Spatial search in a honeycomb network

The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighboring sites are allowed. In this paper, a quantum algorithm for the spatial search problem on a honeycomb lattice with $N$ sites and torus-like boundary conditions. The search algorithm is based on a modified quantum walk on a hexagonal lattice and the general framework proposed by Ambainis, Kempe and Rivosh is used to show that the time complexity of this quantum search algorithm is $O(\sqrt{N \log N})$.Comment: 10 pages, 2 figures; Minor typos corrected, one Reference added. accepted in Math. Structures in Computer Science, special volume on Quantum Computin

Spatial quantum search in a triangular network

The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighboring sites are allowed. We propose a quantum algorithm for the spatial search problem on a triangular lattice with N sites and torus-like boundary conditions. The proposed algortithm is a special case of the general framework for abstract search proposed by Ambainis, Kempe and Rivosh [AKR05] (AKR) and Tulsi [Tulsi08], applied to a triangular network. The AKR-Tulsi formalism was employed to show that the time complexity of the quantum search on the triangular lattice is O(sqrt(N logN)).Comment: 10 pages, 4 Postscript figures, uses sbc-template.sty, appeared in Annals of WECIQ 2010, III Workshop of Quantum Computation and Quantum Informatio

Quantum search by continuous-time quantum walk on t-designs

This work examines the time complexity of quantum search algorithms on combinatorial $t$-designs with multiple marked elements using the continuous-time quantum walk. Through a detailed exploration of $t$-designs and their incidence matrices, we identify a subset of bipartite graphs that are conducive to success compared to random-walk-based search algorithms. These graphs have adjacency matrices with eigenvalues and eigenvectors that can be determined algebraically and are also suitable for analysis in the multiple-marked vertex scenario. We show that the continuous-time quantum walk on certain symmetric $t$-designs achieves an optimal running time of $O(\sqrt{n})$, where $n$ is the number of points and blocks, even when accounting for an arbitrary number of marked elements. Upon examining two primary configurations of marked elements distributions, we observe that the success probability is consistently $o(1)$, but it approaches 1 asymptotically in certain scenarios.Comment: 15 page

Nesting behaviour influences species-specific gas exchange across avian eggshells

Carefully controlled gas exchange across the eggshell is essential for the development of the avian embryo. Water vapour conductance (GH2O) across the shell, typically measured as mass loss during incubation, has been demonstrated to optimally ensure the healthy development of the embryo while avoiding desiccation. Accordingly, eggs exposed to sub-optimal gas exchange have reduced hatching success. We tested the association between eggshell GH2O and putative life-history correlates of adult birds, ecological nest parameters and physical characteristics of the egg itself to investigate how variation in GH2O has evolved to maintain optimal water loss across a diverse set of nest environments. We measured gas exchange through eggshell fragments in 151 British breeding bird species and fitted phylogenetically controlled, general linear models to test the relationship between GH2O and potential predictor parameters of each species. Of our 17 life-history traits, only two were retained in the final model: wet-incubating parent and nest type. Eggs of species where the parent habitually returned to the nest with wet plumage had significantly higher GH2O than those of parents that returned to the nest with dry plumage. Eggs of species nesting in ground burrows, cliffs and arboreal cups had significantly higher GH2O than those of species nesting on the ground in open nests or cups, in tree cavities and in shallow arboreal nests. Phylogenetic signal (measured as Pagel's λ) was intermediate in magnitude, suggesting that differences observed in the GH2O are dependent upon a combination of shared ancestry and species-specific life history and ecological traits. Although these data are correlational by nature, they are consistent with the hypothesis that parents constrained to return to the nest with wet plumage will increase the humidity of the nest environment, and the eggs of these species have evolved a higher GH2O to overcome this constraint and still achieve optimal water loss during incubation. We also suggest that eggs laid in cup nests and burrows may require a higher GH2O to overcome the increased humidity as a result from the confined nest microclimate lacking air movements through the nest. Taken together, these comparative data imply that species-specific levels of gas exchange across avian eggshells are variable and evolve in response to ecological and physical variation resulting from parental and nesting behaviours

A Case Report: Unmasking a Singular Culprit for Cardiogenic Shock: Looking Beyond the Coronary Tree

BACKGROUND: Cardiogenic shock remains challenging in its therapy and aetiology. CASE SUMMARY: A 74-year-old woman admitted for cardiogenic shock requiring mechanical ventilation and high-dose inotropics and vasopressors with an electrocardiogram showing left ventricular (LV) lateral wall ischaemia had diffuse coronary artery disease but TIMI III flow in the coronary tree. An echocardiogram showed a suspicious mass invading the left ventricle and computed tomography scan revealed an advanced lung cancer with LV wall and pulmonary artery invasion as the cardiogenic shock cause. DISCUSSION: When managing cardiogenic shock, it is important to consider different and not obvious diagnosis. A high level of clinical suspicion and multimodality imaging assessment was very important in the present case to attain the diagnosis.info:eu-repo/semantics/publishedVersio

Quantum walk-based search algorithms with multiple marked vertices

The quantum walk is a powerful tool to develop quantum algorithms, which usually are based on searching for a vertex in a graph with multiple marked vertices, Ambainis's quantum algorithm for solving the element distinctness problem being the most shining example. In this work, we address the problem of calculating analytical expressions of the time complexity of finding a marked vertex using quantum walk-based search algorithms with multiple marked vertices on arbitrary graphs, extending previous analytical methods based on Szegedy's quantum walk, which can be applied only to bipartite graphs. Two examples based on the coined quantum walk on two-dimensional lattices and hypercubes show the details of our method.Comment: 12 pages, 1 table, 2 fig