Model Checking Linear Dynamical Systems under Floating-point Rounding

We consider linear dynamical systems under floating-point rounding. In these systems, a matrix is repeatedly applied to a vector, but the numbers are rounded into floating-point representation after each step (i.e., stored as a fixed-precision mantissa and an exponent). The approach more faithfully models realistic implementations of linear loops, compared to the exact arbitrary-precision setting often employed in the study of linear dynamical systems. Our results are twofold: We show that for non-negative matrices there is a special structure to the sequence of vectors generated by the system: the mantissas are periodic and the exponents grow linearly. We leverage this to show decidability of $\omega$-regular temporal model checking against semialgebraic predicates. This contrasts with the unrounded setting, where even the non-negative case encompasses the long-standing open Skolem and positivity problems. On the other hand, when negative numbers are allowed in the matrix, we show that the reachability problem is undecidable by encoding a two-counter machine. Again, this is in contrast to the unrounded setting where point-to-point reachability is known to be decidable in polynomial time

Model Checking Linear Dynamical Systems under Floating-point Rounding

We consider linear dynamical systems under floating-point rounding. In these systems, a matrix is repeatedly applied to a vector, but the numbers are rounded into floating-point representation after each step (i.e., stored as a fixed-precision mantissa and an exponent). The approach more faithfully models realistic implementations of linear loops, compared to the exact arbitrary-precision setting often employed in the study of linear dynamical systems

The Effect of Different Types of Climates on the Spread of COVID-19

Coronavirus disease of 2019 (COVID-19) is the third most common zoonotic disease caused by the coronavirusvirus, SARS in 2002, and Middle East Respiratory Syndrome (MERS) in 2012. The primary origin oftransmission of infection to humans is not well known. However, more prevalence of the disease is caused dueto human-to-human transmission. There are relatively few studies on the impact of climate change on COVID-19 disease in the world. Recognizing the behavioral features of the SARS-CoV-2 virus and its pathogenicity invarious climatic conditions can offer strategies for control measures, preventing the transmission of the disease,and minimizing the potential mortality risk of the virus, which provides a basis for more detailed studies indifferent climatic regions. This study aimed to evaluate the effect of different types of climate on the spread ofCOVID-19

Correction to: Utilization of Waste Glass Micro-particles in Producing Self-Consolidating Concrete Mixtures

Following publication of the original article (Sharifi et al. 2016), the author reported his name has erroneously spelled as Amin Momeni. The full name is Mohammadamin Momeni