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 presents a research survey on the Home Health Care. It is a way of caring for patients who suffer from complex, non-serious diseases and especially evolutionary ones. At their homes, they benefit from medical and paramedical cares that can be only provided by hospitals. This form of treatment has a positive impact on both the patients and the state. To study its evolution as well as its development and to understand the difference in this new mode of care, we have devoted the first part of this investigation for the home health care history. In the second part, based on official data published on the websites of the European and American States, we have analyzed home health care centers, the most recognized ones at the national and internal levels, to distinguish similarities and differences between them and especially to determine their specifications and limitations. To overcome the latter, it is necessary to dig new leads of research; that is why the founders of these institutions have resorted to scientists. The third section covers the state of the art since the 70s. In this part, we have depicted the research work that contributed to resolve home health care problems.

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 the French context of the health expenses control, the operating theatre planning, that represents 9% of hospital's annual budget, presents a stake of first importance. The realization of the operating theatre planning is the fruit of the negotiation between the different actors of the block whose constraints and interests are often different. In this paper, we propose an algorithm of construction of an estimable planning, based on constraints satisfaction programming and whose objective is the minimization of the risk of no realization (RNR) of the planning. We present the results obtained at the time of the implementation of this model on a whole scenario of interventions to plan. Finally, we simulate the proposed planning in order to study the variations of RNR: robustness indicator and other performance productivity indicators.