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

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

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

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

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

Etanercept treatment in corticosteroid-dependent myasthenia gravis

The authors report a prospective pilot trial of etanercept in corticosteroid-dependent autoimmune myasthenia gravis. Eleven patients were enrolled, with eight completing the 6-month trial. Two patients were withdrawn owing to disease worsening, and one patient was withdrawn because of an erythematous skin rash. Six of the eight patients who completed the trial improved, based on quantitative measures of muscle strength and lowering of corticosteroid requirement