Learning High-Dimensional Nonparametric Differential Equations via Multivariate Occupation Kernel Functions

Learning a nonparametric system of ordinary differential equations (ODEs) from $n$ trajectory snapshots in a $d$-dimensional state space requires learning $d$ functions of $d$ variables. Explicit formulations scale quadratically in $d$ unless additional knowledge about system properties, such as sparsity and symmetries, is available. In this work, we propose a linear approach to learning using the implicit formulation provided by vector-valued Reproducing Kernel Hilbert Spaces. By rewriting the ODEs in a weaker integral form, which we subsequently minimize, we derive our learning algorithm. The minimization problem's solution for the vector field relies on multivariate occupation kernel functions associated with the solution trajectories. We validate our approach through experiments on highly nonlinear simulated and real data, where $d$ may exceed 100. We further demonstrate the versatility of the proposed method by learning a nonparametric first order quasilinear partial differential equation.Comment: 22 pages, 3 figures, submitted to Neurips 202

BHPR research: qualitative1. Complex reasoning determines patients' perception of outcome following foot surgery in rheumatoid arhtritis

Background: Foot surgery is common in patients with RA but research into surgical outcomes is limited and conceptually flawed as current outcome measures lack face validity: to date no one has asked patients what is important to them. This study aimed to determine which factors are important to patients when evaluating the success of foot surgery in RA Methods: Semi structured interviews of RA patients who had undergone foot surgery were conducted and transcribed verbatim. Thematic analysis of interviews was conducted to explore issues that were important to patients. Results: 11 RA patients (9 ♂, mean age 59, dis dur = 22yrs, mean of 3 yrs post op) with mixed experiences of foot surgery were interviewed. Patients interpreted outcome in respect to a multitude of factors, frequently positive change in one aspect contrasted with negative opinions about another. Overall, four major themes emerged. Function: Functional ability & participation in valued activities were very important to patients. Walking ability was a key concern but patients interpreted levels of activity in light of other aspects of their disease, reflecting on change in functional ability more than overall level. Positive feelings of improved mobility were often moderated by negative self perception ("I mean, I still walk like a waddling duck”). Appearance: Appearance was important to almost all patients but perhaps the most complex theme of all. Physical appearance, foot shape, and footwear were closely interlinked, yet patients saw these as distinct separate concepts. Patients need to legitimize these feelings was clear and they frequently entered into a defensive repertoire ("it's not cosmetic surgery; it's something that's more important than that, you know?”). Clinician opinion: Surgeons' post operative evaluation of the procedure was very influential. The impact of this appraisal continued to affect patients' lasting impression irrespective of how the outcome compared to their initial goals ("when he'd done it ... he said that hasn't worked as good as he'd wanted to ... but the pain has gone”). Pain: Whilst pain was important to almost all patients, it appeared to be less important than the other themes. Pain was predominately raised when it influenced other themes, such as function; many still felt the need to legitimize their foot pain in order for health professionals to take it seriously ("in the end I went to my GP because it had happened a few times and I went to an orthopaedic surgeon who was quite dismissive of it, it was like what are you complaining about”). Conclusions: Patients interpret the outcome of foot surgery using a multitude of interrelated factors, particularly functional ability, appearance and surgeons' appraisal of the procedure. While pain was often noted, this appeared less important than other factors in the overall outcome of the surgery. Future research into foot surgery should incorporate the complexity of how patients determine their outcome Disclosure statement: All authors have declared no conflicts of interes

A Novel Cross-Disciplinary Multi-Institute Approach to Translational Cancer Research: Lessons Learned from Pennsylvania Cancer Alliance Bioinformatics Consortium (PCABC)

Background The Pennsylvania Cancer Alliance Bioinformatics Consortium (PCABC, http://www.pcabc.upmc.edu ) is one of the first major project-based initiatives stemming from the Pennsylvania Cancer Alliance that was funded for four years by the Department of Health of the Commonwealth of Pennsylvania. The objective of this was to initiate a prototype biorepository and bioinformatics infrastructure with a robust data warehouse by developing a statewide data model (1) for bioinformatics and a repository of serum and tissue samples; (2) a data model for biomarker data storage; and (3) a public access website for disseminating research results and bioinformatics tools. The members of the Consortium cooperate closely, exploring the opportunity for sharing clinical, genomic and other bioinformatics data on patient samples in oncology, for the purpose of developing collaborative research programs across cancer research institutions in Pennsylvania. The Consortium's intention was to establish a virtual repository of many clinical specimens residing in various centers across the state, in order to make them available for research. One of our primary goals was to facilitate the identification of cancer-specific biomarkers and encourage collaborative research efforts among the participating centers. Methods The PCABC has developed unique partnerships so that every region of the state can effectively contribute and participate. It includes over 80 individuals from 14 organizations, and plans to expand to partners outside the State. This has created a network of researchers, clinicians, bioinformaticians, cancer registrars, program directors, and executives from academic and community health systems, as well as external corporate partners - all working together to accomplish a common mission. The various sub-committees have developed a common IRB protocol template, common data elements for standardizing data collections for three organ sites, intellectual property/tech transfer agreements, and material transfer agreements that have been approved by each of the member institutions. This was the foundational work that has led to the development of a centralized data warehouse that has met each of the institutions’ IRB/HIPAA standards. Results Currently, this “virtual biorepository” has over 58,000 annotated samples from 11,467 cancer patients available for research purposes. The clinical annotation of tissue samples is either done manually over the internet or semi-automated batch modes through mapping of local data elements with PCABC common data elements. The database currently holds information on 7188 cases (associated with 9278 specimens and 46,666 annotated blocks and blood samples) of prostate cancer, 2736 cases (associated with 3796 specimens and 9336 annotated blocks and blood samples) of breast cancer and 1543 cases (including 1334 specimens and 2671 annotated blocks and blood samples) of melanoma. These numbers continue to grow, and plans to integrate new tumor sites are in progress. Furthermore, the group has also developed a central web-based tool that allows investigators to share their translational (genomics/proteomics) experiment data on research evaluating potential biomarkers via a central location on the Consortium's web site. Conclusions The technological achievements and the statewide informatics infrastructure that have been established by the Consortium will enable robust and efficient studies of biomarkers and their relevance to the clinical course of cancer. </jats:sec

Global economic burden of unmet surgical need for appendicitis

Background There is a substantial gap in provision of adequate surgical care in many low- and middle-income countries. This study aimed to identify the economic burden of unmet surgical need for the common condition of appendicitis. Methods Data on the incidence of appendicitis from 170 countries and two different approaches were used to estimate numbers of patients who do not receive surgery: as a fixed proportion of the total unmet surgical need per country (approach 1); and based on country income status (approach 2). Indirect costs with current levels of access and local quality, and those if quality were at the standards of high-income countries, were estimated. A human capital approach was applied, focusing on the economic burden resulting from premature death and absenteeism. Results Excess mortality was 4185 per 100 000 cases of appendicitis using approach 1 and 3448 per 100 000 using approach 2. The economic burden of continuing current levels of access and local quality was US $92 492 million using approach 1 and$73 141 million using approach 2. The economic burden of not providing surgical care to the standards of high-income countries was $95 004 million using approach 1 and$75 666 million using approach 2. The largest share of these costs resulted from premature death (97.7 per cent) and lack of access (97.0 per cent) in contrast to lack of quality. Conclusion For a comparatively non-complex emergency condition such as appendicitis, increasing access to care should be prioritized. Although improving quality of care should not be neglected, increasing provision of care at current standards could reduce societal costs substantially

Global economic burden of unmet surgical need for appendicitis

Background There is a substantial gap in provision of adequate surgical care in many low- and middle-income countries. This study aimed to identify the economic burden of unmet surgical need for the common condition of appendicitis. Methods Data on the incidence of appendicitis from 170 countries and two different approaches were used to estimate numbers of patients who do not receive surgery: as a fixed proportion of the total unmet surgical need per country (approach 1); and based on country income status (approach 2). Indirect costs with current levels of access and local quality, and those if quality were at the standards of high-income countries, were estimated. A human capital approach was applied, focusing on the economic burden resulting from premature death and absenteeism. Results Excess mortality was 4185 per 100 000 cases of appendicitis using approach 1 and 3448 per 100 000 using approach 2. The economic burden of continuing current levels of access and local quality was US $92 492 million using approach 1 and$73 141 million using approach 2. The economic burden of not providing surgical care to the standards of high-income countries was $95 004 million using approach 1 and$75 666 million using approach 2. The largest share of these costs resulted from premature death (97.7 per cent) and lack of access (97.0 per cent) in contrast to lack of quality. Conclusion For a comparatively non-complex emergency condition such as appendicitis, increasing access to care should be prioritized. Although improving quality of care should not be neglected, increasing provision of care at current standards could reduce societal costs substantially