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1. Improving Dense Crowd Counting Convolutional Neural Networks using Inverse k-Nearest Neighbor Maps and Multiscale Upsampling [Improving Dense Crowd Counting Convolutional Neural Networks using Inverse k-Nearest Neighbor Maps and Multiscale Upsampling]

   https://doi.org/10.5220/0009156201850195  

   Olmschenk, Greg; Tang, Hao; Zhu, Zhigang (January 2020, 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications)

   Gatherings of thousands to millions of people frequently occur for an enormous variety of events, and automated counting of these high-density crowds is useful for safety, management, and measuring significance of an event. In this work, we show that the regularly accepted labeling scheme of crowd density maps for training deep neural networks is less effective than our alternative inverse k-nearest neighbor (i$$k$$NN) maps, even when used directly in existing state-of-the-art network structures. We also provide a new network architecture MUD-i$$k$$NN, which uses multi-scale upsampling via transposed convolutions to take full advantage of the provided i$$k$$NN labeling. This upsampling combined with the i$$k$$NN maps further improves crowd counting accuracy. Our new network architecture performs favorably in comparison with the state-of-the-art. However, our labeling and upsampling techniques are generally applicable to existing crowd counting architectures. 

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2. An Aggregated Multicolumn Dilated Convolution Network for Perspective-Free Counting

   https://doi.org/10.1109/cvprw.2018.00057  

   Deb, Diptodip; Ventura, Jonathan (June 2018, 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW))

   We propose the use of dilated filters to construct an aggregation module in a multicolumn convolutional neural network for perspective-free counting. Counting is a common problem in computer vision (e.g. traffic on the street or pedestrians in a crowd). Modern approaches to the counting problem involve the production of a density map via regression whose integral is equal to the number of objects in the image. However, objects in the image can occur at different scales (e.g. due to perspective effects) which can make it difficult for a learning agent to learn the proper density map. While the use of multiple columns to extract multiscale information from images has been shown before, our approach aggregates the multiscale information gathered by the multicolumn convolutional neural network to improve performance. Our experiments show that our proposed network outperforms the state-of-the-art on many benchmark datasets, and also that using our aggregation module in combination with a higher number of columns is beneficial for multiscale counting. 

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3. Quantum theory of atoms in molecules in condensed charge density space

   https://doi.org/10.1139/cjc-2019-0086  

   Wilson, Timothy R.; Eberhart, M.E. (November 2019, Canadian Journal of Chemistry)

   By leveraging the fundamental doctrine of the quantum theory of atoms in molecules — the partitioning of the electron charge density (ρ) into regions bounded by surfaces of zero flux — we map the gradient field of ρ onto a two-dimensional space called the gradient bundle condensed charge density ([Formula: see text]). The topology of [Formula: see text] appears to correlate with regions of chemical significance in ρ. The bond wedge is defined as the image in ρ of the basin of attraction in [Formula: see text], analogous to the Bader atom, which is the basin of attraction in ρ. A bond bundle is defined as the union of bond wedges that share interatomic surfaces. We show that maxima in [Formula: see text] typically map to bond paths in ρ, though this is not necessarily always true. This observation addresses many of the concerns regarding the chemical significance of bond critical points and bond paths in the quantum theory of atoms in molecules. 

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4. CONJECTURES ABOUT SIMPLE DYNAMICS FOR SOME REAL NEWTON MAPS ON ℝ2

   https://doi.org/10.1142/S0218348X19500993  

   DE LEO, ROBERTO (September 2019, Fractals)

   We collect from several sources some of the most important results on the forward and backward limits of points under real and complex rational functions, and in particular real and complex Newton maps, in one variable and we provide numerical evidence that the dynamics of Newton maps [Formula: see text] associated to real polynomial maps [Formula: see text] with no complex roots has a complexity comparable with that of complex Newton maps in one variable. In particular such a map [Formula: see text] has no wandering domain, almost every point under [Formula: see text] is asymptotic to a fixed point and there is some non-empty open set of points whose [Formula: see text]-limit equals the set of non-regular points of the Julia set of [Formula: see text]. The first two points were proved by B. Barna in the real one-dimensional case. 

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5. Bounds on the superconducting transition temperature

   https://doi.org/10.1142/S0217984924300047  

   Randeria, Mohit (December 2024, Modern Physics Letters B)

   I summarize recent progress on obtaining rigorous upper bounds on superconducting transition temperature [Formula: see text] in two dimensions independent of pairing mechanism or interaction strength. These results are derived by finding a general upper bound for the superfluid stiffness for a multi-band system with arbitrary interactions, with the only assumption that the external vector potential couples to the kinetic energy and not to the interactions. This bound is then combined with the universal relation between the superfluid stiffness and the Berezinskii–Kosterlitz–Thouless [Formula: see text] in 2D. For parabolic dispersion, one obtains the simple result that [Formula: see text], which has been tested in recent experiments. More generally, the bounds are expressed in terms of the optical spectral weight and lead to stringent constraints for the [Formula: see text] of low-density, strongly correlated superconductors. Results for [Formula: see text] bounds for models of flat-band superconductors, where the kinetic energy vanishes and the vector potential must couple to interactions, are briefly summarized. Upper bounds on [Formula: see text] in 3D remains an open problem, and I describe how questions of universality underlie the challenges in 3D. 

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