Deep Shape Matching

We cast shape matching as metric learning with convolutional networks. We break the end-to-end process of image representation into two parts. Firstly, well established efficient methods are chosen to turn the images into edge maps. Secondly, the network is trained with edge maps of landmark images, which are automatically obtained by a structure-from-motion pipeline. The learned representation is evaluated on a range of different tasks, providing improvements on challenging cases of domain generalization, generic sketch-based image retrieval or its fine-grained counterpart. In contrast to other methods that learn a different model per task, object category, or domain, we use the same network throughout all our experiments, achieving state-of-the-art results in multiple benchmarks.Comment: ECCV 201

Some new results on f-contractions in 0-complete partial metric spaces and 0-complete metric-like spaces

Within this manuscript we generalize the two recently obtained results of O. Popescu and G. Stan, regarding the F-contractions in complete, ordinary metric space to 0-complete partial metric space and 0-complete metric-like space. As Popescu and Stan we use less conditions than D. Wardovski did in his paper from 2012, and we introduce, with the help of one of our lemmas, a new method of proving the results in fixed point theory. Requiring that the function F only be strictly increasing, we obtain for consequence new families of contractive conditions that cannot be found in the existing literature. Note that our results generalize and complement many well-known results in the fixed point theory. Also, at the end of the paper, we have stated an application of our theoretical results for solving fractional differential equations. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Solving fractional differential equations using fixed point results in generalized metric spaces of Perov's type

In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of Đ. Kurepa, a new approach to fixed point problems, by defining generalized metric spaces (also known as vector valued metric spaces), and providing some actual results for the first time. Using the recent approach of coordinate representation for a generalized metric of Jachymski and Klima, we verify in this article some natural properties of generalized metric spaces, already owned by standard metric spaces. Among other results, we show that the theorems of Nemytckii (1936) and Edelstein (1962) are valid in generalized metric spaces, as well. A new application to fractional differential equations is also presented. At the end we state a few open questions for young researchers. © Işık University, Department of Mathematics, 2023; all rights reserved

On ordered topological vector groups - new results

The theory of ordered topological vector spaces has been treated in a great number of articles and books. On the other hand, topological vector groups were introduced and studied by D. A. Raikov [On B-complete topological vector groups, Studia Math. 31 (1968), 296-305] and P. S. Kenderov [On topological vector groups, Mat. Sb. 10 (1970), 531-546]. These are vector spaces with a topology in which addition is continuous, but multiplication by scalars is continuous only if the scalar field is taken with the discrete topology. In this paper we introduce ordered topological vector groups and investigate their structure, in particular exploring them in the case when they need not be locally convex

Unsupervised Monocular Depth Estimation for Night-time Images using Adversarial Domain Feature Adaptation

In this paper, we look into the problem of estimating per-pixel depth maps from unconstrained RGB monocular night-time images which is a difficult task that has not been addressed adequately in the literature. The state-of-the-art day-time depth estimation methods fail miserably when tested with night-time images due to a large domain shift between them. The usual photo metric losses used for training these networks may not work for night-time images due to the absence of uniform lighting which is commonly present in day-time images, making it a difficult problem to solve. We propose to solve this problem by posing it as a domain adaptation problem where a network trained with day-time images is adapted to work for night-time images. Specifically, an encoder is trained to generate features from night-time images that are indistinguishable from those obtained from day-time images by using a PatchGAN-based adversarial discriminative learning method. Unlike the existing methods that directly adapt depth prediction (network output), we propose to adapt feature maps obtained from the encoder network so that a pre-trained day-time depth decoder can be directly used for predicting depth from these adapted features. Hence, the resulting method is termed as "Adversarial Domain Feature Adaptation (ADFA)" and its efficacy is demonstrated through experimentation on the challenging Oxford night driving dataset. Also, The modular encoder-decoder architecture for the proposed ADFA method allows us to use the encoder module as a feature extractor which can be used in many other applications. One such application is demonstrated where the features obtained from our adapted encoder network are shown to outperform other state-of-the-art methods in a visual place recognition problem, thereby, further establishing the usefulness and effectiveness of the proposed approach.Comment: ECCV 202

Some critical remarks on recent results concerning F−contractions in b-metric spaces

This paper aims to correct recent results on a generalized class of F−contractions in the context of b−metric spaces. The significant work consists of repairing some novel results involving F−contraction within the struc-ture of b-metric spaces. Our objective is to take advan-tage of the property (F 1) instead of the four properties viz. (F 1), (F 2), (F 3) and (F 4) applied in the results of Nazam et al. [“Coincidence and common fixed point theorems for four mappings satisfying (αs, F)−contraction", Nonlinear Anal: Model. Control., vol. 23, no. 5, pp. 664–690, 2018]. Our approach of proving the results uti-lizing only the condition (F 1) enriches, improves, and condenses the proofs of a multitude of results in the ex-isting state-of-art. © 2023 M. Younis et al

On the Distribution of Kurepa’s Function

Kurepa’s function and his hypothesis have been investigated by means of numerical simulation. Particular emphasis has been given to the conjecture on its distribution, that should be one of a random uniform distribution, which has been verified for large numbers. A convergence function for the two has been found