Related papers: A Note on a Recent Attempt to Improve the Pin-Fran…
In this short note, we employ well-known results to improve the lower bound for the constant associated with the linear term in the asymptotic expansion of the minimal logarithmic energy on the sphere.
We propose a benchmark to assess the capability of large language models to reason with conventional metaphors. Our benchmark combines the previously isolated topics of metaphor detection and commonsense reasoning into a single task that…
This work introduces a notion of approximate probabilistic trace equivalence for labelled Markov chains, and relates this new concept to the known notion of approximate probabilistic bisimulation. In particular this work shows that the…
Kuzmin-Landau Lemma basic for the bound of sum of exponentials is a nice example of the arithmetization of Analysis. Here we tell the interesting story of this Lemma emphasizing Landau's best constant.
We explore a method for improving the performance of large language models through self-reflection and reinforcement learning. By incentivizing the model to generate better self-reflections when it answers incorrectly, we demonstrate that a…
We study the approximate string matching and regular expression matching problem for the case when the text to be searched is compressed with the Ziv-Lempel adaptive dictionary compression schemes. We present a time-space trade-off that…
This is a brief technical note to clarify the state of lower bounds on regret for reinforcement learning. In particular, this paper: - Reproduces a lower bound on regret for reinforcement learning, similar to the result of Theorem 5 in the…
Probabilistic automata are an extension of nondeterministic finite automata in which transitions are annotated with probabilities. Despite its simplicity, this model is very expressive and many of the associated algorithmic questions are…
We introduce a new Symanzik improved action by adding a 2x2 plaquette in such a way that the Feynman rules in the covariant gauge simplify. We call this the square Symanzik action. Some comparisons with the continuum and the standard Wilson…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does not generally hold. However, under one additional…
In this paper we study some improvements of the classical Hardy inequality. We add to the right hand side of the inequality a term which depends on some Lorentz norms of $u$ or of its gradient and we find the best values of the constants…
A short review is given of some theoretical approaches to CPT violation. A potentially realistic possibility is that small apparent breaking of CPT and Lorentz symmetry could arise at the level of the standard model from spontaneous…
We investigate networks of automata that synchronise over common action labels. A graph synchronisation topology between the automata is defined in such a way that two automata are connected iff they can synchronise over an action. We show…
We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified…
This paper directly builds upon previous work where we introduced new reduced basis a posteriori error bounds for parametrized saddle point problems based on Brezzi's theory. We here sharpen these estimates for the special case of a…
The standard series expansion for the period of a finite amplitude pendulum as a function of energy (and hence amplitude) provides a lower limit on the period when the series is truncated. An adjustment to the last term in the truncated…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
Some modifications of the Luscher algorithm, which reduce the autocorelation time, are proposed and tested.
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…