Tensor network representations from the geometry of entangled states

Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement structure given by a graph of maximally entangled states along the edges that identify the indices of the tensors to be contracted. Recently, more general tensor networks have been considered, where the maximally entangled states on edges are replaced by multipartite entangled states on plaquettes. Both the structure of the underlying graph and the dimensionality of the entangled states influence the computational cost of contracting these networks. Using the geometrical properties of entangled states, we provide a method to construct tensor network representations with smaller effective bond dimension. We illustrate our method with the resonating valence bond state on the kagome lattice.Comment: 35 pages, 9 figure

Improvements In computed tomography perfusion output using complex singular value decomposition and the maximum slope algorithm

OBJECTIVE: Determine if complex singular value decomposition (cSVD) used as preprocessing in the maximum slope algorithm reduces image noise of resultant physiologic parametric images. Noise will be decreased in the parametric maps of cerebral blood flow (CBF), cerebral blood volume (CBV) as compared to the same algorithm and data set with no cSVD applied. MATERIALS AND METHODS: A set of 10 patients (n=15) underwent a total combined 15 CT perfusion studies upon presenting with stroke symptoms. It was determined these patients suffered from occlusions resulting in a prolonged arrival time of blood to the brain. DICOM data files of these patients scans were selected based on this increased arrival delay. We compared the output of estimation calculations for cerebral blood flow (CBF), and cerebral blood volume (CBV), using preprocessing cSVD against the same scan data with no preprocessing cSVD. Image noise was assessed through the calculation of the standard deviation within specific regions of interest copied to specific areas of grey and white matter as well as CSF space. A decrease in the standard deviation values will indicate improvement in the noise level of the resultant images.. Results for the mean value within the regions of interest are expected to be similar between the groups calculated using cSVD and those calculated under the standard method. This will indicate the presence of minimal bias. RESULTS: Between groups of the standard processing method and the cSVD method standard deviation (SD) reductions were seen in both CBF and CBV values across all three ROIs. In grey matter measures of CBV, SD was reduced an average of 0.0034 mL/100g while measures of CBF saw SD reduced by an average of 0.073 mL/100g/min. In samples of white matter, standard deviations of CBV values were reduced on average by 0.0041mL/100g while CBF SD's were reduced by 0.073 mL/100g/min. CSF ROIs in CBV calculations saw SD reductions averaging 0.0047 mL/100g and reductions of 0.074 mL/100g/min in measures of CBF. Bias within CBV calculations was at most minimal as determined by no significant changes in mean calculated values. Calculations of CBF saw large downward bias in the mean values. CONCLUSIONS: The application of the cSVD method to preprocessing of CT perfusion imaging studies produces an effective method of noise reduction. In calculations of CBV, cSVD noise reduction results in overall improvement. In calculations of CBF, cSVD, while effective in noise reduction, caused mean values to be statistically lower than the standard method. It should be noted that there is currently no evaluation of which values can be considered more accurate physiologically. Simulations of the effect of noise on CBF showed a positive correlation suggesting that the CBF algorithm itself is sensitive to the level of noise

NIHSS Scores in Ischemic Small Vessel Disease: A Study in CADASIL

Background: The National Institutes of Health Stroke Scale (NIHSS) is widely used to measure neurological deficits, evaluate the effectiveness of treatment and predict outcome in acute ischemic stroke. It has also been used to measure the residual neurological deficit at the chronic stage after ischemic events. However, the value of NIHSS in ischemic cerebral small vessel disease has not been specifically evaluated. The purpose of this study was to investigate the link between the NIHSS score and clinical severity in a large population of subjects with CADASIL (cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy), a unique model to investigate the pathophysiology and natural history of ischemic small vessel disease. Methods: Demographic and clinical data of 220 patients with one or more lacunar infarcts confirmed by MRI examination and enrolled from a prospective cohort study were analyzed. Detailed neurological examinations, including evaluation of the NIHSS and modified Rankin Scale score (mRS) for evaluating the clinical severity, were performed in all subjects. The sensitivity, specificity, positive and negative predictive values of various NIHSS thresholds to capture the absence of significant disability (mRS = 3, but only 16 (7.3%) had NIHSS >5. All but 1 subject with NIHSS >5 showed mRS >= 3. NIHSS = 3 showed a lower MMSE score than those with mRS = 3 presented either with gait disturbances or MMSE score <25. Conclusions: The present results suggest that the NIHSS cannot reflect the extent of neurological deficit and clinical severity in subjects with lacunar infarctions in the context of a chronic and diffuse small vessel disease. A specific and global neurological scale, including the assessment of cognitive and gait performances, should be developed for ischemic cerebral microangiopathy. Copyright (C) 2012 S. Karger AG, Base

Matrix product decomposition and classical simulation of quantum dynamics in the presence of a symmetry

We propose a refined matrix product state representation for many-body quantum states that are invariant under SU(2) transformations, and indicate how to extend the time-evolving block decimation (TEBD) algorithm in order to simulate time evolution in an SU(2) invariant system. The resulting algorithm is tested in a critical quantum spin chain and shown to be significantly more efficient than the standard TEBD.Comment: 5 pages, 4 figure

Computation of generalized matrix functions

We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra 1(2), 1973, pp. 163-171]. Our algorithms are based on Gaussian quadrature and Golub--Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are performed to illustrate the effectiveness and efficiency of our techniques in computing generalized matrix functions arising in the analysis of networks.Comment: 25 paged, 2 figure

Illicit drug use and cerebral microbleeds in stroke and transient ischemic attack patients

Background: Cerebral microbleeds (CMB) signal cerebral small vessel disease and are associated with ischemic stroke (IS) incidence, recurrence, and complications. While illicit drug use (IDU) is associated with cerebral small vessel disease, the association between CMB and IDU is understudied. We sought to delineate differences in vascular risk factors between IDU and CMB and determine the effect of this relationship on outcomes in IS/transient ischemic attack (TIA) patients. Methods: We included 2001 consecutive IS and TIA patients (years 2009-2018) with a readable T2*gradient-echo MRI sequence. CMB rating followed standardized guidelines and CMB were grouped topographically into lobar, deep or infratentorial. IDU data (history and/or urine toxicology) was available for 1746 patients. The adverse composite outcome included pneumonia, urinary tract infection, deep venous thrombosis or death during hospitalization. Good functional outcome was defined as modified Rankin scale score < 3 and ambulatory on discharge. Univariate analysis was used to assess vascular risk factors and multivariable logistic regression was used to characterize the IDU/CMB relationship on outcomes. Results: We observed IDU in 13.8 % (n=241), and CMB in 32.9% (n=575, 53.8% lobar, 27.3% deep and 18.8% infratentorial). Patients with IDU and at least one CMB were older (53.6±10.5 vs. 56.9±11.5, p=0.04), had a lower BMI (28.1±5.9 vs. 26.6±4.4, p=0.04), and were more likely to have had a previous IS/TIA (25.1% vs. 41.9%, p=0.01). IDU trended higher for those with severe CMB (10+) compared with those without CMB and 1-9 CMB (25% [n=9] vs 14.3% [n=1171] and 12.1% [n=65] respectively; p=0.07) without individual drug deviations from this pattern. Adverse and good functional outcomes were observed in 177 and 905 total patients, respectively. No significant interaction was observed between IDU and CMB with either adverse or functional composite outcomes. Conclusion: IDU prevalence was high in our urban study population, and showed a borderline association with increasing CMB burden. Patients with CMB and IDU history were older and more likely to have had a previous IS/TIA. Further studies are required to clarify the clinical consequences related to the relationship between IDU and CMB.Author Disclosures: B. Petrie: None. H. Lau: None. F. Cajiga-Pena: None. S. Abbas: None. B. Finn: None. K. Dam: None. A. Cervantes-Arslanian: None. T.N. Nguyen: None. H. Aparicio: None. D. Greer: None. J.R. Romero: Speakers' Bureau; Modest; Received speaker honoraria from Ferrer Group