Parallel Algorithms for Constrained Tensor Factorization via the Alternating Direction Method of Multipliers

Tensor factorization has proven useful in a wide range of applications, from sensor array processing to communications, speech and audio signal processing, and machine learning. With few recent exceptions, all tensor factorization algorithms were originally developed for centralized, in-memory computation on a single machine; and the few that break away from this mold do not easily incorporate practically important constraints, such as nonnegativity. A new constrained tensor factorization framework is proposed in this paper, building upon the Alternating Direction method of Multipliers (ADMoM). It is shown that this simplifies computations, bypassing the need to solve constrained optimization problems in each iteration; and it naturally leads to distributed algorithms suitable for parallel implementation on regular high-performance computing (e.g., mesh) architectures. This opens the door for many emerging big data-enabled applications. The methodology is exemplified using nonnegativity as a baseline constraint, but the proposed framework can more-or-less readily incorporate many other types of constraints. Numerical experiments are very encouraging, indicating that the ADMoM-based nonnegative tensor factorization (NTF) has high potential as an alternative to state-of-the-art approaches.Comment: Submitted to the IEEE Transactions on Signal Processin

Conservation of alternative splicing in sodium channels reveals evolutionary focus on release from inactivation and structural insights into gating

Voltage-gated sodium channels are critical for neuronal activity, and highly intolerant to variation. Even mutations that cause subtle changes in the activity these channels are sufficient to cause devastating inherited neurological diseases, such as epilepsy and pain. However, these channels do vary in healthy tissue. Alternative splicing modifies sodium channels, but the functional relevance and adaptive significance of this splicing remain poorly understood. Here we use a conserved alternate exon encoding part of the first domain of sodium channels to compare how splicing modifies different channels, and to ask whether the functional consequences of this splicing have been preserved in different genes. Although the splicing event is highly conserved, one splice variant has been selectively removed from Nav1.1 in multiple mammalian species, suggesting that the functional variation in Nav1.1 is less well-tolerated. We show for three human channels (Nav1.1, Nav1.2 and Nav1.7) splicing modifies the return from inactivated to deactivated states, and the differences between splice variants are occluded by antiepileptic drugs that bind to and stabilize inactivated states. A model based on structural data can replicate these changes, and indicates that splicing may exploit a distinct role of the first domain to change channel availability, and that the first domain of all three sodium channels plays a role in determining the rate at which the inactivation domain dissociates. Taken together, our data suggest that the stability of inactivated states is under tight evolutionary control, but that in Nav1.1 faster recovery from inactivation is associated with negative selection in mammals

Alternative splicing in sodium channels: biophysical and functional effects in NaV1.1, NaV1.2 & NaV1.7

Alternative splicing in voltage-gated sodium channels can affect pathophysiological conditions, including epilepsy and pain. A conserved alternative splicing event in sodium channel genes, including SCN1A, SCN2A and SCN9A, gives rise to the neonatal (5N) and adult (5A) isoforms. Differences in the ratio of 5A/5N in Nav1.1 (encoded by SCN1A) in patients may lead to different predisposition to epilepsy or response to antiepileptic drugs (AED). Previous HEK293T whole-cell voltage-clamp recordings showed that Nav1.1-5N channels recover more quickly from fast inactivation than 5A. However it was unknown whether this effect is conserved in Nav1.2 (encoded by SCN2A) and Nav1.7 (SCN9A) channels, or what the functional consequences of this splicing event are for neurons. This project used whole-cell voltage-clamp recordings on heterologously expressed neonatal and adult channels to compare the biophysical properties of the splice isoforms for all three channel types and their modulation by AEDs. It also used current-clamp and dynamic-clamp recordings on transfected hippocampal cultured neurons to assess the effect of splicing on neuronal properties during epileptiform activity. Biophysical analysis in HEK293T cells revealed that splicing profoundly regulates fast inactivation and channel availability during fast, repetitive stimulation, with neonatal channels showing higher availability compared to adult channels and this difference was conserved among Nav1.1, Nav1.2 and Nav1.7. The change in inactivation imposed by splicing can be modeled as a modification of the stability of the inactivation statein resting channels. This change can be eradicated by administration of the AEDs phenytoin and carbamazepine. Current-clamp recordings in transfected neurons showed that the alternatively spliced variantmodifies the rising phase of action potentials for Nav1.1 and Nav1.2 at high firing frequencies, implying a consistent splice-dependent modulation of channel availability. For Nav1.1 in interneurons, this translated to higher firing frequency for the neonatal isoform, which also conferred a higher maximal firing rate during epileptiform events imposed under dynamic-clamp recordings

Novel mutations in human and mouse SCN4A implicate AMPK in myotonia and periodic paralysis

Mutations in the skeletal muscle channel (SCN4A), encoding the Nav1.4 voltage-gated sodium channel, are causative of a variety of muscle channelopathies, including non-dystrophic myotonias and periodic paralysis. The effects of many of these mutations on channel function have been characterized both in vitro and in vivo. However, little is known about the consequences of SCN4A mutations downstream from their impact on the electrophysiology of the Nav1.4 channel. Here we report the discovery of a novel SCN4A mutation (c.1762A>G; p.I588V) in a patient with myotonia and periodic paralysis, located within the S1 segment of the second domain of the Nav1.4 channel. Using N-ethyl-N-nitrosourea mutagenesis, we generated and characterized a mouse model (named draggen), carrying the equivalent point mutation (c.1744A>G; p.I582V) to that found in the patient with periodic paralysis and myotonia. Draggen mice have myotonia and suffer from intermittent hind-limb immobility attacks. In-depth characterization of draggen mice uncovered novel systemic metabolic abnormalities in Scn4a mouse models and provided novel insights into disease mechanisms. We discovered metabolic alterations leading to lean mice, as well as abnormal AMP-activated protein kinase activation, which were associated with the immobility attacks and may provide a novel potential therapeutic target

Local linear regression with adaptive orthogonal fitting for the wind power application

Short-term forecasting of wind generation requires a model of the function for the conversion of me-teorological variables (mainly wind speed) to power production. Such a power curve is nonlinear and bounded, in addition to being nonstationary. Local linear regression is an appealing nonparametric ap-proach for power curve estimation, for which the model coefficients can be tracked with recursive Least Squares (LS) methods. This may lead to an inaccurate estimate of the true power curve, owing to the assumption that a noise component is present on the response variable axis only. Therefore, this assump-tion is relaxed here, by describing a local linear regression with orthogonal fit. Local linear coefficients are defined as those which minimize a weighted Total Least Squares (TLS) criterion. An adaptive es-timation method is introduced in order to accommodate nonstationarity. This has the additional benefit of lowering the computational costs of updating local coefficients every time new observations become available. The estimation method is based on tracking the left-most eigenvector of the augmented covari-ance matrix. A robustification of the estimation method is also proposed. Simulations on semi-artificial datasets (for which the true power curve is available) underline the properties of the proposed regression and related estimation methods. An important result is the significantly higher ability of local polynomia

Dynamic behavior analysis via structured rank minimization

Human behavior and affect is inherently a dynamic phenomenon involving temporal evolution of patterns manifested through a multiplicity of non-verbal behavioral cues including facial expressions, body postures and gestures, and vocal outbursts. A natural assumption for human behavior modeling is that a continuous-time characterization of behavior is the output of a linear time-invariant system when behavioral cues act as the input (e.g., continuous rather than discrete annotations of dimensional affect). Here we study the learning of such dynamical system under real-world conditions, namely in the presence of noisy behavioral cues descriptors and possibly unreliable annotations by employing structured rank minimization. To this end, a novel structured rank minimization method and its scalable variant are proposed. The generalizability of the proposed framework is demonstrated by conducting experiments on 3 distinct dynamic behavior analysis tasks, namely (i) conflict intensity prediction, (ii) prediction of valence and arousal, and (iii) tracklet matching. The attained results outperform those achieved by other state-of-the-art methods for these tasks and, hence, evidence the robustness and effectiveness of the proposed approach

An Empirical Comparison of Information-Theoretic Criteria in Estimating the Number of Independent Components of fMRI Data

BACKGROUND: Independent Component Analysis (ICA) has been widely applied to the analysis of fMRI data. Accurate estimation of the number of independent components of fMRI data is critical to reduce over/under fitting. Although various methods based on Information Theoretic Criteria (ITC) have been used to estimate the intrinsic dimension of fMRI data, the relative performance of different ITC in the context of the ICA model hasn't been fully investigated, especially considering the properties of fMRI data. The present study explores and evaluates the performance of various ITC for the fMRI data with varied white noise levels, colored noise levels, temporal data sizes and spatial smoothness degrees. METHODOLOGY: Both simulated data and real fMRI data with varied Gaussian white noise levels, first-order auto-regressive (AR(1)) noise levels, temporal data sizes and spatial smoothness degrees were carried out to deeply explore and evaluate the performance of different traditional ITC. PRINCIPAL FINDINGS: Results indicate that the performance of ITCs depends on the noise level, temporal data size and spatial smoothness of fMRI data. 1) High white noise levels may lead to underestimation of all criteria and MDL/BIC has the severest underestimation at the higher Gaussian white noise level. 2) Colored noise may result in overestimation that can be intensified by the increase of AR(1) coefficient rather than the SD of AR(1) noise and MDL/BIC shows the least overestimation. 3) Larger temporal data size will be better for estimation for the model of white noise but tends to cause severer overestimation for the model of AR(1) noise. 4) Spatial smoothing will result in overestimation in both noise models. CONCLUSIONS: 1) None of ITC is perfect for all fMRI data due to its complicated noise structure. 2) If there is only white noise in data, AIC is preferred when the noise level is high and otherwise, Laplace approximation is a better choice. 3) When colored noise exists in data, MDL/BIC outperforms the other criteria