Improved Compressive Sensing Of Natural Scenes Using Localized Random Sampling

Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging

Efficient Image Processing Via Compressive Sensing Of Integrate-And-Fire Neuronal Network Dynamics

Integrate-and-fire (I&F) neuronal networks are ubiquitous in diverse image processing applications, including image segmentation and visual perception. While conventional I&F network image processing requires the number of nodes composing the network to be equal to the number of image pixels driving the network, we determine whether I&F dynamics can accurately transmit image information when there are significantly fewer nodes than network input-signal components. Although compressive sensing (CS) theory facilitates the recovery of images using very few samples through linear signal processing, it does not address whether similar signal recovery techniques facilitate reconstructions through measurement of the nonlinear dynamics of an I&F network. In this paper, we present a new framework for recovering sparse inputs of nonlinear neuronal networks via compressive sensing. By recovering both one-dimensional inputs and two-dimensional images, resembling natural stimuli, we demonstrate that input information can be well-preserved through nonlinear I&F network dynamics even when the number of network-output measurements is significantly smaller than the number of input-signal components. This work suggests an important extension of CS theory potentially useful in improving the processing of medical or natural images through I&F network dynamics and understanding the transmission of stimulus information across the visual system

Theory of the high-frequency chiral optical response in a p_x+ip_y superconductor

The optical Hall conductivity and the polar Kerr angle are calculated as functions of temperature for a two-dimensional chiral p_x+ip_y superconductor, where the time-reversal symmetry is spontaneously broken. The theoretical estimate for the polar Kerr angle agrees by the order of magnitude with the recent experimental measurement in Sr2RuO4 by Xia et al. cond-mat/0607539. The theory predicts that the Kerr angle is proportional to the square of the superconducting energy gap and is inversely proportional to the cube of frequency, which can be verified experimentally.Comment: 4 pages, no figures, RevTeX. V.2: one reference and discussion of horizontal lines of nodes added. V.3: a typo corrected, and one reference added. V.4: two references added and minor stylistic changes made, as in the published versio

Stable topological phases in a family of two-dimensional fermion models

We show that a large class of two-dimensional spinless fermion models exhibit topological superconducting phases characterized by a non-zero Chern number. More specifically, we consider a generic one-band Hamiltonian of spinless fermions that is invariant under both time-reversal, $\mathbb{T}$, and a group of rotations and reflections, $\mathbb{G}$, which is either the dihedral point-symmetry group of an underlying lattice, $\mathbb{G}=D_n$, or the orthogonal group of rotations in continuum, $\mathbb{G}={\rm O}(2)$. Pairing symmetries are classified according to the irreducible representations of $\mathbb{T} \otimes \mathbb{G}$. We prove a theorem that for any two-dimensional representation of this group, a time-reversal symmetry breaking paired state is energetically favorable. This implies that the ground state of any spinless fermion Hamiltonian in continuum or on a square lattice with a singly-connected Fermi surface is always a topological superconductor in the presence of attraction in at least one channel. Motivated by this discovery, we examine phase diagrams of two specific lattice models with nearest-neighbor hopping and attraction on a square lattice and a triangular lattice. In accordance with the general theorem, the former model exhibits only a topological $(p + ip)$-wave state, while the latter shows a doping-tuned quantum phase transition from such state to a non-topological, but still exotic $f$-wave superconductor.Comment: 6 pages, 2 figures, new references adde

Thermodynamic Properties of Generalized Exclusion Statistics

We analytically calculate some thermodynamic quantities of an ideal $g$-on gas obeying generalized exclusion statistics. We show that the specific heat of a $g$-on gas ($g \neq 0$) vanishes linearly in any dimension as $T \to 0$ when the particle number is conserved and exhibits an interesting dual symmetry that relates the particle-statistics at $g$ to the hole-statistics at $1/g$ at low temperatures. We derive the complete solution for the cluster coefficients $b_l(g)$ as a function of Haldane's statistical interaction $g$ in $D$ dimensions. We also find that the cluster coefficients $b_l(g)$ and the virial coefficients $a_l(g)$ are exactly mirror symmetric ($l$=odd) or antisymmetric ($l$=even) about $g=1/2$. In two dimensions, we completely determine the closed forms about the cluster and the virial coefficients of the generalized exclusion statistics, which exactly agree with the virial coefficients of an anyon gas of linear energies. We show that the $g$-on gas with zero chemical potential shows thermodynamic properties similar to the photon statistics. We discuss some physical implications of our results.Comment: 24 pages, Revtex, Corrected typo

Livelihood Strategies of Resource-Poor Farmers in Striga-Infested Areas of Western Kenya.

Striga hermonthica (del) Benth is threatening rural livelihoods in western Kenya where maize is the major food and cash crop. Vulnerability analysis was conducted on a sample of 802 households in eight districts of Nyanza and Western provinces. Farmers perceived Striga as the major cause of poverty and food insecurity. Both household income and child nutrition indicators showed alarming conditions for the majority of households. The coping strategies and informal safety nets were not capable of addressing the vulnerability issue successfully. A logistic regression model of determinants of poverty was estimated to examine the determinants and correlates of poverty. Results revealed certain characteristics of households that were more likely to be poor: poor access to land and farm assets; high dependency ratio; headed by older farmer with low education attainment; no off-farm work, no cash crops; depend on credit; Striga has been on the farm for long, high perceived yield loss to Striga given high dependency on maize for livelihoods; adopt no integrated Striga control options; and live in Bondo and Vihiga districts. The paper concludes with implications for policy to improve the livelihoods of small-scale farmers in the Striga-affected areas of western Kenya. Key words: livelihoods, maize, Striga, Kenya, Logitlivelihoods, maize, Kenya, Striga, logit, Agricultural and Food Policy, Community/Rural/Urban Development, Consumer/Household Economics, Environmental Economics and Policy, Farm Management, Food Consumption/Nutrition/Food Safety, Food Security and Poverty, Health Economics and Policy, Land Economics/Use, Marketing, Productivity Analysis, Research and Development/Tech Change/Emerging Technologies,

Smallholder marketed surplus and input use under transactions costs: maize supply and fertilizer demand in Kenya

This paper assessed the effects of transactions costs—relative to price and non-price factors—on smallholder marketed surplus and input use in Kenya. A selectivity model was used that accounts not only for the effects of fixed and variable transactions costs but also for the role of assets, technology, and support services in promoting input use and generating a marketable surplus. Output supply and input demand responses to changes in transactions costs and price and non-price factors were estimated and decomposed into market entry and intensity. The results showed that while transactions costs indeed have significant negative effects on market participation, cost-mitigating innovations—such as group marketing—are also emerging to mitigate the costs of accessing markets. Output price has no effect on output market entry and only provides incentives for increased supply by sellers. On the other hand, both price and non-price factors have significant influence on adoption and intensity of input use. Overall, the findings suggest that policy options are available other than price policies to promote input use and agricultural surplus.Commercialization, Marketed surplus, Fertilizer use, Transactions cost, Kenya, Agricultural and Food Policy, Agricultural Finance, Consumer/Household Economics, Environmental Economics and Policy, Food Consumption/Nutrition/Food Safety, Food Security and Poverty, Institutional and Behavioral Economics, International Relations/Trade, Marketing, Productivity Analysis, Research and Development/Tech Change/Emerging Technologies, Research Methods/ Statistical Methods,