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Visual-inertial odometry (VIO) has been found to have great value in robot positioning and navigation. However, the existing VIO algorithms rely heavily on excellent lighting environments and the accuracy of robot positioning and navigation is degraded largely in illumination-challenging scenes. A robust visual-inertial navigation method is developed in this paper. We construct an effective low-light image enhancement model using a deep curve estimation network (DCE) and a lightweight convolutional neural network to recover the texture information of dark images. Meanwhile, a brightness consistency inference method based on the Kalman filter is proposed to cope with illumination variations in image sequences. Multiple sequences obtained from UrbanNav and M2DRG datasets are used to test the proposed algorithm. Furthermore, we also conduct a real-world experiment for the proposed algorithm. Both experimental results demonstrate that our algorithm outperforms other state-of-art algorithms. Compared to the baseline algorithm VINS-mono, the tracking time is improved from 22.0% to 68.2% and the localization accuracy is improved from 0.489m to 0.258m on the darkest sequences.

We investigate a family of Dirichlet Laplacians on randomly dented or bulged strips in ℝ²; for this random quantum waveguide model, dense point spectrum with exponentially localized eigenfunctions near its fluctuation boundary at the bottom of the spectrum and Lifshitz asymptotics of the integrated density of states are established. For this purpose, multi-scale analysis in the quite abstract form of [21] is applied, and domain perturbations of the Laplacian are studied.

We prove spectral and dynamical localization on a cubic-lattice quantum graph with a random potential. We use multiscale analysis and show how to obtain the necessary estimates in analogy to the well-studied case of random Schrödinger operators.

The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the nonnegative integers. Using this method we classify, according to such localization properties, all the quantum walks with one defect at the origin, providing explicit expressions for the asymptotic return probabilities to the origin.

We investigate the spectral and dynamical localization of a quantum system of n particles on ℝ^d which are subject to a random potential and interact through a pair potential which may have infinite range. We establish two conditions which ensure spectral and dynamical localization near the bottom of the spectrum of the n-particle system: (i) localization is established in the regime of weak interactions supposing one-particle localization, and (ii) localization is also established under a Lifshitz-tail type condition on the sparsity of the spectrum. In case of polynomially decaying interactions, we provide an upper bound on the number of particles up to which these conditions apply.

We consider the multi-particle tight-binding Anderson model and prove that its lower spectral edge is non-random under some mild assumptions on the inter-particle interaction and the random external potential. We also adapt to the low energy regime the multi-particle multi-scale analysis initially developed by Chulaevsky and Suhov in the high disorder limit, if the marginal probability distribution of the i.i.d. random variables is log-Hölder continuous and we obtain the spectral exponential and strong dynamical localization near the bottom of the spectrum.

We present homotopy theoretic and geometric interpretations of the Kane–Mele invariant for gapped fermionic quantum systems in three dimensions with time-reversal symmetry. We show that the invariant is related to a certain 4-equivalence which lends it an interpretation as an obstruction to a block decomposition of the sewing matrix up to non-equivariant homotopy. We prove a Mayer–Vietoris Theorem for manifolds with ${\mathbb{Z}}_2$-actions which intertwines Real and ${\mathbb{Z}}_2$-equivariant de Rham cohomology groups, and apply it to derive a new localization formula for the Kane–Mele invariant. This provides a unified cohomological explanation for the equivalence between the discrete Pfaffian formula and the known local geometric computations of the index for periodic lattice systems. We build on the relation between the Kane–Mele invariant and the theory of bundle gerbes with ${\mathbb{Z}}_2$-actions to obtain geometric refinements of this obstruction and localization technique. In the preliminary part we review the Freed–Moore theory of band insulators on Galilean spacetimes with emphasis on geometric constructions, and present a bottom-up approach to time-reversal symmetric topological phases.

We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking $N$ values, with $N$ large. These results hold for all energies under an assumption of weak hopping.

Behavioral microsleeps are associated with complete disruption of responsiveness for $\sim 0.5$s to 15s. They can result in injury or death, especially in transport and military sectors. In this study, EEGs were obtained from five nonsleep-deprived healthy male subjects performing a 1h 2D tracking task. Microsleeps were detected in all subjects. Microsleep-related activities in the EEG were detected, characterized, separated from eye closure-related activity, and, via source-space-independent component analysis and power analysis, the associated sources were localized in the brain. Microsleeps were often, but not always, found to be associated with strong alpha-band spindles originating bilaterally from the anterior temporal gyri and hippocampi. Similarly, theta-related activity was identified as originating bilaterally from the frontal-orbital cortex. The alpha spindles were similar to sleep spindles in terms of frequency, duration, and amplitude-profile, indicating that microsleeps are equivalent to brief instances of Stage-2 sleep.

The method to observe the localization of the trace elements in cultured human cell, by the micro Particle Induced X-ray Emission (PIXE) camera, was developed.

The analyzed samples received the eosin staining, which colored the nucleus of cell violet. The scanned areas of the sample with particle irradiation were colored brown by the heat during irradiation. The brown scanned areas were examined by an optical microscope at 400 X magnification and photographed. Then the photo was digitized and loaded into the microcomputer. By microcomputer, the photo of the scanned area was superimposed onto the image of the micro PIXE camera, by matching the scanned area to the image of micro PIXE camera.

This superimposed image enabled us to determine whether the elements exists in cytosol, or in nucleus.

Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve C; we study the moduli problem of parametrizing certain pairs consisting of a sheaf ℰ on S and a map of ℰ to a fixed reference sheaf on S. We prove that the full moduli stack for this problem is representable by a scheme in some cases. Moreover, the moduli stack admits an action by the group C*, and we determine its fixed-point set, which leads to explicit formulas for the rational homology of the moduli space.

Using the method of Witten deformation, we express the basic index of a transversal Dirac operator over a Riemannian foliation as the sum of integers associated to the critical leaf closures of a given foliated bundle map.

Recently, Chang and Li generalized the theory of virtual fundamental class to the setting of semi-perfect obstruction theory. A semi-perfect obstruction theory requires only the local existence of a perfect obstruction theory with compatibility conditions. In this paper, we generalize the torus localization of Graber–Pandharipande [T. Graber and R. Pandharipande, Localization of virtual cycles, Invent. Math.135(2) (1999) 487–518], the cosection localization [Y.-H. Kiem and J. Li, Localizing virtual cycles by cosections, J. Amer. Math. Soc.26(4) (2013) 1025–1050] and their combination [H.-L. Chang, Y.-H. Kiem and J. Li, Torus localization and wall crossing for cosection localized virtual cycles, Adv. Math.308 (2017) 964–986], to the setting of semi-perfect obstruction theory. As an application, we show that the Jiang-Thomas theory [Y. Jiang and R. Thomas, Virtual signed Euler characteristics, preprint (2014), arXiv:1408.2541] of virtual signed Euler characteristic works without the technical quasi-smoothness assumption from derived algebraic geometry.

In this paper, we study some properties of the nth-order weighted reduced Bergman kernels for planar domains, $n\ge 1$. Specifically, we look at Ramadanov type theorems, localization, and boundary behavior of the weighted reduced Bergman kernel and its higher-order counterparts. We also give a transformation formula for these kernels under biholomorphisms.

We present a cellular-automaton model of a reaction-diffusion excitable system with concentration dependent inhibition of the activator, and study the dynamics of mobile localizations (gliders) and their generators. We analyze a three-state totalistic cellular automaton on a two-dimensional lattice with hexagonal tiling, where each cell connects with 6 others. We show that a set of specific rules support spiral glider-guns (rotating activator-inhibitor spirals emitting mobile localizations) and stationary localizations which destroy or modify gliders, along with a rich diversity of emergent structures with computational properties. We describe how structures are created and annihilated by glider collisions, and begin to explore the necessary processes that generate this kind of complex dynamics.

In this paper we study the propagation of acoustic waves in a one-dimensional system with nonstationary chaotic elasticity distribution. The elasticity distribution is assumed to have a power spectrum S(f) ~ 1/f^(2B-3)/(B-1) for B ≥ 1.5. By using a transfer-matrix method we solve the discrete version of the scalar wave equation and compute the Lyapunov exponent. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicate the presence of weak localized acoustic waves for high degree of correlations (B > 2).

We study the nature of collective excitations in classical anharmonic lattices with aperiodic and pseudo-random harmonic spring constants. The aperiodicity was introduced in the harmonic potential by using a sinusoidal function whose phase varies as a power-law, ϕ ∝ n^ν, where n labels the positions along the chain. In the absence of anharmonicity, we numerically demonstrate the existence of extended states and energy propagation for a sufficiently large degree of aperiodicity. Calculations were done by using the transfer matrix formalism (TMF), exact diagonalization and numerical solution of the Hamilton's equations. When nonlinearity is switched on, we numerically obtain a rich framework involving stable and unstable solitons.

In this paper, we investigate the influence of electron-lattice interaction on the stability of uniform electronic wavepackets on chains as well as on several types of fullerenes. We will use an effective nonlinear Schrödinger equation to mimic the electron–phonon coupling in these topologies. By numerically solving the nonlinear dynamic equation for an initially uniform electronic wavepacket, we show that the critical nonlinear coupling above which it becomes unstable continuously decreases with the chain size. On the other hand, the critical nonlinear strength saturates on a finite value in large fullerene buckyballs. We also provide analytical arguments to support these findings based on a modulational instability analysis.

In order to study the information communication ability (i.e. information conductivity) of CodePlex C# community, an Open-Source Online Community (OSOC), we first construct the models of weighted communication networks in 11 periods for the community based on large-scale data collections. Then by using two ways of quantum mapping of complex networks, we analyze the localization properties of information on the maximum connected graphs (named as communication networks) of these weighted networks according to the idea of analyzing the localization properties of an electron on a large cluster. We draw the following conclusions. (1) CodePlex C# OSOC usually has information isolativity. (2) The community has some degree of information communication ability and the ability increases as time goes on. (3) The localization of information on the communication networks in any period induced by its structure is weaker than that induced by its structure together with the connection intensities between its nodes. (4) Our idea and methods can be used to analyze the information communication ability of other online communities.

In this paper, we present a detailed study of the electronic dynamics in systems with correlated disorder generated from the Ornstein–Uhlenbeck process (OU). In short, we used numeric methods for solving the time-dependent Schrödinger equation. We apply a Taylor’s expansion of the evolution operator in order to solve the differential equation. We calculate some typical tools, such as the participation function $\xi (t)$, the mean square displacement $\sigma (t)$ and the probability of return $R(t)$. In our analysis, we show that for low correlations the system behaves as in the standard Anderson model (i.e. all eigenstates are localized). For strong correlations, our results suggest the existence of a quasi-ballistic dynamics.