Finding All Solutions of Equations in Free Groups and Monoids with Involution

The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups as well as the set of all solutions of equations in free monoids with involution in the presence of rational constraints. This became possible due to the recently invented emph{recompression} technique of the second author. He successfully applied the recompression technique for pure word equations without involution or rational constraints. In particular, his method could not be used as a black box for free groups (even without rational constraints). Actually, the presence of an involution (inverse elements) and rational constraints complicates the situation and some additional analysis is necessary. Still, the recompression technique is general enough to accommodate both extensions. In the end, it simplifies proofs that solving word equations is in PSPACE (Plandowski 1999) and the corresponding result for equations in free groups with rational constraints (Diekert, Hagenah and Gutierrez 2001). As a byproduct we obtain a direct proof that it is decidable in PSPACE whether or not the solution set is finite.Comment: A preliminary version of this paper was presented as an invited talk at CSR 2014 in Moscow, June 7 - 11, 201

Disease overarching mechanisms that explain and predict outcome of patients with high cardiovascular risk: rationale and design of the Berlin Long-term Observation of vascular events (BeLOVE) study

BACKGROUND: Cardiovascular disease (CVD) is the leading cause of premature death worldwide. Effective and individualized treatment requires exact knowledge about both risk factors and risk estimation. Most evidence for risk prediction currently comes from population-based studies on first incident cardiovascular events. In contrast, little is known about the relevance of risk factors for the outcome of patients with established CVD or those who are at high risk of CVD, including patients with type 2 diabetes. In addition, most studies focus on individual diseases, whereas less is known about disease overarching risk factors and cross-over risk. AIM: The aim of BeLOVE is to improve short- and long-term prediction and mechanistic understanding of cardiovascular disease progression and outcomes in very high-risk patients, both in the acute as well as in the chronic phase, in order to provide the basis for improved, individualized management. STUDY DESIGN: BeLOVE is an observational prospective cohort study of patients of both sexes aged >18 in selected Berlin hospitals, who have a high risk of future cardiovascular events, including patients with a history of acute coronary syndrome (ACS), acute stroke (AS), acute heart failure (AHF), acute kidney injury (AKI) or type 2 diabetes with manifest target-organ damage. BeLOVE includes 2 subcohorts: The acute subcohort includes 6500 patients with ACS, AS, AHF, or AKI within 2-8 days after their qualifying event, who undergo a structured interview about medical history as well as blood sample collection. The chronic subcohort includes 6000 patients with ACS, AS, AHF, or AKI 90 days after event, and patients with type 2 diabetes (T2DM) and target-organ damage. These patients undergo a 6-8 hour deep phenotyping program, including detailed clinical phenotyping from a cardiological, neurological and metabolic perspective, questionnaires including patient-reported outcome measures (PROMs)as well as magnetic resonance imaging. Several biological samples are collected (i.e. blood, urine, saliva, stool) with blood samples collected in a fasting state, as well as after a metabolic challenge (either nutritional or cardiopulmonary exercise stress test). Ascertainment of major adverse cardiovascular events (MACE) will be performed in all patients using a combination of active and passive follow up procedures, such as on-site visits (if applicable), telephone interviews, review of medical charts, and links to local health authorities. Additional phenotyping visits are planned at 2, 5 and 10 years after inclusion into the chronic subcohort. FUTURE PERSPECTIVE: BeLOVE provides a unique opportunity to study both the short- and long-term disease course of patients at high cardiovascular risk through innovative and extensive deep phenotyping. Moreover, the unique study design provides opportunities for acute and post-acute inclusion and allows us to derive two non-nested yet overlapping sub-cohorts, tailored for upcoming research questions. Thereby, we aim to study disease overarching research questions, to understand crossover risk, and to find similarities and differences between clinical phenotypes of patients at high cardiovascular risk

Protocol of the Berlin Long-term Observation of Vascular Events (BeLOVE): a prospective cohort study with deep phenotyping and long-term follow up of cardiovascular high-risk patients

INTRODUCTION: The Berlin Long-term Observation of Vascular Events is a prospective cohort study that aims to improve prediction and disease-overarching mechanistic understanding of cardiovascular (CV) disease progression by comprehensively investigating a high-risk patient population with different organ manifestations. METHODS AND ANALYSIS: A total of 8000 adult patients will be recruited who have either suffered an acute CV event (CVE) requiring hospitalisation or who have not experienced a recent acute CVE but are at high CV risk. An initial study examination is performed during the acute treatment phase of the index CVE or after inclusion into the chronic high risk arm. Deep phenotyping is then performed after ~90 days and includes assessments of the patient's medical history, health status and behaviour, cardiovascular, nutritional, metabolic, and anthropometric parameters, and patient-related outcome measures. Biospecimens are collected for analyses including 'OMICs' technologies (e.g., genomics, metabolomics, proteomics). Subcohorts undergo MRI of the brain, heart, lung and kidney, as well as more comprehensive metabolic, neurological and CV examinations. All participants are followed up for up to 10 years to assess clinical outcomes, primarily major adverse CVEs and patient-reported (value-based) outcomes. State-of-the-art clinical research methods, as well as emerging techniques from systems medicine and artificial intelligence, will be used to identify associations between patient characteristics, longitudinal changes and outcomes. ETHICS AND DISSEMINATION: The study was approved by the Charité-Universitätsmedizin Berlin ethics committee (EA1/066/17). The results of the study will be disseminated through international peer-reviewed publications and congress presentations. STUDY REGISTRATION: First study phase: Approved WHO primary register: German Clinical Trials Register: https://drks.de/search/de/trial/DRKS00016852; WHO International Clinical Registry Platform: http://apps.who.int/trialsearch/Trial2.aspx?TrialID=DRKS00016852. Recruitment started on July 18, 2017.Second study phase: Approved WHO primary register: German Clinical Trials Register DRKS00023323, date of registration: November 4, 2020, URL: http://www.drks.de/ DRKS00023323. Recruitment started on January 1, 2021

A note on Makanin's algorithm

SIGLETIB Hannover: RO 7333(53) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

UNIF '96. 10. international workshop on unification Extended abstracts

SIGLEAvailable from TIB Hannover: RR 7403(96,91) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Computational treatment of temporal notions -- the CTTN-system

The CTTN-system is a computer program which provides advanced processing or temporal notions. The basic data structures of the CTTN-system are time points, crisp and fuzzy time intervals, labelled partitionings of the time line, durations, and calendar systems. The labelled partitionings are used to model periodic temporal notions, quite regular ones like years, months etc., partially regular ones like timetables, but also very irregular ones like, for example, dates of a conference series. These data structures can be used in the temporal specification language GeTS (GeoTemporal Specifications). GeTS is a functional specification and programming language with a number of built-in constructs for specifying customized temporal notions. CTTN is implemented as a Web server and as a C++ library. This paper gives a short overview over the current state of the system and its components