arXiv research

Study shows diffused interface flows to single diffused balls over time.

Diffuse interface methods have recently been introduced for the task of semi-supervised learning. The underlying model is well-known in materials science but was extended to graphs using a Ginzburg--Landau functional and the graph Laplacian. We here generalize the previously proposed model by a non-smooth potential fun…

We present a graph-based variational algorithm for multiclass classification of high-dimensional data, motivated by total variation techniques. The energy functional is based on a diffuse interface model with a periodic potential. We augment the model by introducing an alternative measure of smoothness that preserves s…

Signed networks contain both positive and negative kinds of interactions like friendship and enmity. The task of node classification in non-signed graphs has proven to be beneficial in many real world applications, yet extensions to signed networks remain largely unexplored. In this paper we introduce the first analysi…

Improved graph-based multiclass classification for multilayer data.

New method steers protein design towards desired properties.

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the fun…

We consider a diffuse interface approximation for the lipid phases of rotationally symmetric two-phase bilayer membranes and rigorously derive its $Γ$-limit. In particular, we prove that limit vesicles are $C^1$ across interfaces, which justifies a regularity assumption that is widely made in formal asymptotic and nume…

New method extracts hidden phases in binary mixtures using tubular tilings.

We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity surfaces. In analyzing this phenomenon, we prove the covariance of surface balances…

We study perturbations of the Allen-Cahn equation and prove the convergence to forced mean curvature flow in the sharp interface limit. We allow for perturbations that are square-integrable with respect to the diffuse surface area measure. We give a suitable generalized formulation for forced mean curvature flow and ap…

PDSim simulates and estimates commodity futures prices using polynomial diffusion models.

A new method uses DMs as priors for imaging problems, offering more accurate reconstructions.

PGEL learns embeddings to diversify protein motifs while maintaining biological function.

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a …

Deep model learns protein interfaces from high-order interactions.

The paper analyzes the score field of diffusion models using Burgers dynamics.

We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from circular interfaces immersed in uniform grids of various resolutions. These multilayer …

GenSBI offers JAX-native SBI methods for natural sciences.

New method learns under latent group sparsity using network dynamics.

Brain-Machine Interfaces (BMIs) have recently emerged as a clinically viable option to restore voluntary movements after paralysis. These devices are based on the ability to extract information about movement intent from neural signals recorded using multi-electrode arrays chronically implanted in the motor cortices of…

Objective: A variety of pattern analysis techniques for model training in brain interfaces exploit neural feature dimensionality reduction based on feature ranking and selection heuristics. In the light of broad evidence demonstrating the potential sub-optimality of ranking based feature selection by any criterion, we …

PHINN: A generative model for rare-event time series using persistent homology

R package for counterfactual explanation methods.

We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based …

New interface explains contextual bandits to non-experts.

Bayesian imaging methods deliver trustworthy probabilities in some cases but struggle with uncertainty quantification.

This paper introduces the probabilistic module interface, which allows encapsulation of complex probabilistic models with latent variables alongside custom stochastic approximate inference machinery, and provides a platform-agnostic abstraction barrier separating the model internals from the host probabilistic inferenc…

We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in $H^{\frac32k +1}$ and the velocity fields in $H^{\frac32k}$. These estimates are obtained using geometric considerations which show th…

Study boundary behavior of limit interfaces in Riemannian manifolds without convexity assumptions.

One of the big restrictions in brain computer interface field is the very limited training samples, it is difficult to build a reliable and usable system with such limited data. Inspired by generative adversarial networks, we propose a conditional Deep Convolutional Generative Adversarial (cDCGAN) Networks method to ge…

Proves long-term smoothness of curved surfaces evolving under specific curvature rules.

In artificial intelligence, we often specify tasks through a reward function. While this works well in some settings, many tasks are hard to specify this way. In deep reinforcement learning, for example, directly specifying a reward as a function of a high-dimensional observation is challenging. Instead, we present an …

A discrete method approximates hyperbolic curvature flow in the plane.

Study on the regularity of $p$-Gauss curvature flow near flat interfaces.

Study stability and bifurcation of liquid interfaces in cylindrical supports.

We address the double bubble problem for the anisotropic Grushin perimeter $P_α$, $α\geq 0$, and the Lebesgue measure in $\mathbb R^2$, in the case of two equal volumes. We assume that the contact interface between the bubbles lays on either the vertical or the horizontal axis. Since no regularity theory is available i…

Interactive Machine Learning is concerned with creating systems that operate in environments alongside humans to achieve a task. A typical use is to extend or amplify the capabilities of a human in cognitive or physical ways, requiring the machine to adapt to the users' intentions and preferences. Often, this takes the…

Analytic patch trees reveal new geometric structures and dimension fields.

LLMs can help explain credit risk models but not autonomously.

Common models for two-phase lipid bilayer membranes are based on an energy that consists of an elastic term for each lipid phase and a line energy at interfaces. Although such an energy controls only the length of interfaces, the membrane surface is usually assumed to be at least $C^1$ across phase boundaries. We consi…

A new method selects important variables for clustering from dependency networks.

This paper uses bandit algorithms to reduce the cost of user interface experimentation in online retail.

New method models dewetting of anisotropic particles using numerical techniques.

We present sktime -- a new scikit-learn compatible Python library with a unified interface for machine learning with time series. Time series data gives rise to various distinct but closely related learning tasks, such as forecasting and time series classification, many of which can be solved by reducing them to relate…

Construct intrinsic Langevin dynamics for rigid inclusions on curved surfaces.

The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations about the parallelization and scalability of realistic problems are often criti…

Brain-Computer Interface (BCI) uses brain signals in order to provide a new method for communication between human and outside world. Feature extraction, selection and classification are among the main matters of concerns in signal processing stage of BCI. In this article, we present our findings about the most effecti…