TY - JOUR
AB - We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness.
AU - Cipolloni, Giorgio
AU - Erdös, László
AU - Schröder, Dominik J
ID - 9412
JF - Electronic Journal of Probability
TI - Fluctuation around the circular law for random matrices with real entries
VL - 26
ER -
TY - JOUR
AB - The dynamics of a triangular magnetocapillary swimmer is studied using the lattice Boltzmann method. We extend on our previous work, which deals with the self-assembly and a specific type of the swimmer motion characterized by the swimmer’s maximum velocity centred around the particle’s inverse viscous time. Here, we identify additional regimes of motion. First, modifying the ratio of surface tension and magnetic forces allows to study the swimmer propagation in the regime of significantly lower frequencies mainly defined by the strength of the magnetocapillary potential. Second, introducing a constant magnetic contribution in each of the particles in addition to their magnetic moment induced by external fields leads to another regime characterized by strong in-plane swimmer reorientations that resemble experimental observations.
AU - Sukhov, Alexander
AU - Hubert, Maxime
AU - Grosjean, Galien M
AU - Trosman, Oleg
AU - Ziegler, Sebastian
AU - Collard, Ylona
AU - Vandewalle, Nicolas
AU - Smith, Ana Sunčana
AU - Harting, Jens
ID - 9411
IS - 4
JF - European Physical Journal E
SN - 12928941
TI - Regimes of motion of magnetocapillary swimmers
VL - 44
ER -
TY - JOUR
AB - We present a computational design system that assists users to model, optimize, and fabricate quad-robots with soft skins. Our system addresses the challenging task of predicting their physical behavior by fully integrating the multibody dynamics of the mechanical skeleton and the elastic behavior of the soft skin. The developed motion control strategy uses an alternating optimization scheme to avoid expensive full space time-optimization, interleaving space-time optimization for the skeleton, and frame-by-frame optimization for the full dynamics. The output are motor torques to drive the robot to achieve a user prescribed motion trajectory. We also provide a collection of convenient engineering tools and empirical manufacturing guidance to support the fabrication of the designed quad-robot. We validate the feasibility of designs generated with our system through physics simulations and with a physically-fabricated prototype.
AU - Feng, Xudong
AU - Liu, Jiafeng
AU - Wang, Huamin
AU - Yang, Yin
AU - Bao, Hujun
AU - Bickel, Bernd
AU - Xu, Weiwei
ID - 9408
IS - 6
JF - IEEE Transactions on Visualization and Computer Graphics
SN - 19410506
TI - Computational design of skinned Quad-Robots
VL - 27
ER -
TY - JOUR
AB - Antibiotic concentrations vary dramatically in the body and the environment. Hence, understanding the dynamics of resistance evolution along antibiotic concentration gradients is critical for predicting and slowing the emergence and spread of resistance. While it has been shown that increasing the concentration of an antibiotic slows resistance evolution, how adaptation to one antibiotic concentration correlates with fitness at other points along the gradient has not received much attention. Here, we selected populations of Escherichia coli at several points along a concentration gradient for three different antibiotics, asking how rapidly resistance evolved and whether populations became specialized to the antibiotic concentration they were selected on. Populations selected at higher concentrations evolved resistance more slowly but exhibited equal or higher fitness across the whole gradient. Populations selected at lower concentrations evolved resistance rapidly, but overall fitness in the presence of antibiotics was lower. However, these populations readily adapted to higher concentrations upon subsequent selection. Our results indicate that resistance management strategies must account not only for the rates of resistance evolution but also for the fitness of evolved strains.
AU - Lagator, Mato
AU - Uecker, Hildegard
AU - Neve, Paul
ID - 9410
IS - 5
JF - Biology letters
TI - Adaptation at different points along antibiotic concentration gradients
VL - 17
ER -
TY - JOUR
AB - This paper presents a method for designing planar multistable compliant structures. Given a sequence of desired stable states and the corresponding poses of the structure, we identify the topology and geometric realization of a mechanism—consisting of bars and joints—that is able to physically reproduce the desired multistable behavior. In order to solve this problem efficiently, we build on insights from minimally rigid graph theory to identify simple but effective topologies for the mechanism. We then optimize its geometric parameters, such as joint positions and bar lengths, to obtain correct transitions between the given poses. Simultaneously, we ensure adequate stability of each pose based on an effective approximate error metric related to the elastic energy Hessian of the bars in the mechanism. As demonstrated by our results, we obtain functional multistable mechanisms of manageable complexity that can be fabricated using 3D printing. Further, we evaluated the effectiveness of our method on a large number of examples in the simulation and fabricated several physical prototypes.
AU - Zhang, Ran
AU - Auzinger, Thomas
AU - Bickel, Bernd
ID - 9376
JF - ACM Transactions on Graphics
KW - multistability
KW - mechanism
KW - computational design
KW - rigidity
TI - Computational design of planar multistable compliant structures
ER -
TY - JOUR
AB - We derive rigorously the leading order of the correlation energy of a Fermi gas in a scaling regime of high density and weak interaction. The result verifies the prediction of the random-phase approximation. Our proof refines the method of collective bosonization in three dimensions. We approximately diagonalize an effective Hamiltonian describing approximately bosonic collective excitations around the Hartree–Fock state, while showing that gapless and non-collective excitations have only a negligible effect on the ground state energy.
AU - Benedikter, Niels P
AU - Nam, Phan Thành
AU - Porta, Marcello
AU - Schlein, Benjamin
AU - Seiringer, Robert
ID - 7901
JF - Inventiones Mathematicae
SN - 00209910
TI - Correlation energy of a weakly interacting Fermi gas
ER -
TY - GEN
AB - For any given positive integer l, we prove that every plane deformation of a circlewhich preserves the 1/2and 1/ (2l + 1) -rational caustics is trivial i.e. the deformationconsists only of similarities (rescalings and isometries).
AU - Kaloshin, Vadim
AU - Koudjinan, Edmond
ID - 9435
TI - Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations of circles
ER -
TY - JOUR
AB - The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing emergent kinetics, but this has received considerably less attention. Using recent advances in automatic differentiation, we show how kinetic pathways can be precisely designed by directly differentiating through statistical physics models, namely free energy calculations and molecular dynamics simulations. We consider two systems that are crucial to our understanding of structural self-assembly: bulk crystallization and small nanoclusters. In each case, we are able to assemble precise dynamical features. Using gradient information, we manipulate interactions among constituent particles to tune the rate at which these systems yield specific structures of interest. Moreover, we use this approach to learn nontrivial features about the high-dimensional design space, allowing us to accurately predict when multiple kinetic features can be simultaneously and independently controlled. These results provide a concrete and generalizable foundation for studying nonstructural self-assembly, including kinetic properties as well as other complex emergent properties, in a vast array of systems.
AU - Goodrich, Carl Peter
AU - King, Ella M.
AU - Schoenholz, Samuel S.
AU - Cubuk, Ekin D.
AU - Brenner, Michael P.
ID - 9257
IS - 10
JF - Proceedings of the National Academy of Sciences
SN - 0027-8424
TI - Designing self-assembling kinetics with differentiable statistical physics models
VL - 118
ER -
TY - JOUR
AB - Given a locally finite set 𝑋⊆ℝ𝑑 and an integer 𝑘≥0, we consider the function 𝐰𝑘:Del𝑘(𝑋)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space.
AU - Edelsbrunner, Herbert
AU - Nikitenko, Anton
AU - Osang, Georg F
ID - 9465
IS - 1
JF - Journal of Geometry
SN - 00472468
TI - A step in the Delaunay mosaic of order k
VL - 112
ER -
TY - JOUR
AB - A key step in understanding the genetic basis of different evolutionary outcomes (e.g., adaptation) is to determine the roles played by different mutation types (e.g., SNPs, translocations and inversions). To do this we must simultaneously consider different mutation types in an evolutionary framework. Here, we propose a research framework that directly utilizes the most important characteristics of mutations, their population genetic effects, to determine their relative evolutionary significance in a given scenario. We review known population genetic effects of different mutation types and show how these may be connected to different evolutionary outcomes. We provide examples of how to implement this framework and pinpoint areas where more data, theory and synthesis are needed. Linking experimental and theoretical approaches to examine different mutation types simultaneously is a critical step towards understanding their evolutionary significance.
AU - Berdan, Emma L.
AU - Blanckaert, Alexandre
AU - Slotte, Tanja
AU - Suh, Alexander
AU - Westram, Anja M
AU - Fragata, Inês
ID - 9470
IS - 12
JF - Molecular Ecology
SN - 09621083
TI - Unboxing mutations: Connecting mutation types with evolutionary consequences
VL - 30
ER -