On the surprising effectiveness of a simple matrix exponential derivative approximation, with application to global SARS-CoV-2.

The continuous-time Markov chain (CTMC) is the mathematical workhorse of evolutionary biology. Learning CTMC model parameters using modern, gradient-based methods requires the derivative of the matrix exponential evaluated at the CTMC's infinitesimal generator (rate) matrix. Motivated by the derivative's extreme computational complexity as a function of state space cardinality, recent work demonstrates the surprising effectiveness of a naive, first-order approximation for a host of problems in computational biology. In response to this empirical success, we obtain rigorous deterministic and probabilistic bounds for the error accrued by the naive approximation and establish a "blessing of dimensionality" result that is universal for a large class of rate matrices with random entries. Finally, we apply the first-order approximation within surrogate-trajectory Hamiltonian Monte Carlo for the analysis of the early spread of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) across 44 geographic regions that comprise a state space of unprecedented dimensionality for unstructured (flexible) CTMC models within evolutionary biology.

Mapping the connectivity-conflict interface to inform conservation.

Balancing the competing, and often conflicting, needs of people and wildlife in shared landscapes is a major challenge for conservation science and policy worldwide. Connectivity is critical for wildlife persistence, but dispersing animals may come into conflict with people, leading to severe costs for humans and animals and impeding connectivity. Thus, conflict mitigation and connectivity present an apparent dilemma for conservation. We present a framework to address this dilemma and disentangle the effects of barriers to animal movement and conflict-induced mortality of dispersers on connectivity. We extend random-walk theory to map the connectivity-conflict interface, or areas where frequent animal movement may lead to conflict and conflict in turn impedes connectivity. We illustrate this framework with the endangered Asian elephant Elephas maximus, a species that frequently disperses out of protected areas and comes into conflict with humans. We mapped expected movement across a human-dominated landscape over the short- and long-term, accounting for conflict mortality. Natural and conflict-induced mortality together reduced expected movement and connectivity among populations. Based on model validation, our conflict predictions that explicitly captured animal movement better explained observed conflict than a model that considered distribution alone. Our work highlights the interaction between connectivity and conflict and enables identification of location-specific conflict mitigation strategies that minimize losses to people, while ensuring critical wildlife movement between habitats. By predicting where animal movement and humans collide, we provide a basis to plan for broad-scale conservation and the mutual well-being of wildlife and people in shared landscapes.

Modeling metastatic progression from cross-sectional cancer genomics data.

MOTIVATION: Metastasis formation is a hallmark of cancer lethality. Yet, metastases are generally unobservable during their early stages of dissemination and spread to distant organs. Genomic datasets of matched primary tumors and metastases may offer insights into the underpinnings and the dynamics of metastasis formation. RESULTS: We present metMHN, a cancer progression model designed to deduce the joint progression of primary tumors and metastases using cross-sectional cancer genomics data. The model elucidates the statistical dependencies among genomic events, the formation of metastasis, and the clinical emergence of both primary tumors and their metastatic counterparts. metMHN enables the chronological reconstruction of mutational sequences and facilitates estimation of the timing of metastatic seeding. In a study of nearly 5000 lung adenocarcinomas, metMHN pinpointed TP53 and EGFR as mediators of metastasis formation. Furthermore, the study revealed that post-seeding adaptation is predominantly influenced by frequent copy number alterations. AVAILABILITY AND IMPLEMENTATION: All datasets and code are available on GitHub at https://github.com/cbg-ethz/metMHN.

Characterization of sleep efficiency transitions in family caregivers.

Family caregivers are at high risk of psychological distress and low sleep efficiency resulting from their caregiving responsibilities. Although psychological symptoms are associated with sleep efficiency, there is limited knowledge about the association of psychological distress with variations in sleep efficiency. We aimed to characterize the short- and long-term patterns of caregivers' sleep efficiency using Markov chain models and compare these patterns between groups with high and low psychological symptoms (i.e., depression, anxiety, and caregiving stress). Based on 7-day actigraphy data from 33 caregivers, we categorized sleep efficiency into three states, < 75% (S1), 75-84% (S2), and ≥ 85% (S3), and developed Markov chain models. Caregivers were likely to maintain a consistent sleep efficiency state from one night to the next without returning efficiently to a normal state. On average, it took 3.6-5.1 days to return to a night of normal sleep efficiency (S3) from lower states, and the long-term probability of achieving normal sleep was 42%. We observed lower probabilities of transitioning to or remaining in a normal sleep efficiency state (S3) in the high depression and anxiety groups compared to the low symptom groups. The differences in the time required to return to a normal state were inconsistent by symptom levels. The long-term probability of achieving normal sleep efficiency was significantly lower for caregivers with high depression and anxiety compared to the low symptom groups. Caregivers' sleep efficiency appears to remain relatively consistent over time and does not show rapid recovery. Caregivers with higher levels of depression and anxiety may be more vulnerable to sustained suboptimal sleep efficiency.

Simulating conversations: A Markov chain model of a central speaker's mnemonic influence over a group of communicating listeners.

Through their selective rehearsal, Central Speakers can reshape collective memory in a group of listeners, both by increasing accessibility for mentioned items (shared practice effects) and by decreasing relative accessibility for related but unmentioned items (socially shared retrieval induced forgetting, i.e., SSRIF). Subsequent networked communication in the group can further modify these mnemonic influences. Extant empirical work has tended to examine such downstream influences on a Central Speaker's mnemonic influence following a relatively limited number of interactions - often only two or three conversations. We develop a set of Markov chain simulations to model the long-term dynamics of such conversational remembering across a variety of group types, based on reported empirical data. These models indicate that some previously reported effects will stabilize in the long-term collective memory following repeated rounds of conversation. Notably, both shared practice effects and SSRIF persist into future steady states. However, other projected future states differ from those described so far in the empirical literature, specifically: the amplification of shared practice effects in communicational versus solo remembering non-conversational groups, the relatively transient impact of social (dis)identification with a Central Speaker, and the sensitivity of communicating networks to much smaller mnemonic biases introduced by the Central Speaker than groups of individual rememberers. Together, these simulations contribute insights into the long-term temporal dynamics of collective memory by addressing questions difficult to tackle using extant laboratory methods, and provide concrete suggestions for future empirical work.

Fitting a stochastic model of intensive care occupancy to noisy hospitalization time series during the COVID-19 pandemic.

Intensive care occupancy is an important indicator of health care stress that has been used to guide policy decisions during the COVID-19 pandemic. Toward reliable decision-making as a pandemic progresses, estimating the rates at which patients are admitted to and discharged from hospitals and intensive care units (ICUs) is crucial. Since individual-level hospital data are rarely available to modelers in each geographic locality of interest, it is important to develop tools for inferring these rates from publicly available daily numbers of hospital and ICU beds occupied. We develop such an estimation approach based on an immigration-death process that models fluctuations of ICU occupancy. Our flexible framework allows for immigration and death rates to depend on covariates, such as hospital bed occupancy and daily SARS-CoV-2 test positivity rate, which may drive changes in hospital ICU operations. We demonstrate via simulation studies that the proposed method performs well on noisy time series data and apply our statistical framework to hospitalization data from the University of California, Irvine (UCI) Health and Orange County, California. By introducing a likelihood-based framework where immigration and death rates can vary with covariates, we find, through rigorous model selection, that hospitalization and positivity rates are crucial covariates for modeling ICU stay dynamics and validate our per-patient ICU stay estimates using anonymized patient-level UCI hospital data.

Causal viewpoint and ensemble interpretation: from physics to the social sciences.

In this article, we assert that, for the construction of quantum physics-analogous (as opposed to quantum math-analogous) probabilistic models of the social (e.g. economics-financial) reality, the use of the notion of causality and the idea of an ensemble of similarly prepared systems in a socially analogous manner could be essential. We give plausibility arguments in favour of this assertion by considering two social situations describable in terms of discrete-time stochastic (i.e. Markov) processes. The first one is an arbitrary economics/financial context expressed as a temporal sequence of actualized social states (e.g. decisions, choices, preferences, etc.). The other one is more specific, involving a generic supply chain context. This article is part of the theme issue 'Thermodynamics 2.0: Bridging the natural and social sciences (Part 1)'.

Analysing ill-conditioned Markov chains.

Discrete state Markov chains in discrete or continuous time are widely used to model phenomena in the social, physical and life sciences. In many cases, the model can feature a large state space, with extreme differences between the fastest and slowest transition timescales. Analysis of such ill-conditioned models is often intractable with finite precision linear algebra techniques. In this contribution, we propose a solution to this problem, namely partial graph transformation, to iteratively eliminate and renormalize states, producing a low-rank Markov chain from an ill-conditioned initial model. We show that the error induced by this procedure can be minimized by retaining both the renormalized nodes that represent metastable superbasins, and those through which reactive pathways concentrate, i.e. the dividing surface in the discrete state space. This procedure typically returns a much lower rank model, where trajectories can be efficiently generated with kinetic path sampling. We apply this approach to an ill-conditioned Markov chain for a model multi-community system, measuring the accuracy by direct comparison with trajectories and transition statistics. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Using Markov chains and temporal alignment to identify clinical patterns in Dementia.

In the healthcare sector, resorting to big data and advanced analytics is a great advantage when dealing with complex groups of patients in terms of comorbidities, representing a significant step towards personalized targeting. In this work, we focus on understanding key features and clinical pathways of patients with multimorbidity suffering from Dementia. This disease can result from many heterogeneous factors, potentially becoming more prevalent as the population ages. We present a set of methods that allow us to identify medical appointment patterns within a cohort of 1924 patients followed from January 2007 to August 2021 in Hospital da Luz (Lisbon), and to stratify patients into subgroups that exhibit similar patterns of interaction. With Markov Chains, we are able to identify the most prevailing medical appointments attended by Dementia patients, as well as recurring transitions between these. To perform patient stratification, we applied AliClu, a temporal sequence alignment algorithm for clustering longitudinal clinical data, which allowed us to successfully identify patient subgroups with similar medical appointment activity. A feature analysis per cluster obtained allows the identification of distinct patterns and characteristics. This pipeline provides a tool to identify prevailing clinical pathways of medical appointments within the dataset, as well as the most common transitions between medical specialities within Dementia patients. This methodology, alongside demographic and clinical data, has the potential to provide early signalling of the most likely clinical pathways and serve as a support tool for health providers in deciding the best course of treatment, considering a patient as a whole.

Stochastic Reaction Networks Within Interacting Compartments.

Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on [Formula: see text], and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes, chemical and otherwise, in homogeneous environments. There are multiple avenues for generalizing away from the assumption that the environment is homogeneous, with the proper modeling choice dependent upon the context of the problem being considered. One such generalization was recently introduced in Duso and Zechner (Proc Nat Acad Sci 117(37):22674-22683 , Duso and Zechner (2020)), where the proposed model includes a varying number of interacting compartments, or cells, each of which contains an evolving copy of the stochastic reaction system. The novelty of the model is that these compartments also interact via the merging of two compartments (including their contents), the splitting of one compartment into two, and the appearance and destruction of compartments. In this paper we begin a systematic exploration of the mathematical properties of this model. We (i) obtain basic/foundational results pertaining to explosivity, transience, recurrence, and positive recurrence of the model, (ii) explore a number of examples demonstrating some possible non-intuitive behaviors of the model, and (iii) identify the limiting distribution of the model in a special case that generalizes three formulas from an example in Duso and Zechner (Proc Nat Acad Sci 117(37):22674-22683 , Duso and Zechner (2020)).

The cost-effectiveness of a virtual intervention to prevent eating disorders in young women in Sweden.

OBJECTIVE: To determine the cost-effectiveness of a virtual version of the Body Project (vBP), a cognitive dissonance-based program, to prevent eating disorders (ED) among young women with a subjective sense of body dissatisfaction in the Swedish context. METHOD: A decision tree combined with a Markov model was developed to estimate the cost-effectiveness of the vBP in a clinical trial population of 149 young women (mean age 17 years) with body image concerns. Treatment effect was modeled using data from a trial investigating the effects of vBP compared to expressive writing (EW) and a do-nothing alternative. Population characteristics and intervention costs were sourced from the trial. Other parameters, including utilities, treatment costs for ED, and mortality were sourced from the literature. The model predicted the costs and quality-adjusted life years (QALYs) related to the prevention of incidence of ED in the modeled population until they reached 25 years of age. The study used both a cost-utility and return on investment (ROI) framework. RESULTS: In total, vBP yielded lower costs and larger QALYs than the alternatives. The ROI analysis denoted a return of US $152 for every USD invested in vBP over 8 years against the do-nothing alternative and US $105 against EW. DISCUSSION: vBP is likely to be cost-effective compared to both EW and a do-nothing alternative. The ROI from vBP is substantial and could be attractive information for decision makers for implementation of this intervention for young females at risk of developing ED. PUBLIC SIGNIFICANCE: This study estimates that the vBP is cost-effective for the prevention of eating disorders among young women in the Swedish setting, and thus is a good investment of public resources.

Asymptotic behavior of mean fixation times in the Moran process with frequency-independent fitnesses.

We derive asymptotic formulae in the limit when population size N tends to infinity for mean fixation times (conditional and unconditional) in a population with two types of individuals, A and B, governed by the Moran process. We consider only the case in which the fitness of the two types do not depend on the population frequencies. Our results start with the important cases in which the initial condition is a single individual of any type, but we also consider the initial condition of a fraction [Formula: see text] of A individuals, where x is kept fixed and the total population size tends to infinity. In the cases covered by Antal and Scheuring (Bull Math Biol 68(8):1923-1944, 2006), i.e. conditional fixation times for a single individual of any type, it will turn out that our formulae are much more accurate than the ones they found. As quoted, our results include other situations not treated by them. An interesting and counterintuitive consequence of our results on mean conditional fixation times is the following. Suppose that a population consists initially of fitter individuals at fraction x and less fit individuals at a fraction [Formula: see text]. If population size N is large enough, then in the average the fixation of the less fit individuals is faster (provided it occurs) than fixation of the fitter individuals, even if x is close to 1, i.e. fitter individuals are the majority.

Operating room design using agent-based simulation to reduce room obstructions.

This study seeks to improve the safety of clinical care provided in operating rooms (OR) by examining how characteristics of both the physical environment and the procedure affect surgical team movement and contacts. We video recorded staff movements during a set of surgical procedures. Then we divided the OR into multiple zones and analyzed the frequency and duration of movement from origin to destination through zones. This data was abstracted into a generalized, agent-based, discrete event simulation model to study how OR size and OR equipment layout affected surgical staff movement and total number of surgical team contacts during a procedure. A full factorial experiment with seven input factors - OR size, OR shape, operating table orientation, circulating nurse (CN) workstation location, team size, number of doors, and procedure type - was conducted. Results were analyzed using multiple linear regression with surgical team contacts as the dependent variable. The OR size, the CN workstation location, and team size significantly affected surgical team contacts. Also, two- and three-way interactions between staff, procedure type, table orientation, and CN workstation location significantly affected contacts. We discuss implications of these findings for OR managers and for future research about designing future ORs.

Modelling a Consultant Workforce for the United Kingdom: needs-based planning for Dental Public Health.

OBJECTIVE: To develop a needs-based workforce planning model to explore specialist workforce capacity and capability for the effective, efficient, and safe provision of services in the United Kingdom (UK); and test the model using Dental Public Health (DPH). BASIC RESEARCH DESIGN: Data from a national workforce survey, national audit, and specialty workshops in 2020 and 2021 set the parameters for a safe effective DPH workforce. A working group drawing on external expertise, developed a conceptual workforce model which informed the mathematical modelling, taking a Markovian approach. The latter enabled the consideration of possible scenarios relating to workforce development. It involved exploration of capacity within each career stage in DPH across a time horizon of 15 years. Workforce capacity requirements were calculated, informed by past principles. RESULTS: Currently an estimated 100 whole time equivalent (WTE) specialists are required to provide a realistic basic capacity nationally for DPH across the UK given the range of organisations, population growth, complexity and diversity of specialty roles. In February 2022 the specialty had 53.55 WTE academic/service consultants, thus a significant gap. The modelling evidence suggests a reduction in DPH specialist capacity towards a steady state in line with the current rate of training, recruitment and retention. The scenario involving increasing training numbers and drawing on other sources of public health trained dentists whilst retaining expertise within DPH has the potential to build workforce capacity. CONCLUSIONS: Current capacity is below basic requirements and approaching 'steady state'. Retention and innovative capacity building are required to secure and safeguard the provision of specialist DPH services to meet the needs of the UK health and care systems.

Flexible transition timing in discrete-time multistate life tables using Markov chains with rewards.

Discrete-time multistate life tables are attractive because they are easier to understand and apply in comparison with their continuous-time counterparts. While such models are based on a discrete time grid, it is often useful to calculate derived magnitudes (e.g. state occupation times), under assumptions which posit that transitions take place at other times, such as mid-period. Unfortunately, currently available models allow very few choices about transition timing. We propose the use of Markov chains with rewards as a general way of incorporating information on the timing of transitions into the model. We illustrate the usefulness of rewards-based multistate life tables by estimating working life expectancies using different retirement transition timings. We also demonstrate that for the single-state case, the rewards approach matches traditional life-table methods exactly. Finally, we provide code to replicate all results from the paper plus R and Stata packages for general use of the method proposed.

Smart Preventive Maintenance of Hybrid Networks and IoT Systems Using Software Sensing and Future State Prediction.

At present, IoT and intelligent applications are developed on a large scale. However, these types of new applications require stable wireless connectivity with sensors, based on several standards of communication, such as ZigBee, LoRA, nRF, Bluetooth, or cellular (LTE, 5G, etc.). The continuous expansion of these networks and services also comes with the requirement of a stable level of service, which makes the task of maintenance operators more difficult. Therefore, in this research, an integrated solution for the management of preventive maintenance is proposed, employing software-defined sensing for hardware components, applications, and client satisfaction. A specific algorithm for monitoring the levels of services was developed, and an integrated instrument to assist the management of preventive maintenance was proposed, which are based on the network of future states prediction. A case study was also investigated for smart city applications to verify the expandability and flexibility of the approach. The purpose of this research is to improve the efficiency and response time of the preventive maintenance, helping to rapidly recover the required levels of service, thus increasing the resilience of complex systems.

Optimal timing of non-pharmaceutical interventions during an epidemic.

In response to the recent outbreak of the SARS-CoV-2 virus governments have aimed to reduce the virus's spread through, inter alia, non-pharmaceutical intervention. We address the question when such measures should be implemented and, once implemented, when to remove them. These issues are viewed through a real-options lens and we develop an SIRD-like continuous-time Markov chain model to analyze a sequence of options: the option to intervene and introduce measures and, after intervention has started, the option to remove these. Measures can be imposed multiple times. We implement our model using estimates from empirical studies and, under fairly general assumptions, our main conclusions are that: (1) measures should be put in place not long after the first infections occur; (2) if the epidemic is discovered when there are many infected individuals already, then it is optimal never to introduce measures; (3) once the decision to introduce measures has been taken, these should stay in place until the number of susceptible or infected members of the population is close to zero; (4) it is never optimal to introduce a tier system to phase-in measures but it is optimal to use a tier system to phase-out measures; (5) a more infectious variant may reduce the duration of measures being in place; (6) the risk of infections being brought in by travelers should be curbed even when no other measures are in place. These results are robust to several variations of our base-case model.

Dollar-Yuan Battle in the World Trade Network.

From the Bretton Woods agreement in 1944 till the present day, the US dollar has been the dominant currency in world trade. However, the rise of the Chinese economy has recently led to the emergence of trade transactions in Chinese yuan. Here, we mathematically analyze how the structure of international trade flows would favor a country to trade whether in US dollar or in Chinese yuan. The trade currency preference of a country is modeled as a binary variable with the properties of a spin in an Ising model. The computation of this trade currency preference is based on the world trade network built from the 2010-2020 UN Comtrade data and is determined by two multiplicative factors: the relative weight of trade volume exchanged by the country with its direct trade partners and the relative weight of its trade partners in global international trade. The performed analysis, based on the convergence of the Ising spin interactions, shows that from 2010 to present a transition took place, and the majority of the world countries would now have a preference to trade in Chinese yuan if one only considers the world trade network structure.

The Role of Gossiping in Information Dissemination over a Network of Agents.

We consider information dissemination over a network of gossiping agents. In this model, a source keeps the most up-to-date information about a time-varying binary state of the world, and n receiver nodes want to follow the information at the source as accurately as possible. When the information at the source changes, the source first sends updates to a subset of m≤n nodes. Then, the nodes share their local information during the gossiping period, to disseminate the information further. The nodes then estimate the information at the source, using the majority rule at the end of the gossiping period. To analyze the information dissemination, we introduce a new error metric to find the average percentage of nodes that can accurately obtain the most up-to-date information at the source. We characterize the equations necessary to obtain the steady-state distribution for the average error and then analyze the system behavior under both high and low gossip rates. We develop an adaptive policy that the source can use to determine its current transmission capacity m based on its past transmission rates and the accuracy of the information at the nodes. Finally, we implement a clustered gossiping network model, to further improve the information dissemination.

Fusions of Consciousness.

What are conscious experiences? Can they combine to form new experiences? What are conscious subjects? Can they combine to form new subjects? Most attempts to answer these questions assume that spacetime, and some of its particles, are fundamental. However, physicists tell us that spacetime cannot be fundamental. Spacetime, they say, is doomed. We heed the physicists, and drop the assumption that spacetime is fundamental. We assume instead that subjects and experiences are entities beyond spacetime, not within spacetime. We make this precise in a mathematical theory of conscious agents, whose dynamics are described by Markov chains. We show how (1) agents combine into more complex agents, (2) agents fuse into simpler agents, and (3) qualia fuse to create new qualia. The possible dynamics of n agents form an n(n-1)-dimensional polytope with nn vertices-the Markov polytopeMn. The total fusions of n agents and qualia form an (n-1)-dimensional simplex-the fusion simplexFn. To project the Markovian dynamics of conscious agents onto scattering processes in spacetime, we define a new map from Markov chains to decorated permutations. Such permutations-along with helicities, or masses and spins-invariantly encode all physical information used to compute scattering amplitudes. We propose that spacetime and scattering processes are a data structure that codes for interactions of conscious agents: a particle in spacetime is a projection of the Markovian dynamics of a communicating class of conscious agents.