Related papers: Canonical block-oriented model
Standard vision models treat objects as independent points in Euclidean space, unable to capture hierarchical structure like parts within wholes. We introduce Worldline Slot Attention, which models objects as persistent trajectories through…
Restricted Boltzmann Machines are generative models that consist of a layer of hidden variables connected to another layer of visible units, and they are used to model the distribution over visible variables. In order to gain a higher…
For $N$-coupled generalized time-dependent oscillators, primary invariants and a generalized invariant are found in terms of classical solutions. Exact quantum motions satisfying the Heisenberg equation of motion are also found. For number…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…
A common framework is provided that comprises classical ordinal item response models as the cumulative, sequential and adjacent categories models as well as nominal response models and item response tree models. The taxonomy is based on the…
Developing realistic and precise models of the electronic properties of organic molecular crystals is crucial for understanding the full range of strongly correlated phases that they exhibit. By using \textit{ab initio} model construction…
The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental…
For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between…
A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family…
We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…
Continuum mechanics can be formulated in the Lagrangian frame (addressing motion of individual continuum particles) or in the Eulerian frame (addressing evolution of fields in an inertial frame). There is a canonical Hamiltonian structure…
A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number…
In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deterministic parabolic equations defined in Euclidean space of…
The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…
The aim of this review is to present the list of by now a significant collection of quantum integrable models, ultralocal as well as nonultralocal, in a systematic way stressing on their underlying unifying algebraic structures. We restrict…
The canonical-type connection on the almost contact manifolds with B-metric is constructed. It is proved that its torsion is invariant with respect to a subgroup of the general conformal transformations of the almost contact B-metric…
Computer vision tasks such as image classification, image retrieval and few-shot learning are currently dominated by Euclidean and spherical embeddings, so that the final decisions about class belongings or the degree of similarity are made…
Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…
We define parafermionic observables in various lattice loop models, including examples where no Kramers-Wannier duality holds. For a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these…