Deep generative modeling for single-cell transcriptomics.

Single-cell transcriptome measurements can reveal unexplored biological diversity, but they suffer from technical noise and bias that must be modeled to account for the resulting uncertainty in downstream analyses. Here we introduce single-cell variational inference (scVI), a ready-to-use scalable framework for the probabilistic representation and analysis of gene expression in single cells ( https://github.com/YosefLab/scVI ). scVI uses stochastic optimization and deep neural networks to aggregate information across similar cells and genes and to approximate the distributions that underlie observed expression values, while accounting for batch effects and limited sensitivity. We used scVI for a range of fundamental analysis tasks including batch correction, visualization, clustering, and differential expression, and achieved high accuracy for each task

based on resting state fMRI

학위논문(박사) -- 서울대학교대학원 : 융합과학기술대학원 분자의학 및 바이오제약학과, 2021.8. 위원석.대부분의 실세계 네트워크에서 네트워크의 구성에 있어서 기하학이 중요한 역할을 하며, 최근 연구에서 구조적 뇌 네트워크는 쌍곡기하적 특성을 가지고 있음이 밝혀졌다. 뇌의 구조와 기능은 밀접한 연관을 지니고 있으므로, 기능적 뇌 네트워크 역시 쌍곡기하적 특성을 지니고 있음을 추정할 수 있다. 이번 연구에서, 우리는 휴식기 뇌 자기공명영상(rs-fMRI)을 통해 추출한 기능적 뇌 커넥톰(connectome)을 분석하여 이 가설을 증명하고자 하였으며, 이를 쌍곡공간에 임베드(embed)함으로써 기능적 뇌 네트워크의 특성을 새로이 조사하고자 하였다. 네트워크의 꼭지점은 274개의 미리 정의된 관심영역(ROI) 혹은 6mm 크기의 복셀(voxel)의 두 가지 스케일로 정의되었으며, 꼭지점 사이의 연결성은 자기공명 영상에서 각 영역의 시간에 따른 BOLD 신호의 상관관계를 측정하고 일정 문턱값(threshold)을 적용함으로서 결정되었다. 먼저 쌍곡기하 네트워크의 특징인 스케일-프리(scale-free)를 만족함을 확인하기 위해, 네트워크의 차수(degree) 분포의 급수성(power-law)을 평가하였다. 차수의 확률분포곡선은 로그-로그 스케일의 그래프에서 우하향하는 직선 모양의 분포를 보였으며, 이는 즉 차수 분포가 차수의 음의 급수함수에 의해 나타내어짐을 의미한다. 이어서 기능적 뇌 네트워크에 가장 적합한 기저 기하를 확인하기 위하여, 그래프를 유클리드, 쌍곡, 구면적 틍성을 가진 다양체들에 임베드하여 임베딩의 충실성 척도(fidelity measure)들을 비교하였다. 임베드 대상이 된 적 다양체들 중, 10차원 및 2차원 쌍곡공간의 평균 뒤틀림(distortion)이 동일 차원의 유클리드 다양체와 비교하여 더 낮았다. 이어, 네트워크를 구체화 및 시각화하고 그 특징을 확인하기 위하여, 네트워크를 이차원의 쌍곡 원판에 1/ℍ2 기하학적 모델에 따라 임베드하였다. 이 이차원의 극좌표 형태의 모델에서 반경 및 각 차원의 좌표는 각각 꼭지점의 연결 인기도 및 유사도를 나타낸다. ROI 수준의 분석에서는 특별히 높은 인기도를 갖는 영역은 관찰되지 않아 임베드된 원판의 중심부에 빈 공간으로 나타났다. 한편 같은 해부학적 엽(lobe)에 속한 영역들은 비슷한 각도 영역 내에 밀집되었으며, 반대측 동일 엽에 속한 영역들 역시 그 각좌표의 분포가 구분되지 않았다. 이는 기능적 뇌 네트워크의 해부학적 연관성과 반대측 동일 엽 간의 기능적 연관성을 나타내는 것으로 볼 수 있다. 또한, 복셀 수준의 분석에서는 소뇌에 속한 복셀들 중 다수가 넓은 각좌표 영역에 흩뿌려진 현상이 나타났으며, 이는 개개 복셀의 기능적 이질성을 시사한다. 또한, 전 영역에 걸쳐 매우 유사한 각좌표를 가진 방사형의 막대 모양의 점의 집합이 관찰되었으며, 높은 기능적 유사성을 가진 복셀들로 볼 수 있다. 복셀 수준의 네트워크에서 뇌의 독립성분 분석(ICA) 의 결과로 나온 성분 네트워크들을 플로팅한 결과, 각 네트워크 성분이 높은 밀집도를 보여 두 방법론 간 결과의 유사성을 확인할 수 있었다. 자폐스펙트럼장애의 ABIDE II 오픈 데이터셋을 이용하여 1/ℍ2 모델에 근거하여, 대조군 환자 그룹과 질병군 환자 개인의 네트워크를 비교하는 분석을 시행한 결과, 질병군에서 다양한 패턴을 보였으나, 그 중 자폐증 진단을 받은 환자에서 피질-선조체 경로의 이상이, 아스퍼거증후군 진단을 받은 환자에서 후위관자고랑 (posterior superior temporal sulcus) 을 포함하는 경로의 이상을 발견할 수 있었다. 분석의 재현성을 확인하기 위하여 같은 네트워크를 대상으로 임베딩 과정을 반복 시행하였을 때, 네트워크 말단의 일부 꼭지점을 제외하면 높은 재현성을 보였다. 영상의 시계열(time series) 내 일관성을 확인하기 위하여 영상을 시간 구간에 따라 분리하여 분석하였을 때, 4구간으로 나눈 시계열 영상에서는 유사한 결과를 얻었으나 30초 길이의 30구간으로 나뉘었을 때는 일관적인 결과가 관찰되지 않았다. 이 연구는 뇌 기능적 네트워크에 대한 분석 중 최초로 기하학적 관점에서 진행된 것이며, 이러한 새로운 관점 및 질병군 대상에서 뇌 네트워크의 이상을 찾기 위한 새로운 방법론을 제시한다는 의의가 있다.For most of the real-world networks, geometry plays an important role in organizing the network, and recent works have revealed that the geometry in the structural brain network is most likely to be hyperbolic. Therefore, it can be assumed that the geometry of the functional brain network would also be hyperbolic. In this study, we analyzed the functional connectomes from functional magnetic resonance imaging (fMRI) to prove this hypothesis and investigate the characteristics of the network by embedding it into the hyperbolic space, by utilizing human connectome project (HCP) dataset for healthy young adults and Autism Brain Imaging Data Exchange II (ABIDE II) dataset for diseased autism subject and control group. Nodes of the network were defined at two different scales: by 274 predefined ROIs and 6mm-sized voxels. The adjacency between the nodes was determined by computing the correlation of the time-series of the BOLD signal of brain regions and binarized by adopting threshold value. First, we aimed to find out whether the network was scale-free by investigating the degree distribution of the functional brain network. The probability distribution function (PDF) versus degree was plotted as a straight line at a log-log scale graph versus the degree of nodes. This indicates that degree distribution is roughly proportional to a power function of degree, or scale-free. To clarify the most fitting underlying geometry of the network, we then embedded the graph into manifolds of Euclidean, hyperbolic, or spherical spaces and compared the fidelity measures of embeddings. The embedding to the hyperbolic spaces yielded a better fidelity measure compared to other manifolds. To get a discrete and visible map and investigate the characteristics of the network, we embedded the network in a two-dimensional hyperbolic disc by the 1/ℍ2 model. The radial and angular dimensions in the embedding is interpreted as popularity and similarity dimensions, respectively. The ROI-wise analysis revealed that no nodes with particularly high popularity were found, which was revealed by a vacant area in the center of the disk. Nodes in the same lobe were more likely to be clustered in narrow similarity dimensions, and the nodes from the homotopic lobes were also functionally clustered. The results indicate the anatomic relevance of the functional brain network and the strong functional coherence of the homotopic area of the cerebral cortex. The voxel-wise analysis revealed additional features. A large number of voxels from the cerebellum were scattered in the whole angular position, which might reflect the functional heterogeneity of the cerebellum in the sub-ROI level. Additionally, multiple rod-shaped substructures of radial direction were found, which indicates sets of voxels with functional similarity. When compared with independent component analysis (ICA)-driven results, each large-scale component of the brain acquired by ICA showed a consistent pattern of embedding between the subjects. To find the abnormality of the network in the diseased patient, we utilized the autistic spectrum disorder (ASD) dataset. The two groups of ASD and the control group were found to be comparable in means of the quality of embedding. We calculated the hyperbolic distance between all edges of the network and searched for the alteration of the distance of the individual brain network. Among the variable results among the networks of ASD group subjects, the alteration of the cortico-striatal pathway in an autism patient and posterior superior temporal sulcus (pSTS) in an Asperger’s syndrome patient were present, respectively. The two different anatomically-scaled layers of the network showed a certain degree of correspondence in terms of degree-degree correlation and spreading pattern of network. But anatomically parcellated ROI did not guarantee the functional similarity between the voxels composing it. Finally, to investigate the reproducibility of the embedding process, we repeatedly performed the embedding process and computed the variance of distance matrices. The result was stable except for end-positioned non-popular nodes. Furthermore, to investigate consistency along time-series of fMRI, we compared network yielded by segments of the time series. The segmented networks showed similar results when divided into four frames, but the result lost consistency when divided into 30 frames of 30 seconds each. This study is the first to investigate the characteristics of the functional brain network on the basis of hyperbolic geometry. We suggest a new method applicable for assessing the network alteration in subjects with a neuropsychiatric disease, and these approaches grant us a new understanding in analyzing the functional brain network with a geometric perspective.1. Introduction 1 1.1. Human brain networks 1 1.1.1. Geometry of human brain networks 2 1.2. Scale-free network 3 1.2.1. Definition of a scale-free network 4 1.3. Embedding of the network in hyperbolic space 5 1.3.1. Hyperbolic spaces and Poincaré disk 5 1.3.2. Geometric model of 1/ℍ2 9 1.4. The aim of the present study 10 2. Methods 12 2.1. Subjects and image acquisition 12 2.1.1. Human connectome project (HCP) dataset 12 2.1.2. Autism Brain Imaging Data Exchange II (ABIDE II) dataset 12 2.2. Preprocessing for resting-state fMRI 15 2.3. Resting-state networks and functional connectivity analysis 16 2.3.1. Analyzing degree distribution 18 2.4. Assessing underlying geometry 18 2.4.1. The three component spaces 18 2.4.2. Embedding into spaces 20 2.5. Embedding of the network in the 1/ℍ2 model 22 2.6. Comparison with ICA-driven method 23 2.7. Assessing the quality of embedding 23 2.8. Abnormality detection in the diseased subject 24 2.9. Assessing variability of analysis 27 3. Results 29 3.1. Global characteristics of the network 29 3.1.1. The degree distribution 31 3.1.2. Determining the threshold value of network 34 3.2. Graph embedding into spaces 36 3.3. 1/ℍ2 model analysis 39 3.4. Quality of the embedding 58 3.5. Alteration of the network in the diseased subject 61 3.6. Variability of results 63 3.6.1. Reproducibility of Mercator 63 3.6.2. Time variance of results 67 4. Discussion 70 4.1. Composition of the network 70 4.2. Scale-freeness of brain network 71 4.3. The underlying geometry of brain network 73 4.4. Hyperbolic plane representation 75 4.4.1. Voxelwise approach 78 4.4.2. Compatibility with ICA 80 4.5. Alteration of the network in ASD subjects 81 4.6. Variability and reproducibility of methods 83 4.7. Further applications 85 5. Conclusion 87 References 89 국문 초록 106박

Four-band non-Abelian topological insulator and its experimental realization

Very recently, increasing attention has been focused on non-Abelian topological charges, e.g. the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple tangled bulk bandgaps and support non-trivial edge states that manifest the non-Abelian topological features. Furthermore, a system with even or odd number of bands will exhibit significant difference in non-Abelian topological classifications. Up to now, there is scant research investigating the even-band non-Abelian topological insulators. Here, we both theoretically explored and experimentally realized a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference from four-dimensional rotation senses on the stereographically projected Clifford tori. We show the evolution of bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way to other even band systems.Comment: Main text and supplementary informatio

On Steady Solutions of a generalized Whitham equation

publishedVersionPaid open acces

Harmonized-Multinational qEEG Norms (HarMNqEEG)

This paper extends the frequency domain quantitative electroencephalography (qEEG) methods pursuing higher sensitivity to detect Brain Developmental Disorders. Prior qEEG work lacked integration of cross-spectral information omitting important functional connectivity descriptors. Lack of geographical diversity precluded accounting for site-specific variance, increasing qEEG nuisance variance. We ameliorate these weaknesses. i) Create lifespan Riemannian multinational qEEG norms for cross-spectral tensors. These norms result from the HarMNqEEG project fostered by the Global Brain Consortium. We calculate the norms with data from 9 countries, 12 devices, and 14 studies, including 1564 subjects. Instead of raw data, only anonymized metadata and EEG cross-spectral tensors were shared. After visual and automatic quality control, developmental equations for the mean and standard deviation of qEEG traditional and Riemannian DPs were calculated using additive mixed-effects models. We demonstrate qEEG "batch effects" and provide methods to calculate harmonized z-scores. ii) We also show that the multinational harmonized Riemannian norms produce z-scores with increased diagnostic accuracy to predict brain dysfunction at school-age produced by malnutrition only in the first year of life. iii) We offer open code and data to calculate different individual z-scores from the HarMNqEEG dataset. These results contribute to developing bias-free, low-cost neuroimaging technologies applicable in various health settings

Towards Remote Gait Analysis: Combining Physics and Probabilistic Models for Estimating Human Joint Mechanics

The connected health movement and remote patient monitoring promise to revolutionize patient care in multiple clinical contexts. In orthopedics, continuous monitoring of human joint and muscle tissue loading in free-living conditions will enable novel insight concerning musculoskeletal disease etiology. These developments are necessary for comprehensive patient characterization, progression monitoring, and personalized therapy. This vision has motivated many recent advances in wearable sensor-based algorithm development that aim to perform biomechanical analyses traditionally restricted to confined laboratory spaces. However, these techniques have not translated to practical deployment for remote monitoring. Several barriers to translation have been identified including complex sensor arrays. Thus, the aim of this work was to lay the foundation for remote gait analysis and techniques for estimating clinically relevant biomechanics with a reduced sensor array. The first step in this process was to develop an open-source platform that generalized the processing pipeline for automated remote biomechanical analysis. The clinical utility of the platform was demonstrated for monitoring patient gait following knee surgery using continuous recordings of thighworn accelerometer data and rectus femoris electromyograms (EMG) during free-living conditions. Individual walking bouts were identified from which strides were extracted and characterized for patient evaluation. A novel, multifactorial asymmetry index was proposed based on temporal, EMG, and kinematic descriptors of gait that was able to differentiate between patients at different stages of recovery and that was more sensitive to recovery time than were indices of cumulative physical activity. The remainder of the work focused on algorithms for estimating joint moment and simulating muscle contraction dynamics using a reduced sensor array. A hybrid technique was proposed that combined both physics and probabilistic models in a complementary fashion. Specifically, the notion of a muscle synergy function was introduced that describes the mapping between excitations from a subset of muscles and excitations from other synergistic muscles. A novel model of these synergy functions was developed that enabled estimation of unmeasured muscle excitations using a measured subset. Data from thigh- and shank-worn inertial sensors were used to estimate segment kinematics and muscle-tendon unit (MTU) lengths using physics-based techniques and a model of the musculoskeletal geometry. These estimates of muscle excitation and MTU length were used as inputs for EMG-driven simulation of muscle contraction. Estimates of muscle force, power, and work as well as net joint moment from the proposed hybrid technique were compared to estimates from laboratory-based techniques. This presents the first sensor-only (four EMG and two inertial sensors) simulation of muscle contraction dynamics and joint moment estimation using machine learning only for estimating unmeasured muscle excitations. This work provides the basis for automated remote biomechanical analysis with reduced sensor arrays; from raw sensor recordings to estimates of muscle moment, force, and power. The proposed hybrid technique requires data from only four EMG and two inertial sensors and work has begun to seamlessly integrate these sensors into a knee brace for monitoring patients following knee surgery. Future work should build on these developments including further validation and design of methods utilizing remotely and longitudinally observed biomechanics for prognosis and optimizing patient-specific interventions

Femtosecond Covariance Spectroscopy

In order to reveal a signal arising from a nonlinear interaction, several spectroscopic techniques are nowadays adopted. In spite of their practical and fundamental differences, they have in common to rely on pulse to pulse consistency to deliver information on a nonlinear process. With the work presented in this thesis we show, instead, that we can successfully leverage upon experimental noise. To achieve this goal, we exploited the fact that a weak nonlinear signal introduces a strong spectral correlation, which can be revealed even when the output spectra fully spectrally and spatially overlap with the excitation pulse. Based on these principles, we proposed a novel approach to a nonlinear spectroscopy experiment, called Femtosecond Covariance Spectroscopy. To provide a solid basis for the validation of the technique, we focused on a third order nonlinear process, inelastic light scattering, which is prompted by the mixing of intense electric fields in a transparent material. The interaction implies that the measured intensity at some point in the transmitted spectrum is statistically related to the intensity at other points of the spectrum, whenever their energy distance coincides with an energy level of the sample involved in the scattering. We performed inelastic light scattering experiments from vibrational modes of a benchmark sample, quartz. We employed a near infrared laser with central wavelength in a transparency region of the sample, and bandwidth larger than its lowest energy vibrational modes. We found in the correlation coefficient sidebands that reproduce the vibrational spectrum of the sample. Their lineshape changes according to the presence or absence of a non modulated portion of the spectrum, heterodyning the scattered radiation. In fact we find that a partial spectral randomization is most efficient in preparing a pulse with no pre-existent correlation, that, at the same time, provides a local oscillator for the sample-induced fluctuations to be amplified. In this scheme, the ultrashort pulse provides, at the same time, intense electric fields to stimulate a response, and noninteracting components to reveal it. The self-heterodyned nature of the acquisition is accounted for in a fully quantum model. The technique can be adapted to a pump - probe scheme by exciting the sample with a separate, intense and spectrally coherent, pump pulse. Our measurements of the average transmitted probe intensity performed using a pump to excite coherent vibrational states, reveal that oscillations in the response are initiated in-phase by the pump and evolve at the vibrational frequencies. Such a response is an ideal candidate to test a covariance based probe, as the spectrum undergoes a red-shift or a blue-shift alternatively in time, and the correlation coefficient is found to oscillate in time at the phonon frequency. The investigation we started with this Thesis aims, primarily, at establishing the signatures in the correlation that resolve a thermal from a coherent vibrational state. In fact, if a quantum optics model describes accurately the results of a standard pump probe experiment on quartz, the theoretical framework must be completed in order to describe a pump probe approach employing randomized pulses and a covariance based retrieval. The experiments have shown that consistent information is present in the correlation maps, but more incisive analytical and conceptual tools are needed to assess the different contributions. The proposed method has proven to be a powerful probing scheme in a optical spectroscopy experiment, and can be successfully translated into the language of stochastic X-ray pulses, complex materials, electronic scattering processes. To fully characterize the FCS technique there are still steps to take. Nonetheless we believe that the present work sets the basis for the development of a technique that successfully conveys information beyond traditional schemes