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

Theoretical Properties of Projection Based Multilayer Perceptrons with Functional Inputs

Many real world data are sampled functions. As shown by Functional Data Analysis (FDA) methods, spectra, time series, images, gesture recognition data, etc. can be processed more efficiently if their functional nature is taken into account during the data analysis process. This is done by extending standard data analysis methods so that they can apply to functional inputs. A general way to achieve this goal is to compute projections of the functional data onto a finite dimensional sub-space of the functional space. The coordinates of the data on a basis of this sub-space provide standard vector representations of the functions. The obtained vectors can be processed by any standard method. In our previous work, this general approach has been used to define projection based Multilayer Perceptrons (MLPs) with functional inputs. We study in this paper important theoretical properties of the proposed model. We show in particular that MLPs with functional inputs are universal approximators: they can approximate to arbitrary accuracy any continuous mapping from a compact sub-space of a functional space to R. Moreover, we provide a consistency result that shows that any mapping from a functional space to R can be learned thanks to examples by a projection based MLP: the generalization mean square error of the MLP decreases to the smallest possible mean square error on the data when the number of examples goes to infinity

Susceptibility to Scams in Older Black and White Adults

Previous reports on racial differences in scam susceptibility have yielded mixed findings, and few studies have examined reasons for any observed race differences. Older Black and White participants without dementia (N = 592) from the Minority Aging Research Study and the Rush Memory and Aging Project who completed a susceptibility to scam questionnaire and other measures were matched according to age, education, sex, and global cognition using Mahalanobis distance. In adjusted models, older Black adults were less susceptible to scams than older White adults (Beta = −0.2496, SE = 0.0649, p = 0.0001). Contextual factors did not mediate and affective factors did not moderate this association. Analyses of specific items revealed Black adults had greater knowledge of scam targeting of older adults and were less likely to pick up the phone for unidentified callers. Older Black adults are less susceptible to scams than demographically-matched older White adults, although the reasons remain unknown

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

On the Non-Existence of Optimal Solutions and the Occurrence of “Degeneracy” in the CANDECOMP/PARAFAC Model

The CANDECOMP/PARAFAC (CP) model decomposes a three-way array into a prespecified number of R factors and a residual array by minimizing the sum of squares of the latter. It is well known that an optimal solution for CP need not exist. We show that if an optimal CP solution does not exist, then any sequence of CP factors monotonically decreasing the CP criterion value to its infimum will exhibit the features of a so-called “degeneracy”. That is, the parameter matrices become nearly rank deficient and the Euclidean norm of some factors tends to infinity. We also show that the CP criterion function does attain its infimum if one of the parameter matrices is constrained to be column-wise orthonormal

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

Motivational modulation of bradykinesia in Parkinson's disease off and on dopaminergic medication.

Motivational influence on bradykinesia in Parkinson's disease may be observed in situations of emotional and physical stress, a phenomenon known as paradoxical kinesis. However, little is known about motivational modulation of movement speed beyond these extreme circumstances. In particular, it is not known if motivational factors affect movement speed by improving movement preparation/initiation or execution (or both) and how this effect relates to the patients' medication state. In the present study, we tested if provision of motivational incentive through monetary reward would speed-up movement initiation and/or execution in Parkinson's disease patients and if this effect depended on dopaminergic medication. We studied the effect of monetary incentive on simple reaction time in 11 Parkinson's disease patients both "off" and "on" dopaminergic medication and in 11 healthy participants. The simple reaction time task was performed across unrewarded and rewarded blocks. The initiation time and movement time were quantified separately. Anticipation errors and long responses were also recorded. The prospect of reward improved initiation times in Parkinson's disease patients both "off" and "on" dopaminergic medication, to a similar extent as in healthy participants. However, for "off" medication, this improvement was associated with increased frequency of anticipation errors, which were eliminated by dopamine replacement. Dopamine replacement had an additional, albeit small effect, on reward-related improvement of movement execution. Motivational strategies are helpful in overcoming bradykinesia in Parkinson's disease. Motivational factors may have a greater effect on bradykinesia when patients are "on" medication, as dopamine appears to be required for overcoming speed-accuracy trade-off and for improvement of movement execution. Thus, medication status should be an important consideration in movement rehabilitation programmes for patients with Parkinson's disease