Euclidean TSP with few inner points in linear space

Given a set of $n$ points in the Euclidean plane, such that just $k$ points are strictly inside the convex hull of the whole set, we want to find the shortest tour visiting every point. The fastest known algorithm for the version when $k$ is significantly smaller than $n$, i.e., when there are just few inner points, works in $O(k^{11\sqrt{k}} k^{1.5} n^{3})$ time [Knauer and Spillner, WG 2006], but also requires space of order $k^{c\sqrt{k}}n^{2}$. The best linear space algorithm takes $O(k! k n)$ time [Deineko, Hoffmann, Okamoto, Woeginer, Oper. Res. Lett. 34(1), 106-110]. We construct a linear space $O(nk^2+k^{O(\sqrt{k})})$ time algorithm. The new insight is extending the known divide-and-conquer method based on planar separators with a matching-based argument to shrink the instance in every recursive call. This argument also shows that the problem admits a quadratic bikernel.Comment: under submissio

Optimal competitiveness for the Rectilinear Steiner Arborescence problem

We present optimal online algorithms for two related known problems involving Steiner Arborescence, improving both the lower and the upper bounds. One of them is the well studied continuous problem of the {\em Rectilinear Steiner Arborescence} ($RSA$). We improve the lower bound and the upper bound on the competitive ratio for $RSA$ from $O(\log N)$ and $\Omega(\sqrt{\log N})$ to $\Theta(\frac{\log N}{\log \log N})$, where $N$ is the number of Steiner points. This separates the competitive ratios of $RSA$ and the Symetric-$RSA$, two problems for which the bounds of Berman and Coulston is STOC 1997 were identical. The second problem is one of the Multimedia Content Distribution problems presented by Papadimitriou et al. in several papers and Charikar et al. SODA 1998. It can be viewed as the discrete counterparts (or a network counterpart) of $RSA$. For this second problem we present tight bounds also in terms of the network size, in addition to presenting tight bounds in terms of the number of Steiner points (the latter are similar to those we derived for $RSA$)

A probability density function generator based on neural networks

© 2019 Elsevier B.V. In order to generate a probability density function (PDF) for fitting the probability distributions of practical data, this study proposes a deep learning method which consists of two stages: (1) a training stage for estimating the cumulative distribution function (CDF) and (2) a performing stage for predicting the corresponding PDF. The CDFs of common probability distributions can be utilised as activation functions in the hidden layers of the proposed deep learning model for learning actual cumulative probabilities, and the differential equation of the trained deep learning model can be used to estimate the PDF. Numerical experiments with single and mixed distributions are conducted to evaluate the performance of the proposed method. The experimental results show that the values of both CDF and PDF can be precisely estimated by the proposed method

Introduction to the special issue: Applications of internet of things

© 2018 by the authors. This editorial introduces the special issue, entitled "Applications of Internet of Things", of Symmetry. The topics covered in this issue fall under four main parts: (I) communication techniques and applications, (II) data science techniques and applications, (III) smart transportation, and (IV) smart homes. Four papers on sensing techniques and applications are included as follows: (1) "Reliability of improved cooperative communication over wireless sensor networks", by Chen et al.; (2) "User classification in crowdsourcing-based cooperative spectrum sensing", by Zhai andWang; (3) "IoT's tiny steps towards 5G: Telco's perspective", by Cero et al.; and (4) "An Internet of things area coverage analyzer (ITHACA) for complex topographical scenarios", by Parada et al. One paper on data science techniques and applications is as follows: "Internet of things: a scientometric review", by Ruiz-Rosero et al. Two papers on smart transportation are as follows: (1) "An Internet of things approach for extracting featured data using an AIS database: an application based on the viewpoint of connected ships", by He et al.; and (2) "The development of key technologies in applications of vessels connected to the Internet", by Tian et al. Two papers on smart home are as follows: (1) "A novel approach based on time cluster for activity recognition of daily living in smart homes", by Liu et al.; and (2) "IoT-based image recognition system for smart home-delivered meal services", by Tseng et al

The cohesin ring concatenates sister DNA molecules

Sister chromatid cohesion, which is essential for mitosis, is mediated by a multi-subunit protein complex called cohesin whose Scc1, Smc1, and Smc3 subunits form a tripartite ring structure. It has been proposed that cohesin holds sister DNAs together by trapping them inside its ring. To test this, we used site-specific cross-linking to create chemical connections at the three interfaces between the ring’s three constituent polypeptides, thereby creating covalently closed cohesin rings. As predicted by the ring entrapment model, this procedure produces dimeric DNA/cohesin structures that are resistant to protein denaturation. We conclude that cohesin rings concatenate individual sister minichromosome DNAs

RGO/Nylon-6 composite mat with unique structural features and electrical properties obtained from electrospinning and hydrothermal process

In this work, the reduced graphene oxide (RGO) sheets were effectively uploaded through nylon-6 fibers using combined process of electrospinning and hydrothermal treatment. Good dispersion of graphene oxide (GO) with nylon-6 solution could allow to upload GO sheets through nylon-6 fibers and facilitate the formation of spider-wave-like nano-nets during electrospinning. GO sheets present on/into nylon-6 spider-wave-like nano-nets were further reduced to RGO using hydrothermal treatment. The impregnated GO sheets into nylon-6 nanofibers and their reduction during hydrothermal treatment were confirmed by FE-SEM, TEM, FT-IR and Raman spectra. The electrical characteristics of pristine nylon-6, GO/nylon-6 and RGO/nylon-6 nanofibers were investigated and it was found that RGO/nylon-6 composite mat had better electrical conductivity than others. The formation of spider-wave-like nano-nets as well as indirect route of incorporation of RGO sheets on electrospun nylon-6 mat may open a new direction for future graphene/polymer electronics. © 2013 The Korean Fiber Society and Springer Science+Business Media Dordrecht

Why Some Interfaces Cannot be Sharp

A central goal of modern materials physics and nanoscience is control of materials and their interfaces to atomic dimensions. For interfaces between polar and non-polar layers, this goal is thwarted by a polar catastrophe that forces an interfacial reconstruction. In traditional semiconductors this reconstruction is achieved by an atomic disordering and stoichiometry change at the interface, but in multivalent oxides a new option is available: if the electrons can move, the atoms don`t have to. Using atomic-scale electron energy loss spectroscopy we find that there is a fundamental asymmetry between ionically and electronically compensated interfaces, both in interfacial sharpness and carrier density. This suggests a general strategy to design sharp interfaces, remove interfacial screening charges, control the band offset, and hence dramatically improving the performance of oxide devices.Comment: 12 pages of text, 6 figure