1438319
Identities and Parseval type relations for the L2-transform
Abstract In the present paper, the authors introduce identities for the L 2 -transform which yield a Parseval type relationship for the L 2 -transform. The Parseval type relationship proven in this paper give rise to useful corollaries for evaluating indefinite integrals of special functions. Some examples are also given as illustrations of the results presented here.
13017049
Identities for the exponential integral and the complementary error transforms
Abstract In the present paper the authors introduce the exponential integral transform and the complementary error transform, then it is shown that the third iterate of the Laplace transform is the exponential integral transform and a modified third iterate of the Laplace transform is the complementary error transform. Some identities involving these new transforms, the Laplace transform and the Stieltjes transform are given. Using the identities, Parseval–Goldstein type results involving these transforms are proved. Some illustrative examples are also given.
10774169
Significance of random neuronal drive
Abstract Effectively random firing occurs frequently in the brain. Random components of neuronal drive are therefore often major influences on activity. We describe here how level of drive, inhibitory/excitatory balance, correlation between input streams, EPSP/IPSP characteristics, the nature of the postsynaptic neuron all affect pattern and level of firing, the influence often interacting in complex ways. Random firing might also be instrumental in facilitating synchronized firing. These factors are possibly important elements of the mechanisms by which some neural networks encode information. Clarifying them might therefore facilitate a deeper understanding of the nature of the neural code.
28101453
HCI Professional Involvement in k-12 Education: On Target or Missing the Mark?
Abstract. The state of learning across geographic, socioeconomic, age, and gender boundaries can be enhanced greatly by Human-Computer Information (HCI) infusion into blended learning [1][2][3] or Course Management System (CMS) software [4][3][5]. The major thrust of this paper is to examine problematic issues examined in popular software such as MoodleTM in which the HCI community could be beneficial. By regarding the ultimate students' goal, i.e. grades, and the desirable benefit of course material understanding, one can develop an understanding of what CMS software needs and CMS software users expect on the high school level.
11160456
Structure of Lateral Inhibition in an Olfactory Bulb Model
It has been shown that mutual lateral inhibition of the projection neurones in the olfactory bulb, mediated by interneurones, serves to tune the representation of odours in the bulb and reduce the overlap between similaz odorants. In this paper we demonstrate that the parameters of the lateral interaction, specifically the relation of synaptic strength to cell separation and the effective overall gain of the network, have a significant effect on the strength and range of lateral inhibition in a simple model of the olfactory bulb.
78402
Composed products and module polynomials over finite fields
Abstract A general notion of composition of polynomials over a finite field was introduced by Brawley and Carlitz (1987). In their paper they developed a unique decomposition theory in two special cases of the composed product, but they left open the question of uniqueness in the general case. This paper settles this open question by proving that irreducibles do indeed decompose uniquely with respect to the general notion and, in doing so, unifies the two separate treatments of Brawley and Carlitz into a single, more general theory. The paper also offers a generalization which unifies into a single theory the notions of ‘belonging to an exponent’ and ‘belonging to a q -polynomial’, which are basic in the theory of finite fields.
10827335
A novel approach for analyzing dynamics in neural networks with saturated characteristics
Current theories about the dynamics of neural networks with nonlinear characteristics and parameterized by set of parameters are mostly based on approximations in one way or another. In this paper we first introduce a rigorous approach which allows us to check in which parameter region a given saturated state is an attractor of the dynamics: a saturated state w=(wi, i=1,...,N)∈{-1,1}N is an attractor of the dynamics if and only if there is a local field gap between neurons in J+(w)={i, wi=1} and J-(w)={i, wi=−1}. Then we apply the result to analyze several models in neural networks. In particular in the Hopfield model we calculate the capacity and give an exact relation between the capacity and the threshold.