344 research outputs found
Computing A Glimpse of Randomness
A Chaitin Omega number is the halting probability of a universal Chaitin
(self-delimiting Turing) machine. Every Omega number is both computably
enumerable (the limit of a computable, increasing, converging sequence of
rationals) and random (its binary expansion is an algorithmic random sequence).
In particular, every Omega number is strongly non-computable. The aim of this
paper is to describe a procedure, which combines Java programming and
mathematical proofs, for computing the exact values of the first 64 bits of a
Chaitin Omega:
0000001000000100000110001000011010001111110010111011101000010000. Full
description of programs and proofs will be given elsewhere.Comment: 16 pages; Experimental Mathematics (accepted
A QUBO formulation for the Tree Containment problem
Phylogenetic (evolutionary) trees and networks are leaf-labeled graphs that
are widely used to represent the evolutionary relationships between entities
such as species, languages, cancer cells, and viruses. To reconstruct and
analyze phylogenetic networks, the problem of deciding whether or not a given
rooted phylogenetic network embeds a given rooted phylogenetic tree is of
recurring interest. This problem, formally know as Tree Containment, is
NP-complete in general and polynomial-time solvable for certain classes of
phylogenetic networks. In this paper, we connect ideas from quantum computing
and phylogenetics to present an efficient Quadratic Unconstrained Binary
Optimization formulation for Tree Containment in the general setting. For an
instance (N,T) of Tree Containment, where N is a phylogenetic network with n_N
vertices and T is a phylogenetic tree with n_T vertices, the number of logical
qubits that are required for our formulation is O(n_N n_T).Comment: final version accepted for publication in Theoretical Computer
Scienc
A Hybrid Quantum-Classical Paradigm to Mitigate Embedding Costs in Quantum Annealing
Despite rapid recent progress towards the development of quantum computers
capable of providing computational advantages over classical computers, it
seems likely that such computers will, initially at least, be required to run
in a hybrid quantum-classical regime. This realisation has led to interest in
hybrid quantum-classical algorithms allowing, for example, quantum computers to
solve large problems despite having very limited numbers of qubits. Here we
propose a hybrid paradigm for quantum annealers with the goal of mitigating a
different limitation of such devices: the need to embed problem instances
within the (often highly restricted) connectivity graph of the annealer. This
embedding process can be costly to perform and may destroy any computational
speedup. In order to solve many practical problems, it is moreover necessary to
perform many, often related, such embeddings. We will show how, for such
problems, a raw speedup that is negated by the embedding time can nonetheless
be exploited to give a real speedup. As a proof-of-concept example we present
an in-depth case study of a simple problem based on the maximum weight
independent set problem. Although we do not observe a quantum speedup
experimentally, the advantage of the hybrid approach is robustly verified,
showing how a potential quantum speedup may be exploited and encouraging
further efforts to apply the approach to problems of more practical interest.Comment: 30 pages, 6 figure
Magnetic trapping of metastable atomic strontium
We report the magnetic trapping of metastable atomic strontium. Atoms
are cooled in a magneto-optical trap (MOT) operating on the dipole allowed
transition at 461 nm. Decay via
continuously loads a magnetic trap formed by the quadrupole magnetic field of
the MOT. Over atoms at a density of cm and
temperature of 1 mK are trapped. The atom temperature is significantly lower
than what would be expected from the kinetic and potential energy of atoms as
they are transferred from the MOT. This suggests that thermalization and
evaporative cooling are occurring in the magnetic trap.Comment: This paper has been accepted by PR
Collisions of cold magnesium atoms in a weak laser field
We use quantum scattering methods to calculate the light-induced collisional
loss of laser-cooled and trapped magnesium atoms for detunings up to 30 atomic
linewidths to the red of the 1S_0-1P_1 cooling transition. Magnesium has no
hyperfine structure to complicate the theoretical studies. We evaluate both the
radiative and nonradiative mechanisms of trap loss. The radiative escape
mechanism via allowed 1Sigma_u excitation is dominant for more than about one
atomic linewidth detuning. Molecular vibrational structure due to
photoassociative transitions to bound states begins to appear beyond about ten
linewidths detuning.Comment: 4 pages with 3 embedded figure
Inter-reader agreement of the PI-QUAL score for prostate MRI quality in the NeuroSAFE PROOF trial
Objectives:
The Prostate Imaging Quality (PI-QUAL) score assesses the quality of multiparametric MRI (mpMRI). A score of 1 means all sequences are below the minimum standard of diagnostic quality, 3 implies that the scan is of sufficient diagnostic quality, and 5 means that all three sequences are of optimal diagnostic quality. We investigated the inter-reader reproducibility of the PI-QUAL score in patients enrolled in the NeuroSAFE PROOF trial.
Methods:
We analysed the scans of 103 patients on different MR systems and vendors from 12 different hospitals. Two dedicated radiologists highly experienced in prostate mpMRI independently assessed the PI-QUAL score for each scan. Interobserver agreement was assessed using Cohen’s kappa with standard quadratic weighting (κw) and percent agreement.
Results:
The agreement for each single PI-QUAL score was strong (κw = 0.85 and percent agreement = 84%). A similar agreement (κw = 0.82 and percent agreement = 84%) was observed when the scans were clustered into three groups (PI-QUAL 1–2 vs PI-QUAL 3 vs PI-QUAL 4–5). The agreement in terms of diagnostic quality for each single sequence was highest for T2-weighted imaging (92/103 scans; 89%), followed by dynamic contrast-enhanced sequences (91/103; 88%) and diffusion-weighted imaging (80/103; 78%).
Conclusion:
We observed strong reproducibility in the assessment of PI-QUAL between two radiologists with high expertise in prostate mpMRI. At present, PI-QUAL offers clinicians the only available tool for evaluating and reporting the quality of prostate mpMRI in a systematic manner but further refinements of this scoring system are warranted
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