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The characteristic function of row contractions and liftings of row contractions are complete invariants up to unitary equivalence for row contractions and liftings of row contractions, respectively. We provide alternate proofs for these…
A key module in neural transformer-based deep architectures is positional encoding. This module enables a suitable way to encode positional information as input for transformer neural layers. This success has been rooted in the use of…
Linear index coding can be formulated as an interference alignment problem, in which precoding vectors of the minimum possible length are to be assigned to the messages in such a way that the precoding vector of a demand (at some receiver)…
We study multivariate integration of functions that are invariant under permutations (of subsets) of their arguments. We find an upper bound for the $n$th minimal worst case error and show that under certain conditions, it can be bounded…
A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show in particular that stationary random…
We expand the classical balayage of measures and subharmonic functions on a system of rays $S$ with a common origin on the complex plane $\mathbb C$. This allows for an arbitrary subharmonic function $v$ of finite order on $\mathbb C$ build…
We prove a partial regularity result for local minimizers of quasiconvex variational integrals with general growth. The main tool is an improved A-harmonic approximation, which should be interesting also for classical growth.
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical…
For a complete noncompact Riemannian manifold with nonnegative Ricci curvature, we show that bounded biharmonic functions are constant and the space consists of biharmonic functions with polynomial growth of a fixed rate is finite…
We establish an optimal regularity result for parametrized two-dimensional stationary varifolds. Namely, we show that the parametrization map is a smooth minimal branched immersion and that the multiplicity function is constant. We provide…
Prior works have demonstrated that implicit representations trained only for reconstruction tasks typically generate encodings that are not useful for semantic tasks. In this work, we propose a method that contextualises the encodings of…
Consistency regularization describes a class of approaches that have yielded state-of-the-art results for semi-supervised classification. While semi-supervised semantic segmentation proved to be more challenging, a number of successful…
We study the relative growth of finitely generated subgroups in finitely generated groups, and the corresponding distortion function of the embeddings. We explore which functions are equivalent to the relative growth functions and…
Let $X=(X_i)_{i\ge 1}$ and $Y=(Y_i)_{i\ge 1}$ be two sequences of independent and identically distributed (iid) random variables taking their values, uniformly, in a common totally ordered finite alphabet. Let LCI$_n$ be the length of the…
We address the problem of learning on sets of features, motivated by the need of performing pooling operations in long biological sequences of varying sizes, with long-range dependencies, and possibly few labeled data. To address this…
In this paper, we study two general classes of optimization algorithms for kernel methods with convex loss function and quadratic norm regularization, and analyze their convergence. The first approach, based on fixed-point iterations, is…
We present a categorical formulation of the Hamiltonian renormalisation programme for quantum field theories, establishing a systematic bridge between functional and lattice renormalisation. To this end, we introduce two categories, $Seq$…
Maximum run-length limited codes are constraint codes used in communication and data storage systems. Insertion/deletion correcting codes correct insertion or deletion errors caused in transmitted sequences and are used for combating…
In literature, it is common to find problems which require a way to encode a finite set of information into a single data; usually means are used for that. An important generalization of means are the so called Aggregation Functions, with a…
Neural encoder-decoder models have been successful in natural language generation tasks. However, real applications of abstractive summarization must consider additional constraint that a generated summary should not exceed a desired…