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This paper proposes an improved prediction update for extended target tracking with the random matrix model. A key innovation is to employ a generalised non-central inverse Wishart distribution to model the state transition density of the target extent; resulting in a prediction update that accounts for kinematic state dependent transformations. Moreover, the proposed prediction update offers an additional tuning parameter c.f. previous works, requires only a single Kullback-Leibler divergence minimisation, and improves overall target tracking performance when compared to state-of-the-art alternatives.
In this paper we obtain a decoupling feature of the random interlacements process $mathcal{I}^u subset mathbb{Z}^d$, at level $u$, $dgeq 3$. More precisely, we show that the trace of the random interlacements process on two disjoint finite sets, $textsf{F}$ and its translated $textsf{F}+x$, can be coupled with high probability of success, when $|x|$ is large, with the trace of a process of independent excursions, which we call the noodle soup process. As a consequence, we obtain an upper bound on the covariance between two $[0,1]$-valued functions depending on the configuration of the random interlacements on $textsf{F}$ and $textsf{F}+x$, respectively. This improves a previous bound obtained by Sznitman in [12].
This is a draft of summary of multi-model algorithm of extended object tracking based on random matrix (RMF-MM).
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD. We find a clear separation of the spectrum of eigenvalues into high chirality, would-be zero modes and others, in accordance with the Index Theorem. We find the expected clustering of the non-zero modes into quartets as we approach the continuum limit. The predictions of random matrix theory for the epsilon regime are well reproduced. We conclude that improved staggered quarks near the continuum limit respond correctly to QCD topology.
We present an improved Standard-Model (SM) prediction for the dilepton decay of the neutral pion. The loop amplitude is determined by the pion transition form factor for $pi^0togamma^*gamma^*$, for which we employ a dispersive representation that incorporates both space-like and time-like data as well as short-distance constraints. The resulting SM branching fraction, $ text{BR}(pi^0to e^+e^-)=6.25(3)times 10^{-8}$ , sharpens constraints on physics beyond the SM, including pseudoscalar and axial-vector mediators.
Exploiting intrinsic structures in sparse signals underpins the recent progress in compressive sensing (CS). The key for exploiting such structures is to achieve two desirable properties: generality (ie, the ability to fit a wide range of signals with diverse structures) and adaptability (ie, being adaptive to a specific signal). Most existing approaches, however, often only achieve one of these two properties. In this study, we propose a novel adaptive Markov random field sparsity prior for CS, which not only is able to capture a broad range of sparsity structures, but also can adapt to each sparse signal through refining the parameters of the sparsity prior with respect to the compressed measurements. To maximize the adaptability, we also propose a new sparse signal estimation where the sparse signals, support, noise and signal parameter estimation are unified into a variational optimization problem, which can be effectively solved with an alternative minimization scheme. Extensive experiments on three real-world datasets demonstrate the effectiveness of the proposed method in recovery accuracy, noise tolerance, and runtime.