Cloth manipulation is a difficult problem mainly because of the non-rigid nature of cloth, which makes a good representation of deformation essential. We present a new representation for the deformation-state of clothes. First, we propose the dGLI disk representation based on topological indices computed for edge segments of the cloth border that are arranged on a circular grid. The heat-map of the dGLI disk uncovers patterns that correspond to features of the cloth state that are consistent for different shapes, sizes or orientation of the cloth. We then abstract these important features from the dGLI disk into a circle, calling it the Cloth StatE representation (CloSE). This representation is compact, continuous, and general for different shapes. We show that this representation is able to accurately predict the fold locations for several simulation clothing datasets. Finally, we also show the strengths of this representation in two relevant applications: semantic labeling and high- and low-level planning. The code and the dataset can be accessed from: https://close-representation.github.io/
Almost all current and future high-contrast imaging instruments will use a Pyramid wavefront sensor (PWFS) as a primary or secondary wavefront sensor. The main issue with the PWFS is its nonlinear response to large phase aberrations, especially under strong atmospheric turbulence. Most instruments try to increase its linearity range by using dynamic modulation, but this leads to decreased sensitivity, most prominently for low-order modes, and makes it blind to petal-piston modes. In the push toward high-contrast imaging of fainter stars and deeper contrasts, there is a strong interest in using the PWFS in its unmodulated form. Here, we present closed-loop lab results of a nonlinear reconstructor for the unmodulated PWFS of the Magellan Adaptive Optics eXtreme (MagAO-X) system based on convolutional neural networks (CNNs). We show that our nonlinear reconstructor has a dynamic range of >600 nm root-mean-square (RMS), significantly outperforming the linear reconstructor that only has a 50 nm RMS dynamic range. The reconstructor behaves well in closed loop and can obtain >80% Strehl at 875 nm under a large variety of conditions and reaches higher Strehl ratios than the linear re
The kernel of analysis, to me anyway, is the following idea: A point is arbitrarily close to a set if every neighborhood of the point intersects the set. Defining ``arbitrarily close'' in this way provides a foundation for classical results in calculus and real analysis dealing with convergence, limits, connectedness, limits, continuity, differentiation, integration, series, and more. This book contains: a thorough introduction to arbitrarily close; an approach to limits and convergence of sequences using arbitrarily close as a key first step; the topology of Euclidean spaces stemming from closed sets; an exploration of the properties of functions like domains, ranges, and images of sets and sequences; and an introduction to basic aspects of continuous functions between Euclidean spaces. Even so, ``arbitrarily close'' reaches deeper than discussed here. The idea is topological in nature and there is much more to explore.
Corporate networks, as induced by interlocking directorates between corporations, provide structures of personal communication at the level of their boards. This paper studies such networks from a perspective of close communication in sub-networks, where each pair of nodes (boards of a corporation) are either neighbours, or have a common neighbour. These correspond to subgraphs of diameter at most 2, designated by us earlier as 2-clubs, with three types (coteries, social circles and hamlets) as degrees of close communication in social networks, within the concept of boroughs of a network. Boroughs are maximal areas and containers of close communication between nodes of a network. This framework is applied in this paper to an analysis of corporate board interlocks between the top 300 European corporations 2010, as studied by Heemkerk (2013), with data provided by him for that purpose. The paper gives results for several perspectives of close communication in the European corporate network of 2010, a year close to the global crash of 2008, as a further elaboration of those given in Heemskerk (2013).
Through an exhaustive search, we produce a 5-parameter family of propagation identities for the closed conformal Killing-Yano equation on 2-forms, which hold on an Einstein cosmological vacuum spacetime in any dimension $n>4$. It is well-known that spacetimes admitting a non-degenerate 2-form of this type are exhausted by the Kerr-NUT-(A)dS family of exact higher dimensional black hole solutions. As a consequence, we identify a set of necessary and sufficient conditions ensuring that the cosmological vacuum development of an initial data set for Einstein's field equations admits a closed conformal Killing-Yano 2-form. We refer to these conditions as \emph{closed conformal Killing-Yano initial data} (cCYKID) equations. The 4-dimensional case is special and is treated separately, where we can also handle the conformal Killing-Yano equation without the closed condition.
Knowledge of the interior density distribution of an asteroid can reveal its composition and constrain its evolutionary history. However, most asteroid observational techniques are not sensitive to interior properties. We investigate the interior constraints accessible through monitoring variations in angular velocity during a close encounter. We derive the equations of motion for a rigid asteroid's orientation and angular velocity to arbitrary order and use them to generate synthetic angular velocity data for a representative asteroid on a close Earth encounter. We develop a toolkit AIME (Asteroid Interior Mapping from Encounters) which reconstructs asteroid density distribution from these data, and we perform injection-retrieval tests on these synthetic data to assess AIME's accuracy and precision. We also perform a sensitivity analysis to asteroid parameters (e.g., asteroid shape and orbital elements), observational set-up (e.g., measurement precision and cadence), and the mapping models used. We find that high precision in rotational period estimates (<~0.27 seconds) are necessary for each cadence, and that low perigees (<~18 Earth radii) are necessary to resolve large-sc
Properties of quantum systems can be estimated using classical shadows, which implement measurements based on random ensembles of unitaries. Originally derived for global Clifford unitaries and products of single-qubit Clifford gates, practical implementations are limited to the latter scheme for moderate numbers of qubits. Beyond local gates, the accurate implementation of very short random circuits with two-local gates is still experimentally feasible and, therefore, interesting for implementing measurements in near-term applications. In this work, we derive closed-form analytical expressions for shadow estimation using brickwork circuits with two layers of parallel two-local Haar-random (or Clifford) unitaries. Besides the construction of the classical shadow, our results give rise to sample-complexity guarantees for estimating Pauli observables. We then compare the performance of shadow estimation with brickwork circuits to the established approach using local Clifford unitaries and find improved sample complexity in the estimation of observables supported on sufficiently many qubits.
The structure of close communication, contacts and association in social networks is studied in the form of maximal subgraphs of diameter 2 (2-clubs), corresponding to three types of close communities: hamlets, social circles and coteries. The concept of borough of a graph is defined and introduced. Each borough is a chained union of 2-clubs of the network and any 2-club of the network belongs to one borough. Thus the set of boroughs of a network, together with the 2-clubs held by them, are shown to contain the structure of close communication in a network. Applications are given with examples from real world network data.
We present an overview of pulsating stars in close binaries, focusing on the question what role the dupliticity plays in triggering and/or modifying stellar oscillations and on how it can help us to interpret the oscillatory behaviour of (one of) the components. We give examples of characteristic types of oscillations observed in binaries: forced oscillations and free oscillations in both, short- and long-period binaries. The importance of studies of oscillations in eclipsing binaries is also pointed out. A list of line-profile and rapid light variables in close binaries with their basic properties is provided. No obvious relations among the orbital eccentricity, orbital frequency, rotational frequency and intrinsic frequencies of oscillations were found. The value and future prospects of asteroseismic studies of binary stars are briefly outlined while the complexity of the problem and its possible complications are also discussed.
In the analysis of social networks many relatively loose and heuristic definitions of 'community' abound. In this paper the concept of closely knit communities is studied as defined by the property that every pair of its members are neighbors or has at least one common neighbor, where the neighboring relationship is based on some more or less durable and stable acquaintance or contact relation. In this paper these are studied in the form of graphs or networks of diameter two (2-clubs). Their structure can be characterized by investigating shortest spanning trees and girth leading to a typology containing just three or, in combination, six types of close communities.
We present the results of a survey of 45 young (<250 Myr), close (<50 pc) stars with the Simultaneous Differential Imager (SDI) implemented at the VLT and the MMT for the direct detection of extrasolar planets. As part of the survey, we observed 54 objects total, of which 45 were close, young stars, 2 were somewhat more distant (<150 pc), very young (<10 Myr) stars, 3 were stars with known radial velocity planets, and 4 were older, very nearby (<20 pc) solar analogues. Our SDI devices use a double Wollaston prism and a quad filter to take images simultaneously at 3 wavelengths surrounding the 1.62 um methane absorption bandhead found in the spectrum of cool brown dwarfs and gas giant planets. In our VLT data, we achieved H band contrasts > 10 mag (5 sigma) at a separation of 0.5" from the primary star on 45% of our targets and H band contrasts of > 9 mag at a separation of 0.5'' on 80% of our targets. With this degree of attenuation, we should be able to image (5sigma detection) a 5 M_{Jup} planet 15 AU from a 70 Myr K1 star at 15 pc or a 5 M_{Jup} planet at 2 AU from a 12 Myr M star at 10 pc. We believe that our SDI images are the highest contrast astronomical
This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian. We discuss several aspects of the slow dynamics in driven systems and emphasize the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions. We also review recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis and discuss relaxation in integrable systems. Finally we overview key experiments probing quantum dynamics in cold atom systems and put them in the context of our current theoretical understanding.
We prove that the probability substitution matrices obtained from a continuous-time Markov chain form a multiplicatively closed set if and only if the rate matrices associated to the chain form a linear space spanning a Lie algebra. The key original contribution we make is to overcome an obstruction, due to the presence of inequalities that are unavoidable in the probabilistic application, that prevents free manipulation of terms in the Baker-Campbell-Haursdorff formula.
We investigate the dynamical behaviour of a holomorphic map on a $f-$invariant subset $\mathcal{C}$ of $U,$ where $f:U \to \mathbb{C}^k.$ We study two cases: when $U$ is an open, connected and polynomially convex subset of $\mathbb{C}^k$ and $\mathcal{C} \subset \subset U,$ closed in $U,$ and when $\partial U$ has a p.s.h. barrier at each of its points and $\mathcal{C}$ is not relatively compact in $U.$ In the second part of the paper, we prove a Birkhoff's type Theorem for holomorphic maps in several complex variables, i.e. given an injective holomorphic map $f,$ defined in a neighborhood of $\overline{U},$ with $U$ star-shaped and $f(U)$ a Runge domain, we prove the existence of a unique, forward invariant, maximal, compact and connected subset of $\overline{U}$ which touches $\partial U.$
Our goal is to develop and test a novel methodology to compute accurate close pair fractions with photometric redshifts. We improve the current methodologies to estimate the merger fraction f_m from photometric redshifts by (i) using the full probability distribution functions (PDFs) of the sources in redshift space, (ii) including the variation in the luminosity of the sources with z in both the selection of the samples and in the luminosity ratio constrain, and (iii) splitting individual PDFs into red and blue spectral templates to deal robustly with colour selections. We test the performance of our new methodology with the PDFs provided by the ALHAMBRA photometric survey. The merger fractions and rates from the ALHAMBRA survey are in excellent agreement with those from spectroscopic work, both for the general population and for red and blue galaxies. With the merger rate of bright (M_B <= -20 - 1.1z) galaxies evolving as (1+z)^n, the power-law index n is larger for blue galaxies (n = 2.7 +- 0.5) than for red galaxies (n = 1.3 +- 0.4), confirming previous results. Integrating the merger rate over cosmic time, we find that the average number of mergers per galaxy since z = 1 is
We link the thermodynamics of colloidal suspensions to the statistics of regular and random packings. Random close packing has defied a rigorous definition yet, in three dimensions, there is near universal agreement on the volume fraction at which it occurs. We conjecture that the common value of phi_rcp, approximately 0.64, arises from a divergence in the rate at which accessible states disappear. We relate this rate to the equation of state for a hard sphere fluid on a metastable, non-crystalline branch.
We experimentally demonstrate atom interferometry using the transverse phase profile of an optical mode. As proof-of-principle, we use the helical phase windings of Hypergeometric Gaussian beams for Ramsey interferometry with ensembles of ballistically-expanding cold Rb87 atoms, and we show that the interferometer can measure rotations induced by a motor with a sensitivity that scales linearly with orbital angular momentum and interferometer time. We characterize the thermal decoherence of the interferometer, deriving and experimentally confirming a closed-form expression for the spatially-varying interferometer visibility arising near the singularity of the helical phase winding, motivating the use of condensed atoms in ring-shaped traps.
There has been significant research effort developing neural-network-based predictors of SQ in recent years. While a primary objective has been to develop non-intrusive, i.e.~reference-free, metrics to assess the performance of SE systems, recent work has also investigated the direct inference of neural SQ predictors within the loss function of downstream speech tasks. To aid in the training of SQ predictors, several large datasets of audio with corresponding human labels of quality have been created. Recent work in this area has shown that speech representations derived from large unsupervised or semi-supervised foundational speech models are useful input feature representations for neural SQ prediction. In this work, a novel and robust SQ predictor is proposed based on feature representations extracted from an ASR model, found to be a powerful input feature for the SQ prediction task. The proposed system achieves higher correlation with human MOS ratings than recent approaches on all NISQA test sets and shows significantly better domain adaption compared to the commonly used DNSMOS metric.
Excellent (<25 mas) H$_α$ images of the star TYC 5709-354-1 led to the discovery of a rare H$_α$ protoplanet. This star was discovered by the WISPIT survey to have a large multi-ring transitional disk, and is hereafter WISPIT 2. Our H$_α$ images of 2025, April 13 and April 16 discovered an accreting (H$_α$ in emission) protoplanet: WISPIT 2b (r=309.43$\pm$1.56 mas; (~54 au deprojected), PA=242.21$\pm$0.41 degrees) likely clearing a dust-free gap between the two brightest dust rings in the transitional disk. Our SNR=12.5 detection gave an H$_α$ ASDI contrast of (6.5$\pm$0.5)x10$^{-4}$ and a H$_α$ line flux of (1.29$\pm$0.28)x10$^{-15}$ erg/s/cm$^2$. We also present L' photometry from LBT/LMIRcam of the planet (L'=15.30$\pm$0.05 mag) which, when coupled with an age of 5.1$^{+2.4}_{-1.3}$ Myr, yields a planet mass estimate of 5.3$\pm$1.0 Mjup from the DUSTY evolutionary models. WISPIT 2b is accreting at 2.25$^{-0.17}_{+3.75}$x10$^{-12}$ Msun/yr. WISPIT 2b is very similar to the other H$_α$ protoplanets in terms of mass, age, flux, and accretion rate. The inclination of the system (${\it i}$=44 degrees) is also, surprisingly, very similar to the other known H$α$ protoplanet systems
The process of carbon burning is vital to understanding late stage stellar evolution of massive stars and the conditions of certain supernovae. Carbon burning is a complex problem, involving quantum tunnelling and nuclear molecular states. Quantum dynamical calculations of carbon burning are presented, combining the time-dependent wave-packet method and the density-constrained time-dependent Hartree-Fock (DC-TDHF) approach. By limiting the contribution of triaxial molecular configurations to fusion, we demonstrate that the DC-TDHF interaction potential successfully explains the appearance of some resonant structures in the sub-barrier fusion cross-section. This result shows the critical role of nucleon-nucleon interactions in the 12C + 12C fusion resonances observed at astrophysical energies.