A Dissociation of Attention and Awareness in Phase-sensitive but Not Phase-insensitive Visual Channels

The elements most vivid in our conscious awareness are the ones to which we direct our attention. Scientific study confirms the impression of a close bond between selective attention and visual awareness, yet the nature of this association remains elusive. Using visual afterimages as an index, we investigate neural processing of stimuli as they enter awareness and as they become the object of attention. We find evidence of response enhancement accompanying both attention and awareness, both in the phase-sensitive neural channels characteristic of early processing stages and in the phase-insensitive channels typical of higher cortical areas. The effects of attention and awareness on phase-insensitive responses are positively correlated, but in the same experiments, we observe no correlation between the effects on phase-sensitive responses. This indicates independent signatures of attention and awareness in early visual areas yet a convergence of their effects at more advanced processing stages

The ‘laws’ of binocular rivalry: 50 years of Levelt’s propositions

It has been fifty years since Levelt’s monograph On Binocular Rivalry (1965) was published, but its four propositions that describe the relation between stimulus strength and the phenomenology of binocular rivalry remain a benchmark for theorists and experimentalists even today. In this review, we will revisit the original conception of the four propositions and the scientific landscape in which this happened. We will also provide a brief update concerning distributions of dominance durations, another aspect of Levelt’s monograph that has maintained a prominent presence in the field. In a critical evaluation of Levelt’s propositions against current knowledge of binocular rivalry we will then demonstrate that the original propositions are not completely compatible with what is known today, but that they can, in a straightforward way, be modified to encapsulate the progress that has been made over the past fifty years. The resulting modified, propositions are shown to apply to a broad range of bistable perceptual phenomena, not just binocular rivalry, and they allow important inferences about the underlying neural systems. We argue that these inferences reflect canonical neural properties that play a role in visual perception in general, and we discuss ways in which future research can build on the work reviewed here to attain a better understanding of these propertie

Наближення мультифрактальних процесів і полів абсолютно неперервними процесами

Визначено абсолютно неперервні процеси, які збігаються до мультифрактального броунівського руху за ймовірністю в просторах типу Бєсова. Одержано результат про збіжність розв'язків стохастичних диференціальних рівнянь з такими процесами до розв'язку рівняння з мультифрактальним броунівським рухом. Аналогічні наближення побудовано для випадку двопараметричних процесів.We define absolute continuous stochastic processes that converge to a multifractal Brownian motion in Besov-type spaces. The convergence of solutions of stochastic differential equations with such processes to a solution of the equation with multifractal Brownian motion is proved. Similar approximations are constructed in the case of two-parameter processes

Flash suppression and flash facilitation in binocular rivalry

We show that previewing one half image of a binocular rivalry pair can cause it to gain initial dominance when the other half is added, a novel phenomenon we term flash facilitation. This is the converse of a known effect called flash suppression, where the previewed image becomes suppressed upon rivalrous presentation. The exact effect of previewing an image depends on both the duration and the contrast of the prior stimulus. Brief, low-contrast prior stimuli facilitate, whereas long, high-contrast ones suppress. These effects have both an eye-based component and a pattern-based component. Our results suggest that, instead of reflecting two unrelated mechanisms, both facilitation and suppression are manifestations of a single process that occurs progressively during presentation of the prior stimulus. The distinction between the two phenomena would then lie in the extent to which the process has developed during prior stimulation. This view is consistent with a neural model previously proposed to account for perceptual stabilization of ambiguous stimuli, suggesting a relation between perceptual stabilization and the present phenomena

Volumes of Restricted Minkowski Sums and the Free Analogue of the Entropy Power Inequality

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality has a counterpart for the free analogue of entropy . The free entropy (introduced recently by the second named author), consistently with Boltzmann's formula $S=k\log W$, was defined via volumes of matricial microstates. Proving the free entropy power inequality naturally becomes a geometric question. Restricting the Minkowski sum of two sets means to specify the set of pairs of points which will be added. The relevant inequality, which holds when the set of "addable" points is sufficiently large, differs from the Brunn-Minkowski inequality by having the exponent $1/n$ replaced by $2/n$. Its proof uses the rearrangement inequality of Brascamp-Lieb-L\"uttinger

Critical exponents of the modified F model

It has been argued (Kadanoff and Wegner 1971) that the existence of continuously variable critical exponents x and x' We consider here a special case of the eight-vertex model and report the result on its exponents and the verification of the scaling relations. This is the modified F model introduced by one of us where the two signs of e5 and eG refer to vertices belonging to the two sublattices A and B respectively. The spontaneous Staggered polarization and the zero-field polarizability are given by where f is the free energy per vertex. The exponents p, y and y' are then defined as usual by the critical behaviours of PO and x near the transition temperature T,. Our first observation is that the eight-vertex model defined by (1) is equivalent to an $ On leave of absence from th

Logarithmically-concave moment measures I

We discuss a certain Riemannian metric, related to the toric Kahler-Einstein equation, that is associated in a linearly-invariant manner with a given log-concave measure in R^n. We use this metric in order to bound the second derivatives of the solution to the toric Kahler-Einstein equation, and in order to obtain spectral-gap estimates similar to those of Payne and Weinberger.Comment: 27 page

The openness conjecture and complex Brunn-Minkowski inequalities

We discuss recent versions of the Brunn-Minkowski inequality in the complex setting, and use it to prove the openness conjecture of Demailly and Koll\'ar.Comment: This is an account of the results in arXiv:1305.5781 together with some background material. It is based on a lecture given at the Abel symposium in Trondheim, June 2013. 13 page

Multi-Timescale Perceptual History Resolves Visual Ambiguity

When visual input is inconclusive, does previous experience aid the visual system in attaining an accurate perceptual interpretation? Prolonged viewing of a visually ambiguous stimulus causes perception to alternate between conflicting interpretations. When viewed intermittently, however, ambiguous stimuli tend to evoke the same percept on many consecutive presentations. This perceptual stabilization has been suggested to reflect persistence of the most recent percept throughout the blank that separates two presentations. Here we show that the memory trace that causes stabilization reflects not just the latest percept, but perception during a much longer period. That is, the choice between competing percepts at stimulus reappearance is determined by an elaborate history of prior perception. Specifically, we demonstrate a seconds-long influence of the latest percept, as well as a more persistent influence based on the relative proportion of dominance during a preceding period of at least one minute. In case short-term perceptual history and long-term perceptual history are opposed (because perception has recently switched after prolonged stabilization), the long-term influence recovers after the effect of the latest percept has worn off, indicating independence between time scales. We accommodate these results by adding two positive adaptation terms, one with a short time constant and one with a long time constant, to a standard model of perceptual switching

Fluctuations for the Ginzburg-Landau ∇ϕ\nabla \phi Interface Model on a Bounded Domain

We study the massless field on $D_n = D \cap \tfrac{1}{n} \Z^2$, where $D \subseteq \R^2$ is a bounded domain with smooth boundary, with Hamiltonian \CH(h) = \sum_{x \sim y} \CV(h(x) - h(y)). The interaction \CV is assumed to be symmetric and uniformly convex. This is a general model for a $(2+1)$-dimensional effective interface where $h$ represents the height. We take our boundary conditions to be a continuous perturbation of a macroscopic tilt: $h(x) = n x \cdot u + f(x)$ for $x \in \partial D_n$, $u \in \R^2$, and $f \colon \R^2 \to \R$ continuous. We prove that the fluctuations of linear functionals of $h(x)$ about the tilt converge in the limit to a Gaussian free field on $D$, the standard Gaussian with respect to the weighted Dirichlet inner product $(f,g)_\nabla^\beta = \int_D \sum_i \beta_i \partial_i f_i \partial_i g_i$ for some explicit $\beta = \beta(u)$. In a subsequent article, we will employ the tools developed here to resolve a conjecture of Sheffield that the zero contour lines of $h$ are asymptotically described by $SLE(4)$, a conformally invariant random curve.Comment: 58 page