Related papers: Symmetry within and between solutions
We demonstrate an unsuspected freedom in physics, by showing an essential unpredictability in the relation between the behavior of clocks on the workbench and explanations of that behavior written in symbols on the blackboard. In theory,…
Many computational problems are unchanged under some symmetry operation. In classical machine learning, this can be reflected with the layer structure of the neural network. In quantum machine learning, the ansatz can be tuned to correspond…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
Consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter and galaxy overdensities can be obtained, both in real and redshift space, thanks to the symmetries enjoyed by the Newtonian equations of…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
Selected applications of symmetry methods in the atmospheric sciences are reviewed briefly. In particular, focus is put on the utilisation of the classical Lie symmetry approach to derive classes of exact solutions from atmospheric models.…
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and on the lattice. They take solutions into solutions and can be…
It has recently been argued that AI models' representations are becoming aligned as their scale and performance increase. Empirical analyses have been designed to support this idea and conjecture the possible alignment of different…
Symmetry breaking in two-dimensional layered materials plays a significant role in their macroscopic electrical, optical, magnetic and topological properties, including but not limited to spin-polarization effects, valley-contrasting…
A symmetry is a `change without change'. As simple as it sounds, this concept is the fundamental cornerstone that unifies all branches of theoretical physics. Virtually all physical laws -- ranging from classical mechanics and…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
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 apply thermodynamics method to generate exact solution with maximum symmetric surface for Einstein equation without solving it. The exact solutions are identified with which people have solved before. The horizons structure of solutions…
Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mirror symmetry} or \emph{Homological mirror symmetry} can be…
In this paper we review two symmetry axioms of special relativity and their connections to each other together with their role in some famous predictions of relativity theory, such as time dilation, length contraction, and the twin paradox.…
Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and…
The established way of looking at special relativity is based on Einstein postulates: the principle of relativity and the constancy of the velocity of light. In the most general geometric approach to the theory of special relativity, the…
Einstein's Equivalence Principle is used with the electromagnetic spectrum to translate meters and seconds into radians and seconds. Based on a unique geometric relationship, a new transformation of velocities and a changed Lorentz…
Galilean symmetry is the natural symmetry of inertial motion that underpins Newtonian physics. Although rigid-body symmetry is one of the most established and fundamental tools in robotics, there appears to be no comparable treatment of…