Interacting non-BPS black holes

We explain how to exploit systematically the structure of nilpotent orbits to obtain a solvable system of equations describing extremal solutions of (super-)gravity theories, i.e. systems that can be solved in a linear way. We present the procedure in the case of the STU model, where we show that all extremal solutions with a flat three-dimensional base are fully described with the help of three different nilpotent orbits: the BPS, the almost-BPS and the composite non-BPS. The latter describes a new class of solutions for which the orientation of half of the constituent branes have been inverted with respect to the BPS one, such that all the centres are intrinsically non-BPS, and interact with each others. We finally recover explicitly the ensemble of the almost-BPS solutions in our formalism and present an explicit two-centre solution of the new class.Comment: 49 page

Symmetric indefinite triangular factorization revealing the rank profile matrix

We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} = \mathbf{L}\mathbf{D}\mathbf{L}^T$ where $\mathbf{P}$ is a permutation matrix, $\mathbf{L}$ is lower triangular with a unit diagonal and $\mathbf{D}$ is symmetric block diagonal with $1{\times}1$ and $2{\times}2$ antidiagonal blocks. The novel algorithm requires $O(n^2r^{\omega-2})$ arithmetic operations. Furthermore, experimental results demonstrate that our algorithm can even be slightly more than twice as fast as the state of the art unsymmetric Gaussian elimination in most cases, that is it achieves approximately the same computational speed. By adapting the pivoting strategy developed in the unsymmetric case, we show how to recover the rank profile matrix from the permutation matrix and the support of the block-diagonal matrix. There is an obstruction in characteristic $2$ for revealing the rank profile matrix which requires to relax the shape of the block diagonal by allowing the 2-dimensional blocks to have a non-zero bottom-right coefficient. This relaxed decomposition can then be transformed into a standard $\mathbf{P}\mathbf{L}\mathbf{D}\mathbf{L}^T\mathbf{P}^T$ decomposition at a negligible cost

On fast multiplication of a matrix by its transpose

We present a non-commutative algorithm for the multiplication of a 2x2-block-matrix by its transpose using 5 block products (3 recursive calls and 2 general products) over C or any finite field.We use geometric considerations on the space of bilinear forms describing 2x2 matrix products to obtain this algorithm and we show how to reduce the number of involved additions.The resulting algorithm for arbitrary dimensions is a reduction of multiplication of a matrix by its transpose to general matrix product, improving by a constant factor previously known reductions.Finally we propose schedules with low memory footprint that support a fast and memory efficient practical implementation over a finite field.To conclude, we show how to use our result in LDLT factorization.Comment: ISSAC 2020, Jul 2020, Kalamata, Greec

Training an interactive humanoid robot using multimodal deep reinforcement learning

Training robots to perceive, act and communicate using multiple modalities still represents a challenging problem, particularly if robots are expected to learn efficiently from small sets of example interactions. We describe a learning approach as a step in this direction, where we teach a humanoid robot how to play the game of noughts and crosses. Given that multiple multimodal skills can be trained to play this game, we focus our attention to training the robot to perceive the game, and to interact in this game. Our multimodal deep reinforcement learning agent perceives multimodal features and exhibits verbal and non-verbal actions while playing. Experimental results using simulations show that the robot can learn to win or draw up to 98% of the games. A pilot test of the proposed multimodal system for the targeted game---integrating speech, vision and gestures---reports that reasonable and fluent interactions can be achieved using the proposed approach

On fast multiplication of a matrix by its transpose

We present a non-commutative algorithm for the multiplication of a block-matrix by its transpose over C or any finite field using 5 recursive products. We use geometric considerations on the space of bilinear forms describing 2×2 matrix products to obtain this algorithm and we show how to reduce the number of involved additions. The resulting algorithm for arbitrary dimensions is a reduction of multiplication of a matrix by its transpose to general matrix product, improving by a constant factor previously known reductions. Finally we propose space and time efficient schedules that enable us to provide fast practical implementations for higher-dimensional matrix products

Preference Dissemination by Sharing Viewpoints: Simulating Serendipity

IC3K 2015 will be held in conjunction with IJCCI 2015International audienceThe Web currently stores two types of content. These contents include linked data from the semantic Web and user contributions from the social Web. Our aim is to represent simplified aspects of these contents within a unified topological model and to harvest the benefits of integrating both content types in order to prompt collective learning and knowledge discovery. In particular, we wish to capture the phenomenon of Serendipity (i.e., incidental learning) using a subjective knowledge representation formalism, in which several " viewpoints " are individually interpretable from a knowledge graph. We prove our own Viewpoints approach by evidencing the collective learning capacity enabled by our approach. To that effect, we build a simulation that disseminates knowledge with linked data and user contributions, similar to the way the Web is formed. Using a behavioral model configured to represent various Web navigation strategies, we seek to optimize the distribution of preference systems. Our results outline the most appropriate strategies for incidental learning, bringing us closer to understanding and modeling the processes involved in Serendipity. An implementation of the Viewpoints formalism kernel is available. The underlying Viewpoints model allows us to abstract and generalize our current proof of concept for the indexing of any type of data set

A race against the clock: Constraining the timing of cometary bombardment relative to Earth's growth

Comets are considered a potential source of inner solar system volatiles, but the timing of this delivery relative to that of Earth's accretion is still poorly understood. Measurements of xenon isotopes in comet 67P/Churyumov-Gerasimenko revealed that comets partly contributed to the Earth's atmosphere. However, there is no conclusive evidence of a significant cometary component in the Earth's mantle. These geochemical constraints would favour a contribution of comets mainly occurring after the last stages of Earth's formation. Here, we evaluate whether dynamical simulations satisfy these constraints in the context of an Early Instability model. We perform dynamical simulations of the solar system, calculate the probability of collision between comets and Earth analogs component embryos through time and estimate the total cometary mass accreted in Earth analogs as a function of time. While our results are in excellent agreement with geochemical constraints, we also demonstrate that the contribution of comets on Earth might have been delayed with respect to the timing of the instability, due to a stochastic component of the bombardment. More importantly, we show that it is possible that enough cometary mass has been brought to Earth after it had finished forming so that the xenon constraint is not necessarily in conflict with an Early Instability scenario. However, it appears very likely that a few comets were delivered to Earth early in its accretion history, thus contributing to the mantle's budget. Finally, we compare the delivery of cometary material on Earth to Venus and Mars. These results emphasize the stochastic nature of the cometary bombardment in the inner solar system.Comment: 26 pages, 12 figure

Subject-variability effects on micron particle deposition in human nasal cavities

Validated computer simulations of the airflow and particle dynamics in human nasal cavities are important for local, segmental and total deposition predictions of both inhaled toxic and therapeutic particles. Considering three, quite different subject-specific nasal airway configurations, micron-particle transport and deposition for low-to-medium flow rates have been analyzed. Of special interest was the olfactory region from which deposited drugs could readily migrate to the central nervous system for effective treatment. A secondary objective was the development of a new dimensionless group with which total particle deposition efficiency curves are very similar for all airway models, i.e., greatly reducing the impact of intersubject variability. Assuming dilute particle suspensions with inhalation flow rates ranging from 7.5 to 20 L/min, the airflow and particle-trajectory equations were solved in parallel with the in-house, multi-purpose Alya program at the Barcelona Supercomputing Center. The geometrically complex nasal airways generated intriguing airflow fields where the three subject models exhibit among them both similar as well as diverse flow structures and wall shear stress distributions, all related to the coupled particle transport and deposition. Nevertheless, with the new Stokes-Reynolds-number group, , the total deposition-efficiency curves for all three subjects and flow rates almost collapsed to a single function. However, local particle deposition efficiencies differed significantly for the three subjects when using particle diameters = 2, 10, and . Only one of the three subject-specific olfactory regions received, at relatively high values of the inertial parameter , some inhaled microspheres. Clearly, for drug delivery to the brain via the olfactory region, a new method of directional inhalation of nanoparticles would have to be implemented.The authors acknowledge Dr. Rick Corley and colleagues at Pacific Northwest National Laboratory for providing the subject B nasal surface geometry and Dr. Edgar Matida and Dr. Matthew Johnson at Carleton University for providing the subject C nasal surface geometryPeer ReviewedPostprint (published version

Investigating the influence of (Deoxy)fluorination on the lipophilicity of non-UV-active fluorinated alkanols and carbohydrates by a new log P determination method

Property tuning by fluorination is very effective for a number of purposes, and currently increasingly investigated for aliphatic compounds. An important application is lipophilicity (log?P) modulation. However, the determination of log?P is cumbersome for non-UV-active compounds. A new variation of the shake-flask log?P determination method is presented, enabling the measurement of log?P for fluorinated compounds with or without UV activity regardless of whether they are hydrophilic or lipophilic. No calibration curves or measurements of compound masses/aliquot volumes are required. With this method, the influence of fluorination on the lipophilicity of fluorinated aliphatic alcohols was determined, and the log?P values of fluorinated carbohydrates were measured. Interesting trends and changes, for example, for the dependence on relative stereochemistry, are reporte