Near-Optimal Complexity Bounds for Fragments of the Skolem Problem

Given a linear recurrence sequence (LRS), specified using the initial conditions and the recurrence relation, the Skolem problem asks if zero ever occurs in the infinite sequence generated by the LRS. Despite active research over last few decades, its decidability is known only for a few restricted subclasses, by either restricting the order of the LRS (upto 4) or by restricting the structure of the LRS (e.g., roots of its characteristic polynomial). In this paper, we identify a subclass of LRS of arbitrary order for which the Skolem problem is easy, namely LRS all of whose characteristic roots are (possibly complex) roots of real algebraic numbers, i.e., roots satisfying x^d = r for r real algebraic. We show that for this subclass, the Skolem problem can be solved in NP^RP. As a byproduct, we implicitly obtain effective bounds on the zero set of the LRS for this subclass. While prior works in this area often exploit deep results from algebraic and transcendental number theory to get such effective results, our techniques are primarily algorithmic and use linear algebra and Galois theory. We also complement our upper bounds with a NP lower bound for the Skolem problem via a new direct reduction from 3-CNF-SAT, matching the best known lower bounds

Computational Fluid Dynamics Analysis of Freeze Drying Process and Equipment

Freeze drying is an important, but expensive, inefficient and time consuming process in the pharmaceutical, chemical and food processing industries. Computational techniques could be a very effective tool in predictive design and analysis of both freeze drying process and equipment. This work is an attempt at using Computational Fluid Dynamics(CFD) and numerical simulations as a tool for freeze drying process and equipment design. Pressure control is critical in freeze dryers, keeping in view the product stability. In industrial freeze dryers, loss of pressure control can lead to loss of an entire batch. Pressure variation within the chamber could also lead to batch inhomogeneity, especially in industrial scale dryers. The low-pressure environment and the relatively small flow velocities make it difficult to quantify the flow structure experimentally. The current work presents a three-dimensional multi-species computational fluid dynamics model for vapor flow in a laboratory scale freeze-dryer validated with experimental data and analytical expressions. The model accounts for the presence of a non-condensable gas such as nitrogen or air using a continuum multi-species model. The flow structure at different sublimation rates, chamber pressures and shelf-gaps are systematically investigated. Emphasis has been placed on accurately predicting the pressure variation across the subliming front. It was found that while the pressure variation increased linearly with sublimation rate in the range of 0.5 kg/hr/m2 to 1.3 kg/hr/m2, the variation was more sensitive at shelf gaps approaching about at 2.1 cm and negligible at gaps close to 9 cm. While the results are found to agree within 10\% of measurements made for the range of shelf gaps and sublimation rates investigated here, the analytical solution is found to be more accurate for smaller shelf gaps. The current work presents an important validation case motivating broader use of CFD in optimizing process and equipment design. A critical component of the freeze drying system is the chamber to pressure duct. A well designed duct, apart from providing smooth flow and lower chamber pressures, should be able to accommodate the peak flow rates without the possibility choking. Here we use computational fluid dynamics as a tool to predict the minimum controllable chamber pressure, maximum sublimation rate, the onset of choking and to suggest better freeze dryer geometry. The main findings include an improved performance concept (IPC) that allowed 11\% improvement in the sublimation rate. The IPC offered a lower minimum controllable pressure at all sublimation rates. A maximum projected improvement because of the combined effect of lower controllable pressure and improved flow throughput is estimated at 14.7\% for the IPC. For the lower condenser temperature, the maximum performance improvement of 8\% was observed at the 50mTorr chamber pressure. Heat transfer to the product is one of the most inefficient step in the Freeze Drying process. While a higher product temperature ensures faster sublimation, it is necessary to maintain it below the collapse temperature for product stability. A quick and reasonable accurate model could accelerate the process design cycle or at the least reduce the number of experimental runs required. Here we present a simplified unsteady heat and mass-transfer model which can be adapted for different equipments and product geometry. The model is compared against experiments, the effect of slice geometry is discussed and the application in a continuous freeze dryer is demonstrated. The model was found to accurately predict the product temperature. However the sublimation rate predictions deviated considerably form experiential studies. It is speculated that the porous structure of the dried cake could play a significant role in the sublimation rates and hence a more complicated model might be required for accurate predictions

Formal analysis of fault tolerant real time multiprocessor allocation and scheduling protocols

Dependable real-time distributed systems rely on allocation and scheduling protocols to satisfy stringent resource and timing constraints. As these protocols have both dependability and real-time attributes, verification of such composite services warrants a rigorous and formal levels of assurance for their correctness. The wide acceptance of formal techniques in the design and development of dependable real-time systems is limited because, most of these formal theories for real-time scheduling have been developed without much regard for their further reuse. This makes the formal specifications and their proof constructs in general difficult to reuse, and to verify or analyze similar or related protocols. To expand the utility of formal techniques, this thesis explores the possibility of effectively defining and then reusing formal theories in order to simplify verification and analysis for a wide spectrum of dependable real-time protocols. We present a modular formal analysis of a fault-tolerant version of a real-time task allocation and scheduling policies. The main aim is to develop a library of formal theories for the identified modules for real-time and dependable services which could be systematically, and if required, repeatedly used to develop different and new composite dependable multiprocessor real-time allocation and scheduling protocols. We demonstrate a rigorous and tool-assisted formal analysis of three multiprocessor real time fault tolerant allocation and scheduling protocols for both periodic and aperiodic task models using the concept of reuasability of previously defined theories. We show the reduced effort in the analysis and verification process by reusing the previously formalized theories. Formal analyses of these protocols have been performed using a mechanized theorem proving environment, called PVS from SRI labs

Global incidence, prevalence, years lived with disability (YLDs), disability-adjusted life-years (DALYs), and healthy life expectancy (HALE) for 371 diseases and injuries in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Background: Detailed, comprehensive, and timely reporting on population health by underlying causes of disability and premature death is crucial to understanding and responding to complex patterns of disease and injury burden over time and across age groups, sexes, and locations. The availability of disease burden estimates can promote evidence-based interventions that enable public health researchers, policy makers, and other professionals to implement strategies that can mitigate diseases. It can also facilitate more rigorous monitoring of progress towards national and international health targets, such as the Sustainable Development Goals. For three decades, the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) has filled that need. A global network of collaborators contributed to the production of GBD 2021 by providing, reviewing, and analysing all available data. GBD estimates are updated routinely with additional data and refined analytical methods. GBD 2021 presents, for the first time, estimates of health loss due to the COVID-19 pandemic. Methods: The GBD 2021 disease and injury burden analysis estimated years lived with disability (YLDs), years of life lost (YLLs), disability-adjusted life-years (DALYs), and healthy life expectancy (HALE) for 371 diseases and injuries using 100 983 data sources. Data were extracted from vital registration systems, verbal autopsies, censuses, household surveys, disease-specific registries, health service contact data, and other sources. YLDs were calculated by multiplying cause-age-sex-location-year-specific prevalence of sequelae by their respective disability weights, for each disease and injury. YLLs were calculated by multiplying cause-age-sex-location-year-specific deaths by the standard life expectancy at the age that death occurred. DALYs were calculated by summing YLDs and YLLs. HALE estimates were produced using YLDs per capita and age-specific mortality rates by location, age, sex, year, and cause. 95% uncertainty intervals (UIs) were generated for all final estimates as the 2·5th and 97·5th percentiles values of 500 draws. Uncertainty was propagated at each step of the estimation process. Counts and age-standardised rates were calculated globally, for seven super-regions, 21 regions, 204 countries and territories (including 21 countries with subnational locations), and 811 subnational locations, from 1990 to 2021. Here we report data for 2010 to 2021 to highlight trends in disease burden over the past decade and through the first 2 years of the COVID-19 pandemic. Findings: Global DALYs increased from 2·63 billion (95% UI 2·44–2·85) in 2010 to 2·88 billion (2·64–3·15) in 2021 for all causes combined. Much of this increase in the number of DALYs was due to population growth and ageing, as indicated by a decrease in global age-standardised all-cause DALY rates of 14·2% (95% UI 10·7–17·3) between 2010 and 2019. Notably, however, this decrease in rates reversed during the first 2 years of the COVID-19 pandemic, with increases in global age-standardised all-cause DALY rates since 2019 of 4·1% (1·8–6·3) in 2020 and 7·2% (4·7–10·0) in 2021. In 2021, COVID-19 was the leading cause of DALYs globally (212·0 million [198·0–234·5] DALYs), followed by ischaemic heart disease (188·3 million [176·7–198·3]), neonatal disorders (186·3 million [162·3–214·9]), and stroke (160·4 million [148·0–171·7]). However, notable health gains were seen among other leading communicable, maternal, neonatal, and nutritional (CMNN) diseases. Globally between 2010 and 2021, the age-standardised DALY rates for HIV/AIDS decreased by 47·8% (43·3–51·7) and for diarrhoeal diseases decreased by 47·0% (39·9–52·9). Non-communicable diseases contributed 1·73 billion (95% UI 1·54–1·94) DALYs in 2021, with a decrease in age-standardised DALY rates since 2010 of 6·4% (95% UI 3·5–9·5). Between 2010 and 2021, among the 25 leading Level 3 causes, age-standardised DALY rates increased most substantially for anxiety disorders (16·7% [14·0–19·8]), depressive disorders (16·4% [11·9–21·3]), and diabetes (14·0% [10·0–17·4]). Age-standardised DALY rates due to injuries decreased globally by 24·0% (20·7–27·2) between 2010 and 2021, although improvements were not uniform across locations, ages, and sexes. Globally, HALE at birth improved slightly, from 61·3 years (58·6–63·6) in 2010 to 62·2 years (59·4–64·7) in 2021. However, despite this overall increase, HALE decreased by 2·2% (1·6–2·9) between 2019 and 2021. Interpretation: Putting the COVID-19 pandemic in the context of a mutually exclusive and collectively exhaustive list of causes of health loss is crucial to understanding its impact and ensuring that health funding and policy address needs at both local and global levels through cost-effective and evidence-based interventions. A global epidemiological transition remains underway. Our findings suggest that prioritising non-communicable disease prevention and treatment policies, as well as strengthening health systems, continues to be crucially important. The progress on reducing the burden of CMNN diseases must not stall; although global trends are improving, the burden of CMNN diseases remains unacceptably high. Evidence-based interventions will help save the lives of young children and mothers and improve the overall health and economic conditions of societies across the world. Governments and multilateral organisations should prioritise pandemic preparedness planning alongside efforts to reduce the burden of diseases and injuries that will strain resources in the coming decades. Funding: Bill & Melinda Gates Foundation

Search for gravitational-lensing signatures in the full third observing run of the LIGO-Virgo network

Gravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational wave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters and sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects

Search for eccentric black hole coalescences during the third observing run of LIGO and Virgo

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass M>70 M⊙) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities 0<e≤0.3 at 0.33 Gpc−3 yr−1 at 90\% confidence level

Ultralight vector dark matter search using data from the KAGRA O3GK run

Among the various candidates for dark matter (DM), ultralight vector DM can be probed by laser interferometric gravitational wave detectors through the measurement of oscillating length changes in the arm cavities. In this context, KAGRA has a unique feature due to differing compositions of its mirrors, enhancing the signal of vector DM in the length change in the auxiliary channels. Here we present the result of a search for U(1)B−L gauge boson DM using the KAGRA data from auxiliary length channels during the first joint observation run together with GEO600. By applying our search pipeline, which takes into account the stochastic nature of ultralight DM, upper bounds on the coupling strength between the U(1)B−L gauge boson and ordinary matter are obtained for a range of DM masses. While our constraints are less stringent than those derived from previous experiments, this study demonstrates the applicability of our method to the lower-mass vector DM search, which is made difficult in this measurement by the short observation time compared to the auto-correlation time scale of DM