Well-Posedness and Symmetries of Strongly Coupled Network Equations

We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered interactions take place at the boundary, i. e., in the nodes of the network. We discuss well-posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions. Finally, we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space, i. e., of symmetries of the associated physical system. Applications to a neurobiological model as well as to a system of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change

Topological Photonics

Topology is revolutionizing photonics, bringing with it new theoretical discoveries and a wealth of potential applications. This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without dissipation even in the presence of impurities. Similarly, new optical mirrors of different wave-vector space topologies have been constructed to support new states of light propagating at their interfaces. These novel waveguides allow light to flow around large imperfections without back-reflection. The present review explains the underlying principles and highlights the major findings in photonic crystals, coupled resonators, metamaterials and quasicrystals.Comment: progress and review of an emerging field, 12 pages, 6 figures and 1 tabl

Bistable Percepts in the Brain: fMRI Contrasts Monocular Pattern Rivalry and Binocular Rivalry

The neural correlates of binocular rivalry have been actively debated in recent years, and are of considerable interest as they may shed light on mechanisms of conscious awareness. In a related phenomenon, monocular rivalry, a composite image is shown to both eyes. The subject experiences perceptual alternations in which the two stimulus components alternate in clarity or salience. The experience is similar to perceptual alternations in binocular rivalry, although the reduction in visibility of the suppressed component is greater for binocular rivalry, especially at higher stimulus contrasts. We used fMRI at 3T to image activity in visual cortex while subjects perceived either monocular or binocular rivalry, or a matched non-rivalrous control condition. The stimulus patterns were left/right oblique gratings with the luminance contrast set at 9%, 18% or 36%. Compared to a blank screen, both binocular and monocular rivalry showed a U-shaped function of activation as a function of stimulus contrast, i.e. higher activity for most areas at 9% and 36%. The sites of cortical activation for monocular rivalry included occipital pole (V1, V2, V3), ventral temporal, and superior parietal cortex. The additional areas for binocular rivalry included lateral occipital regions, as well as inferior parietal cortex close to the temporoparietal junction (TPJ). In particular, higher-tier areas MT+ and V3A were more active for binocular than monocular rivalry for all contrasts. In comparison, activation in V2 and V3 was reduced for binocular compared to monocular rivalry at the higher contrasts that evoked stronger binocular perceptual suppression, indicating that the effects of suppression are not limited to interocular suppression in V1

Adiabatic theorems for generators of contracting evolutions

We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems generated by Lindbladians all the way to classically driven stochastic systems. In all these cases the adiabatic evolution approximates, to lowest order, the natural notion of parallel transport in the manifold of instantaneous stationary states. The dynamics in the manifold of instantaneous stationary states and transversal to it have distinct characteristics: The former is irreversible and the latter is transient in a sense that we explain. Both the gapped and gapless cases are considered. Some applications are discussed.Comment: 31 pages, 4 figures, replaced by the version accepted for publication in CM

Perceptual Rivalry: Reflexes Reveal the Gradual Nature of Visual Awareness

Rivalry is a common tool to probe visual awareness: a constant physical stimulus evokes multiple, distinct perceptual interpretations (“percepts”) that alternate over time. Percepts are typically described as mutually exclusive, suggesting that a discrete (all-or-none) process underlies changes in visual awareness. Here we follow two strategies to address whether rivalry is an all-or-none process: first, we introduce two reflexes as objective measures of rivalry, pupil dilation and optokinetic nystagmus (OKN); second, we use a continuous input device (analog joystick) to allow observers a gradual subjective report. We find that the “reflexes” reflect the percept rather than the physical stimulus. Both reflexes show a gradual dependence on the time relative to perceptual transitions. Similarly, observers' joystick deflections, which are highly correlated with the reflex measures, indicate gradual transitions. Physically simulating wave-like transitions between percepts suggest piece-meal rivalry (i.e., different regions of space belonging to distinct percepts) as one possible explanation for the gradual transitions. Furthermore, the reflexes show that dominance durations depend on whether or not the percept is actively reported. In addition, reflexes respond to transitions with shorter latencies than the subjective report and show an abundance of short dominance durations. This failure to report fast changes in dominance may result from limited access of introspection to rivalry dynamics. In sum, reflexes reveal that rivalry is a gradual process, rivalry's dynamics is modulated by the required action (response mode), and that rapid transitions in perceptual dominance can slip away from awareness

The Spatial Origin of a Perceptual Transition in Binocular Rivalry

When the left and the right eye are simultaneously presented with incompatible images at overlapping retinal locations, an observer typically reports perceiving only one of the two images at a time. This phenomenon is called binocular rivalry. Perception during binocular rivalry is not stable; one of the images is perceptually dominant for a certain duration (typically in the order of a few seconds) after which perception switches towards the other image. This alternation between perceptual dominance and suppression will continue for as long the images are presented. A characteristic of binocular rivalry is that a perceptual transition from one image to the other generally occurs in a gradual manner: the image that was temporarily suppressed will regain perceptual dominance at isolated locations within the perceived image, after which its visibility spreads throughout the whole image. These gradual transitions from perceptual suppression to perceptual dominance have been labeled as traveling waves of perceptual dominance. In this study we investigate whether stimulus parameters affect the location at which a traveling wave starts. We varied the contrast, spatial frequency or motion speed in one of the rivaling images, while keeping the same parameter constant in the other image. We used a flash-suppression paradigm to force one of the rival images into perceptual suppression. Observers waited until the suppressed image became perceptually dominant again, and indicated the position at which this breakthrough from suppression occurred. Our results show that the starting point of a traveling wave during binocular rivalry is highly dependent on local stimulus parameters. More specifically, a traveling wave most likely started at the location where the contrast of the suppressed image was higher than that of the dominant one, the spatial frequency of the suppressed image was lower than that of the dominant one, and the motion speed of the suppressed image was higher than that of the dominant one. We suggest that a breakthrough from suppression to dominance occurs at the location where salience (the degree to which a stimulus element stands out relative to neighboring elements) of the suppressed image is higher than that of the dominant one. Our results further show that stimulus parameters affecting the temporal dynamics during continuous viewing of rival images described in other studies, also affect the spatial origin of traveling waves during binocular rivalry

Roles of contour and surface processing in microgenesis of object perception and visual consciousness

Developments in visual neuroscience and neural-network modeling indicate the existence of separate pathways for the processing of form and surface attributes of a visual object. In line with prior theoretical proposals, it is assumed that the processing of form can be explicit or conscious only as or after the surface property such as color is filled in. In conjunction with extant psychophysical findings, these developments point to interesting distinctions between nonconscious and conscious processing of these attributes, specifically in relation to distinguishable temporal dynamics. At nonconscious levels form processing proceeds faster than surface processing, whereas in contrast, at conscious levels form processing proceeds slower than surface processing. I mplications of separate form and surface processing for current and future psychophysical and neuroscientific research, particularly that relating cortical oscillations to conjunctions of surface and form features, and for cognitive science and philosophy of mind and consciousness are discussed

Meiosis genes in Daphnia pulex and the role of parthenogenesis in genome evolution

<p>Abstract</p> <p>Background</p> <p>Thousands of parthenogenetic animal species have been described and cytogenetic manifestations of this reproductive mode are well known. However, little is understood about the molecular determinants of parthenogenesis. The <it>Daphnia pulex </it>genome must contain the molecular machinery for different reproductive modes: sexual (both male and female meiosis) and parthenogenetic (which is either cyclical or obligate). This feature makes <it>D. pulex </it>an ideal model to investigate the genetic basis of parthenogenesis and its consequences for gene and genome evolution. Here we describe the inventory of meiotic genes and their expression patterns during meiotic and parthenogenetic reproduction to help address whether parthenogenesis uses existing meiotic and mitotic machinery, or whether novel processes may be involved.</p> <p>Results</p> <p>We report an inventory of 130 homologs representing over 40 genes encoding proteins with diverse roles in meiotic processes in the genome of <it>D. pulex</it>. Many genes involved in cell cycle regulation and sister chromatid cohesion are characterized by expansions in copy number. In contrast, most genes involved in DNA replication and homologous recombination are present as single copies. Notably, <it>RECQ2 </it>(which suppresses homologous recombination) is present in multiple copies while <it>DMC1 </it>is the only gene in our inventory that is absent in the <it>Daphnia </it>genome. Expression patterns for 44 gene copies were similar during meiosis <it>versus </it>parthenogenesis, although several genes displayed marked differences in expression level in germline and somatic tissues.</p> <p>Conclusion</p> <p>We propose that expansions in meiotic gene families in <it>D. pulex </it>may be associated with parthenogenesis. Taking into account our findings, we provide a mechanistic model of parthenogenesis, highlighting steps that must differ from meiosis including sister chromatid cohesion and kinetochore attachment.</p

Dynamic Effective Connectivity of Inter-Areal Brain Circuits

Anatomic connections between brain areas affect information flow between neuronal circuits and the synchronization of neuronal activity. However, such structural connectivity does not coincide with effective connectivity (or, more precisely, causal connectivity), related to the elusive question “Which areas cause the present activity of which others?”. Effective connectivity is directed and depends flexibly on contexts and tasks. Here we show that dynamic effective connectivity can emerge from transitions in the collective organization of coherent neural activity. Integrating simulation and semi-analytic approaches, we study mesoscale network motifs of interacting cortical areas, modeled as large random networks of spiking neurons or as simple rate units. Through a causal analysis of time-series of model neural activity, we show that different dynamical states generated by a same structural connectivity motif correspond to distinct effective connectivity motifs. Such effective motifs can display a dominant directionality, due to spontaneous symmetry breaking and effective entrainment between local brain rhythms, although all connections in the considered structural motifs are reciprocal. We show then that transitions between effective connectivity configurations (like, for instance, reversal in the direction of inter-areal interactions) can be triggered reliably by brief perturbation inputs, properly timed with respect to an ongoing local oscillation, without the need for plastic synaptic changes. Finally, we analyze how the information encoded in spiking patterns of a local neuronal population is propagated across a fixed structural connectivity motif, demonstrating that changes in the active effective connectivity regulate both the efficiency and the directionality of information transfer. Previous studies stressed the role played by coherent oscillations in establishing efficient communication between distant areas. Going beyond these early proposals, we advance here that dynamic interactions between brain rhythms provide as well the basis for the self-organized control of this “communication-through-coherence”, making thus possible a fast “on-demand” reconfiguration of global information routing modalities

Anesthetic action on the transmission delay between cortex and thalamus explains the beta-buzz observed under propofol anesthesia

In recent years, more and more surgeries under general anesthesia have been performed with the assistance of electroencephalogram (EEG) monitors. An increase in anesthetic concentration leads to characteristic changes in the power spectra of the EEG. Although tracking the anesthetic-induced changes in EEG rhythms can be employed to estimate the depth of anesthesia, their precise underlying mechanisms are still unknown. A prominent feature in the EEG of some patients is the emergence of a strong power peak in the β–frequency band, which moves to the α–frequency band while increasing the anesthetic concentration. This feature is called the beta-buzz. In the present study, we use a thalamo-cortical neural population feedback model to reproduce observed characteristic features in frontal EEG power obtained experimentally during propofol general anesthesia, such as this beta-buzz. First, we find that the spectral power peak in the α– and δ–frequency ranges depend on the decay rate constant of excitatory and inhibitory synapses, but the anesthetic action on synapses does not explain the beta-buzz. Moreover, considering the action of propofol on the transmission delay between cortex and thalamus, the model reveals that the beta-buzz may result from a prolongation of the transmission delay by increasing propofol concentration. A corresponding relationship between transmission delay and anesthetic blood concentration is derived. Finally, an analytical stability study demonstrates that increasing propofol concentration moves the systems resting state towards its stability threshold