Ilya Pavlyukevich, Georgiy Shevchenko.

Source: Bernoulli, Volume 26, Number 2, 1381--1409.

Abstract:
In this paper, we study the Stratonovich stochastic differential equation $mathrm{d}X=|X|^{alpha }circ mathrm{d}B$, $alpha in (-1,1)$, which has been introduced by Cherstvy et al. ( New J. Phys. 15 (2013) 083039) in the context of analysis of anomalous diffusions in heterogeneous media. We determine its weak and strong solutions, which are homogeneous strong Markov processes spending zero time at $0$: for $alpha in (0,1)$, these solutions have the form egin{equation*}X_{t}^{ heta }=((1-alpha)B_{t}^{ heta })^{1/(1-alpha )},end{equation*} where $B^{ heta }$ is the $ heta $-skew Brownian motion driven by $B$ and starting at $frac{1}{1-alpha }(X_{0})^{1-alpha }$, $ heta in [-1,1]$, and $(x)^{gamma }=|x|^{gamma }operatorname{sign}x$; for $alpha in (-1,0]$, only the case $ heta =0$ is possible. The central part of the paper consists in the proof of the existence of a quadratic covariation $[f(B^{ heta }),B]$ for a locally square integrable function $f$ and is based on the time-reversion technique for Markovian diffusions.

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French translation of "Pillar 3 disclosure requirements - updated framework", December 2018

Spanish version of Press release about Pablo Hernández de Cos appointed as Chairman of Basel Committee on Banking Supervision, 7 March 2019. Pablo Hernández de Cos, nombrado Presidente del Comité de Supervisión Bancaria de Basilea.

Priming refers to the influence that a previously encountered object exerts on future responses to similar objects. For many years, visual priming has been known as a facilitation and sometimes an inhibition effect that lasts for an extended period of time. It contrasts with the recent finding of an oscillated priming effect where facilitation and inhibition alternate over time periodically. Here we developed a computational model of visual priming that combines rhythmic sampling of the environment (attentional oscillation) with active preparation for future events (temporal expectation). Counterintuitively, it shows that both the sustained and oscillated priming effects can emerge from an interaction between attentional oscillation and temporal expectation. The interaction also leads to novel predictions, such as the change of visual priming effects with temporal expectation and attentional oscillation. Reanalysis of two published datasets and the results of two new experiments of visual priming tasks with male and female human participants provide support for the model's relevance to human behavior. More generally, our model offers a new perspective that may unify the increasing findings of behavioral and neural oscillations with the classic findings in visual perception and attention.

SIGNIFICANCE STATEMENT There is increasing behavioral and neural evidence that visual attention is a periodic process that sequentially samples different alternatives in the theta frequency range. It contrasts with the classic findings of sustained facilitatory or inhibitory attention effects. How can an oscillatory perceptual process give rise to sustained attention effects? Here we make this connection by proposing a computational model for a "fruit fly" visual priming task and showing both the sustained and oscillated priming effects can have the same origin: an interaction between rhythmic sampling of the environment and active preparation for future events. One unique contribution of our model is to predict how temporal contexts affects priming. It also opens up the possibility of reinterpreting other attention-related classic phenomena.

The superior colliculus (SC) is arguably the most important visual structure in the mouse brain and is well known for its involvement in innate responses to visual threats and prey items. In other species, the SC plays a central role in voluntary as well as innate visual functions, including crucial contributions to selective attention and perceptual decision-making. In the mouse, the possible role of the SC in voluntary visual choice behaviors has not been established. Here, we demonstrate that the mouse SC of both sexes plays a causal role in visual perceptual decision-making by transiently inhibiting SC activity during an orientation change detection task. First, unilateral SC inhibition-induced spatially specific deficits in detection. Hit rates were reduced, and reaction times increased for orientation changes in the contralateral but not ipsilateral visual field. Second, the deficits caused by SC inhibition were specific to a temporal epoch coincident with early visual burst responses in the SC. Inhibiting SC during this 100-ms period caused a contralateral detection deficit, whereas inhibition immediately before or after did not. Third, SC inhibition reduced visual detection sensitivity. Psychometric analysis revealed that inhibiting SC visual activity significantly increased detection thresholds for contralateral orientation changes. In addition, effects on detection thresholds and lapse rates caused by SC inhibition were larger in the presence of a competing visual stimulus, indicating a role for the mouse SC in visual target selection. Together, our results demonstrate that the mouse SC is necessary for the normal performance of voluntary visual choice behaviors.

SIGNIFICANCE STATEMENT The mouse superior colliculus (SC) has become a popular model for studying the circuit organization and development of the visual system. Although the SC is a fundamental component of the visual pathways in mice, its role in visual perceptual decision-making is not clear. By investigating how temporally precise SC inhibition influenced behavioral performance during a visually guided orientation change detection task, we identified a 100-ms temporal epoch of SC visual activity that is crucial for the ability of mice to detect behaviorally relevant visual changes. In addition, we found that SC inhibition also caused deficits in visual target selection. Thus, our findings highlight the importance of the SC for visual perceptual choice behavior in the mouse.

Behavior can be guided by neuronal activity in visual, auditory, or somatosensory cerebral cortex, depending on task requirements. In contrast to this flexible access of cortical signals, several observations suggest that behaviors depend more on neurons in later areas of visual cortex than those in earlier areas, although neurons in earlier areas would provide more reliable signals for many tasks. We recorded from neurons in different levels of visual cortex of 2 male rhesus monkeys while the animals did a visual discrimination task and examined trial-to-trial correlations between neuronal and behavioral responses. These correlations became stronger in primary visual cortex as neuronal signals in that area became more reliable relative to the other areas. The results suggest that the mechanisms that read signals from cortex might access any cortical area depending on the relative value of those signals for the task at hand.

SIGNIFICANCE STATEMENT Information is encoded by the action potentials of neurons in various cortical areas in a hierarchical manner such that increasingly complex stimulus features are encoded in successive stages. The brain must extract information from the response of appropriate neurons to drive optimal behavior. A widely held view of this decoding process is that the brain relies on the output of later cortical areas to make decisions, although neurons in earlier areas can provide more reliable signals. We examined correlations between perceptual decisions and the responses of neurons in different levels of monkey visual cortex. The results suggest that the brain may access signals in any cortical area depending on the relative value of those signals for the task at hand.

One person has curly hair; one person has straight hair. One person tans, another burns. One person can curl her lip, another can’t. This is all because of our genes and the differences in them. Diversity. It is the spice of life.  

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Tensions are rising on Manitoulin Island because a First Nation is stopping travellers on provincial highways that go through the community. But opinions on M'Chigeeng's attempt to protect its people from COVID-19 are not divided along racial lines. 

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