A new functional role for lateral inhibition in the striatum: Pavlovian conditioning

The striatum has long been implicated in reinforcement learning and has been suggested by several neurophysiological studies as the substrate for encoding the reward value of stimuli. Reward prediction error (RPE) has been used in several basal ganglia models as the underlying learning signal, which leads to Pavlovian conditioning abilities that can be simulated by the Rescorla-Wagner model.

Lateral inhibition between striatal projection neurons was once thought to have a winner-take-all function, useful in selecting between possible actions. However, it has been noted that the necessary reciprocal connections for this interpretation are too few, and the relative strength of these synaptic connections is weak. Still, modeling studies show that lateral inhibition does have an overall suppression effect on striatal activity and may play an important role in striatal processing. 

Neurophysiological recordings show task-relevant ensembles of responsive neurons at specific points in a behavioral paradigm (Barnes et al., 2005), which appear to be induced by lateral inhibition (see Ponzi and Wickens, 2010). We have developed a similarly responding, RPE-based model of the striatum by incorporating lateral inhibition. Model neurons are assigned to either the direct or the indirect pathway but lateral connections occur within and between these groups, leading to competition between both the individual neurons and their pathways. We successfully applied this model to the simulation of Pavlovian phenomena beyond those of the Rescorla-Wagner model, including negative patterning, unovershadowing, and external inhibition

The confined-deconfined interface tension, wetting, and the spectrum of the transfer matrix

The reduced tension $\sigma_{cd}$ of the interface between the confined and the deconfined phase of $SU(3)$ pure gauge theory is determined from numerical simulations of the first transfer matrix eigenvalues. At $T_c = 1/L_t$ we find $\sigma_{cd} = 0.139(4) T_c^2$ for $L_t = 2$. The interfaces show universal behavior because the deconfined-deconfined interfaces are completely wet by the confined phase. The critical exponents of complete wetting follow from the analytic interface solutions of a $\Z(3)$-symmetric $\Phi^4$ model in three dimensions. We find numerical evidence that the confined-deconfined interface is rough.Comment: Talk presented at the International Conference on Lattice Field Theory, Lattice 92, to be published in the proceedings, 4 pages, 4 figures, figures 2,3,4 appended as postscript files, figure 1 not available as a postscript file but identical with figure 2 of Nucl. Phys. B372 (1992) 703, special style file espcrc2.sty required (available from hep-lat), BUTP-92/4

Numerical simulation of heavy fermions in an SU(2)_L x SU(2)_R symmetric Yukawa model

An exploratory numerical study of the influence of heavy fermion doublets on the mass of the Higgs boson is performed in the decoupling limit of a chiral $\rm SU(2)_L \otimes SU(2)_R$ symmetric Yukawa model with mirror fermions. The behaviour of fermion and boson masses is investigated at infinite bare quartic coupling on $4^3 \cdot 8$, $6^3 \cdot 12$ and $8^3 \cdot 16$ lattices. A first estimate of the upper bound on the renormalized quartic coupling as a function of the renormalized Yukawa-coupling is given.Comment: 15 pp + 11 Figures appended as Postscript file

Quark Confinement in the Deconfined Phase

In cylindrical volumes with C-periodic boundary conditions in the long direction, static quarks are confined even in the gluon plasma phase due to the presence of interfaces separating the three distinct high-temperature phases. An effective "string tension" is computed analytically using a dilute gas of interfaces. At T_c, the deconfined-deconfined interfaces are completely wet by the confined phase and the high-temperature "string tension" turns into the usual string tension below T_c. Finite size formulae are derived, which allow to extract interface and string tensions from the expectation value of a single Polyakov loop. A cluster algorithm is built for the 3-d three-state Potts model and an improved estimator for the Polyakov loop is constructed, based on the number of clusters wrapping around the C-periodic direction of the cluster.Comment: 3 pages, Latex, talk presented at Lattice '97, to appear in Nucl. Phys. B (Proc. Suppl.), uses espcrc2.st

Coupling the Deconfining and Chiral Transitions

The Polyakov loop and the chiral condensate are used as order parameters to explore analytically the possible phase structure of finite temperature QCD. Nambu-Jona-Lasinio models in a background temporal gauge field are combined with a Polyakov loop potential in a form suitable for both the lattice and the continuum. Three possible behaviors are found: a first-order transition, a second-order transition, and a region with both transitions.Comment: 4 pages, LaTeX, 4 Postscript Figures, uuencoded, Contribution to Lattice 95 Conference Proceeding

Complete Wetting of Gluons and Gluinos

Complete wetting is a universal phenomenon associated with interfaces separating coexisting phases. For example, in the pure gluon theory, at $T_c$ an interface separating two distinct high-temperature deconfined phases splits into two confined-deconfined interfaces with a complete wetting layer of confined phase between them. In supersymmetric Yang-Mills theory, distinct confined phases may coexist with a Coulomb phase at zero temperature. In that case, the Coulomb phase may completely wet a confined-confined interface. Finally, at the high-temperature phase transition of gluons and gluinos, confined-confined interfaces are completely wet by the deconfined phase, and similarly, deconfined-deconfined interfaces are completely wet by the confined phase. For these various cases, we determine the interface profiles and the corresponding complete wetting critical exponents. The exponents depend on the range of the interface interactions and agree with those of corresponding condensed matter systems.Comment: 15 pages, 5 figure