Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras

This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice), reflection group $W\subset W(S)$, fundamental polyhedron \Cal M of $W$ and an acceptable (corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors orthogonal to faces of \Cal M (simple roots). One can construct the corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by $M$. We show that \goth g has good behavior of imaginary roots, its denominator formula is defined in a natural domain and has good automorphic properties if and only if \goth g has so called {\it restricted arithmetic type}. We show that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus, Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a natural class to study. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the best automorphic properties for the denominator function if they have {\it a lattice Weyl vector $\rho$}. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type with generalized lattice Weyl vector $\rho$ are called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on results and ideas. 31 pages, no figures. AMSTe

Neurophysiophenomenology – predicting emotional arousal from brain arousal in a virtual reality roller coaster

Arousal is a core affect constituted of both bodily and subjective states that prepares an agent to respond to events of the natural environment. While the peripheral physiological components of arousal have been examined also under naturalistic conditions, its neural correlates were suggested mainly on the basis of simplifed experimental designs.   We used virtual reality (VR) to present a highly immersive and contextually rich scenario of roller coaster rides to evoke naturalistic states of emotional arousal. Simultaneously, we recorded EEG to validate the suggested neural correlates of arousal in alpha frequency oscillations (8-12Hz) over temporo-parietal cortical areas. To fnd the complex link between these alpha components and the participants’ continuous subjective reports of arousal, we employed a set of complementary analytical methods coming from machine learning and deep learning

Integrative taxonomic, ecological and genotyping study of charophyte populations from the egyptian western-desert oases and sinai peninsula

Present-day information available on the charophyte macroalgae in Egypt, including their phylogenetic affinities, remains largely incomplete. In this study, nine charophyte populations were collected from different aquatic biotopes across the Egyptian Western-Desert Oases and Sinai Peninsula. All populations were investigated using an integrative polyphasic approach including phylogenetic analyses inferred from the chloroplast-encoded gene (rbcL) and the internal transcribed spacer (ITS1) regions, in parallel with morphotaxonomic assignment, ultrastructure of the oospore walls, and autecology. The specimens identified belonged to the genera Chara, Nitella, and Tolypella, with predominance of the first genus to which five species were assigned though they presented some interesting aberrant taxonomic features: C. aspera, C. contraria, C. globata, C. tomentosa, and C. vulgaris. Based on our integrative study, the globally rare species C. globata was reported for the second time for the whole African continent. The genus Nitella was only represented by N. flagellifera, and based on the available literature, it is a new record for North Africa. Noteworthy, an interesting Tolypella sp., morphologically very similar to T. glomerata, was collected and characterized and finally designated with the working name ‘Tolypella sp. PBA–1704 from a desert, freshwater wetland’, mainly based on its concatenated rbcL+ITS1 phylogenetic position. This study not only improved our understanding on the diversity, biogeography and autecological preferences of charophytes in Egypt, but it also broadened our knowledge on this vulnerable algal group in North Africa, emphasizing the need of more in-depth research work in the future, particularly in the less–impacted desert habitats

The Geometry and Moduli of K3 Surfaces

These notes will give an introduction to the theory of K3 surfaces. We begin with some general results on K3 surfaces, including the construction of their moduli space and some of its properties. We then move on to focus on the theory of polarized K3 surfaces, studying their moduli, degenerations and the compactification problem. This theory is then further enhanced to a discussion of lattice polarized K3 surfaces, which provide a rich source of explicit examples, including a large class of lattice polarizations coming from elliptic fibrations. Finally, we conclude by discussing the ample and Kahler cones of K3 surfaces, and give some of their applications.Comment: 34 pages, 2 figures. (R. Laza, M. Schutt and N. Yui, eds.

Surface-enhanced optical third-harmonic generation in Ag island films

Surface-enhanced optical third-harmonic generation (THG) is observed in silver island films. The THG intensity from Ag nanoparticles is enhanced by more than two orders of magnitude with respect to the THG intensity from a smooth and homogeneous silver surface. This enhancement is attributed to local plasmon excitation and resonance of the local field at the third-harmonic wavelength. The diffuse and depolarized component of the enhanced THG is associated with the third-order hyper-Rayleigh scattering in a 2-D random array of silver nanoparticles.Comment: 4 pages, 2 figure

Neuronal biomarkers of Parkinson's disease are present in healthy aging

The prevalence of Parkinson's disease (PD) increases with aging and both processes share similar cellular mechanisms and alterations in the dopaminergic system. Yet it remains to be investigated whether aging can also demonstrate electrophysiological neuronal signatures typically associated with PD. Previous work has shown that phase-amplitude coupling (PAC) between the phase of beta oscillations and the amplitude of gamma oscillations as well as beta bursts features can serve as electrophysiological biomarkers for PD. Here we hypothesize that these metrics are also present in apparently healthy elderly subjects. Using resting state multichannel EEG measurements, we show that PAC between beta oscillation and broadband gamma activity (50–150 Hz) is elevated in a group of elderly (59–77 years) compared to young volunteers (20–35 years) without PD. Importantly, the increase of PAC is statistically significant even after ruling out confounds relating to changes in spectral power and non-sinusoidal shape of beta oscillation. Moreover, a trend for a higher percentage of longer beta bursts (> 0.2 s) along with the increase in their incidence rate is also observed for elderly subjects. Using inverse modeling, we further show that elevated PAC and longer beta bursts are most pronounced in the sensorimotor areas. Moreover, we show that PAC and longer beta bursts might reflect distinct mechanisms, since their spatial patterns only partially overlap and the correlation between them is weak. Taken together, our findings provide novel evidence that electrophysiological biomarkers of PD may already occur in apparently healthy elderly subjects. We hypothesize that PAC and beta bursts characteristics in aging might reflect a pre-clinical state of PD and suggest their predictive value to be tested in prospective longitudinal studies

Neural excitability and sensory input determine intensity perception with opposing directions in initial cortical responses

Perception of sensory information is determined by stimulus features (e.g., intensity) and instantaneous neural states (e.g., excitability). Commonly, it is assumed that both are reflected similarly in evoked brain potentials, that is, larger amplitudes are associated with a stronger percept of a stimulus. We tested this assumption in a somatosensory discrimination task in humans, simultaneously assessing (i) single-trial excitatory post-synaptic currents inferred from short-latency somatosensory evoked potentials (SEPs), (ii) pre-stimulus alpha oscillations (8-13 Hz), and (iii) peripheral nerve measures. Fluctuations of neural excitability shaped the perceived stimulus intensity already during the very first cortical response (at ~20 ms) yet demonstrating opposite neural signatures as compared to the effect of presented stimulus intensity. We reconcile this discrepancy via a common framework based on the modulation of electro-chemical membrane gradients linking neural states and responses, which calls for reconsidering conventional interpretations of brain potential magnitudes in stimulus intensity encoding

Cardiac activity impacts cortical motor excitability

Human cognition and action can be influenced by internal bodily processes such as heartbeats. For instance, somatosensory perception is impaired both during the systolic phase of the cardiac cycle and when heartbeats evoke stronger cortical responses. Here, we test whether these cardiac effects originate from overall changes in cortical excitability. Cortical and corticospinal excitability were assessed using electroencephalographic and electromyographic responses to transcranial magnetic stimulation while concurrently monitoring cardiac activity with electrocardiography. Cortical and corticospinal excitability were found to be highest during systole and following stronger cortical responses to heartbeats. Furthermore, in a motor task, hand-muscle activity and the associated desynchronization of sensorimotor oscillations were stronger during systole. These results suggest that systolic cardiac signals have a facilitatory effect on motor excitability – in contrast to sensory attenuation that was previously reported for somatosensory perception. Thus, distinct time windows may exist across the cardiac cycle that either optimize perception or action

Testing the effect of depth on the perception of faces in an online study

Faces are socially relevant stimuli that can be distinguished by the spatial arrangements of their visual features. However, face perception has been mostly investigated with static 2D images, which differs from everyday life experience. In an online study, we investigate face perception in two viewing conditions (2D & 3D). We compare the cognitive face space for these conditions, by modeling the acquired human similarity ratings with similarity matrices computed from physical face attributes and feature maps of deep learning-based face recognition models. Lastly, we fit these models to the human similarity judgements to explore relevant facial features between the viewing conditions. Unveiling differences between 2D and 3D perception of faces will further our understanding on the role of stimulus presentation on face processing

Decoding subjective emotional arousal from EEG during an immersive Virtual Reality experience

Immersive virtual reality (VR) enables naturalistic neuroscientific studies while maintaining experimental control, but dynamic and interactive stimuli pose methodological challenges. We here probed the link between emotional arousal, a fundamental property of affective experience, and parieto-occipital alpha power under naturalistic stimulation:37 young healthy adults completed an immersive VR experience, which included rollercoaster rides, while their EEG was recorded. They then continuously rated their subjective emotional arousal while viewing a replay of their experience. The association between emotional arousal and parieto-occipital alpha power was tested and confirmed by (1) decomposing the continuous EEG signal while maximizing the comodulation between alpha power and arousal ratings and by (2) decoding periods of high and low arousal with discriminative common spatial patterns and a Long Short-Term Memory recurrent neural network.We successfully combine EEG and a naturalistic immersive VR experience to extend previous findings on the neurophysiology of emotional arousal towards real-world neuroscience.Competing Interest StatementThe authors have declared no competing interest