Related papers: Dimensional analysis using toric ideals
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
As a preparation for its quantization in the loop formalism, the 2-dimensional gravitation model of Jackiw and Teitelboim is analysed in the classical canonical formalism. The dynamics is of pure constraints as it is well-known. A partial…
We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…
The semiclassical regime of 2D static Dirac matter is obtained from the Dirac equation in curved space-time. To simplify the formulation, the Cartesian space-time geometry parametrization is transformed to isothermal coordinates using…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
A recent development in extreme value modeling uses the geometry of the dataset to perform inference on the multivariate tail. A key quantity in this inference is the gauge function, whose values define this geometry. Methodology proposed…
There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and…
We find the minimal number of independent preparations and measurements certifying the dimension of a classical or quantum system limited to $d$ states, optionally reduced to the real subspace. As a dimension certificate, we use the linear…
Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards…
This paper presents a novel theoretical framework for reducing the computational complexity of multi-model adaptive control/estimation systems through systematic transformation to controllable canonical form. While traditional multi-model…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
A generic massive Thirring Model in three space-time dimensions exhibits a correspondence with a topologically massive bosonized gauge action associated to a self-duality constraint, and we write down a general expression for this…
This paper introduces dimensional analysis in Non-Destructive Testing & Evaluation (NDT&E) problems. This is the first time that this approach is adopted in the framework of NDT&E, and the paper opens to the development of probes and…
We derive and analyze the perturbation series for the classical effective action in quantum statistical mechanics, treated as a toy model for the dimensionally reduced effective action in quantum field theory at finite temperature. The…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
An iterative computer-aided ideation procedure is introduced, building on recent quality-diversity algorithms, which search for diverse as well as high-performing solutions. Dimensionality reduction is used to define a similarity space, in…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
A machine learning technique is proposed for quantifying uncertainty in power system dynamics with spatiotemporally correlated stochastic forcing. We learn one-dimensional linear partial differential equations for the probability density…
Solutions to scalar theories with derivative self-couplings often have regions where non-linearities are important. Given a classical source, there is usually a region, demarcated by the Vainshtein radius, inside of which the classical…
The design of an electrical machine can be quantified and evaluated by Key Performance Indicators (KPIs) such as maximum torque, critical field strength, costs of active parts, sound power, etc. Generally, cross-domain tool-chains are used…