相关论文: The set of toric minimal log discrepancies

Let $\mathcal C\subset(0,1]$ be a set satisfying the descending chain condition. We show that any accumulation point of volumes of log canonical surfaces $(X, B)$ with coefficients in $\mathcal C$ can be realized as the volume of a log…

In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…

We introduce the notion of generalized MR log canonical surfaces and establish the minimal model theory for generalized MR log canonical surfaces in full generality.

We give asymptotic estimates of the variance of the number of integer points in translated thin annuli in any dimension.

This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties and the algebraic moment map. In particular,…

In a previous work, we described the Minimal Model Program in the family of $\Qbb$-Gorenstein projective horospherical varieties, by studying certain continuous changes of moment polytopes of polarized horospherical varieties. Here, we…

Entropic regularization is a method for large-scale linear programming. Geometrically, one traces intersections of the feasible polytope with scaled toric varieties, starting at the Birch point. We compare this to log-barrier methods, with…

One limitation on the performance of optical traps is the noise inherently present in every setup. Therefore, it is the desire of most experimentalists to minimize and possibly eliminate noise from their optical trapping experiments. A step…

We describe a class of affine toric varieties $V$ that are set-theoretically minimally defined by codim $V+1$ binomial equations over fields of any characteristic.

We view difference algebra as the study of algebraic objects in the topos of difference sets. The methods of topos theory and categorical logic enable us to develop difference homological algebra, identify a solid foundation for difference…

In this paper relations among some kinds of cumulative entropies and moments of order statistics are presented. By using some characterizations and the symmetry of a non negative and absolutely continuous random variable X, lower and upper…

The smooth fixed volume discrepancy in the periodic case is studied here. It is proved that the Frolov point sets adjusted to the periodic case have optimal in a certain sense order of decay of the smooth periodic discrepancy. The upper…

We study the fluctuations of ergodic sums using global and local specifications on periodic points. We obtain Lindeberg-type central limit theorems in both situations. As an application, when the system possesses a unique measure of maximal…

In this paper directional derivative sets and differentials of a given set valued map are studied. Relations between the set valued map and compact subsets of the directional derivative sets of the given map are investigated. Upper and…

The idea of slicing divergences has been proven to be successful when comparing two probability measures in various machine learning applications including generative modeling, and consists in computing the expected value of a `base…

Continuous interpolation of real-valued data is characterized by piecewise monotone functions on a compact metric space. Topological total variation of piecewise monotone function f:X->R is a homeomorphism-invariant generalization of 1D…

This paper generalizes sofic entropy theory, in both the topological and measure-theory settings, to actions of locally compact groups. We prove invariance under topological and measure conjugacy of these entropies and establish the…

The smallest deformation of the minimal model M(2,3) that can accommodate Cardy's derivation of the percolation crossing probability is presented. It is shown that this leads to a consistent logarithmic conformal field theory at c=0. A…

We detect, by using symplectic topology, invariant measures with large rotation vectors for a class of Hamiltonian flows.

Mixed $f$-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions and establish some of their properties. Among them are…