Wrinkles form on a thin sheet bonded to a sphere, revealing energy and length scale behaviors.
problem Understanding the wrinkle formation on a thin sheet bonded to a sphere.
method Analyzing the energy of the system with the sheet's thickness as a small parameter, determining leading and next-order behaviors.
result The wrinkling pattern varies with radius, with the number of wrinkles being approximately integer multiples of the sheet thickness.
RGPs connect predictive coding to Bayesian inference, providing a neural substrate.
problem Scalable implementations of Bayesian inference respecting neurobiological constraints.
method Formal connection between predictive coding and Recursive Gaussian Processes (RGPs).
result RGPs intrinsically implement hierarchical Bayesian inference and uncertainty propagation.
We develop a topological model of site-specific recombination that applies to substrates which are the connected sum of two torus links of the form T(2,n)#T(2,m). Then we use our model to prove that all knots and links that can be produced by site-specific recombination on such substrates are contained in one of two…
A learning rule for first-spike times in neural networks reduces energy consumption and reaction times.
problem Energy efficiency and reaction time in neuromorphic systems.
method Derivation of a learning rule for first-spike times in leaky integrate-and-fire neurons, using only input and output spike times.
result Demonstrated that the approach can implement error backpropagation in hierarchical spiking networks and is capable of harnessing neuromorphic system's speed and energy characteristics.
Deep neural networks map brain lesions to deficits for better brain function understanding.
problem Mapping the functional brain organization from pathological lesions.
method Deep generative neural network architectures, specifically variational convolutional volumetric auto-encoders.
result Our model outperforms established methods in lesion-deficit inference across various scenarios.
We develop a model characterizing all possible knots and links arising from recombination starting with a twist knot substrate, extending previous work of Buck and Flapan. We show that all knot or link products fall into three well-understood families of knots and links, and prove that given a positive integer n, the…
Site-specific recombination on supercoiled circular DNA molecules can yield a variety of knots and catenanes. Twist knots are some of the most common conformations of these products and they can act as substrates for further rounds of site-specific recombination. They are also one of the simplest families of knots and …
We develop a topological model of knots and links arising from a single (or multiple processive) round(s) of recombination starting with an unknot, unlink, or (2,m)-torus knot or link substrate. We show that all knotted or linked products fall into a single family, and prove that the size of this family grows linearly …
We establish that equally-spaced smectic configurations enjoy an infinite-dimensional conformal symmetry and show that there is a natural map between them and null hypersurfaces in maximally-symmetric spacetimes. By choosing the appropriate conformal factor it is possible to restore additional symmetries of focal struc…
Graph Element Networks adaptively model spatial processes without prior graph structure.
problem Modeling spatial processes without a priori graphical structure.
method Assign nodes to spatial locations, optimize their connectivity, and use GNNs as a computational substrate.
result Optimized GNN nodes focus on complex parts of the space, allowing generalization and varying precision.
New Heintze-Karcher inequality helps understand droplet shapes.
problem Characterize the shape of droplets inside smooth containers.
method Obtained a new form of the Heintze-Karcher inequality for mean convex hypersurfaces with boundary on curved substrates.
result New mathematical inequality aids in understanding droplet shapes.
A new method approximates deep neural networks using Kalman Filters.
problem Approximating deep neural networks with limited data.
method Matrix Ensemble Kalman Filter-based multi-arm ANN (MEnKF-ANN).
result MEnKF-ANN can adequately approximate LSTM networks and provide uncertainty estimates.
GNNs improve brain activity forecasting in fMRI studies.
problem Understanding neural dynamics in the brain.
method Comparison of GNN architectures for modeling fMRI data.
result GNNs outperform VAR models in robustly scaling to large network studies.
A new hierarchy quantifies agency in systems based on information processing.
problem Lack of a measurable, universal definition for agency in intelligent systems.
method Developed a bottom-up framework based on information processing hierarchy.
result Identified three orders of information processing (I, II, III) as necessary for agency.
AgensFlow learns multi-agent coordination policies from experience.
problem Difficult coordination choices in multi-agent systems built on LLMs.
method Online policy learning from repeated trajectories, treating decisions as learnable.
result Learned routing improves coordination-heavy workflows over static wiring.
Graphs predict reaction conditions for organic chemistry.
problem Predicting specific reaction conditions in organic chemistry.
method Graph Neural Networks (GNNs) for modeling reaction graphs.
result GNNs can identify specific graph features affecting reaction conditions.
Enhances disease progression modeling using LLMs for complex brain connectivity.
problem Inaccurate predictions of disease spread due to oversimplified brain connectivity models.
method Uses LLMs to synthesize multi-modal relationships and learn disease trajectories from longitudinal data.
result Superior prediction accuracy and interpretability compared to traditional methods.
GeomHerd predicts herding behavior before market prices move, using Ricci curvature of agent interaction graphs.
problem Quantifying herding behavior in markets that lags behind actual price movements.
method Develops a geometric framework to track coordination on agent interaction graphs, bypassing lag in price-correlation statistics.
result GeomHerd anticipates herding long before market baselines, with significant lead times in predictions.
Researchers explore non-coherent banding in site-specific recombination.
problem Understanding non-coherent banding in site-specific recombination.
method Survey of recent developments in non-coherent banding on knots.
result Recent advances in non-coherent banding model for site-specific recombination.
Novel graph network learns hierarchical network structure.
problem Lack of information in hierarchical network topology.
method Hierarchical clustering for multiscale decomposition, graph convolutional layers.
result Competitive performance on citation network benchmark.
Selection mechanisms impact market volatility in evolving markets.
problem Determining how selection mechanisms affect market volatility in evolving markets.
method Used a population of evolving zero-intelligence agents and a frequent batch auction price-discovery mechanism to analyze the role of selection mechanisms.
result Local fitness-proportionate selection mechanisms correlate with high correlation between risk-aversion and volatility, while quantile-based selection mechanisms show less correlation.
Boosting classifiers improve accuracy with noisy inputs.
problem Noisy communication or computation degrades boosting classifier accuracy.
method Optimize resource allocation for base classifiers based on importance metrics.
result Optimized noisy boosting classifiers are more robust than bagging.
We show that some pieces of cylinders bounded by two parallel straight-lines bifurcate in a family of periodic non-rotational surfaces with constant mean curvature and with the same boundary conditions. These cylinders are initial interfaces in a problem of microscale range modeling the morphologies that adopt a liquid…
METRO predicts reactions using minimal templates, reducing computational overhead and achieving state-of-the-art results.
problem Predicting possible reaction substrates for complex molecules from simpler precursors.
method METRO (Molecule-Edit Templates for RetrOsynthesis) uses minimal templates to predict reactions efficiently and accurately.
result METRO achieves state-of-the-art results on standard benchmarks, reducing computational overhead.
Adapts MBDOE for real-time parameter estimation in complex systems.
problem Costly posterior inference and design optimization in nonlinear systems.
method Combines DAD with differentiable mechanistic models for real-time parameter estimation.
result Demonstrated on four systems, including a DC motor.
Hierarchical spiking networks resist physical distortions for neuromorphic computing.
problem Distortions in physical neuromorphic implementations of spiking networks.
method Used hierarchical leaky integrate-and-fire neurons to create robust spiking networks.
result Hierarchical spiking networks are robust to physical distortions.
Functional brain networks exhibit dynamics on the sub-second temporal scale and are often assumed to embody the physiological substrate of cognitive processes. Here we analyse the temporal and spatial dynamics of these states, as measured by EEG, with a hidden Markov model and compare this approach to classical EEG mic…
Instrumented data enables causal scientific machine learning
problem Insufficient data for causal scientific machine learning
method Instrumented data with explicit model, uncertainty, and counterfactuals
result Supports causal interventions through Pearl's do-operator
GPMI method interpolates uncertain atrial conduction velocity on non-Euclidean manifolds.
problem Uncertainty in atrial conduction velocity calculations.
method Gaussian Process Manifold Interpolation (GPMI) on human atrial manifolds.
result GPMI accounts for atrial topology and calculates CV uncertainty.
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
problem Simulation of complex 3D geometries with thin features or non-trivial topology.
method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.
result The learned atlas enables different solvers without re-meshing or re-parametrization.
Method improves microbial biomass yield estimation from noisy data.
problem Estimating microbial biomass yields from noisy cell counts and substrate measurements.
method Probabilistic macrochemical modeling to relax cell weight assumptions and improve robustness.
result Model provides accurate uncertainty estimates of key parameters.
This thesis explores emergent intelligence in disordered systems like spin glasses and neural networks.
problem Understanding the principles behind emergent intelligent behaviors in disordered systems.
method Statistical physics approach to charting learning mechanisms and dynamics.
result Uncovering relationships between learning mechanisms and physical dynamics.
Study reveals optimal scaling conditions for photonic neural networks.
problem Impact of reservoir size and learning routines on convergence-speed during learning.
method Used a greedy algorithm to train a photonic neural network for chaotic signals prediction.
result Determined convergence speed of learning as a function of reservoir size and found close to linear scaling.
Quantum systems with scrambling improve temporal information processing, but scaling requires exponential overhead.
problem Scalability and memory retention of quantum reservoirs in temporal information processing.
method Examined a quantum reservoir processing framework with scrambling reservoirs modeled by high-order unitary designs, analyzed in noiseless and noisy settings.
result Memory retention improves exponentially with reservoir size but worsens with reservoir iterations, requiring exponential shot overhead for scaling.
MEGAN models chemical reactions as graph edits, improving synthesis planning.
problem Generating and predicting chemical reactions under constraints.
method End-to-end encoder-decoder neural model inspired by arrow pushing formalism.
result State-of-the-art accuracy in standard benchmarks for retrosynthesis prediction.
The study learns neural update rules by remembering past experiences.
problem Developing efficient online learning rules for neural networks.
method Representing neurons with vectors, using meta-neural networks for updates, and training for remembering past experiences.
result The approach reveals insights into learning rules and could be used for complex tasks like episodic memory.
New method combines brain imaging data from multiple studies to improve cognitive decoding.
problem Low statistical power in individual neuroimaging studies.
method A new methodology to analyze brain responses across tasks without a unified theoretical framework.
result Improves decoding performance for 80% of 35 functional-imaging studies.
The paper models financial order books using geometric shears and directional liquidity.
problem Understanding the geometry and dynamics of financial order books.
method Structural framework modeling liquidity as emergent observables, geometric shears, and directional imbalances.
result The geometry of financial order books can be described by a rigid drift and geometric shear, leading to a gamma-like profile of projected liquidity.
Extended Möbius energy formula for generalized O'Hara's energies.
problem Maintaining Möbius invariance in O'Hara's energies.
method Extended cosine formula for generalized O'Hara's energies.
result Condition for right circle minimization under length-constraint.
The episodic, irregular and asynchronous nature of medical data render them difficult substrates for standard machine learning algorithms. We would like to abstract away this difficulty for the class of time-stamped categorical variables (or events) by modeling them as a renewal process and inferring a probability dens…
Holographic energy equals Hamiltonian energy.
problem Equating holographic and Hamiltonian energies.
method Relative holographic and Hamiltonian energy comparison.
result Holographic energy is identical to Hamiltonian energy.
Token economics improves energy systems with incentives and efficiency.
problem Traditional energy systems have inefficiencies and lack incentives.
method Integrating token economy and blockchain technology.
result Token economic systems enhance energy efficiency and reduce emissions.
Optimizes energy efficiency in wireless sensor networks with limited information.
problem Maximizing energy efficiency in energy harvesting wireless sensor networks with limited channel state information.
method Modeling as a Multi-Armed Bandits problem and developing an Upper Confidence Bound algorithm.
result Significant gains in energy efficiency compared to benchmark schemes.
Reduces energy for 4D submanifolds in R^n.
problem Energy reduction for 4D submanifolds in R^n.
method Connected sum energy reduction for fourth-order Willmore energy.
result Established a connected sum energy reduction for the fourth-order Willmore energy.
Paper tackles energy sharing in ZECs using DRL.
problem Improving energy status of ZECs through agent-based energy sharing.
method Modelled as a multi-agent environment, solved with DRL.
result Agents learn to collaborate and improve ZEC's energy status over time.
Let Ef be the energy of some knot τ for any f from certain class of functions. The problem is to find knots with extremal values of energy. We discuss the notion of the locally perturbed knot. The knot circle minimizes some energies Ef and maximizes some others. So, is there any energy such that the circle ne…
The paper develops a regularity theory for O'hara knot energies, focusing on Möbius energy.
problem Developing a regularity theory for extremal knots of scale invariant knot energies defined by J. O'hara.
method Reinterpreting O'hara knot energies as a nonlinear, nonlocal Lp-energy acting on the unit tangent of the knot parametrization, drawing a connection to the theory of (fractional) harmonic maps into spheres. result Proves regularity for minimizers and critical knots of the scale-invariant O'hara knot energies.
The positive energy theorem is proven for certain spacetimes with irregular curvature.
problem Proving the positive energy theorem for spacetimes with irregular curvature.
method Weak asymptotically anti-de Sitter initial data sets with distributional curvature under weak dominant energy condition.
result Positive energy theorem established for weakly irregular spacetimes.