Del Pezzo surfaces with 1/3(1,1) points

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces.Comment: 42 pages. v2: model construction added of last remaining surface, minor corrections, minor changes to presentation, references adde

Prior movement of one arm facilitates motor adaptation in the other

Many movements in daily life are embedded in motion sequences that involve more than one limb, demanding the motor system to monitor and control different body parts in quick succession. During such movements, systematic changes in the environment or the body might require motor adaptation of specific segments. However, previous motor adaptation research has focused primarily on motion sequences produced by a single limb, or on simultaneous movements of several limbs. For example, adaptation to opposing force fields is possible in unimanual reaching tasks when the direction of a prior or subsequent movement is predictive of force field direction. It is unclear, however, whether multi-limb sequences can support motor adaptation processes in a similar way. In the present study, we investigated whether reaches can be adapted to different force fields in a bimanual motor sequence when the information about the perturbation is associated with the prior movement direction of the other arm. In addition, we examined whether prior perceptual (visual or proprioceptive) feedback of the opposite arm contributes to force field-specific motor adaptation. Our key finding is that only active participation in the bimanual sequential task supports pronounced adaptation. This result suggests that active segments in bimanual motion sequences are linked across limbs. If there is a consistent association between movement kinematics of the linked and goal movement, the learning process of the goal movement can be facilitated. More generally, if motion sequences are repeated often, prior segments can evoke specific adjustments of subsequent movements

Brill–Noether general K3 surfaces with the maximal number of elliptic pencils of minimal degree

We explicitly construct Brill–Noether general K3 surfaces of genus 4, 6 and 8 having the maximal number of elliptic pencils of degrees 3, 4 and 5, respectively, and study their moduli spaces and moduli maps to the moduli space of curves. As an application we prove the existence of Brill–Noether general K3 surfaces of genus 4 and 6 without stable Lazarsfeld–Mukai bundles of minimal c2.publishedVersio

A pp-adic Approach to the Weil Representation of Discriminant Forms Arising from Even Lattices

Suppose that $M$ is an even lattice with dual $M^{*}$ and level $N$. Then the group $Mp_{2}(\mathbb{Z})$, which is the unique non-trivial double cover of $SL_{2}(\mathbb{Z})$, admits a representation $\rho_{M}$, called the Weil representation, on the space $\mathbb{C}[M^{*}/M]$. The main aim of this paper is to show how the formulae for the $\rho_{M}$-action of a general element of $Mp_{2}(\mathbb{Z})$ can be obtained by a direct evaluation which does not depend on ``external objects'' such as theta functions. We decompose the Weil representation $\rho_{M}$ into $p$-parts, in which each $p$-part can be seen as subspace of the Schwartz functions on the $p$-adic vector space $M_{\mathbb{Q}_{p}}$. Then we consider the Weil representation of $Mp_{2}(\mathbb{Q}_{p})$ on the space of Schwartz functions on $M_{\mathbb{Q}_{p}}$, and see that restricting to $Mp_{2}(\mathbb{Z})$ just gives the $p$-part of $\rho_{M}$ again. The operators attained by the Weil representation are not always those appearing in the formulae from 1964, but are rather their multiples by certain roots of unity. For this, one has to find which pair of elements, lying over a matrix in $SL_{2}(\mathbb{Q}_{p})$, belong to the metaplectic double cover. Some other properties are also investigated.Comment: 29 pages, shortened a lo

Gamma Power Is Phase-Locked to Posterior Alpha Activity

Neuronal oscillations in various frequency bands have been reported in numerous studies in both humans and animals. While it is obvious that these oscillations play an important role in cognitive processing, it remains unclear how oscillations in various frequency bands interact. In this study we have investigated phase to power locking in MEG activity of healthy human subjects at rest with their eyes closed. To examine cross-frequency coupling, we have computed coherence between the time course of the power in a given frequency band and the signal itself within every channel. The time-course of the power was calculated using a sliding tapered time window followed by a Fourier transform. Our findings show that high-frequency gamma power (30–70 Hz) is phase-locked to alpha oscillations (8–13 Hz) in the ongoing MEG signals. The topography of the coupling was similar to the topography of the alpha power and was strongest over occipital areas. Interestingly, gamma activity per se was not evident in the power spectra and only became detectable when studied in relation to the alpha phase. Intracranial data from an epileptic subject confirmed these findings albeit there was slowing in both the alpha and gamma band. A tentative explanation for this phenomenon is that the visual system is inhibited during most of the alpha cycle whereas a burst of gamma activity at a specific alpha phase (e.g. at troughs) reflects a window of excitability

Bias adjustment and ensemble recalibration methods for seasonal forecasting: a comprehensive intercomparison using the C3S dataset

This work presents a comprehensive intercomparison of diferent alternatives for the calibration of seasonal forecasts, ranging from simple bias adjustment (BA)-e.g. quantile mapping-to more sophisticated ensemble recalibration (RC) methods- e.g. non-homogeneous Gaussian regression, which build on the temporal correspondence between the climate model and the corresponding observations to generate reliable predictions. To be as critical as possible, we validate the raw model and the calibrated forecasts in terms of a number of metrics which take into account diferent aspects of forecast quality (association, accuracy, discrimination and reliability). We focus on one-month lead forecasts of precipitation and temperature from four state-of-the-art seasonal forecasting systems, three of them included in the Copernicus Climate Change Service dataset (ECMWF-SEAS5, UK Met Ofce-GloSea5 and Météo France-System5) for boreal winter and summer over two illustrative regions with diferent skill characteristics (Europe and Southeast Asia). Our results indicate that both BA and RC methods efectively correct the large raw model biases, which is of paramount importance for users, particularly when directly using the climate model outputs to run impact models, or when computing climate indices depending on absolute values/thresholds. However, except for particular regions and/or seasons (typically with high skill), there is only marginal added value-with respect to the raw model outputs-beyond this bias removal. For those cases, RC methods can outperform BA ones, mostly due to an improvement in reliability. Finally, we also show that whereas an increase in the number of members only modestly afects the results obtained from calibration, longer hindcast periods lead to improved forecast quality, particularly for RC methods.This work has been funded by the C3S activity on Evaluation and Quality Control for seasonal forecasts. JMG was partially supported by the project MULTI-SDM (CGL2015-66583-R, MINECO/FEDER). FJDR was partially funded by the H2020 EUCP project (GA 776613)

A Generalized Framework for Quantifying the Dynamics of EEG Event-Related Desynchronization

Brains were built by evolution to react swiftly to environmental challenges. Thus, sensory stimuli must be processed ad hoc, i.e., independent—to a large extent—from the momentary brain state incidentally prevailing during stimulus occurrence. Accordingly, computational neuroscience strives to model the robust processing of stimuli in the presence of dynamical cortical states. A pivotal feature of ongoing brain activity is the regional predominance of EEG eigenrhythms, such as the occipital alpha or the pericentral mu rhythm, both peaking spectrally at 10 Hz. Here, we establish a novel generalized concept to measure event-related desynchronization (ERD), which allows one to model neural oscillatory dynamics also in the presence of dynamical cortical states. Specifically, we demonstrate that a somatosensory stimulus causes a stereotypic sequence of first an ERD and then an ensuing amplitude overshoot (event-related synchronization), which at a dynamical cortical state becomes evident only if the natural relaxation dynamics of unperturbed EEG rhythms is utilized as reference dynamics. Moreover, this computational approach also encompasses the more general notion of a “conditional ERD,” through which candidate explanatory variables can be scrutinized with regard to their possible impact on a particular oscillatory dynamics under study. Thus, the generalized ERD represents a powerful novel analysis tool for extending our understanding of inter-trial variability of evoked responses and therefore the robust processing of environmental stimuli

Increase of universality in human brain during mental imagery from visual perception

BACKGROUND: Different complex systems behave in a similar way near their critical points of phase transitions which leads to an emergence of a universal scaling behaviour. Universality indirectly implies a long-range correlation between constituent subsystems. As the distributed correlated processing is a hallmark of higher complex cognition, I investigated a measure of universality in human brain during perception and mental imagery of complex real-life visual object like visual art. METHODOLOGY/PRINCIPAL FINDINGS: A new method was presented to estimate the strength of hidden universal structure in a multivariate data set. In this study, I investigated this method in the electrical activities (electroencephalogram signals) of human brain during complex cognition. Two broad groups--artists and non-artists--were studied during the encoding (perception) and retrieval (mental imagery) phases of actual paintings. Universal structure was found to be stronger in visual imagery than in visual perception, and this difference was stronger in artists than in non-artists. Further, this effect was found to be largest in the theta band oscillations and over the prefrontal regions bilaterally. CONCLUSIONS/SIGNIFICANCE: Phase transition like dynamics was observed in the electrical activities of human brain during complex cognitive processing, and closeness to phase transition was higher in mental imagery than in real perception. Further, the effect of long-term training on the universal scaling was also demonstrated