相关论文: Sources of log canonical centers
The matrix of canonical differential equations consists of the 1-$\mathrm{d}\log$-form coefficients obtained by projecting ($n$+1)-$\mathrm{d}\log$-forms onto $n$-$\mathrm{d}\log$-form master integrands. With dual form in relative…
In classical canonical correlation analysis (CCA), the goal is to determine the linear transformations of two random vectors into two new random variables that are most strongly correlated. Canonical variables are pairs of these new random…
We show that if a divisor centered over a point on a smooth surface computes a minimal log discrepancy, then the divisor also computes a log canonical threshold. To prove the result, we study the asymptotic log canonical threshold of the…
Focal loss has recently gained significant popularity, particularly in tasks like object detection where it helps to address class imbalance by focusing more on hard-to-classify examples. This work proposes the focal loss as a distortion…
Sidon sequences and their generalizations have found during the years and especially recently various applications in coding theory. One of the most important applications of these sequences is in the connection of synchronization patterns.…
We describe the set of minimal log discrepancies of toric log varities, and study its accumulation points.
Canonical Correlation Analysis (CCA) has been widely applied to jointly embed multiple views of data in a maximally correlated latent space. However, the alignment between various data perspectives, which is required by traditional…
Let a cluster be a term with a number of patterns occurring in it. We give two accounts of clusters, a geometric one as sets of (node and edge) positions, and an inductive one as pairs of terms with gaps (2nd order variables) and…
Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant…
A system of transformations is associated to a rational point on an elliptic curve. The sequence entropy is connected to the canonical height, and in some cases there is a canonically defined quotient system whose entropy is the canonical…
This is an introduction to cluster algebras and their common triangular bases. These bases are Kazhdan-Lusztig-type and serve as the canonical bases of cluster algebras from the representation-theoretic point of view. We review seeds…
We consider the union of certain irreducible components of cohomological support loci of the canonical bundle, which we call standard. We prove a structure theorem about them and single out some particular cases, recovering and improving…
We show the existence of canonical heights of subvarieties for bounded sequences of morphisms and give some applications.
Two important aspects of semantic parsing for question answering are the breadth of the knowledge source and the depth of logical compositionality. While existing work trades off one aspect for another, this paper simultaneously makes…
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…
It is known that the set of log canonical thresholds (lcts) on any varieties with fixed dimension satisfies the ascending chain condition. Inspired by the foliated minimal model program, it is intriguing to study the foliated version of…
We describe a simple probabilistic method to cross-identify astrophysical sources from different catalogs and provide the probability that a source is associated with a source from another catalog or that it has no counterpart. When the…
We establish the minimal model theory for normal pairs along log canonical locus in the complex analytic setting. This is the complex analytic analog of the previous result by the author.
We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by…
We propose several properties of elliptic lifts of the $K$-theoretic canonical bases for conical symplectic resolutions defined in our previous work. As an example, we construct elliptic lifts of canonical bases for the Hilbert scheme of…