Related papers: Asymmetry in repeated isotropic rotations
Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…
Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted…
We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e.,…
We analytically compute asymptotic expansions of a 1-dimensional sub-manifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us…
We revisit the geometrical meaning of statistical isotropy that is manifest in excursion sets of smooth random fields in two dimensions. Using the contour Minkowski tensor, $\W_1$, as our basic tool we first examine geometrical properties…
A number of physical systems exhibit a particular form of asymptotic conformal invariance: within a particular range of distances, they are characterized by a long-range conformal interaction (inverse square potential), the absence of…
We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…
This work provides a comprehensive theoretical framework for understanding the symmetry properties of High-Resolution NMR spectra. We analyze the conditions under which a spectrum exhibits mirror symmetry (palindromicity). We demonstrate…
Instead of the conventional construction of symmetric and antisymmetric states by abruptly projecting with the symmetrizer or antisymmetrizer, this paper investigates rapid but continuous symmetrization via environment-induced decoherence.…
Due to common architecture designs, symmetries exist extensively in contemporary neural networks. In this work, we unveil the importance of the loss function symmetries in affecting, if not deciding, the learning behavior of machine…
We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…
The probability that two randomly selected phylogenetic trees of the same size are isomorphic is found to be asymptotic to a decreasing exponential modulated by a polynomial factor. The number of symmetrical nodes in a random phylogenetic…
The incompressible three-dimensional Euler equations develop very thin pancake-like regions of exponentially increasing vorticity. The characteristic thickness of such regions decreases exponentially with time, while the other two…
This paper proposes parametric and non-parametric hypothesis testing algorithms for detecting anisotropy -- rotational variance of the covariance function in random fields. Both algorithms are based on resampling mechanisms, which enable…
An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in spectra, ground state spins and isospins is discovered in both odd and even-particle systems. Various types…
Independently trained transformers compute the same function in residual-stream bases that differ by a uniform random rotation on $\mathrm{SO}(d_{\mathrm{model}})$. We call this phenomenon polymorphism: same function, mutually…
Rotating axisymmetric objects amplify incoming waves by superradiant scattering. When enclosed in a cavity, the repeated interaction of a confined field with the object may trigger superradiant instabilities. Rotating binaries are…
These notes describe several loop soup models and their {\it universal behaviour} in dimensions greater or equal to 3. These loop models represent certain classical or quantum statistical mechanical systems. These systems undergo phase…
Quasiconformal maps in the plane are orientation preserving homeomorphisms that satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses of bounded eccentricity. Such maps have many useful geometric distortion…
Rotational smoothing is a phenomenon consisting in a gain of regularity by means of averaging over rotations. This phenomenon is present in operators that regularize only in certain directions, in contrast to operators regularizing in all…