Construction of direction selectivity in V1: from simple to complex cells

Despite detailed knowledge about the anatomy and physiology of the primary visual cortex (V1), the immense number of feed-forward and recurrent connections onto a given V1 neuron make it difficult to understand how the physiological details relate to a given neuron’s functional properties. Here, we focus on a well-known functional property of many V1 complex cells: phase-invariant direction selectivity (DS). While the energy model explains its construction at the conceptual level, it remains unclear how the mathematical operations described in this model are implemented by cortical circuits. To understand how DS of complex cells is constructed in cortex, we apply a nonlinear modeling framework to extracellular data from macaque V1. We use a modification of spike-triggered covariance (STC) analysis to identify multiple biologically plausible "spatiotemporal features" that either excite or suppress a cell. We demonstrate that these features represent the true inputs to the neuron more accurately, and the resulting nonlinear model compactly describes how these inputs are combined to result in the functional properties of the cell. In a population of 59 neurons, we find that both simple and complex V1 cells are selective to combinations of excitatory and suppressive motion features. Because the strength of DS and simple/complex classification is well predicted by our models, we can use simulations with inputs matching thalamic and simple cells to assess how individual model components contribute to these measures. Our results unify experimental observations regarding the construction of DS from thalamic feed-forward inputs to V1: based on the differences between excitatory and inhibitory inputs, they suggest a connectivity diagram for simple and complex cells that sheds light on the mechanism underlying the DS of cortical cells. More generally, they illustrate how stage-wise nonlinear combination of multiple features gives rise to the processing of more abstract visual information

Climate-Vegetation-Feedbacks as a Mechanism for Accelerated Climate Change: The onset of the African Humid Period

Paleo-environmental records and models indicate that the African Humid Period (AHPabruptly ended about 5000-4000 years before present (BP). Some proxies indicate alsan abrupt onset of the AHP between 14,000 and 11,000 BP. How important are local orbitaforcing, ice-sheet forcing, greenhouse gas forcing, and the reorganization of the AtlantiMeridional Overturning Circulation (AMOC) for changes in the African Monsoon/vegetatiosystem? Here we use transient simulations with climate-vegetation models of differencomplexity to identify the factors that control the onset of the African Monsoon/VegetationWe test the following hypothesis:(1) There is no indication for insolation-thresholds for the onset/break of the AHP.(2) Forcing from CO2/ice-sheets significantly controls the climate of North Africa.(3) CO2 fertilization contributes to the vegetation changes over North Africa.(4) A shutdown of the AMOC is as important as orbital insolation for the African Monsoon

Sparse solutions of linear Diophantine equations

We present structural results on solutions to the Diophantine system $A{\boldsymbol y} = {\boldsymbol b}$, ${\boldsymbol y} \in \mathbb Z^t_{\ge 0}$ with the smallest number of non-zero entries. Our tools are algebraic and number theoretic in nature and include Siegel's Lemma, generating functions, and commutative algebra. These results have some interesting consequences in discrete optimization

Time-convolutionless master equation for quantum dots: Perturbative expansion to arbitrary order

The master equation describing the non-equilibrium dynamics of a quantum dot coupled to metallic leads is considered. Employing a superoperator approach, we derive an exact time-convolutionless master equation for the probabilities of dot states, i.e., a time-convolutionless Pauli master equation. The generator of this master equation is derived order by order in the hybridization between dot and leads. Although the generator turns out to be closely related to the T-matrix expressions for the transition rates, which are plagued by divergences, in the time-convolutionless generator all divergences cancel order by order. The time-convolutionless and T-matrix master equations are contrasted to the Nakajima-Zwanzig version. The absence of divergences in the Nakajima-Zwanzig master equation due to the nonexistence of secular reducible contributions becomes rather transparent in our approach, which explicitly projects out these contributions. We also show that the time-convolutionless generator contains the generator of the Nakajima-Zwanzig master equation in the Markov approximation plus corrections, which we make explicit. Furthermore, it is shown that the stationary solutions of the time-convolutionless and the Nakajima-Zwanzig master equations are identical. However, this identity neither extends to perturbative expansions truncated at finite order nor to dynamical solutions. We discuss the conditions under which the Nakajima-Zwanzig-Markov master equation nevertheless yields good results.Comment: 13 pages + appendice

Influence of non-local exchange on RKKY interactions in III-V diluted magnetic semiconductors

The RKKY interaction between substitutional Mn local moments in GaAs is both spin-direction-dependent and spatially anisotropic. In this Letter we address the strength of these anisotropies using a semi-phenomenological tight-binding model which treats the hybridization between Mn d-orbitals and As p-orbitals perturbatively and accounts realistically for the non-local exchange interaction between their spins. We show that exchange non-locality, valence-band spin-orbit coupling, and band-structure anisotropy all play a role in determining the strength of both effects. We use these results to estimate the degree of ground-state magnetization suppression due to frustrating interactions between randomly located Mn ions.Comment: 4 pages RevTeX, 2 figures included, v2: replacement because of font proble

Agriculture, Population, Land and Water Scarcity in a Changing World – The Role of Irrigation

Fertile land and fresh water constitute two of the most fundamental resources for food production. These resources are affected by environmental, political, economic, and technical developments. Regional impacts may transmit to the world through increased trade. With a global forest and agricultural sector model, we quantify the impacts of increased demand for food due to population growth and economic development on potential land and water use. In particular, we investigate producer adaptation regarding crop and irrigation choice, agricultural market adjustments, and changes in the values of land and water.Irrigation, Food supply, Integrated assessment, Water use intensity, Agricultural adaptation, Land scarcity, Partial equilibrium model, Resource /Energy Economics and Policy,