相关论文: Gaps of saddle connection directions for some bran…

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [2] of this work we established that agents cluster around a network…

A translation surface is a surface formed by identifying edges of a collection of polygons in the complex plane that are parallel and of equal length using only translations. We determined that the same circle packing can be realized on…

In this survey we present an extensive research of the vast literature about the Generalized Lambda Distribution (GLD) and propose a hurdle, or two-way, model whose associated distribution is the GLD in order to meet the demand for a highly…

We propose a simple generalization of Schnyder woods from the plane to maps on orientable surfaces of higher genus. This is done in the language of angle labelings. Generalizing results of De Fraysseix and Ossona de Mendez, and Felsner, we…

Techniques are developed for exploring the complete space of intersecting brane models on an orientifold. The classification of all solutions for the widely-studied T^6/Z_2 x Z_2 orientifold is made possible by computing all combinations of…

We study the translation surfaces obtained by considering the unfoldings of the surfaces of Platonic solids. We show that they are all lattice surfaces and we compute the topology of the associated Teichm\"uller curves. Using an algorithm…

Oriented loops on an orientable surface are, up to equivalence by free homotopy, in one-to-one correspondence with the conjugacy classes of the surface's fundamental group. These conjugacy classes can be expressed (not uniquely in the case…

We investigate specific examples of locally-defined real vector-fields on strata of translation surfaces. Integrating SL(2,R)-loci of Veech surfaces along these vector-fields yield interesting new examples of horocyle-invariant ergodic…

In 1986, Oliver Pretzel studied the set of orientations of a connected finite graph $G$ and showed that any two such orientations having the same flow-difference around all closed loops can be obtained from one another by a succession of…

Flat surfaces that correspond to $k$-differentials on compact Riemann surfaces are of finite area provided there is no pole of order $k$ or higher. We denote by \textit{flat surfaces with poles of higher order} those surfaces with flat…

We apply score-based diffusion models to two-dimensional SU(2) lattice pure gauge theory with the Wilson action, extending recent work on U(1) gauge theories. The SU(2) manifold structure is handled through a quaternion parameterization.…

In translation surfaces of finite area (corresponding to holomorphic differentials), directions of saddle connections are dense in the unit circle. On the contrary, saddle connections are fewer in translation surfaces with poles…

We survey the use of dynamics of $SL(2, \R)$-actions to understand gap distributions for various sequences of subsets of $[0, 1)$, particularly those arising from special trajectories of various two-dimensional dynamical systems. We state…

Dilation surfaces are generalizations of translation surfaces where the geometric structure is modelled on the complex plane up to affine maps whose linear part is real. They are the geometric framework to study suspensions of affine…

The distributed setting for Saddle Problems (SPs) has recently emerged as a framework for various modern applications in machine learning and multiagent systems. Despite its relevance, the theoretical foundations of this setting have not…

We consider circles on a translation surface $X$, consisting of points joined to a common center point by a geodesic of length $R$. We show that as $R \to \infty$ these circles distribute to a measure on $X$ which is equivalent to the area.…

We consider distinguishing between two distribution tail models when tails of one model are lighter (or heavier) than those of the other. Two procedures are proposed: one scale-free and one location- and scale-free, and their asymptotic…

We consider various two-leg ladder models exhibiting gapped phases. All of these phases have short-ranged valence bond ground states, and they all exhibit string order. However, we show that short-ranged valence bond ground states divide…

Let $\Gamma < G$ be an arithmetic lattice in a noncompact connected semisimple real algebraic group. For many such $G$ of rank at most $2$, in particular $G = \operatorname{SL}_3(\mathbb R)$, we prove effective equidistribution of large…

We consider the tail distribution of the edge cover time of a specific non-Markov process, $\delta$ once-reinforced random walk, on finite connected graphs, whose transition probability is proportional to weights of edges. Here the weights…