Critical slowing down and hyperuniformity on approach to jamming

Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming and hyperuniformity in frictionless hard-particle packings. Doing so requires one to study very large packings, which can be difficult to jam properly. We modify the rigorous linear programming method of Donev et al. [J. Comp. Phys. 197, 139 (2004)] in order to test for jamming in putatively jammed packings of hard-disks in two dimensions. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes; importantly, these packings appear to be jammed by conventional tests. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming in generating exactly-jammed configurations due to a type of "critical slowing down" as the necessary rearrangements become difficult to realize by numerical protocols. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly-jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for disordered packings with rattlers, we find that when jamming is ensured, our packings are very nearly hyperuniform, and deviations from hyperuniformity correlate with an inability to ensure jamming, suggesting that strict jamming and hyperuniformity are indeed linked. This raises the possibility that the ideal MRJ packings have no rattlers. Our work provides the impetus for the development of packing algorithms that produce large disordered strictly jammed packings that are rattler-free.Comment: 15 pages, 11 figures. Accepted for publication in Phys. Rev.

Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributions

We present a fast, differentially private algorithm for high-dimensional covariance-aware mean estimation with nearly optimal sample complexity. Only exponential-time estimators were previously known to achieve this guarantee. Given $n$ samples from a (sub-)Gaussian distribution with unknown mean $\mu$ and covariance $\Sigma$, our $(\varepsilon,\delta)$-differentially private estimator produces $\tilde{\mu}$ such that $\|\mu - \tilde{\mu}\|_{\Sigma} \leq \alpha$ as long as $n \gtrsim \tfrac d {\alpha^2} + \tfrac{d \sqrt{\log 1/\delta}}{\alpha \varepsilon}+\frac{d\log 1/\delta}{\varepsilon}$. The Mahalanobis error metric $\|\mu - \hat{\mu}\|_{\Sigma}$ measures the distance between $\hat \mu$ and $\mu$ relative to $\Sigma$; it characterizes the error of the sample mean. Our algorithm runs in time $\tilde{O}(nd^{\omega - 1} + nd/\varepsilon)$, where $\omega < 2.38$ is the matrix multiplication exponent. We adapt an exponential-time approach of Brown, Gaboardi, Smith, Ullman, and Zakynthinou (2021), giving efficient variants of stable mean and covariance estimation subroutines that also improve the sample complexity to the nearly optimal bound above. Our stable covariance estimator can be turned to private covariance estimation for unrestricted subgaussian distributions. With $n\gtrsim d^{3/2}$ samples, our estimate is accurate in spectral norm. This is the first such algorithm using $n= o(d^2)$ samples, answering an open question posed by Alabi et al. (2022). With $n\gtrsim d^2$ samples, our estimate is accurate in Frobenius norm. This leads to a fast, nearly optimal algorithm for private learning of unrestricted Gaussian distributions in TV distance. Duchi, Haque, and Kuditipudi (2023) obtained similar results independently and concurrently.Comment: 44 pages. New version fixes typos and includes additional exposition and discussion of related wor

Densest local packing diversity. II. Application to three dimensions

The densest local packings of N three-dimensional identical nonoverlapping spheres within a radius Rmin(N) of a fixed central sphere of the same size are obtained for selected values of N up to N = 1054. In the predecessor to this paper [A.B. Hopkins, F.H. Stillinger and S. Torquato, Phys. Rev. E 81 041305 (2010)], we described our method for finding the putative densest packings of N spheres in d-dimensional Euclidean space Rd and presented those packings in R2 for values of N up to N = 348. We analyze the properties and characteristics of the densest local packings in R3 and employ knowledge of the Rmin(N), using methods applicable in any d, to construct both a realizability condition for pair correlation functions of sphere packings and an upper bound on the maximal density of infinite sphere packings. In R3, we find wide variability in the densest local packings, including a multitude of packing symmetries such as perfect tetrahedral and imperfect icosahedral symmetry. We compare the densest local packings of N spheres near a central sphere to minimal-energy configurations of N+1 points interacting with short-range repulsive and long-range attractive pair potentials, e.g., 12-6 Lennard-Jones, and find that they are in general completely different, a result that has possible implications for nucleation theory. We also compare the densest local packings to finite subsets of stacking variants of the densest infinite packings in R3 (the Barlow packings) and find that the densest local packings are almost always most similar, as measured by a similarity metric, to the subsets of Barlow packings with the smallest number of coordination shells measured about a single central sphere, e.g., a subset of the FCC Barlow packing. We additionally observe that the densest local packings are dominated by the spheres arranged with centers at precisely distance Rmin(N) from the fixed sphere's center.Comment: 45 pages, 18 figures, 2 table

Spherical codes, maximal local packing density, and the golden ratio

The densest local packing (DLP) problem in d-dimensional Euclidean space Rd involves the placement of N nonoverlapping spheres of unit diameter near an additional fixed unit-diameter sphere such that the greatest distance from the center of the fixed sphere to the centers of any of the N surrounding spheres is minimized. Solutions to the DLP problem are relevant to the realizability of pair correlation functions for packings of nonoverlapping spheres and might prove useful in improving upon the best known upper bounds on the maximum packing fraction of sphere packings in dimensions greater than three. The optimal spherical code problem in Rd involves the placement of the centers of N nonoverlapping spheres of unit diameter onto the surface of a sphere of radius R such that R is minimized. It is proved that in any dimension, all solutions between unity and the golden ratio to the optimal spherical code problem for N spheres are also solutions to the corresponding DLP problem. It follows that for any packing of nonoverlapping spheres of unit diameter, a spherical region of radius less than or equal to the golden ratio centered on an arbitrary sphere center cannot enclose a number of sphere centers greater than one more than the number that can be placed on the region's surface.Comment: 12 pages, 1 figure. Accepted for publication in the Journal of Mathematical Physic

Dense sphere packings from optimized correlation functions

Elementary smooth functions (beyond contact) are employed to construct pair correlation functions that mimic jammed disordered sphere packings. Using the g2-invariant optimization method of Torquato and Stillinger [J. Phys. Chem. B 106, 8354, 2002], parameters in these functions are optimized under necessary realizability conditions to maximize the packing fraction phi and average number of contacts per sphere Z. A pair correlation function that incorporates the salient features of a disordered packing and that is smooth beyond contact is shown to permit a phi of 0.6850: this value represents a 45% reduction in the difference between the maximum for congruent hard spheres in three dimensions, pi/sqrt{18} ~ 0.7405, and 0.64, the approximate fraction associated with maximally random jammed (MRJ) packings in three dimensions. We show that, surprisingly, the continued addition of elementary functions consisting of smooth sinusoids decaying as r^{-4} permits packing fractions approaching pi/sqrt{18}. A translational order metric is used to discriminate between degrees of order in the packings presented. We find that to achieve higher packing fractions, the degree of order must increase, which is consistent with the results of a previous study [Torquato et al., Phys. Rev. Lett. 84, 2064, 2000].Comment: 26 pages, 9 figures, 1 table; added references, fixed typos, simplified argument and discussion in Section IV

Phase diagram and structural diversity of the densest binary sphere packings

The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the alpha-x plane of sphere radius ratio alpha and relative concentration x are at the Kepler limit alpha = 1, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao sphere-packing algorithm [S. Torquato and Y. Jiao, Phys. Rev. E 82, 061302 (2010)], we present the most comprehensive determination to date of the phase diagram in (alpha,x) for the densest binary sphere packings. Unexpectedly, we find many distinct new densest packings.Comment: 5 pages, 2 figures. Accepted for publication in Physical Review Letters on August 9th, 201

Polymorphisms in Plasmodium falciparum chloroquine resistance transporter and multidrug resistance 1 genes: parasite risk factors that affect treatment outcomes for P. falciparum malaria after artemether-lumefantrine and artesunate-amodiaquine.

Adequate clinical and parasitologic cure by artemisinin combination therapies relies on the artemisinin component and the partner drug. Polymorphisms in the Plasmodium falciparum chloroquine resistance transporter (pfcrt) and P. falciparum multidrug resistance 1 (pfmdr1) genes are associated with decreased sensitivity to amodiaquine and lumefantrine, but effects of these polymorphisms on therapeutic responses to artesunate-amodiaquine (ASAQ) and artemether-lumefantrine (AL) have not been clearly defined. Individual patient data from 31 clinical trials were harmonized and pooled by using standardized methods from the WorldWide Antimalarial Resistance Network. Data for more than 7,000 patients were analyzed to assess relationships between parasite polymorphisms in pfcrt and pfmdr1 and clinically relevant outcomes after treatment with AL or ASAQ. Presence of the pfmdr1 gene N86 (adjusted hazards ratio = 4.74, 95% confidence interval = 2.29 - 9.78, P < 0.001) and increased pfmdr1 copy number (adjusted hazards ratio = 6.52, 95% confidence interval = 2.36-17.97, P < 0.001 : were significant independent risk factors for recrudescence in patients treated with AL. AL and ASAQ exerted opposing selective effects on single-nucleotide polymorphisms in pfcrt and pfmdr1. Monitoring selection and responding to emerging signs of drug resistance are critical tools for preserving efficacy of artemisinin combination therapies; determination of the prevalence of at least pfcrt K76T and pfmdr1 N86Y should now be routine

The first bite: Imaginaries, promotional publics and the laboratory grown burger

In this paper we analyse a 2013 press conference hosting the world’s first tasting of a laboratory grown hamburger. We explore this as a media event: an exceptional performative moment in which common meanings are mobilised and a connection to a shared centre of reality is offered. We develop our own theoretical contribution – the promotional public – to characterise the affirmative and partial patchwork of carefully selected actors invoked during the burger tasting. Our account draws upon three areas of analysis: interview data with the scientists who developed the burger, media analysis of the streamed press conference itself, and media analysis of the social media tail during and following the event. We argue that the call to witness an experiment is a form of promotion but that such promotional material also offers an address that invokes a public with its attendant tensions.The research leading to this publication has received funding from the European Community’s Seventh Framework Programme (FP7/2007–2013) under grant agreement number 288971 (EPINET). Neil Stephens’ involvement has also received the support of the Economic and Social Research Council (ESRC). His work is part of the Research Programme of the ESRC Genomics Network at Cesagen (ESRC Centre for Economic and Social Aspects of Genomics). Neil Stephens’ work was also supported by the Wellcome Trust (WT096541MA) and a visiting scholarship to CGS Centre for Society and Genomics in The Netherlands, May to July 2011. This support is gratefully acknowledge

A measurement of the millimetre emission and the Sunyaev-Zel'dovich effect associated with low-frequency radio sources

We present a statistical analysis of the millimetre-wavelength properties of 1.4GHz-selected sources and a detection of the Sunyaev–Zel’dovich (SZ) effect associated with the haloes that host them. We stack data at 148, 218 and 277GHz from the Atacama Cosmology Telescope at the positions of a large sample of radio AGN selected at 1.4GHz. The thermal SZ effect associated with the haloes that host the AGN is detected at the 5σ level through its spectral signature, representing a statistical detection of the SZ effect in some of the lowest mass haloes (average M 200 ≈ 10 13 M. h −1 70 ) studied to date. The relation between the SZ effect and mass (based on weak lensing measurements of radio galaxies) is consistent with that measured by Planck for local bright galaxies. In the context of galaxy evolution models, this study confirms that galaxies with radio AGN also typically support hot gaseous haloes. Adding Herschel observations allows us to show that the SZ signal is not significantly contaminated by dust emission. Finally, we analyse the contribution of radio sources to the angular power spectrum of the cosmic microwave background