Publications related to Cross-Intersecting Families of Vectors

Additive and geometric transversality of fractal sets in the integers

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

2024

The Domestic Turn: Politics of Education from New College to The Palazzo Della Sapienza

Marson Korbi

Student accommodation became a problem only a century after the foundation of the first universities in Europe in the 12th century. At the very beginning students had to provide their own lodgings autonomously. In many university cities the situation prove ...

2023

Moments of the number of points in a bounded set for number field lattices

Maryna Viazovska, Vlad Serban, Nihar Prakash Gargava

We examine the moments of the number of lattice points in a fixed ball of volume

V

for lattices in Euclidean space which are modules over the ring of integers of a number field

K

. In particular, denoting by

ω_K

the number of roots of unity in

K

, we ...

arXiv2023

Generative power of a protein language model trained on multiple sequence alignments

Anne-Florence Raphaëlle Bitbol, Umberto Lupo, Damiano Sgarbossa

Computational models starting from large ensembles of evolutionarily related protein sequences capture a representation of protein families and learn constraints associated to protein structure and function. They thus open the possibility for generating no ...

eLIFE SCIENCES PUBL LTD2023

Diversity of radial spin textures in chiral materials

Oleg Yazyev, Daniel Gosalbez Martinez, Alberto Crepaldi

We introduce a classification of the radial spin textures in momentum space that emerge at the high-symmetry points in crystals characterized by nonpolar chiral point groups (D2, D3, D4, D6, T, O). Based on the symmetry constraints imposed by these point g ...

College Pk2023

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

Haoqi Wang, Zhigang Li

We generalize the class vectors found in neural networks to linear subspaces (i.e., points in the Grassmann manifold) and show that the Grassmann Class Representation (GCR) enables simultaneous improvement in accuracy and feature transferability. In GCR, e ...

Ieee Computer Soc2023

ON THE INDEPENDENCE NUMBER OF INTERSECTION GRAPHS OF AXIS-PARALLEL SEGMENTS

Jana Tabea Cslovjecsek

We prove that for any triangle-free intersection graph of n axis-parallel line segments in the plane, the independence number alpha of this graph is at least alpha n/4+ohm(root n). We complement this with a construction of a graph in this class satisfying ...

Ottawa2023

Overflow-free compute memories for edge AI acceleration

David Atienza Alonso, Giovanni Ansaloni, Alexandre Sébastien Julien Levisse, Marco Antonio Rios, Flavio Ponzina

Compute memories are memory arrays augmented with dedicated logic to support arithmetic. They support the efficient execution of data-centric computing patterns, such as those characterizing Artificial Intelligence (AI) algorithms. These architectures can ...

2023

On the Use of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytical Functions for the Calculation of Infinite Sums and the Analysis of Zeroes of Analytical Functions

Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calcul ...

MDPI2023

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

Cross-Intersecting Families of Vectors

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Additive and geometric transversality of fractal sets in the integers

The Domestic Turn: Politics of Education from New College to The Palazzo Della Sapienza

Moments of the number of points in a bounded set for number field lattices

Generative power of a protein language model trained on multiple sequence alignments

Diversity of radial spin textures in chiral materials

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

ON THE INDEPENDENCE NUMBER OF INTERSECTION GRAPHS OF AXIS-PARALLEL SEGMENTS

Overflow-free compute memories for edge AI acceleration

On the Use of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytical Functions for the Calculation of Infinite Sums and the Analysis of Zeroes of Analytical Functions

Fourier non-uniqueness sets from totally real number fields

The Domestic Turn: Politics of Education from New College to The Palazzo Della Sapienza

Generative power of a protein language model trained on multiple sequence alignments

Fourier non-uniqueness sets from totally real number fields

Additive and geometric transversality of fractal sets in the integers

Moments of the number of points in a bounded set for number field lattices

Get the Best of Both Worlds: Improving Accuracy and Transferability by Grassmann Class Representation

Diversity of radial spin textures in chiral materials

ON THE INDEPENDENCE NUMBER OF INTERSECTION GRAPHS OF AXIS-PARALLEL SEGMENTS

Overflow-free compute memories for edge AI acceleration

On the Use of the Generalized Littlewood Theorem Concerning Integrals of the Logarithm of Analytical Functions for the Calculation of Infinite Sums and the Analysis of Zeroes of Analytical Functions