The Pythagoras number of real sum of squares polynomials and sum of square magnitudes of polynomials

In this paper, we conjecture a formula for the value of the Pythagoras number for real multivariate sum of squares polynomials as a function of the (total or coordinate) degree and the number of variables. The conjecture is based on the comparison between the number of parameters and the number of conditions for a corresponding low-rank representation. This is then numerically verified for a number of examples. Additionally, we discuss the Pythagoras number of (complex) multivariate Laurent polynomials that are sum of square magnitudes of polynomials on the $n$ -torus. For both types of polynomials, we also propose an algorithm to numerically compute the Pythagoras number and give some numerical illustrations.     

Compensatability and optimal compensation of systems with white parameters in the delta domain

Using the delta operator, the strengthened discrete-time optimal projection equations for optimal reduced-order compensation of systems with white stochastic parameters are formulated in the delta domain. The delta domain unifies discrete time and continuous time. Moreover, when formulated in this domain, the efficiency and numerical conditioning of algorithms improves when the sampling rate is high. Exploiting the unification, important theoretical results, algorithms and compensatability tests concerning finite and infinite horizon optimal compensation of systems with white stochastic parameters are carried over from discrete time to continuous time. Among others, we consider the finite-horizon time-varying compensation problem for systems with white stochastic parameters and the property mean-square compensatability (ms-compensatability) that determines whether a system with white stochastic parameters can be stabilised by means of a compensator. In continuous time, both of these appear to be new. This also holds for the associated numerical algorithms and tests to verify ms-compensatability. They are illustrated with three numerical examples that reveal several interesting theoretical and numerical issues. A fourth example illustrates the improvement of both the efficiency and numerical conditioning of the algorithms. This is of vital practical importance for digital control system design when the sampling rate is high.     

Iterative spectral unmixing (ISU)

Spectral unmixing techniques strive to find proportions of end-members within a pixel from the observed mixed pixel spectrum and a number of pure end-member spectra of known composition. The outcomes of such analysis are fraction (abundance) images for the selected (pure) end-members and a root mean square (RMS) error estimate representing the difference between the observed mixed spectrum and the calculated mixed spectrum. The RMS image can be used to select additional end-members and re-position existing ones. This is now done manually. In this Letter, an automatediterative approach is proposed using the RMS error image to select additional end-members and re-distribute older ones in order toincrease the accuracy of the spectral unmixing. Optimization criteria are proposed to drive the iterative process including minimization of the average RMS, minimizing the spread of the RMS values, minimizing the spatial structure of the RMS image, minimizing the spatial anisotropy of the RMS image and minimizing the local variance. The preliminary results of the analysis indicate that considerable improvement tothe spectral unmixing results are achieved using the iterative spectral unmixing (ISU) approach.     

Testing two methods for mapping water hyacinth (Eichhornia crassipes) in the Greater Letaba river system,South Africa: discrimination and mapping potential of the polar-orbiting Sentinel-2 MSI and Landsat 8 OLI sensors

ABSTRACT

Early detection and mapping of the spatio-temporal distribution of invasive water hyacinth (Eichhornia crassipes) in inland hydrological systems are vital for a number of water resource management-related reasons. Field surveys and current climate change projections (associated with longer dry spells, and shortened rain seasons) have shown that climate change and the rapid spread of aquatic invasive species are increasingly affecting inland surface water availability in semi-arid regions of Southern Africa. It is upon this premise that accurate, reliable, and timely information on the spatio-temporal distribution and configuration of water hyacinth is required in tracing their evolution and propagation in affected areas as well as in potential vulnerable areas. This work, therefore, attempts to test two robust push-broom multispectral sensors: Landsat 8 Operational Land Imager (OLI) and Sentinel-2 MultiSpectral Instrument (MSI) in identifying, detecting, and mapping the spatial distribution and configuration of invasive water hyacinth in a river system. The results of the study show that water hyacinth in small reservoirs can be mapped with an overall accuracy of 68.44% and 77.56% using Landsat 8 and Sentinel-2 data, respectively. The results further demonstrated the blue, red, red edge (RE) 1, short-wavelength infrared (SWIR)-1, and SWIR-2 of both satellite data sets as the critical and outstanding spectral regions in detecting and mapping water hyacinth from other land-cover types. Overall, the study highlights the unexploited prospects of the new noncommercial multispectral sensors in monitoring invasive species infestation from inland surface waterbodies in semi-arid regions (i.e. smaller reservoirs).     

Lateral Magnetically Modulated Multilayers by Combining Ion Implantation and Lithography

The combination of lithography and ion implantation is demonstrated to be a suitable method to prepare lateral multilayers. A laterally, compositionally, and magnetically modulated microscale pattern consisting of alternating Co (1.6 µm wide) and Co‐CoO (2.4 µm wide) lines has been obtained by oxygen ion implantation into a lithographically masked Au‐sandwiched Co thin film. Magnetoresistance along the lines (i.e., current and applied magnetic field are parallel to the lines) reveals an effective positive giant magnetoresistance (GMR) behavior at room temperature. Conversely, anisotropic magnetoresistance and GMR contributions are distinguished at low temperature (i.e., 10 K) since the O‐implanted areas become exchange coupled. This planar GMR is principally ascribed to the spatial modulation of coercivity in a spring‐magnet‐type configuration, which results in 180° Néel extrinsic domain walls at the Co/Co‐CoO interfaces. The versatility, in terms of pattern size, morphology, and composition adjustment, of this method offers a unique route to fabricate planar systems for, among others, spintronic research and applications.     

Imaging of the optic disc and retinal nerve fiber layer: the effects of age, optic disc area, refractive error, and gender.

We cross-sectionally examined the relationship between age, optic disc area, refraction, and gender and optic disc topography and retinal nerve fiber layer (RNFL) measurements, using optical imaging techniques. One eye from each of 155 Caucasian subjects (age range 23.0-80.8 y) without ocular pathology was included. Measurements were obtained by using the Heidelberg Retina Tomography (HRT), the GDx Nerve Fiber Analyzer, and the Optical Coherence Tomograph (OCT). The effects of age were small (R2 < 17%) and were limited to specific HRT, GDx, and OCT parameters. Disc area was significantly associated with most HRT parameters and isolated GDx and OCT parameters. Refraction and gender were not significantly associated with any optic disc or RNFL parameters. Although effects of age on the optic disc and RNFL are small, they should be considered in monitoring ocular disease. Optic disc area should be considered when cross-sectionally evaluating disc topography and, to a lesser extent, RNFL thickness.     

General expression for pdf of a sum of independent exponential random variables

In order to evaluate exactly the performance of some diversity schemes, the probability density function (pdf) of a sum of independent exponential random variables (r.v.'s) must be known. This paper proposes a simple method to find it by using characteristic function., The resultant pdf is successfully applied to formulate the closed-form BER expression of 2 Tx-J Rx transmit diversity as well as the outage probability of repetition coding.     

Performance analysis of linear MIMO equalizers for multitone DS/SS systems in multipath channels

In [11] the combination of multitone modulation with direct sequence spectrum spreading has been introduced. The performance of a correlation receiver has been evaluated for a multipath channel. In [12] the analysis has been extended to the presence of a multiple access interference. In the present paper we analyze the equalization problem of such a system for a single user scenario. In order to understand the potential of the system we first investigate the steady-state behavior of the MIMO equalizer for an MMSE design. The investigation is carried out for an equalizer following a receiver made of a bank of filters matched to both the symbol shape and the channel, which is a two-path channel. Assuming BPSK symbols an exact expression of the bit error probability before and after equalization is obtained in the form of an integral by means of the characteristic function method. Next adaptive LMS and RLS structures are proposed. The performance of the RLS algorithm is demonstrated.Part of this work has been presented at ICC '95, Seattle, June 1995.This author would like to thank the Belgian NSF for its financial support.This author is a Research assistant of FRIA.     

A Nom historical document recognition system for digital archiving

A Nom historical document recognition system is being developed for digital archiving that uses image binarization, character segmentation, and character recognition. It incorporates two versions of off-line character recognition: one for automatic recognition of scanned and segmented character patterns (7660 categories) and the other for user handwritten input (32,695 categories). This separation is used since including less frequently appearing categories in automatic recognition increases the misrecognition rate without reliable statistics on the Nom language. Moreover, a user must be able to check the results and identify the correct categories from an extended set of categories, and a user can input characters by hand. Both versions use the same recognition method, but they are trained using different sets of training patterns. Recursive X–Y cut and Voronoi diagrams are used for segmentation; k–d tree and generalized learning vector quantization are used for coarse classification; and the modified quadratic discriminant function is used for fine classification. The system provides an interface through which a user can check the results, change binarization methods, rectify segmentation, and input correct character categories by hand. Evaluation done using a limited number of Nom historical documents after providing ground truths for them showed that the two stages of recognition along with user checking and correction improved the recognition results significantly.