DOLPHIn - Dictionary Learning for Phase Retrieval

We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider such a sparse signal prior in the context of phase retrieval, when the sparsifying dictionary is not known in advance. Our algorithm jointly reconstructs the unknown signal - possibly corrupted by noise - and learns a dictionary such that each patch of the estimated image can be sparsely represented. Numerical experiments demonstrate that our approach can obtain significantly better reconstructions for phase retrieval problems with noise than methods that cannot exploit such "hidden" sparsity. Moreover, on the theoretical side, we provide a convergence result for our method

Cosmological implications of a Dark Matter self-interaction energy density

We investigate cosmological constraints on an energy density contribution of elastic dark matter self-interactions characterized by the mass of the exchange particle and coupling constant. Because of the expansion behaviour in a Robertson-Walker metric we investigate self-interacting dark matter that is warm in the case of thermal relics. The scaling behaviour of dark matter self-interaction energy density shows that it can be the dominant contribution (only) in the very early universe. Thus its impact on primordial nucleosynthesis is used to restrict the interaction strength, which we find to be at least as strong as the strong interaction. Furthermore we explore dark matter decoupling in a self-interaction dominated universe, which is done for the self-interacting warm dark matter as well as for collisionless cold dark matter in a two component scenario. We find that strong dark matter self-interactions do not contradict super-weak inelastic interactions between self-interacting dark matter and baryonic matter and that the natural scale of collisionless cold dark matter decoupling exceeds the weak scale and depends linearly on the particle mass. Finally structure formation analysis reveals a linear growing solution during self-interaction domination; however, only non-cosmological scales are enhanced.Comment: 14 pages, 14 figures; version published in Phys. Rev.

Degenerations of ideal hyperbolic triangulations

Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain projective classes of transversely measured singular codimension-one foliations of M. This leads to a combinatorial and geometric variant of well-known constructions by Culler, Morgan and Shalen concerning the character variety of a 3-manifold.Comment: 31 pages, 11 figures; minor changes; to appear in Mathematische Zeitschrif

Gestao de beneficios na etapa de projecto em empreendimentos hospitalares do reino unido [Managing benefits in the design of healthcare favilities in the UK]

Proposal: The healthcare system in the United kingdomis passing through transformation and change for improvement and innovation. Within this context, healthcare facilities are being developed in a complex multi-stakeholder environment, which usually have diverse and conflicting interests and no experience in design. This contributes for difficulties in managing their requirements, leading to low quality of design. Aiming to contribute for the management of these projects, a benefits management model is being developed and introduced in the sector by the University of Salford. This model intends to support the consideration of different stakeholders’ expectations in project development. In this sense, the aim of this paper was to bring discussions about how such approach could be adopted to support the design process within those projects. This research was developed through the participation on the model implementation, in addition to a literature review on benefits management and design approaches that are used in the UK and that could support benefits management in the design process. Main findings are related to a need for anticipating the participation of designers on project development and straightening the relationship between designers and decision makers. As a result, recommendations could be done to support benefits management throughout the design process. Keywords: Design process, project management, benefits realisatio

Generalized multi-photon quantum interference

Non-classical interference of photons lies at the heart of optical quantum information processing. This effect is exploited in universal quantum gates as well as in purpose-built quantum computers that solve the BosonSampling problem. Although non-classical interference is often associated with perfectly indistinguishable photons this only represents the degenerate case, hard to achieve under realistic experimental conditions. Here we exploit tunable distinguishability to reveal the full spectrum of multi-photon non-classical interference. This we investigate in theory and experiment by controlling the delay times of three photons injected into an integrated interferometric network. We derive the entire coincidence landscape and identify transition matrix immanants as ideally suited functions to describe the generalized case of input photons with arbitrary distinguishability. We introduce a compact description by utilizing a natural basis which decouples the input state from the interferometric network, thereby providing a useful tool for even larger photon numbers

Fine-grained complexity of coloring unit disks and balls

On planar graphs, many classic algorithmic problems enjoy a certain "square root phenomenon" and can be solved significantly faster than what is known to be possible on general graphs: for example, Independent Set, 3-Coloring, Hamiltonian Cycle, Dominating Set can be solved in time 2^O(sqrt{n}) on an n-vertex planar graph, while no 2^o(n) algorithms exist for general graphs, assuming the Exponential Time Hypothesis (ETH). The square root in the exponent seems to be best possible for planar graphs: assuming the ETH, the running time for these problems cannot be improved to 2^o(sqrt{n}). In some cases, a similar speedup can be obtained for 2-dimensional geometric problems, for example, there are 2^O(sqrt{n}log n) time algorithms for Independent Set on unit disk graphs or for TSP on 2-dimensional point sets. In this paper, we explore whether such a speedup is possible for geometric coloring problems. On the one hand, geometric objects can behave similarly to planar graphs: 3-Coloring can be solved in time 2^O(sqrt{n}) on the intersection graph of n unit disks in the plane and, assuming the ETH, there is no such algorithm with running time 2^o(sqrt{n}). On the other hand, if the number L of colors is part of the input, then no such speedup is possible: Coloring the intersection graph of n unit disks with L colors cannot be solved in time 2^o(n), assuming the ETH. More precisely, we exhibit a smooth increase of complexity as the number L of colors increases: If we restrict the number of colors to L=Theta(n^alpha) for some 0<=alpha<=1, then the problem of coloring the intersection graph of n unit disks with L colors * can be solved in time exp(O(n^{{1+alpha}/2}log n))=exp( O(sqrt{nL}log n)), and * cannot be solved in time exp(o(n^{{1+alpha}/2}))=exp(o(sqrt{nL})), unless the ETH fails. More generally, we consider the problem of coloring d-dimensional unit balls in the Euclidean space and obtain analogous results showing that the problem * can be solved in time exp(O(n^{{d-1+alpha}/d}log n))=exp(O(n^{1-1/d}L^{1/d}log n)), and * cannot be solved in time exp(n^{{d-1+alpha}/d-epsilon})= exp (O(n^{1-1/d-epsilon}L^{1/d})) for any epsilon>0, unless the ETH fails

Mental health benefits of interactions with nature in children and teenagers: a systematic review

Background It is commonly believed that nature has positive impacts on children’s health, including physical, mental and social dimensions. This review focuses on how accessibility to, exposure to and engagement with nature affects the mental health of children and teenagers. Methods Ten academic databases were used to systematically search and identify primary research papers in English or French from 1990 to 1 March 2017. Papers were included for review based on their incorporation of nature, children and teenagers (0–18 years), quantitative results and focus on mental health. Results Of the 35 papers included in the review, the majority focused on emotional well-being and attention deficit disorder/hyperactivity disorder. Other outcome measures included overall mental health, self-esteem, stress, resilience, depression and health-related quality of life. About half of all reported findings revealed statistically significant positive relationships between nature and mental health outcomes and almost half reported no statistical significance. Conclusions Findings support the contention that nature positively influences mental health; however, in most cases, additional research with more rigorous study designs and objective measures of both nature and mental health outcomes are needed to confirm statistically significant relationships. Existing evidence is limited by the cross-sectional nature of most papers

Extended Successive Convex Approximation for Phase Retrieval with Dictionary Learning

Phase retrieval aims at reconstructing unknown signals from magnitude measurements of linear mixtures. In this paper, we consider the phase retrieval with dictionary learning problem, which includes an additional prior information that the measured signal admits a sparse representation over an unknown dictionary. The task is to jointly estimate the dictionary and the sparse representation from magnitude-only measurements. To this end, we study two complementary formulations and develop efficient parallel algorithms by extending the successive convex approximation framework using a smooth majorization. The first algorithm is termed compact-SCAphase and is preferable in the case of less diverse mixture models. It employs a compact formulation that avoids the use of auxiliary variables. The proposed algorithm is highly scalable and has reduced parameter tuning cost. The second algorithm, referred to as SCAphase, uses auxiliary variables and is favorable in the case of highly diverse mixture models. It also renders simple incorporation of additional side constraints. The performance of both methods is evaluated when applied to blind sparse channel estimation from subband magnitude measurements in a multi-antenna random access network. Simulation results demonstrate the efficiency of the proposed techniques compared to state-of-the-art methods.Comment: This work has been submitted to the IEEE Transactions on Signal Processing for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

Lack of associations between female hormone levels and visuospatial working memory, divided attention and cognitive bias across two consecutive menstrual cycles

Background: Interpretation of observational studies on associations between prefrontal cognitive functioning and hormone levels across the female menstrual cycle is complicated due to small sample sizes and poor replicability. Methods: This observational multisite study comprised data of n = 88 menstruating women from Hannover, Germany, and Zurich, Switzerland, assessed during a first cycle and n = 68 re-assessed during a second cycle to rule out practice effects and false-positive chance findings. We assessed visuospatial working memory, attention, cognitive bias and hormone levels at four consecutive time-points across both cycles. In addition to inter-individual differences we examined intra-individual change over time (i.e., within-subject effects). Results: Estrogen, progesterone and testosterone did not relate to inter-individual differences in cognitive functioning. There was a significant negative association between intra-individual change in progesterone and change in working memory from pre-ovulatory to mid-luteal phase during the first cycle, but that association did not replicate in the second cycle. Intra-individual change in testosterone related negatively to change in cognitive bias from menstrual to pre-ovulatory as well as from pre-ovulatory to mid-luteal phase in the first cycle, but these associations did not replicate in the second cycle. Conclusions: There is no consistent association between women’s hormone levels, in particular estrogen and progesterone, and attention, working memory and cognitive bias. That is, anecdotal findings observed during the first cycle did not replicate in the second cycle, suggesting that these are false-positives attributable to random variation and systematic biases such as practice effects. Due to methodological limitations, positive findings in the published literature must be interpreted with reservation