On the Identity Problem for the Special Linear Group and the Heisenberg Group

We study the identity problem for matrices, i.e., whether the identity matrix is in a semigroup generated by a given set of generators. In particular we consider the identity problem for the special linear group following recent NP-completeness result for SL(2,Z) and the undecidability for SL(4,Z) generated by 48 matrices. First we show that there is no embedding from pairs of words into 3 × 3 integer matrices with determinant one, i.e., into SL(3,Z) extending previously known result that there is no embedding into C^2×2. Apart from theoretical importance of the result it can be seen as a strong evidence that the computational problems in SL(3, Z) are decidable. The result excludes the most natural possibility of encoding the Post correspondence problem into SL(3,Z), where the matrix products extended by the right multiplication correspond to the Turing machine simulation. Then we show that the identity problem is decidable in polynomial time for an important subgroup of SL(3,Z), the Heisenberg group H(3,Z). Furthermore, we extend the decidability result for H(n,Q) in any dimension n. Finally we are tightening the gap on decidability question for this long standing open problem by improving the undecidability result for the identity problem in SL(4, Z) substantially reducing the bound on the size of the generator set from 48 to 8 by developing a novel reduction technique

Reachability problems in low-dimensional nondeterministic polynomial maps over integers

We study reachability problems for various nondeterministic polynomial maps in Zn. We prove that the reachability problem for very simple three-dimensional affine maps (with independent variables) is undecidable and is PSPACE-hard for both two-dimensional affine maps and one-dimensional quadratic maps. Then we show that the complexity of the reachability problem for maps without functions of the form ±x+a0 is lower. In this case the reachability problem is PSPACE for any dimension and if the dimension is not fixed, then the problem is PSPACE-complete. Finally we extend the model by considering maps as language acceptors and prove that the universality problem is undecidable for two-dimensional affine maps

Prevalence and Clinical Characteristics of Recently Diagnosed Type 2 Diabetes Patients with Positive Anti-Glutamic Acid Decarboxylase Antibody

BackgroundLatent autoimmune diabetes in adults (LADA) refers to a specific type of diabetes characterized by adult onset, presence of islet auto-antibodies, insulin independence at the time of diagnosis, and rapid decline in β-cell function. The prevalence of LADA among patients with type 2 diabetes varies from 2% to 20% according to the study population. Since most studies on the prevalence of LADA performed in Korea were conducted in patients who had been tested for anti-glutamic acid decarboxylase antibody (GADAb), a selection bias could not be excluded. In this study, we examined the prevalence and clinical characteristics of LADA among adult patients recently diagnosed with type 2 diabetes.MethodsWe included 462 patients who were diagnosed with type 2 diabetes within 5 years from the time this study was performed. We measured GADAb, fasting insulin level, fasting C-peptide level, fasting plasma glucose level, HbA1c, and serum lipid profiles and collected data on clinical characteristics.ResultsThe prevalence of LADA was 4.3% (20/462) among adult patients with newly diagnosed type 2 diabetes. Compared with the GADAb-negative patients, the GADAb-positive patients had lower fasting C-peptide levels (1.2±0.8 ng/mL vs. 2.0±1.2 ng/mL, P=0.004). Other metabolic features were not significantly different between the two groups.ConclusionThe prevalence of LADA is 4.3% among Korean adult patients with recently diagnosed type 2 diabetes. The Korean LADA patients exhibited decreased insulin secretory capacity as reflected by lower C-peptide levels

Additive Interaction of Hyperglycemia and Albuminuria on Risk of Ischemic Stroke in Type 2 Diabetes: Hong Kong Diabetes Registry

OBJECTIVE—The study aims to test whether biological interaction between hyperglycemia and albuminuria can explain the inconsistent findings from epidemiological studies and clinical trials about effects of hyperglycemia on stroke in type 2 diabetes

Establishing a generalized polyepigenetic biomarker for tobacco smoking

Large-scale epigenome-wide association meta-analyses have identified multiple 'signatures'' of smoking. Drawing on these findings, we describe the construction of a polyepigenetic DNA methylation score that indexes smoking behavior and that can be utilized for multiple purposes in population health research. To validate the score, we use data from two birth cohort studies: The Dunedin Longitudinal Study, followed to age-38 years, and the Environmental Risk Study, followed to age-18 years. Longitudinal data show that changes in DNA methylation accumulate with increased exposure to tobacco smoking and attenuate with quitting. Data from twins discordant for smoking behavior show that smoking influences DNA methylation independently of genetic and environmental risk factors. Physiological data show that changes in DNA methylation track smoking-related changes in lung function and gum health over time. Moreover, DNA methylation changes predict corresponding changes in gene expression in pathways related to inflammation, immune response, and cellular trafficking. Finally, we present prospective data about the link between adverse childhood experiences (ACEs) and epigenetic modifications; these findings document the importance of controlling for smoking-related DNA methylation changes when studying biological embedding of stress in life-course research. We introduce the polyepigenetic DNA methylation score as a tool both for discovery and theory-guided research in epigenetic epidemiology.This article is freely available via Open Access. Click on the Publisher URL to access it via the publisher's site.The Dunedin Longitudinal Study is funded by the New Zealand Health Research Council, the New Zealand Ministry of Business, Innovation, and Employment, the National Institute on Aging (AG032282), and the Medical Research Council (MR/P005918/1). The E-Risk Study is funded by the Medical Research Council (G1002190) and the National Institute of Child Health and Human Development (HD077482). Additional support was provided by a Distinguished Investigator Award from the American Asthma Foundation to Dr. Mill, and by the Jacobs Foundation and the Avielle Foundation. Dr. Arseneault is the Mental Health Leadership Fellow for the U.K. Economic and Social Research Council. Dr. Belsky is a Jacobs Foundation Fellow. This work used a high-performance computing facility partially supported by grant 2016-IDG-1013 (“HARDAC + : Reproducible HPC for Next-generation Genomics”) from the North Carolina Biotechnology Center. Illumina DNA methylation data are accessible from the Gene Expression Omnibus (accession code: GSE105018).pre-print, post-print, publisher's PD

Prediction of interface preferences with a classifier selection approach

Interaction in smart environments should be adapted to the users’ preferences, e.g., utilising modalities appropriate for the situation. While manual customisation of a single application could be feasible, this approach would require too much user effort in the future, when a user interacts with numerous applications with different interfaces, such as e.g. a smart car, a smart fridge, a smart shopping assistant etc. Supporting user groups, jointly interacting with the same application, poses additional challenges: humans tend to respect the preferences of their friends and family members, and thus the preferred interface settings may depend on all group members. This work proposes to decrease the manual customisation effort by addressing the cold-start adaptation problem, i.e., predicting interface preferences of individuals and groups for new (unseen) combinations of applications, tasks and devices, based on knowledge regarding preferences of other users. For predictions we suggest several reasoning strategies and employ a classifier selection approach for automatically choosing the most appropriate strategy for each interface feature in each new situation. The proposed approach is suitable for cases where long interaction histories are not yet available, and it is not restricted to similar interfaces and application domains, as we demonstrate by experiments on predicting preferences of individuals and groups for three different application prototypes: recipe recommender, cooking assistant and car servicing assistant. The results show that the proposed method handles the cold-start problem in various types of unseen situations fairly well: it achieved an average prediction accuracy of 72 ± 1 %. Further studies on user acceptance of predictions with two different user communities have shown that this is a desirable feature for applications in smart environments, even when predictions are not so accurate and when users do not perceive manual customisation as very time-consuming