A laminar organization for selective cortico-cortical communication

The neocortex is central to mammalian cognitive ability, playing critical roles in sensory perception, motor skills and executive function. This thin, layered structure comprises distinct, functionally specialized areas that communicate with each other through the axons of pyramidal neurons. For the hundreds of such cortico-cortical pathways to underlie diverse functions, their cellular and synaptic architectures must differ so that they result in distinct computations at the target projection neurons. In what ways do these pathways differ? By originating and terminating in different laminae, and by selectively targeting specific populations of excitatory and inhibitory neurons, these “interareal” pathways can differentially control the timing and strength of synaptic inputs onto individual neurons, resulting in layer-specific computations. Due to the rapid development in transgenic techniques, the mouse has emerged as a powerful mammalian model for understanding the rules by which cortical circuits organize and function. Here we review our understanding of how cortical lamination constrains long-range communication in the mammalian brain, with an emphasis on the mouse visual cortical network. We discuss the laminar architecture underlying interareal communication, the role of neocortical layers in organizing the balance of excitatory and inhibitory actions, and highlight the structure and function of layer 1 in mouse visual cortex

Quantum ballistic transport in in-plane-gate transistors showing onset of a novel ferromagnetic phase transition

We study one-dimensional transport in focused-ion-beam written in-plane-gate transistors on III-V heterostructures at moderately low temperatures at zero bias without any external magnetic field applied. In accordance with a recent proposal of A. Gold and L. Calmels, Valley- and spin-occupancy instability in the quasi-one-dimensional electron gas, Phil. Mag. Lett. 74, 33-42 (1996) and earlier experimental data, we observe plateaux in the source-drain conductivity considered as a function of the gate voltage, not only at multliples of 2e^2/h but also clearly at e^2/h, just before the channel closes to zero conductivity. This may be interpreted as a many electron effect, namely as a novel ballistic ferromagnetic ground state evading standard descriptions and theorems.Comment: 19 pages, 9 figures, 22 reference

The number of nilpotent semigroups of degree 3

A semigroup is \emph{nilpotent} of degree 3 if it has a zero, every product of 3 elements equals the zero, and some product of 2 elements is non-zero. It is part of the folklore of semigroup theory that almost all finite semigroups are nilpotent of degree 3. We give formulae for the number of nilpotent semigroups of degree 3 with $n\in\N$ elements up to equality, isomorphism, and isomorphism or anti-isomorphism. Likewise, we give formulae for the number of nilpotent commutative semigroups with $n$ elements up to equality and up to isomorphism

Pair correlation functions and limiting distributions of iterated cluster point processes

We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier work by Felsenstein and Shimatani describing a reproducing population. We discuss when closed term expressions of the first and second order moments are available for a given state. In a special case it is known that the pair correlation function for these type of point processes converges as the Markov chain progresses, but it has not been shown whether the Markov chain has an equilibrium distribution with this, particular, pair correlation function and how it may be constructed. Assuming the same reproducing system, we construct an equilibrium distribution by a coupling argument

Deep Gaussian Processes

In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.Comment: 9 pages, 8 figures. Appearing in Proceedings of the 16th International Conference on Artificial Intelligence and Statistics (AISTATS) 201

The Neveu-Schwarz Five-Brane and its Dual Geometries

In this paper we discuss two aspects of duality transformations on the Neveu-Schwarz (NS) 5-brane solutions in type II and heterotic string theories. First we demonstrate that the non-extremal NS 5-brane background is U-dual to its CGHS limit, a two-dimensional black hole times $S^3\times T^5$; an intermediate step is provided by the near horizon geometry which is given by the three-dimensional $BTZ_3$ black hole (being closely related to $AdS_3$) times $S^3\times T^4$. In the second part of the paper we discuss the T-duality between $k$ NS 5-branes and the Taub-NUT spaces respectively ALE spaces, which are related to the resolution of the $A_{k-1}$ singularities of the non-compact orbifold ${\bf C}^2/{\bf Z}_{k}$. In particular in the framework of N=1 supersymmetric gauge theories related to brane box constructions we give the metric dual to two sets of intersecting NS 5-branes. In this way we get a picture of a dual orbifold background ${\bf C}^3/ \Gamma$ which is fibered together out of two N=2 models ($\Gamma={\bf Z}_k\times {\bf Z}_{k'}$). Finally we also discuss the intersection of NS 5-branes with D branes, which can serve as probes of the dual background spaces.Comment: 18pp, added reference

Emergent multipolar spin correlations in a fluctuating spiral - The frustrated ferromagnetic S=1/2 Heisenberg chain in a magnetic field

We present the phase diagram of the frustrated ferromagnetic S=1/2 Heisenberg J_1-J_2 chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states towards spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in two-dimensional $S=1/2$ quantum magnets in a magnetic field.Comment: 4+ pages, 4 figure