stochastic models
John Baez (2014)
"Network Theory".
Presented in Oxford.
Presented at Dagstuhl:
"Categorical Methods
at the Crossroads."
Update:
Links from the book.
Ch.5:
M. Doi (1976) "Second-quantization
representation for classical many-particle
systems" J. Phys. A 9, 1465-1477.
M. Doi (1976) "Stochastic theory of diffusion-
controlled reactions" J. Phys. A 9, 1479-1495.
L. Peliti (1985) "Path integral approach to birth-
death processes on a lattice" J. Phys. 46, 1469-83.
J. Cardy (1996) " Renormalization group
approach to reaction-diffusion problems".
D.C. Mattis, M.L. Glasser (1998) "The uses of
quantum field theory in diffusion-limited reactions"
Rev. Mod. Phys. 70, 979-1001.
U.C. Tauber, M. Howard, B.P. Vollmayr-Lee (2005)
" Applications of field-theoretic renormalization
group methods to reaction-diffusion problems"
Jour. Phys. A 38 (2005), R79.
M.A. Buice, J.D. Cowan (2007) "Field-theoretic
approach to fluctuation effects in neural networks,"
Phys. Rev. E 75, 051919.
M.A. Buice, J.D. Cowan (2009) "Statistical
mechanics of the neocortex," Prog. Biophysics
& Mol. Bio. 99, 53-86.
P.J. Dodd, N.M. Ferguson (2009) "A many-body
field theory approach to stochastic models in
population biology" PLoS ONE 4, e6855.
J.M. Beggs, D. Plenz (2003) "Neuronal avalanches in
neocortical circuits." J. Neurosci. 23(35):11167-77.
Griffith J.S. (1963) "On the stability of
brain-like structures" Biophys. J. 3:299-308.
Ch.11:
Zhi-Ming Ma, M. Röckner "Introduction to the Theory of
(Non-Symmetric) Dirichlet Forms" Springer, Berlin, 1992.
Ch.13:
M.Randic "Symmetry properties of graphs of
interest in chemistry: II: Desargues-Levi graph"
Int. Jour. Quantum Chem. 15 (1997), 663-682.
Ch.14:
Michael W. Newman "The Laplacian Spectrum of Graphs"
M.Sc.Th., Dep. of Math., Univ. of Manitoba, 2000.
Ch.15:
P.G. Doyle, J.L. Snell "Random Walks and Electric Networks"
Mathematical Association of America, Washington DC, 1984.
M. Fukushima "Dirichlet Forms and Markov Processes"
North-Holland, Amsterdam, 1980.
%%%%%%%%%%%%%%%
Additional references
(from J.Cowan's art., NNs book 2014):
Beurle, R.L. (1956) "Properties of a mass of
cells capable of regenerating pulses" Philos.
Trans. R. Soc. Lond. B 240(669), 55-94. (jstore)
Kerner, E. (1957) "A statistical mechanics of inter-
acting species" Bull. Math. Biophys. 19, 121-146.
Grassberger, P., Scheunert, M. (1980) "Fock-space methods
for identical classical objects." Fortschr. Phys. 28, 547-578.
Rose, H. (1980) "Renormalised kinetic theory for nonequilibrium
many-particle classical systems." J. Stat. Phys. 20(4), 415-447.
%% %%
Ohira, T., Cowan, J. (1997) "Stochastic neurodynamics and the system
size expansion." In: Ellacort, S., Anderson, I. (eds.) Proc. of the
1st Int. Conf. on the Math. of NNs, pp. 290-294. Kluwer, Boston.
McKane, A., Newman, T. (2005) "Predator-prey cycles from resonant
amplification of demographic stochasticity" Phys.Rev.Lett.94(21),218102.
Mobilia, M., Georgiev, I., Taüber, U. (2006) "Fluctuations and correlations
in lattice models of predator-prey interactions" Phys.Rev.E 73(4),04093-04096.
Benayoun, M., Cowan, J., van Drongelen, W., Wallace, E. (2010)
"Avalanches in a stochastic model of spiking neurons." PLoS Comput. Biol. 6(7), e1000846.
Buice, M.A., Cowan, J.D., Chow, C.C. (2010) "Systematic fluctuation
expansion for neural network activity equations." Neur. Comp. 22(2), 377-426.
Bressloff, P. (2009) "Stochastic neural field theory and the
system-size expansion." SIAM J. Appl. Math. 70(5), 1488-1521.
P.C. Bressloff (2012) "Spatiotemporal Dynamics of
Continuum Neural Fields" J.Phys.A, 45, 033001. (PDF)
P.C. Bressloff, J.M. Newby (2014) "Path-integrals
and large deviations in stochastic hybrid systems"
Phys.Rev.E, 89, 042701. (PDF)
P.C. Bressloff (2014) "Stochastic Processes in Cell
Biology" Interdisc. Appl. Math. (Springer). The book.
P.C. Bressloff (2009) "Stochastic neural field theory and the
system-size expansion." SIAM J. Appl. Math. 70, 1488-1521. (PDF)
P.C. Bressloff (2009) "Lectures in Mathematical Neuroscience"
In: Math. Biol., AMS, IAS/Park City Math. Ser.(M.A. Lewis,
et al., eds.) 14, 293-398. (PDF)
%%
Moyal, J. (1949) "Stochastic processes and statistical
physics" J. R. Stat. Soc. B 11(2), 150-210.
Abarbanel, H., Broznan, J., Sugar, R., White, A. (1975)
"Reggeon field theory: formulation and use." Phys.Rep.21(3), 119-182.
Grassberger, P., de la Torre, A. (1979) "Reggeon field theory
(Schlögle’s first model) on a lattice: Monte carlo calculations
of critical behaviour." Ann. Phys. 122, 373-396.
Amati, D., Marchesini, G., Ciafoloni, M., Parisi, G. (1976)
"Expanding disc as a dynamical vacuum instability in Reggeon
field theory." Nucl. Phys. B 114, 483-504.
Perelomov, A. (1986) "Generalized Coherent States
and Their Applications." Springer, New York.
"Network Theory".
Presented in Oxford.
Presented at Dagstuhl:
"Categorical Methods
at the Crossroads."
Update:
Links from the book.
Ch.5:
M. Doi (1976) "Second-quantization
representation for classical many-particle
systems" J. Phys. A 9, 1465-1477.
M. Doi (1976) "Stochastic theory of diffusion-
controlled reactions" J. Phys. A 9, 1479-1495.
L. Peliti (1985) "Path integral approach to birth-
death processes on a lattice" J. Phys. 46, 1469-83.
J. Cardy (1996) " Renormalization group
approach to reaction-diffusion problems".
D.C. Mattis, M.L. Glasser (1998) "The uses of
quantum field theory in diffusion-limited reactions"
Rev. Mod. Phys. 70, 979-1001.
U.C. Tauber, M. Howard, B.P. Vollmayr-Lee (2005)
" Applications of field-theoretic renormalization
group methods to reaction-diffusion problems"
Jour. Phys. A 38 (2005), R79.
M.A. Buice, J.D. Cowan (2007) "Field-theoretic
approach to fluctuation effects in neural networks,"
Phys. Rev. E 75, 051919.
M.A. Buice, J.D. Cowan (2009) "Statistical
mechanics of the neocortex," Prog. Biophysics
& Mol. Bio. 99, 53-86.
P.J. Dodd, N.M. Ferguson (2009) "A many-body
field theory approach to stochastic models in
population biology" PLoS ONE 4, e6855.
J.M. Beggs, D. Plenz (2003) "Neuronal avalanches in
neocortical circuits." J. Neurosci. 23(35):11167-77.
Griffith J.S. (1963) "On the stability of
brain-like structures" Biophys. J. 3:299-308.
Ch.11:
Zhi-Ming Ma, M. Röckner "Introduction to the Theory of
(Non-Symmetric) Dirichlet Forms" Springer, Berlin, 1992.
Ch.13:
M.Randic "Symmetry properties of graphs of
interest in chemistry: II: Desargues-Levi graph"
Int. Jour. Quantum Chem. 15 (1997), 663-682.
Ch.14:
Michael W. Newman "The Laplacian Spectrum of Graphs"
M.Sc.Th., Dep. of Math., Univ. of Manitoba, 2000.
Ch.15:
P.G. Doyle, J.L. Snell "Random Walks and Electric Networks"
Mathematical Association of America, Washington DC, 1984.
M. Fukushima "Dirichlet Forms and Markov Processes"
North-Holland, Amsterdam, 1980.
%%%%%%%%%%%%%%%
Additional references
(from J.Cowan's art., NNs book 2014):
Beurle, R.L. (1956) "Properties of a mass of
cells capable of regenerating pulses" Philos.
Trans. R. Soc. Lond. B 240(669), 55-94. (jstore)
Kerner, E. (1957) "A statistical mechanics of inter-
acting species" Bull. Math. Biophys. 19, 121-146.
Grassberger, P., Scheunert, M. (1980) "Fock-space methods
for identical classical objects." Fortschr. Phys. 28, 547-578.
Rose, H. (1980) "Renormalised kinetic theory for nonequilibrium
many-particle classical systems." J. Stat. Phys. 20(4), 415-447.
%% %%
Ohira, T., Cowan, J. (1997) "Stochastic neurodynamics and the system
size expansion." In: Ellacort, S., Anderson, I. (eds.) Proc. of the
1st Int. Conf. on the Math. of NNs, pp. 290-294. Kluwer, Boston.
McKane, A., Newman, T. (2005) "Predator-prey cycles from resonant
amplification of demographic stochasticity" Phys.Rev.Lett.94(21),218102.
Mobilia, M., Georgiev, I., Taüber, U. (2006) "Fluctuations and correlations
in lattice models of predator-prey interactions" Phys.Rev.E 73(4),04093-04096.
Benayoun, M., Cowan, J., van Drongelen, W., Wallace, E. (2010)
"Avalanches in a stochastic model of spiking neurons." PLoS Comput. Biol. 6(7), e1000846.
Buice, M.A., Cowan, J.D., Chow, C.C. (2010) "Systematic fluctuation
expansion for neural network activity equations." Neur. Comp. 22(2), 377-426.
Bressloff, P. (2009) "Stochastic neural field theory and the
system-size expansion." SIAM J. Appl. Math. 70(5), 1488-1521.
P.C. Bressloff (2012) "Spatiotemporal Dynamics of
Continuum Neural Fields" J.Phys.A, 45, 033001. (PDF)
P.C. Bressloff, J.M. Newby (2014) "Path-integrals
and large deviations in stochastic hybrid systems"
Phys.Rev.E, 89, 042701. (PDF)
P.C. Bressloff (2014) "Stochastic Processes in Cell
Biology" Interdisc. Appl. Math. (Springer). The book.
P.C. Bressloff (2009) "Stochastic neural field theory and the
system-size expansion." SIAM J. Appl. Math. 70, 1488-1521. (PDF)
P.C. Bressloff (2009) "Lectures in Mathematical Neuroscience"
In: Math. Biol., AMS, IAS/Park City Math. Ser.(M.A. Lewis,
et al., eds.) 14, 293-398. (PDF)
%%
Moyal, J. (1949) "Stochastic processes and statistical
physics" J. R. Stat. Soc. B 11(2), 150-210.
Abarbanel, H., Broznan, J., Sugar, R., White, A. (1975)
"Reggeon field theory: formulation and use." Phys.Rep.21(3), 119-182.
Grassberger, P., de la Torre, A. (1979) "Reggeon field theory
(Schlögle’s first model) on a lattice: Monte carlo calculations
of critical behaviour." Ann. Phys. 122, 373-396.
Amati, D., Marchesini, G., Ciafoloni, M., Parisi, G. (1976)
"Expanding disc as a dynamical vacuum instability in Reggeon
field theory." Nucl. Phys. B 114, 483-504.
Perelomov, A. (1986) "Generalized Coherent States
and Their Applications." Springer, New York.