with front and rear steering systems. Employing the RP measures, it is concluded that the vehicle feedback control with front steering angles gives superior RP properties in comparison with the feedback loop of the rear steering angles. Based on these results, the penalty weightings in the cost function of the CA unit are determined. Simulation results based on nonlinear seven degrees of freedom vehicle handling model show that the selection of penalty weightings in the CA unit based on the RP properties of the control inputs (front and rear steering angles) improves the RP of the closed-loop.     

Exact,almost and optimal input decoupled (delayed) observers

The core of this paper deals with the construction of input-decoupled observers which seek asymptotic estimation of a desired output variable (a linear combination of state and input) of a time-invariant either continuous- or discrete-time system driven by unknown inputs and disturbances. Exact, almost, optimal (suboptimal) and constrained optimal estimation or filtering problems are formulated and studied. All the problems defined and studied here are inherently interconnected, and have a strong common thread of estimation and filtering in the face of the unknown input and external disturbance signals. They are interconnected from a variety of angles, e.g. they are motivated by one another, methods of obtaining the solvability conditions and their methods of solution rely on one another, etc. Thus, a hierarchy of problems and their solutions is built on top of one another. Some of the problems studied here are known in the literature but not in as general a form as is given here, while a majority of the problems studied here are new. A classical variation of all the above problems is also studied here by introducing an l-step delay in estimating the desired output from the measured output. The underlying philosophy throughout this work has been to study most if not all of the facets of estimation and filtering in one stretch under a single folder. Our study of all the above problems has been guided by three important perspectives: (1) obtaining the solvability conditions, both necessary and sufficient; (2) obtaining optimal performance whenever it applies; and (3) developing sound methodologies to design and construct appropriate observers or filters.     

Eigenvalue assignment by minimal state-feedback gain in LTI multivariable systems

In this article, an improved method for eigenvalue assignment via state feedback in the linear time-invariant multivariable systems is proposed. This method is based on elementary similarity operations, and involves mainly utilisation of vector companion forms, and thus is very simple and easy to implement on a digital computer. In addition to the controllable systems, the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs. Moreover, two types of state-feedback gain matrices can be achieved by this method: (1) the numerical one, which is unique, and (2) the parametric one, in which its parameters are determined in order to achieve a gain matrix with minimum Frobenius norm. The numerical examples are presented to demonstrate the advantages of the proposed method.     

Majorisations for the eigenvectors of graph-adjacency matrices

We develop majorisation results that characterise changes in eigenvector components of a graph's adjacency matrix when its topology is changed. Specifically, for general (weighted, directed) graphs, we characterise changes in dominant eigenvector components for single- and multi-row incrementations. We also show that topology changes can be tailored to set ratios between the components of the dominant eigenvector. For more limited graph classes (specifically, undirected, and reversibly-structured ones), majorisations for components of the subdominant and other eigenvectors upon graph modifications are also obtained.     

Induced-charge electro-osmosis of polymer-containing fluid around a metallic rod

Induced-charge electro-osmotic (ICEO) flow of polymer-containing electrolyte solution around a cylindrical gold-coated stainless steel rod under AC electric field is measured by micro-particle image velocimetry (micro-PIV) for the first time. The ICEO flows as functions of the amount of non-ionic PEG (polyethylene glycol), cationic PDADMA (polydiallyldimethylammonium chloride), and anionic PVSASS (polyvinylsulfonic acid sodium salt) polymers added into the salt solution, frequency, and strength of the AC electric field are measured. The ICEO flow of polymer-containing fluid around the rod is quadrupolar with four vortices and is proportional to the square of imposed electric field. The ICEO flow velocity exponentially decreases with an increased concentration of neutral PEG. Ionic polyelectrolytes significantly increase ICEO velocities due to the enriched net charge within the induced electric double layer arising from the electrostatic interaction between the polarized rod’s surface and the charged polyelectrolytes in ionic polymer solution. In addition, polymer concentration affects the dependence of the ICEO flow on the frequency of AC electric field.