The Arithmetic of Calabi--Yau Manifolds and Mirror Symmetry

We study mirror symmetric pairs of Calabi--Yau manifolds over finite fields. In particular we compute the number of rational points of the manifolds as a function of the complex structure parameters. The data of the number of rational points of a Calabi--Yau $X/\mathbb{F}_q$ can be encoded in a generating function known as the congruent zeta function. The Weil Conjectures (proved in the 1970s) show that for smooth varieties, these functions take a very interesting form in terms of the Betti numbers of the variety. This has interesting implications for mirror symmetry, as mirror symmetry exchanges the odd and even Betti numbers. Here the zeta functions for a one-parameter family of K3 surfaces, $\mathbb{P}_3[4]$, and a two-parameter family of octics in weighted projective space, $\mathbb{P}_4{}^{(1, 1, 2, 2, 2)} [8]$, are computed. The form of the zeta function at points in the moduli space of complex structures where the manifold is singular (where the Weil conjectures apart from rationality are not applicable), is investigated. The zeta function appears to be sensitive to monomial and non-monomial deformations of complex structure (or equivalently on the mirror side, toric and non-toric divisors). Various conjectures about the form of the zeta function for mirror symmetric pairs are made in light of the results of this calculation. Connections with $L$-functions associated to both elliptic and Siegel modular forms are suggested.Comment: Oxford University DPhil thesis, 199 pages, 28 figure

Modulation of speech-in-noise comprehension through transcranial current stimulation with the phase-shifted speech envelope

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/Neural activity tracks the envelope of a speech signal at latencies from 50 ms to 300 ms. Modulating this neural tracking through transcranial alternating current stimulation influences speech comprehension. Two important variables that can affect this modulation are the latency and the phase of the stimulation with respect to the sound. While previous studies have found an influence of both variables on speech comprehension, the interaction between both has not yet been measured. We presented 17 subjects with speech in noise coupled with simultaneous transcranial alternating current stimulation. The currents were based on the envelope of the target speech but shifted by different phases, as well as by two temporal delays of 100 ms and 250 ms. We also employed various control stimulations, and assessed the signal-to-noise ratio at which the subject understood half of the speech. We found that, at both latencies, speech comprehension is modulated by the phase of the current stimulation. However, the form of the modulation differed between the two latencies. Phase and latency of neurostimulation have accordingly distinct influences on speech comprehension. The different effects at the latencies of 100 ms and 250 ms hint at distinct neural processes for speech processing.Peer reviewe

Fast and accurate spike sorting of high-channel count probes with KiloSort

Marius Pachitariu, Nick Steinmetz, Shabnam Kadir, Matteo Carandini, and Kenneth Harris, ‘Fast and accurate spike sorting of high-channel count probes with KiloSort’, Paper presented at the Neural Information Processing Systems (NIPS 2016) Conference, 5 -10 December 2016, Centre Convencions Internacional, Barcelona, Spain, https://papers.nips.cc/book/advances-in-neural-information-processing-systems-29-2016New silicon technology is enabling large-scale electrophysiological recordings in vivo from hundreds to thousands of channels. Interpreting these recordings requires scalable and accurate automated methods for spike sorting, which should minimize the time required for manual curation of the results. Here we introduce KiloSort, a new integrated spike sorting framework that uses template matching both during spike detection and during spike clustering. KiloSort models the electrical voltage as a sum of template waveforms triggered on the spike times, which allows overlapping spikes to be identified and resolved. Unlike previous algorithms that compress the data with PCA, KiloSort operates on the raw data which allows it to construct a more accurate model of the waveforms. Processing times are faster than in previous algorithms thanks to batch-based optimization on GPUs. We compare KiloSort to an established algorithm and show favorable performance, at much reduced processing times. A novel post-clustering merging step based on the continuity of the templates further reduced substantially the number of manual operations required on this data, for the neurons with near-zero error rates, paving the way for fully automated spike sorting of multichannel electrode recordings

Transcranial alternating current stimulation in the theta band but not in the delta band modulates the comprehension of naturalistic speech in noise

© 2020 Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Auditory cortical activity entrains to speech rhythms and has been proposed as a mechanism for online speech processing. In particular, neural activity in the theta frequency band (4–8 ​Hz) tracks the onset of syllables which may aid the parsing of a speech stream. Similarly, cortical activity in the delta band (1–4 ​Hz) entrains to the onset of words in natural speech and has been found to encode both syntactic as well as semantic information. Such neural entrainment to speech rhythms is not merely an epiphenomenon of other neural processes, but plays a functional role in speech processing: modulating the neural entrainment through transcranial alternating current stimulation influences the speech-related neural activity and modulates the comprehension of degraded speech. However, the distinct functional contributions of the delta- and of the theta-band entrainment to the modulation of speech comprehension have not yet been investigated. Here we use transcranial alternating current stimulation with waveforms derived from the speech envelope and filtered in the delta and theta frequency bands to alter cortical entrainment in both bands separately. We find that transcranial alternating current stimulation in the theta band but not in the delta band impacts speech comprehension. Moreover, we find that transcranial alternating current stimulation with the theta-band portion of the speech envelope can improve speech-in-noise comprehension beyond sham stimulation. Our results show a distinct contribution of the theta- but not of the delta-band stimulation to the modulation of speech comprehension. In addition, our findings open up a potential avenue of enhancing the comprehension of speech in noise.Peer reviewe

High-dimensional cluster analysis with the masked EM algorithm

This is an Open Access article published under a Creative Commons Attribution 3.0 Unported (CC BY 3.0) license https://creativecommons.org/licenses/by/3.0/Cluster analysis faces two problems in high dimensions: the "curse of dimensionality" that can lead to overfitting and poor generalization performance and the sheer time taken for conventional algorithms to process large amounts of high-dimensional data. We describe a solution to these problems, designed for the application of spike sorting for nextgeneration, high-channel-count neural probes. In this problem, only a small subset of features provides information about the cluster membership of any one data vector, but this informative feature subset is not the same for all data points, rendering classical feature selection ineffective.We introduce a "masked EM" algorithm that allows accurate and time-efficient clustering of up to millions of points in thousands of dimensions. We demonstrate its applicability to synthetic data and to real-world high-channel-count spike sorting data.Peer reviewe

Characterization of Mononucleated Human Peripheral Blood Cells

Unspecialized cells that can renew themselves and give rise to multiple differentiated cell types are termed stem cells. The objective of this study was to characterize and investigate, through molecular and biochemical analyses, the stemness of cells derived from isolated mononucleated cells that originated from peripheral blood. The isolated mononucleated cells were separated according to their physical characteristics (adherent and suspension), after 4 to 7 days into a 14-day culturing period in complete medium. Our results revealed that adherent and suspension cells were positive for mesenchymal stem cell (MSC) and hematopoietic stem cell (HSC) markers, respectively. Differentiation of adherent cells into osteoblasts was associated with expression of the OPN gene and increasing ALP enzyme activity, while differentiation of suspension cells into osteoclasts was associated with expression of the TRAP gene and increasing TRAP enzyme activity. In conclusion, molecular and biochemical analyses showed that mononucleated cells consist of MSC (adherent) and HSC (suspension), and both cell types are able to differentiate into specialized cells from their respective lineage: osteoblast (MSC) and osteoclast (HSC)

Fast and accurate spike sorting of high-channel count probes with KiloSort

Abstract New silicon technology is enabling large-scale electrophysiological recordings in vivo from hundreds to thousands of channels. Interpreting these recordings requires scalable and accurate automated methods for spike sorting, which should minimize the time required for manual curation of the results. Here we introduce KiloSort, a new integrated spike sorting framework that uses template matching both during spike detection and during spike clustering. KiloSort models the electrical voltage as a sum of template waveforms triggered on the spike times, which allows overlapping spikes to be identified and resolved. Unlike previous algorithms that compress the data with PCA, KiloSort operates on the raw data which allows it to construct a more accurate model of the waveforms. Processing times are faster than in previous algorithms thanks to batch-based optimization on GPUs. We compare KiloSort to an established algorithm and show favorable performance, at much reduced processing times. A novel post-clustering merging step based on the continuity of the templates further reduced substantially the number of manual operations required on this data, for the neurons with nearzero error rates, paving the way for fully automated spike sorting of multichannel electrode recordings