For reprints, please contact:
Russell W. Anderson
rwa@hnc.com
R.W. Anderson, J.B. Badler, and E.L. Keller
Predicting distributions of neural connections in the saccadic system
using a biologically plausible learning rule -- preliminary results.
In: Evolutionary Programming VII:
Proceedings of the Seventh Annual Conference on Evolutionary
Programming (EP98), San Diego, CA, March 25-27, 1998.
V.W. Porto, N. Saravanan, D.E. Waagen, and A.E. Eiben (eds.),
Springer, Berlin, (1998).
Lecture Notes in Computer Science, Vol. 1447 pp. 503-513
Saccades are rapid movements that reposition the eye in space. Several
neural structures involved in saccadic control have been characterized,
providing a unique opportunity for systems-level investigations of the
premotor neural circuitry. This study focuses on the role of the superior
colliculus (SC) in the planning and control of saccadic eye movements
in monkeys. Saccade-related neural activity in the SC is highly
distributed, with saccade displacement commands coded in a topologically-
organized motor map (Robinson 1972; Ottes et al. 1986). Downstream from
the SC, this spatiotemporal code is transformed into the temporal code
necessary to drive the oculomotor neurons. Researchers have postulated
that this transformation is implemented in the projection weights between
the SC and the brainstem saccadic burst generator. Here, an empirical
neural network study is used to predict the topological variation of
these projection weights. Estimates of the spatio-temporal neural activity
in the SC were used as the open-loop inputs to the model. The projection
weights from the SC to excitatory burst neurons (EBNs) in the brainstem
were trained using a biologically plausible evolutionary learning rule
(the chemotaxis algorithm), while well-known features of the downstream
neural structures were fixed. The objective function was defined as the
squared error between the model output and actual eye position
trajectories for several magnitudes of horizontal saccades
(integrated over time). Simulation results predict the excitatory
connections from the SC to EBNs increase in strength or density with
collicular location (from rostral to caudal).
R.W. Anderson, M.S. Ascher, and H.W. Sheppard
Direct HIV cytopathicity cannot account for CD4 decline in AIDS in the presence of homeostasis.
A worst-case dynamical analysis J. AIDS & Human Retrovirology,
17:245-252 (1998)
The central paradox of HIV pathogenesis is that the viral burden (either free or cellular) seems far
too low to deplete the CD4 population by direct killing. Until recently, there were few data
which could be used to critically compare direct and indirect pathogenic theories. Clinical trials
with potent new antiviral agents have measured important kinetic parameters of HIV infection,
including viral and infected cell half-lives. This has led to the construction of explicit models of
direct killing. Using a worst-case dynamical analysis, we show that such cytopathic models are
untenable. Rates of infected cell removal are orders of magnitude too low to significantly
suppress steady state CD4 counts in the face of lymphocyte replenishment, especially in early
infection. Furthermore, the direct cytopathic models, as proposed, predict an extremely variable
disease course across the broad range of observed viral burdens (five orders of magnitude), which
is inconsistent with the relatively small differences in disease progression observed between
patients. In contrast, immunological theories of pathogenesis, such as homeostatic dysregulation
based on immune activation, do not suffer from these difficulties and are more consistent with the
natural history of HIV infection.
R.W. Anderson, E.L. Keller, N.J. Gandhi, and S. Das
Two-dimensional saccade-related population activity in superior
colliculus in monkey.
J. Neurophysiology 80:798-817 (1998).
The two-dimensional distribution of population activity in the superior colliculus (SC) during saccadic eye movements in the monkey was estimated using radial basis functions. In order to make these activity estimates, cells in the deeper layer of the SC were recorded over much of this structure. The dynamic movement field of each cell was determined at 2-ms intervals around the time of saccades for a wide variety of horizontal and oblique movements. Collicular neurons were divided into an overlapping dorsal burst neuron layer and a ventral buildup neuron layer. Cell location on the colliculus was estimated from the optimal target vector for a cell's visual response rather than from the optimal motor vector. The former technique that was found to be more reliable for locating some buildup neurons because it compared well with locations suggested by electrical stimulation. From the movement field data and from the estimates of each cell's anatomic location, the same algorithm was used to compute the two-dimensional population activity in the two layers of the SC during horizontal and oblique saccades. A subset of the sample of neurons, located near the horizontal meridian of the SC, was used to compute one-dimensional dynamic population activity estimates for horizontal saccades to allow direct comparison to previous studies. Statistical analyses on the one-dimensional data indicated that, while there is a shift in the center of gravity of the distributed activity in the buildup layer, there is little support for the theory of a systematic rostral spread of the activity that reaches the rostral limit of the colliculus at saccade end. The two-dimensional results extend the previous one-dimensional estimates of collicular activity. Discharge in the burst layer was found to be invariant in the size with saccade vector and symmetrically arranged about a center of gravity that did not move during saccades. The size of the active area in the buildup layer grew modestly with saccade amplitude while the distribution of activity was skewed toward the rostral end of the SC for saccade larger than 10. There was a clear shift in the center of gravity of the activity that was directed along the horizontal or an oblique meridian of the SC. However, the spread of activity during a saccade was as large or larger in the mediolateral direction as it was in the rostral direction. The results indicate changes in activity occur in an extended zone on the SC in all directions but caudal in the buildup layer during saccades and do not support the idea of a rostrally directed spread of activity as a dynamic control mechanism for saccades.
R.W. Anderson, S. Das, and E.L.Keller.
Estimation of Spatio-temporal Neural Activity
Using Radial Basis Function Networks.
J. Computational Neuroscience ,
5:1-21 (1998).
We report a method using radial basis function (RBF) networks to estimate the time evolution of population activity in topologically-organized neural structures from single-neuron recordings. This is an important problem in neuroscience research, as such estimates may provide insights into systems-level function of these structures. Since single-unit neural data tends to be unevenly sampled and highly variable under identical behavioral conditions, obtaining such estimates is a difficult task. Therefore, we have developed several computational geometry based algorithms for the initial treatment of the data before computing a surface estimation using RBF networks. To illustrate the use of these algorithms, our method is first applied to estimating the movement fields of neurons recorded in the deeper layers of the monkey superior colliculus during rapid (saccadic) eye movements. The method is then expanded to the problem of estimating simultaneous spatio-temporal activity occuring across the superior colliculus during a single movement (the inverse problem). In principle, this methodology could be applied to any neural structure with a regular, two-dimensional organization, provided a sufficient spatial distribution of sampled neurons is available.
R.W. Anderson.
How the adaptive antibodies facilitate the evolution of natural antibodies.
Immunology and Cell Biology, 74(2):286-291 (1996).
I show how Ig specificities, randomly generated in conventional B cells, can come to be expressed
in the genetically-determinate B1 population. Thus the adaptive antibody population facilitates the
evolution of the natural antibody repertoire, in accordance with the Baldwin effect in the
evolution of instinct. I discuss the evolution of these two populations under both the "proximal
usage" and "preferential expression" hypotheses of biased Ig gene segment usage. This process is
independent of theories of B1 function.
M.S. Ascher, H.W. Sheppard, R.W. Anderson, J.F. Krowka, and H.J. Bremermann.
HIV results in the frame -- Paradox Remains.
Nature, 375:196 (1995).
SIR -- The articles by Ho et al.(1) and Wei et al. (2) have been hailed as providing crucial new
information that clarifies the enigma of HIV-mediated pathogenesis (see, for example, refs 3,4).
To the extent that they have estimated equilibrium rate constants and provided an explanation
for rapid development of drug resistance, these studies (1,2) do provide new and important
information. But the central paradox of AIDS pathogenesis remains.
The new studies on the dynamics of HIV infection demonstrate that the underlying rate of virus
production is still 4-20 times lower than the rate of cell turnover. Because each infected cell
produces many virions, and a high proportion of them are known to be defective, there is about
100-1,000 fold more cell death than can be accounted for by the observed rate of virus
production (5). It is a murder scene with far more bodies than bullets.
Instead of addressing this discrepancy, the authors (1,2) suggest that "virus must be
underestimated," or that many more infected cells must be hiding in deep lymphoid organs where
they cannot be observed. Taken at face value, however, these data demonstrate that the CD4
lymphocyte population highly activated and that the fate of uninfected cells may be much more
important in AIDS pathogenesis than that of infected cells. This view is consistent with
observations that the rate of spontaneous apoptosis in the peripheral lymphocytes of HIV
infected individuals is both sharply elevated and at least 10-100 fold higher than the frequency of
productively infected cells (6).
Ho et al. suggest the analogy of a sink, with the tap and drain both equally wide open, which
eventually empties because the "regenerative capacity of the immune system (the tap) is not
infinite" and can't quite keep up. However, the differential between the tap and drain is extremely
small (20-200 x 10^6 cells/day) compared with the overall flow rate (2 x 10^9 cells/day), and
must remain relatively fixed for an average of 10 years, as CD4+ cell loss is roughly linear
throughout most of the natural history of HIV infection (7). Further, this model would predict no
CD4 loss until virus production exceeded a critical threshold, and then an accelerating cell loss
as the virus burden increases.
A more plausible explanation for these data is that a mechanism which finely regulates CD4
replacement makes a slight error, resulting in the failure to completely replace the cells (infected
and uninfected alike) which are lost through programmed cell death, the natural consequence of
immune activation. We have argued that this is exactly what would be expected if the immune
system were exposed to a persistent co-stimulatory T-cell signal caused by the interaction of
gp120 with CD4 (ref. 8). This extra signal causes the control mechanism to sense an elevated
state of immune responsiveness and downregulate the recovery of "memory" cells to prevent
growth of the immune system (9). The result would be an inexorable but steady decay based on
this difference in probability of survival.
Maddox (4) wonders "why, after more than a decade of research, has it only now emerged that
the response of the immune system to infection by HIV is hyperactivity rather than the opposite?".
The answer to this question is that those who would see AIDS as a more-or-less conventional
viral infection have consistently refused to recognize the paradoxes that are clearly evident in the
experimental data. The problem continues.
References
1. Ho, D.D., A.U. Neumann, A.S. Perelson, W. Chen, J.M. Leonard, and M. Markowitz, Rapid
turnover of plasma virions and CD4 lymphocytes in HIV-1 infection. Nature, 373: 123-126 (1995).
2. Wei, X., S.K. Goush, M.E. Taylor, et al. Viral dynamics in human immunodeficiency virus
type 1 infection. Nature, 373:117--122 (1995).
3. Wain-Hobson, S. (1995). Virological mayhem. Nature, 373:102 (1995).
4. Maddox, J. Nature 373,189 (1995)
5. Sheppard, H.W., M.S. Ascher, and J.F. Krowka Viral burden and HIV disease. Nature,
364:291-92.Nature 364,291 (1993).
6. Gougeon, M.L. and Montagnier, L. Apoptosis in AIDS. Science, 260:1269-1270 (1993).
(published erratum appears in Science, 260:1709 (1993))
7. Sheppard, H.W. et al. J. AIDS 7,1159-1166 (1993).
8. Ascher, M.S. and Sheppard, H.W. AIDS as immune system activation II: the panergic imnesia
hypothesis J. AIDS, 3:177-191 (1990).
9. Sheppard, H.W. and M.S. Ascher, The natural history and pathogenesis of HIV infection.
Annu. Rev. Microbiol., 46:533-564 (1992).
R.W. Anderson.
The Baldwin effect.
In: Handbook of Evolutionary Computation
Bock, T., D. Fogel, and Z. Michalewicz, eds. NY: Oxford University Press and IOP Publishing
(1997)
Abstract
The Baldwin effect is a passive evolutionary process, whereby individual learning facilitates
genetic evolution. Baldwinian evolution is distinguished from the more active (and non-biological)
Lamarckian inheritance of acquired characters. This chapter explains the principles underlying the
Baldwin effect and discusses its manifestations in evolutionary algorithms. A first-order analysis
using quantitative genetics is used to illustrate some common misconceptions. When appropriately
implemented, hybrid algorithms can efficiently exploit the Baldwin effect in evolutionary optimization.
1. Interactions Between Learning and Evolution
In the course of an evolutionary optimization, solutions are often generated with low phenotypic
fitness even though the corresponding genotype may be close to an optima. Without additional
information about the local fitness landscape, such genetic ``near misses" would be overlooked
under strong selection. Presumably, one could rank near misses by performing a local search and
scoring them according to distance from the nearest optima. Such evaluations are essentially the
goal of hybrid algorithms (Chapter B1.5; Balakrishnan and Honavar 1995), which combine global
search using evolutionary algorithms and local search using individual learning algorithms.
Hybrid algorithms can exploit learning either actively (via Lamarckian inheritance) or passively
(via the Baldwin effect).
Under Lamarckian algorithms, performance gains from individual learning are mapped back into
the genotype used for the production of the next generation. This is analogous to Lamarckian
inheritance in evolutionary theory --- whereby characters acquired during a parent's lifetime are
passed on to their offspring. Lamarckian inheritance is rejected as a biological mechanism under
the Modern Synthesis, since it is difficult to envision a process by which acquired information can
be transferred into the gametes. Nevertheless, the practical utility of Lamarckian algorithms has
been demonstrated in some evolutionary optimization applications (Ackley and Littman 1994;
Paechter et al. 1995). Of course, these algorithms are limited to problems where a reverse
mapping from the learned phenotype to genotype is possible.
However even under purely Darwinian selection, individual learning influences evolutionary
processes, but the underlying mechanisms are subtle. The ``Baldwin effect" is one such
mechanism, whereby learning facilitates the assimilation of new genetic innovations (Baldwin
1896; Morgan 1896; Osborn 1896; Waddington 1942; Hinton and Nowlan 1987; Maynard Smith
1987; Anderson 1995a; Turney et al. 1996). Learning allows an individual to complete and
exploit partial genetic programs and thereby survive. In other words, learning guides evolution by
assigning ``partial credit" for genetic near misses. Individuals with useful genetic variations are
thus maintained by learning, and the corresponding genes increase in frequency in the subsequent
generation. As genetic components necessary for a complex structure accumulate in the gene
pool, functions that previously required supplemental learning are replaced by
genetically-determinant systems.
Empirical studies can quantify the benefits of incorporating individual learning into evolutionary
algorithms (Belew 1989; French and Messinger 1994; Nolfi et al. 1994; Whitley et al. 1994;
Cecconi et al. 1995). However, a theoretical treatment of the effects of learning on evolution can
strengthen our intuition for when and how to implement such approaches. This chapter
presents an overview of the principles underlying the Baldwin effect, beginning with a brief
history of the elucidation and development in evolutionary biology. Computational models of the
Baldwin effect are reviewed and critiqued. The Baldwin effect is then analyzed using standard
quantitative genetics. Given reasonable assumptions of the effects of learning on fitness and its
associated costs, this theoretical approach builds and strengthens conventional intuition about the
effects of individual learning on evolution. Finally, issues concerning problem formulation,
learning algorithms, and algorithmic design are discussed.
R.W. Anderson
Random-walk learning: A neurobiological correlate to trial-and-error
Progress in Neural Networks, O.M. Omidvar and J. Dayhoff, Eds.,
Academic Press: Boston, Chapter 7,p.221-244 (1998).
Neural network models offer a theoretical testbed for the study of learning at the cellular level.
The only experimentally verified learning rule, Hebb's rule, is extremely limited in its ability to
train networks to perform complex tasks. An identified cellular mechanism responsible for
Hebbian-type long-term potentiation, the NMDA receptor, is highly versatile. Its function and
efficacy are modulated by a wide variety of compounds and conditions and are likely to be
directed by non-local phenomena. Furthermore, it has been demonstrated that NMDA receptors
are not essential for some types of learning. We have shown that another neural network learning
rule, the chemotaxis algorithm, is theoretically much more powerful than Hebb's rule and is
consistent with experimental data. A biased random-walk in synaptic weight space is a learning
rule immanent in nervous activity and may account for some types of learning -- notably the
acquisition of skilled movement.
R.W. Anderson.
Learning and evolution: A quantitative genetics approach
J. of Theoretical Biology, 175:89-101 (1995).
Recent models of the interactions between learning and evolution show that learning increases the
rate at which populations find optima in fixed environments. However, learning ability is only
advantageous in variable environments. In this study, quantitative genetics models are used to
investigate the effects of individual learning on evolution. Two models of populations of learning
individuals are constructed and analyzed. In the first model, the effect of learning is represented as
an increase in the variance of selection. Dynamical equations and equilibrium conditions are
derived for a population of learning individuals under fixed and variable environmental selection.
In the second model, the amount of individual learning effort is regulated by a second gene
specifying the duration of a critical learning period. The second model includes a model of the
learning process to determine the individual fitness costs and benefits accrued during the learning
period. Individuals are then selected for the optimal learning investment. The similarities of the
results from these two models suggest that the net effects of learning on evolution are relatively
independent of the mechanisms underlying the learning process.
R.W. Anderson
On the maternal transmission of immunity: A "molecular attention" hypothesis
Biosystems, 34(1-3):87-105 (1995).
Maternally-derived antibodies can provide passive protection to their offspring. More subtle
phenomena associated with maternal antibodies concern their influence in shaping the immune
repertoire and priming the neonatal immune response. These phenomena suggest that maternal
antibodies play a role in the education of the neonatal immune system. The educational effects are
thought to be mediated by idiotypic interactions among antibodies and B cells in the context of an
idiotypic network. This paper proposes that maternal antibodies trigger localized idiotypic
network activity that serves to amplify and translate information concerning the molecular shapes
of potential antigens. The triggering molecular signals are contained in the binding regions of the
antibody molecules. These antibodies form complexes and are taken up by antigen presenting cells
or retained by follicular dendritic cells and thereby incorporated into more traditional cellular
immune memory mechanisms. This mechanism for maternal transmission of immunity is termed
the molecular attention hypothesis and is contrasted to the dynamic memory hypothesis.
Experiments are proposed that may help indicate which models are more appropriate and will
further our understanding of these intriguing natural phenomena. Finally, analogies are drawn to
attention in neural systems.
R.W. Anderson, A.U. Neumann and A.S. Perelson
A Cayley tree immune network model with antibody dynamics
Bull. Math. Biol., 55(6):1091-1131 (1993).
A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is
formulated and analysed. As in models with B cells only, localized states exist in the network with
limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and
stability of these localized network states are explored as a function of model parameters. As in
previous models that have included antibody, the stability of immune and tolerant localized states
are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody
complex removal. As model parameters are varied, localized steady-states can break down via
two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a
given set of parameters percolation and chaotic attractors can coexist with localized attractors,
and thus there do not exist clear cut boundaries in parameter space that separate regions of
localized attractors from regions of percolation and chaotic attractors. Stable limit cycles, which
are frequent in the two-clone antibody B cell (AB) model, are only observed in highly connected
networks. Also found in highly connected networks are localized chaotic attractors. As in
experiments by Lundkvist et al. (1989. Proc. natn. Acad. Sci. U.S.A. 86, 5074-5078), injection of
Ab1 antibodies into a system operating in the chaotic regime can cause a cessation of fluctuations
of Ab1 and Ab2 antibodies, a phenomenon already observed in the two-clone AB model.
Interestingly, chaotic fluctuations continue at higher levels of the tree, a phenomenon observed by
Lundkvist et al. but not accounted for previously.
R.W. Anderson and V. Vemuri
Neural networks can be used for open-loop, dynamic control
Int'l. J. Neural Networks, 3(3):71-84 (1992).
The use of artificial neural nets to generate control signals for dynamical systems is investigated.
Thus far, attempts to apply neural nets to temporal signal generation have met with limited
success. Training an unconstrained, 'recurrent' network of processing nodes to generate even the
most elementary temporal patterns appears to be prohibitively slow. However, theoretical
analyses of static neural networks demonstrate their power as convenient interpolation devices.
This property is exploited by training the simpler, 'feed-forward' neural networks to generate the
key parameters of the optimal control signal, namely, the switching times. This
methodology is applied to problems in optimal motor control in two stages. First, a network is
trained to generate the appropriate optimal switching times. Second, the networks are trained
directly on the resultant dynamical state trajectory. The latter experiment relies exclusively on
the chemotaxis algorithm, since back-propagation would require calculation of the partial
derivatives back through an unknown plant.
Hans J. Bremermann and R.W. Anderson
Mathematical models of HIV infection. I: Threshold conditions for transmission and host survival
J. of AIDS, 3(12):1129-1134 (1990).
This is the second in a series of papers modeling HIV infections at four interacting levels:
transmission, interaction with the immune system, gene regulation, and selection of mutants. In
the previous paper (Bremermann and Anderson [1989]) models have been motivated and
described verbally and a conjecture about the HIV cytopathic effect, based upon the models (and
a review of the literature) has been stated. In the following we write mathematical equations
about threshold conditions which connect infectivity, length of host survival, and frequency of
acts conducive to transmission. The formula is derived not only for homogeneous populations,
but also for populations of an arbitrary number of subgroups with different frequencies of risk
behavior, different infectivities and latency periods, and different interaction frequencies with
other groups.
F.U. Dowla, S.R. Taylor and R.W. Anderson
Seismic discrimination with artificial neural networks: Preliminary results with regional spectral data
Bull. Seismo. Soc. Amer., 80(5):1346-1373 (1990).
An application of artificial neural networks (ANN) for discrimination between natural earthquakes
and underground nuclear explosions has been studied using distance corrected spectral data of
regional seismic phases. Pn, Pg, and Lg spectra have been analyzed from 83 western U.S.
earthquakes and 87 Nevada Test Site explosions recorded at the four broadband seismic stations
operated by Lawrence Livermore National Laboratory. Distance corrections are applied to the
raw spectral data using existing frequency-dependent Q models for the Basin and Range. The
spectra are sampled logarithmically at 41 points between 0.1 and 10 Hz for each phase and
checked for adequate signal-to-noise ratios (S/N >2). The ANN was implemented on a SUN
4/110 workstation using a backpropagation-feedforward architecture. We find that, using even
simple ANN architectures (82 input units, 1 hidden unit, and 2 output units), powerful
discrimination systems can be designed. In order to regionalize the data characteristics, a separate
neural network was assigned to each station. For this data set, the rate of correct recognition for
untrained data is over 93 per cent for both earthquakes and explosions at any single station. Using
a majority voting scheme with a network of four stations, the rate of recognition is over 97 per
cent. Although the performance of the ANN is similar to that of the Fisher linear discriminant, the
ANN exhibits a number of computational advantages over the conventional method. Finally,
examination of the network weights suggests that, in addition to spectral shape, a criterion that
the ANN utilized to discriminate between the two populations was the Lg/Pg spectral amplitude ratios.
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