Approximating a Wavefunction as an Unconstrained Sum of Slater Determinants

The wavefunction for the multiparticle Schr\"odinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they impose additional structural constraints on the determinants, such as orthogonality between orbitals or an excitation pattern. We present a method without any such constraints, by which we hope to obtain much more efficient expansions, and insight into the inherent structure of the wavefunction. We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. The core procedure is the construction and solution of a matrix-integral system derived from antisymmetric inner products involving the potential operators. We show how to construct and solve this system with computational complexity competitive with current methods.Comment: 30 page

Associations between Quantitative Mobility Measures Derived from Components of Conventional Mobility Testing and Parkinsonian Gait in Older Adults

Objective: To provide objective measures which characterize mobility in older adults assessed in the community setting and to examine the extent to which these measures are associated with parkinsonian gait. Methods: During conventional mobility testing in the community-setting, 351 ambulatory non-demented Memory and Aging Project participants wore a belt with a whole body sensor that recorded both acceleration and angular velocity in 3 directions. We used measures derived from these recordings to quantify 5 subtasks including a) walking, b) transition from sit to stand, c) transition from stand to sit, d) turning and e) standing posture. Parkinsonian gait and other mild parkinsonian signs were assessed with a modified version of the original Unified Parkinson’s Disease Rating Scale (mUPDRS). Results: In a series of separate regression models which adjusted for age and sex, all 5 mobility subtask measures were associated with parkinsonian gait and accounted for 2% to 32% of its variance. When all 5 subtask measures were considered in a single model, backward elimination showed that measures of walking sit to stand and turning showed independent associations with parkinsonian gait and together accounted for more than 35% of its variance. Cross-validation using data from a 2nd group of 258 older adults showed similar results. In similar analyses, only walking was associated with bradykinesia and sway with tremor. Interpretation Quantitative mobility subtask measures vary in their associations with parkinsonian gait scores and other parkinsonian signs in older adults. Quantifying the different facets of mobility has the potential to facilitate the clinical characterization and understanding the biologic basis for impaired mobility in older adults

Motor function in Parkinson's disease and supranuclear palsy: simultaneous factor analysis of a clinical scale in several populations

BACKGROUND: In order to better understand the similarities and differences in the motor behaviour of different groups of patients, their scores on the Motor Examination section of the Unified Parkinson's Disease Rating Scale (UPDRS) were analysed simultaneously. The three groups consisted, respectively, of patients with Parkinson's disease (PD) on medication, patients with Parkinson's disease withdrawn from anti-parkinsonian medication for at least 12 hours, and patients diagnosed with a specific Parkinsonism syndrome: Progressive Supranuclear Palsy (PSP). METHODS: A total of 669 consecutively sampled patients from three separate hospital-based clinics participated (294 PD on medication; 200 PD off medication: 175 PSP). The Motor Examination section of the UPDRS was administered by neurologists at the three participating clinics. The patient scores on each item were recorded. To assess similarities and differences among the components of the UPDRS in these samples, we performed simultaneous or multigroup factor analysis on the covariance matrices of the three groups. In addition, it was investigated whether a single model for the Motor Examination section of the UPDRS could be developed which would be valid for all three groups at the same time. RESULTS: A single six-dimensional factor solution was found that fitted all groups, although this was not straightforward due to differences between the tremor-at-rest variables. The factors were identified as Tremor-at-rest, Postural Tremor, Axial Dysfunctioning, Rigidity, Left Bradykinesia and Right Bradykinesia. The analysis also pointed to a somewhat lower lateralization in bradykinesia for PSP patients. The groups differed in intensity of motor impairment, especially with respect to Tremor-at-Rest, but the overall relationships between the variables were shared by the three groups. In addition, apart from the common factor structure evidence of differences in body part-specific and motor-specific variances was found. CONCLUSION: From a clinical point of view, the analyses showed that using the Motor Examination section of the UPDRS is also appropriate for patients with PSP, because the correlational structure of the items is directly comparable to that of Parkinson's patients. Methodologically, the analysis of all groups together showed that it is possible to evaluate similarities and differences between factor structures in great detail

Integrative analysis of gene expression and copy number alterations using canonical correlation analysis

Supplementary Figure 1. Representation of the samples from the tuning set by their coordinates in the first two pairs of features (extracted from the tuning set) using regularized dual CCA, with regularization parameters tx = 0.9, ty = 0.3 (left panel), and PCA+CCA (right panel). We show the representations with respect to both the copy number features and the gene expression features in a superimposed way, where each sample is represented by two markers. The filled markers represent the coordinates in the features extracted from the copy number variables, and the open markers represent coordinates in the features extracted from the gene expression variables. Samples with different leukemia subtypes are shown with different colors. The first feature pair distinguishes the HD50 group from the rest, while the second feature pair represents the characteristics of the samples from the E2A/PBX1 subtype. The high canonical correlation obtained for the tuning samples with regularized dual CCA is apparent in the left panel, where the two points for each sample coincide. Nevertheless, the extracted features have a high generalization ability, as can be seen in the left panel of Figure 5, showing the representation of the validation samples. 1 Supplementary Figure 2. Representation of the samples from the tuning set by their coordinates in the first two pairs of features (extracted from the tuning set) using regularized dual CCA, with regularization parameters tx = 0, ty = 0 (left panel), and tx = 1, ty = 1 (right panel). We show the representations with respect to both the copy number features and the gene expression features in a superimposed way, where each sample is represented by tw

Testing Gait with Ankle-Foot Orthoses in Children with Cerebral Palsy by Using Functional Mixed-Effects Analysis of Variance

Dr Morrissey is part funded by the NIHR/HEE Senior Clinical Lecturer scheme. Tis report presents independent research part-funded by the National Institute for Health Research (NIHR) CAT SCL-2013-04-00

Combinations of motor measures more strongly predict adverse health outcomes in old age: the rush memory and aging project, a community-based cohort study

<p>Abstract</p> <p>Objective</p> <p>Motor impairment in old age is a growing public-health concern, and several different constructs have been used to identify motor impairments in older people. We tested the hypothesis that combinations of motor constructs more strongly predict adverse health outcomes in older people.</p> <p>Methods</p> <p>In total, 949 people without dementia, history of stroke or Parkinson's disease, who were participating in the Rush Memory and Aging Project (a longitudinal community-based cohort study), underwent assessment at study entry. From this, three constructs were derived: 1) physical frailty based on grip strength, timed walk, body mass index and fatigue; 2) Parkinsonian Signs Score based on the modified motor section of the Unified Parkinson's Disease Rating Scale; and 3) a motor construct, based on nine strength measures and nine motor performances. Disability and cognitive status were assessed annually. A series of Cox proportional-hazards models, controlling for age, sex and education, were used to examine the association of each of these three constructs alone and in various combinations with death, disability and Alzheimer's disease (AD).</p> <p>Results</p> <p>All three constructs were related (mean <it>r </it>= 0.50, all <it>P </it>< 0.001), and when considered individually in separate proportional-hazards models, were associated with risk of death, incident disability and AD. However, when considered together, combinations of these constructs more strongly predicted adverse health outcomes.</p> <p>Conclusions</p> <p>Physical frailty, parkinsonian signs score and global motor score are related constructs that capture different aspects of motor function. Assessments using several motor constructs may more accurately identify people at the highest risk of adverse health consequences in old age.</p

A new class of glycomimetic drugs to prevent free fatty acid-induced endothelial dysfunction

Background: Carbohydrates play a major role in cell signaling in many biological processes. We have developed a set of glycomimetic drugs that mimic the structure of carbohydrates and represent a novel source of therapeutics for endothelial dysfunction, a key initiating factor in cardiovascular complications. Purpose: Our objective was to determine the protective effects of small molecule glycomimetics against free fatty acid­induced endothelial dysfunction, focusing on nitric oxide (NO) and oxidative stress pathways. Methods: Four glycomimetics were synthesized by the stepwise transformation of 2,5­dihydroxybenzoic acid to a range of 2,5­substituted benzoic acid derivatives, incorporating the key sulfate groups to mimic the interactions of heparan sulfate. Endothelial function was assessed using acetylcholine­induced, endotheliumdependent relaxation in mouse thoracic aortic rings using wire myography. Human umbilical vein endothelial cell (HUVEC) behavior was evaluated in the presence or absence of the free fatty acid, palmitate, with or without glycomimetics (1µM). DAF­2 and H2DCF­DA assays were used to determine nitric oxide (NO) and reactive oxygen species (ROS) production, respectively. Lipid peroxidation colorimetric and antioxidant enzyme activity assays were also carried out. RT­PCR and western blotting were utilized to measure Akt, eNOS, Nrf­2, NQO­1 and HO­1 expression. Results: Ex vivo endothelium­dependent relaxation was significantly improved by the glycomimetics under palmitate­induced oxidative stress. In vitro studies showed that the glycomimetics protected HUVECs against the palmitate­induced oxidative stress and enhanced NO production. We demonstrate that the protective effects of pre­incubation with glycomimetics occurred via upregulation of Akt/eNOS signaling, activation of the Nrf2/ARE pathway, and suppression of ROS­induced lipid peroxidation. Conclusion: We have developed a novel set of small molecule glycomimetics that protect against free fatty acidinduced endothelial dysfunction and thus, represent a new category of therapeutic drugs to target endothelial damage, the first line of defense against cardiovascular disease

MRI-based volumetric measurement of the substantia innominata in amnestic MCI and mild AD

The substantia innominata (SI) contains the nucleus basalis of Meynert, which provides the major cholinergic innervation to the entire cortical mantel and the amygdala; degeneration of nucleus basalis neurons correlates with cognitive decline in Alzheimer\u27s disease (AD). However, whether SI atrophy occurs in individuals with amnestic mild cognitive impairment (aMCI) has not been examined thoroughly in vivo. In the present study, we developed a new protocol to measure volumetric changes in the SI from magnetic resonance imaging (MRI) scans. Participants consisted of 27 elderly controls with no cognitive impairment (NCI); 33 individuals with aMCI; and 19 patients with mild AD. SI volumes were traced on three consecutive gapless 1. mm thick coronal slices. Results showed that SI volume was significantly reduced in the mild AD group compared to both NCI and aMCI participants; however, the NCI and aMCI groups did not differ from each other. Furthermore, a decrease in SI volume was related to impaired performance on declarative memory tasks even when attention was controlled. © 2009 Elsevier Inc