Density of monodromy actions on non-abelian cohomology

In this paper we study the monodromy action on the first Betti and de Rham non-abelian cohomology arising from a family of smooth curves. We describe sufficient conditions for the existence of a Zariski dense monodromy orbit. In particular we show that for a Lefschetz pencil of sufficiently high degree the monodromy action is dense.Comment: LaTeX2e, 48 pages, Version substantially revised for publication. A gap in the proof of the density for Lefschetz pencils is fixed. The case of hyperelliptic monodromy is also treated in detai

Looking for a pattern: An MEG study on the abstract mismatch negativity in musicians and nonmusicians

<p>Abstract</p> <p>Background</p> <p>The mismatch negativity (MMN) is an early component of event-related potentials/fields, which can be observed in response to violations of regularities in sound sequences. The MMN can be elicited by simple feature (e.g. pitch) deviations in standard oddball paradigms as well as by violations of more complex sequential patterns. By means of magnetoencephalography (MEG) we investigated if a pattern MMN could be elicited based on global rather than local probabilities and if the underlying ability to integrate long sequences of tones is enhanced in musicians compared to nonmusicians.</p> <p>Results</p> <p>A pattern MMN was observed in response to violations of a predominant sequential pattern (AAAB) within a standard oddball tone sequence consisting of only two different tones. This pattern MMN was elicited even though the probability of pattern deviants in the sequence was as high as 0.5. Musicians showed more leftward-lateralized pattern MMN responses, which might be due to a stronger specialization of the ability to integrate information in a sequence of tones over a long time range.</p> <p>Conclusion</p> <p>The results indicate that auditory grouping and the probability distribution of possible patterns within a sequence influence the expectations about upcoming tones, and that the MMN might also be based on global statistical knowledge instead of a local memory trace. The results also show that auditory grouping based on sequential regularities can occur at a much slower presentation rate than previously presumed, and that probability distributions of possible patterns should be taken into account even for the construction of simple oddball sequences.</p

Non-birational twisted derived equivalences in abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kahler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kahler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov's `homological projective duality.' Along the way, we shall see how `noncommutative spaces' (in Kontsevich's sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.Comment: 54 pages, LaTeX; v2: typo fixe

Processing of Complex Auditory Patterns in Musicians and Nonmusicians

In the present study we investigated the capacity of the memory store underlying the mismatch negativity (MMN) response in musicians and nonmusicians for complex tone patterns. While previous studies have focused either on the kind of information that can be encoded or on the decay of the memory trace over time, we studied capacity in terms of the length of tone sequences, i.e., the number of individual tones that can be fully encoded and maintained. By means of magnetoencephalography (MEG) we recorded MMN responses to deviant tones that could occur at any position of standard tone patterns composed of four, six or eight tones during passive, distracted listening. Whereas there was a reliable MMN response to deviant tones in the four-tone pattern in both musicians and nonmusicians, only some individuals showed MMN responses to the longer patterns. This finding of a reliable capacity of the short-term auditory store underlying the MMN response is in line with estimates of a three to five item capacity of the short-term memory trace from behavioural studies, although pitch and contour complexity covaried with sequence length, which might have led to an understatement of the reported capacity. Whereas there was a tendency for an enhancement of the pattern MMN in musicians compared to nonmusicians, a strong advantage for musicians could be shown in an accompanying behavioural task of detecting the deviants while attending to the stimuli for all pattern lengths, indicating that long-term musical training differentially affects the memory capacity of auditory short-term memory for complex tone patterns with and without attention. Also, a left-hemispheric lateralization of MMN responses in the six-tone pattern suggests that additional networks that help structuring the patterns in the temporal domain might be recruited for demanding auditory processing in the pitch domain

Effects of musical training and event probabilities on encoding of complex tone patterns

Background: The human auditory cortex automatically encodes acoustic input from the environment and differentiates regular sound patterns from deviant ones in order to identify important, irregular events. The Mismatch Negativity (MMN) response is a neuronal marker for the detection of sounds that are unexpected, based on the encoded regularities. It is also elicited by violations of more complex regularities and musical expertise has been shown to have an effect on the processing of complex regularities. Using magnetoencephalography (MEG), we investigated the MMN response to salient or less salient deviants by varying the standard probability (70%, 50% and 35%) of a pattern oddball paradigm. To study the effects of musical expertise in the encoding of the patterns, we compared the responses of a group of non-musicians to those of musicians. Results: We observed significant MMN in all conditions, including the least salient condition (35% standards), in response to violations of the predominant tone pattern for both groups. The amplitude of MMN from the right hemisphere was influenced by the standard probability. This effect was modulated by long-term musical training: standard probability changes influenced MMN amplitude in the group of non-musicians only. Conclusion: This study indicates that pattern violations are detected automatically, even if they are of very low salience, both in non-musicians and musicians, with salience having a stronger impact on processing in the right hemisphere of non-musicians. Long-term musical training influences this encoding, in that non-musicians benefit to a greater extent from a good signal-to-noise ratio (i.e. high probability of the standard pattern), while musicians are less dependent on the salience of an acoustic environment.<br

Modulations of neural activity in auditory streaming caused by spectral and temporal alternation in subsequent stimuli: a magnetoencephalographic study

Background: The aim of the present study was to identify a specific neuronal correlate underlying the preattentive auditory stream segregation of subsequent sound patterns alternating in spectral or temporal cues. Fifteen participants with normal hearing were presented with series’ of two consecutive ABA auditory tone-triplet sequences, the initial triplets being the Adaptation sequence and the subsequent triplets being the Test sequence. In the first experiment, the frequency separation (delta-f) between A and B tones in the sequences was varied by 2, 4 and 10 semitones. In the second experiment, a constant delta-f of 6 semitones was maintained but the Inter-Stimulus Intervals (ISIs) between A and B tones were varied. Auditory evoked magnetic fields (AEFs) were recorded using magnetoencephalography (MEG). Participants watched a muted video of their choice and ignored the auditory stimuli. In a subsequent behavioral study both MEG experiments were replicated to provide information about the participants’ perceptual state. Results: MEG measurements showed a significant increase in the amplitude of the B-tone related P1 component of the AEFs as delta-f increased. This effect was seen predominantly in the left hemisphere. A significant increase in the amplitude of the N1 component was only obtained for a Test sequence delta-f of 10 semitones with a prior Adaptation sequence of 2 semitones. This effect was more pronounced in the right hemisphere. The additional behavioral data indicated an increased probability of two-stream perception for delta-f = 4 and delta-f = 10 semitones with a preceding Adaptation sequence of 2 semitones. However, neither the neural activity nor the perception of the successive streaming sequences were modulated when the ISIs were alternated. Conclusions: Our MEG experiment demonstrated differences in the behavior of P1 and N1 components during the automatic segregation of sounds when induced by an initial Adaptation sequence. The P1 component appeared enhanced in all Test-conditions and thus demonstrates the preceding context effect, whereas N1 was specifically modulated only by large delta-f Test sequences induced by a preceding small delta-f Adaptation sequence. These results suggest that P1 and N1 components represent at least partially-different systems that underlie the neural representation of auditory streaming

Perceptual organization of auditory streaming-task relies on neural entrainment of the stimulus-presentation rate: MEG evidence

Background: Humans are able to extract regularities from complex auditory scenes in order to form perceptually meaningful elements. It has been shown previously that this process depends critically on both the temporal integration of the sensory input over time and the degree of frequency separation between concurrent sound sources. Our goal was to examine the relationship between these two aspects by means of magnetoencephalography (MEG). To achieve this aim, we combined time-frequency analysis on a sensor space level with source analysis. Our paradigm consisted of asymmetric ABA-tone triplets wherein the B-tones were presented temporally closer to the first A-tones, providing different tempi within the same sequence. Participants attended to the slowest B-rhythm whilst the frequency separation between tones was manipulated (0-, 2-, 4- and 10-semitones). Results: The results revealed that the asymmetric ABA-triplets spontaneously elicited periodic-sustained responses corresponding to the temporal distribution of the A-B and B-A tone intervals in all conditions. Moreover, when attending to the B-tones, the neural representations of the A- and B-streams were both detectable in the scenarios which allow perceptual streaming (2-, 4- and 10-semitones). Alongside this, the steady-state responses tuned to the presentation of the B-tones enhanced significantly with increase of the frequency separation between tones. However, the strength of the B-tones related steady-state responses dominated the strength of the A-tones responses in the 10-semitones condition. Conversely, the representation of the A-tones dominated the B-tones in the cases of 2- and 4-semitones conditions, in which a greater effort was required for completing the task. Additionally, the P1 evoked fields’ component following the B-tones increased in magnitude with the increase of inter-tonal frequency difference. Conclusions: The enhancement of the evoked fields in the source space, along with the B-tones related activity of the time-frequency results, likely reflect the selective enhancement of the attended B-stream. The results also suggested a dissimilar efficiency of the temporal integration of separate streams depending on the degree of frequency separation between the sounds. Overall, the present findings suggest that the neural effects of auditory streaming could be directly captured in the time-frequency spectrum at the sensor-space level.<br

Playing and Listening to Tailor-Made Notched Music: Cortical Plasticity Induced by Unimodal and Multimodal Training in Tinnitus Patients

Background. The generation and maintenance of tinnitus are assumed to be based on maladaptive functional cortical reorganization. Listening to modified music, which contains no energy in the range of the individual tinnitus frequency, can inhibit the corresponding neuronal activity in the auditory cortex. Music making has been shown to be a powerful stimulator for brain plasticity, inducing changes in multiple sensory systems. Using magnetoencephalographic (MEG) and behavioral measurements we evaluated the cortical plasticity effects of two months of (a) active listening to (unisensory) versus (b) learning to play (multisensory) tailor-made notched music in nonmusician tinnitus patients. Taking into account the fact that uni- and multisensory trainings induce different patterns of cortical plasticity we hypothesized that these two protocols will have different affects. Results. Only the active listening (unisensory) group showed significant reduction of tinnitus related activity of the middle temporal cortex and an increase in the activity of a tinnitus-coping related posterior parietal area. Conclusions. These findings indicate that active listening to tailor-made notched music induces greater neuroplastic changes in the maladaptively reorganized cortical network of tinnitus patients while additional integration of other sensory modalities during training reduces these neuroplastic effects

Quantization of Fayet-Iliopoulos Parameters in Supergravity

In this short note we discuss quantization of the Fayet-Iliopoulos parameter in supergravity theories. We argue that in supergravity, the Fayet-Iliopoulos parameter determines a lift of the group action to a line bundle, and such lifts are quantized. Just as D-terms in rigid N=1 supersymmetry are interpreted in terms of moment maps and symplectic reductions, we argue that in supergravity the quantization of the Fayet-Iliopoulos parameter has a natural understanding in terms of linearizations in geometric invariant theory (GIT) quotients, the algebro-geometric version of symplectic quotients.Comment: 21 pages, utarticle class; v2: typos and tex issue fixe