A Parametric Propagator for Pairs of Sum Constraints with a Discrete Convexity Property

International audienceWe introduce a propagator for pairs of Sum constraints, where the expressions in the sums respect a form of convexity. This propagator is parametric and can be instantiated for various concrete pairs, including Deviation, Spread, and the conjunction of Linear ≤ and Among. We show that despite its generality , our propagator is competitive in theory and practice with state-of-the-art propagators

Propagators and Violation Functions for Geometric and Workload Constraints Arising in Airspace Sectorisation

Airspace sectorisation provides a partition of a given airspace into sectors, subject to geometric constraints and workload constraints, so that some cost metric is minimised. We make a study of the constraints that arise in airspace sectorisation. For each constraint, we give an analysis of what algorithms and properties are required under systematic search and stochastic local search

Do price trajectory data increase the efficiency of market impact estimation?

Market impact is an important problem faced by large institutional investor and active market participant. In this paper, we rigorously investigate whether price trajectory data from the metaorder increases the efficiency of estimation, from an asymptotic view of statistical estimation. We show that, for popular market impact models, estimation methods based on partial price trajectory data, especially those containing early trade prices, can outperform established estimation methods (e.g., VWAP-based) asymptotically. We discuss theoretical and empirical implications of such phenomenon, and how they could be readily incorporated into practice

Computational Inverse Problems for Partial Differential Equations

The problem of determining unknown quantities in a PDE from measurements of (part of) the solution to this PDE arises in a wide range of applications in science, technology, medicine, and finance. The unknown quantity may e.g. be a coefficient, an initial or a boundary condition, a source term, or the shape of a boundary. The identification of such quantities is often computationally challenging and requires profound knowledge of the analytical properties of the underlying PDE as well as numerical techniques. The focus of this workshop was on applications in phase retrieval, imaging with waves in random media, and seismology of the Earth and the Sun, a further emphasis was put on stochastic aspects in the context of uncertainty quantification and parameter identification in stochastic differential equations. Many open problems and mathematical challenges in application fields were addressed, and intensive discussions provided an insight into the high potential of joining deep knowledge in numerical analysis, partial differential equations, and regularization, but also in mathematical statistics, homogenization, optimization, differential geometry, numerical linear algebra, and variational analysis to tackle these challenges

Multi-scale active shape description in medical imaging

Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed

Selected Topics in Gravity, Field Theory and Quantum Mechanics

Quantum field theory has achieved some extraordinary successes over the past sixty years; however, it retains a set of challenging problems. It is not yet able to describe gravity in a mathematically consistent manner. CP violation remains unexplained. Grand unified theories have been eliminated by experiment, and a viable unification model has yet to replace them. Even the highly successful quantum chromodynamics, despite significant computational achievements, struggles to provide theoretical insight into the low-energy regime of quark physics, where the nature and structure of hadrons are determined. The only proposal for resolving the fine-tuning problem, low-energy supersymmetry, has been eliminated by results from the LHC. Since mathematics is the true and proper language for quantitative physical models, we expect new mathematical constructions to provide insight into physical phenomena and fresh approaches for building physical theories

On Monte Carlo time-dependent variational principles

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Coherent and Measurement-based Feedback in Quantum Mechanics

This thesis is about the theory of quantum feedback control. In particular,it focuses on the theory of coherent feedback-a form of quantum feedback in which no measurements are performed- and how it can be compared with measurement-based feedback. After introducing the background concepts and formalisms, the first part of this thesis is concerned with coherent feedback in the regime of Gaussian quantum systems. We derive a general model for describing Gaussian coherent feedback, and use this to derive a compact description of passive, interferometric coherent feedback. The performance of this model is then evaluated for the task of squeezing a bosonic mode and it is shown that no setup of this kind is able to generate steady-state squeezing of a quadrature beyond the ‘3dB bound’. This performance is compared to the performance of homodyne monitoring which in certain circumstances can out perform the passive coherent feedback setups. After this, we apply our model of Gaussian coherent feedback to optomechanical systems. We investigate the tasks of cooling a mechanical oscillator, generating entanglement between optical and mechanical modes and generating optical and mechanical squeezing. Finally, we develop a unified model of coherent and measurement-based feedback, inspired by collision models and not restricted to Gaussian states. Within this model, we compare the two feedback methods for the tasks of generating low entropy steady-states and simulating unitary evolution on an unknown input state