Homogeneous Map Research Articles

Urban Land Use and Land Cover Classification Using Remotely Sensed SAR Data through Deep Belief Networks

Land use and land cover (LULC) mapping in urban areas is one of the core applications in remote sensing, and it plays an important role in modern urban planning and management. Deep learning is springing up in the field of machine learning recently. By mimicking the hierarchical structure of the human brain, deep learning can gradually extract features from lower level to higher level. The Deep Belief Networks (DBN) model is a widely investigated and deployed deep learning architecture. It combines the advantages of unsupervised and supervised learning and can archive good classification performance. This study proposes a classification approach based on the DBN model for detailed urban mapping using polarimetric synthetic aperture radar (PolSAR) data. Through the DBN model, effective contextual mapping features can be automatically extracted from the PolSAR data to improve the classification performance. Two-date high-resolution RADARSAT-2 PolSAR data over the Great Toronto Area were used for evaluation. Comparisons with the support vector machine (SVM), conventional neural networks (NN), and stochastic Expectation-Maximization (SEM) were conducted to assess the potential of the DBN-based classification approach. Experimental results show that the DBN-based method outperforms three other approaches and produces homogenous mapping results with preserved shape details.

On global inversion of homogeneous maps

Hadamard's global inverse theorem provides conditions for a function to be globally invertible on Rn. In this note we show that the conditions are robust enough for the conclusion to hold even if we relax the conditions by removing the assumption at a finite number of points. As a consequence, we get a global inverse function theorem for homogeneous functions.

An Alignment Strategy for Evolution of Multi-Agent Systems

Developed in this paper is the notion that the collective behavior of swarms can be achieved without explicit peer-to-peer communication among agents. It is based on a recently proposed continuum framework for studying swarms where homogeneous maps are the key. The paper focuses on 2D evolution of a multi-agent system (MAS) that consists of N agents with Nl leaders at the two ends of m lines called leading segments, that are on the boundary of a moving convex domain Ωt. Rest of the (N-Nl) agents, the followers, are distributed along the m leading segments while lying inside the convex domain Ωt. Every follower i is initially located at the intersection of two line segments whose end points define four agents that are adjacent to i. Under this setup if the domain Ωt is transformed under a homogenous mapping and if every follower agent moves in such a way to reach the point of intersection of the two line segments connecting the adjacent agents, then the final formation of the MAS will satisfy the same homogenous map. This alignment strategy has the distinct advantage that the followers do not need the exact positions of the adjacent local agents to stay aligned.

A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map

In this paper we propose a quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map where the Newton method is used to solve an equivalent system of nonlinear equations. The semi-symmetric tensor is introduced to reveal the relation between homogeneous polynomial map and its associated semi-symmetric tensor. Based on this relation a globally and quadratically convergent algorithm is established where the line search is inserted. Some numerical results of this method are reported.

Fine Mapping of the Maize Cross‐Incompatibility Locus Gametophytic Factor 1 (ga1) Using a Homogeneous Population

ABSTRACTPhenotyping of a mapping population is usually the bottleneck that limits the size of the mapping population and mapping resolution. A homogeneous population mapping approach was used for mapping maize (Zea mays L.) gametophytic factor 1 (ga1) that could completely eliminate phenotyping during the mapping process. The strong allele of maize ga1 (Ga1‐S), from popcorn inbred line SDGa25, showed a 100% cross‐incompatibility with the majority of Chinese dent and flint maize. A homogeneous mapping population was developed by crossing an (SDGa25/Jing66) F1 male back to an SDGa25 female. During the pollination process, pollen grains of ga1 were completely excluded from fertilization, and a homogeneous BC1F1 (SDGa25//SDGa25/Jing66) population was created in which only the Ga1‐S/Ga1‐S genotype existed, making phenotyping unnecessary. A total of 2245 individuals of this population were genotyped with SD9 and SD12 markers and 20 recombinants were identified. The Ga1‐S locus was quickly delineated to a 100 Kb region between markers dCS1 and insertion deletion ID7 at position 9,491,422 and 9,591,946 bp based on the B73 RefGen_v2 sequence. By marker‐assisted selection, Ga1‐S was introgressed into parental lines of an elite white waxy maize hybrid by six generations of backcrossing and one generation of selfing. The homozygous Ga1‐S/Ga1‐S hybrid showed full cross‐incompatibility to ga1 maize. The Ga1‐S allele could be used as a biological reproductive barrier in reducing cross‐pollination between different types of maize such as waxy and non‐waxy, genetically modified (GM) and non‐GM maize.

Planar nearrings on the Euclidean plane

Planar near-rings are generalized rings which can serve as coordinate domains for geometric structures in which each pair of nonparallel lines has a unique point of intersection. It is known that all planar nearrings can be constructed from regular groups of automorphisms of groups which can be viewed as the “action groups” of the planar nearring. In this article, we study planar nearrings whose additive group is \({(\mathbb{R}^n,+)}\), in particular, n = 1 and 2. It is natural to study topological planar nearrings in this context, following ideas of the late Kenneth D. Magill, Jr. In the case of n = 1, we characterize all topological planar nearrings by their action groups \({(\mathbb{R}^*, \cdot)}\) or \({(\mathbb{R}^+, \cdot)}\). For n = 2, these action groups and the circle group \({(\mathbb{U}, \cdot)}\) seem to be the most interesting cases, but the last case can be excluded completely. As a consequence, we obtain characterizations of the semi-homogeneous continuous mappings from \({\mathbb{R}^n}\) to \({\mathbb{R}}\) for n = 1 and 2. Such a mapping f enjoys the property that f(f(u)v) = f(u)f(v) for all \({u,v \in \mathbb{R}^n}\). When \({f(\mathbb{R}^n) = \mathbb{R}^+}\), f is a positive homogeneous mapping of degree 1.

Evolution of Multi-Agent Systems as Continua

In this paper, a new framework for evolution of multi-agent systems (MAS) based on principles of continuum mechanics is developed. Agents are treated as mass particles of a continuum whose evolution (both translation and deformation) is modeled as a homeomorphism from a reference to the current configuration. Such a mapping assures that no two mass particles of the continuum occupy the same location at any given time, thus guaranteeing that inter-agent collision is avoided during motion. We show that a special class of mappings whose Jacobian is only time varying and not spatially varying has some desirable properties that are advantageous in studying swarms. Two specific scenarios are studied where the evolution of a swarm from one configuration to another occurs with no inter-agent collisions while avoiding obstacles, under (i) zero inter-agent communication and (ii) local inter-agent communication. In the first case, a desired map is computed by each agent all knowing the positions of a few leader agents in a reference and the desired configurations. In the second case, paths of n + 1 leader agents evolving in an n-D space are known only to the leaders, while positions of follower agents evolve through updates that are based on positions of n + 1 adjacent agent through local communication with them. The latter is based on a set of weights of communication of follower agents that are predicated on certain distance ratios assigned on the basis of the initial formation of the MAS. Properties of homogeneous maps are exploited to characterize the necessary communication protocol.

A strong open mapping theorem for surjections from cones onto Banach spaces

We show that a continuous additive positively homogeneous map from a closed not necessarily proper cone in a Banach space onto a Banach space is an open map precisely when it is surjective. This generalization of the usual Open Mapping Theorem for Banach spaces is then combined with Michael's Selection Theorem to yield the existence of a continuous bounded positively homogeneous right inverse of such a surjective map; a strong version of the usual Open Mapping Theorem is then a special case. As another consequence, an improved version of the analogue of Andô's Theorem for an ordered Banach space is obtained for a Banach space that is, more generally than in Andô's Theorem, a sum of possibly uncountably many closed not necessarily proper cones. Applications are given for a (pre)-ordered Banach space and for various spaces of continuous functions taking values in such a Banach space or, more generally, taking values in an arbitrary Banach space that is a finite sum of closed not necessarily proper cones.

Growing Neural Gas approach for obtaining homogeneous maps by restricting the insertion of new nodes

The Growing Neural Gas model is used widely in artificial neural networks. However, its application is limited in some contexts by the proliferation of nodes in dense areas of the input space. In this study, we introduce some modifications to address this problem by imposing three restrictions on the insertion of new nodes. Each restriction aims to maintain the homogeneous values of selected criteria. One criterion is related to the square error of classification and an alternative approach is proposed for avoiding additional computational costs. Three parameters are added that allow the regulation of the restriction criteria. The resulting algorithm allows models to be obtained that suit specific needs by specifying meaningful parameters.

Factorization Theorems for Homogeneous Maps on Banach Function Spaces and Approximation of Compact Operators

In this paper, we characterize compact linear operators from Banach function spaces to Banach spaces by means of approximations with bounded homogeneous maps. To do so, we undertake a detailed study of such maps, proving a factorization theorem and paying special attention to the equivalent strong domination property involved. Some applications to compact maximal extensions of operators are also given.

Homogeneous maps of Abelian groups

In this paper we study Abelian groups whose homogeneous maps to other Abelian groups are homomorphisms. We consider these groups as modules over the ring of integers and over their endomorphism rings. We also study related issues.

Persistence and extinction of diffusing populations with two sexes and short reproductive season

A model is considered for a spatially distributed population of male and female individuals that mate and reproduce only once in their life during a very short reproductive season. Between birth and mating, females and males move by diffusion on a bounded domain $\Omega$. Mating and reproduction is described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number $\mathcal{R}_0$ that acts as a threshold between extinction and persistence. If $\mathcal{R}_0 <1$, the population dies out while it persists (uniformly weakly) if $\mathcal{R}_0 > 1$. $\mathcal{R}_0$ is the cone spectral radius of a bounded homogeneous map.

Nonlinear Ergodic Theorem for Positively Homogeneous Nonexpansive Mappings in Banach Spaces

Recently, two retractions (projections), which are different from the metric projection and the sunny nonexpansive retraction in a Banach space, were found. In this article, using nonlinear analytic methods and new retractions, we prove a nonlinear ergodic theorem for positively homogeneous and nonexpansive mappings in a uniformly convex Banach space. The limit points are characterized by using new retractions.

Torsion-free Abelian groups of finite rank as endomorphic modules over their endomorphism ring

In the paper, the additivity problem for homogeneous mappings of torsion-free Abelian groups of finite rank is solved and some close problems are considered.

Cubic derivations on Banach algebras

Let A be a Banach algebra and X be a Banach A-bimodule. A mapping D: A⟶X is a cubic derivation if D is a cubic homogeneous mapping, that is, D is cubic and D(λa)=λ 3 D(a) for any complex number λ and all a∈A, and D(ab)=D(a)⋅b 3+a 3⋅D(b) for all a,b∈A. In this paper, we prove the stability of a cubic derivation with direct method. We also employ a fixed point method to establish the stability and the superstability of cubic derivations.

Topological classification of corank 1 map germs from $$\mathbb {R}^{3}$$ R 3 to $$\mathbb {R}^{3}$$ R 3

The link of a real analytic map germ \(f: (\mathbb {R}^{3}, 0) \rightarrow (\mathbb {R}^{3}, 0)\) is obtained by taking the intersection of the image with a small enough sphere \(S^2_\epsilon \) centered at the origin in \(\mathbb {R}^3\). If \(f\) is finitely determined, this link becomes a stable map from \(S^2\) to \(S^2\). In a previous work, we defined the Gauss paragraph which contains all the topological information of the link when the singular set \(S(\gamma )\) is connected. Now, starting from this point, we give a classification of some finitely determined weighted homogeneous map germs with two-jet equivalent to \((x,y,xz)\). In particular, we classify all 2-ruled map germs from \(\mathbb {R}^3\) to \(\mathbb {R}^3\).

Positive eigenvalue-eigenvector of nonlinear positive mappings

We show that an (eventually) strongly increasing and positively homogeneous mapping T defined on a Banach space can be turned into an Edelstein contraction with respect to Hilbert’s projective metric. By applying the Edelstein contraction theorem, a nonlinear version of the famous Krein-Rutman theorem is presented, and a simple iteration process {Tkx/‖Tkx‖} (∀ x ∈ P+) is given for finding a positive eigenvector with positive eigenvalue of T. In particular, the eigenvalue problem of a nonnegative tensor A can be viewed as the fixed point problem of the Edelstein contraction with respect to Hilbert’s projective metric. As a result, the nonlinear Perron-Frobenius property of a nonnegative tensor A is reached easily.

Altered Pattern of Spontaneous Brain Activity in the Patients with End-Stage Renal Disease: A Resting-State Functional MRI Study with Regional Homogeneity Analysis

PurposeTo investigate the pattern of spontaneous neural activity in patients with end-stage renal disease (ESRD) with and without neurocognitive dysfunction using resting-state functional magnetic resonance imaging (rs-fMRI) with a regional homogeneity (ReHo) algorithm.Materials and Methodsrs-fMRI data were acquired in 36 ESRD patients (minimal nephro-encephalopathy [MNE], n = 19, 13 male, 37±12.07 years; non-nephro-encephalopathy [non-NE], n = 17, 11 male, 38±12.13 years) and 20 healthy controls (13 male, 7 female, 36±10.27 years). Neuropsychological (number connection test type A [NCT-A], digit symbol test [DST]) and laboratory tests were performed in all patients. The Kendall's coefficient of concordance (KCC) was used to measure the regional homogeneity for each subject. The regional homogeneity maps were compared using ANOVA tests among MNE, non-NE, and healthy control groups and post hoc t -tests between each pair in a voxel-wise way. A multiple regression analysis was performed to evaluate the relationships between ReHo index and NCT-A, DST scores, serum creatinine and urea levels, disease and dialysis duration.ResultsCompared with healthy controls, both MNE and non-NE patients showed decreased ReHo in the multiple areas of bilateral frontal, parietal and temporal lobes. Compared with the non-NE, MNE patients showed decreased ReHo in the right inferior parietal lobe (IPL), medial frontal cortex (MFC) and left precuneus (PCu). The NCT-A scores and serum urea levels of ESRD patients negatively correlated with ReHo values in the frontal and parietal lobes, while DST scores positively correlated with ReHo values in the bilateral PCC/precuneus, MFC and inferior parietal lobe (IPL) (all P<0.05, AlphaSim corrected). No significant correlations were found between any regional ReHo values and disease duration, dialysis duration and serum creatinine values in ESRD patients (all P>0.05, AlphaSim corrected).ConclusionDiffused decreased ReHo values were found in both MNE and non-NE patients. The progressively decreased ReHo in the default mode network (DMN), frontal and parietal lobes might be trait-related in MNE. The ReHo analysis may be potentially valuable for elucidating neurocognitive abnormalities of ESRD patients and detecting the development from non-NE to MNE.

Image Contrast in Sum Frequency Generation Microscopy Based on Monolayer Order and Coverage

Sum frequency generation imaging microscopy (SFGIM) was used to study a binary system of self-assembled monolayers (SAMs) on evaporated gold. A two-step process that consists of microcontact printing (μCP) and the solution backfilling method is used to generate a sample surface with two distinct SAMs domains. The high contrast chemical identification and the homogeneity map of the SAMs for two different head groups are revealed by processing the three-dimensional images (xy-surface and infrared wavenumbers) obtained from SFGIM. For conformation order analysis, the amplitude ratios of the methylene and methyl symmetric resonance obtained by a nonlinear curve fit of the spatially and spectrally resolved SFG images are used to reconstruct spatial image maps. The conformation order map shows the distribution of gauche defects in SAMs with improved contrast across monodentate and bidentate alkanethiol monolayer regions. The results show that variation of the head group attached on the surface dominantly influences the conformation disorder and surface coverage of the molecules, while the terminal methyl group in both monodentate and bidentate SAMs shows a similar orientation angle.

The Fine Structure of Shape Tuning in Area V4

Previous studies have shown that neurons in area V4 are involved in the processing of shapes of intermediate complexity and are sensitive to curvature. These studies also suggest that curvature-tuned neurons are position invariant. We sought to examine the mechanisms that endow V4 neurons with these properties. Consistent with previous studies, we found that response rank order to the most- and least-preferred stimuli was preserved throughout the receptive field. However, a fine-grained analysis of shape tuning revealed a surprising result: V4 neurons tuned to highly curved shapes exhibit very limited translation invariance. At a fine spatial scale, these neurons exhibit local variation in orientation. In contrast, neurons that prefer straight contours exhibit spatially invariant orientation-tuning and homogenous fine-scale orientation maps. Both of these patterns are consistent with a simple orientation-pooling model, with tuning for straight or curved shapes resulting, respectively, from pooling of homogenous or heterogeneous orientation signals inherited from early visual areas.