Object-Based Burned Area Mapping with Extreme Gradient Boosting Using Sentinel-2 Imagery

The Sentinel-2 satellites are providing an unparalleled wealth of high-resolution remotely sensed information with a short revisit cycle, which is ideal for mapping burned areas both accurately and timely. This paper proposes an automated methodology for mapping burn scars using pairs of Sentinel-2 imagery, exploiting the state-of-the-art eXtreme Gradient Boosting (XGB) machine learning framework. A large database of 64 reference wildfire perimeters in Greece from 2016 to 2019 is used to train the classifier. An empirical methodology for appropriately sampling the training patterns from this database is formulated, which guarantees the effectiveness of the approach and its computational efficiency. A difference (pre-fire minus post-fire) spectral index is used for this purpose, upon which we appropriately identify the clear and fuzzy value ranges. To reduce the data volume, a super-pixel segmentation of the images is also employed, implemented via the QuickShift algorithm. The cross-validation results showcase the effectiveness of the proposed algorithm, with the average commission and omission errors being 9% and 2%, respectively, and the average Matthews correlation coefficient (MCC) equal to 0.93.

A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

In this paper, we construct a new Roper-Suffridge extension operator Φn^r,β1,,βn（f）（z） = F（z） = （（rf（z1/r）/z1）^β1z1,（rf（z1/r）/z1）^β2z2,...,（rf（z1/r）/z1）^βnzn）＇,where f is a normalized locally biholomorphic function on the unit disc D, r = sup{｜z1｜ ： z =（z1, ···, zn） ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.

ROPER-SUFFRIDGE EXTENSION OPERATOR ON A REINHARDT DOMAIN

Let pj ∈ N and pj≥ 1, j = 2, …, k, k ≥ 2 be a fixed positive integer. We introduce a Roper-Suffridge extension operator on the following Reinhardt domain ΩN ={z =（z1, z′2,…, z′k）′∈ C × C^n2×…× Cnk： ｜z1｜^2＋ ｜｜z2｜｜2^p2＋ … ＋ ｜｜zk ｜｜k^pk〈 1} given〈1} give by F（z）=（f（z1）＋f＇（z1）∑j=2 kPj（zj,（f＇（z1））1/p2 z2＇,…,（f＇（z1））1/pkzk＇）＇, where f is a normaljized biholomorphic function k（z） =（f（z1） ＋ f′（z1）=2 on the unit disc D, and for 2 ≤ j ≤ k, Pj ： C^nj→ C is a homogeneous polynomial of degree pj and zj =（zj1, …, zjnj）′∈ C^nj, nj ≥ 1, pj ≥ 1,｜｜zj｜｜j =（∑l=1 nj｜zjl｜^pj）1/pj. In this paper, some conditions for Pjare found under which the loperator p ｜zjl｜pj=1reserves the properties of almost starlikeness of order α, starlikeness of order αand strongly starlikeness of order α on ΩN, respectively.

Automated Burned Scar Mapping Using Sentinel-2 Imagery

The Sentinel-2 satellites are providing an unparalleled wealth of high-resolution remotely sensed information with a short revisit cycle, which is ideal for mapping burned areas both accurately and timely. However, the high detail and volume of information provided actually encumbers the automation of the mapping process, at least for the level of automation required to map systematically wildfires on a national level. This paper proposes a fully automated methodology for mapping burn scars using Sentinel-2 data. Information extracted from a pair of Sentinel-2 images, one pre-fire and one post-fire, is jointly used to automatically label a set of training patterns via two empirical rules. An initial pixel-based classification is derived using this training set by means of a Support Vector Machine (SVM) classifier. The latter is subsequently smoothed following a multiple spectral-spatial classification (MSSC) approach, which increases the mapping accuracy and thematic consistency of the final burned area delineation. The proposed methodology was tested on six recent wildfire events in Greece, selected to cover representative cases of the Greek ecosystems and to present challenges in burned area mapping. The lowest classification accuracy achieved was 92%, whereas Matthews correlation coefficient (MCC) was greater or equal to 0.85.

TENSOR SUM AND DYNAMICAL SYSTEMS

In this paper we introduce the concept of tensor sum semigroups. Also we have given the examples of tensor sum operators which induce dynamical system on weighted locally convex function spaces.

Additive Maps Preserving Similarity of Operators on Banach Spaces

Let X be an infinite-dimensional complex Banach space and denote by B（X） the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B（X） onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B（X） such that either Φ（T） = cATA^-1 ＋ ψ（T）I for all T, or Φ（T） = cAT＊A^-1 ＋ ψ（T）I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero.

Maps on Positive Cones of C^(*)-algebras

We prove that a surjective map(on the positive cones of unital C^(*)-algebras)preserves the minimum spectrum values of harmonic means if and only if it has a Jordan *-isomorphism extension to the whole algebra.We represent weighted geometric mean preserving bijective maps on the positive cones of prime C^(*)-algebras in terms of Jordan *-isomorphisms of the algebras.We also characterize order isomorphisms and orthoisomorphisms of the projection lattice of the von Neumann algebra of all bounded linear operators on a Hilbert space,answering an open question arisen by Dye.Finally,we give a description for Fuglede-Kadison determinant preserving maps on the positive cone of a finite von Neumann algebra and improve Gaal and Nayak’s work on this topic.

Development and prospects of the fire space monitoring system in Kazakhstan

This article provides a brief description of the fire space monitoring system in Kazakhstan, including the GIS-technology incorporated in its structure. The system performs operative space monitoring of fire areas and burnt areas, mapping of large fire areas, analysis of seasonal and long-term dynamics of burnt areas, and estimation of fire risk zones. Examples of output information obtained from space monitoring of fires are given. Possible directions of development of fire space monitoring in Kazakhstan are specified.