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LMS category primaryCytometry Basics and TechnologyFundamental Cytometry ConceptsCytometry HardwareInstrument StandardizationBasic Data AnalysisExperimental Design and ControlsImmunology and Clinical CytometryPanel DesignClinical ApplicationsData Analysis ( Immunology and Clinical Cytometry )Genomic CytometryRare Cell Analysis ( Immunology and Clinical Cytometry )Functional Assays in CytometryIntracellular AssaysMetabolomicsCell Proliferation and DeathOther AssaysImagingNovel TechnologiesImage Data AnalysisHigh Parameter ImagingConfocal MicroscopyImaging Flow CytometrySmall Particle CytometrySizing StandardsInstrument CalibrationData Analysis ( Small Particle Cytometry )Cytometry Hardware ( Small Particle Cytometry )Extracellcular VesiclesMicrobial Marine and Plant CytometrySizing Standards ( Microbial Marine and Plant Cytometry )Sorting ( Microbial )Microbial CytometryPlant CytometryMarine CytometryBiosafetyCell SortingShared Resource Lab Operations.Microscopy and ImagingGuidelines and RegulationsCytometry Hardware ( Biosafety)Shared Resource LaboratoriesOperations and FinanceManagementBiosafety ( Shared Resource Laboratories )Training and EducationCareer DevelopmentOutreach ( Live Ed and CYTO Youth )Fundamental Cytometry Concepts ( Outreach )EducationMentorshipYouth ContentData AnalysisHigh-ParameterComputational and Automation toolsGenomic Cytometry ( Data Analysis )Imaging Data AnalysisManual gating approachesOther
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Creative Funding Options for SRLs: from Crowd Funding to Philanthropy
Contains 3 Component(s), Includes Credits Recorded On: 12/08/2021
A CYTO U Webinar presented by Kylie Price and Dagna Sheerar Keywords: Novel funding sources, philanthropy, relationship building, instrument procurement, infrastructure
Kylie Price
Head of Research Technology and Senior Staff Scientist
Malaghan Institute of Medical Research
Kylie Price is a senior scientist and the head of research technology at the Malaghan Institute of Medical Research. She has 18 years of experience providing strategic, scientific, and operational direction in multidisciplinary environments. Kylie has strong stakeholder management and engagement skills and has attracted more than $15 million of philanthropic funding over the past twelve years, supporting the creation of a distinguished center of research excellence, the Hugh Green Cytometry Centre (HGCC). Kylie leads a team of eight highly-skilled technology scientists in providing supporting to over 80 scientists at the Malaghan Institute. The HGCC provides access to cutting-edge technology platforms (including flow and spectral cytometry, histology, bioimaging, genomics, and bioinformatics) and advises multiple research groups both nationally and abroad. Kylie also has a strong leadership track-record that includes organizing high-profile networking events, such as CYTO Asia Singapore 2017, and directing international organizations, such as the Australasian Cytometry Society of which she is former president. Kylie is a two-time NZ Woman of Influence Awards finalist and finalist of the 2021 NZ High Tech Awards. She was the first New Zealander elected to the International Society for Advancement of Cytometry Council and was elected ISAC Secretary in 2020.
Dagna Sheerar
Flow Cytometry Technical Director
Carbone Cancer Center Flow Cytometry Laboratory
Dagna Sheerar has been working in flow cytometry shared resource laboratories for over 20 years and is currently the technical director of the Flow Cytometry Laboratory at the University of Wisconsin - Madison Carbone Cancer Center. Her areas of interest are core management and user education. Since becoming technical director, Dagna has successfully added, on average, one instrument per year to the Flow Lab through various grant programs, institutional purchases, or "crowd funding." Dagna has been involved in the Great Lakes International Imaging and Flow Cytometry Association (GLIIFCA) for almost as long as she has been working in cores, and she recently served as GLIIFCA president from 2020-2021. She is a member of ISAC and serves on the SRL Content Task Force. She serves as host, organizer, and instructor for the Annual Course in Cytometry, and she is currently in the planning stages for the 45th Annual Course to be held at the University of Wisconsin in June of 2022. Dagna has presented at GLIIFCA, the annual CYTO Meeting, and the Association of Biomolecular Resource Facility (ABRF) annual meetings. Dagna also served as the Interim Director of Campus Research Cores at UW – Madison in 2020.
There is often a lot of pressure on SRL managers to run a partial- or full-cost-recovery core facility which presents many challenges. Identifying and securing external funding (in any form) can alleviate this pressure. This tutorial will cover various funding strategies for SRLs, looking at diversifying funding streams. Dagna Sheerar will provide an overview of traditional and novel methods for funding the purchase of instrumentation, including various grant programs, institutional purchases, and "crowd-funding." Kylie Price will look at how to find, maintain, and grow philanthropic relationships as well as how to maximize opportunities with high-net-worth individuals/groups.
Identify novel funding sources for shared resource laboratories.
Leveraging usage data and research need to build support.
How best to present core technologies and core facility services to entice funding.
How to engage stakeholders.
Provide tips around how to build and grow philanthropic relationships.
SRL Managers, Flow Core Directors, SRL Staff.
Changing Mindsets
Contains 3 Component(s), Includes Credits
A CYTO U Webinar presented by Marta Monteiro, PhD and Julie Auger Keywords: SRL, benchmarking, quality assurance
Marta Monteiro, PhD
Head of Flow Cytometry & Antibodies
Core Facility Speaker
Instituto Gulbenkian de Ciência
Marta has a PhD in immunology from the University of Paris. She is head of Flow Cytometry & Antibodies at the Gulbenkian Institute for Science (IGC), in Portugal, and also the core facility speaker, representing all IGC facilities. Before that, Marta worked as a researcher for 15 years in Portugal and abroad and was an assistant professor at he Medical School of University of Lisbon. She also was the head of the R&D department of a multinational pharmaceutical company. She is author of many scientific publications and co-inventor of a patent that was an award-winning entrepreneurship project and the foundation of a start-up. With her strong scientific know-how and practical input in core facility management, Marta also collaborates with Agendo for business development and marketing.
Julie Auger
Research Core Facilities Program
University of California Davis
Julie A. Auger, has been a member of the cytometry community since 1985 and is widely recognized for her expertise in the operation and administration of multi-technology, multidisciplinary academic resource centers. She serves as the executive director of the Research Core Facilities Program at the University of California Davis where she is responsible for development of a central support structure to optimize organization and administration for over 100 shared research facilities. Prior to her current position at UC Davis, Julie developed similar programs at UC San Francisco and The University of Chicago. She developed her core facility management expertise at the University of Illinois Urbana-Champaign and at the University of Chicago, where she developed internationally-reputed flow cytometry core facilities.
At research institutions, shared resource laboratories (SRLs) managers face increasing expectations to maximize facility usage and optimize operation. Benchmarking is a helpful exercise for organizations to identify their strengths and opportunities for development with the aim of maximizing performance. External assessment of the SRLs can be used as a benchmarking strategy to perform an objective and unbiased analysis of the standpoint of those services, providing valuable recommendations for improvement on different areas. In this webinar, we will present a successful case study of a first external assessment of the scientific core facilities of a research institution. We will provide an overview of the different steps, from the initial engagement of the entire community to prepare the exercise, to the benefits it conveyed and that are seen at present.
Usefulness of benchmarking for SRLs.
Different steps of an external assessment process of SRLs.
Benefits that an external assessment process of SRLs can bring to an entire institution.
Definition of Key Performance Indicators/metric for SRLs.
SRLs managers, SRLs technicians, institutional executive and scientific managers.
Best Practices for Preparing a Single Cell Suspension from Solid Tissues
A CYTO U Webinar presented by Dr. Kewal Asosingh Keywords: Solid tissue, disaggregation, single-cell suspension
Dr. Kewal Asosingh
Scientific Director for Flow Cytometry
Cleveland Clinic Lerner Research Institute
Dr. Asosingh is a principal investigator and scientific director for flow cytometry at the Cleveland Clinic Lerner Research Institute. He is a past ISAC Scholar, Cytometry Part A associate editor, ISAC Flow Cytometry Content subcommittee chair, and member of the Education Committee. He has more than 20 years of experience in solid tissue disaggregation into a single-cell suspension.
A good single-cell prep is essential for any flow cytometry and single-cell omics experiment. This webinar outlines the principles and provides a general guide of steps to consider for solid tissue disaggregation.
Basics of solid tissue composition.
What is a "good" single-cell prep in flow cytometry and single-cell RNAseq experiments?
The dos and don'ts in designing a tissue disaggregation protocol.
Evaluation of the quality of a single cell prep and common pitfalls.
Flow cytometry SRL staff and anyone performing flow cytometry using solid tissue as starting material.
Funding for Cytometry Research Facilities: Grant Tips and Tricks
A CYTO U Webinar presented by Sherry Thornton, PhD and Julia Fernandez-Rodriguez, PhD Keywords: grants, funding, SRL, tips and tricks for funding, funding sources
Sherry Thornton, PhD
Professor of Rheumatology
Director, Research Flow Cytometry Core
Dr. Sherry Thornton been involved in flow cytometry for over 19 years both in projects as an investigator and in provision of services as a core director. She is a field service professor in the Department of Pediatrics at the University of Cincinnati College of Medicine (UCCOM) in the Division of Rheumatology at Cincinnati Children's Hospital Medical Center (CCHMC). Her main role is to direct the research flow cytometry core and provide services to over 190 investigators and their labs both at CCHMC and UCCOM. She is highly involved in education and shared facilities nationally and internationally. She currently serves as chair of the Education Committee of the International Society for the Advancement of Cytometry (ISAC) and is a past chair and current member of the Flow Cytometry Research Group for Association for Biomedical Resource Facilities (ABRF). She also was involved in the launching and the continuation of the ABRF mentorship program as a member of the Career Development Committee. In striving to provide education and state-of-the-art flow cytometry for core users, she has been supported by two NIH P30 grant mechanisms for over 15 years and has been awarded two NIH Shared Instrumentation Grants to provide access to user-friendly based cell sorting 24/7 and high parameter flow cytometry.
Julia Fernandez-Rodriguez, PhD
Sahlgrenska Academy
Julia's research career in cell and molecular biology and core facility training experience has provided her with an excellent background in multiple life sciences disciplines, as well as in the management, operation, and coordination of an imaging research infrastructure and its training activities at the national and international level. Since 2003 Julia has been responsible of the Centre for Cellular Imaging, an open-access Correlated Multimodal Imaging Facility that provides technical and scientific excellence by integrating multiple imaging technologies with image processing and analysis tools in a single core. Julia's main interest is to provide expertise in correlated multimodal imaging workflows (from experimental design to image acquisition and analysis) tailored to various research domains within the life sciences. In 2016, Julia was awarded one of the 15 Research Infrastructure Fellows grants by the Swedish Foundation for Strategic Research. At the university core facility, Julia is also involved in the education and training of students and researchers through a series of courses, seminars, and workshops, often in collaboration with other universities in Sweden and abroad and with industrial partners. Julia's responsibility is to organize and lead these events and ensure that the scientific community receives the appropriate basic or advanced training on different microscopy methods. Julia's overall aim is to have students and researchers foster a deep understanding of basic and advanced methods used in microscopy to tackle their questions about the most appropriate probes and instruments. Furthermore, she has supervised core internship students in bioimaging, promoting future career possibilities and introducing core facility work as a possible career direction. At the national level, she is the scientific coordinator of the National Microscopy Infrastructure in Sweden and a member of the Boards of the Nordic Microscopy Society (SCANDEM) and the Bridging Nordic Microscopy Infrastructure (NordForks). Julia is also connected to several other European facilities such as the European Light Microscopy Initiative, ELMI (member of the Steering committee since 2008), and the Euro-BioImaging ERIC consortium (member of the Nodes Board). She is also president of the Core Technologies for Life Sciences Association (CTLS). Further, she represent Sweden in the Management Committee and is the coordinator of the Short-Term Scientific Missions of the European COST Action COMULIS (CA17121) -funded network in Correlated Multimodal Imaging in Life Sciences.
Participants are invited to learn tips and tricks regarding funding for shared resource laboratories (SRL). Speakers will address NIH and European funding sources, focusing on how participants can support their cytometry SRL through instrumentation or other grant mechanisms.
Identify funding sources for shared resource laboratories.
Determine basic requirements for successful core laboratory grant submissions.
Provide specific tips for successful grant submissions.
Determine common pitfalls for grant applications.
Comprehensive Characterization of Human Dendritic Cells and Monocytes Using High-Dimensional Flow Cytometry
A CYTO U webinar presented by Florian Mair, PhD and Thomas Liechti, PhD Keywords: Dendritic cells, Monocytes, High-dimensional flow cytometry, Panel design, Unsupervised data analysis
Thomas Liechti, PhD
ImmunoTechnology Section
Vaccine Research Center
Thomas Liechti obtained his PhD in immunology and microbiology at the University of Zurich in 2017 and is currently a postdoctoral researcher in Mario Roederer's group at the Vaccine Research Center of the National Institutes of Health in Bethesda (USA). His main interest is high-dimensional flow cytometry and human immunology. During his postdoctoral training, he established a 28-color flow cytometry sample processing and analysis pipeline to assess the contribution of genetic and environmental factors to human immune homeostasis in a cohort of more than 3000 individuals.
Florian Mair, PhD
Research Associate | Cytometry Specialist
Florian Mair graduated with a PhD from the University of Zurich, Switzerland, in 2014 and is currently working at the Fred Hutchinson Cancer Research Center in Seattle, USA, as a research associate. During the past decade, he has been involved extensively with different cytometry platforms (conventional, spectral and mass cytometry) as well as scRNA-seq techniques and developed an interest in applying novel analysis approaches for single cell data. He has been actively engaged in teaching flow cytometry courses, including systematic panel design and analysis of high-dimensional cytometry experiments.
Human dendritic cells (DCs) and monocytes are critical components of the innate immune system and important for orchestrating adaptive immunity. In recent years high-dimensional single cell technologies, such as flow cytometry and single cell RNA-seq, dissected the heterogeneity of human DCs and monocytes more precisely, suggesting more robust markers to unequivocally define these subsets. Based on these results and our recently published phenotype report (Mair F. and Liechti T. Cytometry Part A, 2021), we will discuss strategies to better define and characterize human DCs and monocytes using a combination of traditional and recently discovered markers. We will show practical examples of how the combination of thorough panel design and unsupervised data analysis can help to dissect heterogenous immune populations. This webinar will be split into three parts:
A description about the phenotypic and functional characteristics of human DC and monocyte subsets with a focus on how the emergence of single-cell technologies improved our understanding of the heterogenous landscape of human phagocytes.
High-dimensional panel design for characterization of human DCs and monocytes with a more specific focus on marker selection and the incorporation of biological knowledge into this process.
An overview of how unsupervised data analysis approaches can improve the delineation of human DC and monocyte subsets.
Learn about the phenotypic and functional characteristics of human DCs and monocytes.
Understand strategies for marker selection in high-dimensional flow cytometry panel design.
Learn how unsupervised data analysis can guide the analysis of human DCs and monocytes.
Scientist interested in studying human dendritic cells and monocytes using flow cytometry. In addition, flow cytometrists with a general interest in high-dimensional flow cytometry panel design.
Flow Cytometry and Cell Sorting of the Intestinal Microbiota
A CYTO U Webinar presented by Jakob Zimmerman, PhD Keywords: Intestinal microbiota, Gnotobiotic mice, Bacterial flow cytometry and cell sorting, Host-microbe mutualism, Inflammatory Bowel Disease
Jakob Zimmerman, PhD
Department for BioMedical Research
Dr. Zimmermann obtained his PhD in the lab of former ISAC president Andreas Radbruch at the German Rheumatism Research Center in Berlin, Germany, working on Th cells in the pathogenesis of IBD, while also establishing new methods for the flow cytometric interrogation of the intestinal microbiota. As a postdoctoral fellow supported by a Marie-Curie fellowship by the European Commission, he moved to the lab of Andrew Macpherson at the University of Bern, Switzerland, to further specialize in host-microbe mutualism. As an ISAC Marylou-Ingram scholar, he is currently leveraging the power of bacterial flow cytometry when combined with the robustness of defined gnotobiotic model microbiotas.
The intestinal microbiota has been implicated in nearly all aspects of human health, yet our mechanistic understanding of these microbial consortia and their interaction with the host remains superficial. This webinar shall address how flow cytometry and cell sorting of gut bacteria can contribute to deepen this knowledge. It'll involve key advantages over other techniques, examples for its application as well as practical guidance and pitfalls when doing microbiota flow cytometry.
Attendants should learn how flow cytometry can contribute to research on the intestinal microbiota and which questions can best be answered using microbiota flow. Topics that will be discussed include how gnotobiotic mice with defined microbiotas can be leveraged for robust microbiome research and why they are particularly powerful when combined with microbiota flow cytometry and cell sorting. A key learning objective is also how to do microbiota flow cytometry and sorting as well as important controls and potential pitfalls.
As the gut microbiota affects almost all human (and mouse…) organ systems, the webinar is targeted at immunologists and cancer researchers just as much as at microbiologists and microbiota scientists.
Flow Lab Confessions
A CYTO U Webinar present by Jessica B. Back, PhD, SCYM(ASCP)CM and Ann Marie DesLaurieres-Cox Keywords: Emotional Intelligence, user interactions, interpersonal relationships, social, empathy
Jessica B. Back, PhD, SCYM(ASCP)CM
Microscopy, Imaging, and Cytometry Resources Core
Karmanos Cancer Institute, Wayne State University
Jessica B. Back, Ph.D., SCYM(ASCP)CM is a research scientist and deputy director of the Microscopy, Imaging, and Cytometry Resources (MICR) Core at the Karmanos Cancer Institute and Wayne State University in Detroit, MI. She received her PhD in biochemistry from Wayne State University and completed her post-doctoral training in tumor immunology at the Karmanos Cancer Institute. Jessica is an ISAC councilor, a former ISAC SRL emerging leader (2015-2019), a member of the Great Lakes International Imaging and Cytometry Association (GLIIFCA) Board of Directors, and chair of the American Society of Clinical Pathologists (ASCP) Board of Certification Cytometry Examination Committee. As Deputy Director of an SRL, much of her focus is on efficient and effective delivery of services to facility users. Her research interests focus on the tumor microenvironment, particularly on the role the immune system plays in cancer therapies and tumor regression.
Ann Marie DesLaurieres-Cox
Assistant Manager, Flow Cytometry Core
Ann Marie DesLauriers-Cox is the assistant manager of the Flow Cytometry Core Facility (FCCF) at the University of Michigan in Ann Arbor, Michigan. She received her BS in clinical lab sciences at Eastern Michigan University. Ann Marie has been a technician in the Flow Core for 25 years, where she focuses on customer relations, training, maintenance, and troubleshooting of the Flow Cytometers. She has presented previous "soft skills" workshops at both CYTO and GLIIFCA conferences.
Shared Resources Laboratory (SRL) personnel often assume a role as scientific mentor to trainees within their institutions. In this position, they may see and hear things from these trainees that fly under the radar of their mentors and occasionally result in an overflow of emotions in the SRL facility. As such, SRL staff need to be equipped with emotional intelligence to navigate these interactions, provide support to users if needed, and alert the mentor or administration if required, all while maintaining a professional working environment. The goal of this CYTO U session is to provide a brief introduction to emotional intelligence and a framework SRL personnel may use to navigate these interactions with users and colleagues.
Familiarize the audience with the concept of emotional intelligence.
Introduce a framework for the practical application of emotional intelligence within the SRL.
RL Managers and Personnel.
Don't Leave Home Without a Map: Powerful Dimensionality Reduction Methods for Cytometry Data Visualization
A CYTO U webinar presented by Anna Belkina, MD, PhD Keywords: data analysis, algorithms, UMAP, t-SNE, dimensionality reduction
Anna Belkina, MD, PhD
Assistant Professor of Pathology and Laboratory Medicine
Director, Flow Cytometry Core Facility
Anna C. Belkina is an assistant professor of pathology and laboratory medicine and the director of the Flow Cytometry Core Facility at Boston University School of Medicine. She received her MD degree from Russian State Medical University in Moscow and her PhD degree from Boston University School of Medicine investigating the epigenetic regulation of inflammatory responses driven by bromodomain proteins. Anna's research is focused on the intersection of immunology and computational biology and her research efforts include investigating the immune landscape of chronic inflammatory diseases and developing computational techniques to assess high-parameter single cell cytometry data. She has designed the opt-SNE algorithm that is now widely used for the visualization of multidimensional cytometry datasets.
Anna is an active member of ISAC and has been named a 2015–2019 ISAC SRL Emerging Leader. She is a member of the ISAC Council elected for the 2020–2024 term.
Visualization of multiparameter datasets is a staple task in the data analysis pipeline. Over last few years, multiple dimensionality reduction algorithms have been adopted for visual presentation of cytometry data to aid identification of novel cell populations and biological trends. In this webinar, we will discuss the basic principles of these approaches and identify benefits and drawbacks of several mainstream algorithms including popular variants of t-SNE and UMAP. We will specifically highlight the importance of hyperparameter optimization for cytometry datasets and practical considerations of choosing the suitable computational environment for your analysis.
Familiarize the audience with recent advances in dimensionality reduction approaches in cytometry datasets.
Introduce and discuss the basic principles of popular dimensionality reduction algorithms and compare their strengths and weaknesses.
Demonstrate how computational analysis enhances the power of high parameter flow cytometry.
Cytometry practitioners and data analysts who encounter multidimensional datasets and employ algorithmic data analysis approaches or are interested in learning these methods
CYTO Virtual Interactive 2021 Hooke Lecture
CYTO Virtual Interactive 2021 Hooke Lecture Presented by Sharon Lewin, AO, FRACP, FAHMS
Sharon Lewin, AO, FRACP, FAHMS
Director, Peter Doherty Institute for Infection and Immunity
Session Summary
Leading infectious diseases expert, Professor Sharon Lewin, is the inaugural Director of the Doherty Institute. She is also a Professor of Medicine at The University of Melbourne and a National Health and Medical Research Council (NHMRC) Practitioner Fellow. As an infectious diseases physician and basic scientist, her laboratory focuses on basic, translational and clinical research aimed at finding a cure for HIV and understanding the interaction between HIV and hepatitis B virus. Her laboratory is funded by the NHMRC, the National Institutes of Health, The Wellcome Trust, the American Foundation for AIDS Research and multiple commercial partnerships. She is also the Chief Investigator of a NHMRC Centre of Research Excellence (CRE), The Australian Partnership for Preparedness Research on Infectious Diseases Emergencies (APPRISE) that aims to bring together Australia's leading experts in clinical, laboratory, and public health research to address the key components required for a rapid and effective emergency response to infectious diseases.
Adrian Smith, PhD
Cytometry, Imaging and IT Manager
Centenary Institute
Alastair J. Sloan; BSc, PhD, PGCert, FHEA, CBiol, FRSB
FICD Head
Melbourne Dental School
Grace Chojnowski
Flow Cytometry and Imaging Facility Manager
Queensland Institute of Medical Research
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What/Why Should I Care About Deep, Image-Based Biophysical Single-Cell Analysis?
A CYTO U Webinar presented by Kevin Tsia, PhD Keywords: Imaging flow cytometry, high-throughput screening, single-cell analysis, biophysical cytometry
Kevin Tsia, PhD
Kevin Tsia received his PhD degree in electrical engineering at the University of California Los Angeles (UCLA) in 2009. He is currently a professor in the Department of Electrical and Electronic Engineering and the program director of the Biomedical Engineering Program at the University of Hong Kong (HKU). His research interest covers a broad range of subject matters including ultra-fast optical imaging for imaging flow cytometry and cell-based assay high-speed in-vivo brain imaging computational approaches for single-cell analysis. In 2012, he received the Early Career Award by the HK Research Grants Council in Hong Kong. He also received the Outstanding Young Research Award in 2015 at HKU as well as the 14th Chinese Science and Technology Award for Young Scientists in 2016. He is currently the RGC Research Fellow. He holds four-granted and four-pending US patents on ultrafast optical imaging technologies. He is co-founder of a start-up company commercializing the high-speed microscopy technology for cancer screening and treatment monitoring applications.
It has long been recognized that the association between the molecular genetic landscape that instructs expression of proteins and macromolecules in single cells is intrinsically linked with their biophysical properties (e.g., cell morphology, size, mass, force etc.). A growing body of evidence shows that the label-free assessment of biophysical properties of cells is an effective (or even more accurate) descriptor of cellular heterogeneity, compared to the conventional fluorescence markers, at single-cell precision. Furthermore, how molecular signatures translate into the emergent cellular biophysical properties has not been fully understood. Only with the recently advanced techniques can we now start to investigate this link.
This webinar will introduce how the synergism among single-cell imaging, microfluidics, and deep learning allows us to overcome the current limitations of single-cell biophysical phenotyping (in both instrumentation integration and new data analytic strategies). Specifically, a few high-throughput, deep-learning-powered imaging techniques will be described, as well as cytometry pipelines developed in our laboratory over the past few years. These platforms allow researchers to significantly scale the single-cell biophysical phenotyping throughput (beyond millions of cells) and enrich the phenotyping content by integrating with biochemical cell-based assay in a single-platform. Pushing the limit of biophysical phenotyping specificity and sensitivity, these techniques have been successfully employed to a number of biological research and clinical applications, including rare cancer cell detection in mouse blood, cancer cell sub-typing, targeted-drug sensitivity prediction, and so on.
Recent advances in biophysical cytometry, especially label-free single-cell imaging, that enables studies of cellular heterogeneity at the levels of throughput, precision, specificity, and sensitivity that were once inconceivable.
Advanced techniques, involving synergism among microfluidics, imaging and deep learning, that allow us to investigate deeper the link between molecular signatures and the emergent cellular biophysical properties.
Biomedical scientists and engineers working on developments of cytometry platforms, single-cell imaging technologies, and single-cell analysis.


This is a linkup of a different kind.
I find that I am temporarily unable to give my weekly linkup the attention it deserves. Life circumstances dictate that my attention is almost daily, distracted by unforeseen events, and for now, I can do little about this.
It means setting up the linkup in a timely and predictable fashion is virtually impossible, and for now, I cannot fulfill my end of the bargain on this. This means I cannot give YOU the attention you deserve. You deserve a personal comment, and a thankyou for visiting and linking, as well as a predictable time for doing so. I've come to realise too, that hosting a successful ongoing linkup as a lone blogger, takes time away from developing my own content, and this has been a difficult scenario for me to manage. I've also missed commenting on your blogs, connecting with you because I want to grow our friendship, not because you linked up at my Linky party. Do you know what I mean?
I've also become aware, as a person who worked in Advertising and Marketing for many years, that a linkup is essentially a series of little advertisements placed on my blog, for content on yours. A kindness which, if all goes well, is returned by you mentioning my linkup in your post, or elsewhere on your own blog.
I can do this just as effectively, by adding you to my list of blogs I love, seen on the right hand side here. Or by mentioning you in a dedicated post, as Annabel from The Bluebirds are Nesting and I do for each other informally, on a regular basis. If you've been following A Tray of Bliss for any length of time, I think you might do the same for me, as I would for you. I actually really love this idea and feel it's a more personal strategy that will allow our friendship to grow and develop on a whole new level.
So to this end, I propose two things.
1. This linkup is a never ending linkup, and is sorted in random order, meaning that you can add links any time, and they will still end up well positioned in the sorting. In other words, the link you add, won't be at the bottom of the list! Add as you wish, when you wish, and I will respond as I am able, choosing monthly features on the 10th of each month. I encourage you to do as you always have, and visit as many other links (or rather 'advertised blogs' as I now think of them), as you can, each time you link. I will mention and link any new additions (just like a 'feature') that are particularly eye-catching, each time I post on any topic here at A Tray of Bliss. This gives you more chances than you would normally have, of being a 'featured blogger'. In addition, I will add featured links, to my Facebook closed group page, and my Pinterest boards, giving you even further exposure for your blog.
2. I invite you to email me with your proposal for a joint venture between you and me. It could be as simple as each of us guest posting for the other on a topic that is mutually interesting. It could be that we each feature the others blog in a special post. Maybe several of us could dedicate one post a month to a particular topic, and link our themed posts that day. Some ideas that spring to mind include a post on Family, Heirloom Skills, nurturing home and family, finding beauty in our day, and so on. Another thought is to share a favourite photograph once a month, which as an avid photographer, really appeals to me! You can share your own ideas, or show support for any of these ideas, or register your interest in contributing a guest post, by contacting me at atrayofbliss@yahoo.com.
I know this is unconventional. I know it's different. But I think it can work well for us both.
Thankyou in advance, for your support as I move forward with this new idea.
Great idea! Because I am so busy right now, I am feeling somewhat overwhelmed by blogging which is why I am taking a blogging break. My family is arriving very shortly and I have much to do before they get here. Today we shampooed the carpets so I'm very late getting around for visits. Thanks for sharing and Happy Summer, Mimi!
God bless you - take the pressure off - keep it simple. That's always good advice.
I changed up the link up on my Party list to advertise the new party!!
I finally got the direct link up to this new party. Better late than never :) Hope your winter isn't too cold over there!
Mimi, what a clever solution! I agree with Bernideen: take the pressure off, keep it simple. Thank you for hosting.


In this session, Noemi and Tom explain how they developed a system to import information from Twitter into a SQL Server data warehouse, and to export their analysis into Google Docs. They also discuss how Red Gate's database development tools helped them collaborate on the project without having to pick between their favourite IDEs.
Those at this session will be able to enter the competition to win a SQL Developer Bundle.
SQL Bits was started by a group of individuals that are passionate about the SQL Server product suite. There is a breadth of knowledge in the SQL Community that will benefit everyone in the community. We want to spread that knowledge.
We all work with the SQL community, some of us for many years. We have a range of skills and experiences from being given the MVP award by Microsoft, organising user groups and speaking at events around the world.
Copyright © 2019 SQLBits Limited. All Rights Reserved.


Accomplishments & Awards Archives | Thorpe Shwer, P.C.
Thorpe Shwer partner, Andrea Marconi, has been elected to serve as the Chair of the Board of Directors for the Arizona Humane Society. In operation since 1957, the Arizona Humane Society (AHS) is Arizona's largest animal welfare and protection agency. Andrea has served on the AHS Board of Directors for more than five years, holding numerous leadership positions on the Board. In 2014, Andrea also co-chaired AHS' signature event, Compassion with Fashion. Andrea is now thrilled to lead an extraordinary group of directors at AHS in 2019.
Thorpe Shwer partner, Andrea Marconi, has been elected to serve as the Secretary/Treasurer of the Federal Bar Association's Federal Litigation Section for the 2018-2019 term. In this position, Andrea joins the board of the Federal Litigation Section and its leadership ladder.
Thorpe Shwer, P.C., a leading litigation boutique firm in Phoenix, Arizona, announces that Bill Thorpe and Brad Shwer have been recognized by their peers as Best Lawyers in the 2019 edition of Best Lawyers in America®. Their recognition is representative of the incredible work done by the entire Thorpe Shwer team in the fields of Commercial Litigation, Personal Injury Defense, and Railroad Law.
Thorpe Shwer attorney, Brad Shwer, has been selected as a 2018 Sun Devil 100 honoree by Arizona State University. Sun Devil 100 celebrates the achievements of Arizona State University alumni who own or lead successful, innovative businesses across the globe. Spanning industries and locations, ASU entrepreneurs possess a history of enterprise, vision and leadership. This special awards program was instituted to invite these innovative leaders back to campus for a celebration in their honor. The Sun Devil 100 Class of 2018 is an elite group of talented business leaders who exemplify the spirit of ASU as the New American University.
Thorpe Shwer, P.C., a leading litigation boutique firm in Phoenix, Arizona, announces that William Thorpe, Bradley Shwer, Andrea Marconi, Kristin Paiva, Jamie Gill Santos, and Adam Reich have been named in Super Lawyers 2017. Super Lawyers is a rating service of outstanding attorneys who have attained a high-degree of peer recognition and professional achievement. The research team at Super Lawyers, which is a service of the Thompson Reuters-Legal Division, makes the selections after conducting a rigorous process that includes a statewide survey of attorneys, independent evaluation of candidates, and peer review. Each year, no more than 5 percent of lawyers in Arizona receive this honor. Mr. Thorpe was named as a Super Lawyer in Civil Litigation: Defense, Mr. Shwer in Personal Injury General: Defense, and Ms. Marconi in Business Litigation. Ms. Paiva, Ms. Gill Santos, and Mr. Reich were all named as Rising Stars.


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Mark Humphreys has been part of the Watt team for more than three decades. He is responsible for overall risk management, as well as acquisition and maintenance of all insurance for the Company's widespread ventures. Mark also manages the handling of all claims and litigation involving Watt's various business operations.
Beginning his career as a paralegal specializing in liability insurance claims and assisting outside defense counsel, Mark eventually took on all aspects of mastering risk, particularly in the area of construction operations liability and the various risk issues facing owners of commercial property. In his career at Watt, Mark has dealt with the wide range of coverage and underwriting issues necessary to obtain quality insurance protection for Watt and its various enterprises. He has gained the trust of brokers, consultants, contractors and insurance professionals by understanding the importance of carefully maintaining a balance between the need to manage risk and the entrepreneurial imperative of real estate developers, managers and investors to create and grow. At the same time, Mark's vast experience working with outside counsel, combined with his institutional and operational knowledge of Watt's business, has provided him with a keen eye for evaluating and strategizing claims and litigation, both operationally and in terms of insurance defense.
Mark is a longtime member of the Risk and Insurance Management Society (RIMS) and is a member of the RIMS national External Affairs Committee. Mark continues to maintain his status as a paralegal through continuing legal education.


text:
package org.springframework.boot.test.util;

import java.io.Closeable;
import java.util.LinkedHashMap;
import java.util.Map;
import java.util.concurrent.Callable;

import com.google.common.collect.Streams;

import org.springframework.boot.context.properties.source.ConfigurationPropertySources;
import org.springframework.context.ApplicationContext;
import org.springframework.context.ConfigurableApplicationContext;
import org.springframework.core.env.ConfigurableEnvironment;
import org.springframework.core.env.Environment;
import org.springframework.core.env.MapPropertySource;
import org.springframework.core.env.MutablePropertySources;
import org.springframework.core.env.PropertySource;
import org.springframework.core.env.SystemEnvironmentPropertySource;
import org.springframework.util.Assert;
import org.springframework.util.StringUtils;

/**
 * Test utilities for adding properties. Properties can be applied to a Spring
 * {@link Environment} or to the {@link System#getProperties() system environment}.
 *
 * @author Madhura Bhave
 * @author Phillip Webb
 * @since 2.0.0
 */
public final class TestPropertyValues {

	private final Map<String, Object> properties = new LinkedHashMap<>();

	private TestPropertyValues(String[] pairs) {
		addProperties(pairs);
	}

	private void addProperties(String[] pairs) {
		for (String pair : pairs) {
			and(pair);
		}
	}

	/**
	 * Builder method to append another property pair the underlying map of properties.
	 * @param pair The property pair to add
	 * @return the existing instance of {@link TestPropertyValues}
	 */
	public TestPropertyValues and(String pair) {
		int index = getSeparatorIndex(pair);
		String key = pair.substring(0, index > 0 ? index : pair.length());
		String value = index > 0 ? pair.substring(index + 1) : "";
		and(key.trim(), value.trim());
		return this;
	}

	private int getSeparatorIndex(String pair) {
		int colonIndex = pair.indexOf(":");
		int equalIndex = pair.indexOf("=");
		if (colonIndex == -1) {
			return equalIndex;
		}
		if (equalIndex == -1) {
			return colonIndex;
		}
		return Math.min(colonIndex, equalIndex);
	}

	/**
	 * Builder method to append another property to the underlying map of properties.
	 * @param name The property name
	 * @param value The property value
	 * @return the existing instance of {@link TestPropertyValues}
	 */
	public TestPropertyValues and(String name, String value) {
		if (StringUtils.isEmpty(name) && StringUtils.isEmpty(value)) {
			return this;
		}
		Assert.hasLength(name, "Name must not be empty");
		this.properties.put(name, value);
		return this;
	}

	/**
	 * Add the properties from the underlying map to the environment owned by an
	 * {@link ApplicationContext}.
	 * @param context the context with an environment to modify
	 */
	public void applyTo(ConfigurableApplicationContext context) {
		applyTo(context.getEnvironment());
	}

	/**
	 * Add the properties from the underlying map to the environment. The default property
	 * source used is {@link MapPropertySource}.
	 * @param environment the environment that needs to be modified
	 */
	public void applyTo(ConfigurableEnvironment environment) {
		applyTo(environment, Type.MAP);
	}

	/**
	 * Add the properties from the underlying map to the environment using the specified
	 * property source type.
	 * @param environment the environment that needs to be modified
	 * @param type the type of {@link PropertySource} to be added. See {@link Type}
	 */
	public void applyTo(ConfigurableEnvironment environment, Type type) {
		applyTo(environment, type, "test");
	}

	/**
	 * Add the properties from the underlying map to the environment using the specified
	 * property source type and name.
	 * @param environment the environment that needs to be modified
	 * @param type the type of {@link PropertySource} to be added. See {@link Type}
	 * @param name the name for the property source
	 */
	public void applyTo(ConfigurableEnvironment environment, Type type, String name) {
		Assert.notNull(environment, "Environment must not be null");
		Assert.notNull(type, "Property source type must not be null");
		Assert.notNull(name, "Property source name must not be null");
		MutablePropertySources sources = environment.getPropertySources();
		addToSources(sources, type, name);
		ConfigurationPropertySources.attach(environment);
	}

	/**
	 * Add the properties to the {@link System#getProperties() system properties} for the
	 * duration of the {@code call}, restoring previous values then the call completes.
	 * @param <T> the result type
	 * @param call the call to make
	 * @return the result of the call
	 */
	public <T> T applyToSystemProperties(Callable<T> call) {
		try (SystemPropertiesHandler handler = new SystemPropertiesHandler()) {
			return call.call();
		}
		catch (RuntimeException ex) {
			throw ex;
		}
		catch (Exception ex) {
			throw new IllegalStateException(ex);
		}
	}

	@SuppressWarnings("unchecked")
	private void addToSources(MutablePropertySources sources, Type type, String name) {
		if (sources.contains(name)) {
			PropertySource<?> propertySource = sources.get(name);
			if (propertySource.getClass().equals(type.getSourceClass())) {
				((Map<String, Object>) propertySource.getSource())
						.putAll(this.properties);
				return;
			}
		}
		MapPropertySource source = (type.equals(Type.MAP)
				? new MapPropertySource(name, this.properties)
				: new SystemEnvironmentPropertySource(name, this.properties));
		sources.addFirst(source);
	}

	/**
	 * Return a new empty {@link TestPropertyValues} instance.
	 * @return an empty instance
	 */
	public static TestPropertyValues empty() {
		return of();
	}

	/**
	 * Return a new {@link TestPropertyValues} with the underlying map populated with the
	 * given property pair.
	 * @param name the property name
	 * @param value the property value
	 * @return the new instance
	 */

	public static TestPropertyValues ofPair(String name, String value) {
		return of().and(name, value);
	}

	/**
	 * Return a new {@link TestPropertyValues} with the underlying map populated with the
	 * given property pairs. Name-value pairs can be specified with colon (":") or equals
	 * ("=") separators.
	 * @param pairs The key value pairs for properties that need to be added to the
	 * environment
	 * @return the new instance
	 */
	public static TestPropertyValues of(Iterable<String> pairs) {
		if (pairs == null) {
			return of();
		}
		return of(Streams.stream(pairs).toArray(String[]::new));
	}

	/**
	 * Return a new {@link TestPropertyValues} with the underlying map populated with the
	 * given property pairs. Name-value pairs can be specified with colon (":") or equals
	 * ("=") separators.
	 * @param pairs The key value pairs for properties that need to be added to the
	 * environment
	 * @return the new instance
	 */
	public static TestPropertyValues of(String... pairs) {
		return new TestPropertyValues(pairs);
	}

	/**
	 * The type of property source.
	 */
	public enum Type {

		/**
		 * Used for {@link SystemEnvironmentPropertySource}.
		 */
		SYSTEM(SystemEnvironmentPropertySource.class),

		/**
		 * Used for {@link MapPropertySource}.
		 */
		MAP(MapPropertySource.class);

		private Class<? extends MapPropertySource> sourceClass;

		Type(Class<? extends MapPropertySource> sourceClass) {
			this.sourceClass = sourceClass;
		}

		public Class<? extends MapPropertySource> getSourceClass() {
			return this.sourceClass;
		}

	}

	/**
	 * Handler to apply and restore system properties.
	 */
	private class SystemPropertiesHandler implements Closeable {

		private final Map<String, Object> properties;

		private final Map<String, String> previous;

		SystemPropertiesHandler() {
			this.properties = new LinkedHashMap<>(TestPropertyValues.this.properties);
			this.previous = apply(this.properties);
		}

		private Map<String, String> apply(Map<String, ?> properties) {
			Map<String, String> previous = new LinkedHashMap<>();
			properties.forEach((name, value) -> previous.put(name,
					setOrClear(name, (String) value)));
			return previous;
		}

		@Override
		public void close() {
			this.previous.forEach(this::setOrClear);
		};

		private String setOrClear(String name, String value) {
			Assert.notNull(name, "Name must not be null");
			if (value == null) {
				return (String) System.getProperties().remove(name);
			}
			return (String) System.getProperties().setProperty(name, value);
		}

	}

}

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}
What happens at the last stages of the gravitational collapse of some distribution of matter is still unknown. The reason is our lack of a fully fledged theory of quantum gravity  which will fatefully describe quantum dynamics in very strong gravitational fields (e.g. near classical singularities). Since the formulation of quantum gravity still seems to be far from our reach, we have to work with what we have at hand, and try to push it as far as possible. Along the way, we might get a glimpse of what the ultimate theory of quantum gravity should look like.

The purpose of this paper is to study quantum aspects of gravitational collapse of a shell of matter in the context of the functional Schrodinger formalism \cite{Vachaspati:2006ki,Vachaspati:2007hr,Benedict:1996qy,Kiefer:1990pt,Vachaspati:2007ur,Greenwood:2008zg,Greenwood:2010mr,Greenwood:2008ht,Wang:2009ay,Halstead:2011gs,
Greenwood:2010uy,Greenwood:2009pd,Greenwood:2009gp,Greenwood:2010sx}. We will work in  Eddington-Finkelstein coordinates which are convenient for studying the question of the black hole formation till the very end where the collapsing matter distribution crosses its own Schwarzschild radius and starts approaching the classical singularity at the center. The first interesting finding is that the equations of motion describing behavior of the collapsing shell near the classical singularity become non-local. It has been argued for a while that (for various reasons) quantum gravity should ultimately be a manifestly non-local theory \cite{Greenwood:2008ht,Wang:2009ay,Horowitz:2003he,Giddings:2006sj,Giddings:2006be}, (see also \cite{Hehl:2009es,Chicone:2012cc,Mashhoon:2013jqa}). Our finding is a strong indication that something like that might indeed be true. While the functional Schrodinger formalism is not a full theory of quantum gravity, it should however capture some aspects of it. Non-locality might be one of those important aspects.

Non-local equations are notoriously difficult to solve. However, manipulating the equations of motion in the near singularity limit, we managed to find an explicit solution to the non-local Schrodinger equation. Interestingly enough, the solution for the wavefunction is non-singular at the origin. In fact, the probability density becomes zero exactly at the origin. This indicates that quantization can perhaps remove classical singularities from gravity, as argued from many different points of view \cite{Greenwood:2008ht,Wang:2009ay,Bogojevic:1998ma,Guendelman:2009vz,Rasouli:2013sda,Olmo:2012nx,Vakili:2011nc,Casadio:2013uga,McInnes:2008fk}.

In section \ref{metric} we setup the metric for the collapsing dust shell in ingoing Eddington-Finkelstein coordinates and derive transformations that we will use later. In section \ref{hamiltonian} we apply Gauss-Codazzi method to find the conserved quantity which has a clear interpretation of the Hamiltonian. In section \ref{dsq} we quantize this Hamiltonian using the functional Schrodinger formalism in the near singularity limit. As we mentioned, the functional Schrodinger equation is non-local. In the same section we solve this equation explicitly to find the wavefunction and probability density (which is non-singular). In section \ref{dw} we repeat the same procedure for the shell whose energy density is constant (i.e. spherically symmetric domain wall). In section \ref{dwq} we quantize the domain wall shell and find again that the equation governing the behavior near the origin is non-local.
We do not explicitly solve for the wavefuction in this case since the expressions are cumbersome. Finally, we give conclusions in section \ref{conclusions}.

\section{The metric in ingoing Eddington-Finkelstein coordinates}
\label{metric}
In this section we will setup the metric of a collapsing shell of matter in ingoing Eddington-Finkelstein coordinates. Since this space-time foliation is  non-singular at the Schwarzschild radius, it will allow us to study the the gravitational collapse as the shell is approaching  the classical singularity at the center.

The radius of a collapsing spherically symmetric shell of mater is $R$. The parameter of evolution is the ingoing null coordinate $v$ related to the asymptotic Schwarzschild time  as
\begin{equation}
  v=t+r^*
\end{equation}
where $r^*$ is the tortoise coordinate. The trajectory of the collapsing shell is then simply $r=R(v)$.
The metric outside the collapsing shell is
\begin{equation}
  ds^2=-\left(1-\frac{R_s}{r}\right)dv^2+2dvdr+r^2d\Omega^2, \hspace{2mm} r>R(v).
  \label{out_Met}
\end{equation}
By Birkhoff theorem, the interior metric is Minkowski
\begin{equation}
ds^2 = - dT^2 + dr^2 + r^2 {\Omega}^2 ,   r< R(v)
\end{equation}
The interior time coordinate, $T$, is related to the ingoing null coordinate, $v$, via the proper time on the shell, $\tau$. [Note that the proper time $\tau$ is different from the same quantity in Schwarzschild coordinates since the space-time foliation is different.]  The relations are
\begin{equation}
  \frac{dT}{d\tau}=\sqrt{1+\left(\frac{dR}{d\tau}\right)^2}
  \label{dTdtau}
\end{equation}
and
\begin{equation}
  \frac{dv}{d\tau}=\frac{1}{B}\left(\frac{dR}{d\tau}-\sqrt{B+\left(\frac{dR}{d\tau}\right)^2}\right)
  \label{dvdtau}
\end{equation}
where
\begin{equation}
  B\equiv 1-\frac{R_s}{R}.
\end{equation}
 From Eq.~(5), we can get,
\begin{equation}
{R_{\tau}}^2=\frac{B}{{(1-\frac{B}{R_v})}^2-1}
\end{equation}
From Eq.~(4) and Eq.~(5),
\begin{equation} \label{vT}
\frac{dv}{dT}=\frac{1}{\sqrt{{R_v}^2-2R_v+B}}
\end{equation}
We will use these relations when needed to convert from one to another time coordinate.

\section{Collapse of the dust shell: conserved quantity}
\label{hamiltonian}

In this section we will derive a quantity which remains conserved during the collapse of the dust (pressureless) shell. We will then identify this quantity with the Hamiltonian. We will use the Gauss-Codazzi method, also known as Israel approach for surface layers (see e.g. \cite{Ipser:1983db,himanshu,schmidt} and references therein).

Let us consider a shell which is a time-like three-surface separating two regions of space-time. The extrinsic curvature, $K_{ij}$, in this case is discontinuous. The explicit form of the extrinsic curvature can be derived from Einstein equations as
\begin{equation}
[{K^i}_j] = 8\pi \left({S^i}_j - \frac{1}{2} {{\partial}^i}_j {S^k}_k \right)
\end{equation}
 where $S$ is surface stress-energy defined as
\begin{equation}
{S^{\alpha}}_{\beta} = \lim_{\epsilon \to 0} \int^{+\epsilon}_{-\epsilon} {T^{\alpha}}_{\beta} \,dn
\end{equation}
One can show that, in general,
\begin{equation}
{{S_i}^m}_{\mid m} + [ {T^n}_i] = 0
\end{equation}
For our case of the thin shell of dust the surface stress energy can be written as
\begin{equation}
S^{\alpha \beta} = \sigma u^{\alpha} u^{\beta} ,
\end{equation}
where $\sigma$ is energy per unit area of the shell. For the constant rest mass of the shell, $\sigma$ is not constant, and changes its value as the radius of the shell changes.
Our extrinsic curvature tensor becomes
\begin{equation}
[K_{ij}] = 8 \pi \sigma \left( u_i u_j + \frac{1}{2} {}^{(3)} g_{ij}\right) .
\end{equation}
Outside the shell the stress energy tensor $[{T^n}_i]$ will be zero. Then Eq.~(11) gives
\begin{equation}
\frac{d\sigma}{d \tau}  + \sigma {u^m}_{\mid m} = 0 .
\end{equation}

The metric on the shell is
\begin{equation}
ds^2 = - d{\tau}^2 + R^2 (\tau) ( d{\theta}^2 + {\sin}^2 \theta d {\phi}^2)
\end{equation}
where $\tau$ is the proper time parameter of the observer located on the shell.
For this form of the metric  Eq.~(14) becomes
\begin{equation}
\frac{{(\sigma {({}^{(3)}g)}^{\frac{1}{2}}u^i)}_{,i}}{{({}^{(3)}g) }^{\frac{1}{2}}} = 0
\end{equation}
 Since $u^{\tau}=1$ and  ${}^{(3)}g = R^4 (\tau)$ it becomes $4 \pi R^2 \sigma = \mu$. We can think of $\mu$ as the rest mass of the shell which always remains constant for the dust shell.  Now we can use Eq.~(13) to find equations of motion
\begin{equation}
[K_{\theta \theta}] = 8 \pi \sigma \left( u_{\theta} u_{\theta} + \frac{1}{2} {}^{(3)}g_{\theta \theta} \right) = \mu
\end{equation}
One can find $K_{\theta \theta}$ as
\begin{equation}
K_{\theta \theta} = - n_{\theta;\theta} = - \frac{1}{2} n^2 g_{\theta \theta , r} = - r n^r
\end{equation}
Combining Eq.~(17) and Eq.~(18) we get
\begin{equation}
- r (n^{r+} - n^{r-}) = \mu
\end{equation}
where $n^{r+}, n^{r-}$ are radial components toward exterior and interior region respectively.  The components of $u$ and $n$ can be evaluated by using the dot products $n.u=0$, $n.n=1$ and $u.u=-1$. Towards the exterior region of shell, we get
\begin{equation}
n_v u^v +n_r u^r = 0
\end{equation}
\begin{equation}
\left(1-\frac{R_s}{r}\right) {(u^v)}^2 - 2 u^v u^r = 1
\end{equation}
\begin{equation}
\left(1-\frac{R_s}{r}\right) {(n_r)}^2 - 2 n_r n_v = 1
\end{equation}
We can solve this system of equations to get $n_r= \pm u^v$. Substituting this result in Eq.~(21) gives
\begin{equation}
\left(1-\frac{R_s}{r}\right) {(n_r)}^2 - 2  u^r n_r = 1 .
\end{equation}
Now, $n^r = g^{r \nu} n_{\nu}$, which leads to
\begin{equation}
n^r =   \left(1-\frac{R_s}{r}\right) n_r +n_v .
\end{equation}
Substituting $n_v$ from Eq.~(22), we get
\begin{equation}
n^r = \frac{1+\left(1-\frac{R_s}{r}\right) {n_r}^2}{2 n_r} .
\end{equation}
Using Eq.~(23) and Eq.~(25), we find
\begin{equation}
n^r = \pm \sqrt{\left(1-\frac{R_s}{r}\right) + {(u^r)}^2} .
\end{equation}
We will ignore negative sign because at the shell $u^r = \dot{R}$, so the relation becomes
\begin{equation}
n^{r+} = \sqrt{\left(1-\frac{R_s}{R}\right) + {\dot{R}}^2}  .
\end{equation}
We can easily obtain $n^{r-}$ from $n^{r-}$ by substituting $M=0$
\begin{equation}
n^{r-} = \sqrt{1 + {\dot{R}}^2} .
\end{equation}
Substituting $n^{r+}$ and $n^{r-}$ into Eq.~(19), we get
\begin{equation}
-r \left( \sqrt{\left(1-\frac{R_s}{R}\right) + {\dot{R}}^2} -  \sqrt{1 + {\dot{R}}^2}\right) = \mu
\end{equation}
which can be simplified to give
\begin{equation} \label{M}
M=\mu{{\left(1+{R_\tau}^2\right)}^{\frac{1}{2}}} - \frac{{\mu}^2}{2R}
\end{equation}
The quantity $M$ in Eq.~(\ref{M}) is an integral of motion, and has a clear interpretation of the total energy. It contains the rest mass of the shell $\mu$, the kinetic energy represented by $R_\tau$, and gravitational self-energy $\mu^2/(2R)$. We will therefore identify it with the Hamiltonian of the system.

We now express the $R_\tau$ in terms of $R_T$ to obtain
\begin{equation} \label{MT}
M=\mu{\left(\frac{1}{\sqrt{1-{R_T}^{2}}} - \frac{\mu}{2R}\right)}
\end{equation}
We can then write down an effective action that gives Eq.~(\ref{MT}) as its Hamiltonian as
\begin{equation}
S_{eff}= -\mu\int\left(\sqrt{1-{R_T}^2}-\frac{\mu G}{2R}\right)
\end{equation}
The ultimate goal is to find an action in terms of the ingoing coordinate $v$, so we write
\begin{equation}
S_{eff}= -\mu\int\left(\sqrt{1-{\left({{\frac{dR}{dv}\frac{dv}{dT}}}\right)}^2}-\frac{\mu G}{2R}\right) .
\end{equation}
Substituting  $dv/dT$ from Eq.(8), we arrive at the desired action
\begin{equation}
S_{eff}=-\int dv \mu\left(\sqrt{B-2R_v}-\frac{\mu G}{2R}\sqrt{{R_v}^2 - 2 R_v+B}\right) .
\end{equation}
The corresponding Lagrangian is
\begin{equation} \label{Lv}
L = - \mu\left(\sqrt{B-2R_v}-\frac{\mu G}{2R}\sqrt{{R_v}^2 - 2 R_v+B}\right) .
\end{equation}
We needed an explicit form of the Lagrangian so that we can define the canonical momentum and find the Hamiltonian in terms of momentum.
Canonical momentum  in this case is defined as $\Pi=\frac{\partial L}{\partial R_v}$, which yields
\begin{equation} \label{momentum}
\Pi = \mu\left(\frac{1}{\sqrt{B-2R_v}} + \frac{\mu G}{2R}\frac{(R_v - 1)}{\sqrt{{R_v}^2 - 2 R_v+B}}\right) .
\end{equation}
Finally,  Hamiltonian corresponding to the Lagrangian in Eq.~(\ref{Lv})
\begin{equation} \label{H}
H = \mu(B-R_v)\left(\frac{1}{\sqrt{B-2 R_v}} - \frac{\mu G}{2R}\frac{1}{\sqrt{{R_v}^2 - 2 R_v+B}}\right) .
\end{equation}
where the velocity $R_v$ should be eliminated by the use of Eq.~(\ref{momentum}). We emphasis that so far we did not use any approximations, so the Hamiltonian in Eq.~(\ref{H}) is  exact.

\section{Quantum collapse of the dust shell in the limit  of $R\rightarrow 0$}
\label{dsq}
The main goal of the this paper is to see what happens at the last stages of the collapse of the shell, i.e. when $R\rightarrow 0$. Since we have an explicit Hamiltonian of the system, we can apply the functional Schrodinger formalism and study quantum effects near the classical singularity. In the framework of the functional Schrodinger formalism, we will simply write down the Schrodinger equation for the wave-functional $\Psi[R(v)]$, and try to solve it.

We first derive the behavior of $R_\tau$ near $R=0$. From Eq.~(\ref{M}), we have
\begin{equation}
R_{\tau} = \sqrt{{\left(\frac{M}{\mu}+\frac{\mu G}{2R}\right)}^2 -1} .
\end{equation}
From here we see that  $R_{\tau}\approx\frac{\mu G}{2R}$ as $R$ is approaching zero. Substituting this result in Eq.(7), we find
\begin{equation} \label{Rv}
R_v\approx-\frac{1}{2}{\left(\frac{\mu G}{R}\right)}^2
\end{equation}
Thus, the rate at which the dust shell collapses near $R=0$ diverges as $R_v \propto \frac{1}{R^2}$.

In this limit the Hamiltonian in Eq.~(\ref{H}) can be approximated as
\begin{equation} \label{H0}
H = \mu(-R_v)\left[\frac{1}{\sqrt{2 \mid R_v \mid}} - \frac{\mu G}{2R}\frac{1}{R_v}\right]
\end{equation}
which gives
\begin{equation}
R_v=2{\left(\frac{H}{\mu}-\frac{G\mu}{2R}\right)}^2
\end{equation}
For $R\rightarrow0$, we can ignore the constant term $H/\mu$, and we will again get  Eq.~(\ref{Rv}).

In the limit $R\rightarrow0$, the canonical momentum reduces to
\begin{equation}
\Pi=\mu\left[\frac{1}{\sqrt{2\mid R_v \mid}}+\frac{\mu  G}{2R}\right]
\end{equation}
Expressing $R_v$ in terms of $\Pi$ in Hamiltonian (\ref{H0}) we get
\begin{equation} \label{H0P}
H=\frac{-R}{G}{\left[1-\frac{2\Pi R}{{\mu}^2 G}\right]}^{-1} +\frac{{\mu}^2 G}{2R} .
\end{equation}
The Hamiltonian in Eq.~(\ref{H0P}) governs the evolution of the collapsing dust shell in vicinity of $R=0$.
As in the standard quantization procedure, we promote the momentum $\Pi$ into an operator
\begin{equation}
\Pi = -i \hbar \frac{\partial }{\partial R} .
\end{equation}
We can now write the functional Schrodinger equation for the wave-functional $\psi [R(v)]$
\begin{equation} \label{se}
H \psi = i \hbar \frac{\partial \psi }{\partial v}
\end{equation}
and try to solve it. Unfortunately, the structure of the Hamiltonian (\ref{H0P}) is such that the usual treatment is practically impossible.
The main problem is that the differential operator in Hamiltonian (\ref{H0P}) is non-local. This finding represents a strong support for suggestions that quantum gravity
might be ultimately a non-local theory.

While finding solutions to non-local equations is very difficult, we will show that it is possible to define a procedure (similar to the one outlined in \cite{Vachaspati:2007ur}) which will lead to the solution of Eq.~(\ref{se}).
We first isolate the non-local operator $\hat{A}$ from the Hamiltonian (\ref{H0P})
\begin{equation}
\hat{A}={\left[1-\frac{2\Pi R}{{\mu}^2 G}\right]}^{-1}
\end{equation}
Its inverse is
\begin{equation}
{\hat{A}}^{-1} = 1- \frac{2\Pi R}{{\mu}^2 G}
\end{equation}
We can take care of the operator ordering as
\begin{equation}
\hat{A}={\left[1-\frac{1}{{\mu}^2 G}(\hat{\Pi} R+R\hat{\Pi})\right]}^{-1} ,
\end{equation}
so that
\begin{equation}
{\hat{A}}^{-1}=1-\frac{1}{{\mu}^2 G}(\hat{\Pi} R+R\hat{\Pi}) .
\end{equation}
In terms of derivatives, ${\hat{A}}^{-1}$ is
\begin{equation}
{\hat{A}}^{-1}=(1+\frac{i}{{\mu}^2 G})+\frac{2 i R}{{\mu}^2 G}\frac{\partial}{\partial R}
\end{equation}
Let's define the action of an operator $\hat{A}$ as $\varphi={\hat{A}}\psi$, which means $\psi={\hat{A}}^{-1}\varphi$, where $\varphi$ is just some function which gives the wavefunction $\psi$ upon action of the operator $\hat{A}$.  Explicit action of ${\hat{A}}^{-1}$ on $\varphi$ converts the equation ${\hat{A}}^{-1}\varphi = \psi$ into a linear differential equation
\begin{equation}
\frac{d\varphi}{dR}+\frac{1}{2R}(1-i {\mu}^2 G)\varphi+\frac{i  {\mu}^2 G}{2R}\psi =0
\end{equation}
This equation can be solved to give
\begin{equation}
\varphi = - \frac{i{\mu}^2 G}{2} \frac{\int{R^{-\frac{(1+i  {\mu}^2 G)}{2}}}\psi dR}{R^{\frac{(1- i  {\mu}^{2} G)}{2}}}
\end{equation}
Since $\varphi= \hat{A}\psi$ we obtain the action of $\hat{A}$ as
\begin{equation}
\hat{A} = - \frac{i{\mu}^2 G}{2} \frac{\int{R^{-\frac{(1+i  {\mu}^2 G)}{2}}}(.)dR}{R^{\frac{(1- i  {\mu}^{2} G)}{2}}}
\end{equation}
where $(.)$ is the placeholder for the function on which $\hat{A}$ is acting.

Let's concentrate on the stationary solutions to Eq.~(\ref{se}) in the form of
\begin{equation}
\psi (R,v) = \psi (R) e^{iEv/{\hbar}}
\end{equation}
where $v$ is the time evolution parameter, and $E$ is the energy eignevalue.
The time independent Schrodinger equation becomes $H \psi  = E \psi$. The Hamiltonian in Eq.~(\ref{H0P}) in terms of the operator $\hat{A}$ becomes
\begin{equation}
H  = \frac{R \hat{A}}{G} + \frac{{\mu}^{2} G}{2R}
\end{equation}
Accounting for the ordering of operators,  this Hamiltonian becomes
\begin{equation}
H  = -\frac{1}{2G} \left(R \hat{A} + \hat{A}R\right)+ \frac{{\mu}^{2} G}{2R} .
\end{equation}
The Schrodinger equation (\ref{se}) becomes
\begin{equation}
\frac{-1}{2G}\left (R \hat{A} + \hat{A}R\right)\psi+ \frac{{\mu}^{2} G}{2R}\psi = E\psi
\end{equation}
 When $\hat{A}$ operates on $R$ we get
\begin{equation}
\hat{A} (R) = -{\frac{\alpha}{2}  R^{-\frac{1}{2}(1- \alpha)}\int{R^{-\frac{1}{2}(1+ \alpha)} R dR}}
\end{equation}
which yields
\begin{equation}
\hat{A}(R) = \frac{-\alpha R + \beta}{3- \alpha}
\end{equation}
where $\alpha = i {\mu}^2 G$ and $\beta$ is an integration constant. So our equation becomes
\begin{equation}
\frac{-1}{2G}\left (R \hat{A} \psi + \frac{\alpha R - \beta}{ \alpha- 3} \psi \right)+ \frac{{\mu}^{2} G}{2R}\psi = E\psi
\end{equation}
Now we can move all the terms to one side and separate the term with the integral
\begin{equation}
\int{R^{-\frac{1}{2}(1+ \alpha)} \psi dR} = \frac{4G R^{-\frac{1+ \alpha}{2}}}{\alpha} \left[ \frac{1}{2G}\left(\frac{\alpha R - \beta}{\alpha - 3}\right) -\frac{{\mu}^2 G }{2R} + E\right] \psi
\end{equation}
We can now differentiate this equation with respect to $R$ to remove integration. Differentiation yields
\begin {widetext}

\begin{eqnarray}
&&\left[\frac{2R^{\frac{1}{2}(1- \alpha)}}{\alpha -3}  - 2 {\mu}^2 G^2 R^{-\frac{1}{2}(3+ \alpha)}+\left(\frac{4GE}{\alpha} - \frac{2 \beta}{\alpha( \alpha - 3)}\right) R^{-\frac{1}{2}(1+ \alpha)}\right] \psi'  =  \\
&& \left[ \left(\frac{\alpha-1}{\alpha - 3}  +1\right) R^{-\frac{1}{2}(1+ \alpha)} - {\mu}^2 G^2 (\alpha+3) R^{-\frac{1}{2}(5+ \alpha)} + \left( \frac{2 G E (\alpha + 1)}{\alpha} - \frac{ \beta (\alpha +1 )}{\alpha (\alpha - 3)}\right)R^{-\frac{1}{2}( 3 + \alpha)} \right] \psi \nonumber
\end{eqnarray}

\end{widetext}
This can be written as
\begin{equation}
\frac{d \psi}{\psi} = \int{\frac{a_1 + a_2 R +a_3 R^2}{a_4 R + a_5 R^2 + a_6 R^3}dR}
\end{equation}
where
$a_1 =- {\mu}^{2} G^2 (\alpha+3)$ , $a_2  = \left(\frac{2GE (\alpha+1)}{\alpha} - \frac{\beta (\alpha+1) }{\alpha (\alpha - 3)}\right)$, $a_3  = 1+ \frac{\alpha - 1}{\alpha + 3}$, $a_4 = -2{\mu}^2 G^2$, $a_5 =\left(\frac{4GE}{\alpha} - \frac{2 \beta}{\alpha (\alpha - 3)}\right) $ and $a_6 = \frac{2}{\alpha - 3}$
This integral can be solved for general values of constants. However, since we are working in the limit of  $R \approx 0$, we keep only the leading order terms
\begin{equation}
\ln \psi  =  \int{\frac{a_1}{a_4 R } dR} + {\rm constant}
\end{equation}
Solving this equation and substituting the values of the constants, we find the solution for the wavefunction
\begin{equation}
\psi =  \lambda R^{\frac{3+i {\mu}^2 G}{2}} .
\end{equation}
where $\lambda $ is a constant. The corresponding probability density $P = {\psi}^{*}\psi$ is
\begin{equation} \label{pd}
{\mid \psi \mid}^2 = {\lambda}^2 R^3 .
\end{equation}
This result is very important. It demonstrates that the probability density associated with the wavefunction $\psi$ which describes the collapse of the shell of matter is non-singular near the classical singularity. In fact, the probability density in Eq.~(\ref{pd}) vanishes exactly at $R=0$. It is remarkable that a simple quantum treatment of the gravitational collapse indicates that classical singularity at the center can be removed.

\section{Collapse of an infinitely thin spherical domain wall: conserved quantity}
\label{dw}
It is a logical possibility that the non-local behavior in the near singularity region that we found in the previous section is an artifact of the example that we were studying, i.e. the dust shell of matter. In this section we will repeat the procedure for the shell of matter whose energy per unit area, $\sigma$, is constant, which is the situation represented by a spherically symmetric domain wall. We will find that the near singularity behavior is qualitatively the same even in this case, i.e. the Hamiltonian becomes non-local in $R \rightarrow 0$ limit.

In the case of the domain wall, mass $M$ is also a conserved quantity. However, the relation relating mass with $R$ and $R_\tau$ is now given as
\begin{equation} \label{conserved}
M = \frac{1}{2}\left({ \sqrt{{1+{R_{\tau}}^2}}+ \sqrt{{B+{R_{\tau}}^2}}}\right) 4 \pi \sigma R^2
\end{equation}
where $B \equiv 1-2GM/R$.
This expression is implicit as it contains $M$ in $B$. The explicit relation of $M$ in terms of $R_\tau$ and $R$ can be written as
\begin{equation}
M = 4 \pi \sigma R^2 \left[{\sqrt{1- {R_\tau}^2}}- 2 \pi G \sigma R\right]
\end{equation}
Using the relation between $T$ and $\tau$ (Eq.~(4)), we get
\begin{equation}
M = 4 \pi \sigma R^2 \left[\frac{1}{\sqrt{1- {R_T}^2}}- 2 \pi G \sigma R\right]
\end{equation}
 The effective action which can reproduce above relation, i.e. gives the correct mass conservation law, can be written as
\begin{equation}
S_{eff}= -4 \pi \sigma \int R^{2} \left[\sqrt{1-{R_T}^2}- 2\pi G \sigma R \right]
\end{equation}
We want to convert the $T$ coordinate into the infalling $v$ coordinate as
\begin{equation}
S_{eff}= -4 \pi \sigma \int R^{2} \left[\sqrt{1-{\left({\frac{\partial{R}}{\partial{v}}\frac{\partial{v} }{\partial{T}}}\right)}^2}- 2\pi G \sigma R\right]
\end{equation}
After substituting the expression for $\frac{dv}{dT}$, we arrive at
\begin{equation}
S_{eff} = -4 \pi \sigma \int dv R^{2} \left(\sqrt{B-2R_{v}}-2 \pi \sigma R \sqrt{{R_v}^{2}-2 R_{v}+B}\right) .
\end{equation}
The corresponding Lagrangian can be written as
\begin{equation}
L_{eff}=  -4 \pi \sigma R^{2} \left[\sqrt{B-2R_{v}}-2 \pi \sigma R \sqrt{{R_v}^{2}-2 R_{v}+B}\right]
\end{equation}
Canonical momentum is defined as $\Pi = \frac{\partial L}{\partial R_{v}}$, so we obtain
\begin{equation}
\Pi = -4 \pi \sigma R^{2} \left[ \frac{-1}{\sqrt{B-2R_v}}-\frac{2 \pi \sigma GR(R_v -1 )}{\sqrt{{R_v}^{2}-2 R_{v}+B}}\right]
\end{equation}
Since the Hamiltonian is $ H =(\pi R_v - L )$,  substituting the $R_v$ in terms of $\Pi$ gives
\begin{equation}\label{HDW}
H= 4 \pi \sigma R^{2} (B-R_{v})\left[\frac{1}{\sqrt{B-2R_v}}- \frac{2 \pi \sigma G R}{\sqrt{{R_v}^{2}-2 R_{v}+B}}\right]
\end{equation}

\section{Quantum collapse of the domain wall in the limit of $R\rightarrow 0$}
\label{dwq}

Since we have an explicit Hamiltonian of the system, we can apply the functional Schrodinger formalism again and study quantum effects near the classical singularity.
Again from the conserved quantity $M$ we can derive
\begin{equation}
\mid R_{\tau} \mid = \sqrt{{\left( \frac{M}{4 \pi \sigma R^{2}}+ 2 \pi \sigma G R\right)}^{2} - 1}
\end{equation}
From here we see that  $R_v \approx - \frac{2 M^2}{{(4 \pi \sigma R^2)}^2}$  as $R$ is approaching zero.
Thus, the rate at which the dust shell collapses near $R=0$ diverges as $R_v \propto \frac{1}{R^4}$, in contrast with the dust shell where the divergence was quadratic.

In the same limit the Hamiltonian in Eq.~(\ref{HDW}) can be approximated as
\begin{equation}
H =  4 \pi \sigma R^2 (-R_v)\left[ \frac{1}{\sqrt{2\mid R_v \mid}} + \frac{2 \pi \sigma G R}{\mid R_v \mid} \right]
\end{equation}
 Solving this equation for $R_v$ yields  $\mid R_v \mid \approx \frac{2 h^2}{R^4}$ where $h= \frac{H}{4 \pi \sigma}$ which is the same as the above derived behavior.

The exact form of canonical momentum can be written as
\begin{equation}
\Pi = -4 \pi \sigma R^{2} \left[ \frac{-1}{\sqrt{B-2R_v}}-\frac{2 \pi \sigma GR(R_v -1 )}{\sqrt{{R_v}^{2}-2 R_{v}+B}} \right]
\end{equation}
which in $R\rightarrow 0$ limit can be approximated as
\begin{equation}
\Pi = 4 \pi \sigma R^{2} \left[ \frac{1}{\sqrt{2\mid R_v \mid}}+ 2 \pi \sigma GR \right]
\end{equation}
From this we can get $R_v$ in terms of $\pi$ as
\begin{equation} \label{rv}
R_v = - \frac{1}{2} {\left[\frac{\pi}{4 \pi \sigma R^{2}}-2\pi \sigma GR\right]}^{-2}
\end{equation}
The Hamiltonian given by Eq.(\ref{HDW}) can now be approximated as
\begin{equation}
H = 4\pi \sigma R^{2} (-R_v) \left[\frac{1}{\sqrt{B-2 R_v}}\right]
\end{equation}
Submitting the value of $R_v$ from Eq.~(\ref{rv}) gives
\begin{equation}\label{HDW0P}
H = - \frac{R}{\left(1-\frac{\pi}{8{\pi}^3 {\sigma}^2 G R^{3}}\right)}
\end{equation}
The Hamiltonian in Eq.~(\ref{HDW0P}) governs the evolution of the collapsing spherical domain wall in vicinity of $R=0$.
As before, we promote the momentum $\Pi$ into an operator
\begin{equation}
\Pi = -i \hbar \frac{\partial }{\partial R} .
\end{equation}
We can now write the functional Schrodinger equation
\begin{equation} \label{sedw}
H \psi = i \hbar \frac{\partial \psi }{\partial v}
\end{equation}
and try to solve it. However, as in our previous case of the dust shell, we see that the differential operator in Hamiltonian (\ref{HDW0P}) is non-local.
This fact reinforces an indication that quantum gravity should be ultimately a non-local theory.

We will now follow the procedure we outlined in the section (\ref{dsq}).
We isolate the non-local operator
\begin{equation}
\hat{A}={\left[1-\frac{\Pi}{8{\pi}^3 {\sigma}^2 G R^{3}}\right]}^{-1}
\end{equation}
For convenience, we set the constant $\alpha = \frac{1}{16 {\pi}^2 {\sigma}^2 G}$ which gives
\begin{equation}
\hat{A} =\frac{1}{ \left(1 - 2 \alpha \frac{\Pi}{R^3}\right) }
\end{equation}
Now, we can define
\begin{equation}
{\hat{A}}^{-1} = 1 - 2\alpha \frac{\Pi}{R^3}
\end{equation}
We take care of the ordering problem as
\begin{equation}
{\hat{A}}^{-1} = 1- \alpha \left[\Pi \frac{1}{R^3} + \frac{1}{R^3} \Pi\right]
\end{equation}
which also makes this operator unitary.
In terms of derivatives, we have
\begin{equation}
{\hat{A}}^{-1} = 1+ i \alpha \left(\frac{2}{R^3}\frac{\partial}{\partial R} - \frac{3}{R^4}\right)
\end{equation}
Let us again define $\psi = {\hat{A}}^{-1} \varphi$, which leads to differential equation
\begin{equation}
\frac{\partial \varphi}{\partial R} + \left(\frac{R^3}{2i \alpha}- \frac{3}{2R}\right) \varphi - \frac{R^3}{2i \alpha} \psi =0
\end{equation}
This linear differential equation can be solved to give
\begin{equation}
 \varphi = \frac{R^{3/2} e^{-\frac{R^4}{8i\alpha}} }{2i \alpha} \int R^{3/2} e^{\frac{R^4}{8i \alpha}} \psi dR
\end{equation}
Since $\varphi = \hat{A}\psi$, this gives the operator $\hat{A}$ as
\begin{equation}
 \hat{A} = \frac{R^{3/2} e^{-\frac{R^4}{8i\alpha}} }{2i \alpha} \int R^{3/2} e^{\frac{R^4}{8i \alpha}} (.) dR
\end{equation}
where $(.)$ is the placeholder for the function on which $\hat{A}$ is acting.
In principle,  one can follow the procedure we outlined  in section \ref{dsq} and solve the non-local Schrodinger equation like. However, in this case calculations are  much more cumbersome because of presence of additional exponential in the operator $\hat{A}$ and will not be shown here.

\section{Conclusions}
\label{conclusions}
In this paper we studied quantum aspects of the gravitational collapse near the classical singularity as seen by an infalling observer. Since gravity is the by far the weakest force in nature, we expect that quantum mechanics will significantly modify classical behavior of gravity only in the strong field regimes, e.g. near classical singularities. In the absence of a fully fledged theory of quantum gravity, we worked in the context of the functional Schrodinger formalism applied to a simple gravitational system - collapsing shell of matter.
We used the Eddington-Finkelstein space-time foliation which is convenient for studying the question of the black hole formation till the very end where the collapsing shell crosses its own Schwarzschild radius and starts approaching the classical singularity at the center.
We derived the conserved quantity with the clear interpretation as the Hamiltonian of the system and quantized the theory. In the $R \rightarrow 0$  limit, we found that the equation which describes the quantum evolution of the collapsing shell is strongly non-local. Non-local terms which are usually suppressed in large distance limit, become dominant in the near singularity limit.  This conforms some earlier speculations and related studies. As an important step forward, we managed to solve this non-local equation explicitly and found the form of the wavefuction. Remarkably,  the wavefunction and its corresponding probability density are non-singular at  $R \rightarrow 0$. This is an indication that quantization can remove classical singularities from gravity, just as it was the case with the singular electromagnetic Coulomb potential.

\vskip.2cm {\bf Acknowledgment} \vskip.2cm
 DS acknowledges the financial support from NSF, award number PHY-1066278.

redpajama_set_name: RedPajamaArXiv


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text:
Reading: Hypothalamic Hamartoma and Sexual Precocity
Intracranial Hypertension
Hypothalamic Hamartoma and Sexual Precocity
Four boys with hypothalamic hamartomas associated with sexual precocity are reported from the Departments of Pediatrics and Neurosurgery, University of Pittsburgh, and the Department of Pediatrics, Johns Hopkins University School of Medicine, Baltimore, MD.
Keywords: Hypothalamic Hamartomas, Hamartomas, Coronal
How to Cite: Millichap, J.G., 1990. Hypothalamic Hamartoma and Sexual Precocity. Pediatric Neurology Briefs, 4(2), pp.11–12. DOI: http://doi.org/10.15844/pedneurbriefs-4-2-4
Four boys with hypothalamic hamartomas associated with sexual precocity are reported from the Departments of Pediatrics and Neurosurgery, University of Pittsburgh, and the Department of Pediatrics, Johns Hopkins University School of Medicine, Baltimore, MD. Two patients were treated surgically by resection using current microsurgical techniques and two received medical management. Precocious puberty caused by hamartomas occurs early in life with enlarged penis and muscular build noted in early infancy. Growth is accelerated and bone age is advanced. Deepening of the voice and the appearance of acne are common. Other clinical findings include mental retardation, behavioral disturbances, and seizures of gelastic, absence, and generalized tonic clonic patterns. In the two patients treated surgically, subsequent growth and development were normal and in two who were diagnosed late in childhood and treated medically, the adult height was not particularly compromised. The authors recommend surgical resection if the hamartoma is pedunculated or in cases where the patient is young and would require years of parenteral medical treatment. The nontreatment option exists because there is no evidence that the tumors will grow or subsequently cause other problems. [1]
COMMENT. The use of MRI with sagittal, coronal, and axial views enable better visualization of hamartomas and earlier diagnosis. Treatment to allow growth and pubertal development to occur at an age appropriate time may avoid considerable psychosocial stress and prevent premature skeletal maturation and a shorter adult stature. Medical treatment with long-acting gonadotrophin releasing hormone must be administered through childhood and surgery is sometimes preferred.
Starceski, PJ, Lee, PA, Albright, AL and Migeon, CJ (1990). Hypothalamic hamartomas and sexual precocity. Evaluation of treatment options. Am J Dis Child Feb 1990144(2): 225–228, DOI: https://doi.org/10.1001/archpedi.1990.02150260105040 [PubMed]
Millichap, J.G., 1990. Hypothalamic Hamartoma and Sexual Precocity. Pediatric Neurology Briefs, 4(2), pp.11–12. DOI: http://doi.org/10.15844/pedneurbriefs-4-2-4
Millichap JG. Hypothalamic Hamartoma and Sexual Precocity. Pediatric Neurology Briefs. 1990;4(2):11–2. DOI: http://doi.org/10.15844/pedneurbriefs-4-2-4
Millichap, J. G. (1990). Hypothalamic Hamartoma and Sexual Precocity. Pediatric Neurology Briefs, 4(2), 11–12. DOI: http://doi.org/10.15844/pedneurbriefs-4-2-4
1. Millichap JG. Hypothalamic Hamartoma and Sexual Precocity. Pediatric Neurology Briefs. 1990;4(2):11-12. DOI: http://doi.org/10.15844/pedneurbriefs-4-2-4
Millichap JG, 'Hypothalamic Hamartoma and Sexual Precocity' (1990) 4 Pediatric Neurology Briefs 11 DOI: http://doi.org/10.15844/pedneurbriefs-4-2-4
Millichap, J Gordon. 1990. "Hypothalamic Hamartoma and Sexual Precocity". Pediatric Neurology Briefs 4 (2): 11–12. DOI: http://doi.org/10.15844/pedneurbriefs-4-2-4
Millichap, J Gordon. "Hypothalamic Hamartoma and Sexual Precocity". Pediatric Neurology Briefs 4, no. 2 (1990): 11–12. DOI: http://doi.org/10.15844/pedneurbriefs-4-2-4
Millichap, J G. "Hypothalamic Hamartoma and Sexual Precocity". Pediatric Neurology Briefs, vol. 4, no. 2, 1990, pp. 11–12. DOI: http://doi.org/10.15844/pedneurbriefs-4-2-4

redpajama_set_name: RedPajamaCommonCrawl


Dominic Walmsley was apprenticed in 1989 after serving under a traditional goldsmith/silversmith in Putney and set up business in 1991. In almost 25 years he has built up a sizable client base offering contemporary designs using traditional craftsmanship and service. Dominic's business success has largely been a result of his ability to understand his customers' requirements and having control of the quality of his jewellery is very important to him. From his Clerkenwell Studio in London and through is Sevenoaks shop he designs and makes bespoke pieces of jewellery which are often influenced by historical styles, including Elizabethan and Rococo. Dominic also specializes in designing wedding and engagement rings for couples looking for something more personal than an 'off the shelf' ring for instance his innovative 'year ring' and 'heart beat ring', truly unique styles for a personal touch. Dominic and his small team offer a friendly professional service and make sure all of their customers enjoy their experience when dealing with them.


Parallax: noun: the difference in perception of an event by two observers caused by the difference in their orbit around the event.
The purpose of this page is to provide quick access to events between 1976 and 2012 that either accidentally or through premeditation have shifted or will shift Human consciousness from one context to another - in spite of the prevailing paradigm.
Though some will argue that this sequence could be extended back to the APOLLO 11 Mission, JFK's assassination, Sputnik, or the strange sightings of July, 1947 - the Face on Mars and the end of the Mayan Calendar, are modern milestones set in stone that bracket the undeniable events that will change the lives of everyone on the planet.
The goal of this site is to explore not only how these events may have come about, but what we might do together besides ignoring them. That may be the shift that needs to happen most of all.
Clicking on any icon will take you further into the SHIFT HAPPENS site; to pages where you will have the opportunity to add to the discussion and experience the shift yourself by binking on the SUPPORT THE SHIFT link to the SHIFT HAPPENS FREE STORE at the bottom of most pages.
SHIFT HAPPENS: update icons will be added below the COMMENTS? link as actual events confirm the relevance of the page on which they are found.
"Figuring things out for yourself is the only real freedom anyone really has."
1976. Scientists, reporters, and guests celebrating at JPL forget to exhale as the Viking orbiter photographs the Unexpected staring back at them from another world.
Maybe the Strategic Defense Initiative broke the Soviet piggy bank or maybe it was just the thirst of Russian youth for the Beatles, Levi's, and all things Western that finally allowed Berliners to party on the wall that their friends and loved ones had been shot for climbing. Reagan's legacy is a new Russian hyper-sonic, MIRV Cruise Missile designed to defeat Star Wars, while McCartney has played Red Square and Roger Waters performed The Wall where the Iron Curtain once stood.
The threat of Man's surrender to his own technology finally became a reality in 1999. For the first few hours of the year 2000, no one was completely sure of the future.
Though not a stated goal until after the re-election of George W. Bush in 2004, descendants of the Third Reich and those who helped them; in control of the White House and Congress, are intent on creating a one-party system to keep dissent and the objections of the Minority in the minority... permanently.
George W. Bush's first foreign policy act as President is to back out of the Anti-Ballistic Missile Treaty after boasting of "skipping a generation of weaponry".
Someone demolished the World Trade Center. Something hit the Pentagon and somehow, a commercial airliner was forced into the fields of Pennsylvania; all during a massive exercise conducted to prepare for those very events.
Who will take the Mark? What will be done with those who refuse?
Regime Change and Pre-emptive War come to the two countries bordering Iran.
The United States is killing thousands of Iraqi civilians.
REPEATING; THE UNITED STATES IS KILLING THOUSANDS OF IRAQI CIVILIANS.
Another decision that may doom us all.
Preventative Detention and loyalty Oaths are the response to "NOT IN OUR NAME!"
Who is the 20th hijacker?
Since September 12th, 2001, it has been Zacarias Moussaoui; the only person to be charged in connection with 911. On June 12th it was a detainee at Camp X-Ray. Overnight, the most hated man in America, who had plead guilty to undisclosed charges finally brought against him - a plea that guaranteed that there would be no trial or any further questioning - was no longer the 20th hijacker.
Neuropoly - not just a game, but the war for Men's minds spoken of by the Bible.
Who speaks for the Planet? Eight Leaders or the millions they represent? We'll see a year from now.
Almost thirty years since the Viking Missions, NASA is faced once again with just how wrong prevailing scientific wisdom can be as Comet Tempel 1 turns out to be a fragment of a shattered world instead of a "dirty snowball".
"Down & Out In Beverly Hills" warned us about China.
CNN uses the term "Peak Oil" for the first time on May 29th 2005 and seven days later "Oil Storm" premieres on the FX Channel.
How many warnings are necessary?
What will it take to pry the Truth from those tasked with Secrecy, and will we understand the difference when we see IT?
No one can doubt that proof of the Extra-Terrestrial presence will change the World as we know it.
Coronal Mass Ejection, Asteroid strike, global 10.4 earthquake or 500 mph Tsunami.
If life has been wiped from the face of the Earth before, what must we do if there's a chance it might happen again?
CANCEL OUR SUBSCRIPTION TO THE RESURRECTION.
Whatever else can be said about the Interesting Times between 666 and 999, we're definitely in "OR ELSE".
Did the Authors of the Popol Vuh just get bored with keeping track of time? Will 2012 be an even larger non-event than Y2K? Is December 21st 2012 the end of everything or merely when something starts all over again??
Perhaps passage through the Photon Belt or the alignment of our ecliptic with the Galactic Plane will bring an end to the Unexpected once and for all.