Power of Randomization in Automata on Infinite Strings

Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata that process input strings of infinite length. Based on the threshold chosen for the acceptance probability, different classes of languages can be defined. In this paper, we present a number of results that clarify the power of such machines and properties of the languages they define. The broad themes we focus on are as follows. We present results on the decidability and precise complexity of the emptiness, universality and language containment problems for such machines, thus answering questions central to the use of these models in formal verification. Next, we characterize the languages recognized by PBAs topologically, demonstrating that though general PBAs can recognize languages that are not regular, topologically the languages are as simple as \omega-regular languages. Finally, we introduce Hierarchical PBAs, which are syntactically restricted forms of PBAs that are tractable and capture exactly the class of \omega-regular languages

Towards Logical Specification of Statistical Machine Learning

We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification performance, robustness, and fairness of classifiers by using epistemic logic. Then we show some relationships among properties of classifiers and those between classification performance and robustness, which suggests robustness-related properties that have not been formalized in the literature as far as we know. To formalize fairness properties, we define a notion of counterfactual knowledge and show techniques to formalize conditional indistinguishability by using counterfactual epistemic operators. As far as we know, this is the first work that uses logical formulas to express statistical properties of machine learning, and that provides epistemic (resp. counterfactually epistemic) views on robustness (resp. fairness) of classifiers.Comment: SEFM'19 conference paper (full version with errors corrected

REGULATION OF EXPRESSION OF MULTIPLE BETA- GLUCOSIDASES OF ASPERGILLUS TERREUS AND THEIR PURIFICATION AND CHARACTERIZATION

This study reports the regulation and purification of -glucosidases from a thermotolerant Aspergillus terreus AN1 strain, previously reported for efficient deinking of composite paper waste. The differential expression of four -glucosidase isoforms, in response to carbon sources in production medium, was studied by electrophoretically resolving proteins by polyacrylamide gel electro-phoresis analysis (PAGE) and developing zymograms using methylum-belliferyl -D glucoside as substrate. Three -glucosidases (GI, GII & GIII) were purified using chromatographic techniques. SDS-PAGE revealed the respective molecular masses of GI, GII, and GIII, as 29, 43, and 98 KDa, and isoelectric point (pI) to be 2.8, 3.7, and 3.0. The -glucosidases exhibited diverse pH and temperature optima as well as stability. -Glucosidase I (GI) specifically recog-nized pNP--glucopyranoside (pNPG) as a substrate, whereas, -glucosidase II (GII) and III (GIII) also showed activities against cellobiose and salicin. In contrast to GII and GIII, the activity of GI was positively influenced in the presence of hexoses/pentoses and alcohols. Km and Vmax for hydrolysis of pNPG by GI, GII, andGIII were found to be 14.2 mM and 166.9 µmol -1mg protein -1, 4.37 mM, and 34.7 µmol -1mg proteins -1, and 11.1 mM and 378.7µ mol -1 mg protein -1, respectively

REACHABILITY UNDER CONTEXTUAL LOCKING ∗

Vol. 9(3:21)2013, pp. 1–17 www.lmcs-online.or

Book of Abstracts of the 2nd International Conference on Applied Mathematics and Computational Sciences (ICAMCS-2022)

It is a great privilege for us to present the abstract book of ICAMCS-2022 to the authors and the delegates of the event. We hope that you will find it useful, valuable, aspiring, and inspiring. This book is a record of abstracts of the keynote talks, invited talks, and papers presented by the participants, which indicates the progress and state of development in research at the time of writing the research article. It is an invaluable asset to all researchers. The book provides a permanent record of this asset. Conference Title: 2nd International Conference on Applied Mathematics and Computational SciencesConference Acronym: ICAMCS-2022Conference Date: 12-14 October 2022Conference Organizers: DIT University, Dehradun, IndiaConference Mode: Online (Virtual

Management of coronary disease in patients with advanced kidney disease

BACKGROUND Clinical trials that have assessed the effect of revascularization in patients with stable coronary disease have routinely excluded those with advanced chronic kidney disease. METHODS We randomly assigned 777 patients with advanced kidney disease and moderate or severe ischemia on stress testing to be treated with an initial invasive strategy consisting of coronary angiography and revascularization (if appropriate) added to medical therapy or an initial conservative strategy consisting of medical therapy alone and angiography reserved for those in whom medical therapy had failed. The primary outcome was a composite of death or nonfatal myocardial infarction. A key secondary outcome was a composite of death, nonfatal myocardial infarction, or hospitalization for unstable angina, heart failure, or resuscitated cardiac arrest. RESULTS At a median follow-up of 2.2 years, a primary outcome event had occurred in 123 patients in the invasive-strategy group and in 129 patients in the conservative-strategy group (estimated 3-year event rate, 36.4% vs. 36.7%; adjusted hazard ratio, 1.01; 95% confidence interval [CI], 0.79 to 1.29; P=0.95). Results for the key secondary outcome were similar (38.5% vs. 39.7%; hazard ratio, 1.01; 95% CI, 0.79 to 1.29). The invasive strategy was associated with a higher incidence of stroke than the conservative strategy (hazard ratio, 3.76; 95% CI, 1.52 to 9.32; P=0.004) and with a higher incidence of death or initiation of dialysis (hazard ratio, 1.48; 95% CI, 1.04 to 2.11; P=0.03). CONCLUSIONS Among patients with stable coronary disease, advanced chronic kidney disease, and moderate or severe ischemia, we did not find evidence that an initial invasive strategy, as compared with an initial conservative strategy, reduced the risk of death or nonfatal myocardial infarction

Health status after invasive or conservative care in coronary and advanced kidney disease

BACKGROUND In the ISCHEMIA-CKD trial, the primary analysis showed no significant difference in the risk of death or myocardial infarction with initial angiography and revascularization plus guideline-based medical therapy (invasive strategy) as compared with guideline-based medical therapy alone (conservative strategy) in participants with stable ischemic heart disease, moderate or severe ischemia, and advanced chronic kidney disease (an estimated glomerular filtration rate of <30 ml per minute per 1.73 m2 or receipt of dialysis). A secondary objective of the trial was to assess angina-related health status. METHODS We assessed health status with the Seattle Angina Questionnaire (SAQ) before randomization and at 1.5, 3, and 6 months and every 6 months thereafter. The primary outcome of this analysis was the SAQ Summary score (ranging from 0 to 100, with higher scores indicating less frequent angina and better function and quality of life). Mixed-effects cumulative probability models within a Bayesian framework were used to estimate the treatment effect with the invasive strategy. RESULTS Health status was assessed in 705 of 777 participants. Nearly half the participants (49%) had had no angina during the month before randomization. At 3 months, the estimated mean difference between the invasive-strategy group and the conservative-strategy group in the SAQ Summary score was 2.1 points (95% credible interval, 120.4 to 4.6), a result that favored the invasive strategy. The mean difference in score at 3 months was largest among participants with daily or weekly angina at baseline (10.1 points; 95% credible interval, 0.0 to 19.9), smaller among those with monthly angina at baseline (2.2 points; 95% credible interval, 122.0 to 6.2), and nearly absent among those without angina at baseline (0.6 points; 95% credible interval, 121.9 to 3.3). By 6 months, the between-group difference in the overall trial population was attenuated (0.5 points; 95% credible interval, 122.2 to 3.4). CONCLUSIONS Participants with stable ischemic heart disease, moderate or severe ischemia, and advanced chronic kidney disease did not have substantial or sustained benefits with regard to angina-related health status with an initially invasive strategy as compared with a conservative strategy