On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

From music to mathematics and backwards: introducing algebra, topology and category theory into computational musicology

International audienceDespite a long historical relationship between mathematics and music, the interest of mathematicians is a recent phenomenon. In contrast to statistical methods and signal-based approaches currently employed in MIR (Music Information Research), the research project described in this paper stresses the necessity of introducing a structural multidisciplinary approach into computational musicology making use of advanced mathematics. It is based on the interplay between three main mathematical disciplines: algebra, topology and category theory. It therefore opens promising perspectives on important prevailing challenges, such as the automatic classification of musical styles or the solution of open mathematical conjectures, asking for new collaborations between mathematicians, computer scientists, musicologists, and composers. Music can in fact occupy a strategic place in the development of mathematics since music-theoretical constructions can be used to solve open mathematical problems. The SMIR project also differs from traditional applications of mathematics to music in aiming to build bridges between different musical genres, ranging from contemporary art music to popular music, including rock, pop, jazz and chanson. Beyond its academic ambition, the project carries an important societal dimension stressing the cultural component of 'mathemusical' research, that naturally resonates with the underlying philosophy of the “Imagine Maths”conference series. The article describes for a general public some of the most promising interdisciplinary research lines of this project

Perceptual impairment and psychomotor control in virtual laparoscopic surgery

Background: It is recognised that one of the major difficulties in performing laparoscopic surgery is the translation of two-dimensional video image information to a three-dimensional working area. However, research has tended to ignore the gaze and eye-hand coordination strategies employed by laparoscopic surgeons as they attempt to overcome these perceptual constraints. This study sought to examine if measures related to tool movements, gaze strategy, and eye-hand coordination (the quiet eye) differentiate between experienced and novice operators performing a two-handed manoeuvres task on a virtual reality laparoscopic surgical simulator (LAP Mentor™). Methods: Twenty-five right-handed surgeons were categorised as being either experienced (having led more than 60 laparoscopic procedures) or novice (having performed fewer than 10 procedures) operators. The 10 experienced and 15 novice surgeons completed the "two-hand manoeuvres" task from the LAP Mentor basic skills learning environment while wearing a gaze registration system. Performance, movement, gaze, and eye-hand coordination parameters were recorded and compared between groups. Results: The experienced surgeons completed the task significantly more quickly than the novices, used significantly fewer movements, and displayed shorter tool paths. Gaze analyses revealed that experienced surgeons spent significantly more time fixating the target locations than novices, who split their time between focusing on the targets and tracking the tools. A more detailed analysis of a difficult subcomponent of the task revealed that experienced operators used a significantly longer aiming fixation (the quiet eye period) to guide precision grasping movements and hence needed fewer grasp attempts. Conclusion: The findings of the study provide further support for the utility of examining strategic gaze behaviour and eye-hand coordination measures to help further our understanding of how experienced surgeons attempt to overcome the perceptual difficulties inherent in the laparoscopic environment. © 2011 The Author(s).published_or_final_versionSpringer Open Choice, 21 Feb 201

Psychomotor control in a virtual laparoscopic surgery training environment: gaze control parameters differentiate novices from experts

Background: Surgical simulation is increasingly used to facilitate the adoption of technical skills during surgical training. This study sought to determine if gaze control parameters could differentiate between the visual control of experienced and novice operators performing an eye-hand coordination task on a virtual reality laparoscopic surgical simulator (LAP Mentor™). Typically adopted hand movement metrics reflect only one half of the eye-hand coordination relationship; therefore, little is known about how hand movements are guided and controlled by vision. Methods: A total of 14 right-handed surgeons were categorised as being either experienced (having led more than 70 laparoscopic procedures) or novice (having performed fewer than 10 procedures) operators. The eight experienced and six novice surgeons completed the eye-hand coordination task from the LAP Mentor basic skills package while wearing a gaze registration system. A variety of performance, movement, and gaze parameters were recorded and compared between groups. Results: The experienced surgeons completed the task significantly more quickly than the novices, but only the economy of movement of the left tool differentiated skill level from the LAP Mentor parameters. Gaze analyses revealed that experienced surgeons spent significantly more time fixating the target locations than novices, who split their time between focusing on the targets and tracking the tools. Conclusion: The findings of the study provide support for the utility of assessing strategic gaze behaviour to better understand the way in which surgeons utilise visual information to plan and control tool movements in a virtual reality laparoscopic environment. It is hoped that by better understanding the limitations of the psychomotor system, effective gaze training programs may be developed. © 2010 The Author(s).published_or_final_versionSpringer Open Choice, 01 Dec 201

Conscious monitoring and control (reinvestment) in surgical performance under pressure.

Research on intraoperative stressors has focused on external factors without considering individual differences in the ability to cope with stress. One individual difference that is implicated in adverse effects of stress on performance is "reinvestment," the propensity for conscious monitoring and control of movements. The aim of this study was to examine the impact of reinvestment on laparoscopic performance under time pressure

Gaze training enhances laparoscopic technical skill acquisition and multi-tasking performance: A randomized, controlled study

Background: The operating room environment is replete with stressors and distractions that increase the attention demands of what are already complex psychomotor procedures. Contemporary research in other fields (e.g., sport) has revealed that gaze training interventions may support the development of robust movement skills. This current study was designed to examine the utility of gaze training for technical laparoscopic skills and to test performance under multitasking conditions. Methods: Thirty medical trainees with no laparoscopic experience were divided randomly into one of three treatment groups: gaze trained (GAZE), movement trained (MOVE), and discovery learning/control (DISCOVERY). Participants were fitted with a Mobile Eye gaze registration system, which measures eye-line of gaze at 25 Hz. Training consisted of ten repetitions of the "eye-hand coordination" task from the LAP Mentor VR laparoscopic surgical simulator while receiving instruction and video feedback (specific to each treatment condition). After training, all participants completed a control test (designed to assess learning) and a multitasking transfer test, in which they completed the procedure while performing a concurrent tone counting task. Results: Not only did the GAZE group learn more quickly than the MOVE and DISCOVERY groups (faster completion times in the control test), but the performance difference was even more pronounced when multitasking. Differences in gaze control (target locking fixations), rather than tool movement measures (tool path length), underpinned this performance advantage for GAZE training. Conclusions: These results suggest that although the GAZE intervention focused on training gaze behavior only, there were indirect benefits for movement behaviors and performance efficiency. Additionally, focusing on a single external target when learning, rather than on complex movement patterns, may have freed-up attentional resources that could be applied to concurrent cognitive tasks. © 2011 The Author(s).published_or_final_versionSpringer Open Choice, 21 Feb 201