Treatment of backscattering in a gas of interacting fermions confined to a one-dimensional harmonic atom trap

An asymptotically exact many body theory for spin polarized interacting fermions in a one-dimensional harmonic atom trap is developed using the bosonization method and including backward scattering. In contrast to the Luttinger model, backscattering in the trap generates one-particle potentials which must be diagonalized simultaneously with the two-body interactions. Inclusion of backscattering becomes necessary because backscattering is the dominant interaction process between confined identical one-dimensional fermions. The bosonization method is applied to the calculation of one-particle matrix elements at zero temperature. A detailed discussion of the validity of the results from bosonization is given, including a comparison with direct numerical diagonalization in fermionic Hilbert space. A model for the interaction coefficients is developed along the lines of the Luttinger model with only one coupling constant $K$. With these results, particle densities, the Wigner function, and the central pair correlation function are calculated and displayed for large fermion numbers. It is shown how interactions modify these quantities. The anomalous dimension of the pair correlation function in the center of the trap is also discussed and found to be in accord with the Luttinger model.Comment: 19 pages, 5 figures, journal-ref adde

Effects of V1 surround modulation tuning on visual saliency and the tilt illusion

Neurons in the primary visual cortex respond to oriented stimuli placed in the center of their receptive field, yet their response is modulated by stimuli outside the receptive field (the surround). Classically, this surround modulation is assumed to be strongest if the orientation of the surround stimulus aligns with the neuron's preferred orientation - irrespective of the actual center stimulus. This neuron-dependent surround modulation has been used to explain a wide range of psychophysical phenomena, such as biased tilt perception and saliency of stimuli with contrasting orientation. However, several neurophysiological studies have shown that for most neurons surround modulation is instead center-dependent: it is strongest if the surround orientation aligns with the center stimulus. As the impact of such center-dependent modulation on the population level is unknown, we examine this using computational models. We find that with neuron-dependent modulation the biases in orientation coding, commonly used to explain the tilt illusion, are larger than psychophysically reported, but disappear with center-dependent modulation. Therefore we suggest that a mixture of the two modulation types is necessary to quantitatively explain the psychophysically observed biases. Next, we find that under center-dependent modulation average population responses are more sensitive to orientation differences between stimuli, which in theory could improve saliency detection. However, this effect depends on the specific saliency model. Overall, our results thus show that center-dependent modulation reduces coding bias, while possibly increasing the sensitivity to salient features

Feedforward Inhibition and Synaptic Scaling – Two Sides of the Same Coin?

Feedforward inhibition and synaptic scaling are important adaptive processes that control the total input a neuron can receive from its afferents. While often studied in isolation, the two have been reported to co-occur in various brain regions. The functional implications of their interactions remain unclear, however. Based on a probabilistic modeling approach, we show here that fast feedforward inhibition and synaptic scaling interact synergistically during unsupervised learning. In technical terms, we model the input to a neural circuit using a normalized mixture model with Poisson noise. We demonstrate analytically and numerically that, in the presence of lateral inhibition introducing competition between different neurons, Hebbian plasticity and synaptic scaling approximate the optimal maximum likelihood solutions for this model. Our results suggest that, beyond its conventional use as a mechanism to remove undesired pattern variations, input normalization can make typical neural interaction and learning rules optimal on the stimulus subspace defined through feedforward inhibition. Furthermore, learning within this subspace is more efficient in practice, as it helps avoid locally optimal solutions. Our results suggest a close connection between feedforward inhibition and synaptic scaling which may have important functional implications for general cortical processing

Histone H3 Localizes to the Centromeric DNA in Budding Yeast

During cell division, segregation of sister chromatids to daughter cells is achieved by the poleward pulling force of microtubules, which attach to the chromatids by means of a multiprotein complex, the kinetochore. Kinetochores assemble at the centromeric DNA organized by specialized centromeric nucleosomes. In contrast to other eukaryotes, which typically have large repetitive centromeric regions, budding yeast CEN DNA is defined by a 125 bp sequence and assembles a single centromeric nucleosome. In budding yeast, as well as in other eukaryotes, the Cse4 histone variant (known in vertebrates as CENP-A) is believed to substitute for histone H3 at the centromeric nucleosome. However, the exact composition of the CEN nucleosome remains a subject of debate. We report the use of a novel ChIP approach to reveal the composition of the centromeric nucleosome and its localization on CEN DNA in budding yeast. Surprisingly, we observed a strong interaction of H3, as well as Cse4, H4, H2A, and H2B, but not histone chaperone Scm3 (HJURP in human) with the centromeric DNA. H3 localizes to centromeric DNA at all stages of the cell cycle. Using a sequential ChIP approach, we could demonstrate the co-occupancy of H3 and Cse4 at the CEN DNA. Our results favor a H3-Cse4 heterotypic octamer at the budding yeast centromere. Whether or not our model is correct, any future model will have to account for the stable association of histone H3 with the centromeric DNA