Skip Navigation



Logic Journal of IGPL Advance Access published online on October 30, 2009

Logic Journal of IGPL, doi:10.1093/jigpal/jzp046
This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Supplementary Data
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Simen, P.
Right arrow Articles by Polk, T.
Social Bookmarking
 Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A symbolic/subsymbolic interface protocol for cognitive modeling

Patrick Simen

Princeton Neuroscience Institute, Princeton University, Princeton, NJ.
E-mail: psimen{at}princeton.edu

Thad Polk

Department of Psychology, University of Michigan, Ann Arbor, MI.
E-mail: tpolk{at}umich.edu

Researchers studying complex cognition have grown increasingly interested in mapping symbolic cognitive architectures onto subsymbolic brain models. Such a mapping seems essential for understanding cognition under all but the most extreme viewpoints (namely, that cognition consists exclusively of digitally implemented rules; or instead, involves no rules whatsoever). Making this mapping reduces to specifying an interface between symbolic and subsymbolic descriptions of brain activity. To that end, we propose parameterization techniques for building cognitive models as programmable, structured, recurrent neural networks. Feedback strength in these models determines whether their components implement classically subsymbolic neural network functions (e.g., pattern recognition), or instead, logical rules and digital memory. These techniques support the implementation of limited production systems. Though inherently sequential and symbolic, these neural production systems can exploit principles of parallel, analog processing from decision-making models in psychology and neuroscience to explain the effects of brain damage on problem solving behavior.

Key Words: problem solving • production system • neural network • diffusion • decision making • symbolic • subsymbolic



References

    Ackley DH, Hinton GE, Sejnowski TJ. A learning algorithm for Boltzmann machines. Cognitive Science (1985) 9:147–169.[CrossRef][Web of Science]

    Aldridge JW, Berridge KC. Coding of serial order by neostriatal neurons: a ‘natural action’ approach to movement sequence. Journal of Neuroscience (1998) 18(7):2777–2787.[Abstract/Free Full Text]

    Alexander GE, DeLong MR, Strick PL. Parallel organization of functionally segregated circuits linking basal ganglia and cortex. Annual Review of Neuroscience (1986) 9:357–381.[CrossRef][Web of Science][Medline]

    Amit D, Gutfreund H, Sompolinsky H. Storing infinite numbers of patterns in a spin-glass model of neural networks. Physical Review Letters (1985) 5:1530–1533.

    Anderson J, Lebiere C. The Atomic Components of Thought (1998) Lawrence-Erlbaum Associates.

    Anderson JA, Silverstein JW, Ritz SA, Jones RS. Distinctive features, categorical perception, and probability learning: some applications of a neural model. Psychological Review (1977) 84:413–451.[CrossRef][Web of Science]

    Anderson JR, Bothell D, Byrne MD, Douglass S, Lebiere C, Qin Y. An integrated theory of mind. Psychological Review (2004) 111(4):1036–1060.[CrossRef][Web of Science][Medline]

    Arrow KJ. A difficulty in the concept of social welfare. Journal of Political Economy (1950) 58(4):328–346.[CrossRef][Web of Science]

    Bader S, Hitzler P, Holldobler S, Witzel A. The Core method for first-order logic programs (2007) Heidelberg: Springer. Ch. 9.

    Bishop C. Pattern recognition and machine learning (2006) New York, NY: Springer.

    Bogacz R, Brown E, Moehlis J, Holmes P, Cohen JD. The physics of optimal decision making: a formal analysis of models of performance in two-alternative forced choice tasks. Psychological Review (2006) 113(4):700–765.[CrossRef][Web of Science][Medline]

    Bogacz R, Gurney K. The basal ganglia and cortex implement optimal decision making between alternative actions. Neural Computation (2007) 19:442–477.[CrossRef][Web of Science][Medline]

    Botvinick MM, Braver TS, Barch DM, Carter CS, Cohen JD. Conflict monitoring and cognitive control. Psychological Review (2001) 108(3):624–652.[CrossRef][Web of Science][Medline]

    Braver TS, Cohen JD. On the control of control: the role of dopamine in regulating prefrontal function and working memory. In: Control of Cognitive Processes: Attention and Performance XVIII—Monsell S, Driver J, eds. (2000) MIT Press.

    Brown E, Gao J, Holmes P, Bogacz R, Gilzenrat M, Cohen JD. Simple neural networks that optimize decisions. International Journal of Bifurcation and Chaos (2005) 15(3):803–826.[CrossRef][Web of Science]

    Carlin D, Bonerba J, Phipps M, Alexander G, Shapiro M, Grafman J. Planning impairments in frontal lobe dementia and frontal lobe lesion patients. Neuropsychologia (2000) 38:655–665.[CrossRef][Web of Science][Medline]

    Cohen JD, Dunbar K, McClelland JL. On the control of automatic processes: a parallel distributed processing account of the Stroop effect. Psychological Review (1990) 97(3):332–361.[CrossRef][Web of Science][Medline]

    Cohen M, Grossberg S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man and Cybernetics (1983) 13:815–826.[Web of Science]

    Cooper R, Shallice T. Contention scheduling and the control of routine activities. Cognitive Neuropsychology (2000) 17(4):297–338.[CrossRef][Web of Science]

    Cowan JD. A Mathematical Theory of Central Nervous Activity (1967) University of London. Ph.D. thesis.

    Cragg BG, Temperley HNV. Memory – The analogy with ferromagnetic hysteresis. Brain (1955) 78(2):304–315.[Free Full Text]

    Cybenko G. Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals, and Systems (1989) 2:303–314.[CrossRef]

    Dayan P, Abbott LF. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (2001) Cambridge, MA: MIT Press.

    Dehaene S, Changeux J. A hierarchical neuronal network for planning behavior. Proceedings of the National Academy of Sciences, USA (1997) 94:13293–13298.[Abstract/Free Full Text]

    Desimone R, Duncan J. Neural mechanisms of selective visual attention. Annual Review of Neuroscience (1995) 18:193–222.[CrossRef][Web of Science][Medline]

    Eliasmith C, Anderson CH. Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems (2003) Cambridge, MA: MIT Press.

    Feldman JA, Ballard DH. Connectionist models and their properties. Cognitive Science (1982) 6:205–254.[CrossRef][Web of Science]

    Frank MJ, Loughry B, O’Reilly RC. Interactions between frontal cortex and basal ganglia in working memory: a computational model. Cognitive, Affective and Behavioral Neuroscience (2001) 1(2):137–160.[CrossRef]

    Franklin GF, Powell JD, Emami-Naeini A. Feedback Control of Dynamic Systems (1994) New York: Addison-Wesley.

    Frey PW, Sears RJ. Model of conditioning incorporating the Rescorla-Wagner associative axiom, a dynamic attention process, and a catastrophe rule. Psychological Review (1978) 85:321–340.[CrossRef][Web of Science]

    Gardiner CW. Handbook of stochastic methods (2004) 3rd Edition. New York, NY: Springer-Verlag.

    Gerstner W. Population dynamics of spiking neurons: fast transients, asynchronous states, and locking. Neural Computation (2000) 12:43–89.[CrossRef][Web of Science][Medline]

    Goel V, Pullara SD, Grafman J. A computational model of frontal lobe dysfunction: working memory and the tower of hanoi task. Cognitive Science (2001) 25:287–313.[CrossRef][Web of Science]

    Gold JI, Shadlen MN. Neural computations that underlie decisions about sensory stimuli. Trends in Cognitive Science (2001) 5(1):10–16.[CrossRef][Web of Science][Medline]

    Gold JI, Shadlen MN. Banburismus and the brain: decoding the relationship between sensory stimuli, decisions, and reward. Neuron (2002) 36(2):299–308.[CrossRef][Web of Science][Medline]

    Gray RM, Neuhoff DL. Quantization. IEEE Transactions on Information Theory (1998) 44:2325–2383.[CrossRef][Web of Science]

    Green DM, Swets JA. Signal Detection Theory and Psychophysics (1966) New York: Wiley.

    Grice GR. Application of a variable criterion model to auditory reaction time as a function of the type of catch trial. Perception and Psychophysics (1972) 102:103–107.

    Grossberg S. Biological competition: Decision rules, pattern formation and oscillations. Proceedings of the National Academy of Sciences U S A (1980a) 77(4):2338–2342.[Abstract/Free Full Text]

    Grossberg S. How does a brain build a cognitive code? Psychological Review (1980b) 87:1–51.[CrossRef][Web of Science][Medline]

    Grossberg S. A psychophysiological theory of reinforcement, drive, motivation and attention. Journal of Theoretical Neurobiology (1982) 1:286–369.

    Grossberg S. Competitive learning: from interactive activation to adaptive resonance. Cognitive Science (1987) 11:23–63.[CrossRef][Web of Science]

    Hammer B, Hitzler P, eds. Perspectives of Neural-Symbolic Integration (2007) Heidelberg: Springer.

    Hanes DP, Schall JD. Neural control of voluntary movement initiation. Science (1996) 274(5286):427–430.[Abstract/Free Full Text]

    Harth EM, Csermely TJ, Beek B, Lindsay RD. Brain functions and neural dynamics. Journal of Theoretical Biology (1970) 26:93–120.[CrossRef][Web of Science][Medline]

    Hartline HK, Ratliff F. Inhibitory interaction of receptor units in the eye of Limulus. Journal of General Physiology (1957) 40(3):357–376.[Abstract/Free Full Text]

    Hayes J. Introduction to Digital Logic Design (1993) New York, NJ: Addison-Wesley.

    Hertz J, Krogh A, Palmer RG. Introduction to the Theory of Neural Computation (1991) Redwood City, CA: Addison Wesley. Vol. 1 of Santa Fe Institute Studies in the Sciences of Complexity Lecture Notes.

    Higham DJ. An algorithmic introduction to numerical simulation of stochastic differential equations. Society for Industrial and Applied Mathematics Review (2001) 43(3):525–546.

    Hodgkin AL, Huxley AF. Resting and action potentials in single nerve fibres. Journal of Physiology (1945) 104:176–195.[Free Full Text]

    Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Neurophysiology (London) (1952) 117:500–544.

    Holland JH. Escaping brittleness: the possibilities of general-purpose learning algorithms applied to parallel rule-based systems. In: Machine Learning: An Artificial Intelligence Approach—Michalski RS, Carbonell JG, Mitchell TM, eds. (1986a) 2. Los Altos, CA: Morgan Kaufmann.

    Holland JH. A mathematical framework for studying learning in classifier systems. Physica D (1986b) 2:307–317.

    Holmes P, Brown E, Moehlis J, Bogacz R, Gao J, Aston-Jones G. Optimal decisions: from neural spikes, through stochastic differential equations, to behavior. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science (2005) 88(10):2496–2503.

    Hopfield JJ. Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences, USA (1984) 81:3088–3092.[Abstract/Free Full Text]

    Hopfield JJ, Tank DW. "neural" computation of decisions in optimization problems. Biological Cybernetics (1985) 52:141–152.[Web of Science][Medline]

    Hummel JE, Holyoak KJ. Distributed representations of structure: a theory of analogical access and mapping. Psychological Review (1997) 104(3):427–466.[CrossRef][Web of Science]

    Jordan DW, Smith P. Nonlinear Ordinary Differential Equations (1999) 3rd Edition. New York, NY: Oxford University Press.

    Just MA, Carpenter PA. A capacity theory of comprehension: individual differences in working memory. Psychological Review (1992) 99(1):122–149.[CrossRef][Web of Science][Medline]

    Kieras D, Meyer D. An overview of the EPIC architecture for cognition and performance with application to human-computer interaction. Human Computer Interaction (1997) 12(4):391–438.[CrossRef][Web of Science]

    Kimberg DY, Farah MJ. A unified account of cognitive impairments following frontal lobe damage: the role of working memory in complex, organized behavior. Journal of Experimental Psychology: General (1993) 122:411–428.[CrossRef][Web of Science][Medline]

    Kleene SC. Representation of events in nerve nets and finite automata. In: Automata Studies—Shannon CE, McCarthy J, eds. (1956) Princeton, NJ: Princeton University Press. 3–41.

    Laird J, Congdon CB. The Soar User's Manual (2006) 8th Edition. Ann Arbor, Michigan: Electrical Engineering and Computer Science Department.

    Laird J, Newell A, Rosenbloom P. Soar: an architecture for general intelligence. Artificial Intelligence (1987) 33(1):1–64.[CrossRef][Web of Science]

    Laird J, Rosenbloom P, Newell A. Chunking in Soar: the anatomy of a general learning mechanism. Machine Learning (1986) 1:11–46.

    Laming DRJ. Information theory of choice reaction time (1968) New York: Wiley.

    Lapique L. Recherches quantitatives sur l’excitation électrique des nerfs traitée comme une polarization. Journal of Physiology, Pathology and Genetics (1907) 9:620–635.

    Loewenstein Y, Seung HS. Operant matching is a generic outcome of synaptic plasticity based on the covariance between reward and neural activity. Proceedings of the National Academy of Sciences U S A (2006) 103(41):15224–15229.[Abstract/Free Full Text]

    Luce RD. Response Times: Their Role in Inferring Elementary Mental Organization (1986) New York: Oxford University Press.

    Marcus G. The Algebraic Mind: Integrating Connectionism and Cognitive Science, cambridge, ma Edition (2001) MIT Press.

    Marr D. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information (1982) San Francisco: W. H. Freeman and Company.

    McClelland JL, Rumelhart DE. An interactive activation model of context effects in letter perception: Part 1. An account of basic findings. Psychological Review (1981) 99:375–407.

    McCulloch W, Pitts W. A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics (1943) 5:115–133.[CrossRef]

    McMillen T, Holmes P. The dynamics of choice among multiple alternatives. Journal of Mathematical Psychology (2006) 50:30–57.[CrossRef][Web of Science]

    Mead C. Analog VLSI and Neural Systems (1989) New York: Addison-Wesley.

    Meck WH. Neuropharmacology of timing and time perception. Cognitive Brain Research (1996) 3:227–42.[CrossRef][Medline]

    Meyer DE, Kieras DE. A computational theory of executive cognitive processes and multiple-task performance: Part 1. basic mechanisms. Psychological Review (1997) 104:3–65.[CrossRef][Web of Science][Medline]

    Miller E, Cohen JD. An integrative theory of prefrontal cortex function. Annual Review of Neuroscience (2001) 24:167–202.[CrossRef][Web of Science][Medline]

    Miller GA. The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological Review (1956) 63:81–97.[CrossRef][Web of Science][Medline]

    Miller GA, Galanter E, Pribram KH. Plans and the Structure of Behavior (1960) Rinehart & Winston: Holt.

    Montague PR, Berns GS. Neural economics and the biological substrates of valuation. Neuron (2002) 36:265–284.[CrossRef][Web of Science][Medline]

    Nakahara H, Doya K. Near-saddle-node bifurcation behavior as dynamics in working memory for goal-directed behavior. Neural Computation (1998) 10:113–132.[CrossRef][Web of Science][Medline]

    Newell A. Unified Theories of Cognition (1990) Cambridge, MA: Harvard University Press.

    Newell A, Simon H. Human Problem-Solving (1972) Englewood Cliffs, NJ: Prentice Hall.

    Newell A, Simon HA. GPS: A program that simulates human thought. In: Computers and Thought—Feigenbaum EA, ed. (1963) New York: McGraw-Hill.

    Oksendal B. Stochastic Differential Equations (2003) Springer.

    Oppenheim AV, Willsky AS. Signals and systems (1996) 2nd Edition. New York, NY: Prentice Hall.

    O’Reilly RC, Busby RS. Generalizable relational binding from coarse-coded distributed representations. In: Advances in Neural Information Processing—Dietterich T, Becker S, Ghahramani Z, eds. (2002) 14. Cambridge, MA: MIT Press.

    O’Reilly RC, Munakata Y. Computational Explorations in Cognitive Neuroscience: Understanding the Mind by Simulating the Brain (2000) MIT Press.

    Owen AM, Downes JJ, Sahakian BJ, Polkey CE, Robbins TW. Planning and spatial working memory following frontal lobe lesions in man. Neuropsychologia (1990) 28(10):1021–1034.[CrossRef][Web of Science][Medline]

    Owen AM, James M, Leigh PN, Summers BA, Marsden CD, Quinn NP, Lange KW, Robbins TW. Fronto-striatal cognitive deficits at different stages of parkinson's disease. Brain (1992) 115(1727-1751).

    Owen AM, Sahakian BJ, Hodges JR, Summers BA, Polkey CE, Robbins TW. Dopamine-dependent frontostriatal planning deficits in early parkinson's disease. Neuropsychology (1995) 9(1):126–140.[CrossRef][Web of Science]

    Polk TA, Drake RM, Jonides JJ, Smith MR, Smith EE. Attention enhances the neural processing of relevant features and suppresses the processing of irrelevant features in humans: a functional magnetic resonance imaging study of the Stroop task. Journal of Neuroscience (2008) 28:13786–13792.[Abstract/Free Full Text]

    Polk TA, Simen PA, Lewis RL, Freedman EG. A computational approach to control in complex cognition. Cognitive Brain Research (2002) 15(1):71–83.[CrossRef][Medline]

    Poor HV. An Introduction to Signal Detection and Estimation (1994) New York: Springer-Verlag.

    Ratcliff R. A theory of memory retrieval. Psychological Review (1978) 85:59–108.[CrossRef][Web of Science]

    Ratcliff R, Rouder JN. Modeling response times for two-choice decisions. Psychological Science (1998) 9:347–356.[CrossRef][Web of Science]

    Reddi BAJ, Carpenter RHS. The influence of urgency on decision time. Nature (2000) 3(8):827–830.[Web of Science]

    Ritter H, Haschke R, Steil JJ. A dual interaction perspective for robot cognition: grasping as a ‘‘Rosetta Stone’’. In: Perspectives of Neural-Symbolic Integration—Hammer B, Hitzler P, eds. (2007) Berlin: Springer. 159–178.

    Roe RM, Busemeyer JR, Townsend JT. Multialternative decision field theory: a dynamic connectionist model of decision making. Psychological Review (2001) 108(2):370–392.[CrossRef][Web of Science][Medline]

    Roitman JD, Shadlen MN. Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task. Journal of Neuroscience (2002) 22(21):9475–9489.[Abstract/Free Full Text]

    The perceptron: a probabilistic model for information storage and organization in the brain. Psychological Review (1958) 65:386–408. reprinted in Anderson and Rosenfeld(1988).[CrossRef][Web of Science][Medline]

    Rumelhart DE, Hinton GE, Williams RJ. Learning representations by backpropagating errors. Nature (1986) 323:533–536.[CrossRef][Web of Science]

    Seung HS, Lee DD, Reis BY, Tank DW. The autapse: a simple illustration of short-term analog memory storage by tuned synaptic feedback. Journal of Computational Neuroscience (2000) 9:171–185.[CrossRef][Web of Science][Medline]

    Shadlen MN, Newsome WT. The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. Journal of Neuroscience (1998) 18(10):3870–3896.[Abstract/Free Full Text]

    Shadlen MN, Newsome WT. Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey. Journal of Neurophysiology (2001) 86(4):1916–1936.[Abstract/Free Full Text]

    Shallice T. Specific impairments in planning. Philosophical Transactions of the Royal Society of London, Series B (1982) 298:199–209.[Abstract/Free Full Text]

    Shastri L, Ajjanagadde V. From simple associations to systematic reasoning: a connectionist representation of rules, variables and dynamic bindings using temporal synchrony. Behavioral and Brain Sciences (1993) 16:417–494.[Web of Science]

    Simen PA, Cohen JD, in press. Explicit melioration by a neural diffusion model. Brain Research.

    Simen PA, Cohen JD, Holmes P. Rapid decision threshold modulation by reward rate in a neural network. Neural Networks (2006) 19:1013–1026.[CrossRef][Web of Science][Medline]

    Simen PA, Polk TA, Lewis RL, Freedman E. A computational account of latency impairments in problem solving by Parkinson's patients. (2004) 273–279. In: Proceedings of the International Conference on Cognitive Modeling.

    Simen PA, Polk TA, Lewis RL, Freedman EG. Universal computation by networks of model cortical columns. (2003) 230–235. In: Proceedings of the International Joint Conference on Neural Networks.

    Simon HA. The functional equivalence of problem solving skills. Cognitive Psychology (1975) 7:268–288.[CrossRef][Web of Science]

    Sipser M. Introduction to the Theory of Computation (1997) Boston, MA: PWS Publishing Co.

    Smith PL, Ratcliff R. Psychology and neurobiology of simple decisions. Trends in Neuroscience (2004) 27:161–168.[CrossRef][Web of Science][Medline]

    Soltani A, Wang XJ. A biophysically based neural model of matching law behavior: melioration by stochastic synapses. Journal of Neuroscience (2006) 26(14):3731–3744.[Abstract/Free Full Text]

    Sparso J, Furber S. Principles of Asynchronous Circuit Design (2002) Springer.

    Stone M. Models for choice reaction time. Psychometrika (1960) 25:251–260.[CrossRef][Web of Science]

    Sun R, Coward LA, Zenzen MJ. On levels of cognitive modeling. Philosophical Psychology (2005) 18(5):613–637.[CrossRef][Web of Science]

    Sutherland I, Ebergen J. Computers without clocks. Scientific American (2002) 62–69.

    Sutton RS, Barto AG. Reinforcement Learning (1998) Cambridge, MA: MIT Press.

    Thom R. Structural Stability and Morphogenesis: An Outline of a General Theory of Models (1989) Reading, MA: Addison-Wesley.

    Touretzky DS. BoltzCONS: dynamic symbol structures in a connectionist network. Artificial Intelligence (1990) 46:5–46.[CrossRef][Web of Science]

    Touretzky DS, Hinton GE. A distributed connectionist production system. Cognitive Science (1988) 12(3):423–466.[CrossRef][Web of Science]

    Usher M, McClelland JL. The time course of perceptual choice: the leaky, competing accumulator model. Psychological Review (2001) 108(3):550–592.[CrossRef][Web of Science][Medline]

    Von Neumann JV, Morgenstern O. Theory of Games and Economic Behavior (1944) Princeton, N.J.: Princeton University Press.

    Wald A, Wolfowitz J. Optimum character of the sequential probability ratio test. Annals of Mathematical Statistics (1948) 19:326–339.[CrossRef][Web of Science]

    Wang XJ. Synaptic reverberation underlying mnemonic persistent activity. Trends in Neuroscience (2001) 24(8):455–463.[CrossRef][Web of Science][Medline]

    Wang XJ. Probabilistic decision making by slow reverberation in cortical circuits. Neuron (2002) 36(5):955–968.[CrossRef][Web of Science][Medline]

    Ward G, Allport A. Planning and problem-solving using the five-disc tower of london task. Quarterly Journal of Experimental Psychology Section A: Human Experimental Psychology (1997) 50:49–78.[Web of Science]

    Williams RJ, Zipser D. A learning algorithm for continually running fully recurrent neural networks. Neural Computation (1989) 1:270–280.[CrossRef]

    Wilson HR, Cowan JD. Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal (1972) 12:1–24.[Web of Science][Medline]

    Wong KF, Wang XJ. A recurrent network mechanism of time integration in perceptual decisions. Journal of Neuroscience (2006) 26(4):1314–1328.[Abstract/Free Full Text]


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?



This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Supplementary Data
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Simen, P.
Right arrow Articles by Polk, T.
Social Bookmarking
 Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?