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Physical Review E 2014年第3期89卷 032717-032717页

作者： Tao Han Trevor P. Bailey Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

Due to a thermodynamic coupling between the two leaflets comprising a lipid bilayer, compositional lipid domains residing within opposing leaflets are often found in registry. If the system is perturbed by displacing one domain relative to the other, diffusive and advective lipid fluxes are established to restore equilibrium and reestablish domain overlap. In this work, we focus on the advective part of the process, and first derive an analytical expression for the hydrodynamic drag coefficient associated with the advective flow for the special case of perfect domain overlap. The resulting expression identifies parameter regions where sliding friction between the leaflets dominates over viscous dissipation within the leaflets or vice versa. It is shown that in all practically relevant cases, sliding friction between the leaflets is the dominant factor. Finally, we investigate the domain separation dependence of the hydrodynamic drag coefficient via direct simulations of a continuum diffuse interface model, and provide useful empirical expressions for its behavior.

关键词： HYDRODYNAMICS BILAYER lipid membranes DRAG coefficient ENERGY dissipation SLIDING friction FLUX (Energy)

Lipid Microdomains: Structural Correlations, Fluctuations, and Formation Mechanisms

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Physical Review Letters 2010年第11期104卷 118101-118101页

作者： Jun Fan Maria Sammalkorpi Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

Compositional lipid microdomains (“lipid rafts”) in mammalian plasma membranes are believed to facilitate many important cellular processes. While several physically distinct scenarios predicting the presence of finite-sized microdomains in vivo have been proposed in the past, direct experimental verification or falsification of model predictions has remained elusive. Herein, we demonstrate that the combination of the spatial correlation and temporal fluctuation spectra of the lipid domains can be employed to unambiguously differentiate between the existing theoretical scenarios. Furthermore, the differentiation of the raft formation mechanisms using this methodology can be achieved by collecting data at physiologically relevant conditions without the need to tune control parameters.

关键词： Cell membranes

Bounds on the MMSE of “bad” LDPC codes at rates above capacity

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Bounds on the MMSE of “bad” LDPC codes at rates above capa...

Annual Allerton Conference on Communication, Control, and Computing

作者： Amir Bennatan A. Robert Calderbank Shlomo Shamai Program in Applied and Computational Mathematics (PACM) Princeton University USA Technion Israel Institute of Technology Haifa Haifa IL

We present bounds on the minimum mean square error (MMSE) of LDPC codes at rates above capacity. One potential application for MMSE estimation involves cooperative communication. A relay following a compress-and-forward (CF) strategy could first compute an estimate of the transmitted codeword, to reduce the level of noise in the retransmitted signal. Our first bound is based on an analysis of the LDPC belief-propagation decoder. A second bound relies on the relationship between the mutual information and the MMSE, which was discovered by Guo et al. . We compute our bounds for ldquobadrdquo LDPC codes (requiring SNRs that are far above the Shannon limit, for reliable communications to be possible) and show that such codes substantially outperform ldquogoodrdquo codes. This advantage of ldquobadrdquo codes implies an interesting degree of freedom in the design of codes for cooperative communications.

关键词： Parity check codes Relays Decoding Mutual information Context Mean square error methods Noise reduction Noise level Channel capacity mathematics

Critical dynamics in multicomponent lipid membranes

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Physical Review E 2009年第2期80卷 020902(R)-020902(R)页

作者： Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes both in vivo and in vitro lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, the roles of membrane and exterior fluid hydrodynamics on domain formation kinetics have received less attention. A case in point is the impact of hydrodynamics on the dynamics of compositional heterogeneities in lipid membranes in the vicinity of a critical point. In this Rapid Communication it is argued that the asymptotic dynamic behavior of a lipid membrane system in the vicinity of a critical point is strongly influenced by hydrodynamic interactions. More specifically, a mode-coupling argument is developed which predicts a scaling behavior of lipid transport coefficients near the critical point for both symmetric and asymmetric bilayers immersed in a bulk fluid.

关键词： Hydrodynamics

The Nystrom Extension for Signals Defined on a Graph

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The Nystrom Extension for Signals Defined on a Graph

International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Ayelet Heimowitz Yonina C. Eldar The Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Electrical Engineering Technion Haifa Israel

ISBN: (纸本)9781538646595

In this paper we introduce a computationally efficient solution to the problem of graph signal interpolation. Our solution is derived using the Nyström extension and is due to the properties of the Markov matrix which we use as our graph shift operator, inspired by diffusion maps. We focus on graph signals that are smooth over the graph. This assumption cements the relationship between the graph and the graph signal. We experimentally verify our suggested framework on the MNIST data set of handwritten digits.

关键词： Markov processes Signal processing Interpolation Laplace equations Symmetric matrices Image edge detection Eigenvalues and eigenfunctions

MOMENT-BASED METRICS FOR MOLECULES COMPUTABLE FROM CRYO-EM IMAGES

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arXiv 2024年

作者： Zhang, Andy Mickelin, Oscar Kileel, Joe Verbeke, Eric J. Marshall, Nicholas F. Gilles, Marc Aurèle Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Oden Institute University of Texas At Austin AustinTX78712 United States Department of Mathematics Oregon State University CorvallisOR97331 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Single particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution 3-D structure of biological macromolecules from many noisy and randomly oriented projection images. One notable approach to 3-D reconstruction, known as Kam's method, relies on the moments of the 2-D images. Inspired by Kam's method, we introduce a rotationally invariant metric between two molecular structures, which does not require 3-D alignment. Further, we introduce a metric between a stack of projection images and a molecular structure, which is invariant to rotations and reflections and does not require performing 3-D reconstruction. Additionally, the latter metric does not assume a uniform distribution of viewing angles. We demonstrate uses of the new metrics on synthetic and experimental datasets, highlighting their ability to measure structural similarity. Copyright © 2024, The Authors. All rights reserved.

关键词： Method of moments

Machine learning based non-Newtonian fluid model with molecular fidelity

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arXiv 2020年

作者： Lei, Huan Wu, Lei Weinan, E. Department of Computational Mathematics Science & Engineering Department of Statistics & Probability Michigan State University MI48824 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We introduce a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics model directly from a micro-scale description. Polymer solution is used as an example to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the micro-scale polymer configurations and their macro-scale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the micro-scale model and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN2), takes the form of conventional non-Newtonian fluid dynamics models, with a new form of the objective tensor derivative. Numerical results demonstrate the accuracy of DeePN2. Copyright © 2020, The Authors. All rights reserved.

关键词： Viscous flow

MONGE-AMPÈRE FLOW FOR GENERATIVE MODELING

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arXiv 2018年

作者： Zhang, Linfeng Weinan, E. Wang, Lei Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University United States Center for Data Science Peking University Beijing Institute of Big Data Research Beijing100871 China Institute of Physics Chinese Academy of Sciences Beijing100190 China

We present a deep generative model, named Monge-Ampère flow, which builds on continuous-time gradient flow arising from the Monge-Ampère equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Ampère flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative model by designing suitable scalar potential functions. We apply the approach to unsupervised density estimation of the MNIST dataset and variational calculation of the two-dimensional Ising model at the critical point. This approach brings insights and techniques from Monge-Ampère equation, optimal transport, and fluid dynamics into reversible flow-based generative models. Copyright © 2018, The Authors. All rights reserved.

关键词： Statistical mechanics

Energy stability of the Charney-DeVore quasi-geostrophic equation for atmospheric blocking

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arXiv 2021年

作者： Chen, Zhi-Min Xiong, Xiangming School of Mathematics and Statistics Shenzhen University Shenzhen518060 China The Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Charney and DeVore [J. Atmos. Sci. 36 (1979), 1205-1216] found multiple equilibrium states as a consequence of bottom topography in their pioneering work on the quasi-geostrophic barotropic flow over topography in a β-plane channel. In the present paper, we prove that the basic flow is asymptotically stable in a parameter region, including the flat topography situation, which excludes the existence of multiple equilibrium states therein. Moreover, we show that an additional condition on the average zonal force or the average zonal velocity is indispensable to the well-posedness of the Charney–DeVore quasi-geostrophic equation. Coexistence of at least three equilibrium states is confirmed by a pseudo-arclength continuation method for different topographic amplitudes. The stabilities of the equilibrium states are examined by high-resolution direct numerical simulations. © 2021, CC BY-NC-ND.

关键词： Astrophysics

A trace theorem for sobolev spaces on the sierpinski gasket

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arXiv 2019年

作者： CAO, SHIPING LI, SHUANGPING STRICHARTZ, ROBERT S. TALWAI, PREM Department of Mathematics Cornell University Ithaca14853 United States Program in Applied and Computational Mathematics Princeton University NJ08544-1000 United States

We give a discrete characterization of the trace of a class of Sobolev spaces on the Sierpinski gasket to the bottom line. This includes the L2 domain of the Laplacian as a special case. In addition, for Sobolev spaces of low orders, including the domain of the Dirichlet form, the trace spaces are Besov spaces on the *** Codes 28A80 Copyright © 2019, The Authors. All rights reserved.

关键词： Sobolev spaces