The Complexity of Gradient Descent: CLS = PPAD ∩\cap PLS

We study search problems that can be solved by performing Gradient Descent on a bounded convex polytopal domain and show that this class is equal to the intersection of two well-known classes: PPAD and PLS. As our main underlying technical contribution, we show that computing a Karush-Kuhn-Tucker (KKT) point of a continuously differentiable function over the domain $[0,1]^2$ is PPAD $\cap$ PLS-complete. This is the first natural problem to be shown complete for this class. Our results also imply that the class CLS (Continuous Local Search) - which was defined by Daskalakis and Papadimitriou as a more "natural" counterpart to PPAD $\cap$ PLS and contains many interesting problems - is itself equal to PPAD $\cap$ PLS

The NORMAN Association and the European Partnership for Chemicals Risk Assessment (PARC): let’s cooperate! [Commentary]

The Partnership for Chemicals Risk Assessment (PARC) is currently under development as a joint research and innovation programme to strengthen the scientific basis for chemical risk assessment in the EU. The plan is to bring chemical risk assessors and managers together with scientists to accelerate method development and the production of necessary data and knowledge, and to facilitate the transition to next-generation evidence-based risk assessment, a non-toxic environment and the European Green Deal. The NORMAN Network is an independent, well-established and competent network of more than 80 organisations in the field of emerging substances and has enormous potential to contribute to the implementation of the PARC partnership. NORMAN stands ready to provide expert advice to PARC, drawing on its long experience in the development, harmonisation and testing of advanced tools in relation to chemicals of emerging concern and in support of a European Early Warning System to unravel the risks of contaminants of emerging concern (CECs) and close the gap between research and innovation and regulatory processes. In this commentary we highlight the tools developed by NORMAN that we consider most relevant to supporting the PARC initiative: (i) joint data space and cutting-edge research tools for risk assessment of contaminants of emerging concern; (ii) collaborative European framework to improve data quality and comparability; (iii) advanced data analysis tools for a European early warning system and (iv) support to national and European chemical risk assessment thanks to harnessing, combining and sharing evidence and expertise on CECs. By combining the extensive knowledge and experience of the NORMAN network with the financial and policy-related strengths of the PARC initiative, a large step towards the goal of a non-toxic environment can be taken

The NORMAN Suspect List Exchange (NORMAN-SLE): facilitating European and worldwide collaboration on suspect screening in high resolution mass spectrometry

Background: The NORMAN Association (https://www.norman-.network.com/) initiated the NORMAN Suspect List Exchange (NORMAN-SLE; https://www.norman-.network.com/nds/SLE/) in 2015, following the NORMAN collaborative trial on non-target screening of environmental water samples by mass spectrometry. Since then, this exchange of information on chemicals that are expected to occur in the environment, along with the accompanying expert knowledge and references, has become a valuable knowledge base for "suspect screening" lists. The NORMAN-SLE now serves as a FAIR (Findable, Accessible, Interoperable, Reusable) chemical information resource worldwide.Results: The NORMAN-SLE contains 99 separate suspect list collections (as of May 2022) from over 70 contributors around the world, totalling over 100,000 unique substances. The substance classes include per- and polyfluoroalkyl substances (PFAS), pharmaceuticals, pesticides, natural toxins, high production volume substances covered under the European REACH regulation (EC: 1272/2008), priority contaminants of emerging concern (CECs) and regulatory lists from NORMAN partners. Several lists focus on transformation products (TPs) and complex features detected in the environment with various levels of provenance and structural information. Each list is available for separate download. The merged, curated collection is also available as the NORMAN Substance Database (NORMAN SusDat). Both the NORMAN-SLE and NORMAN SusDat are integrated within the NORMAN Database System (NDS). The individual NORMAN-SLE lists receive digital object identifiers (DOIs) and traceable versioning via a Zenodo community (https:// zenodo.org/communities/norman-.sle), with a total of > 40,000 unique views, > 50,000 unique downloads and 40 citations (May 2022). NORMAN-SLE content is progressively integrated into large open chemical databases such as PubChem (https://pubchem.ncbi.nlm.nih.gov/) and the US EPA's CompTox Chemicals Dashboard (https://comptox. epa.gov/dashboard/), enabling further access to these lists, along with the additional functionality and calculated properties these resources offer. PubChem has also integrated significant annotation content from the NORMAN-SLE, including a classification browser (https://pubchem.ncbi.nlm.nih.gov/classification/#hid=101).Conclusions: The NORMAN-SLE offers a specialized service for hosting suspect screening lists of relevance for the environmental community in an open, FAIR manner that allows integration with other major chemical resources. These efforts foster the exchange of information between scientists and regulators, supporting the paradigm shift to the "one substance, one assessment" approach. New submissions are welcome via the contacts provided on the NORMAN-SLE website (https://www.norman-.network.com/nds/SLE/)

The role of open abdomen in non-trauma patient : WSES Consensus Paper

The open abdomen (OA) is defined as intentional decision to leave the fascial edges of the abdomen un-approximated after laparotomy (laparostomy). The abdominal contents are potentially exposed and therefore must be protected with a temporary coverage, which is referred to as temporal abdominal closure (TAC). OA use remains widely debated with many specific details deserving detailed assessment and clarification. To date, in patients with intra-abdominal emergencies, the OA has not been formally endorsed for routine utilization; although, utilization is seemingly increasing. Therefore, the World Society of Emergency Surgery (WSES), Abdominal Compartment Society (WSACS) and the Donegal Research Academy united a worldwide group of experts in an international consensus conference to review and thereafter propose the basis for evidence-directed utilization of OA management in non-trauma emergency surgery and critically ill patients. In addition to utilization recommendations, questions with insufficient evidence urgently requiring future study were identified.Peer reviewe

The NORMAN Suspect List Exchange (NORMAN-SLE): Facilitating European and worldwide collaboration on suspect screening in high resolution mass spectrometry

Background: The NORMAN Association (https://www.norman-network.com/) initiated the NORMAN Suspect List Exchange (NORMAN-SLE; https://www.norman-network.com/nds/SLE/) in 2015, following the NORMAN collaborative trial on non-target screening of environmental water samples by mass spectrometry. Since then, this exchange of information on chemicals that are expected to occur in the environment, along with the accompanying expert knowledge and references, has become a valuable knowledge base for “suspect screening” lists. The NORMAN-SLE now serves as a FAIR (Findable, Accessible, Interoperable, Reusable) chemical information resource worldwide. Results: The NORMAN-SLE contains 99 separate suspect list collections (as of May 2022) from over 70 contributors around the world, totalling over 100,000 unique substances. The substance classes include per- and polyfluoroalkyl substances (PFAS), pharmaceuticals, pesticides, natural toxins, high production volume substances covered under the European REACH regulation (EC: 1272/2008), priority contaminants of emerging concern (CECs) and regulatory lists from NORMAN partners. Several lists focus on transformation products (TPs) and complex features detected in the environment with various levels of provenance and structural information. Each list is available for separate download. The merged, curated collection is also available as the NORMAN Substance Database (NORMAN SusDat). Both the NORMAN-SLE and NORMAN SusDat are integrated within the NORMAN Database System (NDS). The individual NORMAN-SLE lists receive digital object identifiers (DOIs) and traceable versioning via a Zenodo community (https://zenodo.org/communities/norman-sle), with a total of > 40,000 unique views, > 50,000 unique downloads and 40 citations (May 2022). NORMAN-SLE content is progressively integrated into large open chemical databases such as PubChem (https://pubchem.ncbi.nlm.nih.gov/) and the US EPA’s CompTox Chemicals Dashboard (https://comptox.epa.gov/dashboard/), enabling further access to these lists, along with the additional functionality and calculated properties these resources offer. PubChem has also integrated significant annotation content from the NORMAN-SLE, including a classification browser (https://pubchem.ncbi.nlm.nih.gov/classification/#hid=101). Conclusions: The NORMAN-SLE offers a specialized service for hosting suspect screening lists of relevance for the environmental community in an open, FAIR manner that allows integration with other major chemical resources. These efforts foster the exchange of information between scientists and regulators, supporting the paradigm shift to the “one substance, one assessment” approach. New submissions are welcome via the contacts provided on the NORMAN-SLE website (https://www.norman-network.com/nds/SLE/)

The NORMAN Suspect List Exchange (NORMAN-SLE): facilitating European and worldwide collaboration on suspect screening in high resolution mass spectrometry

The NORMAN Association (https://www.norman-network.com/) initiated the NORMAN Suspect List Exchange (NORMAN-SLE; https://www.norman-network.com/nds/SLE/) in 2015, following the NORMAN collaborative trial on non-target screening of environmental water samples by mass spectrometry. Since then, this exchange of information on chemicals that are expected to occur in the environment, along with the accompanying expert knowledge and references, has become a valuable knowledge base for "suspect screening" lists. The NORMAN-SLE now serves as a FAIR (Findable, Accessible, Interoperable, Reusable) chemical information resource worldwide.The NORMAN-SLE project has received funding from the NORMAN Association via its joint proposal of activities. HMT and ELS are supported by the Luxembourg National Research Fund (FNR) for project A18/BM/12341006. ELS, PC, SEH, HPHA, ZW acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 101036756, project ZeroPM: Zero pollution of persistent, mobile substances. The work of EEB, TC, QL, BAS, PAT, and JZ was supported by the National Center for Biotechnology Information of the National Library of Medicine (NLM), National Institutes of Health (NIH). JOB is the recipient of an NHMRC Emerging Leadership Fellowship (EL1 2009209). KVT and JOB acknowledge the support of the Australian Research Council (DP190102476). The Queensland Alliance for Environmental Health Sciences, The University of Queensland, gratefully acknowledges the financial support of the Queensland Department of Health. NR is supported by a Miguel Servet contract (CP19/00060) from the Instituto de Salud Carlos III, co-financed by the European Union through Fondo Europeo de Desarrollo Regional (FEDER). MM and TR gratefully acknowledge financial support by the German Ministry for Education and Research (BMBF, Bonn) through the project “Persistente mobile organische Chemikalien in der aquatischen Umwelt (PROTECT)” (FKz: 02WRS1495 A/B/E). LiB acknowledges funding through a Research Foundation Flanders (FWO) fellowship (11G1821N). JAP and JMcL acknowledge financial support from the NIH for CCSCompendium (S50 CCSCOMPEND) via grants NIH NIGMS R01GM092218 and NIH NCI 1R03CA222452-01, as well as the Vanderbilt Chemical Biology Interface training program (5T32GM065086-16), plus use of resources of the Center for Innovative Technology (CIT) at Vanderbilt University. TJ was (partly) supported by the Dutch Research Council (NWO), project number 15747. UFZ (TS, MaK, WB) received funding from SOLUTIONS project (European Union’s Seventh Framework Programme for research, technological development and demonstration under Grant Agreement No. 603437). TS, MaK, WB, JPA, RCHV, JJV, JeM and MHL acknowledge HBM4EU (European Union’s Horizon 2020 research and innovation programme under the grant agreement no. 733032). TS acknowledges funding from NFDI4Chem—Chemistry Consortium in the NFDI (supported by the DFG under project number 441958208). TS, MaK, WB and EMLJ acknowledge NaToxAq (European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 722493). S36 and S63 (HPHA, SEH, MN, IS) were funded by the German Federal Ministry for the Environment, Nature Conservation and Nuclear Safety (BMU) Project No. (FKZ) 3716 67 416 0, updates to S36 (HPHA, SEH, MN, IS) by the German Federal Ministry for the Environment, Nature Conservation, Nuclear Safety and Consumer Protection (BMUV) Project No. (FKZ) 3719 65 408 0. MiK acknowledges financial support from the EU Cohesion Funds within the project Monitoring and assessment of water body status (No. 310011A366 Phase III). The work related to S60 and S82 was funded by the Swiss Federal Office for the Environment (FOEN), KK and JH acknowledge the input of Kathrin Fenner’s group (Eawag) in compiling transformation products from European pesticides registration dossiers. DSW and YDF were supported by the Canadian Institutes of Health Research and Genome Canada. The work related to S49, S48 and S77 was funded by the MAVA foundation; for S77 also the Valery Foundation (KG, JaM, BG). DML acknowledges National Science Foundation Grant RUI-1306074. YL acknowledges the National Natural Science Foundation of China (Grant No. 22193051 and 21906177), and the Chinese Postdoctoral Science Foundation (Grant No. 2019M650863). WLC acknowledges research project 108C002871 supported by the Environmental Protection Administration, Executive Yuan, R.O.C. Taiwan (Taiwan EPA). JG acknowledges funding from the Swiss Federal Office for the Environment. AJW was funded by the U.S. Environmental Protection Agency. LuB, AC and FH acknowledge the financial support of the Generalitat Valenciana (Research Group of Excellence, Prometeo 2019/040). KN (S89) acknowledges the PhD fellowship through Marie Skłodowska-Curie grant agreement No. 859891 (MSCA-ETN). Exposome-Explorer (S34) was funded by the European Commission projects EXPOsOMICS FP7-KBBE-2012 [308610]; NutriTech FP7-KBBE-2011-5 [289511]; Joint Programming Initiative FOODBALL 2014–17. CP acknowledges grant RYC2020-028901-I funded by MCIN/AEI/1.0.13039/501100011033 and “ESF investing in your future”, and August T Larsson Guest Researcher Programme from the Swedish University of Agricultural Sciences. The work of ML, MaSe, SG, TL and WS creating and filling the STOFF-IDENT database (S2) mostly sponsored by the German Federal Ministry of Education and Research within the RiSKWa program (funding codes 02WRS1273 and 02WRS1354). XT acknowledges The National Food Institute, Technical University of Denmark. MaSch acknowledges funding by the RECETOX research infrastructure (the Czech Ministry of Education, Youth and Sports, LM2018121), the CETOCOEN PLUS project (CZ.02.1.01/0.0/0.0/15_003/0000469), and the CETOCOEN EXCELLENCE Teaming 2 project supported by the Czech ministry of Education, Youth and Sports (No CZ.02.1.01/0.0/0.0/17_043/0009632).Peer reviewe

The Complexity of Gradient Descent: CLS = PPAD ∩\cap PLS

We study search problems that can be solved by performing Gradient Descent on a bounded convex polytopal domain and show that this class is equal to the intersection of two well-known classes: PPAD and PLS. As our main underlying technical contribution, we show that computing a Karush-Kuhn-Tucker (KKT) point of a continuously differentiable function over the domain $[0,1]^2$ is PPAD $\cap$ PLS-complete. This is the first natural problem to be shown complete for this class. Our results also imply that the class CLS (Continuous Local Search) - which was defined by Daskalakis and Papadimitriou as a more "natural" counterpart to PPAD $\cap$ PLS and contains many interesting problems - is itself equal to PPAD $\cap$ PLS

The Complexity of Computing KKT Solutions of Quadratic Programs

It is well known that solving a (non-convex) quadratic program is NP-hard. We show that the problem remains hard even if we are only looking for a Karush-Kuhn-Tucker (KKT) point, instead of a global optimum. Namely, we prove that computing a KKT point of a quadratic polynomial over the domain [0,1]n is complete for the class CLS = PPAD∩PLS