The paper explores metrics and models for analyzing biological shapes.
problem Analyzing biological shapes using mathematical metrics.
method Review of Riemannian metrics and evolution equations, focusing on diffeomorphic shape analysis.
result Introduction of a new class of metrics involving optimization of a growth tensor.
The paper introduces a new method to measure the shape relations between biological objects using r-parallel sets.
problem The influence of neighboring objects on the shape and function of biological objects.
method The authors develop a theory based on spatial point processes to measure the geometrical interaction between objects.
result The proposed measures provide detailed information about the shape of individual objects and their interactions.
Paper develops a new method to analyze 3D tree-like objects.
problem Analyzing complex geometrical and topological variations in 3D tree-like objects.
method Extended SRVF representation and new metric for tree-shaped 3D objects.
result Captures full elasticity and topological variations of branches.
Convolutional Neural Networks (CNNs) have become the state-of-the-art method to learn from image data. However, recent research shows that they may include a texture and colour bias in their representation, contrary to the intuition that they learn the shapes of the image content and to human biological learning. Thus,…
Efficient method for shape modeling invariant to rigid motion.
problem Statistical shape modeling for rigidly moving shapes.
method Non-Euclidean Lie group analysis of metric distortion and curvature.
result Outperforms state-of-the-art classifiers in sparse data.
The paper classifies self-replicating 3D shapes using algebraic models.
problem Understanding self-replicating 3D shapes.
method Using idempotents in the (2+1)-cobordism category to classify 3-manifolds.
result A classification theorem for self-replicating 3-manifolds.
Symmetry principles help in creating better AI representations.
problem Creating efficient and generalizable AI representations.
method Using symmetry transformations to guide representation learning.
result Symmetry principles improve data efficiency and generalizability in AI.
New tool for summarizing time-varying data shapes.
problem Understanding dynamic data shapes.
method Introducing crocker stacks for time-varying metric spaces.
result Demonstrated utility in parameter identification task.
New origami structures adapt to over 100 shapes with minimal actuation.
problem Limited shape-morphing capabilities in metamaterials and robotics.
method Hierarchical origami based on polyhedrons, using simple actuation.
result Single structure adapts to over 103 configurations with few actuations.
Defines metrics to compare neural network representations.
problem Comparing neural network representations across different architectures and tasks.
method Developed a family of metric spaces and modified existing measures to quantify representational dissimilarity.
result Identified relationships between neural representations and anatomical features.
Machine learning methods struggle with geometric data, but shape space analysis provides a framework for studying and analyzing geometric variability.
problem Machine learning methods struggle with geometric data
method Shape space analysis provides a mathematical and computational framework
result Characterizes shape variability, compares geometric objects, and analyzes structural trajectories
Study connects hyperbolic geometry to membrane shapes.
problem Understanding the shapes of biological membranes.
method Relates geometry of hyperbolic space to Helfrich model.
result Establishes a connection between membrane shapes and hyperbolic geometry.
The paper analyzes the emergence of almost-honeycomb structures in low-energy planar clusters.
problem Understanding the formation of shapes resembling honeycombs in low-energy configurations.
method Detailed quantitative estimates and a revision of the global isoperimetric principle for honeycomb clusters.
result The majority of chambers in low-energy planar clusters are generalized hexagons, closely resembling regular hexagons.
The key idea of current deep learning methods for dense prediction is to apply a model on a regular patch centered on each pixel to make pixel-wise predictions. These methods are limited in the sense that the patches are determined by network architecture instead of learned from data. In this work, we propose the dense…
Helical ribbons arise in many biological and engineered systems, often driven by anisotropic surface stress, residual strain, and geometric or elastic mismatch between layers of a laminated composite. A full mathematical analysis is developed to analytically predict the equilibrium deformed helical shape of an initiall…
Two-sample tests improve on existing methods for microtubule data.
problem Testing differences between two groups of filament data.
method Optimal lifts and manifold stability theorem applied to microtubule data.
result New tests outperform existing methods on simulated and real data.
Deep learning algorithms for connectomics rely upon localized classification, rather than overall morphology. This leads to a high incidence of erroneously merged objects. Humans, by contrast, can easily detect such errors by acquiring intuition for the correct morphology of objects. Biological neurons have complicated…
The Procrustes distance is used to quantify the similarity or dissimilarity of (3-dimensional) shapes, and extensively used in biological morphometrics. Typically each (normalized) shape is represented by N landmark points, chosen to be homologous (i.e. corresponding to each other), as far as possible, and the Procrust…
Stochasticity is key for machine learning's robustness and generalizability.
problem Machine learning's need for robustness and generalizability.
method Review of ML literature and biological intelligence.
result Stochasticity is a critical ingredient for intelligent systems in ML.
Neurons predict future scalar inputs by learning top modes of lag vectors.
problem Predicting future scalar inputs with physiological delays.
method Normal Mode Decomposition to extract independently evolving modes.
result Temporal filters of neurons correspond to left eigenvectors of a generalized eigenvalue problem.
Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse covariance matrix. We utilize a novel projected gradient method, which is faster …
Physics-informed methods infer spatial dynamics from static snapshots, but limits exist.
problem Inferring spatial dynamics from static molecular patterns.
method Combining flexible representations with mechanistic constraints, analyzing structural identifiability, and adapting physics-informed schemes.
result Static spatial patterns can identify spatially varying dynamics, but limits exist due to modeling choices.
The amoebas associated to algebraic varieties are certain concave regions in the Euclidean space whose shape reminds biological amoebas. This term was formally introduced to Mathematics in 1994 by Gelfand, Kapranov and Zelevinski. Some traces of amoebas were appearing from time to time, even before the formal introduct…
Optimal algorithm selects biological models without prior info.
problem Determining the correct biological model without prior knowledge.
method Systems biology models and likelihood-free inference.
result Improved model selection performance over conventional methods.
Researchers develop flexible kernels for biological sequences with guaranteed reliability.
problem Challenges in applying machine learning to biological sequences, including unreliable methods.
method Theoretical analysis and development of modified kernels to ensure reliability and accuracy.
result Developed kernels that are universal, characteristic, and metrize the space of distributions for biological sequences.
In the brain, learning signals change over time and synaptic location, and are applied based on the learning history at the synapse, in the complex process of neuromodulation. Learning in artificial neural networks, on the other hand, is shaped by hyper-parameters set before learning starts, which remain static through…
New learning algorithm mimics biological neural networks.
problem Biologically implausible backpropagation for directed neural networks.
method Introduces new neuronal dynamics and learning rule for arbitrary architectures, sparsity-inducing pruning method, and dynamical-systems characterization.
result Prunes irrelevant connections and improves learning efficiency.
SENA-discrepancy-VAE interprets latent causal factors in biological pathways.
problem Interpreting latent causal factors in biological pathways.
method SENA-discrepancy-VAE, a model based on discrepancy-VAE, that produces interpretable latent causal factors.
result Sena-discrepancy-VAE achieves comparable predictive performance with non-interpretable counterparts while providing biologically meaningful causal factors.
Deep learning applied to biological data mining.
problem Mining complex biological data from diverse sources.
method Artificial neural networks, deep learning architectures.
result Deep learning techniques improve pattern recognition in biological data.
Biological networks are a very convenient modelling and visualisation tool to discover knowledge from modern high-throughput genomics and postgenomics data sets. Indeed, biological entities are not isolated, but are components of complex multi-level systems. We go one step further and advocate for the consideration of …
Scalable GPLVM reduces complexity in scRNA-seq data, accounting for technical and biological confounders.
problem Complexity and confounders in scRNA-seq data hamper interpretation.
method Extended Gaussian process latent variable model (GPLVM) to handle large datasets.
result Framework reconstructs latent signatures and captures disease-specific gene expression.
DeepSIBA predicts biological effects of chemical structures using graph neural networks.
problem Predicting biological effects of chemical structures for drug discovery.
method Siamese Graph Convolutional Neural Networks for structure-biological effect mapping.
result Highly accurate predictions of biological effects for structurally dissimilar compounds.
New methods improve uncertainty quantification in dynamic biological systems.
problem Uncertainty in dynamic biological models due to nonlinearity and parameter sensitivity.
method Conformal inference methods for non-asymptotic guarantees.
result Enhanced robustness and scalability for diverse biological data structures.
Proposes a novel network-based neighborhood regression for biological systems.
problem Lack of comprehensive analysis on biological modules using both global and local network data.
method Develops a community-wise least square optimization approach to analyze gene modules and their regulatory strength.
result Achieves exact minimax optimality and linear consistency in identifying gene module associations.
Machine learning and topological data analysis identify unique geometric and topological features of human papillae.
problem Identifying unique features of human papillae across individuals.
method 3D microscopic scans, machine learning, discrete differential geometry, computational topology, persistent homology.
result Persistent homology features of papillae shape predict papillae type with high accuracy and can identify individuals with high accuracy.
New method constructs geometric flat outputs for robotic systems using symmetry.
problem Finding flat outputs for arbitrary robotic systems remains an open question.
method Employing symmetry directly to construct a flat output.
result Demonstrated geometric flat outputs for various robotic systems.
AR algorithm simplifies backpropagation with improved scalability and biological plausibility.
problem Improving backpropagation algorithms for complex neural networks and biological plausibility.
method Introducing learnable backwards weights and avoiding nonlinear derivative computations; relaxing frozen feedforward pass assumption.
result Simplified AR algorithm maintains performance on complex CNN architectures and challenging datasets.
We solve a lifecycle model in which the consumer's chronological age does not move in lockstep with calendar time. Instead, biological age increases at a stochastic non-linear rate in time like a broken clock that might occasionally move backwards. In other words, biological age could actually decline. Our paper is ins…
Algorithm optimizes biological sequences using bootstrapped training with a score-conditioned generator.
problem Optimizing biological sequences for a black-box score function.
method Bootstrapped training of score-conditioned generator (BootGen) algorithm.
result Our method outperforms competitive baselines on biological sequential design tasks.
Recent advances in neuroscience have revealed many principles about neural processing. In particular, many biological systems were found to reconfigure/recruit single neurons to generate multiple kinds of decisions. Such findings have the potential to advance our understanding of the design and optimization process of …
Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This work is about empirically supported mathematical ideas behind splitting and merging…
Backpropagation is the workhorse of deep learning, however, several other biologically-motivated learning rules have been introduced, such as random feedback alignment and difference target propagation. None of these methods have produced a competitive performance against backpropagation. In this paper, we show that bi…
Fault-tolerant neural networks inspired by biological error correction codes.
problem Achieving reliable computation with unreliable neurons.
method Using biological error correction codes from grid cells in the mammalian cortex to develop a fault-tolerant neural network.
result Noisy biological neurons operate below a fault-tolerance threshold, suggesting a mechanism for reliable computation in the brain.
This paper tackles infinite-dimensional diffusion bridge simulation using operator learning.
problem Challenges in simulating diffusion bridges for modeling natural data due to intractable drift terms and continuous data representations.
method Merges score matching techniques with operator learning to directly learn infinite-dimensional bridges.
result Demonstrates high efficacy in simulating diffusion bridges for various applications, including real-world biological data.
Probabilistic graphical models (PGMs) have become a popular tool for computational analysis of biological data in a variety of domains. But, what exactly are they and how do they work? How can we use PGMs to discover patterns that are biologically relevant? And to what extent can PGMs help us formulate new hypotheses t…
New learning rules for wide neural networks without backpropagation.
problem Training wide neural networks efficiently and without backpropagation.
method Input-weight alignment driven by gradient descent in the NTK regime.
result Biologically-motivated learning rules equivalent to backpropagation in wide networks.
We present an analysis of the problem of identifying biological context and associating it with biochemical events in biomedical texts. This constitutes a non-trivial, inter-sentential relation extraction task. We focus on biological context as descriptions of the species, tissue type and cell type that are associated …
Double descent observed in tree-based models for genomic prediction.
problem Understanding the generalization behavior of tree-based models in machine learning.
method Systematic variation of model complexity in a genomic prediction task using whole-genome sequencing data.
result Double descent emerges only when complexity is scaled jointly across learner capacity and ensemble size.