TY - JOUR
TI - On asymptotic properties of several classes of operators
AU - Campbell, Stephen L.
AU - Gellar, R.
T2 - Proceedings of the American Mathematical Society
DA - 1977///
PY - 1977///
VL - 66
IS - 1
SP - 79–84
ER -
TY - JOUR
TI - Linear operators for which T*T and T+T* commute II
AU - Campbell, Stephen L.
AU - Geller, R.
T2 - Transactions of the American Mathematical Society
DA - 1977///
PY - 1977///
VL - 226
SP - 305–319
ER -
TY - JOUR
TI - Small solutions of a non-linear equation in Banach space for a degenerate case
AU - Shearer, M.
T2 - Proceedings of the Royal Society of Edinburgh: Section A Mathematics
AB - Synopsis The existence of zeroes of an operator in Banach space near a. known zero is examined, when the non-degeneracy condition of Magnus [1] is violated, and replaced by a condition which is called simple-degeneracy. Criteria are given which help determine the number and the structure of curves of zeroes of the operator, passing through the known zero. These conditions and results are interpreted in terms of bifurcation theory. By considering several different cases, it is shown that the failure of various conditions frequently employed in the Lyapunov–Schmidt method may be overcome using the idea of simple-degeneracy.
DA - 1977///
PY - 1977///
DO - 10.1017/s0308210500016802
VL - 79
IS - 1-2
SP - 35-49
J2 - Proceedings of the Royal Society of Edinburgh: Section A Mathematics
LA - en
OP -
SN - 0308-2105 1473-7124
UR - http://dx.doi.org/10.1017/s0308210500016802
DB - Crossref
ER -
TY - RPRT
TI - Stability analysis and correction of pathological behavior of neural networks
AU - Silverstein, Jack
A3 - Division of Applied Mathematics, Brown University
C6 - 48
DA - 1977///
PY - 1977///
M1 - 48
M3 - Pattern Analysis Report
PB - Division of Applied Mathematics, Brown University
SN - 48
ER -
TY - CONF
TI - Vowel pre-processing with a neurally based model
AU - Anderson, J.
AU - Silverstein, J.
AU - Ritz, S.
T2 - IEEE International Conference on Acoustics, Speech, and Signal Processing
AB - We assume that (1) nervous system activity is most usefully represented as the set of simultaneous individual neuron activities in a group of neurons, (2) different memory traces make use of the same synapses and (3) synapses associate two patterns of neural activity by incrementing synaptic connectivity proportional to the product of pre- and post-synaptic activity (a Hebbian rule). We extend this model by (1) introducting positive feedback of a set of neurons onto itself and (2) allowing the individual neurons to saturate. Positive feedback forces the pattern of neural activity into stable corners of a high dimensionality hypercube. The model has behavior reminiscent of 'categorical perception' in that large regions of initial neural activity will end in the same corner. We wish to demonstrate that this model can serve as an efficient pre-processer, which takes a noisy stimulus, a spoken vowel, and puts it in a noise free standard form. As a test, we used acoustic representations of nine spoken Dutch vowels. We apply the model, and show that after several thousand learning trials, input vowels, initially close together, are associated with separate stable corners.
C2 - 1977///
C3 - ICASSP '77. IEEE International Conference on Acoustics, Speech, and Signal Processing
DA - 1977///
DO - 10.1109/icassp.1977.1170257
PB - Institute of Electrical and Electronics Engineers
UR - http://dx.doi.org/10.1109/icassp.1977.1170257
ER -
TY - JOUR
TI - Distinctive features, categorical perception, and probability learning: Some applications of a neural model.
AU - Anderson, James A.
AU - Silverstein, Jack W.
AU - Ritz, Stephen A.
AU - Jones, Randall S.
T2 - Psychological Review
AB - A previously proposed model for memory based on neurophysiolo gical considerations is reviewed. We assume that (a) nervous system activity is usefully represented as the set of simultaneous individual neuron activities in a group of neurons; (b) different memory traces make use of the same synapses; and (c) synapses associate two patterns of neural activity by incrementing synaptic connectivity proportionally to the product of pre- and postsynaptic activity, forming a matrix of synaptic connectivities. We extend this model by (a) introducing positive feedback of a set of neurons onto itself and (b) allowing the individual neurons to saturate. A hybrid model, partly analog and partly binary, arises. The system has certain characteristics reminiscent of analysis by distinctive features. Next, we apply the model to categorical perception. Finally, we discuss probability learning. The model can predict overshooting, recency data, and probabilities occurring in systems with more than two events with reasonably good accuracy.
DA - 1977/9//
PY - 1977/9//
DO - 10.1037/0033-295x.84.5.413
VL - 84
IS - 5
SP - 413-451
J2 - Psychological Review
LA - en
OP -
SN - 1939-1471 0033-295X
UR - http://dx.doi.org/10.1037/0033-295x.84.5.413
DB - Crossref
ER -
TY - JOUR
TI - Spectral Analysis of Networks with Random Topologies
AU - Grenander, Ulf
AU - Silverstein, Jack W.
T2 - SIAM Journal on Applied Mathematics
AB - A class of neural models is introduced in which the topology of the neural network has been generated by a controlled probability model. It is shown that the resulting linear operator has a spectral measure that converges in probability to a universal one when the size of the net tends to infinity: a law of large numbers for the spectra of such operators. The analytical treatment is accompanied by omputational experiments.
DA - 1977/3//
PY - 1977/3//
DO - 10.1137/0132041
VL - 32
IS - 2
SP - 499-519
J2 - SIAM J. Appl. Math.
LA - en
OP -
SN - 0036-1399 1095-712X
UR - http://dx.doi.org/10.1137/0132041
DB - Crossref
ER -
TY - JOUR
TI - On continuity of the Moore-Penrose and Drazin generalized inverses
AU - Campbell, Stephen L.
T2 - Linear Algebra and its Applications
AB - Let A be an m × n matrix. It is shown that if a matrix Â comes close to satisfying the definition of the Moore-Penrose generalized inverse of A,A†, then ┆Â–A†┆ is small. Norm estimates are given which make precise what is close. The Drazin generalized inverse is also considered.
DA - 1977///
PY - 1977///
DO - 10.1016/0024-3795(77)90079-9
VL - 18
IS - 1
SP - 53-57
J2 - Linear Algebra and its Applications
LA - en
OP -
SN - 0024-3795
UR - http://dx.doi.org/10.1016/0024-3795(77)90079-9
DB - Crossref
ER -
TY - JOUR
TI - Linear Systems of Differential Equations with Singular Coefficients
AU - Campbell, Stephen L.
T2 - SIAM Journal on Mathematical Analysis
AB - Differential equations of the form $A\dot x + Bx = f$ are studied where A, B are $m \times n$ matrices. Explicit solutions are derived for several cases of interest. One such case is when there exists a scalar $\lambda $ such that $\lambda A + B$ is of full rank. Another includes the case when A, B are normal matrices and one is positive semidefinite. The application of these results to linear autonomous control processes is discussed.
DA - 1977/11//
PY - 1977/11//
DO - 10.1137/0508081
VL - 8
IS - 6
SP - 1057-1066
J2 - SIAM J. Math. Anal.
LA - en
OP -
SN - 0036-1410 1095-7154
UR - http://dx.doi.org/10.1137/0508081
DB - Crossref
ER -
TY - JOUR
TI - Convolution and H‐equations for operator‐valued functions with applications to neutron transport theory
AU - Kelley, C. T.
T2 - Journal of Mathematical Physics
AB - The Wiener–Hopf factorization of certain-valued functions is related to operator-valued generalizations of Chandrasekhar’s H-functions. These functions satisfy a nonlinear system and may be computed by an iterative scheme. A general transport equation is solved in terms of these functions. The equation for steady-state transport in one space dimension with isotropic scattering and continuous energy dependence is discussed as an application.
DA - 1977/4//
PY - 1977/4//
DO - 10.1063/1.523305
VL - 18
IS - 4
SP - 764-769
J2 - Journal of Mathematical Physics
LA - en
OP -
SN - 0022-2488 1089-7658
UR - http://dx.doi.org/10.1063/1.523305
DB - Crossref
ER -