Related papers: Multiscale Modeling, Homogenization and Nonlocal E…
Heterogeneous data from multiple populations, sub-groups, or sources is often represented as a ``mixture model'' with a single latent class influencing all of the observed covariates. Heterogeneity can be resolved at multiple levels by…
The macroscopic behavior of the solution of a coupled system of partial differential equations arising in the modeling of reaction-diffusion processes in periodic porous media is analyzed. Our mathematical model can be used for studying…
There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
Model merging aims to integrate multiple expert models into a single model that inherits their complementary strengths without incurring the inference-time cost of ensembling. Recent progress has shown that merging can be highly effective…
Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript…
ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…
Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging…
The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity…
We develop a mesoscopic modeling framework for diffusion in a crowded environment, particularly targeting applications in the modeling of living cells. Through homogenization techniques we effectively coarse-grain a detailed microscopic…
We introduce a fresh scheme based on the local hidden variable models to quantify nonlocality for arbitrarily high-dimensional quantum systems. Our scheme explores the minimal amount of white noise that must be added to the system in order…
How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links…
In this paper, we propose a multicontinuum homogenization approach for nonlinear problems involving dynamically evolving multiscale media. The main idea of the proposed approach is that one of the fine-scale variables defines continua. It…
Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…
A new possible version of multisimultaneous causality is proposed, and real experiments allowing us to decide between this view and quantum mechanical retrocausation are further discussed. The interest of testing quantum mechanics against…
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate…
Datasets with a mixture of numerical and categorical attributes are routinely encountered in many application domains. In this work we examine an approach to clustering such datasets using homogeneity analysis. Homogeneity analysis…
Urbanization has a strong impact on the health and wellbeing of populations across the world. Predictive spatial modeling of urbanization therefore can be a useful tool for effective public health planning. Many spatial urbanization models…
We present a new theoretical and numerical assessment methodology for a one-dimensional process chain with general applicability to management problems such as the optimization of decision chains or production chains. The process is thereby…
A growing number of applications involve settings where, in order to infer heterogeneous effects, a researcher compares various units. Examples of research designs include children moving between different neighborhoods, workers moving…