Bogdanov-Takens bifurcation of codimension 33 in the Gierer-Meinhardt model

Bifurcation of the local Gierer-Meinhardt model is analyzed in this paper. It is found that the degenerate Bogdanov-Takens bifurcation of codimension 3 happens in the model, except that teh saddle-node bifurcation and the Hopf bifurcation. That was not reported in the existing results about this model. The existence of equilibria, their stability, the bifurcation and the induced complicated and interesting dynamics are explored in detail, by using the stability analysis, the normal form method and bifurcation theory. Numerical results are also presented to validate theoretical results

Toward a semi-self-paced EEG brain computer interface: decoding initiation state from non-initiation state in dedicated time slots.

Brain computer interfaces (BCIs) offer a broad class of neurologically impaired individuals an alternative means to interact with the environment. Many BCIs are "synchronous" systems, in which the system sets the timing of the interaction and tries to infer what control command the subject is issuing at each prompting. In contrast, in "asynchronous" BCIs subjects pace the interaction and the system must determine when the subject's control command occurs. In this paper we propose a new idea for BCI which draws upon the strengths of both approaches. The subjects are externally paced and the BCI is able to determine when control commands are issued by decoding the subject's intention for initiating control in dedicated time slots. A single task with randomly interleaved trials was designed to test whether it can be used as stimulus for inducing initiation and non-initiation states when the sensory and motor requirements for the two types of trials are very nearly identical. Further, the essential problem on the discrimination between initiation state and non-initiation state was studied. We tested the ability of EEG spectral power to distinguish between these two states. Among the four standard EEG frequency bands, beta band power recorded over parietal-occipital cortices provided the best performance, achieving an average accuracy of 86% for the correct classification of initiation and non-initiation states. Moreover, delta band power recorded over parietal and motor areas yielded a good performance and thus could also be used as an alternative feature to discriminate these two mental states. The results demonstrate the viability of our proposed idea for a BCI design based on conventional EEG features. Our proposal offers the potential to mitigate the signal detection challenges of fully asynchronous BCIs, while providing greater flexibility to the subject than traditional synchronous BCIs

A Fuzzy Mining Algorithm for Association-Rule Knowledge Discovery

Due to increasing use of very large database and data warehouses, discovering useful knowledge from transactions is becoming an important research area. On the other hand, using fuzzy classification in data mining has been developed in recent years. Hong and Lee proposed a general learning method that automatically derives fuzzy if-then rules and membership functions from a set of given training examples using a decision table. But it is complex if there are many attributes or if the predefined unit is small. Hong and Chen improve it by first selecting relevant attributes and building appropriate initial membership functions. Based on Hong’s heuristic algorithm of membership functions and Apriori approach, we propose a fuzzy mining algorithm to explore association rules from given quantitative transactions. Experimental results on Iris data show that the proposed algorithm effectively induces more association rules

Noncollinearity-modulated electronic properties of the monolayer CrI3_3

Introducing noncollinear magnetization into a monolayer CrI$_3$ is proposed to be an effective approach to modulate the local electronic properties of the two-dimensional (2D) magnetic material. Using first-principles calculation, we illustrate that both the conduction and valence bands in the monolayer CrI$_3$ are lowered down by spin spiral states. The distinct electronic structure of the monolayer noncollinear CrI$_3$ can be applied in nanoscale functional devices. As a proof of concept, we show that a magnetic domain wall can form a one-dimensional conducting channel in the 2D semiconductor via proper gating. Other possible applications such as electron-hole separation and identical quantum dots are also discussed

Formation of in-volume nanogratings with sub-100 nm periods in glass by femtosecond laser irradiation

We present direct experimental observation of the morphological evolution during the formation of nanogratings with sub-100-nm periods with the increasing number of pulses. Theoretical simulation shows that the constructive interference of the scattering light from original nanoplanes will create an intensity maximum located between the two adjacent nanoplanes, resulting in shortening of the nanograting period by half. The proposed mechanism enables explaining the formation of nanogratings with periods beyond that predicted by the nanoplasmonic model.Comment: 4 pages, 3 figure