Optimising Matrix Product State Simulations of Shor's Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on $r$, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.Comment: 8 pages, 2 figures, 2 tables. v2 using PDFLaTeX compiler. v3 to include extra references. v4 for publication in Quantu

The Insula and Its Epilepsies

Insular seizures are great mimickers of seizures originating elsewhere in the brain. The insula is a highly connected brain structure. Seizures may only become clinically evident after ictal activity propagates out of the insula with semiology that reflects the propagation pattern. Insular seizures with perisylvian spread, for example, manifest first as throat constriction, followed next by perioral and hemisensory symptoms, and then by unilateral motor symptoms. On the other hand, insular seizures may spread instead to the temporal and frontal lobes and present like seizures originating from these regions. Due to the location of the insula deep in the brain, interictal and ictal scalp electroencephalogram (EEG) changes can be variable and misleading. Magnetic reso- nance imaging, magnetic resonance spectroscopy, magnetoencephalography, positron emission tomography, and single-photon computed tomography imaging may assist in establishing a diagnosis of insular epilepsy. Intracranial EEG recordings from within the insula, using stereo-EEG or depth electrode techniques, can prove insular seizure origin. Seizure onset, most commonly seen as low-voltage, fast gamma activity, however, can be highly localized and easily missed if the insula is only sparsely sampled. Moreover, seizure spread to the contralateral insula and other brain regions may occur rapidly. Extensive sampling of the insula with multiple electrode trajectories is necessary to avoid these pitfalls. Understanding the functional organization of the insula is helpful when interpreting the semiology produced by insular seizures. Electrical stimulation mapping around the central sulcus of the insula results in paresthesias, while stimulation of the posterior insula typically produces painful sensations. Visceral sensations are the next most common result of insular stimulation. Treatment of insular epilepsy is evolving, but poses challenges. Surgical resections of the insula are effective but risk significant morbidity if not carefully planned. Neurostimulation is an emerging option for treatment, especially for seizures with onset in the posterior insula. The close association of the insula with marked autonomic changes has led to interest in the role of the insula in sudden unexpected death in epilepsy and warrants additional study with larger patient cohorts

Synthesis and Characterization of β-Cyclodextrin/alginate Nanoparticle as a Novel Drug Delivery System

The aim of this work was to study a novel nanoparticle system formed from alginate and β-cyclodextrin by ionotropic gelation method and to evaluate their potential for the association and delivery of drugs. The nanoparticles were prepared by electrostatic interactions between Ca2+/alginate gel and β-cyclodextrin. Morphology and structure characterization of nanoparticles was investigated by scanning electron micrographs (SEM), transmission electron microscope (TEM), Fourier transform infrared spectra (FTIR). The nanoparticle size was about 50 – 80 nm and their structure quite regular and consistent. Ketoprofen, chosen as a model drug, was incorporated into the nanocarriers with association efficiency of 50.7 % and loading efficiency of 5.7 %. Ketoprofen released from the nanoparticles was 57 % at pH 7.4 and 69 % at pH 5.0 for 4 h

Relativistic Coulomb Sum Rules for (e,e′)(e,e^\prime)

A Coulomb sum rule is derived for the response of nuclei to $(e,e^\prime)$ scattering with large three-momentum transfers. Unlike the nonrelativistic formulation, the relativistic Coulomb sum is restricted to spacelike four-momenta for the most direct connection with experiments; an immediate consequence is that excitations involving antinucleons, e.g., $N{\bar N}$ pair production, are approximately eliminated from the sum rule. Relativistic recoil and Fermi motion of target nucleons are correctly incorporated. The sum rule decomposes into one- and two-body parts, with correlation information in the second. The one-body part requires information on the nucleon momentum distribution function, which is incorporated by a moment expansion method. The sum rule given through the second moment (RCSR-II) is tested in the Fermi gas model, and is shown to be sufficiently accurate for applications to data.Comment: 32 pages (LaTeX), 4 postscript figures available from the author

The hyperon mean free paths in the relativistic mean field

The $\Lambda$- and $\Xi^-$-hyperon mean free paths in nuclei are firstly calculated in the relativistic mean field (RMF) theory. The real parts of the optical potential are derived from the RMF approach, while the imaginary parts are obtained from those of nucleons with the relations: $U^{\mathrm{IY}}_{\mathrm{S}} = \alpha_{\sigma \mathrm{Y}}\cdot U_{\mathrm{S}}^{\mathrm{IN}}$ and $U^{\mathrm{IY}}_{\mathrm{V}} = \alpha_{\omega \mathrm{Y}}\cdot U_{\mathrm{V}}^{\mathrm{IN}}$ . With the assumption, the depth of the imaginary potential for $\Xi^-$ is $W_{\Xi}\simeq-$ 3.5 MeV, and for $\Lambda$ is $W_{\Lambda}\simeq-$ 7 MeV at low incident energy. We find that, the hyperon mean free path decreases with the increase of the hyperon incident energies, from 200 MeV to 800 MeV; and in the interior of the nuclei, the mean free path is about $2\sim 3$ fm for $\Lambda$, and about $4\sim 8$ fm for $\Xi^-$, depending on the hyperon incident energy.Comment: 5 figures, 6 page

Order in extremal trajectories

Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the trajectories of the archetypical chaotic system, the baker's map. We show that, out of all irregular trajectories, a large-deviation requirement selects (isolated) orbits that are periodic or quasiperiodic. We discuss what the relevance of this calculation may be for dynamical systems and for glasses

Competing magnetic fluctuations in Sr3Ru2O7 probed by Ti doping

We report the effect of nonmagnetic Ti4+ impurities on the electronic and magnetic properties of Sr3Ru2O7. Small amounts of Ti suppress the characteristic peak in magnetic susceptibility near 16 K and result in a sharp upturn in specific heat. The metamagnetic quantum phase transition and related anomalous features are quickly smeared out by small amounts of Ti. These results provide strong evidence for the existence of competing magnetic fluctuations in the ground state of Sr3Ru2O7. Ti doping suppresses the low temperature antiferromagnetic interactions that arise from Fermi surface nesting, leaving the system in a state dominated by ferromagnetic fluctuations.Comment: 5 pages, 4 figures, 1 tabl

Hybrid Focal Stereo Networks for Pattern Analysis in Homogeneous Scenes

In this paper we address the problem of multiple camera calibration in the presence of a homogeneous scene, and without the possibility of employing calibration object based methods. The proposed solution exploits salient features present in a larger field of view, but instead of employing active vision we replace the cameras with stereo rigs featuring a long focal analysis camera, as well as a short focal registration camera. Thus, we are able to propose an accurate solution which does not require intrinsic variation models as in the case of zooming cameras. Moreover, the availability of the two views simultaneously in each rig allows for pose re-estimation between rigs as often as necessary. The algorithm has been successfully validated in an indoor setting, as well as on a difficult scene featuring a highly dense pilgrim crowd in Makkah.Comment: 13 pages, 6 figures, submitted to Machine Vision and Application