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pro vyhledávání: '"Pontiveros, Gonzalo Fiz"'
Despite recent advancements in Machine Learning, many tasks still involve working in low-data regimes which can make solving natural language problems difficult. Recently, a number of text augmentation techniques have emerged in the field of Natural
Externí odkaz:
http://arxiv.org/abs/2302.12784
The proliferation of DeepFake technology is a rising challenge in today's society, owing to more powerful and accessible generation methods. To counter this, the research community has developed detectors of ever-increasing accuracy. However, the abi
Externí odkaz:
http://arxiv.org/abs/2210.03683
Let the random variable $X\, :=\, e(\mathcal{H}[B])$ count the number of edges of a hypergraph $\mathcal{H}$ induced by a random $m$ element subset $B$ of its vertex set. Focussing on the case that $\mathcal{H}$ satisfies some regularity condition we
Externí odkaz:
http://arxiv.org/abs/1910.12835
We show that the Right-Angled Coxeter group $C=C(G)$ associated to a random graph $G\sim \mathcal{G}(n,p)$ with $\frac{\log n + \log\log n + \omega(1)}{n} \leq p < 1- \omega(n^{-2})$ virtually algebraically fibers. This means that $C$ has a finite in
Externí odkaz:
http://arxiv.org/abs/1703.01207
The Ramsey number r(K_s,Q_n) is the smallest positive integer N such that every red-blue colouring of the edges of the complete graph K_N on N vertices contains either a red n-dimensional hypercube, or a blue clique on s vertices. Answering a questio
Externí odkaz:
http://arxiv.org/abs/1306.0461
The areas of Ramsey theory and random graphs have been closely linked ever since Erd\H{o}s' famous proof in 1947 that the 'diagonal' Ramsey numbers $R(k)$ grow exponentially in $k$. In the early 1990s, the triangle-free process was introduced as a mo
Externí odkaz:
http://arxiv.org/abs/1302.6279
The Ramsey number r(K_3,Q_n) is the smallest integer N such that every red-blue colouring of the edges of the complete graph K_N contains either a red n-dimensional hypercube, or a blue triangle. Almost thirty years ago, Burr and Erd\H{o}s conjecture
Externí odkaz:
http://arxiv.org/abs/1302.3840
Autor:
Pontiveros, Gonzalo Fiz
We consider the problem of sums of dilates in groups of prime order. We show that given $A\subset \Z{p}$ of sufficiently small density then $$\big| \lambda_{1}A+\lambda_{2}A+...+ \lambda_{k}A \big| \,\ge\,\bigg(\sum_{i}|\lambda_{i}|\bigg)|A|- o(|A|),
Externí odkaz:
http://arxiv.org/abs/1203.2659
Autor:
Pontiveros, Gonzalo Fiz
Let $A$ be a random subset of $\mathbb{Z}_{N}$ obtained by including each element of $\mathbb{Z}_{N}$ in $A$ independently with probability $p$. We say that $A$ is \emph{linear} if the only Freiman homomorphisms are given by the restrictions of funct
Externí odkaz:
http://arxiv.org/abs/1004.3709