Low-complexity RLS algorithms using dichotomous coordinate descent iterations

In this paper, we derive low-complexity recursive least squares (RLS) adaptive filtering algorithms. We express the RLS problem in terms of auxiliary normal equations with respect to increments of the filter weights and apply this approach to the exponentially weighted and sliding window cases to derive new RLS techniques. For solving the auxiliary equations, line search methods are used. We first consider conjugate gradient iterations with a complexity of O(N-2) operations per sample; N being the number of the filter weights. To reduce the complexity and make the algorithms more suitable for finite precision implementation, we propose a new dichotomous coordinate descent (DCD) algorithm and apply it to the auxiliary equations. This results in a transversal RLS adaptive filter with complexity as low as 3N multiplications per sample, which is only slightly higher than the complexity of the least mean squares (LMS) algorithm (2N multiplications). Simulations are used to compare the performance of the proposed algorithms against the classical RLS and known advanced adaptive algorithms. Fixed-point FPGA implementation of the proposed DCD-based RLS algorithm is also discussed and results of such implementation are presented

Molecular Dynamics Studies on the Buffalo Prion Protein

It was reported that buffalo is a low susceptibility species resisting to prion diseases, which are invariably fatal and highly infectious neurodegenerative diseases that affect a wide variety of species. In molecular structures, TSE neurodegenerative diseases are caused by the conversion from a soluble normal cellular prion protein, predominantly with alpha-helices, into insoluble abnormally folded infectious prions, rich in beta-sheets. This paper studies the molecular structure and structural dynamics of buffalo prion protein, in order to reveal the reason why buffalo are resistant to prion diseases. We first did molecular modeling of a homology structure constructed by one mutation at residue 143 from the Nuclear Magnetic Resonance structure of bovine and cattle PrP(124-227); immediately we found for buffalo PrPC(124-227) there are 5 hydrogen bonds at Asn143, but at this position bovine/cattle do not have such hydrogen bonds. Same as that of rabbits, dogs or horses, our molecular dynamics studies also confirmed there is a strong salt bridge ASP178-ARG164 (O-N) keeping the beta2-alpha2 loop linked in buffalo. We also found there is a very strong hydrogen bond SER170-TYR218 linking this loop with the C-terminal end of alpha-helix H3. Other information such as (i) there is a very strong salt bridge HIS187-ARG156 (N-O) linking alpha-helices H2 and H1 (if mutation H187R is made at position 187 then the hydrophobic core of PrPC will be exposed), (ii) at D178, there is a hydrogen bond Y169-D178 and a polar contact R164-D178 for BufPrPC instead of a polar contact Q168-D178 for bovine PrPC, (iii) BufPrPC owns 3-10 helices at 125-127, 152-156 and in the beta2-alpha2 loop respectively, and (iv) in beta2-alpha2 loop there are strong pi-contacts, etc, has been discovered