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We develop the theory of Energy Conserving Descent (ECD) and introduce ECDSep, a gradient-based optimization algorithm able to tackle convex and non-convex optimization problems. The method is based on the novel ECD framework of optimization as physical evolution of a suitable chaotic energy-conserving dynamical system, enabling analytic control of the distribution of results - dominated at low loss - even for generic high-dimensional problems with no symmetries. Compared to previous realizations of this idea, we exploit the theoretical control to improve both the dynamics and chaos-inducing elements, enhancing performance while simplifying the hyper-parameter tuning of the optimization algorithm targeted to different classes of problems. We empirically compare with popular optimization methods such as SGD, Adam and AdamW on a wide range of machine learning problems, finding competitive or improved performance compared to the best among them on each task. We identify limitations in our analysis pointing to possibilities for additional improvements., Comment: 15 pages + appendices, full code available

Let $G$ be a non-compact classical semisimple Lie group and let $G/V$ be the adjoint orbit with respect to a fixed element in $G$. These manifolds can be equipped with an almost-K\"ahler structure and we provide explicit formulae for the existence of special almost-complex structures on $G/V$ purely in terms of the combinatorics of the associated Vogan diagram. The formulae are given separately for Lie groups whose Lie algebras are of type $A_{\ell}$, $B_{\ell}$, $C_{\ell}$, $D_{\ell}$, where $\ell$ denotes the rank of the Lie algebra., Comment: 28 pages

BACKGROUND: Considering the growing genitourinary (GU) cancer population undergoing systemic treatment with immune checkpoint inhibitors (ICIs) in the context of the COVID-19 pandemic, we planned a clinical audit in 24 Italian institutions treating GU malignancies. OBJECTIVE: The primary objective was investigating the clinical impact of COVID-19 in GU cancer patients undergoing ICI-based therapy during the first outbreak of SARS-CoV-2 contagion in Italy. DESIGN, SETTING, AND PARTICIPANTS: The included centers were 24 Oncology Departments. Two online forms were completed by the responsible Oncology Consultants, respectively, for metastatic renal cell carcinoma (mRCC) and metastatic urothelial carcinoma (mUC) patients receiving at least one administration of ICIs between 31 January 2020 and 30 June 2020. RESULTS AND LIMITATION: In total, 287 mRCC patients and 130 mUC patients were included. The COVID-19 incidence was, respectively, 3.5%, with mortality 1%, in mRCC patients and 7.7%, with mortality 3.1%, in mUC patients. In both groups, 40% of patients developing COVID-19 permanently discontinued anticancer treatment. The pre-test SARS-CoV-2 probability in the subgroup of patients who underwent nasal/pharyngeal swab ranged from 14% in mRCC to 26% in mUC. The main limitation of the work was its nature of audit: data were not recorded at the single-patient level. CONCLUSION: GU cancer patients undergoing active treatment with ICIs have meaningful risk factors for developing severe events from COVID-19 and permanent discontinuation of therapy after the infection. Treatment delays due to organizational issues during the pandemic were unlikely to affect the treatment outcome in this population.

We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented using SAGE graph convolution layers, and trained using an advantage actor critic (A2C) agent. We present two variants, one for finding an edge separator that minimizes the normalized cut or quotient cut, and one that finds a small vertex separator. The vertex separators are then used to construct a nested dissection ordering to permute a sparse matrix so that its triangular factorization will incur less fill-in. The partitioning quality is compared with partitions obtained using METIS and SCOTCH, and the nested dissection ordering is evaluated in the sparse solver SuperLU. Our results show that the proposed method achieves similar partitioning quality as METIS and SCOTCH. Furthermore, the method generalizes across different classes of graphs, and works well on a variety of graphs from the SuiteSparse sparse matrix collection.

We study the almost Kaehler geometry of adjoint orbits of non-compact real semisimple Lie groups endowed with the Kirillov-Kostant-Souriau symplectic form and a canonically defined almost complex structure. We give explicit formulas for the Chern-Ricci form, the Hermitian scalar curvature and the Nijenhuis tensor in terms of root data. We also discuss when the Chern-Ricci form is a multiple of the symplectic form, and when compact quotients of these orbits are of Kaehler type., 42 pages. Exposition improved. Appendix enhanced with more tables and more data. Many typos fixed

This report finds its origin in the observation of the activities implemented (operated) within the framework of the courts (courses, prices, yards) of biology of a sixth year of high school ASSP. We realized that many pupil of this class feels (experiences) difficulties of understanding in biology. Furthermore it seems that the skills of communication in the reference table of the high school diploma Support (Accompaniment) Care and human services are not necessarily to work within the framework of the training(formation) during the courts (courses, prices, yards) on the high school. We thus set up the tutelage between peers because he allows to individualize the transmission of the knowledges, to take into account more the difficulties of each, to answer the difficulties of understanding but also to work the skills in communication. Indeed by activating the expression of the knowledge and the exchange the tutelage thus allows to organize the mental activity and to structure and to develop so its capacities of communication. This shape of tutelage can be formalized or not and we thus are to ask in what the diverse forms of tutelage allow to develop the skills of communications specific to the pupils of the Tub(Ferry,High school diploma) ASSP? To verify this hypothesis we thus built a questionnaire of self-assessment of the skills in communication allowing to see the global evolution and by sub-skill (sub-competence) of communication to refine the understanding of the impact of the diverse forms of tutelage. We subjected (submitted) this questionnaire upstream and downstream to the implementation of the device(plan). The results (profits) show us contrary to our hypotheses of departure that the formal tutelage does not improve the global skills in communication and that the reduction is essentially due to the sub-skills "production and search (research) for feedback of understanding" and "capacities to detect incoherence". The informal tutelage allows to improve the global skills and more specifically the sub-skills "métacognition" and the capacities to detect incoherence. Both train(form) some tutelage improve the sub-skill (sub-competence) "perception (collection) of one in the group". Certainly that the too stiff frame of the formal tutelage locks every pupil into a role (guardian or tutored) to the detriment of the relation between peers. It stays in an asymmetric relation which does not facilitate the interactions and thus the development of the skills.; Ce mémoire trouve son origine dans l’observation des activités mises en œuvre dans le cadre des cours de biologie d’une classe de première ASSP. Nous nous sommes rendu compte que beaucoup d’élève de cette classe éprouve des difficultés de compréhension en biologie. De plus il apparait que les compétences de communication dans le référentiel du baccalauréat Accompagnement Soins et services à la personne ne sont pas forcément travailler dans le cadre de la formation pendant les cours au lycée. Nous avons donc mis en place le tutorat entre pairs car il permet d’individualiser la transmission des savoirs, de prendre davantage en compte les difficultés de chacun, de répondre aux difficultés de compréhension mais aussi de travailler les compétences en communication. En effet en activant l’expression du savoir et l’échange le tutorat permet donc d’organiser l’activité mentale et de structurer et de développer ainsi ses capacités de communication. Cette forme de tutorat peut être formalisé ou non et nous nous sommes donc demander en quoi les diverses formes de tutorat permettent de développer les compétences de communications spécifiques aux élèves du Bac ASSP ? Pour vérifier cette hypothèse nous avons donc construit un questionnaire d’autoévaluation des compétences en communication permettant de voir l’évolution globale et par sous-compétence de communication pour affiner la compréhension de l’impact des diverses formes de tutorat. Nous avons soumis ce questionnaire en amont et en aval de la mise en place du dispositif. Les résultats nous montrent contrairement à nos hypothèses de départ que le tutorat formel n’améliore pas les compétences globales en communication et que la baisse est essentiellement due aux sous-compétences « production et recherche de feedback de compréhension » et « capacités à détecter des incohérences ». Le tutorat informel permet d’améliorer les compétences globales et plus spécifiquement les sous-compétences « métacognition » et capacités à détecter des incohérences. Les deux forment du tutorat améliore la sous-compétence « perception de soi dans le groupe ». Certainement que le cadre trop rigide du tutorat formel enferme chaque élève dans un rôle (tuteur ou tutoré) au détriment de la relation entre pairs. Il reste dans une relation asymétrique qui ne facilite pas les interactions et donc le développement des compétences.