Emergency Departments (EDs) must operate in environments characterized by uncertainty and resource constraints. One of their critical challenges is dual-resource scheduling, that is, synchronizing two resources at the same time on a task. For example, taking a blood sample from a child patient requires two nurses, one to take the sample and another to prevent the patient from moving. Addressing this challenge requires structured approaches capable of ensuring both synchronization and prioritization based on patient urgency. This study explores two distinct optimization models for dual-resource scheduling in EDs, namely, a Mixed Integer Linear Programming (MILP) and a Constraint Programming (CP). The MILP model leverages a linear formulation to globally optimize scheduling and resource synchronization, while the CP model exploits constraint satisfaction techniques to handle task dependencies and resource constraints. We test both models on the same case study. Their comparison highlights key differences in computational complexity, variable representation and constraint formulation. The results demonstrate that neither model consistently outperforms the other, but rather, their effectiveness depends on instance size and problem-specific characteristics.

The Emergency Department (ED) is a principal sector in the hospital that has to make crucial decisions effectively under uncertainties to ensure that the patients receive good quality care. Improving decision-making in ED, especially the resource scheduling decision, becomes one research interest. A promising approach to improve decision-making is by utilising Digital Twin (DT). This context of decision-making in DT is both (i) an opportunity given by the DT which provides data close to real-time and (ii) constrained by the DT which forces to make decisions dynamically rather than statically. That is, our research contributes to the decision layer of DT. More precisely, we propose a decentralised organisation to enhance the resource scheduling decision-making process in ED. This is a multi-agent system with a local dynamic resource scheduling based on a Mixed Integer Linear Programming (MILP) model. This proposition is compared to two other organisations, which are a centralised organisation that optimises the dynamic scheduling MILP globally, and the FIFO sequencing currently performed in the paediatric ED of the University Hospital Centre in Saint-Étienne, France. The results show that the proposed decentralised organisation provides good results quickly and seems promising for improving resource scheduling decision-making in ED with DT support. Note to Practitioners—This research provides an initial study on the approach to improve the decision-making process in the Emergency Department (ED) of the hospital by using Digital Twin (DT). We focus more on improving resource scheduling decisions, which is a part of the decision layer of DT. We propose a decentralised organisation based on a multi-agent approach for solving the resource scheduling problem. Each resource agent, i.e. nurse, can run a local dynamic resource scheduling based on a Mixed Integer Linear Programming (MILP) model. Through our proposition with a centralised model and current practice in ED based on the triage-based First in First Out (FIFO) rule, we can see that our decentralised organisation is a favourable decision organisation in the context of decision improvement with DT, as it is capable of providing favourable results in a short time. This research will be further extended by including different resources and tasks in ED to make the model closer to reality in ED.

Improving the resolution of a VRP instance often requires knowledge extracted from the instance itself. However, very little work focuses on analyzing or exploiting the topology of the point cloud associated with this instance. In this work, we aim to fill this gap by proposing the characterization of generators of the homological group of the VRP instance that represent natural cycles (tours). To improve the connection between these generators representing tours and optimal or exact tours, we morphologically deform the point cloud of the instance before-hand. The results obtained are clearly encouraging, showing a strong connection between generators obtained by polynomially bounded complexity and optimal or exact tours.

Clustering is an unsupervised machine learning method giving insights on data without early knowledge. Classes of data are return by assembling similar elements together. Giving the increasing of the available data, this method is now applied in a lot of fields with various data types. Here, we propose to explore the case of time series clustering. Indeed, time series are one of the most classic data type, and are present in various fields such as medical or finance. This kind of data can be pre-processed by of dimension reduction methods, such as the recent UMAP algorithm. In this paper, a benchmark of time series clustering is created, comparing the results with and without UMAP as a pre-processing step. UMAP is used to enhance clustering results. For completeness, three different clustering algorithms and two different geometric representation for the time series (Classic Euclidean geometry, and Riemannian geometry on the Stiefel Manifold) are applied. The results are compared with and without UMAP as a pre-processing step on the databases available at UCR Time Series Classification Archive www.cs.ucr.edu/~eamonn/time_series_data/.

Giving process information through spectral considerations has been tackled for decades. We propose, in this paper, a new way of dealing with such an objective by giving hidden information topology of the spectral measure of non-stationary and periodically correlated processes. We used first the Kolmogorov decomposition which is a natural extension of the Naimark operator theory to obtain a sequence of rotation matrices called the dilation matrices. These matrices carry all the spectral information of the process and belong to SO(n) or SU(n) with respect to, respectively, the real or complex nature of the periodically correlated processes studied. In order to give a topological interpretation of the positioning of these matrices on the space of rotation matrices, we have applied a persistent homology technique and next exposed fundamental attributes. We showed that different types of periodically correlated processes are endowed with a point cloud structure that can be easily discriminated by topological and information features.

Excessive admissions at the emergency department (ED) is a phenomenon very closely linked to the propagation of viruses. It is a cause of overcrowding for EDs and a public health problem. The aim of this work is to give EDs' leaders more time for decision making during this period. Based on the admissions time series associated with specific clinical diagnoses, we will first perform a detrended fluctuation analysis to obtain the corresponding variability time series. Next, we will embed this time series on a manifold to obtain a point cloud representation and use topological data analysis through persistent homology technic to propose two early real-time indicators. One is the early indicator of abnormal arrivals at the ED whereas the second gives the information on the time index of the maximum number of arrivals. The performance of the detectors is parameter dependent and it can evolve each year. That is why we also propose to solve a biobjective optimization problem to track the variations of this parameter.

This paper focuses on the estimation of voltage sags in three-phase power systems. Specifically, it proposes a new approach for estimating the amplitude and phase angle of the sag based on the Unconditional Maximum Likelihood technique. As opposed to other techniques, this approach is well suited for signals with amplitude and/or phase modulation such as those encountered in smart grid applications. Simulation and experimental results illustrate the effectiveness of the proposed approach.

When epidemics occur, such as is the case for bronchiolitis in the Pediatric Emergency Department (ED), the patient flow in the ED incontestably increases and can lead to crowding. We bypassed this difficulty of forecasting patient flow with aggregated weekly or monthly data by tackling the problem from a different point of view. We used daily data to build a multiperiod Serfling-based model. This model is hereinafter assimilated to normal ED flow. We then used the fourth-order moment of distribution of the time series, obtained from the difference between the estimated model and the real data, to provide an early index announcing abnormal ED patient flow. This index is parameter-dependent and we provide criterion to assist in selecting the optimal parameters. A simple program based on this methodology has been developed and has been given to the pediatric physicians for testing. Thanks to this index, the Pediatric ED was able to anticipate crowding almost three weeks before the height of the bronchiolitis epidemic.

In certain direction-of-arrival (DOA) estimation scenarios some of the source directions are known to the operator even before measurements are acquired. It is then undesirable to use regular DOA-algorithms which waste data-samples estimating the known directions. Additionally, in some applications it is known that the signals emanating from the known directions are uncorrelated with those coming from the unknown directions. In this article we present a novel algorithm which exploits the combination of such prior knowledge in a manner more efficient (in terms of accuracy) than any algorithm known to the authors. Through numerical Monte-Carlo simulations we show the estimator to attain the theoretical accuracy bound for significantly lower signal-to-noise ratios than current state-of-the-art methods. Additionally we show the proposed algorithm to treat the stricter problem of entirely uncorrelated emitters better than current state of the art.

Recently, an optimal Prior-knowledge method for DOA estimation has been proposed. This method solely estimates a subset of DOA's accounting known ones. The global idea is to maximize the orthogonality between an estimated signal subspace and noise subspace by constraining the orthogonal noise-made projector to only project onto the desired unknown signal subspace. As it could be surprising, no deflation process is used for. Understanding how it is made possible needs to derive the variance for the DOA estimates. During the derivation, oblique projection operators and their first order derivatives appear and are needed. Those operators show in consequence how the optimal Prior-knowledge criterion can focus only on DOA's of interest and how the optimality is reached.

In certain applications involving direction of arrival (DOA) estimation the operator may have a-priori information on some of the DOAs. This information could refer to a target known to be present at a certain position or to a reflection. In this study, the authors investigate a methodology for array processing that exploits the information on the known DOAs for estimating the unknown DOAs as accurately as possible. Algorithms are presented that can efficiently handle the case of both correlated and uncorrelated sources when the receiver is a uniform linear array. The authors find a major improvement in estimator accuracy in feasible scenarios, and they compare the estimator performance to the corresponding theoretical stochastic Cramér–Rao bounds as well as to the performance of other methods capable of exploiting such prior knowledge. In addition, real data from an ultra-sound array is applied to the investigated estimators.

In a number of direction of arrival (DOA) estimation applications there exists prior knowledge about the sources whose bearings are to be determined. We study the case when this prior information concerns some of the source positions and their correlation state, which is a relevant case in, for example, RADAR scenarios where stationary objects exists in the regions of interest. Traditional DOA methods are not designed to exploit such information, and thus cannot obtain the highest theoretical accuracy. We present a method that can utilize in an asymptotically efficient manner both knowledge on some source positions and that the source signals are uncorrelated.

In the context of the direction-of-arrival (DOA) estimation problem, we can sometimes assume the a priori knowledge of M-S DOA among M. Some authors have propose to incorporate this a priori knowledge to better estimate the DOA of interest (ie., the unknown ones). In a previous work, the authors have proposed two prior MinNorm schemes based on oblique projection which allow the integration of this prior-knowledge. In particular, numerical and theoretical expressions of the variances have been derived. In this work, we go further into the analysis already given. We first focus on the asymptotic (large number of sensors) behavior of the standard, the constrained and the prior versions of the MinNorm algorithm and we show that in this case the exploitation of a prior-knowledge is not beneficial. Next, we derive closed-form approximations of the variance of these algorithms in case of two closely-spaced sources for small/moderate number of sensors and we show that the prior-MinNorm algorithms based on oblique projection is much more insensitive to the proximity of the DOA as compared to the standard and the constrained MinNorm algorithms. Finally, these theoretical analysis are checked against computer simulations by means of Monte-Carlo runs.

Many works has been made in the context of the recursive or sequential MUSIC algorithm for bearing estimation. Indeed, in some difficult scenarios as for closely spaced bearings, correlated sources and at low SNRs, the accuracy of the MUSIC algorithm can be improved by sequentially cancel the previous estimated bearings. In this paper, we propose a new algorithm, called zero-forcing based sequential MUSIC, which efficiently tackles this problem.