1987. Daniel Amit 1938-2007. (Ising model) ferromagnetic. (e.g., S.K. model) + spin-glass state. (Hopfield model) + memory states. Systems of spin-like elements may dynamically relax governed by the Hamiltonian towards increasingly complex “discrete” attractor states. A. B. C.
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Daniel Amit 1938-2007
(e.g., S.K. model) + spin-glass state
(Hopfield model) + memory states
Systems of spin-like elements may dynamically relax
governed by the
towards increasingly complex “discrete” attractor states
showed how to extend the mathematical analysis of spin-glasses
into a new “statistical physics” of Hopfield attractor networks
and the saddle-point equations
that describe the equilibrium
reached by relaxational dynamics
DS (disordered state)
SG (spin glass)
yielding finally a phase-diagram
+RS (retrieval memory state)
storage load = p / N
are spin-glass effects really relevant to understanding realistic
Threshold-linear neural network (Hopfield)
Threshold-linear spin glass
Ramón y Cajal
La reazione nera
The Braitenberg model
N pyramidal cells
√N cells each
A pical synapses
B asal synapses
(O’Kane & Treves, 1992)
updated to remove the
‘memory glass’ problem
(Fulvi Mari & Treves, 1998)
Reduced to a Potts model
(Kropff & Treves, 2005)
Potts units with dilute
..but all cortical modules
share the same organization…
Local attractor states (=S)
“0” state included
S+1 Potts states
Global activity patterns
Sparse global patterns
Sparse Potts patterns
pc S ?!?!
pc CS 2 !!
Each MF terminates in several hundreds rosettes
Each rosette has the dendrites of 28 GCs
Each GC receives from 4 rosettes (MFs)
There are 450 times more GCs than MFs
In humans, there are 3x1010 GCs,
each making about 300 PF synapse,
for a total 1013 storage locations
on some 5x107 Purkinje cells.
Nature411, 189 - 193 (2001); doi:10.1038/35075564
Nature 411, 189 - 193 (2001)
Scalable architecture in mammalian brains
DAMON A. CLARK*†, PARTHA P. MITRA‡ & SAMUEL S.-H. WANG*
* Department of Molecular Biology and† Department of Physics, Princeton University, Princeton, New Jersey 08544, USA‡ Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, New Jersey 07974, USA
Correspondence and requests for materials should be addressed to S.S.-H.W. (e-mail: [email protected]).
Comparison of mammalian brain parts has often focused on differences in absolute size, revealing only a general tendency for all parts to grow together. Attempts to find size-independent effects using body weight as a reference variable obscure size relationships owing to independent variation of body size and give phylogenies of questionable significance. Here we use the brain itself as a size reference to define the cerebrotype, a species-by-species measure of brain composition. With this measure, across many mammalian taxa the cerebellum occupies a constant fraction of the total brain volume (0.13 0.02), arguing against the hypothesis that the cerebellum acts as a computational engine principally serving the neocortex. Mammalian taxa can be well separated by cerebrotype, thus allowing the use of quantitative neuroanatomical data to test evolutionary relationships. Primate cerebrotypes have progressively shifted and neocortical volume fractions have become successively larger in lemurs and lorises, New World monkeys, Old World monkeys, and hominoids, lending support to the idea that primate brain architecture has been driven by directed selection pressure. At the same time, absolute brain size can vary over 100-fold within a taxon, while maintaining a relatively uniform cerebrotype. Brains therefore constitute a scalable architecture.
The telencephalon of tetrapods in evolution.Striedter GF.Department of Psychobiology, University of California, Irvine 92697-4550, USA.Numerous scientists have sought a homologue of mammalian isocortex in sauropsids (reptiles and birds) and a homologue of sauropsid dorsal ventricular ridge in mammals. Although some of the proposed theories were enormously influential, alternative theories continued to coexist, primarily because the striking differences in pallial organization between adult mammals, sauropsids, and amphibians enabled different authors to enlist different subsets of similarity data in support of different hypotheses of putative homology. A phylogenetic analysis based on parsimony cannot discriminate between such alternative hypotheses of putative homology, because sauropsids and mammals are sister groups. One solution to this dilemma is to include embryological patterns of telencephalic organization in the comparative analysis. Because early developmental stages in different taxa tend to resemble each other more than the adults do, the embryological data may reveal intermediate patterns of organization that provide unambiguous support for a single hypothesis of putative homology. The validity of this putative homology may then be supported by means of a phylogenetic analysis based on parsimony. A comparative analysis of pallial organization that includes embryological data suggests the following set of homologies. The lateral cortex in reptiles is homologous to the piriform cortex in birds and mammals. The anterior dorsal ventricular ridge in reptiles is probably homologous to the neostriatum and ventral hyperstriatum in birds and to the endopiriform nucleus in mammals. The posterior dorsal ventricular ridge in reptiles is most likely homologous to the archistriatum in birds and to the pallial amygdala in mammals. The pallial thickening in reptiles is probably homologous to the dorsal and intercalated portions of the hyperstriatum in birds and to the claustrum proper in mammals. Finally, the dorsal cortex in reptiles is probably homologous to the accessory hyperstriatum and parahippocampal area in birds and to the isocortex in mammals. These hypotheses of homology imply relatively minor evolutionary changes in development but major changes in neuronal connections. Most significantly, they imply the independent elaboration of thalamic sensory projections to derivatives of the lateral and dorsal pallia in sauropsids and mammals, respectively. They also imply the independent evolution of lamination in the pallium of birds and mammals.
cutting-edge, in cerebellar technology?
DG input sparsifier
Tonic output firing
100’s Myrs old
that we fail