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Let $S$ be the random walk obtained from "coin turning" with some sequence $\{p_n\}_{n\ge 1}$, as introduced in [6]. In this paper we investigate the scaling limits of $S$ in the spirit of the classical Donsker invariance principle, both for the heating and for the cooling dynamics. We prove that an invariance principle, albeit with a non-classical scaling, holds for "not too small" sequences, the order const$\cdot n^{-1}$ (critical cooling regime) being the threshold. At and below this critical order, the scaling behavior is dramatically different from the one above it. The same order is also the critical one for the Weak Law of Large Numbers to hold. In the critical cooling regime, an interesting process emerges: it is a continuous, piecewise linear, recurrent process, for which the one-dimensional marginals are Beta-distributed. We also investigate the recurrence of the walk and its scaling limit, as well as the ergodicity and mixing of the $n$th step of the walk., Comment: 47 pages, 4 figures

According to observations, different visual objects have different salient features in different scenarios. Even for the same object, its salient shape and appearance features may change greatly from time to time in a long-term tracking task. Motivated by them, we proposed an end-to-end feature fusion framework based on Siamese network, named FF-Siam, which can effectively fuse different features for adaptive visual tracking. The framework consists of four layers. A feature extraction layer is designed to extract the different features of the target region and search region. The extracted features are then put into a weight generation layer to obtain the channel weights, which indicate the importance of different feature channels. Both features and the channel weights are utilized in a template generation layer to generate a discriminative template. Finally, the corresponding response maps created by the convolution of the search region features and the template are applied with a fusion layer to obtain the final response map for locating the target. Experimental results demonstrate that the proposed framework achieves state-of-the-art performance on the popular Temple-Color, OTB50 and UAV123 benchmarks.

Local feature descriptors have been widely used in fine-grained visual object search thanks to their robustness in scale and rotation variation and cluttered background. However, the performance of such descriptors drops under severe illumination changes. In this paper, we proposed a Discriminative and Contrast Invertible (DCI) local feature descriptor. In order to increase the discriminative ability of the descriptor under illumination changes, a Laplace gradient based histogram is proposed. A robust contrast flipping estimate is proposed based on the divergence of a local region. Experiments on fine-grained object recognition and retrieval applications demonstrate the superior performance of DCI descriptor to others.

It is well known that when the fused silica is irradiated with focused femtosecond laser beams, space selective chemical etching can be achieved. The etching rate depends sensitively on the polarization of the laser. Surprisingly, we observe that by chirping the Fourier-transform-limited femtosecond laser pulses to picosecond pulses, the polarization dependence of the etching rate disappears, whereas an efficient etching rate can still be maintained. Observation with a scanning electron microscope reveals that the chirped pulses can induce interconnected nanocracks in the irradiated areas which facilitates efficient introduction of the etchant into the microchannel. The reported technology is of great use for fabrication of three-dimensional (3D) microfluidic systems and glass-based 3D printing., Comment: 9 pages, 5 figures, 1 table

Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with a^2 in A for all a in A. In two recent papers by the authors and Neal, a theory for these spaces was developed. It was shown there that much of the theory of associative operator algebras, in particularly surprisingly much of the associative theory from several recent papers of the first author and coauthors, generalizes to Jordan operator algebras. In the present paper we complete this task, giving several results which generalize the associative case in these papers, relating to unitizations, real positivity, hereditary subalgebras, and a couple of other topics. We also solve one of the three open problems stated at the end of our earlier joint paper on Jordan operator algebras., Comment: 10 pages

Examples of operator algebras with involution include the operator $*$-algebras occurring in noncommutative differential geometry studied recently by Mesland, Kaad, Lesch, and others, several classical function algebras, triangular matrix algebras, (complexifications) of real operator algebras, and an operator algebraic version of the {\em complex symmetric} operators studied by Garcia, Putinar, Wogen and others. We investigate the general theory of involutive operator algebras, and give many applications., Comment: 37 pages

The existence of electronic coherence can fundamentally change the scenario of nonlinear interaction of light with quantum systems such as atoms and molecules, which, however, has escaped from observation in the investigations of strong field nonlinear optics in the past several decades. Here, we report on the generation of electronic quantum coherence by strong field ionization of nitrogen molecules in an intense 800 nm laser field. The coherence is experimentally revealed by observing a resonant four-wave mixing process in which the two pump pulses centered at 800 nm and 1580 nm wavelengths are temporally separated from each other. The experimental observation is further reproduced by calculating the nonlinear polarization response of N_2^+ ions using a three-level quantum model. Our result suggests that strong field ionization provides a unique approach to generating a fully coherent molecular wavepacket encapsulating the rotational, vibrational, and electronic states., Comment: 23 pages, 5 figures