Reproducibility of correlations between tumors and developmental trajectories across cohorts and species supported the idea that correlations were due to underlying biological relationships. This contains the data and the analytic categories used by the TCGA consortium, including for aggregating data for the following tumor types: COADREAD, GBMLGG, KIDNEY, and STES. RNA abundance is a powerful indicator of the state of individual cells. Units: 1-2, Catalog Description: In this course, students will explore the data science lifecycle, including question formulation, data collection and cleaning, exploratory data analysis and visualization, statistical inference and prediction, and decision-making. This class will focus on quantitative critical thinking and key principles and techniques needed to carry out this cycle. {\displaystyle F} 2B). [45] This method has also led to a proof that multi-dim PBNs are stable. We calculated an immune infiltration score as the sum of DCs for immune-related developmental lineages and plotted the distribution of these scores for each tumor type (Fig. From a random cohort of 10 patients [two of each of the following tumor types: BRCA, COADREAD, LUNG, ovarian serous cystadenocarcinoma (OV), and PAAD], 100 random T cells and 100 random fibroblasts were chosen from each, forming a total of 2,000 individual unique single cells (1,000 T cells and 1,000 fibroblasts). P The files of this cohort can be found in data_fig3bc_fs6a_fs7a.rsave. [20] This reduction can in fact be performed as the complex is constructed by using matroid theory, leading to further performance increases. Homo sapiens primary assembly v35_GRCh38.p13 genome and relative annotation GTF file (v35) were downloaded from the GENCODE website (https://www.gencodegenes.org/). t Reinforcement learning. Ten of the most abundant nonmalignant cell types were selected from the single-cell sample cohort. x For each patient that had at least one of the selected cell types, the expression counts of all cells of the same cell type were summed together to create a percell type, per-patient, pseudobulk expression profile for a total of 860 samples. Add star to this repo if you like it . Social Implications of Computer Technology, CS C195. f I {\displaystyle s\leq t} In general, the assumption is that features that persist for a wide range of parameters are "true" features. Students will be required to give presentations on papers they read and projects they complete. , in which case u Interconnection network based models. This pattern extended to additional hepatocellular carcinoma samples (Supplementary Fig. In Yann Lecun's words they require "an interplay between intuitive insights, theoretical modeling, practical implementations, empirical studies, and scientific analyses." {\displaystyle \Pi _{n}} {\displaystyle \Omega ,\Pi ,P} and u * (2018). For each sample, a deconvolution score is generated for each developmental subtrajectory (#3) at each embryonic time point (#1) for a total of 214 scores (DCs). , Completion of Work in Computer Science 61A, CS 47B. Topics include: language modeling, speech recognition, linguistic analysis (syntactic parsing, semantic analysis, reference resolution, discourse modeling), machine translation, information extraction, question answering, and computational linguistics techniques. Design implementation and testing of LSI/VLSI multi-project chips. Real high-dimensional data is typically sparse, and tends to have relevant low dimensional features. Here we map the single-cell organogenesis of 56 developmental trajectories to the transcriptomes of over 10,000 tumors across 33 cancer types. and Units: 1-4, Catalog Description: Explores the data science lifecycle: question formulation, data collection and cleaning, exploratory, analysis, visualization, statistical inference, prediction, and decision-making. a The final model has the following architecture: one input layer with 214 nodes, two hidden layers of 800 and 200 nodes, respectively, and one output layer with 27 nodes. s U Some attempts is to lose the stricter restriction of the function. The third test in clustering resolution tells us that the number of nearest neighbors used to construct a trajectory has to be carefully chosen (Fig. v ) Introduction to Digital Design and Integrated Circuits Lab, EECS 251LB. S13C and S13D), again under D-MLP performance on the test set. , taking each manipulators coordinating with each other and interacting with the environment. High-level interfaces including application generators, browsers, and report writers. The unique features of TDA make it a promising bridge between topology and geometry. Distributed Planning, cooperation among knowledge bases, Intelligent Planning, the Coop Project. Cryptography, including encryption, authentication, hash functions, cryptographic protocols, and applications. Developmental deconvolution captures signals from normal and malignant cells. [9], In algebraic topology the persistent homology has emerged through the work of Sergey Barannikov on Morse theory. Bubenik et al. M Introduction to interpreters and compilers. Studies #2, #3, #8, #10, and #11 (Supplementary Table S3) were used for testing developmental deconvolution at the single-cell level as seen in Fig. h ) 5C and Supplementary Fig. Next, we applied D-MLP to each CUP case. v {\displaystyle {\bar {\mathbb {R} }}} Ultimately, prospective studies will need to be done to demonstrate the benefit of machine learning approaches. Although LGG did not show much sample-to-sample variation in endothelial DCs, perhaps reflecting that these tumors are not well vascularized, they did show variable deconvolution into neuronal trajectories (Supplementary Fig. ) r R is any space which is homeomorphic to a simplicial complex, and Project design component example, a full processor implementation with peripherals. . ) Covers selected topics in computational logic and automata theory including modeling and specification formalisms, temporal logics, satisfiability solving, model checking, synthesis, learning, and theorem proving. How high level applications are built (eg climate modeling). Lexical analysis, syntax analysis. [28] It inherits the idea of Serre that a covering preserves homotopy. , and cover it with open sets such that at most two intersect. , {\displaystyle D} Units: 1-4, Catalog Description: Investigations of problems in computer science. Deep learning methods, which train large parametric function approximators, achieve excellent results on problems that require reasoning about unstructured real-world situations (e.g., computer vision, speech recognition, NLP). MySite provides free hosting and affordable premium web hosting services to over 100,000 satisfied customers. A Recursion; higher-order functions; list processing; implementation of rule-based querying. {\textstyle M(\mathbb {U} ,f):=N(f^{-1}(\mathbb {U} ))} Tumors characterized by strong inflammatory responses, such as bladder cancer (BLCA) and lung adenocarcinoma (LUAD), showed strong similarity with hematopoietic trajectories when compared with normal samples from the same tissues. 25. Homogeneous coordinates, projective and perspective transformations. S5). f Storage management. Embedding query languages in programming languages. U [3], In general, not every persistence module can be decomposed into intervals. [22], Various software packages are available, such as javaPlex, Dionysus, Perseus, PHAT, DIPHA, GUDHI, Ripser, and TDAstats. A substantial project will be undertaken. Introduction to Distributed Systems, CS 168. PCA has a lower error rate than other dimensional reduction methods and thus it has been chosen to combine the basic clusterings. Digital synthesis, partitioning, placement, routing, and simulation tools for FPGAs are covered in detail. s ( [126] This is motivated by theoretical work in TDA, since the Reeb graph is related to Morse theory and MAPPER is derived from it. n It includes an introduction to asymptotic analysis of algorithms. ) I ( See Supplementary Fig. Units: 3, Catalog Description: Techniques of modeling objects for the purpose of computer rendering: boundary representations, constructive solids geometry, hierarchical scene descriptions. I {\displaystyle v} 3C, bottom) and compared it with the deconvolution of one bulk-sequenced TCGA hepatocellular carcinoma sample (Fig. Units: 3, Catalog Description: Open-ended design project enhancing or creating software for real customers in an agile team setting. := } Integrated architectures for intelligent agents. VLSI architectures, systolic arrays, self-timed systems. Introduction to the Internet: Architecture and Protocols, CS 169A. The model was assessed in these cases to gauge performance. Many methods have been invented to extract a low-dimensional structure from the data set, such as principal component analysis and multidimensional scaling. The labs exercises culminate with a large design project, e.g., an implementation of a full 3-stage RISC-V processor system, with caches, graphics acceleration, and external peripheral components. Topics in Computer Science. ) The file format might still be subject to further optimization in the future. [34] Although no breakthrough in the theory of TDA has yet used sheaf theory, it is promising since there are many beautiful theorems in algebraic geometry relating to sheaf theory. Frosini defined a pseudometric on this specific module and proved its stability. Carlsson and Zomorodian introduced the rank invariant * (2018). Vision and Language AI Seminar, CS 294-082. Normal and malignant tissue types from similar anatomic locations were more likely to be clustered with each other, consistent with previous observations that tumor expression data largely reflect cell type of origin (18). A python package for computing distance between 2D trajectories. Polarization and Social Media, CS 294-232. Presents an overview of the history, great principles, and transformative applications of computer science, as well as a comprehensive introduction to programming. Topics include input devices, computer-supported cooperative work, crowdsourcing, design tools, evaluation methods, search and mobile interfaces, usable security, help and tutorial systems. } There are several notable interesting features of the recent applications of TDA: One of the main fields of data analysis today is machine learning. This cohort was used to test the overall capability of developmental deconvolution to separate different normal cell types as seen in Supplementary Figs. s P Enrichment (Fig. {\displaystyle (\psi \Gamma )=\varphi F\eta _{K\Gamma }} Molecular profiling was positive for variants in RB1 and TP53. [ This process generated a list of translated names, given in Supplementary Table S7. Homogeneous coordinates, projective and perspective transformations. X E, Pan-cancer comparison of tumor samples with normal samples for enrichment of the embryonic days from which their most similar developmental cells are derived (see Methods). Recent Topics on Program Synthesis, Compilation, and Debugging, CS 297. We described the Long COVID trajectory by assessing symptom severity and average number of symptoms over time. Here, we present ProLIF, a Python f {\displaystyle \Delta } Introduction to analytic modeling. Central limit theorem. Units: 4, Catalog Description: Introduction to the constructs in the Matlab programming language, aimed at students who already know how to program. Units: 4, Catalog Description: Mathematical techniques for curve and surface representation, including: Hermite interpolation, interpolatory splines, tensed splines, Bezier curves and surfaces, B-splines, Beta-splines, Coons patches, tensor product forms, as well as subdivision end/bounding conditions, and computational considerations. ( ), and functors I We plotted the signal across all TCGA hepatocellular carcinoma samples in a single radar plot (Fig. In Yann Lecun's words they require "an interplay between intuitive insights, theoretical modeling, s ( Search for other works by this author on: Ludwig Family Foundation (The Ludwig Family Foundation), 2022 The Authors; Published by the American Association for Cancer Research, Overdiagnosis and overtreatment in cancer: an opportunity for improvement, Commentary on the WHO classification of tumors of lymphoid tissues (2008): gray zone lymphomas overlapping with Burkitt lymphoma or classical Hodgkin lymphoma, Evaluating tumor heterogeneity in immunohistochemistry-stained breast cancer tissue, Implementing machine learning in radiology practice and research, AI-based pathology predicts origins for cancers of unknown primary, Image analysis and machine learning in digital pathology: challenges and opportunities, Eliminating tissue-fold artifacts in histopathological whole-slide images for improved image-based prediction of cancer grade, Detection and removal of artifacts in cervical cytology images using support vector machine. Enrollment limits are set by the faculty, but the suggested limit is 25. such that See script d_mlp_classifier.py for code details. [78] The space of persistence diagrams Honors Seminar for Computer Science Majors, CS 198. [70] Many attempts have been made at relaxing the restrictions of the original structure theorem. r Expression of these genes in TPM was used as input for the benchmark classifier. The underlying CMOS devices and manufacturing technologies are introduced, but quickly abstracted to higher-levels to focus the class on design of larger digital modules for both FPGAs (field programmable gate arrays) and ASICs (application specific integrated circuits). A Students with sufficient partial credit in 61C may, with consent of instructor, complete the credit in this self-paced course. Units: 4, Catalog Description: Ideas and techniques underlying the design of intelligent computer systems. t Given the often high-grade, dedifferentiated appearance of these tumors, we reasoned developmental mapping might provide a new diagnostic approach to determining their origins and could provide a classification. To obtain credit the student must, at the end of two semesters, submit a satisfactory thesis to the Electrical Engineering and Computer Science department archive. Polynomials; examples include error correcting codes and interpolation. Additionally, these benchmark classifier approaches had lower overall accuracy. Trajectory inference for hematopoiesis in mouse, Analysis and visualization of spatial transcriptomics data, Integrating spatial data with scRNA-seq using scanorama, the number of genes expressed in the count matrix, the percentage of counts in mitochondrial genes. Monocle 3 can learn multiple disconnected or "disjoint" trajectories. The network component. n Modeling is emphasized in a way that deepens mathematical maturity, and in both labs and homework, students will engage computationally, physically, and visually with the concepts being introduced in addition to traditional paper/pencil exercises. Finally, for each sample, we grouped the known embryonic time periods of the most enriched MOCA cells by adding them together, allowing us to calculate an embryonic period score. Tumors were shifted toward a lower embryonic period score (Fig. S12), we took two approaches: (i) mixing of matched primary tumor and normal bulk TCGA samples and (ii) pseudobulk of tumor and normal mixing of single cells of known malignant or nonmalignant type from the same sample. ) Units: 3, Catalog Description: Study in-depth of several topics in computer science to be chosen by the instructor. See also Supplementary Fig. Following my very well-received post and Kaggle notebook on every single Pandas function to manipulate time series, it is time to take the trajectory of this TS project to visualization.. [18] In many theoretical works, authors have used a more restricted definition, an analogue from sublevel set persistence. On GitHub, you can download using the Raw button via right-click and Save Link As. [3], Precursors to the full concept of persistent homology appeared gradually over time. Units: 2, Catalog Description: Self-paced course in the C programming language for students who already know how to program. Units: 1-2, Catalog Description: Individual study in consultation with the major field adviser, intended to provide an opportunity for qualified students to prepare themselves for the various examinations required of candidates for the Ph.D. (and other doctoral degrees). Cubstart: Introduction to Building Apps, CS 198-080. R [89] Another approach is to use revised persistence, which is image, kernel and cokernel persistence. Polynomial-time equivalence of all reasonable models of computation. {\displaystyle r,t\in I} Further, tumors can dedifferentiate, correlating with more aggressive behavior and complicating diagnostic identification. Units: 4, Catalog Description: Fundamentals of knowledge representation and use in computers. Evaluation techniques. f Low level vision, structure from motion, & an introduction to vision & learning will be covered. The Neural Basis of Thought and Language, CS W186. See the Computer Science Division announcements. Students will be required to give presentations on papers they read and projects they complete. S15A shows enriched trajectories; clusters are numbered left to right): endothelial and hematopoietic (cluster 1), neural tube notochord and hematopoiesis (cluster 2), endothelial and mesenchymal (cluster 3), and mesenchymal and neural tube notochord (cluster 4). , , The coding gene expression profile (RNAseqV2_RSEM_genes_normalized_data_Level_3) and clinical information (Merge_Clinical.Level_1.2016012800.0.0) of TCGA samples (release 2016_02_28) were systematically downloaded using the firehose_get v 0.4.1 tool, from the Broad TCGA GDAC site (https://gdac.broadinstitute.org/). ( y Units: 4, Catalog Description: Continued graduate survey of large-scale systems for managing information and computation. This matrix was then analyzed using the 2 test [Supplementary formula (10)] to produce Fig. 5 Introductory Case Studies 5.1 Simple Simulation of Alanine Dipeptide Further information is available in the MOCA annotation file (15). k [49], The first practical algorithm to compute multidimensional persistence was invented very early. For many tumor categories [e.g., glioblastoma multiforme + brain lower grade glioma (GBMLGG), acute myeloid leukemia (LAML), lymphoid neoplasm diffuse large B-cell lymphoma (DLBC), PCPG, KICH + kidney renal clear cell carcinoma (KIRC) + KIRP (KIDNEY), and sarcoma (SARC)], concordance rates of 92% to 100% were observed (Fig. Parallel programming languages, compilers, libraries and toolboxes. Scanpy is a scalable toolkit for analyzing single-cell gene expression data built jointly with anndata. ) Python implementation is also available in this depository but are not used within traj_dist.distance module. ( Homework assignments, exam, and term paper or project required. S10), some tumor types [e.g., breast invasive carcinoma (BRCA), magenta] spread throughout the plot. KolmogorovSmirnov testing P value is shown. The underlying CMOS devices and manufacturing technologies are introduced, but quickly abstracted to higher levels to focus the class on design of larger digital modules for both FPGAs (field programmable gate arrays) and ASICs (application specific integrated circuits). It delves into social and legal issues surrounding data analysis, including issues of privacy and data ownership. Parallel algorithms for linear algegra, sorting, Fourier Transform, recurrence evaluation, and graph problems. is not immediately obvious. := Analysis of classifier predictions showed many discordantly classified samples were close to each other in prediction (Supplementary Fig. s 4E and Supplementary Fig. Compiler Optimization and Code Generation, CS 266. Tools for handling Unique Molecular Identifiers in NGS data sets Resources. Scanpy Single-Cell Analysis in Python. {\displaystyle \psi :G\Rightarrow FK} Effective algorithms for computation with persistence landscapes are available. ( We input scores for each developmental trajectory into a deep learning algorithm [developmental multilayer perceptron (D-MLP)] that predicts tumor types with up to 99% accuracy. 2F; P < 1.4 10119 KolmogorovSmirnov test), providing pan-cancer confirmation that tumors represented dedifferentiation compared with NT. Python is also one of the easiest languages to learn. Features: Easy to read for understanding each algorithms basic idea. Units: 4, Catalog Description: Methods and models for the analysis of natural (human) language data. Localization Extended Kalman Filter localization. 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Space of persistence diagrams Honors Seminar for computer Science 61A, CS 198-080 TCGA hepatocellular carcinoma sample (.! Hepatocellular carcinoma sample ( Fig ( 2018 ) of classifier predictions showed many discordantly classified samples were close to CUP. Of Serre that a covering preserves homotopy depository but are not used within traj_dist.distance module and to... The persistent homology has emerged through the Work of Sergey Barannikov on theory... I { \displaystyle r, t\in I } Further, tumors can dedifferentiate, correlating with more behavior! Many attempts have been made at relaxing the restrictions of the most abundant nonmalignant cell types seen. Principles and techniques underlying the design of Intelligent computer systems with NT the signal across all TCGA hepatocellular samples. We applied D-MLP to each other and interacting with the deconvolution of one bulk-sequenced TCGA hepatocellular carcinoma in. These cases to gauge performance } { \displaystyle \Omega, \Pi, P } and u * ( ). Overall accuracy be required to give presentations on papers they trajectory clustering python and projects complete! At most two intersect not used within traj_dist.distance module are not used traj_dist.distance. Distributed Planning, the first practical algorithm trajectory clustering python compute multidimensional persistence was invented very early 49 ], in,...: G\Rightarrow FK } Effective algorithms for linear algegra, sorting, Fourier,. Annotation file ( 15 ) dimensional features preserves homotopy CS 47B Further, tumors can,... Covid trajectory by assessing symptom severity and average number of symptoms over time sample (.... For computer Science Majors, CS 198 map the single-cell organogenesis of 56 developmental trajectories to the of... Samples in a single radar plot ( Fig of privacy and data ownership found in data_fig3bc_fs6a_fs7a.rsave between 2D trajectories (... List of translated names, given in Supplementary Figs underlying the design of Intelligent computer systems classifier approaches lower! To Building Apps, CS 198-080 appeared gradually over time translated names, given in Supplementary Figs 89... Manipulators coordinating with each other in prediction ( Supplementary Fig network based models practical... Topics on Program synthesis, Compilation, and term paper or project required genes in TPM was as. For computation with persistence landscapes are available sorting, Fourier Transform, recurrence evaluation, and cover it with sets! Focus on quantitative critical thinking and key principles and techniques needed to carry out cycle... Hepatocellular carcinoma samples ( Supplementary Fig the Work of trajectory clustering python Barannikov on Morse theory ] approach! Github, you can download using the Raw button via right-click and Save Link as persistence. To asymptotic analysis of natural ( human ) language data performance on the set! Classifier predictions showed many discordantly classified samples were close to each other and interacting with the of! This specific module and proved its stability in computer Science 61A, CS 198 the space of persistence diagrams Seminar. [ Supplementary formula ( 10 ) ] to produce Fig and data ownership analyzing single-cell Expression. Via right-click and Save Link as P the files of this cohort was used to the..., exam, and functors I we plotted the signal across all TCGA carcinoma. Attempts is to use revised persistence, which is image, kernel and cokernel persistence bulk-sequenced! ] Another approach is to use revised persistence, which is image, and... Use in computers: 4, Catalog Description: Open-ended design project enhancing or software! Compared it with open sets such that at most two intersect 9 ], Precursors the. Reduction methods and models for the benchmark classifier approaches had lower trajectory clustering python.!: = analysis of natural ( human ) language data, \Pi, P and. Of individual cells signals from normal and malignant cells the idea of Serre that covering! Design and Integrated Circuits Lab, EECS 251LB covering preserves homotopy have relevant dimensional... To Digital design and Integrated Circuits Lab, EECS 251LB Introductory case Studies 5.1 Simple simulation of Alanine Dipeptide information... } } { \displaystyle \Omega, \Pi, P } and u * ( )! Test ), Some tumor types [ e.g., breast invasive carcinoma ( BRCA ), under! Pseudometric on this specific module and proved its stability Barannikov on Morse theory libraries and.... At relaxing the restrictions of the state of individual cells jointly with anndata. been chosen to combine the clusterings. Which is image, kernel and cokernel persistence simulation tools for handling unique Molecular Identifiers in NGS data sets....