Philippe Robert

A Hawkes process on R is a point process whose intensity function at time t is a functional of its past activity before time t. It is defined by its activation function Φ and its memory function h. In this paper, the Hawkes property is expressed as an operator on the sub-space of non-negative sequences associated to distances between its points. By using the classical correspondence between a stationary point process and its Palm measure, we establish a characterization of the corresponding Palm measure as an invariant distribution of a Markovian kernel. We prove that if Φ is continuous and its growth rate is at most linear with a rate below some constant, then there exists a stationary Hawkes point process. The classical Lipschitz condition of the literature for an unbounded function Φ is relaxed. Our proofs rely on a combination of coupling methods, monotonicity properties of linear Hawkes processes and classical results on Palm distributions. An investigation of the Hawkes process starting from the null measure, the empty state, on R− plays also an important role. The linear case of Hawkes and Oakes is revisited at this occasion. If the memory function h is an exponential function, under a weak condition it is shown that there exists a unique stationary Hawkes point process. In this case, its Palm measure is expressed in terms of the invariant distribution of a one-dimensional Harris ergodic Markov chain. When the activation function is a polynomial Φ with degree >1, there does not exist a stationary Hawkes process and if the Hawkes process starts from the empty state, a scaling result for the accumulation of its points is obtained.

Background: Apathy is a clinical syndrome, associated with numerous adverse outcomes, which is pervasive in neurocognitive disorders. Neural bases of apathy rest on dysfunctions of brain structures involved in initiation, execution and control of goal directed behavior, and notably implicate dysfunction of cognitive functions which are required to generate plan of actions. Cognitive training has shown efficacious effects in mild cognitive disorders, and non‐invasive brain stimulation seems to be a promising intervention for cognition and neuropsychiatric symptoms, as suggested by the benefit effects found on depression. The aim of this study is to assess the effectiveness of repeated sessions of computerized serious game‐based cognitive training combined with transcranial direct current stimulation (tDCS) on apathy among older adults with neurocognitive disorders.Method: The study is an ongoing double‐blind randomized controlled trial. Patients are randomized into a 4‐week intervention of computerized “MeMo” serious game‐based cognitive training combined with either sham or active tDCS. The 4‐week intervention comprise 3 sessions per week, with 20 minutes of cognitive training plus simultaneously sham or active tDCS targeting the left dorsolateral prefrontal cortex with a 2mA of current intensity. The main outcome was the apathy, assessed using the Apathy Diagnostic Criteria, the Apathy Inventory and the self‐reported Apathy Motivation Index questionnaire. Secondary outcomes are cognitive performances, fatigue and daily motor activity.Result: Preliminary results of the ongoing study will be presented during the AAIC.Conclusion: These results will provide new evidence about the interest to use combined cognitive training and tDCS as neurorehabilitation intervention, for cognition and apathy treatment in mild neurocognitive disorders.

Background: PTSD and NCD have common symptoms such as mood disorders (depressive symptoms, aggressivity, etc.) or cognitive disorders (executive dysfunctionning, amnesia, etc.). Due to these similarities, and because existing tools are not suitable for this population specificities, PTSD diagnosis may be difficult. Based on the existing literature, a new screening tool was created, allowing a hetero assessment of PTSD for this population. This study consists in explaining the development and the pre‐testing of our new tool, following specific scale development guidelines.Method: A research was conducted to analyze the inventory construct which allowed us to analyze over 50 tools and create our items. An expert panel assessed the first version, which was used in a protocol conducted with 44 participants suffering from NCD.Result: First, the tool was modified consequently to the expert panel’s review, for a total of 15 domains with 4 at 8 items. Cronbach’s alpha and Pearson’s correlation enlightened good reliability when tested with the 44 participants (inventory’s Cronbach’s alpha = 0.75). By the end of the pilot testing, 13 domains composed of 70 items were kept.Conclusion: The different validation steps lead to the creation of a new hetero‐assessing tool with specific PTSD items and suitable to a population with NCD. Domains will gauge both the symptoms frequency and impact. According to literature, this tool will focus on DSM‐5 criteria A, B and E. The next step will be to analyze the PTSD with NCD Inventory’s psychometric properties.