Self-Paced Learning: an Implicit Regularization Perspective

Self-paced learning (SPL) mimics the cognitive mechanism of humans and animals that gradually learns from easy to hard samples. One key issue in SPL is to obtain better weighting strategy that is determined by minimizer function. Existing methods usually pursue this by artificially designing the explicit form of SPL regularizer. In this paper, we focus on the minimizer function, and study a group of new regularizer, named self-paced implicit regularizer that is deduced from robust loss function. Based on the convex conjugacy theory, the minimizer function for self-paced implicit regularizer can be directly learned from the latent loss function, while the analytic form of the regularizer can be even known. A general framework (named SPL-IR) for SPL is developed accordingly. We demonstrate that the learning procedure of SPL-IR is associated with latent robust loss functions, thus can provide some theoretical inspirations for its working mechanism. We further analyze the relation between SPL-IR and half-quadratic optimization. Finally, we implement SPL-IR to both supervised and unsupervised tasks, and experimental results corroborate our ideas and demonstrate the correctness and effectiveness of implicit regularizers.Comment: 12 pages, 3 figure

The investigation of saccade parallel programming using a novel double-step paradigm: an fMRI study

Introduction: This study investigated the neuronal mechanisms of saccade target remapping and decision- making process in relation to parallel programming of saccades. Our previous study (Hu & Walker, 2011) showed that the frontal and parietal eye fields were both involved in pre-programmed of saccade sequences. It has been suggested that the representation of the second saccade goal in the double-step paradigm may involve the process of saccade target re-mapping (Duhamel, Colby, & Goldberg, 1992). In this study, we have developed a novel double-step paradigm enable us to be able to examine the neuronal mechanism underlying saccade target remapping process that required for second saccades to be executed correctly. Methods: Fifteen participants completed a novel double-step task in a 3T MRI scanner. Anatomical scans (T1 weighted) were acquired for each participant before the functional scans (TR = 1830 ms, TE = 5.5ms, resolution = 256*256, flip angle of 11°, number of slices = 160, field of view = 256*256). Functional data were collected from the whole brain using echo-planar (EPI) images with voxel size of 3*3*3 mm (TR = 3000 ms, TE = 32 ms, resolution = 64*64, field of view = 192*192, flip angle = 90°, number of slices = 42). For each participant, 73 volumes were acquired in an interleaved sequence per session. Different double-step saccade trials were as follows: 1) saccades required both target remapping and change-of-plan (saccade to an alternative target); 2) saccades required target remapping but no change-of-plan; 3) saccades required change-of-plan but not target remapping (when a return saccade to the origin or a saccade to an alternative target with vector the same as the original one was made); 4) saccades required neither target remapping nor change-of-plan. Contrasting the BOLD signal between these trial types examined the neural basis of the saccade target remapping and change-of-plan processes. Results: FMRI data were analyzed using SPM5 (functional imaging laboratory, UCL, 2005) based on Matlab 6.5 (The MathWorks, 2002). Realignment (2nd Degree B-Spline interpolation), normalization (MNI space) and spatial smoothing (8mm Gaussian smoothing kernel) were carried out as data pre- processing. First level analysis used general linear model (GLM) and each trial type was modelled as one regressor in addition to the six head movement regressors. Four key contrast were carried out to examine the cognitive process of interest: saccade target remapping & change-of-plan processes. Results showed that the right superior parietal, temporal and hippocampus regions were involved in saccade target remapping. Left lateral prefrontal, left pre-motor region, right ventromedial frontal cortex, right frontal eye fields and bilateral parietal eye fields were involved in saccade target decision processes. Behavioural results supported the view that second saccades could be partially preprogrammed, in parallel with the first step, regardless if a change-of-plan was required or not. Conclusions: In conclusion, the findings support the role of the superior parietal region in the saccade target remapping process while the hippocampus area may be involved as a temporal storage to store the original vectors required for the spatial remapping process. The saccade target decision process required a network of both prefrontal executive function regions and saccade related regions

Initial-boundary value problems for Poiseuille flow of nematic liquid crystal via full Ericksen-Leslie model

In this paper, we study the initial-boundary value problem for the Poiseuille flow of hyperbolic-parabolic Ericksen-Leslie model of nematic liquid crystals in one space dimension. Due to the quasilinearity, the solution of this model in general forms cusp singularity. We prove the global existence of H\"older continuous solution, which may include cusp singularity, for initial-boundary value problems with different types of boundary conditions.Comment: 36 pages, 3 figure

Event-related potential measures of the intending process: Time course and related ERP components

<p>Abstract</p> <p>Background</p> <p>The intending process plays an important part to the successful completion of many daily activities. However, few researchers have paid attention to this issue. This study was set to investigate the time course and the electrophysiological evidence of the intending process with a cue-respond task.</p> <p>Methods</p> <p>Event-related potentials (ERPs) were recorded while participants were performing different cued conditions (deceptive, truthful, and watch-only). The time course of intending process was analyzed through the different effect of the cue stimuli.</p> <p>Results</p> <p>The P2 component, that appeared between 200 and 400 ms after the cue was onset, can be observed in the intended conditions (deceptive, truthful), but cannot be found in un-intended condition (watch-only). The mean amplitude in P2 between the truthful and deceptive conditions was consistent with previous studies. P2 was thought to be the reflection of the intention process.</p> <p>Conclusions</p> <p>The results suggested that the intention process happened 200 to 400 ms after the cue stimuli was onset, and the P2 in the posterior scalp during this period could be a specific component that related with the process of intention.</p

Nitrate transporters in leaves and their potential roles in foliar uptake of nitrogen dioxideâ€

While plant roots are specialized organs for the uptake and transport of water and nutrients, the absorption of gaseous or liquid mineral elements by aerial plant parts has been recognized since more than one century. Nitrogen (N) is an essential macronutrient which generally absorbed either as nitrate (NO(−)(3)) or ammonium (NH(+)(4)) by plant roots. Gaseous nitrogen pollutants like N dioxide (NO(2)) can also be absorbed by plant surfaces and assimilated via the NO(−)(3) assimilation pathway. The subsequent NO(−)(3) flux may induce or repress the expression of various NO(−)(3)-responsive genes encoding for instance, the transmembrane transporters, NO(−)(3)/NO(−)(2) (nitrite) reductase, or assimilatory enzymes involved in N metabolism. Based on the existing information, the aim of this review was to theoretically analyze the potential link between foliar NO(2) absorption and N transport and metabolism. For such purpose, an overview of the state of knowledge on the NO(−)(3) transporter genes identified in leaves or shoots of various species and their roles for NO(−)(3) transport across the tonoplast and plasma membrane, in addition to the process of phloem loading is briefly provided. It is assumed that a NO(2)-induced accumulation of NO(−)(3)/NO(−)(2) may alter the expression of such genes, hence linking transmembrane NO(−)(3) transporters and foliar uptake of NO(2). It is likely that NRT1/NRT2 gene expression and species-dependent apoplastic buffer capacity may be also related to the species-specific foliar NO(2) uptake process. It is concluded that further work focusing on the expression of NRT1 (NRT1.1, NRT1.7, NRT1.11, and NRT1.12), NRT2 (NRT2.1, NRT2.4, and NRT2.5) and chloride channel family genes (CLCa and CLCd) may help us elucidate the physiological and metabolic response of plants fumigated with NO(2)