Quantum annealing for systems of polynomial equations

Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct matrix inversion or iteratively with judicious preconditioning. However, the convergence of iterative algorithms is highly variable and depends, in part, on the condition number. We present a direct method for solving general systems of polynomial equations based on quantum annealing, and we validate this method using a system of second-order polynomial equations solved on a commercially available quantum annealer. We then demonstrate applications for linear regression, and discuss in more detail the scaling behavior for general systems of linear equations with respect to problem size, condition number, and search precision. Finally, we define an iterative annealing process and demonstrate its efficacy in solving a linear system to a tolerance of $10^{-8}$.Comment: 11 pages, 4 figures. Added example for a system of quadratic equations. Supporting code is available at https://github.com/cchang5/quantum_poly_solver . This is a post-peer-review, pre-copyedit version of an article published in Scientific Reports. The final authenticated version is available online at: https://www.nature.com/articles/s41598-019-46729-

Cellulose Nanoparticles are a Biodegradable Photoacoustic Contrast Agent for Use in Living Mice.

Molecular imaging with photoacoustic ultrasound is an emerging field that combines the spatial and temporal resolution of ultrasound with the contrast of optical imaging. However, there are few imaging agents that offer both high signal intensity and biodegradation into small molecules. Here we describe a cellulose-based nanoparticle with peak photoacoustic signal at 700 nm and an in vitro limit of detection of 6 pM (0.02 mg/mL). Doses down to 0.35 nM (1.2 mg/mL) were used to image mouse models of ovarian cancer. Most importantly, the nanoparticles were shown to biodegrade in the presence of cellulase both through a glucose assay and electron microscopy

A geometric model of a V-slit Sun sensor correcting for spacecraft wobble

A V-Slit sun sensor is body-mounted on a spin-stabilized spacecraft. During injection from a parking or transfer orbit to some final orbit, the spacecraft may not be dynamically balanced. This may result in wobble about the spacecraft spin axis as the spin axis may not be aligned with the spacecraft's axis of symmetry. While the widely used models in Spacecraft Attitude Determination and Control, edited by Wertz, correct for separation, elevation, and azimuthal mounting biases, spacecraft wobble is not taken into consideration. A geometric approach is used to develop a method for measurement of the sun angle which corrects for the magnitude and phase of spacecraft wobble. The algorithm was implemented using a set of standard mathematical routines for spherical geometry on a unit sphere

Information entropy as a measure of the quality of a nuclear density distribution

The information entropy of a nuclear density distribution is calculated for a number of nuclei. Various phenomenological models for the density distribution using different geometry are employed. Nuclear densities calculated within various microscopic mean field approaches are also employed. It turns out that the entropy increases on going from crude phenomenological models to more sophisticated (microscopic) ones. It is concluded that the larger the information entropy, the better the quality of the nuclear density distribution. An alternative approach is also examined: the net information content i.e. the sum of information entropies in position and momentum space $S_{r}+S_{k}$. It is indicated that $S_{r}+S_{k}$ is a maximum, when the best fit to experimental data of the density and momentum distributions is attained.Comment: 12 pages, LaTex, no figures, Int. J. of Mod. Phys. E in pres

Roles of proton-neutron interactions in alpha-like four-nucleon correlations

An extended pairing plus QQ force model, which has been shown to successfully explain the nuclear binding energy and related quantities such as the symmetry energy, is applied to study the alpha-like four-nucleon correlations in 1f_{7/2} shell nuclei. The double difference of binding energies, which displays a characteristic behavior at $N \approx Z$, is interpreted in terms of the alpha-like correlations. Important roles of proton-neutron interactions forming the alpha-like correlated structure are discussed.Comment: 10 pages, 2 figures, RevTex, submitted to Phys. Rev.

Confronting mitigation deterrence in low-carbon scenarios

Carbon dioxide removal (CDR) features heavily in low-carbon scenarios, where it often substitutes for emission reductions in both the near-term and long-term, enabling temperature targets to be met at lower cost. There are major concerns around the scale of CDR deployment in many low-carbon scenarios, and the risk that anticipated future CDR could dilute incentives to reduce emissions now, a phenomenon known as mitigation deterrence. Here we conduct an in-depth analysis into the relationship between emissions reduction and emissions removal in a global integrated assessment model. We explore the impact of CDR on low-carbon scenarios, illustrating how the pathway for the 2020s is highly sensitive to assumptions around CDR availability. Using stochastic optimisation, we demonstrate that accounting for uncertainty in future CDR deployment provides a strong rationale to increase rates of mitigation in the 2020s. A 20% chance of CDR deployment failure requires additional emissions reduction in 2030 of 3–17 GtCO2. Finally, we introduce new scenarios which demonstrate the risks of mitigation deterrence and the benefits of formally separating CDR and emissions reduction as climate strategies. Continual mitigation deterrence across the time-horizon leads to the temperature goals being breached by 0.2–0.3 °C. If CDR is treated as additional to emissions reduction, up to an additional 700–800 GtCO2 can be removed from the atmosphere by 2100, reducing end-of-century warming by up to 0.5 °C. This could put sub-1.5 °C targets within reach but requires that CDR is additional to, rather than replaces, emission reductions

A Magnetic Bead-Based Sensor for the Quantification of Multiple Prostate Cancer Biomarkers.

Novel biomarker assays and upgraded analytical tools are urgently needed to accurately discriminate benign prostatic hypertrophy (BPH) from prostate cancer (CaP). To address this unmet clinical need, we report a piezeoelectric/magnetic bead-based assay to quantitate prostate specific antigen (PSA; free and total), prostatic acid phosphatase, carbonic anhydrase 1 (CA1), osteonectin, IL-6 soluble receptor (IL-6sr), and spondin-2. We used the sensor to measure these seven proteins in serum samples from 120 benign prostate hypertrophy patients and 100 Gleason score 6 and 7 CaP using serum samples previously collected and banked. The results were analyzed with receiver operator characteristic curve analysis. There were significant differences between BPH and CaP patients in the PSA, CA1, and spondin-2 assays. The highest AUC discrimination was achieved with a spondin-2 OR free/total PSA operation--the area under the curve was 0.84 with a p value below 10(-6). Some of these data seem to contradict previous reports and highlight the importance of sample selection and proper assay building in the development of biomarker measurement schemes. This bead-based system offers important advantages in assay building including low cost, high throughput, and rapid identification of an optimal matched antibody pair