Deriving Finite Sphere Packings

Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for deriving all packings of n spheres in R3 satisfying minimal rigidity constraints (≥ 3 contacts per sphere and ≥ 3n − 6 total contacts). We derive such packings for n ≤ 10 and provide a preliminary set of maximum contact packings for 10 < n ≤ 20. The resultant set of packings has some striking features; among them are the following: (i) all minimally rigid packings for n ≤ 9 have exactly 3n−6 contacts; (ii) nonrigid packings satisfying minimal rigidity constraints arise for n ≥ 9; (iii) the number of ground states (i.e., packings with the maximum number of contacts) oscillates with respect to n; (iv) for 10 ≤ n ≤ 20 there are only a small number of packings with the maximum number of contacts, and for 10 ≤ n < 13 these are all commensurate with the hexagonal close-packed lattice. The general method presented here may have applications to other related problems in mathematics, such as the Erdos repeated distance problem and Euclidean distance matrix completion problems.Engineering and Applied SciencesPhysic

Minimal Energy Clusters of Hard Spheres with Short Range Attractions

We calculate the ground states of hard-sphere clusters, in which n identical hard spherical particles bind by isotropic short-ranged attraction. Combining graph theoretic enumeration with basic geometry, we analytically solve for clusters of n9 the degeneracy decreases due to the formation of structures with >3n-6 contacts. Interestingly, for n=10 and possibly at n=11 and n=12, the ground states of this system are subsets of hexagonal close-packed crystals. The ground states are not icosahedra at n=12 and n=13. We relate our results to the structure and thermodynamics of suspensions of colloidal particles with short-ranged attractions.Engineering and Applied SciencesMolecular and Cellular BiologyPhysic

The Free-Energy Landscape of Clusters of Attractive Hard Spheres

The study of clusters has provided the most tangible link between local geometry and bulk condensed matter. But experiments have not yet systematically explored the thermodynamics of even the smallest clusters. Here we present experimental measurements of the structures and free energies of colloidal clusters in which the particles act as hard spheres with short-range attractions. We find that highly symmetric clusters are strongly suppressed by rotational entropy, while the most stable clusters have anharmonic vibrational modes or extra bonds. Many of these are subsets of close-packed lattices. As the number of particles increases from 6 to 10 we observe the emergence of a complex free energy landscape with a small number of ground states and many local minima.Engineering and Applied SciencesPhysic

Physical Ageing of the Contact Line on Colloidal Particles at Liquid Interfaces

Young's law predicts that a colloidal sphere in equilibrium with a liquid interface will straddle the two fluids, its height above the interface defined by an equilibrium contact angle. This equilibrium analysis has been used to explain why colloids often bind to liquid interfaces, an effect first observed a century ago by Ramsden and Pickering and later exploited in a wide range of material processes, including emulsification, water purification, mineral recovery, encapsulation, and the making of nanostructured materials. But little is known about the dynamics of binding. Here we show that the adsorption of polystyrene microspheres to a water-oil interface is characterized by a sudden breach and an unexpectedly slow relaxation. Particles do not reach equilibrium even after 100 seconds, and the relaxation appears logarithmic in time, suggesting that complete equilibration may take months. Surprisingly, viscous dissipation appears to play little role. Instead, the observed dynamics, which bear strong resemblance to aging in glassy systems, agree well with a model describing activated hopping of the contact line over nanoscale surface heterogeneities. These results may provide clues to longstanding questions on colloidal interactions at an interface.Engineering and Applied SciencesPhysic

Fine and Large Coulomb Diamonds in a Silicon Quantum Dot

We experimentally study the transport properties of silicon quantum dots (QDs) fabricated from a highly doped n-type silicon-on-insulator wafer. Low noise electrical measurements using a low temperature complementary metal-oxide-semiconductor (LTCMOS) amplifier are performed at 4.2 K in liquid helium. Two series of Coulomb peaks are observed: long-period oscillations and fine structures, and both of them show clear source drain voltage dependence. We also observe two series of Coulomb diamonds having different periodicity. The obtained experimental results are well reproduced by a master equation analysis using a model of double QDs coupled in parallel.Comment: 5 pages, 4 figures, to appear in Jpn. J. Appl. Phy

AnoA: A Framework For Analyzing Anonymous Communication Protocols

Anonymous communication (AC) protocols such as the widely used Tor network have been designed to provide anonymity over the Internet to their participating users. While AC protocols have been the subject of several security and anonymity analyses in the last years, there still does not exist a framework for analyzing complex systems, such as Tor, and their different anonymity properties in a unified manner. In this work we present AnoA: a generic framework for defining, analyzing, and quantifying anonymity properties for AC protocols. In addition to quantifying the (additive) advantage of an adversary in an indistinguishability-based definition, AnoA uses a multiplicative factor, inspired from differential privacy. AnoA enables a unified quantitative analysis of well-established anonymity properties, such as sender anonymity, sender unlinkability, and relationship anonymity. AnoA modularly specifies adversarial capabilities by a simple wrapper-construction, called adversary classes. We examine the structure of these adversary classes and identify conditions under which it suffices to establish anonymity guarantees for single messages in order to derive guarantees for arbitrarily many messages. We coin this condition single-challenge reducability. This then leads us to the definition of Plug\u27n\u27Play adversary classes (PAC), which are easy to use, expressive, and single-challenge reducable. Additionally, we show that our framework is compatible with the universal composability (UC) framework. Leveraging a recent security proof about Tor, we illustrate how to apply AnoA to a simplified version of Tor against passive adversaries

p45 NF-E2 regulates syncytiotrophoblast differentiation by post-translational GCM1 modifications in human intrauterine growth restriction

AbstractPlacental insufficiency jeopardizes prenatal development, potentially leading to intrauterine growth restriction (IUGR) and stillbirth. Surviving fetuses are at an increased risk for chronic diseases later in life. IUGR is closely linked with altered trophoblast and placental differentiation. However, due to a paucity of mechanistic insights, suitable biomarkers and specific therapies for IUGR are lacking. The transcription factor p45 NF-E2 (nuclear factor erythroid derived 2) has been recently found to regulate trophoblast differentiation in mice. The absence of p45 NF-E2 in trophoblast cells causes IUGR and placental insufficiency in mice, but mechanistic insights are incomplete and the relevance of p45 NF-E2 for human syncytiotrophoblast differentiation remains unknown. Here we show that p45 NF-E2 negatively regulates human syncytiotrophoblast differentiation and is associated with IUGR in humans. Expression of p45 NF-E2 is reduced in human placentae complicated with IUGR compared with healthy controls. Reduced p45 NF-E2 expression is associated with increased syncytiotrophoblast differentiation, enhanced glial cells missing-1 (GCM1) acetylation and GCM1 desumoylation in IUGR placentae. Induction of syncytiotrophoblast differentiation in BeWo and primary villous trophoblast cells with 8-bromo-adenosine 3′,5′-cyclic monophosphate (8-Br-cAMP) reduces p45 NF-E2 expression. Of note, p45 NF-E2 knockdown is sufficient to increase syncytiotrophoblast differentiation and GCM1 expression. Loss of p45 NF-E2 using either approach resulted in CBP-mediated GCM1 acetylation and SENP-mediated GCM1 desumoylation, demonstrating that p45 NF-E2 regulates post-translational modifications of GCM1. Functionally, reduced p45 NF-E2 expression is associated with increased cell death and caspase-3 activation in vitro and in placental tissues samples. Overexpression of p45 NF-E2 is sufficient to repress GCM1 expression, acetylation and desumoylation, even in 8-Br-cAMP exposed BeWo cells. These results suggest that p45 NF-E2 negatively regulates differentiation and apoptosis activation of human syncytiotrophoblast by modulating GCM1 acetylation and sumoylation. These studies identify a new pathomechanism related to IUGR in humans and thus provide new impetus for future studies aiming to identify new biomarkers and/or therapies of IUGR.</jats:p