A Convex Optimization Framework for Almost Budget Balanced Allocation of a Divisible Good

We address the problem of allocating a single divisible good to a number of agents. The agents have concave valuation functions parameterized by a scalar type. The agents report only the type. The goal is to find allocatively efficient, strategy proof, nearly budget balanced mechanisms within the Groves class. Near budget balance is attained by returning as much of the received payments as rebates to agents. Two performance criteria are of interest: the maximum ratio of budget surplus to efficient surplus, and the expected budget surplus, within the class of linear rebate functions. The goal is to minimize them. Assuming that the valuation functions are known, we show that both problems reduce to convex optimization problems, where the convex constraint sets are characterized by a continuum of half-plane constraints parameterized by the vector of reported types. We then propose a randomized relaxation of these problems by sampling constraints. The relaxed problem is a linear programming problem (LP). We then identify the number of samples needed for ``near-feasibility'' of the relaxed constraint set. Under some conditions on the valuation function, we show that value of the approximate LP is close to the optimal value. Simulation results show significant improvements of our proposed method over the Vickrey-Clarke-Groves (VCG) mechanism without rebates. In the special case of indivisible goods, the mechanisms in this paper fall back to those proposed by Moulin, by Guo and Conitzer, and by Gujar and Narahari, without any need for randomization. Extension of the proposed mechanisms to situations when the valuation functions are not known to the central planner are also discussed. Note to Practitioners-Our results will be useful in all resource allocation problems that involve gathering of information privately held by strategic users, where the utilities are any concave function of the allocations, and where the resource planner is not interested in maximizing revenue, but in efficient sharing of the resource. Such situations arise quite often in fair sharing of internet resources, fair sharing of funds across departments within the same parent organization, auctioning of public goods, etc. We study methods to achieve near budget balance by first collecting payments according to the celebrated VCG mechanism, and then returning as much of the collected money as rebates. Our focus on linear rebate functions allows for easy implementation. The resulting convex optimization problem is solved via relaxation to a randomized linear programming problem, for which several efficient solvers exist. This relaxation is enabled by constraint sampling. Keeping practitioners in mind, we identify the number of samples that assures a desired level of ``near-feasibility'' with the desired confidence level. Our methodology will occasionally require subsidy from outside the system. We however demonstrate via simulation that, if the mechanism is repeated several times over independent instances, then past surplus can support the subsidy requirements. We also extend our results to situations where the strategic users' utility functions are not known to the allocating entity, a common situation in the context of internet users and other problems.

Cerebroprotective activity of Wedelia calendulacea on global cerebral ischemia in rats

The present study was to investigate the effect of W. calendulacea on ischemia and reperfusion-induced cerebral injury. Cerebral ischemia was induced by occluding right and left common carotid arteries (global cerebral ischemia) for 30 min followed by reperfusion for 1 h and 4 h individually. Various biochemical alterations, produced subsequent to the application of bilateral carotid artery occlusion (BCAO) followed by reperfusion viz. increase in lipid peroxidation (LPO), hydrogen peroxide (H(2)O(2)), and decrease in reduced glutathione (GSH), catalase (CAT) and superoxide dismutase (SOD), level in the brain tissue, Western blot analysis (Cu-Zn-SOD and CAT) and assessment of cerebral infarct size were measured. All those enzymes are markedly reversed and restored to near normal level in the groups pre-treated with W. calendulacea (250 and 500 mg/kg given orally in single and double dose/day for 10 days) in dose-dependent way. The effect of W. calendulacea had increased significantly the protein expression of copper/zinc superoxide dismutase (Cu-Zn-SOD) and CAT in cerebral ischemia. W. claendulacea was markedly decrease cerebral infarct damages but results are not statistically significant. It can be concluded that W. calendulacea possesses a neuroprotective activity against cerebral ischemia in rat.

SURE-FAST BILATERAL FILTERS

Edge-preserving smoothing is widely used in image processing and bilateral filtering is one way to achieve it. Bilateral filter is a nonlinear combination of domain and range filters. Implementing the classical bilateral filter is computationally intensive, owing to the nonlinearity of the range filter. In the standard form, the domain and range filters are Gaussian functions and the performance depends on the choice of the filter parameters. Recently, a constant time implementation of the bilateral filter has been proposed based on raisedcosine approximation to the Gaussian to facilitate fast implementation of the bilateral filter. We address the problem of determining the optimal parameters for raised-cosine-based constant time implementation of the bilateral filter. To determine the optimal parameters, we propose the use of Stein's unbiased risk estimator (SURE). The fast bilateral filter accelerates the search for optimal parameters by faster optimization of the SURE cost. Experimental results show that the SURE-optimal raised-cosine-based bilateral filter has nearly the same performance as the SURE-optimal standard Gaussian bilateral filter and the Oracle mean squared error (MSE)-based optimal bilateral filter.

Optimal parameter selection for bilateral filters using Poisson unbiased risk estimate

Bilateral filters perform edge-preserving smoothing and are widely used for image denoising. The denoising performance is sensitive to the choice of the bilateral filter parameters. We propose an optimal parameter selection for bilateral filtering of images corrupted with Poisson noise. We employ the Poisson's Unbiased Risk Estimate (PURE), which is an unbiased estimate of the Mean Squared Error (MSE). It does not require a priori knowledge of the ground truth and is useful in practical scenarios where there is no access to the original image. Experimental results show that quality of denoising obtained with PURE-optimal bilateral filters is almost indistinguishable with that of the Oracle-MSE-optimal bilateral filters.

Bilateral smoothing of gradient vector field and application to image segmentation

Medical image segmentation finds application in computer-aided diagnosis, computer-guided surgery, measuring tissue volumes, locating tumors, and pathologies. One approach to segmentation is to use active contours or snakes. Active contours start from an initialization (often manually specified) and are guided by image-dependent forces to the object boundary. Snakes may also be guided by gradient vector fields associated with an image. The first main result in this direction is that of Xu and Prince, who proposed the notion of gradient vector flow (GVF), which is computed iteratively. We propose a new formalism to compute the vector flow based on the notion of bilateral filtering of the gradient field associated with the edge map - we refer to it as the bilateral vector flow (BVF). The range kernel definition that we employ is different from the one employed in the standard Gaussian bilateral filter. The advantage of the BVF formalism is that smooth gradient vector flow fields with enhanced edge information can be computed noniteratively. The quality of image segmentation turned out to be on par with that obtained using the GVF and in some cases better than the GVF.

A strategy-proof and budget-balanced mechanism for carbon footprint reduction by global companies

The problem addressed in this paper is concerned with an important issue faced by any green aware global company to keep its emissions within a prescribed cap. The specific problem is to allocate carbon reductions to its different divisions and supply chain partners in achieving a required target of reductions in its carbon reduction program. The problem becomes a challenging one since the divisions and supply chain partners, being autonomous, may exhibit strategic behavior. We use a standard mechanism design approach to solve this problem. While designing a mechanism for the emission reduction allocation problem, the key properties that need to be satisfied are dominant strategy incentive compatibility (DSIC) (also called strategy-proofness), strict budget balance (SBB), and allocative efficiency (AE). Mechanism design theory has shown that it is not possible to achieve the above three properties simultaneously. In the literature, a mechanism that satisfies DSIC and AE has recently been proposed in this context, keeping the budget imbalance minimal. Motivated by the observation that SBB is an important requirement, in this paper, we propose a mechanism that satisfies DSIC and SBB with slight compromise in allocative efficiency. Our experimentation with a stylized case study shows that the proposed mechanism performs satisfactorily and provides an attractive alternative mechanism for carbon footprint reduction by global companies.

BILATERAL EDGE DETECTORS

We propose to employ bilateral filters to solve the problem of edge detection. The proposed methodology presents an efficient and noise robust method for detecting edges. Classical bilateral filters smooth images without distorting edges. In this paper, we modify the bilateral filter to perform edge detection, which is the opposite of bilateral smoothing. The Gaussian domain kernel of the bilateral filter is replaced with an edge detection mask, and Gaussian range kernel is replaced with an inverted Gaussian kernel. The modified range kernel serves to emphasize dissimilar regions. The resulting approach effectively adapts the detection mask according as the pixel intensity differences. The results of the proposed algorithm are compared with those of standard edge detection masks. Comparisons of the bilateral edge detector with Canny edge detection algorithm, both after non-maximal suppression, are also provided. The results of our technique are observed to be better and noise-robust than those offered by methods employing masks alone, and are also comparable to the results from Canny edge detector, outperforming it in certain cases.

Balanced Excitatory and Inhibitory Synaptic Currents Promote Efficient Coding and Metabolic Efficiency

A balance between excitatory and inhibitory synaptic currents is thought to be important for several aspects of information processing in cortical neurons in vivo, including gain control, bandwidth and receptive field structure. These factors will affect the firing rate of cortical neurons and their reliability, with consequences for their information coding and energy consumption. Yet how balanced synaptic currents contribute to the coding efficiency and energy efficiency of cortical neurons remains unclear. We used single compartment computational models with stochastic voltage-gated ion channels to determine whether synaptic regimes that produce balanced excitatory and inhibitory currents have specific advantages over other input regimes. Specifically, we compared models with only excitatory synaptic inputs to those with equal excitatory and inhibitory conductances, and stronger inhibitory than excitatory conductances (i.e. approximately balanced synaptic currents). Using these models, we show that balanced synaptic currents evoke fewer spikes per second than excitatory inputs alone or equal excitatory and inhibitory conductances. However, spikes evoked by balanced synaptic inputs are more informative (bits/spike), so that spike trains evoked by all three regimes have similar information rates (bits/s). Consequently, because spikes dominate the energy consumption of our computational models, approximately balanced synaptic currents are also more energy efficient than other synaptic regimes. Thus, by producing fewer, more informative spikes approximately balanced synaptic currents in cortical neurons can promote both coding efficiency and energy efficiency.

Proper holomorphic mappings of balanced domains in C-n

We extend a well-known result, about the unit ball, by H. Alexander to a class of balanced domains in . Specifically: we prove that any proper holomorphic self-map of a certain type of balanced, finite-type domain in , is an automorphism. The main novelty of our proof is the use of a recent result of Opshtein on the behaviour of the iterates of holomorphic self-maps of a certain class of domains. We use Opshtein's theorem, together with the tools made available by finiteness of type, to deduce that the aforementioned map is unbranched. The monodromy theorem then delivers the result.

Directional bilateral filters for smoothing fluorescence microscopy images

Images obtained through fluorescence microscopy at low numerical aperture (NA) are noisy and have poor resolution. Images of specimens such as F-actin filaments obtained using confocal or widefield fluorescence microscopes contain directional information and it is important that an image smoothing or filtering technique preserve the directionality. F-actin filaments are widely studied in pathology because the abnormalities in actin dynamics play a key role in diagnosis of cancer, cardiac diseases, vascular diseases, myofibrillar myopathies, neurological disorders, etc. We develop the directional bilateral filter as a means of filtering out the noise in the image without significantly altering the directionality of the F-actin filaments. The bilateral filter is anisotropic to start with, but we add an additional degree of anisotropy by employing an oriented domain kernel for smoothing. The orientation is locally adapted using a structure tensor and the parameters of the bilateral filter are optimized for within the framework of statistical risk minimization. We show that the directional bilateral filter has better denoising performance than the traditional Gaussian bilateral filter and other denoising techniques such as SURE-LET, non-local means, and guided image filtering at various noise levels in terms of peak signal-to-noise ratio (PSNR). We also show quantitative improvements in low NA images of F-actin filaments. (C) 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.

Patch-based and multiresolution optimum bilateral filters for denoising images corrupted by Gaussian noise

We propose optimal bilateral filtering techniques for Gaussian noise suppression in images. To achieve maximum denoising performance via optimal filter parameter selection, we adopt Stein's unbiased risk estimate (SURE)-an unbiased estimate of the mean-squared error (MSE). Unlike MSE, SURE is independent of the ground truth and can be used in practical scenarios where the ground truth is unavailable. In our recent work, we derived SURE expressions in the context of the bilateral filter and proposed SURE-optimal bilateral filter (SOBF). We selected the optimal parameters of SOBF using the SURE criterion. To further improve the denoising performance of SOBF, we propose variants of SOBF, namely, SURE-optimal multiresolution bilateral filter (SMBF), which involves optimal bilateral filtering in a wavelet framework, and SURE-optimal patch-based bilateral filter (SPBF), where the bilateral filter parameters are optimized on small image patches. Using SURE guarantees automated parameter selection. The multiresolution and localized denoising in SMBF and SPBF, respectively, yield superior denoising performance when compared with the globally optimal SOBF. Experimental validations and comparisons show that the proposed denoisers perform on par with some state-of-the-art denoising techniques. (C) 2015 SPIE and IS&T

Joint Bilateral Filtering based Non-local Means Image Denoising

This paper proposes a denoising algorithm which performs non-local means bilateral filtering. As existing literature suggests, non-local means (NLM) is one of the widely used denoising techniques, but has a critical drawback of smoothing of edges. In order to improve this, we perform fast and efficient NLM using Approximate Nearest Neighbour Fields and improve the edge content in denoising by formulating a joint-bilateral filter. Using the proposed joint bilateral, we are able to denoise smooth regions using the NLM approach and efficient edge reconstruction is obtained from the bilateral filter. Furthermore, to avoid tedious parameter selection, we carry out a noise estimation before performing joint bilateral filtering. The proposed approach is observed to perform well on high noise images.

Stabilization of Collective Motion in Synchronized, Balanced and Splay Phase Arrangements on a Desired Circle

This paper proposes a design methodology to stabilize collective circular motion of a group of N-identical agents moving at unit speed around individual circles of different radii and different centers. The collective circular motion studied in this paper is characterized by the clockwise rotation of all agents around a common circle of desired radius as well as center, which is fixed. Our interest is to achieve those collective circular motions in which the phases of the agents are arranged either in synchronized, in balanced or in splay formation. In synchronized formation, the agents and their centroid move in a common direction while in balanced formation, the movement of the agents ensures a fixed location of the centroid. The splay state is a special case of balanced formation, in which the phases are separated by multiples of 2 pi/N. We derive the feedback controls and prove the asymptotic stability of the desired collective circular motion by using Lyapunov theory and the LaSalle's Invariance principle.

On Fast Bilateral Filtering Using Fourier Kernels

It was demonstrated in earlier work that, by approximating its range kernel using shiftable functions, the nonlinear bilateral filter can be computed using a series of fast convolutions. Previous approaches based on shiftable approximation have, however, been restricted to Gaussian range kernels. In this work, we propose a novel approximation that can be applied to any range kernel, provided it has a pointwise-convergent Fourier series. More specifically, we propose to approximate the Gaussian range kernel of the bilateral filter using a Fourier basis, where the coefficients of the basis are obtained by solving a series of least-squares problems. The coefficients can be efficiently computed using a recursive form of the QR decomposition. By controlling the cardinality of the Fourier basis, we can obtain a good tradeoff between the run-time and the filtering accuracy. In particular, we are able to guarantee subpixel accuracy for the overall filtering, which is not provided by the most existing methods for fast bilateral filtering. We present simulation results to demonstrate the speed and accuracy of the proposed algorithm.