Pattern avoidance in partial words over a ternary alphabet

Blanched-Sadri and Woodhouse in 2013 have proven the conjecture of Cassaigne, stating that any pattern with $m$ distinct variables and of length at least $2^m$ is avoidable over a ternary alphabet and if the length is at least $3\cdot 2^{m-1}$ it is avoidable over a binary alphabet. They conjectured that similar theorems are true for partial words – sequences, in which some characters are left “blank”. Using method of entropy compression, we obtain the partial words version of the theorem for ternary words

Pathwidth and nonrepetitive list coloring

A vertex coloring of a graph is nonrepetitive if there is no path in the graph whose first half receives the same sequence of colors as the second half. While every tree can be nonrepetitively colored with a bounded number of colors (4 colors is enough), Fiorenzi, Ochem, Ossona de Mendez, and Zhu recently showed that this does not extend to the list version of the problem, that is, for every $\ell \geq 1$ there is a tree that is not nonrepetitively $\ell$-choosable. In this paper we prove the following positive result, which complements the result of Fiorenzi et al.: There exists a function $f$ such that every tree of pathwidth $k$ is nonrepetitively $f(k)$-choosable. We also show that such a property is specific to trees by constructing a family of pathwidth-2 graphs that are not nonrepetitively $\ell$-choosable for any fixed $\ell$.Comment: v2: Minor changes made following helpful comments by the referee

I don't want to miss a thing : learning dynamics and effects of feedback type and monetary incentive in a paired associate deterministic learning task

Effective functioning in a complex environment requires adjusting of behavior according to changing situational demands. To do so, organisms must learn new, more adaptive behaviors by extracting the necessary information from externally provided feedback. Not surprisingly, feedback-guided learning has been extensively studied using multiple research paradigms. The purpose of the present study was to test the newly designed Paired Associate Deterministic Learning task (PADL), in which participants were presented with either positive or negative deterministic feedback. Moreover, we manipulated the level of motivation in the learning process by comparing blocks with strictly cognitive, informative feedback to blocks where participants were additionally motivated by anticipated monetary reward or loss. Our results proved the PADL to be a useful tool not only for studying the learning process in a deterministic environment, but also, due to the varying task conditions, for assessing differences in learning patterns. Particularly, we show that the learning process itself is influenced by manipulating both the type of feedback information and the motivational significance associated with the expected monetary reward

Threshold ECDSA for Decentralized Asset Custody

The surge of interest in decentralization-enabling technologies sparked by the recent success of Bitcoin and other blockchains has led to several new challenges in cryptography and protocol design. One such challenge concerns the widely used digital signature scheme -- ECDSA -- that has in particular been chosen to secure transactions in Bitcoin and several other blockchain systems. To empower decentralized interoperability between such blockchains one would like to implement distributed custody over Bitcoin accounts, which technically can be realized via a threshold ECDSA protocol. Even though several threshold ECDSA protocols already exist, as we argue, due to lack of robustness in signature generation, they are not well suited for deployment scenarios with large committees of parties, out of which a significant fraction might be malicious or prone to DDoS attacks. We propose a new threshold ECDSA protocol that improves upon the state-of-the-art solutions by enabling robustness and fault attributability during signature generation. In addition to that, we improve the signing time and bandwidth of previous solutions by moving expensive operations that are oblivious to the signed message to a separate setup phase. Finally, we back our theoretical results via an empirical evaluation of our protocol in large-scale experiments in LAN and WAN settings

Saying "yes" when you want to say "no" : pupil dilation reflects evidence accumulation in a visual working memory recognition task

A number of studies have shown that the pupil dilates during stimuli recognition and decision-making. Yet, little is known about the interaction between recognition memory and decision processes. Here, we investigated the possible link between pupil response and decision-related factors during a visual recognition task. Forty-eight volunteers took part in the study. The experimental task was based on the Deese-Roediger-McDermott paradigm designed to study false recognitions. Participants were shown different sets of two meaningless objects. After seeing each set, they were asked to determine whether the subsequent probe (positive, lure or negative) was already presented. We had found that the pupil dilated more and slower, and the reaction time was extended, when the upcoming choice was against individual response bias. Such a result indicates that recognition and rejection in memory tasks could be seen as two behavioral alternatives supported by evidence accumulation, in line with decision-making models. This interpretation was upheld with the drift-diffusion modelling based on pupil data. A similar pattern was observed for errors - larger pupil sizes before incorrect responses were accompanied by longer reaction times. Furthermore, before correct reactions, especially in participants differentiating more accurately between the old and new stimuli, pupil dilation was increasing faster, indicating swifter evidence accumulation. Taking into account the link between cognitive pupillary reflex and norepinephrine release, we conclude that similarly to decision making, reactions in memory tasks may partly depend on the locus coeruleus activity, which is the principal site for norepinephrine synthesis

Delta-gamma coupling as a potential neurophysiological mechanism of fluid intelligence

Electrophysiological investigations have pointed out significant yet weak correlations between intelligence and oscillatory brain activity, including the spectral power, frequency, complexity, synchrony, and coherence of electroencephalographic (EEG) signals, however neglecting the interplay between fast and slow neuronal oscillations underlying information transfer in the brain. We found that fluid intelligence level (gf) depends on the precise synchronization of fast oscillations to a specific time window of slow brain rhythms. Specifically, by examining EEG recordings of 50 people in resting state as well as during performance at two gf tasks we found converging evidence that high-gf participants display stronger Phase-Amplitude Coupling (PAC) related to an increased concentration of gamma (~ 36 Hz) spectral power at the descending phase of delta oscillations (~ 3 Hz). Delta-gamma PAC strength explained 35% variance in scores on multiple gf tests, outperforming six alternative EEG-based predictors including spectral power, complexity and amplitude-amplitude coupling. Present results suggest PAC as a neurophysiological substrate of gf in humans, offering novel insight about the role of slow and fast brain rhytms in high-order cognition, as well as a potential new target for neuromodulatory interventions in the healthy and pathological brain