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skilled non-academics; more normal gender diversity) + \item Challenging (in fact, often intractable) problems + \item Teamwork + \item Use different skills than in research (interpersonal skills and empathy; communication) +\end{itemize} +\end{frame} + +\begin{frame}{Dislikes} +\begin{itemize} +\item Less control over your time + \item Constant need to manage up and down + \item Stress + \item Frustration +\end{itemize} +\end{frame} + +\begin{frame}{Thoughts on academia} + \begin{itemize} + \item Academic careers are long. Some people get stuck and get unhappy, then make everyone around them unhappy. Math particularly impermeable. + \item Academic institutions are far too tolerant of bad behavior; people work around it and manage it. + \item Lack of diversity and failure to make progress on it taints the enterprise. Deep problems and no progress on them. + \end{itemize} +\end{frame} + +\begin{frame}{Jackson Labs} + \begin{itemize} + \item Founded in 1929 in Bar Harbor, Maine. + \item World center for mouse genetics. Supplier of laboratory mice to the world -- 3M per year shipped world wide. + \item Mouse genome database contains enormous amount of information on mice and their genetic profiles. + \item 26 Nobel Prizes associated with JAX. + \item New CT facility has 350 employees focused on precision medicine and cancer. + \item About 90 million in NIH funding and 256M per year in mouse business. + \end{itemize} +\end{frame} +\begin{frame}{JAX, cont'd} + \begin{itemize} + \item 30 faculty: 10:1 staff to faculty ratio. Huge IT infrastrcture, imaging and sequencing base staffed by Ph.D.'s. + \item LOTS of jobs. Very diverse group of postdocs and research scientists including biologists, physicsts, computer scientists and some mathematicians. + \item Very different than a university because they are GROWING and HIRING all the time. + \item JAX, or places like it, worth thinking about for math Ph.D.'s if they want to do science as an alternative to NSA or Finance jobs outside academia. + \end{itemize} +\end{frame} + + +\begin{frame}{1. Diagnosis and the Human Phenotype Ontology} +\begin{block}{} +A human mendelian disease is a disorder that is attributable to a mutation in a single gene. Such diseases +are inherited according to the classical laws of mendelian genetics. \textit{Sickle cell anemia}, caused by the change of +a single nucleotide on chromosome 11, is an example of such a disease. +\end{block} +\begin{block}{} +The website \href{http://www.omim.org}{Online Mendelian Inheritance in Man} summarizes information +about ``Mendelian Diseases'' It identifies over 5000 conditions for which the cause is a change in a single gene. +Of the over 30000 genes in humans, 3500 genes have known mutations that cause disease. +\end{block} +\begin{block}{} +Many of these diseases cause a constellation of abnormalities making them difficult to diagnose. +\end{block} +\end{frame} +\begin{frame} +\begin{block}{} + The Human Phenotype Ontology (HPO) is a directed acyclic graph $HPO$ + nodes are 'symptoms.' More specific symptoms are child nodes of + more general ones. The ontology is carefully curated to reflect + standard medical terminology. +\end{block} +\begin{block}{} +The HPO was initially constructed by Peter Robinson and his group at +Charite hospital in Berlin. Robinson is now at JAX. +\end{block} +\end{frame} +\begin{frame} +A disease $d$ is characterized by a finite set of symptoms (nodes of the HPO) and therefore by its spanning +subtree $HPO(d)\subset HPO$. +\begin{center} +Angleman's Disease +\end{center} +\begin{tabular}{m{1.5in}m{3in}} +\includegraphics[width=1.5in]{angleman_symptoms.png} & \includegraphics[width=2.5in]{anglemanI.png}\cr +\end{tabular} +\end{frame} +\begin{frame} +A doctor examining a patient identifies a list of symptoms $S$, which in turn determine a spanning subtree +$HPO(S)$. + +\begin{problem} Given a symptom subtree $HPO(S)$, find a set of diseases (subtrees $HPO(D)$), scored by some type of likelihood measure, that are consistent with the symptoms. +\end{problem} + +Complications: +\begin{itemize} +\item Doctor may give more general version of a symptom, rather than the most specific one. +\item Doctor may miss some symptoms, or they may be rare even among people with a disease. +\item Doctor may add unrelated symptoms. +\end{itemize} +\end{frame} +\begin{frame}{Semantic Similarity} + In 1995 Resnick proposed a similarity measure for ontologies based on the ``information content'' of a node. + \begin{itemize} + \item Given a node (symptom) $m$, let $\mathcal{A}(m)$ be the set of diseases that are associated with that node -- meaning some descendant of that node is a specific symptom of the disease. + \item Assign weights to the edges of the DAG by setting the weight of $n\to m$ to be $\log |\mathcal{A}(m)|-\log |\mathcal{A}(n)|$. + \item The information content $IC(n)$ of a node $n$ is the sum of the weights of the edges from the node to the root (along any path). + \end{itemize} + + \end{frame} +\begin{frame} +\begin{block}{} + The Resnick similarity between two sub-DAG's $X$ and $Y$ is $(H(X,Y)+H(Y,X))/2$ + where + $$ + H(X,Y)=\frac{1}{|X|}\sum_{x\in X} \max_{y\in Y} IC(z(x,y)) + $$ + where $z$ is the common ancestor of $x$ and $y$ with the greatest $IC$. +\end{block} +\begin{block}{} + \textit{A new method to measure the semantic similarity from query phenotypic abnormalities to diseases based on the human phenotype ontology}, in \textit{BMC Bioinformatics 2018}, lists six other + 'distance measures' between subtrees of a DAG, and adds a new one. + There are many others. +\end{block} +\end{frame} +\begin{frame} +More sophisticated models under development: +\begin{enumerate} +\item incorporate information about the relative frequencies of symptoms in patients with the disease +\item attempt to incorporate information about genetic variants into the diagnosis. +\end{enumerate} + +Common validation technique is to test against simulated data. +\begin{problem} +Formally characterize the differences, strengths, weaknesses of these different approaches. +\end{problem} +\end{frame} +\begin{frame}{2. Analysis of single cell RNA experiment data} + Two seconds on human molecular genetics. +\begin{center} + \includegraphics[width=3in]{dna.png} +\end{center} +\end{frame} +\begin{frame}{RNA-seq} +\begin{itemize} +\item In 'Bulk RNA sequencing' (RNA-seq) researchers take a sample of a particular tissue type, sequence the RNA in the sample by cutting it up into pieces and aligning the pieces against a reference genome. +\item They count the fragments of RNA that line up against a particular gene and use that as a measure of the relative activation level of that particular gene AVERAGED OVER THE CELLS IN THE SAMPLE. +\item Typical experiments: + \begin{itemize} + \item Take cells before and after treatment with a drug and look to see if the expression profile has changed. + \item Compare expression profile of normal and cancer cells and look for genes that are amplified or repressed in cancer; these might suggest biochemical pathways for drug targeting. + \end{itemize} +\end{itemize} +\end{frame} +\begin{frame} + \begin{itemize} + \item + Typical experiment might have 3 or 4 controls, 3 or 4 treatment cases, and 30000 genes. So for Bulk RNA sequencing the problem is to identify which of those 30000 genes differ between the controls and treatment cases. +\item Although this technology is perhaps only 10 years old, it is now standard and there are established techniques for this. +\end{itemize} +\end{frame} +\begin{frame}{Single Cell RNA-Seq} + In single cell RNA-seq, \textit{individual cells} are captured to obtain a cell by cell expression profile. + \begin{itemize} + \item Cells are caught in droplets and RNA in each droplet gets a unique sequence identifying the droplet attached; plus each RNA molecule gets a unique sequence identifying the molecule. + \item Then these pieces are amplified (replicated many times). The resulting 'library' gets sequenced. + \item In this way one can count the number of RNA molecules from each gene in each cell. + \item Some nice, elementary use of error correcting codes takes place here.' + \end{itemize} +\begin{center} + \includegraphics[width=1.75in]{10XSingleCellDetail.png} +\end{center} +\end{frame} +\begin{frame} +\begin{center} + \includegraphics[width=3in]{10xSingleCellOverview.png} + + 10x Genomics droplet high-throughput single cell platform +\end{center} +\end{frame} +\begin{frame}{Single Cell Data} +\begin{block}{} + The output from a single cell experiment is an $N\times K$ sparse integer matrix. Here $N$, the number of cells, could range from a few hundred to a few million, and $K$, the number of genes, is on the order of $30000$. The $(i,j)$-th entry of the matrix is the activation level of gene $j$ in cell $i$. +\end{block} +\begin{block}{} + Goals for these experiments are: + \begin{itemize} + \item Obtain fine structure among classes of cells based on their expression profiles. + \item Understand developmental history and reconstruct development. + \item Understand tumor heterogeneity and its relationship to chemotherapy response (*) + \item Many other things.... + \end{itemize} +\end{block} +\end{frame} +\begin{frame}{Outline of Analysis} + \begin{enumerate} + \item Clean up the data by throwing out cells with few detected genes and genes that hardly ever show up. + \item Normalize the data by cell to account for the different levels of sequencing success. + \item Do a first round of dimensionality reduction by identifying genes that show a lot of variance + \item Use a second round of dimensionality reduction to two or three dimensions (PCA, tSNE, or UMAP) + \item Cluster the results + \item Look at the gene profiles of each cluster to try to find genetic markers for each cluster. + \item Figure out the biological implications. + \end{enumerate} + + + + +\end{frame} +\begin{frame} + \begin{center} + \includegraphics[width=3in]{blood.png} + + Immune cell types in blood from \textit{Massively parallel digital transcriptional profiling of single cells} by Zheng, et. al., Nature Comm. 8, 2017. +\end{center} +\end{frame} + +\begin{frame}{Challenges with scRNA data} + \begin{block}{Sparsity} + There is considerable activity in the literature over some basic questions about how to analyze single cell data. + Much of this comes from the sparsity of the data. + \begin{enumerate} + \item How to distinguish between genes that have low (or zero) expression and + genes that show up with zero expression for technical reasons? + \item How to properly normalize the data by cell when there is so much variation in the total count per cell? + \item How to identify subpopulations within the data when the subpopulations could be distinguished by differential expression of only a very small number of the 30000 genes being profiled? + \end{enumerate} +\end{block} +\end{frame} + +\begin{frame} + More questions: + \begin{enumerate} + \item What is the proper statistical model for this data? I count more than 10 proposals that have been published in different studies. + \item How sensitive are the common dimensionality reduction algorithms used for clustering to the different choices one makes for normalization and to the possible dropout of some values? + \item How to integrate this data with 'bulk' sequencing data or other types of data. + \end{enumerate} +\end{frame} +\begin{frame}{Very recent: random matrix theory applied to single cell data} +\begin{block}{} +The paper \textit{Quasi-universality in single-cell sequencing data}, by Aparicio, Bordyuh, Blumberg, and Rabadan, looks +at the spectra of matrices arising from single cell experiments through the lens of random matrix theory. +\end{block} +\begin{block}{} +One formulates a 'null hypothesis' that the matrix of data is random, and and can identify a signal by identifying the the extent that the eigenvalue distribution of the correlation matrix differs from the universal distribution that one expect. +\end{block} +\begin{block}{} +The sparsity of the data matrices is an obstacle to this and needs to be accounted for. +\end{block} +\end{frame} +\begin{frame}{More on random matrices and single cell data} +From the paper cited above. +\begin{center} +\includegraphics[width=4in]{RMT2.png} +\end{center} +\end{frame} +\begin{frame}{Structure of single cell data from random matrix perspective} +From the paper cited above. +\begin{center} +\includegraphics[width=4.5in]{RMT1.png} +\end{center} +\end{frame} + + +\begin{frame}{Some thoughts about graduate education in math} + + Goal is to train successful research mathematicians, but students need to protect their economic mobility as a hedge against exploitation. Not clear what long-term future of academic jobs will be. + + \begin{itemize} + \item (Not a radical idea) Insist on knowledge of programming. + \item Include some statistics in the core curriculum for mathematicians. + \item Find a way to include group projects in the curriculum. + \item Math in general is pretty good about time-to-degree but in academia in general students have to get through fast. + \end{itemize} + \end{frame} + +\end{document} + + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff --git a/Wisconsin/wisconsin.txt b/Wisconsin/wisconsin.txt new file mode 100644 index 0000000..088232a --- /dev/null +++ b/Wisconsin/wisconsin.txt @@ -0,0 +1,179 @@ +After more than 10 years in administration, including 9 as Dean of +Arts and Sciences and 1 as interim Provost at UConn, I have returned +to my faculty position. I am spending a year as a visiting scientist +at the Jackson Laboratory for Genomic Medicine (JAX-GM) in Farmington, +Connecticut, trying to get a grip on some of the mathematical problems +of interest to researchers in cancer genomics. In this talk, I will offer some personal +observations about being a mathematician and a high-level administrator, talk a bit about +the research environment at an independent research institute like JAX-GM, outline +a few problems that I've begun to learn about, and conclude with a +discussion of how these experiences have shaped my view of graduate training in mathematics. + +Observations as an administrator +Challenges/pleasures of administration: + intellectual diversity + other types of diversity + truly intractable problems + teamwork + opportunity to be a force for good +issues: + - doubts about the curriculum + - isolation of the department + - stubbornly slow process of diversification + +broader observations: + -- length of academic career is a challenge for many people; change can be good. + -- relative impermeability of academic mathematics + + +Jackson Labs + +Founded 1929 in Bar Harbor Maine +Originally supported by Edsel Ford and Roscoe Jackson (Hudson Motor cars) +Home of mouse genetics +26 Nobel Prizes associated with JAX +George Snell, JAX Faculty, won in 1980 for genetics of the immunte system. +Huge business in mice -- 3M mice per year +88M per year grant support +256M per year in the mouse business and other services +Mouse genome database +New facility in Connecticut dedicated to 'precision medicine' + -- 350 employees + ~ 30 faculty + huge technical support infrastructure + -- information technology and "computational services" + -- imaging + -- sequencing + +Math departments think of NSA or Finance as places where there are jobs for PhD's. +Place like JAX offers a research environment (no teaching) but can be a steady job -- compare +for example with a permanenent teaching faculty job. + +Here's a sample job ad: + +Responsibilities + +The successful candidate will develop and apply computational methods +for genomic data analyses, have novel opportunities at the +intersection of algorithms, data interpretation, and experimental +design in close collaboration with the experimental team in the +lab. The applicant is expected to have Ph.D. in computational biology, +cancer genomics, or a similar discipline, and demonstrate strong +computing expertise, publication, and communication skills. We also +consider exceptional applicants who are new to computational biology, +including statistics, applied math, physics, and computer science. + +Qualifications + + PhD. in a quantitative area: computational biology, computer science, statistics, physics and applied math + + Programming in R, Python, Perl or C++ + + Experience in genomic dataset analysis and integration + + Three (3) years of postdoctoral training or equivalent research experience, and demonstrated meritorious scientific performance. + + Strong publication record (two or more peer-reviewed publications). + + Ability to integrate and apply feedback in a professional manner, prioritize and drive to results with a high emphasis on quality, and work as part of a team. + + Proven ability to analyze and synthesize information, and demonstrated resourcefulness in finding appropriate solutions to problems and initiative in presenting alternatives and implementing solutions to ensure effective change and/or eliminate or mitigate potential negative effects. + + Exceptional organizational and project management skills, including the ability to plan, schedule, and successfully carry out multiple projects at the same time to successful conclusion with minimal supervision. + +Quality orientated including delivering accuracy and attention to detail. + + +Some examples of people at JAX -- many non-biologists -- changing field draws in people from lots of areas. + +Jeff Chuang (Assoc Prof, faculty member) PhD from MIT in statistical physics +Bill Flynn, "Application computational scientist", PhD in Physics (large molecules) from Rutgers +Vida Ravanmehr, PhD in Electrical/Computer Engineering (working on error correcting codes) BA/MA in Applied Math +Peter Robinson (Professor), BA and MS in Computer Science, MD from Penn. + +But not many math PhD's (pure or applied) overall. + +What are they working on? + +Many different things, but here are two examples of problems. + +1. (Robinson group) The Human Phenotype Ontology (HPO) + +Phenotype = symptom. HPO is a large directed acyclic graph, where each node represents a symptom/phenotype and they are classified +from general to specific. Items ("terms") in the HPO are curated by experts. +For example: +[Term] +id: HP:0010082 +name: Symphalangism affecting the distal phalanx of the hallux +synonym: "Fused outermost bone of big toe" EXACT layperson [ORCID:0000-0001-5208-3432] +xref: UMLS:C4024063 +is_a: HP:0001859 ! Distal foot symphalangism +is_a: HP:0010053 ! Abnormality of the distal phalanx of the hallux +is_a: HP:0010091 ! Symphalangism affecting the proximal phalanx of the hallux +is_a: HP:0010191 ! Symphalangism affecting the distal phalanges of the toes +created_by: doelkens +creation_date: 2009-05-29T12:16:28Z + +DAG is annotated by (mendelian genetic) diseases (So a disease is a subtree of the ontology) + +Possible applications: +useful for clinical studies because it nails down symptoms in a systematic nomenclature. +Can be used for more interesting problems -- given a set of symptoms, find potential diseases consistent with those symptoms. +This type of reasoning problem from ontologies has a long history. +(give examples) + +Also used to identify cross-species similarities and to find appropriate animal models +And to try to pair specific genetic variants with diseases. + +2. (Chuang group) broader problem: tumor evolution. Typical tumor is made up of subpopulations of cells with common +genetic profile. Some of these subpopulations might be susceptible to treatment with a particular chemotherapy agent +to which others are resistant. + +Patient-derived xenografts (PDX): take tumors from people, grow them in immuno suppressed mice so there is space to experiment on them. + +Some attempts to reconstruct history of cell populations using ideas from evolutionary biology, but still an active area of research + +Management of PDX studies is a large complicated business. + +Key tool is sequencing -- different types -- DNA, RNA, single-cell. +My current project is to look at issues in single cell RNA sequencing, so here is a brief overview. + +Recall how genetics works: DNA -> mRNA -> protein +Different cells in your body have same* DNA but different expression profiles -- different levels of mRNA and so different collection of proteins. + +Prior technology (RNA-seq) looked at a sample from a mixture of cells and computed the relative abundance of different mRNA molecules. +So a typical RNA-seq experiment might take 3 replicates of a control and 3 of a treatment (say drugs or whatever) and compute the expression levels +of the genes in the two cases, then try to draw conclusions. So you have a matrix with 30000 genes and six samples. Various strategies to extract +meaning from this situation. + +single-cell works differently. Cells get sequenced one at a time and you get an expression profile for all of the genes for each cell. +Result might be an integer matrix of 3000 cells by 30000 genes. Each integer counts the number of mRNA associated with that gene. + +BUT: the data is confounded because the small amounts of material in each cell mean that many things DON't get counted that should. So the +matrix has lots and lots of zeros. + +A typical goal is: + -- to cluster the cells by their expression profiles; + -- identify the genes whose expression levels characterize the clusters; + -- find a biological interpretation for these genes. + +In the context of tumor heterogeneity, perhaps the clusters might be associated with certain biochemical pathways that can be targeted with particular drugs. + +Example of one associated statistical model (there are many proposals for this): + +Typical approach would be to use principal componenet analysis or some fancier method to reduce the dimension and identify clusters. + +Problem: How to deal with the issues of: + -- normalization of the data + -- what effect does the dropout have on the dimensionality reduction? + -- should one try to impute the zero values? if so, how? + + + + + + + + + + diff --git a/docs/README.md b/docs/README.md index bc9e1e6..ed74d90 100644 --- a/docs/README.md +++ b/docs/README.md @@ -9,6 +9,6 @@ Storrs, Connecticut 06269 - [Counting Trees @ UConn Math Club, February 2018](./talk.pdf) - [ECM Method @ Connecticut Number Theory Week, June, 2018](./ctnt2018.pdf) - [Random Walk methods @ JAX working group on graph embedding, July 2018](./graphE.pdf) - +- [Lessons Learned and New Perspectives @ UW-Madison Math Colloquium, October, 2018](./wisconsin.pdf) [Jump to GitHub repository](http://github.uconn.edu/jet08013/Talks.git) diff --git a/docs/wisconsin.pdf b/docs/wisconsin.pdf new file mode 100644 index 0000000..d648705 Binary files /dev/null and b/docs/wisconsin.pdf differ