Space Version Research Articles

Gravitational redshift and asymmetric redshift-space distortions for stacked clusters

We derive the expression for the observed redshift in the weak field limit in the observer's past light cone, including all relativistic terms up to second order in velocity. We then apply it to compute the cluster–galaxy cross-correlation functions (CGCF) using N-body simulations. The CGCF is asymmetric along the line of sight owing to the presence of the small second-order terms such as the gravitational redshift (GRedshift). We identify two systematics in the modelling of the GRedshift signal in stacked clusters. First, it is affected by the morphology of dark matter haloes and the large-scale cosmic-web. The non-spherical distribution of galaxies around the central halo and the presence of neighbouring clusters systematically reduce the GRedshift signal. This bias is approximately 20 per cent for Mmin ≃ 1014 M⊙ h−1, and is more than 50 per cent for haloes with Mmin ≃ 2 × 1013 M⊙ h−1 at r > 4 Mpc h−1. Secondly, the best-fitting GRedshift profiles as well as the profiles of all other relativistic terms are found to be significantly different in velocity space compared to their real space versions. We find that the relativistic Doppler redshift effect, like other second-order effects, is subdominant to the GRedshift signal. We discuss some subtleties relating to these effects in velocity space. We also find that the S/N of the GRedshift signal increases with decreasing halo mass.

Borwein–Preiss vector variational principle

This article extends to the vector setting the results of our previous work Kruger et al. (2015) which refined and slightly strengthened the metric space version of the Borwein-Preiss variational principle due to Li and Shi, J. Math. Anal. Appl. 246(1), 308-319 (2000). We introduce and characterize two seemingly new natural concepts of epsilon-minimality, one of them dependent on the chosen element in the ordering cone and the fixed "gauge-type" function.

Operator Inequalities of Morrey Spaces Associated with Karamata Regular Variation

Karamata regular variation is a basic tool in stochastic process and the boundary blow-up problems for partial differential equations (PDEs). Morrey space is closely related to study of the regularity of solutions to elliptic PDEs. The aim of this paper is trying to bring together these two areas and this paper is intended as an attempt at motivating some further research on these areas. A version of Morrey space associated with Karamata regular variation is introduced. As application, some estimates of operators, especially one-sided operators, on these spaces are considered.

Optimal Control of a Semidiscrete Cahn--Hilliard--Navier--Stokes System with Nonmatched Fluid Densities

This paper is concerned with the distributed optimal control of a time-discrete Cahn--Hilliard--Navier--Stokes system with variable densities. It focuses on the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the Navier--Stokes equation. By proposing a suitable time-discretization, energy estimates are proved, and the existence of solutions to the primal system and of optimal controls is established for the original problem as well as for a family of regularized problems. The latter correspond to Moreau--Yosida-type approximations of the double-obstacle potential. The consistency of these approximations is shown, and first-order optimality conditions for the regularized problems are derived. Through a limit process with respect to the regularization parameter, a stationarity system for the original problem is established. The resulting system corresponds to a function space version of C-s...

Singular twisted sums generated by complex interpolation

We present new methods to obtain singular twisted sums X ⊕ Ω X X\oplus _\Omega X (i.e., exact sequences 0 → X → X ⊕ Ω X → X → 0 0\to X\to X\oplus _\Omega X \to X\to 0 in which the quotient map is strictly singular) when X X is an interpolation space arising from a complex interpolation scheme and Ω \Omega is the induced centralizer. Although our methods are quite general, we are mainly concerned with the choice of X X as either a Hilbert space or Ferenczi’s uniformly convex Hereditarily Indecomposable space. In the first case, we construct new singular twisted Hilbert spaces (which includes the only known example so far: the Kalton-Peck space Z 2 Z_2 ). In the second case we obtain the first example of an H.I. twisted sum of an H.I. space. During our study of singularity we introduce the notion of a disjointly singular twisted sum of Köthe function spaces and construct several examples involving reflexive p p -convex Köthe function spaces (which includes the function space version of the Kalton-Peck space Z 2 Z_2 ). We then use Rochberg’s description of iterated twisted sums to show that there is a sequence F n \mathcal F_n of H.I. spaces so that F m + n \mathcal F_{m+n} is a singular twisted sum of F m \mathcal F_m and F n \mathcal F_n , while for l > n l>n the direct sum F n ⊕ F l + m \mathcal F_n \oplus \mathcal F_{l+m} is a nontrivial twisted sum of F l \mathcal F_l and F m + n \mathcal F_{m+n} .

A comparison study on active learning integrated ensemble approaches in sentiment analysis

One of the most challenging problems of sentiment analysis on social media is that labelling huge amounts of instances can be very expensive. Active learning has been proposed to overcome this problem and to provide means for choosing the most useful training instances. In this study, we introduce active learning to a framework which is comprised of most popular base and ensemble approaches for sentiment analysis. In addition, the implemented framework contains two ensemble approaches, i.e. a probabilistic algorithm and a derived version of Behavior Knowledge Space (BKS) algorithm. The Shannon Entropy approach was utilized for choosing among training data during active learning process and it was compared with maximum disagreement method and random selection of instances. It was observed that the former method causes better accuracies in less number of iterations. The above methods were tested on Cornell movie review dataset and a popular multi-domain product review dataset.

A note on Huang–Zhao theorem on intersecting families with large minimum degree

Using the linear algebra method Huang and Zhao proved that if n>2k and F is an intersecting n-vertex k-uniform hypergraph with minimum degree at least n−2k−2, then F is the star. In this note we present an elementary, combinatorial proof of this result for the case n≥3k. We also prove a vector space version of the Huang–Zhao result along the same line as their proof.

Binary Cockroach Swarm Optimization for Combinatorial Optimization Problem

The Cockroach Swarm Optimization (CSO) algorithm is inspired by cockroach social behavior. It is a simple and efficient meta-heuristic algorithm and has been applied to solve global optimization problems successfully. The original CSO algorithm and its variants operate mainly in continuous search space and cannot solve binary-coded optimization problems directly. Many optimization problems have their decision variables in binary. Binary Cockroach Swarm Optimization (BCSO) is proposed in this paper to tackle such problems and was evaluated on the popular Traveling Salesman Problem (TSP), which is considered to be an NP-hard Combinatorial Optimization Problem (COP). A transfer function was employed to map a continuous search space CSO to binary search space. The performance of the proposed algorithm was tested firstly on benchmark functions through simulation studies and compared with the performance of existing binary particle swarm optimization and continuous space versions of CSO. The proposed BCSO was adapted to TSP and applied to a set of benchmark instances of symmetric TSP from the TSP library. The results of the proposed Binary Cockroach Swarm Optimization (BCSO) algorithm on TSP were compared to other meta-heuristic algorithms.

Validation of TANSO-FTS/GOSAT XCO<sub>2</sub> and XCH<sub>4</sub> glint mode retrievals using TCCON data from near-ocean sites

Abstract. The thermal And near infrared sensor for carbon observations Fourier transform spectrometer (TANSO-FTS) on board the Greenhouse Gases Observing Satellite (GOSAT) applies the normal nadir mode above the land (“land data”) and sun glint mode over the ocean (“ocean data”) to provide global distributions of column-averaged dry-air mole fractions of CO2 and CH4, or XCO2 and XCH4. Several algorithms have been developed to obtain highly accurate greenhouse gas concentrations from TANSO-FTS/GOSAT spectra. So far, all the retrieval algorithms have been validated with the measurements from ground-based Fourier transform spectrometers from the Total Carbon Column Observing Network (TCCON), but limited to the land data. In this paper, the ocean data of the SRPR, SRFP (the proxy and full-physics versions 2.3.5 of SRON/KIT's RemoTeC algorithm), NIES (National Institute for Environmental Studies operational algorithm version 02.21) and ACOS (NASA's Atmospheric CO2 Observations from Space version 3.5) are compared with FTIR measurements from five TCCON sites and nearby GOSAT land data.For XCO2, both land and ocean data of NIES, SRFP and ACOS show good agreement with TCCON measurements. Averaged over all TCCON sites, the relative biases of ocean data and land data are −0.33 and −0.13 % for NIES, 0.03 and 0.04 % for SRFP, 0.06 and −0.03 % for ACOS, respectively. The relative scatter ranges between 0.31 and 0.49 %. For XCH4, the relative bias of ocean data is even less than that of the land data for the NIES (0.02 vs. −0.35 %), SRFP (0.04 vs. 0.20 %) and SRPR (−0.02 vs. 0.06 %) algorithms. Compared to the results for XCO2, the XCH4 retrievals show larger relative scatter (0.65–0.81 %).

Efficient Representation of Pattern Databases Using Acyclic Random Hypergraphs

A popular way to create domain-independent heuristic functions is by using abstraction, where an abstract (coarse) version of the state space is derived from the original state space. An abstraction-based heuristic is usually implemented using a pattern database, a lookup table of (abstract state, heuristic value) pairs. Efficient representation and compression of pattern databases has been the topic of substantial ongoing research. In this paper, we present a novel domain-independent algorithm for this purpose using acyclic r-partite random hypergraphs. The theoretical and experimental results show that our proposed algorithm provides a consistent representation that works well across planning problem domains and provides a good trade-off between space usage and lookup time. Thus, it is suitable to be a standard efficient representation for pattern databases and a benchmark method for other pattern database representation/compression methods.

A discrete extension of the Blaschke rolling ball theorem

The rolling ball theorem asserts that given a convex body $$K\subset \mathbb {R}^d$$ in Euclidean space and having a $$C^2$$ -smooth surface $$\partial K$$ with all principal curvatures not exceeding $$c>0$$ at all boundary points, then K necessarily has the property that to each boundary point there exists a ball $$B_r$$ of radius $$r=1/c$$ , fully contained in K and touching $$\partial K$$ at the given boundary point from the inside of K. In the present work we prove a discrete analogue of the result on the plane. We consider a certain discrete condition on the curvature, namely that to any boundary points $$\mathbf{x},\mathbf{y}\in \partial K$$ with $$|\mathbf{x}-\mathbf{y}|\le \tau $$ , the angle $$\varphi (\mathbf{n}_\mathbf{x},\mathbf{n}_\mathbf{y}):= \arccos \langle \mathbf{n}_\mathbf{x},\mathbf{n}_\mathbf{y}\rangle $$ of any unit outer normals $$\mathbf{n}_\mathbf{x},\mathbf{n}_\mathbf{y}$$ at $$\mathbf{x}$$ and at $$\mathbf{y}$$ , resp., does not exceed a given angle $$\varphi $$ . Then we construct a corresponding body, $$M(\tau ,\varphi )$$ , which is to lie fully within K while containing the given boundary point $$\mathbf{x}\in \partial K$$ . In dimension $$d=2$$ , that is, on the plane, M is almost a regular n-gon, and the result allows to recover the precise form of Blaschke’s Rolling Ball Theorem in the limit. Similarly, we consider the dual type discrete Blaschke theorems ensuring certain circumscribed polygons. In the limit, the discrete theorem enables us to provide a new proof for a strong result of Strantzen assuming only a.e. existence and lower estimations on the curvature. For $$d\ge 3$$ , directly we can derive only a weaker, quasi-precise form of the discrete inscribed ball theorem, while no space version of the circumscribed ball theorem is found. However, at least the higher dimensional smooth cases follow already from the plane versions of the smooth theorems, which obtain as limiting cases also from our discrete versions.

Extending smooth cyclic group actions on the Poincaré homology sphere

Let $X_0$ denote a compact, simply-connected smooth $4$-manifold with boundary the Poincar\'e homology $3$-sphere $\Sigma(2,3,5)$ and with even negative definite intersection form $Q_{X_0}=E_8$. We show that free $\mathbb{Z}/p$ actions on $\Sigma(2,3,5)$ do not extend to smooth actions on $X_0$ with isolated fixed points for any prime $p>7$. The approach is to study the equivariant version of the Yang-Mills instanton-one moduli space for $4$-manifolds with cylindrical ends. As an application we show that for $p>7$ a smooth $\mathbb{Z}/p$ action on $\#^8 S^2 \times S^2$ with isolated fixed points does not split along a free action on $\Sigma(2,3,5)$. The results hold for $p=7$ if the action is homologically trivial.

Euclidean signature semi-classical methods for bosonic field theories: interacting scalar fields

Elegant 'microlocal' methods have long since been extensively developed for the analysis of conventional Schroedinger eigenvalue problems. For technical reasons though these methods have not heretofore been applicable to quantum field theories. In this article however we initiate a 'Euclidean signature semi-classical' program to extend the scope of these analytical techniques to encompass the study of self-interacting scalar fields in 1 + 1, 2 + 1 and 3 + 1 dimensions. The basic microlocal approach entails, first of all, the solution of a single, nonlinear equation of Hamilton-Jacobi type followed by the integration (for both ground and excited states) of a sequence of linear 'transport' equations along the 'flow' generated by the 'fundamental solution' to the aforementioned Hamilton-Jacobi equation. Using a combination of the direct method of the calculus of variations, elliptic regularity theory and the Banach space version of the implicit function theorem we establish, in a suitable function space setting, the existence, uniqueness and global regularity of this needed 'fundamental solution' to the relevant, Euclidean signature Hamilton-Jacobi equation for the systems under study. Our methods are applicable to (massive) scalar fields with polynomial self-interactions of renormalizable type. They can, as we shall show elsewhere, also be applied to Yang-Mills fields in 2 + 1 and 3 + 1 dimensions.

Hypertelescopes: potential science gains, current testing and prospects in space

In the way of giant dilute telescopes, the hypertelescope is a many-aperture interferometer, which provides direct high resolution images with efficient light concentration. Pending future versions in space, a prototype terrestrial hypertelescope is under test in a high valley of the southern Alps. A moving focal gondola, suspended 101 m above small static mirrors, is driven under computer control with millimeter accuracy. The coude focus at ground level has been qualified by observing a Vega image focused by one of the mirrors and transmitted through the gondola. Upgrades under way for multi-beam interference include full autoguiding, the installation of several cameras on the gondola and adaptive optics for cophasing. Science observing is expected to begin in a few years, and other potential sites are considered for a larger meta-aperture, in the kilometer range. Future space versions, utilizing a 10–1000 km flotilla of small mirrors, are also considered and proposed to NASA and ESA, but require different technical developments.

Initial-value semiclassical propagators for the Wigner phase space representation: Formulation based on the interpretation of the Moyal equation as a Schrödinger equation.

We formulate various semiclassical propagators for the Wigner phase space representation from a unified point of view. As is shown in several studies, the Moyal equation, which is an equation of motion for the Wigner distribution function, can be regarded as the Schrödinger equation of an extended Hamiltonian system where its "position" and "momentum" correspond to the middle point of two points of the original phase space and the difference between them, respectively. Then we show that various phase-space semiclassical propagators can be formulated just by applying existing semiclassical propagators to the extended system. As a result, a phase space version of the Van Vleck propagator, the initial-value Van Vleck propagator, the Herman-Kluk propagator, and the thawed Gaussian approximation are obtained. In addition, we numerically compare the initial-value phase-space Van Vleck propagator, the phase-space Herman-Kluk propagator, and the classical mechanical propagation as approximation methods for the time propagation of the Wigner distribution function in terms of both accuracy and convergence speed. As a result, we find that the convergence speed of the Van Vleck propagator is far slower than others as is the case of the Hilbert space, and the Herman-Kluk propagator keeps its accuracy for a long period compared with the classical mechanical propagation while the convergence speed of the latter is faster than the former.

Carleson measures and balayage for Bergman spaces of strongly pseudoconvex domains

Given a bounded strongly pseudoconvex domain D in with smooth boundary, we characterize -Bergman Carleson measures for , , and . As an application, we show that the Bergman space version of the balayage of a Bergman Carleson measure on D belongs to BMO in the Kobayashi metric.

Borwein–Preiss variational principle revisited

In this article, we refine and slightly strengthen the metric space version of the Borwein–Preiss variational principle due to Li and Shi (2000) [12], clarify the assumptions and conclusions of their Theorem 1 as well as Theorem 2.5.2 in Borwein and Zhu (2005) [4] and streamline the proofs. Our main result, Theorem 3 is formulated in the metric space setting. When reduced to Banach spaces (Corollary 9), it extends and strengthens the smooth variational principle established in Borwein and Preiss (1987) [3] along several directions.

A MRI study of the lesser trochanteric version and its relationship to proximal femoral osseous anatomy.

The purpose of this study is to quantify the lesser trochanteric version and determine the angle and the relationship between lesser trochanter and femoral neck version. Investigate the influence of the lesser trochanter version in the width of ischiofemoral space. Two hundred and fifty asymptomatic hips were evaluated with axial magnetic resonance image. The lesser trochanter version was calculated. The difference between the femoral neck version and the lesser trochanter version formed the angle between each structure. The width of ischiofemoral space was measured and its relationship with the lesser trochanter version was determined. The mean lesser trochanter version was −24° ± 11.5° (range, − 54° to + 17°) with a coefficient variation of 47.45%. The mean femoral neck version measured 14.0° ± 10.8° (range, −16° to 50°), with a coefficient variation of 81.32%. The lesser trochanter/femora neck angle was 38.4° ± 9.6° (range, 8° to 67°), coefficient variation of 30%, with a moderate correlation between the structures (r = 0.63, P < 0.01). The mean ischiofemoral space was 22.9.0 ± 7.0 mm (range, 10.3 to 55 mm), and a weak correlation was found between ischiofemoral space and lesser trochanteric version (r = −0.16, P < 0.05). The lesser trochanteric version showed a high variation with a moderate relationship with the femoral neck version. The lesser trochanteric version does not influence the width of the ischiofemoral space.

Entries of indefinite Nevanlinna matrices

In the early 1950’s M.G.Krein characterised those entire functions which are an entry of some Nevanlinna matrix, and those pairs of entire functions which are a row of some such matrix. In connection with Pontryagin space versions of Krein’s theory of entire operators and de Branges’ theory of Hilbert spaces of entire functions, an indefinite analogue of Nevanlinna matrices plays a role. In this paper we extend the mentioned characterisations to the indefinite situation and investigate the geometry of associated reproducing kernel Pontryagin spaces. AMS MSC 2010: 46C20, 34B20, 30D10, 30D15

Holographic Skyrmions

Skyrmions are topological solitons that describe baryons within a nonlinear theory of pions. In holographic QCD, baryons correspond to topological solitons in a bulk theory with an extra spatial dimension. Thus, the three-dimensional Skyrmion lifts to a four-dimensional holographic Skyrmion in the bulk. We begin this review with a description of the simplest example of this correspondence, where the holographic Skyrmion is exactly the self-dual Yang–Mills instanton in flat space. This places an old result of Atiyah and Manton within a holographic framework and reveals that the associated Skyrme model extends the nonlinear pion theory to include an infinite tower of vector mesons, with specific couplings for a BPS theory. We then describe the more complicated curved space version that arises from the string theory construction of Sakai and Sugimoto. The basic concepts remain the same but the technical difficulty increases as the holographic Skyrmion is a curved space version of the Yang–Mills instanton, so self-duality and integrability are lost. Finally, we turn to a low-dimensional analog of holographic Skyrmions, where aspects such as multi-baryons and finite baryon density are amenable to both numerical computation and an approximate analytic treatment.