Algorithms and Lower Bounds for De Morgan Formulas of Low-Communication Leaf Gates

The class FORMULA[s]∘G consists of Boolean functions computable by size- s De Morgan formulas whose leaves are any Boolean functions from a class G. We give lower bounds and (SAT, Learning, and pseudorandom generators ( PRG s )) algorithms for FORMULA[n 1.99 ]∘G, for classes G of functions with low communication complexity . Let R (k) G be the maximum k -party number-on-forehead randomized communication complexity of a function in G. Among other results, we show the following: • The Generalized Inner Product function GIP k n cannot be computed in FORMULA[s]° G on more than 1/2+ε fraction of inputs for s=o(n 2 /k⋅4 k ⋅R (k) (G)⋅log⁡(n/ε)⋅log⁡(1/ε)) 2 ). This significantly extends the lower bounds against bipartite formulas obtained by [62]. As a corollary, we get an average-case lower bound for GIP k n against FORMULA[n 1.99 ]∘PTF k −1 , i.e., sub-quadratic-size De Morgan formulas with degree-k-1) PTF ( polynomial threshold function ) gates at the bottom. Previously, it was open whether a super-linear lower bound holds for AND of PTFs. • There is a PRG of seed length n/2+O(s⋅R (2) (G)⋅log⁡(s/ε)⋅log⁡(1/ε)) that ε-fools FORMULA[s]∘G. For the special case of FORMULA[s]∘LTF, i.e., size- s formulas with LTF ( linear threshold function ) gates at the bottom, we get the better seed length O(n 1/2 ⋅s 1/4 ⋅log⁡(n)⋅log⁡(n/ε)). In particular, this provides the first non-trivial PRG (with seed length o(n)) for intersections of n halfspaces in the regime where ε≤1/n, complementing a recent result of [45]. • There exists a randomized 2 n-t #SAT algorithm for FORMULA[s]∘G, where t=Ω(n\√s⋅log 2 ⁡(s)⋅R (2) (G))/1/2. In particular, this implies a nontrivial #SAT algorithm for FORMULA[n 1.99 ]∘LTF. • The Minimum Circuit Size Problem is not in FORMULA[n 1.99 ]∘XOR; thereby making progress on hardness magnification, in connection with results from [14, 46]. On the algorithmic side, we show that the concept class FORMULA[n 1.99 ]∘XOR can be PAC-learned in time 2 O(n/log n) .

Integrity monitoring for precise orbit determination of LEO satellites

Due to an increasing requirement for high accuracy orbital information for low Earth orbit (LEO) satellites, precise orbit determination (POD) of LEO satellites is a topic of growing interest. To assure the safety and reliability of the applications requiring high accuracy LEO orbits in near-real-time, integrity monitoring (IM) is an essential operation of the POD process. In this contribution, the IM strategy for LEO POD in both the kinematic and reduced-dynamic modes is investigated. The overbounding parameters of the signal-in-space range error are investigated for the GPS products provided by the International GNSS Service’s Real-Time Service and the Multi-GNSS Advanced Demonstration of Orbit and Clock Analysis service. Benefiting from the dynamic models used and the improved model strength, the test results based on the data of the LEO satellite GRACE FO-1 show that the average-case mean protection levels (PLs) can be reduced from about 3–4 m in the kinematic mode to about 1 m in the reduced-dynamic mode in the radial, along-track and cross-track directions. The overbounding mean values of the SISRE play the dominant role in the final PLs. In the reduced-dynamic mode and average-case projection, the IM availabilities reach above 99% in the radial, along-track and cross-track directions with the alert limit (AL) set to 2 m. The values are still above 98% with the AL set to 4 m, when the duty cycle of tracking is reduced to 40%, e.g., in the case of power limits for miniature satellites such as CubeSats.

Socio-economic substantiation of expediency of seasonal influenza vaccine prophylaxis among medical workers

The purpose of this study is to determine the socio-economic effectiveness of seasonal influenza vaccine prophylaxis among health professionals based on the analysis of the morbidity with temporal disability (MTD) and the financial benefits of this preventive measure. The study included the collection and analysis of information on MTD and direct and indirect costs of influenza treatment compared to vaccine prophylaxis in “Dnipropetrovsk Regional Perinatal Center with Hospital” Dnipropetrovsk Regional Council” (ME “DRPC with Hospital” DRC”) during 2017-2020 (3 epidemic seasons). To assess the consequences of vaccine prophylaxis, the analysis of MTD indicators was performed, and the index and coefficient of anti-epidemic effectiveness were used. The economic effect was determined on the basis of the cost-benefit method using the analysis algorithm in the form of a “decision tree”. The information base for the analysis was the accounting and reporting and financial and economic documentation of the health care institution (HCI). The analysis of influenza MTD during the observation period revealed that all studied morbidity rates (number of cases per 100 employees; number of days per 100 employees; average case duration) were statistically significantly lower in vaccinated compared to unvaccinated (p<0.001). Precautionary number of cases of MTD for influenza in the last year of observation (2019-2020) was 11.07 (95% CI 6.68-15.46) per 100 employees; days – 96.23 (95% CI 81.86-110.60) per 100 employees. The index of anti-epidemic efficiency during the study increased by 2.37 (95% CI 1.95-2.79), the coefficient of anti-epidemic effectiveness – by 15.16% (95% CI 11.17-18.01). The economic efficiency of vaccination of 69.44% of employees for one epidemic season (2019-2020) amounted to a total of UAH 248,976 or UAH 494 (56%) benefits per employee. The study proved the high medical, social and economic effectiveness of vaccine prophylaxis in HCI. Medical efficiency consists in a significant reduction in the morbidity with temporary disability, high levels and a tendency to increase the indicators of anti-epidemic efficiency. The economic effect is defined as the available monetary benefit from the vaccine prophylaxis. The resulting savings are the basis for optimizing the use of resources of the medical institution, including labor.

Trends in Surgical Case Volume During Pacific Partnership Missions Onboard USNS Mercy

ABSTRACT Introduction Since 2006, the U.S. Navy has conducted six Pacific Partnership (PP) missions throughout Southeast Asia on board the U.S. Naval Ship Mercy (T-AH 19). This study describes trends in overall and surgical specialty operative volumes to better understand the burden of surgical disease treated during these humanitarian and civic assistance (HCA) operations. This information can assist medical planners and surgical leaders involved in future humanitarian missions. Materials and Methods Following approval from the Naval Medical Center San Diego Institutional Review Board, a retrospective review of surgical case data was performed for the six PP missions from 2006 to 2018. Data collected included patient demographics, Current Procedural Terminology codes, and surgical specialty. The primary outcome was surgical case volume per specialty. Secondary outcomes included surgical staffing per mission and overall trends in operative volume. Results A total of 3,826 operative procedures were performed during the study period. Mission years in which case volume for both general surgery and ophthalmology were below their respective medians were associated with the least total surgical services to host nations (HNs). The number of active duty Navy surgeons varied with each mission; however, the staffing for a PP mission generally included at least two general surgeons, one ophthalmologist, one plastic surgeon, one pediatric surgeon, one orthopedic surgeon, one otolaryngologist, one oral surgeon, one urologist, and one obstetrician–gynecologist. Case volume per surgeon was highest in 2006 (50 cases per surgeon) and decreased after 2006, reaching an all-time low during the 2018 PP mission (10 cases per surgeon). Pediatric surgery and plastic surgery had the highest average case volumes per surgeon at 58 and 46 cases per surgeon, respectively, while oromaxillofacial surgery and neurosurgery had the lowest average case volumes per surgeon at 9 and 14 cases per surgeon, respectively. Conclusions Operative volume on military HCA missions is greatly influenced by the priorities of the HN, the mission focus, the number of individuals from the HN that present for screening, and the availability of personnel and resources available on the hospital ship. Future mission planning should optimize general surgery and ophthalmology staffing and essential equipment, as total mission case volumes were highly dependent upon the productivity of these two specialties. Careful determination of the surgical needs of HNs should serve as a guide for the selection of subspecialists to maximize effectiveness in future military HCA missions.

Explaining Neighbourhood Variations in the Incidence of Dengue Fever in Jeddah City, Saudi Arabia

The rapid growth and development of cities is a contributing factor to the rise and persistence of dengue fever (DF) in many areas around the world. Many studies have examined how neighbourhood environmental conditions contribute to dengue fever and its spread, but have not paid enough attention to links between socio-economic conditions and other factors, including population composition, population density, the presence of migrant groups, and neighbourhood environmental conditions. This study examines DF and its distribution across 56 neighbourhoods of Jeddah City, Saudi Arabia, where the incidence of dengue remains high. Using stepwise multiple regression analysis it focuses on the key ecological correlates of DF from 2006-2009, the years of the initial outbreak. Neighbourhood variations in average case rates per 10,000 population (2006–2009) were largely predicted by the Saudi gender ratio and socio-economic status (SES), the respective beta coefficients being 0.56 and 0.32 (p < 0.001). Overall, 77.1% of cases occurred in the poorest neighbourhoods. SES effects, however, are complex and were partly mediated by neighbourhood population density and the presence of migrant groups. SES effects persisted after controls for both factors, suggesting the effect of other structural factors and reflecting a lack of DF awareness and the lack of vector control strategies in poorer neighbourhoods. Neighbourhood environmental conditions, as measured by the presence of surface water, were not significant. It is suggested that future research pay more attention to the different pathways that link neighbourhood social status to dengue and wider health outcomes.

COVID-19 Pandemic: Public Health Risk Assessment and Risk Mitigation Strategies

A newly emerged respiratory viral disease called severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) is also known as pandemic coronavirus disease (COVID-19). This pandemic has resulted an unprecedented global health crisis and devastating impact on several sectors of human lives and economies. Fortunately, the average case fatality ratio for SARS-CoV-2 is below 2%, much lower than that estimated for MERS (34%) and SARS (11%). However, COVID-19 has a much higher transmissibility rate, as evident from the constant increase in the count of infections worldwide. This article explores the reasons behind how COVID-19 was able to cause a global pandemic crisis. The current outbreak scenario and causes of rapid global spread are examined using recent developments in the literature, epidemiological features relevant to public health awareness, and critical perspective of risk assessment and mitigation strategies. Effective pandemic risk mitigation measures have been established and amended against COVID-19 diseases, but there is still much scope for upgrading execution and coordination among authorities in terms of organizational leadership’s commitment and diverse range of safety measures, including administrative control measures, engineering control measures, and personal protective equipment (PPE). The significance of containment interventions against the COVID-19 pandemic is now well established; however, there is a need for its effective execution across the globe, and for the improvement of the performance of risk mitigation practices and suppression of future pandemic crises.

Memory and communication efficient algorithm for decentralized counting of nodes in networks

Node counting on a graph is subject to some fundamental theoretical limitations, yet a solution to such problems is necessary in many applications of graph theory to real-world systems, such as collective robotics and distributed sensor networks. Thus several stochastic and naïve deterministic algorithms for distributed graph size estimation or calculation have been provided. Here we present a deterministic and distributed algorithm that allows every node of a connected graph to determine the graph size in finite time, if an upper bound on the graph size is provided. The algorithm consists in the iterative aggregation of information in local hubs which then broadcast it throughout the whole graph. The proposed node-counting algorithm is on average more efficient in terms of node memory and communication cost than its previous deterministic counterpart for node counting, and appears comparable or more efficient in terms of average-case time complexity. As well as node counting, the algorithm is more broadly applicable to problems such as summation over graphs, quorum sensing, and spontaneous hierarchy creation.