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A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatorially finite, cancellative, commutative monoids to be…
We classify Fano threefolds with only terminal singularities whose canonical class is Cartier and divisible by 2, and satisfying an additional assumption that the $G$-invariant part of the Weil divisor class group is of rank 1 with respect…
Few-shot, fine-grained classification requires a model to learn subtle, fine-grained distinctions between different classes (e.g., birds) based on a few images alone. This requires a remarkable degree of invariance to pose, articulation and…
Mixtures of Mallows models are a popular generative model for ranking data coming from a heterogeneous population. They have a variety of applications including social choice, recommendation systems and natural language processing. Here we…
We determine the groups of minimal order in which all groups of order n can embedded for 1 < n < 16. We further determine the order of a minimal group in which all groups or order n or less can be embedded, also for 1 < n < 16.
Consider a primitive polynomial $f$ in two variables, thought of as a map from the affine plane to the affine line. We study the minimimal compactification of $f$; from our result one deduces in particular that if one of the fibers of $f$…
Few-shot learning has attracted intensive research attention in recent years. Many methods have been proposed to generalize a model learned from provided base classes to novel classes, but no previous work studies how to select base…
We present consistent algorithms for multiclass learning with complex performance metrics and constraints, where the objective and constraints are defined by arbitrary functions of the confusion matrix. This setting includes many common…
Calculations of the number of equivalence classes of Sudoku boards has to this point been done only with the aid of a computer, in part because of the unnecessarily large symmetry group used to form the classes. In particular, the…
We study surface representatives of homology classes of finite complexes which minimize certain complexity measures, including its genus and Euler characteristic. Our main result is that up to surgery at nullhomotopic curves minimizers are…
We answer the question which conjunctive queries are uniquely characterized by polynomially many positive and negative examples, and how to construct such examples efficiently. As a consequence, we obtain a new efficient exact learning…
The problem of computing a representation for a real polynomial as a sum of minimum number of squares of polynomials can be casted as finding a symmetric positive semidefinite real matrix (Gram matrix) of minimum rank subject to linear…
Two matrices are said to be principal minor equivalent if they have equal corresponding principal minors of all orders. We give a characterization of principal minor equivalence and a deterministic polynomial time algorithm to check if two…
A consistent exposition of the arguments and constructions of the method of maximal singularities, the aim of which is to describe birational iso/automorphisms of Fano varieties and Fano fibrations. The principal elements of the method are…
We give lower bounds for the degree of the discriminant with respect to y of separable polynomials f in K[x,y] over an algebraically closed field of characteristic zero. Depending on the invariants involved in the lower bound, we give a…
We describe an algorithm, implemented in Python, which can enumerate any permutation class with polynomial enumeration from a structural description of the class. In particular, this allows us to find formulas for the number of permutations…
With an easily applicable criterion based on permutation symmetries of (identically prepared) replicas of quantum states we identify distinct entanglement classes in high-dimensional multi- partite systems. The different symmetry properties…
Chains of minimal degree rational curves have been used as an important tool in the study of Fano manifolds. Their own geometric properties, however, have not been studied much. The goal of the paper is to introduce an infinitesimal method…
We classify all wormhole singularities, i.e. cyclic quotient surface singularities admitting at least two extremal P-resolutions, thereby solving an open problem posed by Urz\'ua. Our approach introduces a new combinatorial framework based…
The category $\bcalNT$ was defined in \cite{Lobos2}, it is a category whose objects are commutative nil graded algebras over a field, defined by presentation encoded by triangular matrices. A natural problem related to this category is to…