Study confirms neck condition for budding vesicles of any shape.
problem Understanding the shape of budding vesicles with two-phase domains.
method Derived shape equation and linking conditions, refined conjecture, proved for asymmetric vesicles.
result Mean curvature condition holds for all membrane segments adjacent to the neck in budding vesicles.
This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact solutions to the governing equations of open lipid membranes; (iii) neck condition o…
Study derives the limit of lipid bilayer membranes, proving their smooth transition across interfaces.
problem Understanding the smooth transition of lipid bilayer membranes across interfaces.
method Rigorous derivation of the Γ-limit for rotationally symmetric two-phase bilayer membranes. result Limit membranes are C1 across interfaces and can consist of multiple topological spheres. Study improves models of lipid bilayer curvature and elasticity.
problem Accurately modeling curvature and elasticity of lipid bilayers.
method Computed bending energy and forces on triangulated meshes using four schemes.
result Proposed extensions enhance models for shape transformation and non-axisymmetric shapes.
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly trained with backpropagation, like a neural network. Even though this continuity …
Updated VESICLE-CNN for faster synapse detection.
problem Slow patch-based synapse detection.
method Fully convolutional approach using dilated convolutions.
result 600x speedup at test time with no loss in accuracy.
BUDS balances privacy and utility by shuffling data, achieving strong privacy with minimal loss.
problem Balancing privacy and utility in crowd-sourced statistical databases.
method One-hot encoding, iterative shuffling, loss estimation, risk minimization.
result Achieves ε=0.02 for privacy, maintaining a privacy bound of ε=ln[t/((n1−1)S)]. Teaches math, physics, and machine learning using Calabi-Yau spaces.
problem Understanding Calabi-Yau spaces in geometry, physics, and machine learning.
method Lecture series, colloquia, and seminars.
result Pedagogical introduction to computational geometry, physical implications, and data science of Calabi-Yau manifolds.
Theory and methods for particle dynamics in curved lipid membranes.
problem Understanding particle behavior in curved lipid membranes.
method Developed theory and computational methods for hydrodynamic coupling.
result Membrane curvature and topology affect particle mobility.
This review reports some theoretical results on the Geometry of membranes. The governing equations to describe equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are derived from the variation of free energies of these structures. Some analytic solutions to these e…
Recent theoretical advances in elasticity of membranes following Helfrich's famous spontaneous curvature model are summarized in this review. The governing equations describing equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are presented. Several analytic solut…
We address the geometric Cauchy problem for surfaces associated to the membrane shape equation describing equilibrium configurations of vesicles formed by lipid bilayers. This is the Euler-Lagrange equation of the Canham-Helfrich-Evans elastic curvature energy subject to constraints on the enclosed volume and the surfa…
New flows model distributions on Riemannian manifolds without domain knowledge.
problem Limited modeling of distributions on Riemannian manifolds.
method Riemannian convex potential maps using optimal transport.
result These flows can model standard distributions on spheres and tori.
Paper proposes a method to train neural networks incrementally using cloud computing despite disconnections and resource outages.
problem Frequent disconnections and resource outages in cloud computing and local machines hinder deep learning model training.
method Introduces an incremental learning framework that allows continuous training of neural networks even with interruptions.
result Demonstrates that incremental learning can maintain progress and train neural networks effectively despite interruptions.
New method infers centromere locations in yeast using Hi-C data.
problem Difficulty in inferring centromere locations in yeast.
method Simulation-based inference using Hi-C data and simulated contact maps.
result Infers stochastic locations of all centromeres in budding yeast.
Automatically updates both network weights and architecture.
problem Manual selection of network architecture limits flexibility and efficiency.
method Continuous parameterization of network depth and automatic adjustment of architecture and weights.
result Correctly adjusts network complexity to task complexity.
Lipid necks, large curvature bridges, are shown to be metastable.
problem Understanding the energetically prohibitive yet ubiquitous lipid necks in cell membranes.
method Geometric triality approach to demonstrate metastability.
result Lipid necks can exist for finite but potentially long times without stabilizing mechanisms.
Locally learned synaptic failure enables complete Bayesian inference.
problem Bayesian inference in neural networks.
method Biologically constrained neural network with synaptic failure and lateral inhibition.
result Synaptic failure allows sampling from both epistemic and aleatoric distributions.
Fusion of transformer networks using optimal transport for improved performance.
problem Improving performance of transformer-based models through fusion.
method Exploiting optimal transport for soft alignment of transformer components.
result Consistently outperforms vanilla fusion and individual parent models.
Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an energetic point of view in recent years. Such pores permit targeted delivery of dru…
Deep learning aids water science by tackling complex data challenges.
problem Interdisciplinary challenges in water research.
method Application of deep learning techniques to water science problems.
result Deep learning can reveal emergent behaviors of problem-specific units.