Related papers: Breaking Symmetry with Different Orderings
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a provably deterministic polynomial-time algorithm to accomplish…
A characterization of the symmetry algebra of the $n$th order ordinary differential equations (ODEs) with maximal symmetry and all third order linearizable ODEs is given. This is used to show that such an algebra $\mathfrak{g}$ determines…
Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…
Gravitational properties of a hedge-hog type topological defect in two extra dimensions are considered in General Relativity employing a vector as the order parameter. All previous considerations were done using the order parameter in the…
Using symmetry as an inductive bias in deep learning has been proven to be a principled approach for sample-efficient model design. However, the relationship between symmetry and the imperative for equivariance in neural networks is not…
We present a new approach to termination analysis of logic programs. The essence of the approach is that we make use of general orderings (instead of level mappings), like it is done in transformational approaches to logic program…
When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints…
Models of spontaneous breaking of electroweak symmetry by a strong interaction do not have fine tuning/hierarchy problem. They are conceptually elegant and use the only mechanism of spontaneous breaking of a gauge symmetry that is known to…
An algorithm for solving first order ODEs, by systematically determining symmetries of the form [ xi = F(x), eta = P(x) y + Q(x) ], where xi d/dx + eta d/dy is the symmetry generator - is presented. To these {\it linear} symmetries one can…
A combinatorial Gray code for a set of combinatorial objects is a sequence of all combinatorial objects in the set so that each object is derived from the preceding object by changing a small part. In this paper we design a Gray code for…
Graph-structured data is central to many scientific and industrial domains, where the goal is often to optimize objectives defined over graph structures. Given the combinatorial complexity of graph spaces, such optimization problems are…
Contrary to canonical expectations we show that lattice translational symmetry breaking often accompanies uniformly ordered flux phases. We demonstrate this phenomena by studying a spinless-fermion model on a square latttice with…
Diagram chasing is not an easy task. The coherence holds in a generalized sense if we have a mechanical method to judge whether given two morphisms are equal to each other. A simple way to this end is to reform a concerned category into a…
We propose a novel ray reordering technique to accelerate the ray tracing process by encoding and sorting rays prior to traversal. Instead of spatial coordinates, our method encodes rays according to the cuts of the hierarchical…
The goal of inductive logic programming is to search for a hypothesis that generalises training data and background knowledge. The challenge is searching vast hypothesis spaces, which is exacerbated because many logically equivalent…
We present a new solution to the Hierarchy Problem utilizing non-linearly realized discrete symmetries. The cancelations occur due to a discrete symmetry that is realized as a shift symmetry on the scalar and as an exchange symmetry on the…
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…
The solution of a class of third order ordinary differential equations possessing two parameter Lie symmetry group is obtained by group theoretic means. It is shown that reduction to quadratures is possible according to two scenarios: 1) if…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…