A new formulation of compartmental epidemic modelling for arbitrary distributions of incubation and removal times

The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are more flexible, yet do not allow for arbitrary distributions. We present a new formulation, focussing on the SEIR concept that allows to include general distributions of incubation and removal times. We compare the solution to two types of agent-based model simulations, a spatially homogeneous one where infection occurs by proximity, and a model on a scale-free network with varying clustering properties, where the infection between any two agents occurs via their link if it exists. We find good agreement in both cases. Furthermore a family of asymptotic solutions of the equations is found in terms of a logistic curve, which after a non-universal time shift, fits extremely well all the microdynamical simulations. The formulation allows for a simple numerical approach; software in Julia and Python is provided.Comment: 21 pages, 11 figures. v2 matches published version: improved presentation (including title, abstract and references), results and conclusions unchange

Non-perturbative running of quark masses in three-flavour QCD

We present our preliminary results for the computation of the non-perturbative running of renormalized quark masses in $N_f = 3$ QCD, between the electroweak and hadronic scales, using standard finite-size scaling techniques. The computation is carried out to very high precision, using massless $\mathcal{O}(a)$-improved Wilson quarks. Following the strategy adopted by the ALPHA Collaboration for the running coupling, different schemes are used above and below a scale $\mu_0 \sim m_b$, which differ by using either the Schr\"odinger Functional or Gradient Flow renormalized coupling. We discuss our results for the running in both regions, and the procedure to match the two schemes.Comment: 7 pages, 3 figures, 34th annual International Symposium on Lattice Field Theor

Prospects and status of quark mass renormalization in three-flavour QCD

We present the current status of a revised strategy to compute the running of renormalized quark masses in QCD with three flavours of massless O(a) improved Wilson quarks. The strategy employed uses the standard finite-size scaling method in the Schr\"odinger functional and accommodates for the non-perturbative scheme-switch which becomes necessary at intermediate renormalized couplings as discussed in [arXiv:1411.7648].Comment: 7 pages, 3 figures, 1 table; Proceedings of the 33rd International Symposium on Lattice Field Theory, 14-18 July 2015, Kobe, Japa

Non-perturbative quark mass renormalisation and running in Nf=3N_f=3 QCD

We determine from first principles the quark mass anomalous dimension in Nf=3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and non-perturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless O(a)-improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with O(a)-improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about 1%.Comment: 41 pages, 10 tables, 7 figures, published version (minimal text improvements

Train Timetable Design for Shared Railway Systems using a Linear Programming Approach to Approximate Dynamic Programming

In the last 15 years, the use of rail infrastructure by different train operating companies (shared railway system) has been proposed as a way to improve infrastructure utilization and to increase efficiency in the railway industry. Shared use requires coordination between the infrastructure manager and multiple train operators in a competitive framework, so that regulators must design appropriate capacity pricing and allocation mechanisms. However, the resulting capacity utilization from a given mechanism in the railway industry cannot be known in the absence of operations. Therefore assessment of capacity requires the determination of the train timetable, which eliminates any potential conflicts in bids from the operators. Although there is a broad literature that proposes train timetabling methods for railway systems with single operators, there are few models for shared competitive railway systems. This paper proposes a train timetabling model for shared railway systems that explicitly considers network effects and the existence of multiple operators requesting to operate several types of trains traveling along different routes in the network. The model is formulated and solved both as a mixed integer linear programming (MILP) problem (using a commercial solver) and as a dynamic programming (DP) problem. We solve the DP formulation with a novel algorithm based on a linear programming (LP) approach to approximate dynamic programming (ADP) that can solve much larger problems than are computationally intractable with commercial MILP solvers. The model simulates the optimal decisions by an infrastructure manager for a shared railway system with respect to a given objective function and safety constraints. This model can be used to evaluate alternative capacity pricing and allocation mechanism. We demonstrate the method for one possible capacity pricing and allocation mechanism, and show how the competing demands and the decisions of the infrastructure manager under this mechanism impact the operations on a shared railway system for all stakeholders

An approximate dynamic programming approach for designing train timetables

Traditional approaches to solving the train timetabling problem—the optimal allocation of when each train arrives and departs each station—have relied on Mixed-Integer Programming (MIP) approaches. We propose an alternative formulation for this problem based on the modeling and algorithmic framework of approximate dynamic programming. We present a Q-learning algorithm in order to tractably solve the high-dimensional problem. We compare the performance of several variants of this approach, including discretizing the state and the action spaces, and continuous function approximation with global basis functions. We demonstrate the algorithms on two railway system cases, one minimizing energy consumption subject to punctuality constraints, and one maximizing capacity subject to safety constraints. We demonstrate that the ADP algorithm converges rapidly to an optimal solution, and that the number of iterations required increases linearly in the size of the rail system, in contrast with MIP approaches whose computation time grows exponentially. We also show that an additional benefit to the ADP approach is the intuition gained from visualizing the Q-factor functions, which graphically capture the intuitive tradeoffs between efficiency and constraints in both examples

Rail Infrastructure Manager Problem: Analyzing Capacity Pricing and Allocation in Shared Railway System

This paper proposes a train timetabling model for shared railway systems. The model is formulated as a mixed integer linear programming problem and solved both using commercial software and a novel algorithm based on approximate dynamic programming. The results of the train timetabling model can be used to simulate and evaluate the behavior of the infrastructure manager in shared railway systems under different capacity pricing and allocation mechanisms. This would allow regulators and decision makers to identify the implications of these mechanisms for different stakeholders considering the specific characteristics of the system

Home care routing and scheduling problem with teams’ synchronization

Funding Information: This work is funded by Portuguese funds through the FCT - Fundação para a Ciência e a Tecnologia , I.P., under the scope of the projects UIDB/00297/2020 (Center for Mathematics and Applications), UIDB/00097/2020 (CEGIST), and the PhD scholarship grant SFRH/BD/148773/2019 . Publisher Copyright: © 2023 The AuthorsThe demand for home care (HC) services has steadily been growing for two main types of services: healthcare and social care. If, for the former, caregivers' skills are of utter importance, in the latter caregivers are not distinguishable in terms of skills. This work focuses social care and models caregivers' synchronization as a means of improving human resources management. Moreover, in social care services, several visits need to be performed in the same day since patients are frequently alone and need assistance throughout the day. Depending on the patient's autonomy, some tasks have to be performed by two caregivers (e.g. assist bedridden patients). Therefore, adequate decision support tools are crucial for assisting managers (often social workers) when designing operational plans and to efficiently assign caregivers to tasks. This paper advances the literature by 1) considering teams of one caregiver that can synchronize to perform tasks requiring two caregivers (instead of having teams of two caregivers), 2) simultaneously modelling daily continuity of care and teams' synchronization, and 3) associating dynamic time windows to teams' synchronizations introducing scheduling flexibility while minimize service and travel times. These concepts are embedded into a daily routing and scheduling MIP model, deciding on the number of caregivers and on the number and type of teams to serve all patient tasks. The main HC features of the problem, synchronization and continuity of care, are evaluated by comparing the proposed planning with the current situation of a home social care service provider in Portugal. The results show that synchronization is the feature that most increases efficiency with respect to the current situation. It evidences a surplus in working time capacity by proposing plans where all requests can be served with a smaller number of caregivers. Consequently, new patients from long waiting lists can now be served by the “available” caregivers.publishersversionpublishe

Non-perturbative quark mass renormalisation and running in Nf = 3 QCD

We determine from first principles the quark mass anomalous dimension in Nf= 3 QCD between the electroweak and hadronic scales. This allows for a fully non-perturbative connection of the perturbative and non-perturbative regimes of the Standard Model in the hadronic sector. The computation is carried out to high accuracy, employing massless O(a)-improved Wilson quarks and finite-size scaling techniques. We also provide the matching factors required in the renormalisation of light quark masses from lattice computations with O(a)-improved Wilson fermions and a tree-level Symanzik improved gauge action. The total uncertainty due to renormalisation and running in the determination of light quark masses in the SM is thus reduced to about 1