Related papers: A Pathway Idea in Model Building
The purpose of this paper is to give an introduction to the field of Schema Theory written by a mathematician and for mathematicians. In particular, we endeavor to to highlight areas of the field which might be of interest to a…
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
Human beings learn causal models and constantly use them to transfer knowledge between similar environments. We use this intuition to design a transfer-learning framework using object-oriented representations to learn the causal…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
Many classic questions of structural theory concern discrete changes, such as the formation or dissolution of groups, role turnover, or faction realignment. Here, we consider a basic framework combining prior work on change paths and recent…
Highway driving invariably combines high speeds with the need to interact closely with other drivers. Prediction methods enable autonomous vehicles (AVs) to anticipate drivers' future trajectories and plan accordingly. Kinematic methods for…
Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a…
In branching simulation, a novel approach to simulation presented in this paper, a multiplicity of plausible scenarios are concurrently developed and implemented. In conventional simulations of complex systems, there arise from time to time…
To better understand the structure and function of complex systems, researchers often represent direct interactions between components in complex systems with networks, assuming that indirect influence between distant components can be…
The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…
This article mediates an mathematical insight to the theory of vehicular headways measured on signalized crossroads. Considering both, mathematical and empirical substances of the socio-physical system studied, we firstly formulate several…
Stepwise inference protocols, such as scratchpads and chain-of-thought, help language models solve complex problems by decomposing them into a sequence of simpler subproblems. Despite the significant gain in performance achieved via these…
We present for mental processes the program of mathematical mapping which has been successfully realized for physical processes. We emphasize that our project is not about mathematical simulation of brain's functioning as a complex physical…
A methodology that seeks to enhance model prediction performance is presented. The method involves generating multiple auxiliary models that capture relationships between attributes as a function of each other. Such information serves to…
Air traffic can be significantly disrupted by weather. Pathfinder operations involve assigning a designated aircraft to assess whether airspace that was previously impacted by weather can be safely traversed through. Despite relatively…
We study particle hopping on a two-leg ladder where a particle can jump to their immediate neighbours, one at a time, with rates that depend on the occupation of the departure site and a neighbouring site on the other leg. For specific…
The theory of linear transports along paths in vector bundles, generalizing the parallel transports generated by linear connections, is developed. The normal frames for them are defined as ones in which their matrices are the identity…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
Additive models (AMs) have sparked a lot of interest in machine learning recently, allowing the incorporation of interpretable structures into a wide range of model classes. Many commonly used approaches to fit a wide variety of potentially…