Related papers: Fano schemes of generic intersections and machine …
We compute the quantum Euler class of Fano complete intersections X in a projective space. In particular, we prove a recent conjecture of A. Buch and R. Pandharipande. Finally we apply our result to obtain formulas for the virtual Tevelev…
We propose a new probabilistic programming language for the design and analysis of perception systems, especially those based on machine learning. Specifically, we consider the problems of training a perception system to handle rare events,…
We propose an analogue of Dubrovin's conjecture for the case where Fano manifolds have quantum connections of exponential type. It includes the case where the quantum cohomology rings are not necessarily semisimple. The conjecture is…
We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields of arbitrary characteristic. Our results imply that unirational parametrizations of most Fano hypersurfaces need to have enormously…
Understanding how nano- or micro-scale structures and material properties can be optimally configured to attain specific functionalities remains a fundamental challenge. Photonic metasurfaces, for instance, can be spectrally tuned through…
Standard clustering techniques assume a common configuration for all features in a dataset. However, when dealing with multi-view or longitudinal data, the clusters' number, frequencies, and shapes may need to vary across features to…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
The Fano resonance is a widespread wave scattering phenomenon associated with a peculiar asymmetric and ultra-sharp line shape, which has found applications in a large variety of prominent optical devices. While its substantial sensitivity…
The idea of a finite collection of closed sets having "strongly regular intersection" at a given point is crucial in variational analysis. We show that this central theoretical tool also has striking algorithmic consequences. Specifically,…
This work studies the problem of learning under both large datasets and large-dimensional feature space scenarios. The feature information is assumed to be spread across agents in a network, where each agent observes some of the features.…
We investigate within a coarse-grained model the conditions leading to the appearance of Fano resonances or anti-resonances in the conductance spectrum of a generic molecular junction with a side group (T-junction). By introducing a simple…
For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs…
Recently supervised machine learning has been ascending in providing new predictive approaches for chemical, biological and materials sciences applications. In this Perspective we focus on the interplay of machine learning algorithm with…
Motivation: Sequence mapping is the cornerstone of modern genomics. However, most existing sequence mapping algorithms are insufficiently general. Results: We introduce context schemes: a method that allows the unambiguous recognition of a…
Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…
Congruences, or $2$-parameter families of lines in $3$-space are of interest in many situations, in particular in geometric optics. In this paper we consider elements of their geometry which are invariant under affine changes of…
The knowledge that data lies close to a particular submanifold of the ambient Euclidean space may be useful in a number of ways. For instance, one may want to automatically mark any point far away from the submanifold as an outlier or to…
We consider seven fundamental properties of cellular embeddings of graphs in compact surfaces, and show that each property can be associated with a point of the Fano plane $F$, in such a way that allowable combinations of properties…
We study the probability that an $(n - m)$-dimensional linear subspace in $\mathbb{P}^n$ or a collection of points spanning such a linear subspace is contained in an $m$-dimensional variety $Y \subset \mathbb{P}^n$. This involves a strategy…
A visual system has to learn both which features to extract from images and how to group locations into (proto-)objects. Those two aspects are usually dealt with separately, although predictability is discussed as a cue for both. To…