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This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for regulatory networks, and the class of functions studied here captures a key feature of biological network dynamics, namely that a subset of one or more variables, under certain conditions, can dominate the value of a Boolean function, to the exclusion of all others. These functions have rich mathematical properties to be explored. The paper shows how the number and type of such sets influence a function's behavior and define a new measure for the canalizing strength of any Boolean function. We further connect the concept of collective canalization with the well-studied concept of the average sensitivity of a Boolean function. The relationship between Boolean functions and the dynamics of the networks they form is important in a wide range of applications beyond biology, such as computer science, and has been studied with statistical and simulation-based methods. But the rich relationship between structure and dynamics remains largely unexplored, and this paper is intended as a contribution to its mathematical foundation., Comment: 17 pages, 3 figures

People are more likely to interact with other people of their ethnicity—a phenomenon known as ethnic homophily. In the United States, people of color are known to hold proportionately more high-contact jobs and are thus more at risk of virus infection. At the same time, these ethnic groups are on average younger than the rest of the population. This gives rise to interesting disease dynamics and non-trivial trade-offs that should be taken into consideration when developing prioritization strategies for future mass vaccine roll-outs.Here, we study the spread of COVID-19 through the U.S. population, stratified by age, ethnicity, and occupation, using a detailed, previously-developed compartmental disease model. Based on historic data from the U.S. mass COVID-19 vaccine roll-out that began in December 2020, we show, (i) how ethnic homophily affects the choice of optimal vaccine allocation strategy, (ii) that, notwithstanding potential ethical concerns, differentiating by ethnicity in these strategies can improve outcomes (e.g., fewer deaths), and (iii) that the most likely social context in the United States is very different from the standard assumptions made by models which do not account for ethnicity and this difference affects which allocation strategy is optimal.HighlightsA social mixing model accounting for ethnic homophily and variable job-related risk level is developed.A scenario that differs strongly from standard homogeneous mixing assumptions best matches U.S. ethnicity-specific death and case counts.Two trade-offs are explored: Should (i) old or young, and (ii) people of color or White and Asian people first receive COVID-19 vaccines?Exhaustive simulation of a compartmental disease model identifies the optimal allocation strategy for different demographic groups.Optimal strategies depend on the underlying mixing pattern and strategies that differentiate vaccine access by ethnicity outperform others.

Serosurveys are an important tool to estimate the true extent of the current SARS-CoV-2 pandemic. So far, most serosurvey data have been analyzed with cutoff-based methods, which dichotomize individual measurements into sero-positives or negatives based on a predefined cutoff. However, mixture model methods can gain additional information from the same serosurvey data. Such methods refrain from dichotomizing individual values and instead use the full distribution of the serological measurements from pre-pandemic and COVID-19 controls to estimate the cumulative incidence. This study presents an application of mixture model methods to SARS-CoV-2 serosurvey data from the SEROCoV-POP study from April and May 2020 in Geneva (2766 individuals). Besides estimating the total cumulative incidence in these data (8.1% (95% CI: 6.8%–9.9%)), we applied extended mixture model methods to estimate an indirect indicator of disease severity, which is the fraction of cases with a distribution of antibody levels similar to hospitalized COVID-19 patients. This fraction is 51.2% (95% CI: 15.2%–79.5%) across the full serosurvey, but differs between three age classes: 21.4% (95% CI: 0%–59.6%) for individuals between 5 and 40 years old, 60.2% (95% CI: 21.5%–100%) for individuals between 41 and 65 years old and 100% (95% CI: 20.1%–100%) for individuals between 66 and 90 years old. Additionally, we find a mismatch between the inferred negative distribution of the serosurvey and the validation data of pre-pandemic controls. Overall, this study illustrates that mixture model methods can provide additional insights from serosurvey data., Epidemics, 39, ISSN:1878-0067, ISSN:1755-4365

BackgroundAnticipating an initial shortage of vaccines for COVID-19, the Centers for Disease Control (CDC) in the United States developed priority vaccine allocations for specific demographic groups in the population. This study evaluates the performance of the CDC vaccine allocation strategy with respect to multiple potentially competing vaccination goals (minimizing mortality, cases, infections, and years of life lost (YLL)), under the same framework as the CDC allocation: four priority vaccination groups and population demographics stratified by age, comorbidities, occupation and living condition (congested or non-congested).MethodsWe developed a compartmental disease model that incorporates key elements of the current pandemic including age-varying susceptibility to infection, age-varying clinical fraction, an active case-count dependent social distancing level, and time-varying infectivity (accounting for the emergence of more infectious virus strains). Under this model, the CDC allocation strategy is compared to all other possibly optimal allocations that stagger vaccine roll-out in up to four phases (17.5 million strategies).ResultsThe CDC allocation strategy performed well in all vaccination goals but never optimally. Under the developed model, the CDC allocation deviated from the optimal allocations by small amounts, with 0.19% more deaths, 4.0% more cases, 4.07% more infections, and 0.97% higher YLL, than the respective optimal strategies. The CDC decision to not prioritize the vaccination of individuals under the age of 16 was optimal, as was the prioritization of health-care workers and other essential workers over non-essential workers. Finally, a higher prioritization of individuals with comorbidities in all age groups improved outcomes compared to the CDC allocation.InterpretationThe developed approach can be used to inform the design of future vaccine allocation strategies in the United States, or adapted for use by other countries seeking to optimize the effectiveness of their vaccine allocation strategies.FundingThe authors received no funding for this work.Research in contextEvidence before this studyThe Centers for Disease Control and Prevention (CDC) prioritized population groups for vaccination based on available scientific evidence, the feasibility of different implementation strategies, and ethical considerations. We searched PubMed using the query “(((COVID) AND (vaccin*)) AND (model)) AND ((priorit*) OR alloc*)” up to June 15, 2021, with no date or language restrictions. The search identified 190 articles, of which 15 used predictive models to evaluate the efficacy of vaccine allocation strategies in achieving vaccination campaign goals such as reducing mortality or incidence. All studies compared only a small number of specific, expertise-based allocations. Most studies stratified the population by age, while some considered additional characteristics such as occupation or comorbidity status, but none took into account all characteristics included in the CDC vaccine prioritizations.Added value of this studyWe developed a compartmental disease model that takes into account several important components of the COVID-19 pandemic, and stratifies the U.S. population by all characteristics included in the CDC vaccine prioritization recommendations. In a novel global optimization approach, we compared the CDC recommendations to all potentially optimal strategies (17.5 million strategies) that also stagger the vaccine roll-out in four phases. The CDC allocation strategy performed well in all considered outcome measures, but never optimally; a higher prioritization of individuals with comorbidities in all age groups improved outcomes. The CDC decision to initially not vaccinate children, as well as the prioritization of health-care workers and other essential workers over non-essential workers proved optimal under all outcome measures.Implications of all the available evidenceOur study identifies and compares the optimal vaccine allocation strategies for several competing vaccination goals. The developed global optimization approach can be used to inform the design of future vaccine allocation strategies in the United States and elsewhere.

This paper provides a collection of mathematical and computational tools for the study of robustness in nonlinear gene regulatory networks, represented by time- and state-discrete dynamical systems taking on multiple states. The focus is on networks governed by nested canalizing functions (NCFs), first introduced in the Boolean context by S. Kauffman. After giving a general definition of NCFs we analyze the class of such functions. We derive a formula for the normalized average $c$-sensitivities of multistate NCFs, which enables the calculation of the Derrida plot, a popular measure of network stability. We also provide a unique canonical parametrized polynomial form of NCFs. This form has several consequences. We can easily generate NCFs for varying parameter choices, and derive a closed form formula for the number of such functions in a given number of variables, as well as an asymptotic formula. Finally, we compute the number of equivalence classes of NCFs under permutation of variables. Together, the results of the paper represent a useful mathematical framework for the study of NCFs and their dynamic networks., Comment: 15 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1304.3707

The European project broadband radio access for IP-based networks (BRAIN) investigates system concepts to provide wireless broadband access to a new QoS-based Internet. As basis for the BRAIN radio access, HiperLAN/2 (H/2) is considered. In this paper, we propose functions enhancing the H/2 radio interface to support IP QoS. The focus is on the system ability to schedule the various connections dedicated for IP traffic according to their QoS requirements, whereby the specific characteristics of the wireless access such as transmission error control (EC) and link adaptation will be taken into account.

In order to gain better understanding of the mechanistic pathway leading to chain propagation and termination in Fischer-Tropsch type reactions, complexes with sp 3 -and sp 2 -hybridized carbon-metal bonds were reacted with carbon monoxide and mixtures of hydrogen and carbon monoxide. In all our experiments only the insertion of one CO was observed. The second part of this paper deals with homogeneous hydrogenation of carbon monoxide at high pressures. Clusters and complexes of Group VIII elements of the Periodic Table were used as catalysts. A variety of oxygenated compounds such as methyl formate, methyl acetate, ethyl formate, methanol, ethanol, n-propyl alcohol, propylene glycols, ethylene glycol and glycerine was formed to varying degrees. The mechanism of the cobalt catalyzed reactions is discussed and non-cluster but bimetallic intermediates are proposed for the key steps.

The reactions of the anionic carbene complexes [(CO)nMCOPh]- (M = Fe, Cr, Mo, W) with ethene are described. The iron and chromium complexes yield predominantly propiophenone, formed by ethene insertion into the MCOPh moiety. For instance, [cis-PPh3(CO)4CrCOPh][Li · 2Et2O] gave 63% yield of propiophenone. At 150°C, a double insertion of ethene, leading to CH3CH2CH(CH3)COPh, is observed. At this temperature products incorporating an odd number of carbon atoms, viz.: CH3CH2CH2COPh, CH3CH(CH3)COPh, CH3CH2CH2CH(CH3)COPh are also formed and have been isolated in up to 15% yield; a metathetic reaction path and ethene insertion are proposed to account for their formation.