As a synthesis of a legacy of cerebellar models, we have developed a new general cerebellar module incorporating all major cell types and connections. It has two key features: 1. reciprocal connections between cerebellar nuclear cells and the inferior olive result in a stable learning system driving the cerebellum to mirror sensory input to the olive; and 2. synaptic eligibility effects a time-...

ByteSub is a key module in the AES hardware architectures. Most of the ByteSub design is accomplished by look-up table method. To reduce the complexity of AES module and improve the performance and security, we propose a novel dynamic ByteSub generator, which is composed of finite field inverse and multipliers. In our design, look-up table method is no more essential to the ByteSub hardware arc...

Our final project will be designing and implementing an audio system in which the audio signal is input, wirelessly transmitted, audio filtered and equalized. The audio is inputted through a microphone and is digitized using an Analog-To-Digital converter with the LM4550 AC’97 Codec. The audio signal is then compressed using the Discrete Cosine Transform (DCT) and is wirelessly transmitted and ...

In his important paper "Coverings of p-adic symmetric regions" [Dr], Drinfeld showed that the p-adic upper half plane and its higher dimensional analogues serve as moduli spaces for certain rigidified formal groups with quaternionic multiplications. Given a formal group of the proper type, together with rigidifying data, over, say, a ring R on which p is nilpotent, Drinfeld constructs an R-valu...

The aim of this note is to classify all weakly closed unipotent subgroups in the split Chevalley groups. In an application we show under some mild assumptions on the characteristic that 2 dimX + dim cg(X) < dim g for X a non-trivial unipotent subgroup of the connected simple algebraic group G. This shows the failure of the analogue of the so called “2F-condition” for finite groups for the adjoi...

4. Describe the D-module extD(M,D) in terms of generators and relations. 5. Prove that extD(M,D) is a 1-dimensional Q(a, k, ω, ζ)-vector space. Give a basis ρ(Λ) of extD(M,D), where ρ : D 3 −→ D3/(RD4) denotes the canonical projection. 6. Deduce that ρ(Λ) generates extD(M,D), i.e., ext 1 D(M,D) is a cyclic D-module. 7. Consider the matrix P = (R − Λ) ∈ D3×5. Show that P admits a left-inverse ov...

This paper gives a necessary and sufficient condition for the image of Specht module under inverse Schur functor to be isomorphic dual Weyl in characteristic 2, an elementary proof that this isomorphism holds all cases other characteristics. These results are new characteristics 2 3. We deduce some examples indecomposable modules 2. When does not hold, is still quotient module, we prove additio...

Efficient parameter identification is an important issue for mechanistic agro-hydrological models with a complex and nonlinear property. In this study, we presented an efficient global methodology of sensitivity analysis and parameter estimation for a physically-based agro-hydrological model (SWAP-EPIC). The LH-OAT based module and the modified-MGA based module were developed for parameter sens...