Cross-Intersecting Families of Vectors

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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 ...

We initiate the study of certain families of L-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values L( 2 1 , chi a )L( 21 , chi b ) for arbitrary ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

A polyhedral graph is a 3-connected planar graph. We find the least possible order p(k, a) of a polyhedral graph containing a k-independent set of size a for all positive integers k and a. In the case k =1 and a even, we prove that the extremal graphs are ...

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 ...

Inspired by the work of Lang-Trotter on the densities of primes with fixed Frobenius traces for elliptic curves defined over Q and by the subsequent generalization of Cojocaru-Davis-Silverberg-Stange to generic abelian varieties, we study the analogous que ...

In this paper we investigate pointed (q, g, n)-Boltzmann loop-decorated maps with loops traversing only inner triangular faces. Using peeling exploration Budd (2018) modified to this setting we show that its law in the non-generic critical phase can be cod ...

Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in substructured for ...

We use birational geometry to show that the existence of rational points on proper rationally connected varieties over fields of characteristic 0 is a consequence of the existence of rational points on terminal Fano varieties. We discuss several consequenc ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

We discuss some properties of generative models for word embeddings. Namely, (Arora et al., 2016) proposed a latent discourse model implying the concentration of the partition function of the word vectors. This concentration phenomenon led to an asymptotic ...

We study Byzantine collaborative learning, where n nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and f < n nodes can behave arbitrarily. We prove that collaborati ...

Computational protein design has emerged as a powerful tool capable of identifying sequences compatible with pre-defined protein structures. The sequence design protocols, implemented in the Rosetta suite, have become widely used in the protein engineering ...

We provide an introduction to Gaussian process regression (GPR) machinelearning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of in ...

Conformal field theory lies at the heart of two central topics in theoretical high energy physics: the study of quantum gravity and the mapping of quantum field theories through the renormalization group. In this thesis we explore a technique to study conf ...

Cross-Intersecting Families of Vectors

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Additive and geometric transversality of fractal sets in the integers

Toroidal families and averages of L-functions, I

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

Independence numbers of polyhedral graphs

Fourier non-uniqueness sets from totally real number fields

The Lang-Trotter conjecture for products of non-CM elliptic curves

The exploration process of critical Boltzmann planar maps decorated by a triangular O(n) loop model

Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning

On rationally connected varieties over C1 fields of characteristic 0

A Functional Perspective on Information Measures

Further results on latent discourse models and word embeddings

Collaborative Learning in the Jungle (Decentralized, Byzantine, Heterogeneous, Asynchronous and Nonconvex Learning)

A Rosetta-based protein design protocol converging to natural sequences

Gaussian Process Regression for Materials and Molecules

Nonperturbative Mellin Amplitudes