Formula For Function Research Articles

Reconstruction of Three-Dimensional Images Based on Estimation of Spinning Target Parameters in Radar Network

A high-resolution three-dimensional (3D) image reconstruction method for a spinning target is proposed in this paper and the anisotropy is overcome by fusing different observation information acquired from the radar network. The proposed method will reconstruct the 3D scattering distribution, and the mapping of the reconstructed 3D image onto the imaging plane is identical to the two-dimensional (2D) imaging result. At first, the range compression and inverse radon transform is employed to produce the 2D image of the spinning target. In addition, the process of mapping the spinning target onto the imaging plane is analyzed and the mapping formulas which are to map the point onto the 2D image plane are derived. After the micro-Doppler signature about which every reconstructed point in 2D imaging result is extracted by the Radon transform, the extended Hough transform is adopted to calculate an important parameter about the micro-Doppler signature, and the 3D image reconstruction model for the spinning target is constructed based on the radar network. Finally, the algorithm for solving the reconstruction model is proposed and the 3D image of the spinning target is obtained. Some simulation results are given to illustrate the effectiveness of the proposed method, and results show that the mean square error (MSE) relatively holds a steady trend when the signal-to-noise ratio (SNR) is higher than −10 dB and the MSE of the reconstructed 3D target image is less than 0.15 when SNR is at the level of −10 dB.

A 3D image reconstruction technique for spinning targets based on Radar networks

ABSTRACTA three-dimensional (3D) image reconstruction method for the spinning target based on the radar network is proposed in this letter and the design concept is sourced from the similarity of the two-dimensional (2D) imaging result with the target’s mapping on the imaging plane. The proposed method has the capacity to generate 3D image of the spinning target by reconstructing the scattering distribution in 3D Cartesian space. Firstly, the inverse Radon transform is applied to obtain the imaging result of the spinning target and the mapping formulas for mapping the air points onto the 2D image plane are derived. In addition, the radar network 3D image reconstruction model for the spinning target is constructed and the corresponding algorithm for solving the reconstruction model is proposed. Finally, some experiment results are given to verify the effectiveness of the proposed method.

Some isolation results for f-harmonic maps on weighted Riemannian manifolds with boundary

In this paper, we study f -harmonic (respectively, ( p , f ) -harmonic) maps on a compact weighted Riemannian manifold of nonempty boundary and of positive Bakry–Émery Ricci curvature. We first establish a Bochner–Reilly formula for such maps and deduce therefrom some immediate isolation results. In addition, using a weighted Sobolev inequality obtained in [12] , we prove that, under some energy level depending on the Bakry–Émery curvature of the initial manifold and on the sectional curvature of the final one, the only f -harmonic (respectively, ( p , f ) -harmonic) maps are the constant ones. A gap property of the energy density of f -harmonic maps from a weighted Riemannian manifold to a unit sphere is also obtained.

Residues for maps generically transverse to distributions

We show a residues formula for maps generically transversal to regular holomorphic distributions.

Large Scale Structure in Redshift Space

The mapping of dark matter clustering from real space to redshift space introduces the anisotropic property to the measured density power spectrum in redshift space, known as the redshift space distortion effect. The mapping formula is intrinsically non-linear, which is complicated by the higher order polynomials due to indefinite cross correlations between the density and velocity fields, and the Finger–of–God effect due to the randomness of the peculiar velocity field. Whilst the full higher order polynomials remain unknown, the other systematics can be controlled consistently within the same order truncation in the expansion of the mapping formula, as shown in this paper. The systematic due to the unknown non–linear density and velocity fields is removed by separately measuring all terms in the expansion directly using simulations. The uncertainty caused by the velocity randomness is controlled by splitting the FoG term into two pieces, 1) the “one–point” FoG term being independent of the separation vector between two different points, and 2) the “correlated” FoG term appearing as an indefinite polynomials which is expanded in the same order as all other perturbative polynomials. We introduce the recent progress on understanding this mapping, and the application for the future analysis to reveal the nature of cosmic acceleration.

Hybrid modeling of redshift space distortions

The observed power spectrum in redshift space appears distorted due to the peculiar motion of galaxies, known as redshift-space distortions (RSD). While all the effects in RSD are accounted for by the simple mapping formula from real to redshift spaces, accurately modeling redshift-space power spectrum is rather difficult due to the non-perturbative properties of the mapping. Still, however, a perturbative treatment may be applied to the power spectrum at large-scales, and on top of a careful modeling of the Finger-of-God effect caused by the small-scale random motion, the redshift-space power spectrum can be expressed as a series of expansion which contains the higher-order correlations of density and velocity fields. In our previous work [JCAP 8 (Aug., 2016) 050], we provide a perturbation-theory inspired model for power spectrum in which the higher-order correlations are evaluated directly from the cosmological N-body simulations. Adopting a simple Gaussian ansatz for Finger-of-God effect, the model is shown to quantitatively describe the simulation results. Here, we further push this approach, and present an accurate power spectrum template which can be used to estimate the growth of structure as a key to probe gravity on cosmological scales. Based on the simulations, we first calibrate the uncertainties and systematics in the pertrubation theory calculation in a fiducial cosmological model. Then, using the scaling relations, the calibrated power spectrum template is applied to a different cosmological model. We demonstrate that with our new template, the best-fitted growth functions are shown to reproduce the fiducial values in a good accuracy of 1% at k<0.18 Mpc-1 for cosmologies with different Hubble parameters.

Detecting Changes in the Environment Based on Full Posterior Distributions Over Real-Valued Grid Maps

To detect changes in an environment, one has to decide whether a set of recent observations is incompatible with a set of previous observations. For binary, lidar-based grid maps, this is essentially the case when the laser beam traverses a voxel that has been observed as occupied, or when the beam is reflected by a voxel that has been observed as empty. However, in real-world environments, some voxels are neither completely occupied nor completely free. These voxels have to be modeled by real-valued variables, whose estimation is an inherently statistical process. Thus, it is nontrivial to decide whether two sets of observations emerge from the same underlying true map values, and hence from an unchanged environment. Our main idea is to account for the statistical nature of the estimation by leveraging the full map posteriors instead of only the most likely maps. Closed-form solutions of posteriors over real-valued grid maps have been introduced recently. We leverage a similarity measure on these posteriors to score each point in time according to the probability that it constitutes a change in the hidden map value. While the proposed approach works for any type of real-valued grid map that allows the computation of the full posterior, we provide all formulas for the well-known reflection maps and the recently introduced decay-rate maps. We introduce and compare different similarity measures and show that our method significantly outperforms baseline approaches in simulated and real-world experiments.

Bijections for planar maps with boundaries

We present bijections for planar maps with boundaries. In particular, we obtain bijections for triangulations and quadrangulations of the sphere with boundaries of prescribed lengths. For triangulations we recover the beautiful factorized formula obtained by Krikun using a (technically involved) generating function approach. The analogous formula for quadrangulations is new. We also obtain a far-reaching generalization for other face-degrees. In fact, all the known enumerative formulas for maps with boundaries are proved bijectively in the present article (and several new formulas are obtained).Our method is to show that maps with boundaries can be endowed with certain “canonical” orientations, making them amenable to the master bijection approach we developed in previous articles. As an application of our enumerative formulas, we note that they provide an exact solution of the dimer model on rooted triangulations and quadrangulations.

Metric Properties of Level Surfaces of Hölder Mappings Defined on Two-Step Carnot Groups

For a model case of Holder mappings of two-step nilpotent graded groups, the metric properties of level surfaces are established. A version of the coarea formula for noncontact mappings is deduced as an application.

Simulation Analysis of the Variation of Bearing Vibration Performance Based on Fuzzy Set Theory (Part I: Theory)

Based on the fuzzy set theory, a method for bearing vibration performance variation analysis is proposed. Firstly, the original vibration data of the bearing is grouped and the fuzzy similarity relation matrix is constructed by the linear mapping formula. The fuzzy similarity relation matrix in the engineering practice is transformed into the fuzzy equivalence matrix of the spatial vector by the transfer closure method. Then, The equivalence coefficient of the fuzzy equivalence relation matrix is compared with the set threshold to diagnose the variation of bearing vibration performance.

Simulation Analysis of the Variation of Bearing Vibration Performance Based on Fuzzy Set Theory (Part II: Experiment)

Based on the fuzzy set theory, a method for bearing vibration performance variation analysis is proposed. Firstly, the original vibration data of the bearing is grouped and the fuzzy similarity relation matrix is constructed by the linear mapping formula. The fuzzy similarity relation matrix in the engineering practice is transformed into the fuzzy equivalence matrix of the spatial vector by the transfer closure method. Then, The equivalence coefficient of the fuzzy equivalence relation matrix is compared with the set threshold to diagnose the variation of bearing vibration performance.

A note on the spectral deformation of harmonic maps from $${\varvec{S}}^{\varvec{2}}$$ S 2 into the unitary group

In Ferreira et al. (Math Z 266:953–978, 2010), together with J. C. Wood, the authors gave a completely explicit formula for all harmonic maps from 2-spheres to the unitary group U(n) in terms of freely chosen meromorphic functions on $$S^2$$ . The simplest harmonic maps are the isotropic ones. Using Morse theory Burstall and Guest (Math Ann 309:541–572, 1997) showed that the harmonic maps are partitioned into classes labeled by the isotropic ones. In this work, using the formula for harmonic maps aforementioned, we describe explicitly this procedure, showing how all harmonic maps can be built from the isotropic ones.

Perceptual video quality metric for compression artefacts: from two‐dimensional to omnidirectional

In this study, the perceptual video quality (PVQ) for the vogue 360-degree video with compression artefacts viewed on the visual reality (VR) head-mounted display (HMD) is obtained for the first time by an elaborately designed subjective experiment. The characteristic of the PVQ of omnidirectional (360-degree) video on the VR HMD and PC monitor is then investigated. The PVQ on the HMD is found to be linearly related to the video coding quality (VCQ) on the PC monitor. A quality evaluation model is then proposed based on the mapping formula and a new assessment parameter, where the impact of the video resolution and display device is involved. In this way, the traditional video quality assessment metrics for two-dimensional video can be extended to assess the PVQ of the 360-degree video viewed on the HMD. At last, the video structural similarity metric is taken as an example to predict the input of the proposed model, i.e. the VCQ of the 360-degree video. Experimental results demonstrate that the proposed model can effectively and conveniently solve the challenge of PVQ assessment for the 360-degree video with compression distortions on the HMD.

Diagnosis of Vibration Variation of Bearing Based on Fuzzy Set Theory (Part I: Theory)

Based on the fuzzy set theory, a method for diagnosing the variation of bearing vibration performance is proposed. Firstly, the original signal data of the bearing vibration acceleration are grouped to obtain the samples, and then the standard deviation, the average membership, the distance and the closeness degree of each sample are calculated as the sample indicators values. The sample indicators values are processed in the order of magnitude and form fuzzy similarity relation matrix by the linear mapping formula, then the fuzzy similarity relation matrix is transformed into fuzzy equivalence matrix by using the transfer closure method, and the equivalence coefficient in the fuzzy equivalence relation matrix is compared with the set threshold. Finally, the variation of bearing vibration performance is diagnosed.

Counting rooted 4-regular unicursal planar maps

A map is 4-regular unicursal if all its vertices are 4-valent except two odd-valent vertices. This paper investigates the number of rooted 4-regular unicursal planar maps and presents some formulae for such maps with four parameters: the number of edges, the number of inner faces and the valencies of the two odd vertices.

Moving-centre monotonicity formulae for minimal submanifolds and related equations

Monotonicity formulae play a crucial role for many geometric PDEs, especially for their regularity theories. For minimal submanifolds in a Euclidean ball, the classical monotonicity formula implies that if such a submanifold passes through the centre of the ball, then its area is at least that of the equatorial disk. Recently Brendle and Hung proved a sharp area bound for minimal submanifolds when the prescribed point is not the centre of the ball, which resolved a conjecture of Alexander, Hoffman and Osserman. Their proof involves asymptotic analysis of an ingeniously chosen vector field, and the divergence theorem.In this article we prove a sharp ‘moving-centre’ monotonicity formula for minimal submanifolds, which implies the aforementioned area bound. We also describe similar moving-centre monotonicity formulae for stationary p-harmonic maps, mean curvature flow and the harmonic map heat flow.

Scaling limits of random outerplanar maps with independent link-weights

La limite d’échelle des cartes planaires extérieures simples a été établie par Caraceni via une bijection de Bonichon, Gavoille et Hanusse. Dans ce papier, nous construisons une nouvelle bijection entre les cartes planaires extérieures, et les arbres décorés par des suites ordonnées de dissections de polygones enracinées. Nous utilisons cette décomposition pour obtenir une nouvelle preuve, plus courte, du résultat de Caraceni, qui s’étend en outre au cadre général de la percolation de premier passage. Nous obtenons des bornes précises sur la queue de distribution du diamètre des cartes planaires extérieures, et retrouvons les formules d’énumération asymptotiques de ces cartes. Nos méthodes nous permettent également de traiter le cas de sous-classes comme les cartes planaires extérieures biparties.

Monotonicity formulas for extrinsic triharmonic maps and the triharmonic Lane–Emden equation

We derive monotonicity formulas and ε-regularity results for extrinsic triharmonic maps and triharmonic Lane–Emden equations. As an application, we prove partial regularity results for both types of equations in the supercritical regime.

Comparative efficacy and tolerability of pharmacological and somatic interventions in adult patients with treatment-resistant depression: a systematic review and network meta-analysis

Objective: Major depressive disorder (MDD) affects about 10–15% of the general population in a lifetime. A considerable number of patients fail to achieve full symptom remission despite adequate treatment and are considered treatment resistant (TRD). The current study compared the relative efficacy and tolerability of pharmacological and somatic TRD interventions by means of a Bayesian network meta-analysis.Research design and methods: An electronic literature search of MEDLINE, MEDLINE In-Process, EMBASE, PsycInfo, EconLit and Cochrane Library databases for trials published between September 2003 and September 2014 was conducted. Key outcomes extracted were disease severity change from baseline, response and remission rates at various timepoints and discontinuation due to adverse events.Results: Of the 3876 abstracts identified, 31 publications/randomised controlled trials (RCTs) were included in the analysis; 19 RCTs investigating 13 pharmacological interventions and 12 RCTs investigating electroconvulsive therapy (ECT) and repetitive transcranial magnetic stimulation (rTMS). The evidence synthesis investigating efficacy outcomes of TRD treatments demonstrated superior efficacy for ketamine compared to pharmacological and somatic interventions at 2 weeks after treatment initiation. At 4, 6 and 8 weeks, quetiapine augmentation (800 mg/day) and risperidone augmentation were found to be the first and second best treatments, respectively. Networks were small for response rate and remission rate outcomes at most timepoints. The most tolerable treatment was lamotrigine augmentation showing a comparable profile to placebo/sham.Conclusions: This analysis revealed scarcity of long-term data on sustained remission that would allow a comparative long-term efficacy assessment. Key limitations of the analysis can be considered the search timeframe and the use of mapping formula for the depression scores.

Enumeration of 4-regular one-face maps

We obtain explicit formulas for enumerating rooted and unrooted 4-regular one-face maps on genus g surfaces. For rooted maps the result is combinatorially derived from Chapuy’s vertex cutting bijection and has a simple sum-free form similar to analogous formulas for general and cubic one-face maps. To enumerate unrooted maps we apply the approach of Liskovets, Mednykh and Nedela of reducing the problem to counting rooted maps on orbifolds. We show that for 4-regular one-face maps the set of orbifolds to be considered has a simple description, which allows us to obtain the final formula in an explicit form of a sum over 3 integer indices.