Catalytic space: Non-determinism and hierarchy

Catalytic computation, defined by Buhrman, Cleve, Koucký, Loff and Speelman (STOC 2014), is a space-bounded computation where in addition to our working memory we have an exponentially larger auxiliary memory which is full; the auxiliary memory may be used throughout the computation, but it must be restored to its initial content by the end of the computation. Motivated by the surprising power of this model, we set out to study the non-deterministic version of catalytic computation. We establish that non-deterministic catalytic log-space is contained in ZPP, which is the same bound known for its deterministic counterpart, and we prove that non-deterministic catalytic space is closed under complement (under a standard derandomization assumption). Furthermore, we establish hierarchy theorems for non-deterministic and deterministic catalytic computation

Limits of Quantum Speed-Ups for Computational Geometry and Other Problems: Fine-Grained Complexity via Quantum Walks

Many computational problems are subject to a quantum speed-up: one might find that a problem having an Opn3q-time or Opn2q-time classic algorithm can be solved by a known Opn1.5q-time or Opnq-time quantum algorithm. The question naturally arises: how much quantum speed-up is possible? The area of fine-grained complexity allows us to prove optimal lower-bounds on the complexity of various computational problems, based on the conjectured hardness of certain natural, well-studied problems. This theory has recently been extended to the quantum setting, in two independent papers by Buhrman, Patro and Speelman [7], and by Aaronson, Chia, Lin, Wang, and Zhang [1]. In this paper, we further extend the theory of fine-grained complexity to the quantum setting. A fundamental conjecture in the classical setting states that the 3SUM problem cannot be solved by (classical) algorithms in time Opn2´εq, for any ε ą 0. We formulate an analogous conjecture, the Quantum-3SUM-Conjecture, which states that there exist no sublinear Opn1´εq-time quantum algorithms for the 3SUM problem. Based on the Quantum-3SUM-Conjecture, we show new lower-bounds on the time complexity of quantum algorithms for several computational problems. Most of our lower-bounds are optimal, in that they match known upper-bounds, and hence they imply tight limits on the quantum speedup that is possible for these problems. These results are proven by adapting to the quantum setting known classical fine-grained reductions from the 3SUM problem. This adaptation is not trivial, however, since the original classical reductions require pre-processing the input in various ways, e.g. by sorting it according to some order, and this pre-processing (provably) cannot be done in sublinear quantum time. We overcome this bottleneck by combining a quantum walk with a classical dynamic data-structure having a certain “history-independence” property. This type of construction has been used in the past to prove upper bounds, and here we use it for the first time as part of a reduction. This general proof strategy allows us to prove tight lower bounds on several computational-geometry problems, on Convolution-3SUM and on the 0-Edge-Weight-Triangle problem, conditional on the Quantum-3SUM-Conjecture. We believe this proof strategy will be useful in proving tight (conditional) lower-bounds, and limits on quantum speed-ups, for many other problems

MRI-based biomechanical parameters for carotid artery plaque vulnerability assessment.

Carotid atherosclerotic plaques are a major cause of ischaemic stroke. The biomechanical environment to which the arterial wall and plaque is subjected to plays an important role in the initiation, progression and rupture of carotid plaques. MRI is frequently used to characterize the morphology of a carotid plaque, but new developments in MRI enable more functional assessment of carotid plaques. In this review, MRI based biomechanical parameters are evaluated on their current status, clinical applicability, and future developments. Blood flow related biomechanical parameters, including endothelial wall shear stress and oscillatory shear index, have been shown to be related to plaque formation. Deriving these parameters directly from MRI flow measurements is feasible and has great potential for future carotid plaque development prediction. Blood pressure induced stresses in a plaque may exceed the tissue strength, potentially leading to plaque rupture. Multi-contrast MRI based stress calculations in combination with tissue strength assessment based on MRI inflammation imaging may provide a plaque stress-strength balance that can be used to assess the plaque rupture risk potential. Direct plaque strain analysis based on dynamic MRI is already able to identify local plaque displacement during the cardiac cycle. However, clinical evidence linking MRI strain to plaque vulnerability is still lacking. MRI based biomechanical parameters may lead to improved assessment of carotid plaque development and rupture risk. However, better MRI systems and faster sequences are required to improve the spatial and temporal resolution, as well as increase the image contrast and signal-to-noise ratio.This is the author accepted manuscript. The final version is available from Schattauer via http://dx.doi.org/10.1160/TH15-09-071

The role of migration and demographic change in small island futures

Low-lying atoll islands are especially threatened by anticipated sea-level rise, and migration is often mentioned as a potential response of these island societies. Further, small island states are developing population, economic and adaptation policies to plan the future. Policies, such as raising of islands or land reclamation, require a long-term vision on populations and migration. However, population and migration systems in small island settings are poorly understood. To address this deficiency requires an approach that considers changing environmental and socio-economic factors and individual migration decision-making. This article introduces the conceptual model of migration and explores migration within one small island nation, the Maldives, as an example. Agent-based simulations of internal migration from 1985–2014 are used as a basis to explore a range of potential demographic futures up to 2050. The simulations consider a set of consistent demographic, environmental, policy and international migration narratives, which describe a range of key uncertainties. The capital island Malé has experienced significant population growth over the last decades, growing from around 67,000 to 153,000 inhabitants from 2000 to 2014, and comprising about 38 percent of the national population in 2014. In all future narratives, which consider possible demographic, governance, environmental and globalization changes, the growth of Malé continues while many other islands are effectively abandoned. The analysis suggests that migration in the Maldives has a strong inertia, and radical change to the environmental and/or socio-economic drivers would be needed for existing trends to change. Findings from this study may have implications for national development and planning for climate change more widely in island nations

A continuous-discontinuous model for crack branching

This is the peer reviewed version of the following article: Tamayo, E. [et al.]. A continuous-discontinuous model for crack branching. "International journal for numerical methods in engineering", 5 Octubre 2019, vol. 120, núm. 1, p. 86-104, which has been published in final form at https://doi.org/10.1002/nme.6125. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A new continuous-discontinuous model for fracture that accounts for crack branching in a natural manner is presented. It combines a gradient-enhanced damage model based on nonlocal displacements to describe diffuse cracks and the extended finite element method (X-FEM) for sharp cracks. Its most distinct feature is a global crack tracking strategy based on the geometrical notion of medial axis: the sharp crack propagates following the direction dictated by the medial axis of a damage isoline. This means that, if the damage field branches, the medial axis automatically detects this bifurcation, and a branching sharp crack is thus easily obtained. In contrast to other existing models, no special crack-tip criteria are required to trigger branching. Complex crack patterns may also be described with this approach, since the X-FEM enrichment of the displacement field can be recursively applied by adding one extra term at each branching event. The proposed approach is also equipped with a crack-fluid pressure, a relevant feature in applications such as hydraulic fracturing or leakage-related events. The capabilities of the model to handle propagation and branching of cracks are illustrated by means of different two-dimensional numerical examples.Peer ReviewedPostprint (author's final draft

High shear stress relates to intraplaque haemorrhage in asymptomatic carotid plaques

AbstractBackground and aimsCarotid artery plaques with vulnerable plaque components are related to a higher risk of cerebrovascular accidents. It is unknown which factors drive vulnerable plaque development. Shear stress, the frictional force of blood at the vessel wall, is known to influence plaque formation. We evaluated the association between shear stress and plaque components (intraplaque haemorrhage (IPH), lipid rich necrotic core (LRNC) and/or calcifications) in relatively small carotid artery plaques in asymptomatic persons.MethodsParticipants (n = 74) from the population-based Rotterdam Study, all with carotid atherosclerosis assessed on ultrasound, underwent carotid MRI. Multiple MRI sequences were used to evaluate the presence of IPH, LRNC and/or calcifications in plaques in the carotid arteries. Images were automatically segmented for lumen and outer wall to obtain a 3D reconstruction of the carotid bifurcation. These reconstructions were used to calculate minimum, mean and maximum shear stresses by applying computational fluid dynamics with subject-specific inflow conditions. Associations between shear stress measures and plaque composition were studied using generalized estimating equations analysis, adjusting for age, sex and carotid wall thickness.ResultsThe study group consisted of 93 atherosclerotic carotid arteries of 74 participants. In plaques with higher maximum shear stresses, IPH was more often present (OR per unit increase in maximum shear stress (log transformed) = 12.14; p = 0.001). Higher maximum shear stress was also significantly associated with the presence of calcifications (OR = 4.28; p = 0.015).ConclusionsHigher maximum shear stress is associated with intraplaque haemorrhage and calcifications