Sparse coding

Jortner, R.A., Farivar, S.S., Laurent, G. A Simple Connectivity Scheme for Sparse Coding in an Olfactory System. J. Neurosci. 27, 1659-1669 (2007)... 

A common approach for sparse coding (see for example Lewicki and Sejnowski, 2000) is to use mathematical optimisation to find the best code for signal/image representation. Before coming to the optimisation function, we need to define the norms of a vector. 

The highest level of integration would be to establish one large set of equations and to apply one solution process to both thermal and airflow-related variables. Nevertheless, a very sparse matrix must be solved, and one cannot use the reliable and well-proven solvers of the present codes anymore. Therefore, a separate solution process for thermal and airflow parameters respectively remains the most promising approach. This seems to be appropriate also for the coupling of computational fluid dynamics (CFD) with a thermal model. ... 

Diagnosis and procedure codes may reflect reimbursement strategies instead of clinically accurate diagnoses Limited information on important covariates Sparse outcomes data Lack of representativeness Lack of structure for research purposes... 

SQP. This is a sister code to GRG2 and available from the same source. The interfaces to SQP are very similar to those of GRG2. SQP is useful for small problems as well as large sparse ones, employing sparse matrix structures throughout. The implementation and performance of SQP are documented in Fan, et al. (1988). 

The field was comprehensively reviewed by Duff (25) in 1977. The design features of sparse matrix codes are discussed by Duff and Reid (26) and the need for suitable user interfaces is the subject of a paper by George and Liu (27). Generally the goal of the... 

The expression is easily coded, since T<0>, Eq. 41, and the r 1 are known. It simplifies for substitution on a principal plane or axis and for symmetrically equivalent multiple substitution, because several of the elements of the matrix T will then vanish. It is clear from Eq. 45 that the derivatives are nonvanishing only for those atoms a that have actually been substitued in the particular isotopomer s. Therefore, the Jacobian matrix X generated from these derivatives is, in general, a sparse matrix. 

Since this matrix is a sparse matrix, it is not economical to be explicitly used in computer programming. In order to save computer memory, the authors used the technique of the bond list, which encodes the position and the value of the non-zero elements in the upper-triangle (or lower-triangle) of the matrix. Thus, each member in the bond list is coded by (i,j, with i and j referring... 

At present, there are serious limitations to the use of geochemical codes to study clay mineral solution-equilibria. These include the sparse and often dubious clay mineral stabilities given in program data bases and the fact that water analyses rarely include reliable data for both dissolved Si and Al. Also, dissolved Al is usually below detection above pH 5 to 6. When reported at higher pH s, aluminum is mostly present in suspended form, as suggested by Example 9.3. For such reasons, many researchers still prefer using graphic methods to depict the stabilities and behavior of clay minerals. 

An obvious disadvantage of the procedure outlined above is that a relatively large amount of memory is needed. It should also be noted that the method is most advantageous for complete reference functions. For simple reference wavefunctions the matrices Aij, C, etc., become very sparse. This sparsity cannot be exploited fully in a vectorized computer code. It may, therefore, be more efficient to use other techniques in such cases. 

Cosson et al. (54) provided another improvement for allometric scaling by using the PK/PD population approach. This approach enables one to use sparse and unbalanced data, which is most often the case in animal studies. Using this approach, they were able to estimate all allometric parameters and all interindividual variabilities in the population and for each species. An example of their code for implementation in NONMEM is presented in their publication (54). 

The recent application of sparse-matrix techniques combined with computer optimization (vectorization) techniques has, however, improved the speed of Gear s code substantially, so that this advanced algorithm can now be used to study complex problems in multi-dimensional models (see e.g., the SMVGEAR package developed by Jacobson (1995 1998) and Jacobson and Turco, 1994). 

Jacobson, M.Z., and R.P. Turco, SMVGEAR A sparse-matrix vectorized gear code for atmospheric models. Atmos Environ 28A, 273, 1994. 

In the last decade, there have been many studies about the emergence of synchronous activity in spiking neural networks [16]. In a recent paper, Bdrgers and Kopell [17] have addressed the case of a network with sparse and random conneetivity between two populations of theta neurons, one excitatory and the other inhibitory. However, their network is limited to excitatory to inhibitory and inhibitory to excitatory connections and the dynamical behaviour is studied at the population level only. In contrast, we address here a more complex situation in which spike adaptation and inhibitory to inhibitory connectivity are likely to play a role in the dynamics and we address both population and individual neuron levels. In order to understand how the firings of PNs and LNs get synchronized, we will first study two simple cases a PN which has received inhibition and a LN which has received excitation. While unraveling progressively the behaviour of individual neurons, we will be able to explain the dynamical construction of the neural code. 

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