Towards a Framework for Nonlinear Predictive Control using Derivative-Free Optimization

The use of derivative-based solvers to compute solutions to optimal control problems with non-differentiable cost or dynamics often requires reformulations or relaxations that complicate the implementation or increase computational complexity. We present an initial framework for using the derivative-free Mesh Adaptive Direct Search (MADS) algorithm to solve Nonlinear Model Predictive Control problems with non-differentiable features without the need for reformulation. The MADS algorithm performs a structured search of the input space by simulating selected system trajectories and computing the subsequent cost value. We propose handling the path constraints and the Lagrange cost term by augmenting the system dynamics with additional states to compute the violation and cost value alongside the state trajectories, eliminating the need for reconstructing the state trajectories in a separate phase. We demonstrate the practicality of this framework by solving a robust rocket control problem, where the objective is to reach a target altitude as close as possible, given a system with uncertain parameters. This example uses a non-differentiable cost function and simulates two different system trajectories simultaneously, with each system having its own free final time.Comment: Accepted for presentation at the 7th IFAC Conference on Nonlinear Model Predictive Contro

Noroviruses subvert the core stress granule component G3BP1 to promote viral VPg-dependent translation.

Knowledge of the host factors required for norovirus replication has been hindered by the challenges associated with culturing human noroviruses. We have combined proteomic analysis of the viral translation and replication complexes with a CRISPR screen, to identify host factors required for norovirus infection. The core stress granule component G3BP1 was identified as a host factor essential for efficient human and murine norovirus infection, demonstrating a conserved function across the Norovirus genus. Furthermore, we show that G3BP1 functions in the novel paradigm of viral VPg-dependent translation initiation, contributing to the assembly of translation complexes on the VPg-linked viral positive sense RNA genome by facilitating ribosome recruitment. Our data uncovers a novel function for G3BP1 in the life cycle of positive sense RNA viruses and identifies the first host factor with pan-norovirus pro-viral activity

Common non-synonymous SNPs associated with breast cancer susceptibility: findings from the Breast Cancer Association Consortium.

Candidate variant association studies have been largely unsuccessful in identifying common breast cancer susceptibility variants, although most studies have been underpowered to detect associations of a realistic magnitude. We assessed 41 common non-synonymous single-nucleotide polymorphisms (nsSNPs) for which evidence of association with breast cancer risk had been previously reported. Case-control data were combined from 38 studies of white European women (46 450 cases and 42 600 controls) and analyzed using unconditional logistic regression. Strong evidence of association was observed for three nsSNPs: ATXN7-K264R at 3p21 [rs1053338, per allele OR = 1.07, 95% confidence interval (CI) = 1.04-1.10, P = 2.9 × 10(-6)], AKAP9-M463I at 7q21 (rs6964587, OR = 1.05, 95% CI = 1.03-1.07, P = 1.7 × 10(-6)) and NEK10-L513S at 3p24 (rs10510592, OR = 1.10, 95% CI = 1.07-1.12, P = 5.1 × 10(-17)). The first two associations reached genome-wide statistical significance in a combined analysis of available data, including independent data from nine genome-wide association studies (GWASs): for ATXN7-K264R, OR = 1.07 (95% CI = 1.05-1.10, P = 1.0 × 10(-8)); for AKAP9-M463I, OR = 1.05 (95% CI = 1.04-1.07, P = 2.0 × 10(-10)). Further analysis of other common variants in these two regions suggested that intronic SNPs nearby are more strongly associated with disease risk. We have thus identified a novel susceptibility locus at 3p21, and confirmed previous suggestive evidence that rs6964587 at 7q21 is associated with risk. The third locus, rs10510592, is located in an established breast cancer susceptibility region; the association was substantially attenuated after adjustment for the known GWAS hit. Thus, each of the associated nsSNPs is likely to be a marker for another, non-coding, variant causally related to breast cancer risk. Further fine-mapping and functional studies are required to identify the underlying risk-modifying variants and the genes through which they act.BCAC is funded by Cancer Research UK (C1287/A10118, C1287/A12014) and by the European Community’s Seventh Framework Programme under grant agreement n8 223175 (HEALTH-F2–2009-223175) (COGS). Meetings of the BCAC have been funded by the European Union COST programme (BM0606). Genotyping of the iCOGS array was funded by the European Union (HEALTH-F2-2009-223175), Cancer Research UK (C1287/A10710), the Canadian Institutes of Health Research for the ‘CIHR Team in Familial Risks of Breast Cancer’ program and the Ministry of Economic Development, Innovation and Export Trade of Quebec (PSR-SIIRI-701). Additional support for the iCOGS infrastructure was provided by the National Institutes of Health (CA128978) and Post-Cancer GWAS initiative (1U19 CA148537, 1U19 CA148065 and 1U19 CA148112—the GAME-ON initiative), the Department of Defence (W81XWH-10-1-0341), Komen Foundation for the Cure, the Breast Cancer Research Foundation, and the Ovarian Cancer Research Fund. The ABCFS and OFBCR work was supported by grant UM1 CA164920 from the National Cancer Institute (USA). The content of this manuscript does not necessarily reflect the views or policies of the National Cancer Institute or any of the collaborating centers in the Breast Cancer Family Registry (BCFR), nor does mention of trade names, commercial products or organizations imply endorsement t by the US Government or the BCFR. The ABCFS was also supported by the National Health and Medical Research Council of Australia, the New South Wales Cancer Council, the Victorian Health Promotion Foundation (Australia) and the Victorian Breast Cancer Research Consortium. J.L.H. is a National Health and Medical Research Council (NHMRC) Senior Principal Research Fellow and M.C.S. is a NHMRC Senior Research Fellow. The OFBCR work was also supported by the Canadian Institutes of Health Research ‘CIHR Team in Familial Risks of Breast Cancer’ program. The ABCS was funded by the Dutch Cancer Society Grant no. NKI2007-3839 and NKI2009-4363. The ACP study is funded by the Breast Cancer Research Trust, UK. The work of the BBCC was partly funded by ELAN-Programme of the University Hospital of Erlangen. The BBCS is funded by Cancer Research UK and Breakthrough Breast Cancer and acknowledges NHS funding to the NIHR Biomedical Research Centre, and the National Cancer Research Network (NCRN). E.S. is supported by NIHR Comprehensive Biomedical Research Centre, Guy’s & St. Thomas’ NHS Foundation Trust in partnership with King’s College London, UK. Core funding to the Wellcome Trust Centre for Human Genetics was provided by the Wellcome Trust (090532/Z/09/Z). I.T. is supported by the Oxford Biomedical Research Centre. The BSUCH study was supported by the Dietmar-Hopp Foundation, the Helmholtz Society and the German Cancer Research Center (DKFZ). The CECILE study was funded by the Fondation de France, the French National Institute of Cancer (INCa), The National League against Cancer, the National Agency for Environmental l and Occupational Health and Food Safety (ANSES), the National Agency for Research (ANR), and the Association for Research against Cancer (ARC). The CGPS was supported by the Chief Physician Johan Boserup and Lise Boserup Fund, the Danish Medical Research Council and Herlev Hospital.The CNIO-BCS was supported by the Genome Spain Foundation the Red Temática de Investigación Cooperativa en Cáncer and grants from the Asociación Española Contra el Cáncer and the Fondo de Investigación Sanitario PI11/00923 and PI081120). The Human Genotyping-CEGEN Unit, CNIO is supported by the Instituto de Salud Carlos III. D.A. was supported by a Fellowship from the Michael Manzella Foundation (MMF) and was a participant in the CNIO Summer Training Program. The CTS was initially supported by the California Breast Cancer Act of 1993 and the California Breast Cancer Research Fund (contract 97-10500) and is currently funded through the National Institutes of Health (R01 CA77398). Collection of cancer incidence e data was supported by the California Department of Public Health as part of the statewide cancer reporting program mandated by California Health and Safety Code Section 103885. HAC receives support from the Lon V Smith Foundation (LVS39420). The ESTHER study was supported by a grant from the Baden Württemberg Ministry of Science, Research and Arts. Additional cases were recruited in the context of the VERDI study, which was supported by a grant from the German Cancer Aid (Deutsche Krebshilfe). The GENICA was funded by the Federal Ministry of Education and Research (BMBF) Germany grants 01KW9975/5, 01KW9976/8, 01KW9977/0 and 01KW0114, the Robert Bosch Foundation, Stuttgart, Deutsches Krebsforschungszentrum (DKFZ), Heidelberg Institute for Prevention and Occupational Medicine of the German Social Accident Insurance, Institute of the Ruhr University Bochum (IPA), as well as the Department of Internal Medicine , Evangelische Kliniken Bonn gGmbH, Johanniter Krankenhaus Bonn, Germany. The HEBCS was supported by the Helsinki University Central Hospital Research Fund, Academy of Finland (132473), the Finnish Cancer Society, The Nordic Cancer Union and the Sigrid Juselius Foundation. The HERPACC was supported by a Grant-in-Aid for Scientific Research on Priority Areas from the Ministry of Education, Science, Sports, Culture and Technology of Japan, by a Grant-in-Aid for the Third Term Comprehensive 10-Year strategy for Cancer Control from Ministry Health, Labour and Welfare of Japan, by a research grant from Takeda Science Foundation , by Health and Labour Sciences Research Grants for Research on Applying Health Technology from Ministry Health, Labour and Welfare of Japan and by National Cancer Center Research and Development Fund. The HMBCS was supported by short-term fellowships from the German Academic Exchange Program (to N.B), and the Friends of Hannover Medical School (to N.B.). Financial support for KARBAC was provided through the regional agreement on medical training and clinical research (ALF) between Stockholm County Council and Karolinska Institutet, the Stockholm Cancer Foundation and the Swedish Cancer Society. The KBCP was financially supported by the special Government Funding (EVO) of Kuopio University Hospital grants, Cancer Fund of North Savo, the Finnish Cancer Organizations, the Academy of Finland and by the strategic funding of the University of Eastern Finland. kConFab is supported by grants from the National Breast Cancer Foundation , the NHMRC, the Queensland Cancer Fund, the Cancer Councils of New South Wales, Victoria, Tasmania and South Australia and the Cancer Foundation of Western Australia. The kConFab Clinical Follow Up Study was funded by the NHMRC (145684, 288704, 454508). Financial support for the AOCS was provided by the United States Army Medical Research and Materiel Command (DAMD17-01-1-0729), the Cancer Council of Tasmania and Cancer Foundation of Western Australia and the NHMRC (199600). G.C.T. and P.W. are supported by the NHMRC. LAABC is supported by grants (1RB-0287, 3PB-0102, 5PB-0018 and 10PB-0098) from the California Breast Cancer Research Program. Incident breast cancer cases were collected by the USC Cancer Surveillance Program (CSP) which is supported under subcontract by the California Department of Health. The CSP is also part of the National Cancer Institute’s Division of Cancer Prevention and Control Surveillance, Epidemiology, and End Results Program, under contract number N01CN25403. LMBC is supported by the ‘Stichting tegen Kanker’ (232-2008 and 196-2010). The MARIE study was supported by the Deutsche Krebshilfe e.V. (70-2892-BR I), the Federal Ministry of Education Research (BMBF) Germany (01KH0402), the Hamburg Cancer Society and the German Cancer Research Center (DKFZ). MBCSG is supported by grants from the Italian Association ciation for Cancer Research (AIRC) and by funds from the Italian citizens who allocated a 5/1000 share of their tax payment in support of the Fondazione IRCCS Istituto Nazionale Tumori, according to Italian laws (INT-Institutional strategic projects ‘5 × 1000’). The MCBCS was supported by the NIH grants (CA122340, CA128978) and a Specialized Program of Research Excellence (SPORE) in Breast Cancer (CA116201), the Breast Cancer Research Foundation and a generous gift from the David F. and Margaret T. Grohne Family Foundation and the Ting Tsung and Wei Fong Chao Foundation. MCCS cohort recruitment was funded by VicHealth and Cancer Council Victoria. The MCCS was further supported by Australian NHMRC grants 209057, 251553 and 504711 and by infrastructure provided by Cancer Council Victoria. The MEC was supported by NIH grants CA63464, CA54281, CA098758 and CA132839. The work of MTLGEBCS was supported by the Quebec Breast Cancer Foundation, the Canadian Institutes of Health Research (grant CRN-87521) and the Ministry of Economic Development, Innovation and Export Trade (grant PSR-SIIRI-701). MYBRCA is funded by research grants from the Malaysian Ministry of Science, Technology and Innovation (MOSTI), Malaysian Ministry of Higher Education (UM.C/HlR/MOHE/06) and Cancer Research Initiatives Foundation (CARIF). Additional controls were recruited by the Singapore Eye Research Institute, which was supported by a grant from the Biomedical Research Council (BMRC08/1/35/19,tel:08/1/35/19./550), Singapore and the National medical Research Council, Singapore (NMRC/CG/SERI/2010). The NBCS was supported by grants from the Norwegian Research council (155218/V40, 175240/S10 to A.L.B.D., FUGE-NFR 181600/ V11 to V.N.K. and a Swizz Bridge Award to A.L.B.D.). The NBHS was supported by NIH grant R01CA100374. Biological sample preparation was conducted the Survey and Biospecimen Shared Resource, which is supported by P30 CA68485. The OBCS was supported by research grants from the Finnish Cancer Foundation, the Sigrid Juselius Foundation, the Academy of Finland, the University of Oulu, and the Oulu University Hospital. The ORIGO study was supported by the Dutch Cancer Society (RUL 1997-1505) and the Biobanking and Biomolecular Resources Research Infrastructure (BBMRI-NLCP16). The PBCS was funded by Intramural Research Funds of the National Cancer Institute, Department of Health and Human Services, USA. pKARMA is a combination of the KARMA and LIBRO-1 studies. KARMA was supported by Ma¨rit and Hans Rausings Initiative Against Breast Cancer. KARMA and LIBRO-1 were supported the Cancer Risk Prediction Center (CRisP; www.crispcenter.org), a Linnaeus Centre (Contract ID 70867902) financed by the Swedish Research Council. The RBCS was funded by the Dutch Cancer Society (DDHK 2004-3124, DDHK 2009-4318). SASBAC was supported by funding from the Agency for Science, Technology and Research of Singapore (A∗STAR), the US National Institute of Health (NIH) and the Susan G. Komen Breast Cancer Foundation KC was financed by the Swedish Cancer Society (5128-B07-01PAF). The SBCGS was supported primarily by NIH grants R01CA64277, R01CA148667, and R37CA70867. Biological sample preparation was conducted the Survey and Biospecimen Shared Resource, which is supported by P30 CA68485. The SBCS was supported by Yorkshire Cancer Research S305PA, S299 and S295. Funding for the SCCS was provided by NIH grant R01 CA092447. The Arkansas Central Cancer Registry is fully funded by a grant from National Program of Cancer Registries, Centers for Disease Control and Prevention (CDC). Data on SCCS cancer cases from Mississippi were collected by the Mississippi Cancer Registry which participates in the National Program of Cancer Registries (NPCR) of the Centers for Disease Control and Prevention (CDC). The contents of this publication are solely the responsibility of the authors and do not necessarily represent the official views of the CDC or the Mississippi Cancer Registry. SEARCH is funded by a programme grant from Cancer Research UK (C490/A10124) and supported by the UK National Institute for Health Research Biomedical Research Centre at the University of Cambridge. The SEBCS was supported by the BRL (Basic Research Laboratory) program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (2012-0000347). SGBCC is funded by the National Medical Research Council Start-up Grant and Centre Grant (NMRC/CG/NCIS /2010). The recruitment of controls by the Singapore Consortium of Cohort Studies-Multi-ethnic cohort (SCCS-MEC) was funded by the Biomedical Research Council (grant number: 05/1/21/19/425). SKKDKFZS is supported by the DKFZ. The SZBCS was supported by Grant PBZ_KBN_122/P05/2004. K. J. is a fellow of International PhD program, Postgraduate School of Molecular Medicine, Warsaw Medical University, supported by the Polish Foundation of Science. The TNBCC was supported by the NIH grant (CA128978), the Breast Cancer Research Foundation , Komen Foundation for the Cure, the Ohio State University Comprehensive Cancer Center, the Stefanie Spielman Fund for Breast Cancer Research and a generous gift from the David F. and Margaret T. Grohne Family Foundation and the Ting Tsung and Wei Fong Chao Foundation. Part of the TNBCC (DEMOKRITOS) has been co-financed by the European Union (European Social Fund – ESF) and Greek National Funds through the Operational Program ‘Education and Life-long Learning’ of the National Strategic Reference Framework (NSRF)—Research Funding Program of the General Secretariat for Research & Technology: ARISTEIA. The TWBCS is supported by the Institute of Biomedical Sciences, Academia Sinica and the National Science Council, Taiwan. The UKBGS is funded by Breakthrough Breast Cancer and the Institute of Cancer Research (ICR). ICR acknowledges NHS funding to the NIHR Biomedical Research Centre. Funding to pay the Open Access publication charges for this article was provided by the Wellcome Trust.This is the advanced access published version distributed under a Creative Commons Attribution License 2.0, which can also be viewed on the publisher's webstie at: http://hmg.oxfordjournals.org/content/early/2014/07/04/hmg.ddu311.full.pdf+htm

Fine-Scale Mapping of the 4q24 Locus Identifies Two Independent Loci Associated with Breast Cancer Risk

Background: A recent association study identified a common variant (rs9790517) at 4q24 to be associated with breast cancer risk. Independent association signals and potential functional variants in this locus have not been explored. Methods: We conducted a fine-mapping analysis in 55,540 breast cancer cases and 51,168 controls from the Breast Cancer Association Consortium. Results: Conditional analyses identified two independent association signals among women of European ancestry, represented by rs9790517 [conditional P = 2.51 × 10−4; OR, 1.04; 95% confidence interval (CI), 1.02–1.07] and rs77928427 (P = 1.86 × 10−4; OR, 1.04; 95% CI, 1.02–1.07). Functional annotation using data from the Encyclopedia of DNA Elements (ENCODE) project revealed two putative functional variants, rs62331150 and rs73838678 in linkage disequilibrium (LD) with rs9790517 (r2 ≥ 0.90) residing in the active promoter or enhancer, respectively, of the nearest gene, TET2. Both variants are located in DNase I hypersensitivity and transcription factor–binding sites. Using data from both The Cancer Genome Atlas (TCGA) and Molecular Taxonomy of Breast Cancer International Consortium (METABRIC), we showed that rs62331150 was associated with level of expression of TET2 in breast normal and tumor tissue. Conclusion: Our study identified two independent association signals at 4q24 in relation to breast cancer risk and suggested that observed association in this locus may be mediated through the regulation of TET2. Impact: Fine-mapping study with large sample size warranted for identification of independent loci for breast cancer risk

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio

Numerical methods for model predictive control

There has been an increased interest in controlling complex systems using Model Predictive Control (MPC). However, the use of resource-constrained computing platforms in these systems has slowed the adoption of MPC. This thesis focuses on increasing the efficiency of numerical methods for MPC in terms of resource usage and solution time, while also simplifying the design process. We first show how block Toeplitz operators can be used to link the linear MPC matrices to the transfer function of the predicted system, resulting in horizon-independent bounds on the condition number of the condensed Hessian and the upper iteration bound for the Fast Gradient Method (FGM). We derive a horizon-independent preconditioner that produces up to a 9x speedup for the FGM while reducing the preconditioner computation time by up to 50,000x compared to an existing preconditioner. We propose a new method for computing the minimum number of fractional bits needed to ensure the FGM with fixed-point arithmetic is stable, with an example showing decreases of up to 77% in resource usage and 50% in the computational energy when using this method on a Field Programmable Gate Array. Finally, we present a framework using the derivative-free Mesh Adaptive Direct Search method to solve nonlinear MPC problems with non-differentiable features or quantized variables without the need for complex or costly reformulations. We augment the system dynamics with additional states to compute the Lagrange cost term and the violation of the path constraints along the state trajectory, and then perform a structured search of the input space using a single-shooting simulation of the system dynamics. We demonstrate this framework on a robust Goddard rocket problem with a non-differentiable cost and a quantized thrust input, where we achieve an altitude within 40m of the target, while other methods are unable to get closer than 180m.Open Acces

Conditions for Digit Stability in Iterative Methods Using the Redundant Number Representation

Iterative methods play an important role in science and engineering applications, with uses ranging from linear system solvers in finite element methods to optimization solvers in model predictive control. Recently, a new computational strategy for iterative methods called ARCHITECT was proposed by Li et al. in [1] that uses the redundant number representation to create "stable digits" in the Most-significant Digits (MSDs) of an iterate, allowing the future iterations to assume the stable MSDs have not changed their value, eliminating the need to recompute them. In this work, we present a theoretical analysis of how these "stable digits" arise in iterative methods by showing that a Fejér monotone sequence in the redundant number representation can develop stable MSDs in the elements of the sequence as the sequence grows in length. This property of Fejér monotone sequences allows us to expand the class of iterative methods known to have MSD stability when using the redundant number representation to include any fixed-point iteration of a contractive Lipschitz continuous function. We then show that this allows for the theoretical guarantee of digit stability not just in the Jacobi method that was previously analyzed by Li et al. in [2], but also in other commonly used methods such as Newton's method

Conditions for Digit Stability in Iterative Methods Using the Redundant Number Representation

Iterative methods play an important role in science and engineering applications, with uses ranging from linear system solvers in finite element methods to optimization solvers in model predictive control. Recently, a new computational strategy for iterative methods called ARCHITECT was proposed by Li et al. in [1] that uses the redundant number representation to create "stable digits" in the Most-significant Digits (MSDs) of an iterate, allowing the future iterations to assume the stable MSDs have not changed their value, eliminating the need to recompute them. In this work, we present a theoretical analysis of how these "stable digits" arise in iterative methods by showing that a Fejer monotone sequence in the redundant number representation can develop stable MSDs in the elements of the sequence as the sequence grows in length. This property of Fejer monotone sequences allows us to expand the class of iterative methods known to have MSD stability when using the redundant number representation to include any fixed-point iteration of a contractive Lipschitz continuous function. We then show that this allows for the theoretical guarantee of digit stability not just in the Jacobi method that was previously analyzed by Li et al. in [2], but also in other commonly used methods such as Newton's method