15,220 research outputs found
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
Analytic theory of fiber-optic Raman polarizers
The Raman polarizer is a Raman amplifier which not only amplifies but also re-polarizes light. We propose a relatively simple and analytically tractable model - the ideal Raman polarizer, for describing the operation of this device. The model efficiently determines key device parameters such as the degree of polarization, the alignment parameter, the gain and the RIN variance
Factors of sums and alternating sums involving binomial coefficients and powers of integers
We study divisibility properties of certain sums and alternating sums
involving binomial coefficients and powers of integers. For example, we prove
that for all positive integers , , and any
nonnegative integer , there holds {align*} \sum_{k=0}^{n_1}\epsilon^k
(2k+1)^{2r+1}\prod_{i=1}^{m} {n_i+n_{i+1}+1\choose n_i-k} \equiv 0 \mod
(n_1+n_m+1){n_1+n_m\choose n_1}, {align*} and conjecture that for any
nonnegative integer and positive integer such that is odd, where .Comment: 14 pages, to appear in Int. J. Number Theor
On the least common multiple of -binomial coefficients
In this paper, we prove the following identity \lcm({n\brack 0}_q,{n\brack
1}_q,...,{n\brack n}_q) =\frac{\lcm([1]_q,[2]_q,...,[n+1]_q)}{[n+1]_q},
where denotes the -binomial coefficient and
. This result is a -analogue of an identity of
Farhi [Amer. Math. Monthly, November (2009)].Comment: 5 page
Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems
Many modern nonlinear control methods aim to endow systems with guaranteed
properties, such as stability or safety, and have been successfully applied to
the domain of robotics. However, model uncertainty remains a persistent
challenge, weakening theoretical guarantees and causing implementation failures
on physical systems. This paper develops a machine learning framework centered
around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and
unmodeled dynamics in general robotic systems. Our proposed method proceeds by
iteratively updating estimates of Lyapunov function derivatives and improving
controllers, ultimately yielding a stabilizing quadratic program model-based
controller. We validate our approach on a planar Segway simulation,
demonstrating substantial performance improvements by iteratively refining on a
base model-free controller
Attraction between like-charged colloidal particles induced by a surface a density - functional analysis
We show that the first non-linear correction to the linearised
Poisson-Boltzman n (or DLVO) theory of effective pair interactions between
charge-stabilised, co lloidal particles near a charged wall leads to an
attractive component of entro pic origin. The position and depth of the
potential compare favourably with rec ent experimental measurementsComment: 12 pages including 2 figures. submitted to physical review letter
Chemotaxis of Arbacia punctulata spermatozoa to resact, a peptide from the egg jelly layer
Resact, a peptide of known sequence isolated from the jelly layer of Arbacia punctulata eggs, is a potent chemoattractant for A. punctulata spermatozoa. The chemotactic response is concentration dependent, is abolished by pretreatment of the spermatozoa with resact, and shows an absolute requirement for millimolar external calcium. A. punctulata spermatozoa do not respond to speract, a peptide isolated from the jelly layer of Strongylocentrotus purpuratus eggs. This is the first report of animal sperm chemotaxis in response to a defined egg-derived molecule
Colour Relations in Form
The orthodox monadic determination thesis holds that we represent colour relations by virtue of representing colours. Against this orthodoxy, I argue that it is possible to represent colour relations without representing any colours. I present a model of iconic perceptual content that allows for such primitive relational colour representation, and provide four empirical arguments in its support. I close by surveying alternative views of the relationship between monadic and relational colour representation
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