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We derive generalized spin models for the development of feedforward cortical architecture from a Hebbian synaptic learning rule in a two layer neural network with nonlinear weight constraints. Our model takes into account the effects of lateral interactions in visual cortex combining local excitation and long range effective inhibition. Our approach allows the principled derivation of developmental rules for low-dimensional feature maps, starting from high-dimensional synaptic learning rules. We incorporate the effects of smooth nonlinear constraints on net synaptic weight projected from units in the thalamic layer (the fan-out) and on the net synaptic weight received by units in the cortical layer (the fan-in). These constraints naturally couple together multiple feature maps such as orientation preference and retinotopic organization. We give a detailed illustration of the method applied to the development of the orientation preference map as a special case, in addition to deriving a model for joint pattern formation in cortical maps of orientation preference, retinotopic location, and receptive field width. We show that the combination of Hebbian learning and center-surround cortical interaction naturally leads to an orientation map development model that is closely related to the XY magnetic lattice model from statistical physics. The results presented here provide justification for phenomenological models studied in Cowan and Friedman (Advances in neural information processing systems 3, 1991), Thomas and Cowan (Phys Rev Lett 92(18):e188101, 2004) and provide a developmental model realizing the synaptic weight constraints previously assumed in Thomas and Cowan (Math Med Biol 23(2):119-138, 2006).

Forty evaluable patients with malignant lymphoma (ML) were treated with bisantrene at a dose of 260 mg/m2 every 3 weeks (18 patients) or 208 mg/m2 every 3 weeks (22 patients). The initial dose rate was determined on the basis of expected myelosuppression. Patients were heavily pretreated and had advanced disease (92% had stage IV). The overall response rate was 10% and included 1 partial response (PR) in 17 patients with Hodgkin's disease (HD), 1 PR and 1 complete response (CR) in 5 patients with favorable histology in non-Hodgkin's lymphoma (NHL), and 1 PR in 18 patients with unfavorable histology in NHL. Neutropenia (WBC less than or equal to 3000 cells/microliter) was the most common toxicity, occurring in 50% of patients. Phlebitis was a common side effect in patients treated with bisantrene administered by way of peripheral veins. Bisantrene has limited activity in heavily pretreated patients with HD or unfavorable histology in NHL. The role of bisantrene for treatment of NHL with favorable histology or for treatment at an earlier point in the natural history of ML is unknown.

Neuronal activity in a two-dimensional net is analyzed in the neighborhood of an instability. Bifurcation theory and group theory are used to demonstrate the existence of a variety of doubly-periodic patterns, hexagons, rolls, etc., as solutions to the field equations for the net activity. It is suggested that these simple geometric patterns are the cortical concomitants of the "form constants" seen during visual hallucinosis.

A model for the interactions of cortical neurons is derived and analyzed. It is shown that small amplitude spatially inhomogeneous standing oscillations can bifurcate from the rest state. In a periodic domain, traveling wave trains exist. Stability of these patterns is discussed in terms of biological parameters. Homoclinic and heteroclinic orbits are demonstrated for the space-clamped system.