Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable to verify multivariate nonlinear polynomial and non-polynomial inequalities on rectangular domains. One of the main features of our work is an efficient implementation of the verification procedure which can prove non-trivial high-dimensional inequalities in several seconds. We developed the verification tool as a part of the Flyspeck project (a formal proof of the Kepler conjecture). The Flyspeck project includes about 1000 nonlinear inequalities. We successfully tested our method on more than 100 Flyspeck inequalities and estimated that the formal verification procedure is about 3000 times slower than an informal verification method implemented in C++. We also describe future work and prospective optimizations for our method.Comment: 15 page

Satisfiability Modulo Transcendental Functions via Incremental Linearization

In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted in the abstract space, which is described in terms of the combined theory of linear arithmetic on the rationals with uninterpreted functions, and are incrementally axiomatized by means of upper- and lower-bounding piecewise-linear functions. Suitable numerical techniques are used to ensure that the abstractions of the transcendental functions are sound even in presence of irrationals. Our experimental evaluation on benchmarks from verification and mathematics demonstrates the potential of our approach, showing that it compares favorably with delta-satisfiability /interval propagation and methods based on theorem proving

Psychometric Properties of the Farsi Version of Posttraumatic Growth Inventory for Children-Revised in Iranian Children with Cancer

Objective: Coping with childhood cancer, as a stressful incident, can lead to a growth in various aspects of the child's life. Therefore, this study aims to validate Posttraumatic Growth Inventory for Children-Revised (PTGI-C-R) in children with cancer. Methods: This methodological research was carried out in referral children hospitals in Tehran. PTGI-C-R was translated and back-translated. Content and face validity were assessed. Confirmatory factor analysis (CFA) was performed on 200 children with inclusion criteria, using LISREL V8.5. Due to the rejection of the model, an exploratory factor analysis (EFA) was done, using SPSS V21. The correlation of posttraumatic growth (PTG) with the variables, i.e., age and gender, was investigated. Results: Some writing changes were made in phrases in the sections concerning face and content validity. CFA rejected the five-factor model due to the undesirable fit indices. Therefore, an EFA was used and the three-factor model was not approved, either despite the statistical appropriateness or due to the lack of similarity between the items loaded on factors. The results also indicated a significant relationship between PTG and age (r = 0.13, P = 0.05). There is no significant relationship between PTG and gender (z = -1.35, P = 0.83). Conclusions: PTGI-C-R does not have desirable psychometric properties in Iranian children with cancer and may not be able to reflect all the aspects of PTG experienced by them. Therefore, it cannot be used as an appropriate scale, and it is necessary to develop and validate a specific tool through a qualitative study. © 2021 Wolters Kluwer Medknow Publications. All rights reserved

Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

Tissue-resident, extravascular Ly6c- monocytes are critical for inflammation in the synovium

Monocytes are abundant immune cells that infiltrate inflamed organs. However, the majority of monocyte studies focus on circulating cells, rather than those in tissue. Here, we identify and characterize an intravascular synovial monocyte population resembling circulating non-classical monocytes and an extravascular tissue-resident monocyte-lineage cell (TR-MC) population distinct in surface marker and transcriptional profile from circulating monocytes, dendritic cells, and tissue macrophages that are conserved in rheumatoid arthritis (RA) patients. TR-MCs are independent of NR4A1 and CCR2, long lived, and embryonically derived. TR-MCs undergo increased proliferation and reverse diapedesis dependent on LFA1 in response to arthrogenic stimuli and are required for the development of RA-like disease. Moreover, pathways that are activated in TR-MCs at the peak of arthritis overlap with those that are downregulated in LFA1-/- TR-MCs. These findings show a facet of mononuclear cell biology that could be imperative to understanding tissue-resident myeloid cell function in RA.</p

Global, regional, and national burden of stroke and its risk factors, 1990-2019 : a systematic analysis for the Global Burden of Disease Study 2019

Background Regularly updated data on stroke and its pathological types, including data on their incidence, prevalence, mortality, disability, risk factors, and epidemiological trends, are important for evidence-based stroke care planning and resource allocation. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) aims to provide a standardised and comprehensive measurement of these metrics at global, regional, and national levels. Methods We applied GBD 2019 analytical tools to calculate stroke incidence, prevalence, mortality, disability-adjusted life-years (DALYs), and the population attributable fraction (PAF) of DALYs (with corresponding 95% uncertainty intervals [UIs]) associated with 19 risk factors, for 204 countries and territories from 1990 to 2019. These estimates were provided for ischaemic stroke, intracerebral haemorrhage, subarachnoid haemorrhage, and all strokes combined, and stratified by sex, age group, and World Bank country income level. Findings In 2019, there were 12·2 million (95% UI 11·0–13·6) incident cases of stroke, 101 million (93·2–111) prevalent cases of stroke, 143 million (133–153) DALYs due to stroke, and 6·55 million (6·00–7·02) deaths from stroke. Globally, stroke remained the second-leading cause of death (11·6% [10·8–12·2] of total deaths) and the third-leading cause of death and disability combined (5·7% [5·1–6·2] of total DALYs) in 2019. From 1990 to 2019, the absolute number of incident strokes increased by 70·0% (67·0–73·0), prevalent strokes increased by 85·0% (83·0–88·0), deaths from stroke increased by 43·0% (31·0–55·0), and DALYs due to stroke increased by 32·0% (22·0–42·0). During the same period, age-standardised rates of stroke incidence decreased by 17·0% (15·0–18·0), mortality decreased by 36·0% (31·0–42·0), prevalence decreased by 6·0% (5·0–7·0), and DALYs decreased by 36·0% (31·0–42·0). However, among people younger than 70 years, prevalence rates increased by 22·0% (21·0–24·0) and incidence rates increased by 15·0% (12·0–18·0). In 2019, the age-standardised stroke-related mortality rate was 3·6 (3·5–3·8) times higher in the World Bank low-income group than in the World Bank high-income group, and the age-standardised stroke-related DALY rate was 3·7 (3·5–3·9) times higher in the low-income group than the high-income group. Ischaemic stroke constituted 62·4% of all incident strokes in 2019 (7·63 million [6·57–8·96]), while intracerebral haemorrhage constituted 27·9% (3·41 million [2·97–3·91]) and subarachnoid haemorrhage constituted 9·7% (1·18 million [1·01–1·39]). In 2019, the five leading risk factors for stroke were high systolic blood pressure (contributing to 79·6 million [67·7–90·8] DALYs or 55·5% [48·2–62·0] of total stroke DALYs), high bodymass index (34·9 million [22·3–48·6] DALYs or 24·3% [15·7–33·2]), high fasting plasma glucose (28·9 million [19·8–41·5] DALYs or 20·2% [13·8–29·1]), ambient particulate matter pollution (28·7 million [23·4–33·4] DALYs or 20·1% [16·6–23·0]), and smoking (25·3 million [22·6–28·2] DALYs or 17·6% [16·4–19·0]). Interpretation The annual number of strokes and deaths due to stroke increased substantially from 1990 to 2019, despite substantial reductions in age-standardised rates, particularly among people older than 70 years. The highest age-standardised stroke-related mortality and DALY rates were in the World Bank low-income group. The fastest growing risk factor for stroke between 1990 and 2019 was high body-mass index. Without urgent implementation of effective primary prevention strategies, the stroke burden will probably continue to grow across the world, particularly in low-income countries