Related papers: Divisors computing the minimal log discrepancy on …
We use the theory of motivic integration for singular spaces to give a characterization of minimal log discrepencies in terms of the codimension of certain subsets of spaces of arcs. This is done for arbitrary pairs $(X,Y)$, with $X$ normal…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.
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…
In this largely-expository note, we describe a class of divisors on elliptic curves that index the inflection points of linear series arising (as subspaces of holomorphic sections) from line bundles on $\mathbb{P}^1$ via pullback along the…
We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a…
Minimal log discrepancies (mld's) are related not only to termination of log flips, and thus to the existence of log flips but also to the ascending chain condition (acc) of some global invariants and invariants of singularities in the Log…
We give asymptotic estimates for the mean number of divisors of integers without small prime factors, integers with bounded ratios of consecutive divisors, and for practical numbers. In the last case, this confirms a conjecture of…
In this book chapter we survey known approaches and algorithms to compute discrepancy measures of point sets. After providing an introduction which puts the calculation of discrepancy measures in a more general context, we focus on the…
We classify two-dimensional toric log germs in terms of their minimal log discrepancy.
Measuring device is proposed for determining a linear dimension. The device comprises three associated longitudinally moving parts one of which is a scale. The integer part of the device reading is being taken from the standard millimeter…
We prove that each divisorial contraction to a curve between terminal threefolds is a weighted blow-up under a suitable embedding. Moreover, we give a classification of the weighted blow-ups assuming that the curve is smooth.
Calculating and categorizing the similarity of curves is a fundamental problem which has generated much recent interest. However, to date there are no implementations of these algorithms for curves on surfaces with provable guarantees on…
This work provides a comprehensive exploration of various methods in solving incompressible flows using a projection method, and their relation to the occurrence and management of checkerboard oscillations. It employs an algebraic…
Inspired by the boolean discrepancy problem, we study the following optimization problem which we term \textsc{Spherical Discrepancy}: given $m$ unit vectors $v_1, \dots, v_m$, find another unit vector $x$ that minimizes $\max_i \langle x,…
We report a new type of drop instability, where the density difference between the drop and the solvent is negative. We show that the drop falls inside the solvent down to a minimum height, then fragmentation takes place and secondary…
In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute…
We use intersection theory, degeneration techniques and jet schemes to study log canonical thresholds. Our first result gives a lower bound for the log canonical threshold of a pair in terms of the log canonical threshold of the image by a…
The law of the iterated logarithm for discrepancies of geometric progressions with small ratios is proved.
This paper deals with the problem of soft guessing under log-loss distortion (logarithmic loss) that was recently investigated by [Wu and Joudeh, IEEE ISIT, pp. 466--471, 2023]. We extend this problem to soft guessing allowing errors, i.e.,…