Related papers: Cartesian Frames
Modern order and lattice theory provides convenient mathematical tools for pattern mining, in particular for condensed irredundant representations of pattern spaces and their efficient generation. Formal Concept Analysis (FCA) offers a…
Active inference is a mathematical framework for understanding how agents (biological or artificial) interact with their environments, enabling continual adaptation and decision-making. It combines Bayesian inference and free energy…
The intent of control argumentation frameworks is to specifically model strategic scenarios from the perspective of an agent by extending the standard model of argumentation framework in a way that takes unquantified uncertainty regarding…
Simulation is widely used to make model-based predictions, but few approaches have attempted this technique in dynamic physical environments of medium to high complexity or in general contexts. After an introduction to the cognitive science…
Cai et al. have recently proposed change structures as a semantic framework for incremental computation. We generalise change structures to arbitrary cartesian categories and propose the notion of change action model as a categorical model…
We introduce Forecasting Argumentation Frameworks (FAFs), a novel argumentation-based methodology for forecasting informed by recent judgmental forecasting research. FAFs comprise update frameworks which empower (human or artificial) agents…
Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel…
Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…
We propose an alternative and unifying framework for decision-making that, by using quantum mechanics, provides more generalised cognitive and decision models with the ability to represent more information than classical models. This…
We introduce probabilistic frames to study finite frames whose elements are chosen at random. While finite tight frames generalize orthonormal bases by allowing redundancy, independent, uniformly distributed points on the sphere…
The Polymorphic Combinatorial Framework (PCF) leverages Large Language Models (LLMs) and mathematical frameworks to guide the meta-prompt enabled design of solution spaces and adaptive AI agents for complex, dynamic environments. Unlike…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
Multi-agent models are a suitable starting point to model complex social interactions. However, as the complexity of the systems increase, we argue that novel modeling approaches are needed that can deal with inter-dependencies at different…
A single quantum system, such as a hydrogen atom, can transmit a Cartesian coordinate frame (three axes). For this it has to be prepared in a superposition of states belonging to different irreducible representations of the rotation group.…
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the…
Organization concepts and models are increasingly being adopted for the design and specification of multi-agent systems. Agent organizations can be seen as mechanisms of social order, created to achieve global (or organizational) objectives…
We introduce matrix and its block to the Dung's theory of argumentation frameworks. It is showed that each argumentation framework has a matrix representation, and the common extension-based semantics of argumentation framework can be…
In this paper, we present a novel general framework grounded in the factor graph theory to solve kinematic and dynamic problems for multi-body systems. Although the motion of multi-body systems is considered to be a well-studied problem and…
Rational agents acting as observers use ``knowables'' to construct a vision of the outside world. Thereby, they are bound by the information exchanged with what they consider to be objects. The cartesian cut or, in modern terminology, the…
Financial structures such as securitisations, insurance contracts, and other hierarchical claims systems can be interpreted as deterministic allocation mechanisms acting on stochastic inflow processes. This paper develops a general…