Related papers: Multiscale Modeling, Homogenization and Nonlocal E…
Marginal problems naturally arise in a variety of different fields: basically, the question is whether some marginal/partial information is compatible with a joint probability distribution. To this aim, the characterization of marginal sets…
This short course offers a new perspective on randomized algorithms for matrix computations. It explores the distinct ways in which probability can be used to design algorithms for numerical linear algebra. Each design template is…
How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to…
Subword tokenizers trained on multilingual corpora naturally produce overlapping tokens across languages. Does token overlap facilitate cross-lingual transfer or instead introduce interference between languages? Prior work offers mixed…
Subword tokenization introduces a computational layer in language models where many distinct token sequences decode to the same surface form and preserve meaning, yet induce different internal computations. Despite this non-uniqueness,…
We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these…
Whole-cell computational models aim to predict cellular phenotypes from genotype by representing the entire genome, the structure and concentration of each molecular species, each molecular interaction, and the extracellular environment.…
Modelling uncertainty in Machine Learning models is essential for achieving safe and reliable predictions. Most research on uncertainty focuses on output uncertainty (predictions), but minimal attention is paid to uncertainty at inputs. We…
Motivated by genome-wide association studies, we consider a standard linear model with one additional random effect in situations where many predictors have been collected on the same subjects and each predictor is analyzed separately.…
Bell's theorem shows that local measurements on entangled states give rise to correlations incompatible with local hidden variable models. The degree of quantum nonlocality is not maximal though, as there are even more nonlocal theories…
In this work we further develop a nonlocal calculus theory (initially introduced in [5]) associated with singular fractional-type operators which exhibit kernels with finite support of interactions. The applicability of the framework to…
Which nonlocal correlations can be obtained, when a party has access to more than one subsystem? While traditionally nonlocality deals with spacelike separated parties, this question becomes important with quantum technologies that connect…
The relationships between diversity, productivity and scale determine much of the structure and robustness of complex biological and social systems. While arguments for the link between specialization and productivity are common, diversity…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…
Hierarchical modeling provides a framework for modeling the complex interactions typical of problems in applied statistics. By capturing these relationships, however, hierarchical models also introduce distinctive pathologies that quickly…
Biological and artificial information processing systems form representations of the world that they can use to categorize, reason, plan, navigate, and make decisions. How can we measure the similarity between the representations formed by…
The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate…
Many complex systems can be modeled as multiagent systems in which the constituent entities (agents) interact with each other. The global dynamics of such a system is determined by the nature of the local interactions among the agents.…
The question how an agent is affected by its embodiment has attracted growing attention in recent years. A new field of artificial intelligence has emerged, which is based on the idea that intelligence cannot be understood without taking…