186,617 research outputs found
Statistical inference for Bures-Wasserstein barycenters
No full textIn this work we introduce the concept of Bures--Wasserstein barycenter , that is essentially a Fréchet mean of some distribution supported on a subspace of positive semi-definite -dimensional Hermitian operators . We allow a barycenter to be constrained to some affine subspace of , and we provide conditions ensuring its existence and uniqueness. We also investigate convergence and concentration properties of an empirical counterpart of in both Frobenius norm and Bures--Wasserstein distance, and explain, how the obtained results are connected to optimal transportation theory and can be applied to statistical inference in quantum mechanics
Place navigation in rats guided by a vestibular and kinesthetic orienting gradient.
No full textThe role of the slope of terrain in orientation was examined in rats trained to find, among 4 equidistant feeders, the 1 located in the upper left quadrant of a 10% tilted arena (1-m radius). Rats started from the center in light and with randomly changing slope direction reached the correct goal in 90% of 1st choices after 29 sessions. The same rats maintained 83% correct choices when the experiment was conducted in darkness. On a horizontal arena, their performance became random. After training, successful navigation was also observed (71% correct 1st choices) when the rats were started from different points at about 30 cm from the wall. This finding suggests that the slope of terrain may be used to establish a cognitive map based primarily on kinesthetic and vestibular signals. The flexibility of such a map seems to be rather limited, however, because changing the goal position with respect to inclination requires prolonged retraining
Exact Bures probabilities that two quantum bits are classically correlated
No full textIn previous studies, we have explored the ansatz that the volume
elements of the Bures metrics over
quantum systems
might serve as prior distributions, in analogy with the
(classical) Bayesian role of the volume elements ("Jeffreys' priors")
of Fisher information metrics.
Continuing this work, we obtain exact Bures prior
probabilities that the members of
certain low-dimensional subsets of the fifteen-dimensional
convex set of
density matrices are separable
or classically
correlated.
The main analytical tools employed are symbolic integration and
a formula of Dittmann (J. Phys. A 32, 2663 (1999))
for Bures metric
tensors.
This study complements an earlier one (J. Phys. A 32,
5261 (1999)) in which numerical
(randomization) -but not integration -methods
were used to estimate Bures separability probabilities for
unrestricted
and density matrices.
The exact values adduced here for pairs of quantum bits (qubits),
typically, well exceed the estimate () there, but
this disparity may be attributable to our
focus on special low-dimensional subsets.
Quite remarkably, for
the q= 1 and states inferred using the
principle of maximum nonadditive (Tsallis)
entropy, the Bures probabilities
of separability are both equal to .
For the Werner qubit-qutrit
and qutrit-qutrit
states, the probabilities
are vanishingly small, while in the qubit-qubit case it is
Cahier de Bures (Paris)
No full textCahier de Bures (Paris). In: Archives Parlementaires de 1787 à 1860 - Première série (1787-1799) sous la direction de Emile Laurent et Jérôme Mavidal. Tome IV - Etats généraux ; Cahiers des sénéchaussées et bailliages. Paris : Librairie Administrative P. Dupont, 1879. pp. 383-385
Cahier de Bures (Paris)
No full textCahier de Bures (Paris). In: Archives Parlementaires de 1787 à 1860 - Première série (1787-1799) sous la direction de Emile Laurent et Jérôme Mavidal. Tome IV - Etats généraux ; Cahiers des sénéchaussées et bailliages. Paris : Librairie Administrative P. Dupont, 1879. pp. 383-385
Genome size and GC Content Evolution of Festuca: Ancestral Expansion and Subsequent Reduction.
No full text† Background and Aims Plant evolution is well known to be frequently associated with remarkable changes in genome size and composition; however, the knowledge of long-term evolutionary dynamics of these processes still remains very limited. Here a study is made of the fine dynamics of quantitative genome evolution in Festuca (fescue), the largest genus in Poaceae (grasses).
† Methods Using flow cytometry (PI, DAPI), measurements were made of DNA content (2C-value), monoploid genome size (Cx-value), average chromosome size (C/n-value) and cytosine þ guanine (GC) content of 101 Festuca taxa and 14 of their close relatives. The results were compared with the existing phylogeny based on ITS and trnL-F sequences.
† Key Results The divergence of the fescue lineage from related Poeae was predated by about a 2-fold monoploid genome and chromosome size enlargement, and apparent GC content enrichment. The backward reduction of these parameters, running parallel in both main evolutionary lineages of fine-leaved and broad-leaved fescues, appears to diverge among the existing species groups. The most dramatic reductions are associated with the most recently and rapidly evolving groups which, in combination with recent intraspecific genome size variability, indicate that the reduction process is probably ongoing and evolutionarily young. This dynamics may be a consequence of GCrich
retrotransposon proliferation and removal. Polyploids derived from parents with a large genome size and high GC content (mostly allopolyploids) had smaller Cx- and C/n-values and only slightly deviated from parental GC content, whereas polyploids derived from parents with small genome and low GC content (mostly autopolyploids) generally had a markedly increased GC content and slightly higher Cx- and C/n-values.
†Conclusions The present study indicates the high potential of general quantitative characters of the genome for understanding the long-term processes of genome evolution, testing evolutionary hypotheses and their usefulness for large-scale genomic projects. Taken together, the results suggest that there is an evolutionary advantage for small genomes in Festuca
Applications of the Bures-Wasserstein Distance in Linear Metric Learning
No full textMetric Learning has proved valuable in information retrieval and classification problems, with many algorithms using statistical formulations to their advantage. Optimal Transport, a powerful framework for computing distances between probability distributions, has seen significant uptake in Machine Learning and some applications in Metric Learning. The Bures-Wasserstein distance, a particular formulation of Optimal Transport, has seen limited application in Metric Learning despite being well suited to the field. In this thesis Linear Metric Learning algorithms incorporating the Bures-Wasserstein distance are developed, utilising its novel properties. The first set of algorithms we contribute use the Bures-Wasserstein distance for learning linear metrics using Cyclic Projections, Riemannian barycenters and gradient-based algorithms. The convergence properties and classification performance of these algorithms are then compared to benchmark Linear Metric Learning algorithms. Our algorithms achieve competitive classification performance on feature and image datasets and converge reliability.
The second set of contributions extend Linear Metric Learning with the Bures-Wasserstein distance to a low-rank context to address issues related to scalability. An extension of the previous Cyclic Projections algorithm and a Riemannian optimisation method are developed. Convergence and classification experiments analogous to the full-rank case are conducted to examine how the reduced rank affects both of these performance metrics. Both algorithms converge reliably under a variety of synthetic conditions. Reduction in rank generally decreased the training time for algorithms until effects caused by the size of the training data dominated. Reducing rank either left classification error unchanged or increased it. With respect to other low-rank Linear Metric Learning algorithms our algorithms again performed competitively with respect to classification error.
The last set of contributions consider Linear Metric Learning on Symmetric Positive Definite (SPD) matrices. Some datasets are expressed as or are suited to a SPD representation. As such, Metric Learning algorithms that respect the structure of these matrices have found success when adapted to this kind of data. Another extension of the Cyclic Projections algorithm is developed to use the Generalised Bures-Wasserstein distance on SPD matrices. Two other methods based on a ground metric formulation of the Bures-Wasserstein distance for learning linear metrics on SPD data are also introduced. One ground metric formulation uses an approximation (inspired by the Sinkhorn distance) to increase its scalability. Convergence experiments on synthetic problems adapted to SPD matrices are conducted on the ground metric algorithms to establish their convergence properties. Classification experiments are also conducted with respect to several types of SPD data. While the Cyclic Projections method is competitive, the ground metric algorithms have poor performance. Despite their poor classification performance, the approximation method does evaluate faster than the Generalised Bures-Wasserstein distance, potentially offering some scalability improvements.</p
High-level mission specification for multiple robots
No full textMobile robots are increasingly used in our everyday life to autonomously realize missions. A variety of languages has been proposed to support roboticists in the systematic development of robotic applications, ranging from logical languages with well-defined semantics to domain-specific languages with user-friendly syntax. The characteristics of both of them have distinct advantages, however, developing a language that combines those advantages remains an elusive task. We present PROMISE, a novel language that enables domain experts to specify missions on a high level of abstraction for teams of autonomous robots in a user-friendly way, while having well-defined semantics. Our ambition is to permit users to specify high-level goals instead of a series of specific actions the robots should perform. The language contains a set of atomic tasks that can be executed by robots and a set of operators that allow the composition of these tasks in complex missions. The language is supported by a standalone tool that permits mission specification through a textual and a graphical interface and that can be integrated within a variety of frameworks. We integrated PROMISE with a software platform providing functionalities such as motion control and planning. We conducted experiments to evaluate the correctness of the specification and execution of complex robotic missions with both simulators and real robots. We also conducted two user studies to assess the simplicity of PROMISE. The results show that PROMISE effectively supports users to specify missions for robots in a user-friendly manner
On the Bures distance and the Uhlmann transition probability of states on a von Neumann algebra
No full textSimple expressions for the Bures distance and the Uhlmann transition probability of states on a von Neumann algebra are obtained. Based on these expressions, certain properties are immediately derived.</p
Towards a monophyletic classification of Cardueae: restoration of the genus Lophiolepis (= Cirsium p.p.) and new circumscription of Epitrachys
No full textUsing molecular data and representative species coverage, we confirmed the monophyly of Cirsium sect. Eriolepis and, therefore, we propose to treat it as a separate genus (Lophiolepis). Besides, based on molecular and morphological evidence we segregate Cirsium italicum into the separate genus Epitrachys, sister to a large clade including Carduus, Cirsium s.l. and several allied genera. The name of a new hybrid genus (Lophiocirsium) is also published. Overall, 129 new combinations in Lophiolepis one in Epitrachys and one in Lophiocirsium are proposed
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