相关论文: A simpler way of imposing simplicity constraints

The Barrett-Crane model for the SO(4,C) general relativity is systematically derived. This procedure makes rigorous the calculation of the Barrett-Crane intertwiners from the Barrett-Crane constraints of both real and complex Riemannian…

Monte Carlo algorithms are barely considered in spin foam quantum gravity. Due to the quantum nature of spin foam amplitudes one cannot readily apply them, and the present sign problem is a threat to convergence and thus efficiency. Yet,…

We formulate the spin foam representation of discrete SU(2) gauge theory as a product of vertex amplitudes each of which is the spin network generating function of the boundary graph dual to the vertex. In doing so the sums over spins have…

Experimental limits on supersymmetry and similar theories are difficult to set because of the enormous available parameter space and difficult to generalize because of the complexity of single points. Therefore, more phenomenological,…

The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…

Probabilistic graphical models compactly represent joint distributions by decomposing them into factors over subsets of random variables. In Bayesian networks, the factors are conditional probability distributions. For many problems, common…

Diffusion models struggle to produce samples that respect constraints, a common requirement in scientific applications. Recent approaches have introduced regularization terms in the loss or guidance methods during sampling to enforce such…

Spin foam models for gravity or BF theory can be constructed by path integral formulation of the classical discrete models formulated on simplicial manifolds. Using this, we discuss the rigorous construction of Lorentzian spin foam models…

An attractive mechanism to specify global constraints in rostering and other domains is via formal languages. For instance, the Regular and Grammar constraints specify constraints in terms of the languages accepted by an automaton and a…

Deep neural networks exhibit a simplicity bias, a well-documented tendency to favor simple functions over complex ones. In this work, we cast new light on this phenomenon through the lens of the Minimum Description Length principle,…

We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the…

Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian…

We study perturbation theory for spin foam models on triangulated manifolds. Starting with any model of this sort, we consider an arbitrary perturbation of the vertex amplitudes, and write the evolution operators of the perturbed model as…

In this paper we present a new approach to modeling finite set domain constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We show that it is possible to construct an efficient set domain propagator which compactly…

We provide the Barrett-Crane spin foam model for quantum gravity with a discrete action principle, consisting in the usual BF term with discretized simplicity constraints which in the continuum turn topological BF theory into gravity. The…

We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…

Numerical analysis has no satisfactory method for the more realistic optimization models. However, with constraint programming one can compute a cover for the solution set to arbitrarily close approximation. Because the use of constraint…

We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…

Fefferman-Graham ambient construction can be formulated as $\mathfrak{sp}(2)$-algebra relations on three Hamiltonian constraint functions on ambient space. This formulation admits a simple extension that leads to higher-spin fields, both…

Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon Sowa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given…