Related papers: The minimal log discrepancy

Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…

We prove that many of the results of the LMMP hold for $3$-folds over fields of characteristic $p>5$ which are not necessarily perfect. In particular, the existence of flips, the cone theorem, the contraction theorem for birational extremal…

Hidden regular variation defines a subfamily of distributions satisfying multivariate regular variation on $\mathbb{E} = [0, \infty]^d \backslash \{(0,0, ..., 0) \} $ and models another regular variation on the sub-cone $\mathbb{E}^{(2)} =…

Event logs are widely used for anomaly detection and prediction in complex systems. Existing log-based anomaly detection methods usually consist of four main steps: log collection, log parsing, feature extraction, and anomaly detection,…

A common task in physics, information theory, and other fields is the analysis of properties of subsystems of a given system. Given the covariance matrix $M$ of a system of $n$ coupled variables, the covariance matrices of the subsystems…

We present here a unit-log-symmetric model based on the bivariate log-symmetric distribution. It is a flexible family of distributions over the interval $(0, 1)$. We then discuss its mathematical properties such as stochastic…

We discuss the log minimal model theory for log surfaces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the…

We study discrepancy minimization for vectors in $\mathbb{R}^n$ under various settings. The main result is the analysis of a new simple random process in multiple dimensions through a comparison argument. As corollaries, we obtain bounds…

The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…

In this paper we give a new point of view for optimizing the definitions related to the study of singularities of normal varieties, introduced in [dFH09] and further studied in [Urb12a] and [Urb12b], in relation to the Minimal Model…

We establish maximal trees and graphs for the difference of average distance and proximity proving thus the corresponding conjecture posed in [4]. We also establish maximal trees for the difference of average eccentricity and remoteness and…

Log-concave distributions include some important distributions such as normal distribution, exponential distribution and so on. In this note, we show inequalities between two Lp-norms for log-concave distributions on the Euclidean space.…

We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in $\mathbb{R}^d$. Our study covers both the case where the true underlying density is…

In this paper we study the regularity and the boundedness of the minima of two classes of functionals of the calculus of variations

As is well known, the "usual discrepancy" is defined for a normal Q-Gorenstein variety. By using this discrepancy we can define a canonical singularity and a log canonical singularity. In the same way, by using a new notion, Mather-Jacobian…

Let $M$ be a compact manifold of dimension at least 2. If $M$ admits a minimal homeomorphism then $M$ admits a minimal noninvertible map.

The statistical properties of local alignment algorithms with gaps are analyzed theoretically for uncorrelated and correlated DNA sequences. In the vicinity of the log-linear phase transition, the statistics of alignment with gaps is shown…

We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree…

The simple interpretation of the minimum distance of a linear code obtained by De Boer and Pellikaan, and later refined by the second author, is further developed through the study of various finitely generated graded modules. We use the…

The log-density method is a powerful algorithmic framework which in recent years has given rise to the best-known approximations for a variety of problems, including Densest-$k$-Subgraph and Bipartite Small Set Vertex Expansion. These…