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pro vyhledávání: '"Roger Baker"'
Autor:
Roger Baker, Stefano Pontone, Marco Lauriola, Rossella Palma, Cristina Panetta, Manuela Tomai
Publikováno v:
BMJ Open, Vol 12, Iss 2 (2022)
Externí odkaz:
https://doaj.org/article/27bfe7bec02846d6b2372d97f9097b83
Autor:
Treutlein, Johannes, Choi, Dami, Betley, Jan, Anil, Cem, Marks, Samuel, Grosse, Roger Baker, Evans, Owain
One way to address safety risks from large language models (LLMs) is to censor dangerous knowledge from their training data. While this removes the explicit information, implicit information can remain scattered across various training documents. Cou
Externí odkaz:
http://arxiv.org/abs/2406.14546
Learning With Opponent-Learning Awareness (LOLA) (Foerster et al. [2018a]) is a multi-agent reinforcement learning algorithm that typically learns reciprocity-based cooperation in partially competitive environments. However, LOLA often fails to learn
Externí odkaz:
http://arxiv.org/abs/2210.10125
Autor:
Roger Baker
Publikováno v:
Acta Mathematica Hungarica. 165:316-325
Let $$p \ge 1$$ . We give upper and lower bounds for $$\begin{aligned} {M}_{p}(N): = \bigg \Vert \mathop {\mathrm{sup}}\limits _{0 \le t \le 1} \bigg | {\sum _{n=1}^N} {e}(nx + n^{2}t)\bigg |\bigg \Vert _{L^{p}[0,1]}^{p} \end{aligned}$$ that are of t
Autor:
Roger Baker, David Masser
Publikováno v:
International Mathematics Research Notices.
In this paper we give a refinement of the one-dimensional form of Bilu’s Equidistribution Theorem together with some examples and applications. These include an explicit bound for the sum of the $e^{i\theta }$ taken over all conjugates $re^{i\theta
Autor:
Roger Baker, Glyn Harman
Publikováno v:
Mathematika. 67:447-467
Let c > 0.55. Every large n can be written in the form p +ab, where p is prime, a and b are significantly smaller than x^1/2 and ab is less than n^c. This strengthens a result of Heath-Brown, which has the requirement c>3/4. We introduce the idea of
Autor:
Roger Baker
Publikováno v:
Acta Arithmetica. 200:429-438
An asymptotic formula is given for the number of y-smooth numbers up to x in a Beatty sequence corresponding to an irrational number of finite type.
Autor:
Roger Baker
Publikováno v:
Cell and Gene Therapy Insights. 6:9-15
Autor:
Roger Baker
Publikováno v:
Functiones et Approximatio Commentarii Mathematici. 64
We consider the solutions to the inequality \[|p_1^c + \cdots + p_s^c - R| 1$, $c \not\in \mb N$ and $\eta$ is a small positive number; $R$ is large). We obtain new ranges of $c$ for which this has many solutions in primes $p_1, \ldots, p_s$, for $s
Autor:
Roger Baker, David Masser
Publikováno v:
Bulletin of the London Mathematical Society. 51:853-867
The well-known Siegel Lemma gives an upper bound $cU^{m/(n−m)}$ for the size of the smallest non-zero integral solution of a linear system of $m \ge 1$ equations in $n > m$ unknowns whose coefficients are integers of absolute value at most $U \ge 1