Compact Map Research Articles

An uncertainty principle for star formation – IV. On the nature and filtering of diffuse emission

Abstract Diffuse emission is observed in galaxies in many tracers across the electromagnetic spectrum, including tracers of star formation, such as H α and ultraviolet (UV), and tracers of gas mass, such as carbon monoxide (CO) transition lines and the 21-cm line of atomic hydrogen (H i). Its treatment is key to extracting meaningful information from observations such as cloud-scale star formation rates. Finally, studying diffuse emission can reveal information about the physical processes taking place in the interstellar medium, such as chemical transitions and the nature of stellar feedback (through the photon escape fraction). We present a physically motivated method for decomposing astronomical images containing both diffuse emission and compact regions of interest, such as H ii regions or molecular clouds, into diffuse and compact component images through filtering in Fourier space. We have previously presented a statistical method for constraining the evolutionary timeline of star formation and mean separation length between compact star-forming regions with galaxy-scale observations. We demonstrate how these measurements are biased by the presence of diffuse emission in tracer maps and that by using the mean separation length as a critical length-scale to separate diffuse emission from compact emission, we are able to remove its biasing effect. Furthermore, this method provides, without the need for interferometry or ancillary spectral data, a measurement of the diffuse emission fraction in input tracer maps and decomposed diffuse and compact emission maps for further analysis.

The Bishop–Phelps–Bollobás property for Lipschitz maps

In this paper, we introduce and study a Lipschitz version of the Bishop–Phelps–Bollobás property (Lip-BPB property). This property deals with the possibility of making a uniformly simultaneous approximation of a Lipschitz map F and a pair of points at which F almost attains its norm by a Lipschitz map G and a pair of points such that G strongly attains its norm at the new pair of points. We first show that if M is a finite pointed metric space and Y is a finite-dimensional Banach space, then the pair (M,Y) has the Lip-BPB property, and that both finiteness assumptions are needed. Next, we show that if M is a uniformly Gromov concave pointed metric space (i.e. the molecules of M form a set of uniformly strongly exposed points), then (M,Y) has the Lip-BPB property for every Banach space Y. We further prove that this is the case for finite concave metric spaces, ultrametric spaces, and Hölder metric spaces. The extension of the Lip-BPB property from (M,R) to some Banach spaces Y and some results for compact Lipschitz maps are also discussed.

Iterates of a compact holomorphic map on a finite rank homogeneous ball

Iterates of a compact holomorphic map on a finite rank homogeneous ball

ACTION RECOGNITION USING UNDECIMATED DUAL TREE COMPLEX WAVELET TRANSFORM FROM DEPTH MOTION MAPS / DEPTH SEQUENCES

Abstract. Accumulating the motion information from a video sequence is one of the highly challenging and significant phase in Human Action Recognition. To achieve this, several classical and compact representations are proposed by the research community with proven applicability. In this paper, we propose a compact Depth Motion Map based representation methodology with hastey striding, consisely accumulating the motion information. We extract Undecimated Dual Tree Complex Wavelet Transform features from the proposed DMM, to form an efficient feature descriptor. We designate a Sequential Extreme Learning Machine for classifying the human action secquences on benchmark datasets, MSR Action 3D dataset and DHA Dataset. We empirically prove the feasability of our method under standard protocols, achieving proven results.

Operator p-compact mappings

We introduce the classes of operator p-compact mappings and completely right p-nuclear operators, which are natural extensions to the operator space framework of their corresponding Banach operator ideals. We relate these two classes, define natural operator space structures and study several properties of these ideals. We show that the class of operator ∞-compact mappings in fact coincides with a notion already introduced by Webster in the nineties (in a very different language). This allows us to provide an operator space structure to Webster's class.

Positive Solutions of Elliptic Boundary Value Problems and Applications to Population Dynamics

In this paper, we investigate the dynamics of population inhabiting a favorable environment surrounded by a region where survival is impossible. We use a parabolic partial differential equation with nonlinearity changing signs to describe the dynamics. By using a recent result on the existence of nonzero fixed point for r-nowhere normal-outward compact maps, we establish new results on existence of nonzero nonnegative or positive steady-state solutions of such boundary value problems. Additionally, we obtain the convergence of positive solutions of such parabolic boundary value problems in the Banach space $$C^1$$, which is different from the previous results that considered weak convergence or uniform convergence.

Optimizing compaction calculation for improved probabilistic 2D mapping

ABSTRACTIntegration of all available data in reservoir characterization is critically important. 2D mapping is a reliable and robust technique that allows integration of multiple secondary data, including geological and geophysical surfaces and maps, to generate realistic summaries of reservoir quality at each location in an area of interest with an associated measure of uncertainty. This is achieved in 2D mapping with a more straightforward implementation, requiring significantly less time and fewer resources than three‐dimensional modelling. In this paper, we propose an approach for the empirical calculation and optimization of differential compaction maps by leveraging existing well control for the use in 2D mapping. Success of the proposal is demonstrated through tests of accuracy, precision and fairness of the local uncertainty distributions for 100 new stratigraphical wells drilled in the Christina Lake and Kirby East area.

A generalization of Krasnosel'skii compression fixed point theorem by using star convex sets

AbstractIn the framework of fixed point theory, many generalizations of the classical results due to Krasnosel'skii are known. One of these extensions consists in relaxing the conditions imposed on the mapping, working with k-set contractions instead of continuous and compact maps. The aim of this work if to study in detail some fixed point results of this type, and obtain a certain generalization by using star convex sets.

On a theorem of Terzioğlu

The theory of compact linear operators acting on a Banach space has a classical core and is familiar to many. Perhaps less known is the characterization theorem of Terzioglu for compact maps. This theorem has a number of important connections that deserves illumination. In this paper we survey Terzioglu's characterization theorem for compact maps and some of its consequences. We also prove a similar characterization theorem for Q role=presentation> Q Q Q -compact maps.

Bio-inspired Analysis of Deep Learning on Not-So-Big Data Using Data-Prototypes

Deep artificial neural networks are feed-forward architectures capable of very impressive performances in diverse domains. Indeed stacking multiple layers allows a hierarchical composition of local functions, providing efficient compact mappings. Compared to the brain, however, such architectures are closer to a single pipeline and require huge amounts of data, while concrete cases for either human or machine learning systems are often restricted to not-so-big data sets. Furthermore, interpretability of the obtained results is a key issue: since deep learning applications are increasingly present in society, it is important that the underlying processes be accessible and understandable to every one. In order to target these challenges, in this contribution we analyze how considering prototypes in a rather generalized sense (with respect to the state of the art) allows to reasonably work with small data sets while providing an interpretable view of the obtained results. Some mathematical interpretation of this proposal is discussed. Sensitivity to hyperparameters is a key issue for reproducible deep learning results, and is carefully considered in our methodology. Performances and limitations of the proposed setup are explored in details, under different hyperparameter sets, in an analogous way as biological experiments are conducted. We obtain a rather simple architecture, easy to explain, and which allows, combined with a standard method, to target both performances and interpretability.

Compact snapshot image mapping spectrometer for unmanned aerial vehicle hyperspectral imaging

Due to the surge in the development of unmanned aerial vehicles (UAVs) and small spacecraft (CubeSats and SmallSats) in recent years, there has been a push to develop miniaturized instrumentation to be incorporated on such platforms. A compact hyperspectral imager integrated with these vehicles provides a cost-effective platform for a range of environmental sensing applications that include the monitoring of vegetation, urban development, and lightning. We present the snapshot hyperspectral imaging system (SNAP-IMS), requiring no scanning and capable of integration with a UAV. The collected hyperspectral data cube is 350 × 400 × 55 (x , y , λ) and is acquired within a single camera exposure. The system (288 mm × 150 mm × 160 mm) weighs 3.6 kg (7.9 lb), and its power consumption is marginal as there are no scanning components. Experimental testing included several flights over an area covered by diverse types of vegetation and man-made structures. Data cubes are recorded at a 1/100 s integration time, which mitigated motion-related artifacts. The low size, mass, and power consumption of the imager can enable longer and higher flights at smaller drone sizes and allow easy, portable spectral imaging. Imaging results and the system description are presented and discussed.

Coincidence theory for set-valued maps via compactness principles

A variety of coincidence type results are presented for set-valued maps on Hausdorff topological spaces. Our theory is based on coincidence results (in fact fixed point results) for compact maps.

SOME PROPERTIES OF STRONGLY PARACOMPACT MAPPINGS

In this paper, we continue our study of strongly paracompact mappings, see [2]. More properties of strongly paracompact mappings are obtained. It is proved that paracompact locally compact regular mappings are strongly paracompact. And every paracompact locally compact mapping is a disjoint union of closed and open Lindel?f mappings.

Positive Solutions of One-Dimensional p-Laplacian Problems with Superlinearity

We study one-dimensional p-Laplacian problems and answer the unsolved problem. Our method is to study the property of the operator, the concavity of the solutions and the continuity of the first eigenvalues. By the above study, the main difficulty is overcome and the fixed point theorem can be applied for the corresponding compact maps. An affirmative answer is given to the unsolved problem with superlinearity. A global growth condition is not imposed on the nonlinear term f. The assumptions of this paper are more general than the usual, thus the existing results cannot be utilized. Some recent results are improved from weak solutions to classical solutions and from p ≥ 2 to p ∈ ( 1 , ∞ ) .

Unification of local and nonlocal models within a stable integral formulation for analysis of defects

Employing the discrete Cauchy-Born rule with the principle of virtual work done, a generalized model is formulated with the hope to unify local and nonlocal continuum frameworks. Despite the conventional mapping of the microscopic bond from the undeformed configuration, the consistent derivation requires a transformation on the Average Deviation of Lattice (ADL) vector in the region of influence. The new conversion proffers flexibility to the framework for the analysis of nonuniform distribution of particles in the field. We also found a compact mapping matrix which converts surface-based forces (stresses) to the nonlocal body-based forces. The transformation matrix allows reconstructing continuum models at a lower length scale in a discrete setting. To see the credibility of the model, fracture evolution in SCB specimen made of Polymethyl methacrylate (PMMA) is simulated, and the results are compared with experiments which admit an acceptable agreement.

Boolean loops with compact left inner mapping groups are profinite

A compact, Hausdorff and totally disconnected loop is called a boolean loop. In this note, we prove that a boolean loop with compact left inner mapping group is profinite.

The Schauder and Krasnoselskii Fixed-Point Theorems on a Frechet Space

In this manuscript, we study some fixed-point theorems of the Schauder and Krasnoselskii type in a Frechet topological vector space E. We prove a fixed-point theorem which is for every weakly compact map from a closed bounded convex subset of a Frechet topological vector space having the Dunford–Pettis property into itself has a fixed point. Using our results, we will establish a new version of the Krasnoselskii fixed-point theorem.

Existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale

Let T be a periodic time scale. The purpose of this paper is to use Krasnoselskii's fixed point theorem to prove the existence of positive periodic solutions for nonlinear neutral dynamic equations with variable coefficients on a time scale. We invert these equations to construct a sum of a contraction and a compact map which is suitable for applying the Krasnoselskii's theorem. The results obtained here extend the work of Candan <cite>c1</cite>.

Schauder's Theorem and the method of a priori bounds

We first recall simple proofs relying on the Schauder Fixed Point Theorem of the Nonlinear Alternative, the Leray-Schauder Alternative and the Coincidence Alternative for compact maps on normed spaces. We present also an alternative for compact maps defined on convex subsets of normed spaces. Those alternatives permit to apply the method of a priori bounds to obtain results establishing the existence of solutions to differential equations. Using those alternatives, we present some new proofs of existence results for first order differential equations.

Embodied hands

Humans move their hands and bodies together to communicate and solve tasks. Capturing and replicating such coordinated activity is critical for virtual characters that behave realistically. Surprisingly, most methods treat the 3D modeling and tracking of bodies and hands separately. Here we formulate a model of hands and bodies interacting together and fit it to full-body 4D sequences. When scanning or capturing the full body in 3D, hands are small and often partially occluded, making their shape and pose hard to recover. To cope with low-resolution, occlusion, and noise, we develop a new model called MANO ( hand Model with Articulated and Non-rigid defOrmations ). MANO is learned from around 1000 high-resolution 3D scans of hands of 31 subjects in a wide variety of hand poses. The model is realistic, low-dimensional, captures non-rigid shape changes with pose, is compatible with standard graphics packages, and can fit any human hand. MANO provides a compact mapping from hand poses to pose blend shape corrections and a linear manifold of pose synergies. We attach MANO to a standard parameterized 3D body shape model (SMPL), resulting in a fully articulated body and hand model (SMPL+H). We illustrate SMPL+H by fitting complex, natural, activities of subjects captured with a 4D scanner. The fitting is fully automatic and results in full body models that move naturally with detailed hand motions and a realism not seen before in full body performance capture. The models and data are freely available for research purposes at http://mano.is.tue.mpg.de.