Centroidal bases in graphs

We introduce the notion of a centroidal locating set of a graph $G$, that is, a set $L$ of vertices such that all vertices in $G$ are uniquely determined by their relative distances to the vertices of $L$. A centroidal locating set of $G$ of minimum size is called a centroidal basis, and its size is the centroidal dimension $CD(G)$. This notion, which is related to previous concepts, gives a new way of identifying the vertices of a graph. The centroidal dimension of a graph $G$ is lower- and upper-bounded by the metric dimension and twice the location-domination number of $G$, respectively. The latter two parameters are standard and well-studied notions in the field of graph identification. We show that for any graph $G$ with $n$ vertices and maximum degree at least~2, $(1+o(1))\frac{\ln n}{\ln\ln n}\leq CD(G) \leq n-1$. We discuss the tightness of these bounds and in particular, we characterize the set of graphs reaching the upper bound. We then show that for graphs in which every pair of vertices is connected via a bounded number of paths, $CD(G)=\Omega\left(\sqrt{|E(G)|}\right)$, the bound being tight for paths and cycles. We finally investigate the computational complexity of determining $CD(G)$ for an input graph $G$, showing that the problem is hard and cannot even be approximated efficiently up to a factor of $o(\log n)$. We also give an $O\left(\sqrt{n\ln n}\right)$-approximation algorithm

The dynamical structure of the MEO region: long-term stability, chaos, and transport

It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Recent studies have shown that the occurrence and nature of the resonances driving these dynamics depend chiefly on the frequencies of nodal and apsidal precession and the rate of regression of the Moon's nodes. Woven throughout the inclination and eccentricity phase space is an exceedingly complicated web-like structure of lunisolar secular resonances, which become particularly dense near the inclinations of the navigation satellite orbits. A clear picture of the physical significance of these resonances is of considerable practical interest for the design of disposal strategies for the four constellations. Here we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions, and trace the topological organization of the manifolds on which the chaotic motions take place. We present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. As the semi-major axis of the satellite is receding, we observe a transition from stable Nekhoroshev-like structures at three Earth radii, where regular orbits dominate, to a Chirikov regime where resonances overlap at five Earth radii. From a numerical estimation of the Lyapunov times, we find that many of the inclined, nearly circular orbits of the navigation satellites are strongly chaotic and that their dynamics are unpredictable on decadal timescales.Comment: Submitted to Celestial Mechanics and Dynamical Astronomy. Comments are greatly appreciated. 28 pages, 15 figure

Near-seafloor magnetic signatures unveil serpentinization dynamics at ultramafic-hosted hydrothermal sites

A near-seafloor magnetic and bathymetric survey conducted by the autonomous underwater vehicle AutoSub 6000 over intermediate-temperature, ultramafic-hosted Von Damm Vent Field (Mid-Cayman spreading center, Caribbean Sea) revealed a moderate positive magnetic anomaly, in accordance with the magnetic response of other known ultramafic-hosted hydrothermal vent fields. However, compared with low-temperature ultramafic-hosted hydrothermal activity, the magnetic signature of this intermediate-temperature site indicates a slightly stronger magnetization contrast between the hydrothermal system and its host, but it remains considerably weaker than at high-temperature ultramafic-hosted hydrothermal vent fields. This observation highlights the nonlinear increase of magnetization production with temperature, as iron partitions into weakly magnetic brucite under 200 °C, but magnetite dominates above this temperature, leading to a sudden increase in the magnetic signature of a site. Our study is consistent with recent laboratory experiments and unveils the dynamics of the serpentinization reaction, enabling fine tuning of the magnetic technique for remotely locating hydrothermal systems. In addition to refining our understanding of the magnetic behavior of hydrothermal vent fields, these new results also reveal the orientation of the fluid pathway feeding the hydrothermal site and indicate the nonvertical structure of the complex network of fissures within the host rock and its associated tectonic feature—an oceanic core complex

Soil drought anomalies in MODIS GPP of a Mediterranean broadleaved evergreen forest

The Moderate Resolution Imaging Spectroradiometer (MODIS) yields global operational estimates of terrestrial gross primary production (GPP). In this study, we compared MOD17A2 GPP with tower eddy flux-based estimates of GPP from 2001 to 2010 over an evergreen broad-leaf Mediterranean forest in Southern France with a significant summer drought period. The MOD17A2 GPP shows seasonal variations that are inconsistent with the tower GPP, with close-to-accurate winter estimates and significant discrepancies for summer estimates which are the least accurate. The analysis indicated that the MOD17A2 GPP has high bias relative to tower GPP during severe summer drought which we hypothesized caused by soil water limitation. Our investigation showed that there was a significant correlation (R-2 = 0.77, p < 0.0001) between the relative soil water content and the relative error of MOD17A2 GPP. Therefore, the relationship between the error and the measured relative soil water content could explain anomalies in MOD17A2 GPP. The results of this study indicate that careful consideration of the water conditions input to the MOD17A2 GPP algorithm on remote sensing is required in order to provide accurate predictions of GPP. Still, continued efforts are necessary to ascertain the most appropriate index, which characterizes soil water limitation in water-limited environments using remote sensing

6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains

Recent work has established a uniform characterization of most 6D SCFTs in terms of generalized quivers with conformal matter. Compactification of the partial tensor branch deformation of these theories on a $T^2$ leads to 4D $\mathcal{N} = 2$ SCFTs which are also generalized quivers. Taking products of bifundamental conformal matter operators, we present evidence that there are large R-charge sectors of the theory in which operator mixing is captured by a 1D spin chain Hamiltonian with operator scaling dimensions controlled by a perturbation series in inverse powers of the R-charge. We regulate the inherent divergences present in the 6D computations with the associated 5D Kaluza--Klein theory. In the case of 6D SCFTs obtained from M5-branes probing a $\mathbb{C}^{2}/\mathbb{Z}_{K}$ singularity, we show that there is a class of operators where the leading order mixing effects are captured by the integrable Heisenberg $XXX_{s=1/2}$ spin chain with open boundary conditions, and similar considerations hold for its $T^2$ reduction to a 4D $\mathcal{N}=2$ SCFT. In the case of M5-branes probing more general D- and E-type singularities where generalized quivers have conformal matter, we argue that similar mixing effects are captured by an integrable $XXX_{s}$ spin chain with $s>1/2$. We also briefly discuss some generalizations to other operator sectors as well as little string theories.Comment: v2: 51 pages, 5 figures, typos corrected, clarifications and references adde

Super-Spin Chains for 6D SCFTs

Nearly all 6D superconformal field theories (SCFTs) have a partial tensor branch description in terms of a generalized quiver gauge theory consisting of a long one-dimensional spine of quiver nodes with links given by conformal matter; a strongly coupled generalization of a bifundamental hypermultiplet. For theories obtained from M5-branes probing an ADE singularity, this was recently leveraged to extract a protected large R-charge subsector of operators, with operator mixing controlled at leading order in an inverse large R-charge expansion by an integrable spin $s$ Heisenberg spin chain, where $s$ is determined by the $\mathfrak{su}(2)_{R}$ R-symmetry representation of the conformal matter operator. In this work, we show that this same structure extends to the full superconformal algebra $\mathfrak{osp}(6,2|1)$. In particular, we determine the corresponding Bethe ansatz equations which govern this super-spin chain, as well as distinguished subsectors which close under operator mixing. Similar considerations extend to 6D little string theories (LSTs) and 4D $\mathcal{N} = 2$ SCFTs with the same generalized quiver structures.Comment: 35 pages + appendices, 7 figure

Drag force as a function of cross section and angle of attack. A hydraulic laboratory dataset for numerical validation

This data relates to a set of hydraulic laboratory experiments in which the flow around four cross-sections was investigated. Each cross section was examined at four angles of attack (0, 5, 10, 90°), seven velocities (0–0.7 m/s in 0.1 m/s steps) and two flow directions. The data is primarily from an array of load cell which monitored the loading on the cross-sections during testing in six degrees of freedom during testing. Video and photographs are also included

Error correcting code using tree-like multilayer perceptron

An error correcting code using a tree-like multilayer perceptron is proposed. An original message \mbi{s}^0 is encoded into a codeword \boldmath{y}_0 using a tree-like committee machine (committee tree) or a tree-like parity machine (parity tree). Based on these architectures, several schemes featuring monotonic or non-monotonic units are introduced. The codeword \mbi{y}_0 is then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by noise. The analytical performance of these schemes is investigated using the replica method of statistical mechanics. Under some specific conditions, some of the proposed schemes are shown to saturate the Shannon bound at the infinite codeword length limit. The influence of the monotonicity of the units on the performance is also discussed.Comment: 23 pages, 3 figures, Content has been extended and revise