Should Egalitarians Expropriate Philanthropists?

Wealthy individuals often voluntarily provide public goods that the poor also consume. Such philanthropy is perceived as legitimizing one’s wealth. Governments routinely exempt the rich from taxation on grounds of their charitable expenditure. We examine the normative logic of this exemption. We show that, rather than reducing it, philanthropy may aggravate absolute inequality in welfare achievement, while leaving the change in relative inequality ambiguous. Additionally, philanthropic preferences may increase the effectiveness of policies to redistribute income, instead of weakening them. Consequently, the general normative case for exempting the wealthy from expropriation, on grounds of their public goods contributions, appears dubious.community, public goods, inequality, distribution, philanthropy, egalitarianism

A Sparse Johnson--Lindenstrauss Transform

Dimension reduction is a key algorithmic tool with many applications including nearest-neighbor search, compressed sensing and linear algebra in the streaming model. In this work we obtain a {\em sparse} version of the fundamental tool in dimension reduction --- the Johnson--Lindenstrauss transform. Using hashing and local densification, we construct a sparse projection matrix with just $\tilde{O}(\frac{1}{\epsilon})$ non-zero entries per column. We also show a matching lower bound on the sparsity for a large class of projection matrices. Our bounds are somewhat surprising, given the known lower bounds of $\Omega(\frac{1}{\epsilon^2})$ both on the number of rows of any projection matrix and on the sparsity of projection matrices generated by natural constructions. Using this, we achieve an $\tilde{O}(\frac{1}{\epsilon})$ update time per non-zero element for a $(1\pm\epsilon)$-approximate projection, thereby substantially outperforming the $\tilde{O}(\frac{1}{\epsilon^2})$ update time required by prior approaches. A variant of our method offers the same guarantees for sparse vectors, yet its $\tilde{O}(d)$ worst case running time matches the best approach of Ailon and Liberty.Comment: 10 pages, conference version

On sampling nodes in a network

Random walk is an important tool in many graph mining applications including estimating graph parameters, sampling portions of the graph, and extracting dense communities. In this paper we consider the problem of sampling nodes from a large graph according to a prescribed distribution by using random walk as the basic primitive. Our goal is to obtain algorithms that make a small number of queries to the graph but output a node that is sampled according to the prescribed distribution. Focusing on the uniform distribution case, we study the query complexity of three algorithms and show a near-tight bound expressed in terms of the parameters of the graph such as average degree and the mixing time. Both theoretically and empirically, we show that some algorithms are preferable in practice than the others. We also extend our study to the problem of sampling nodes according to some polynomial function of their degrees; this has implications for designing efficient algorithms for applications such as triangle counting

On additive approximate submodularity

A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function evaluation might not be exact. In this paper we study how close such approximately submodular functions are to truly submodular functions. We show that an approximately submodular function defined on a ground set of n elements is pointwise-close to a submodular function. This result also provides an algorithmic tool that can be used to adapt existing submodular optimization algorithms to approximately submodular functions. To complement, we show an lower bound on the distance to submodularity. These results stand in contrast to the case of approximate modularity, where the distance to modularity is a constant, and approximate convexity, where the distance to convexity is logarithmic

Method Development and Validation for the Simultaneous Estimation of Ilaprazole and Domperidone in Capsule Dosage Form by UPLC

AIM: To develop and validate a new method for the simultaneous determination of Ilaprazole and Domperidone in capsule dosage form by Ultra Performance Liquid Chromatography [UPLC].OBJECTIVE: The literature review revealed that there are several methods reported for the estimation Ilaprazole and Domperidone alone or in combination with other drugs in their pharmaceutical dosage forms but none of the method available for the estimation of these drugs in the selected pharmaceutical dosage form by this intended method (UPLC). It is common to administer two or more drugs in a single formulation and it may be to reduce the number of medicaments to be taken at a time for better patient compliance. It is a challenging task for the analyst to develop a simple analytical method for simultaneous estimation of multiple drug formulations with desired degree of accuracy and precision. In the present work attempts have been made to develop Rapid UPLC method of analysis for a simultaneous estimation of selected two drugs in capsule dosage form. Hence on the basis of the literature survey, it was thought to develop a precise, accurate, simple, rapid and reliable method for estimation of Ilaprazole and Domperidone in capsules dosage form using the following technique of UPLC. SUMMARY: From the literature review it was found that no UPLC method was carried out for the simultaneous determination of Domperidone and Ilaprazole in capsule dosage form. Various trials were conducted by varying the wavelength, column, mobile phase, and flow rate and injection volume and the parameters for UPLC method for the determination of DPD and IPZcapsule dosage form were optimized. The scope of the present work is to expand the optimization of the chromatographic conditions and to develop new RP-UPLC method. A series of mobile phases were tried and among the various mobile phase comprising of mixture of Water : Methanol : ACN : Acetic Acid (30:20:50:0.3) (pH 5.0, adjusted with Triethylamine) was chosen as an ideal mobile phase, since it a good resolution and peak shapes with perfect optimization. The detection was carried out at 288 nm by using PDA detector. The flow rate was optimized at 0.4 ml/min. The Specificity of DPD and IPZ were shown in Chromatograms. There was no interference in this method and good separation between all peaks. It means no impurity was interfered and also reveals that commonly used excipients and additives present in the capsule dosage form were not interfering in the proposed methods. It was also found that the retention time of sample DPD and IPZ were identical corresponding to standard DPD and IPZ. The system suitability was found within the limits. The % RSD for DPD and IPZ were found 0.381% and 0.388% respectively. Theoretical plates, resolution and Asymmetry factor also found suitable.The linearity obtained from calibration graph shows that DPD and IPZ were linear in the range of (9.79-14.68) mg/ml and (3.20-4.81) mg/ml respectively. Correlation coefficient in the range of (9.79-14.68)mg/ml for DPD and (3.20-4.81) mg/ml for IPZ were calculated and found 0.999 and 0.999 respectively. In assay of marketed formulation the percentage purity of DPD and IPZ were found 102.53 % and 100.00% respectively which indicate that the method can be used to determine the percentage purity of Domperidone and Ilaprazole in capsule dosage form. Accuracy study was carried out by spiking method where calculated known amount of standard were added for different Percentage levels (100% - 130%). The average percentage recovery for DPD and IPZ was found to be 99.75% and 99.20% respectively. The average percentage RSD for DPD and IPZ was found to be 0.05% and 0.07% respectively. The limits of % recovery studies are in the range of 98-102% and the results found that recovery values of pure drugs from the solution were as well, which indicates that the method is accurate. Method Precision was assessed by repeatability tests (6 determinations at the level of 100% concentration). The % RSD for the area and assay of DPD found to be 0.01 and 0.02 respectively. The % RSD for the area and assay of IPZ was found to be 0.01 and 0.2 respectively. Hence method is precise for DPD and IPZ. The complete data regarding the precision was shown in table11. Based on standard deviation response (standard deviation of y intercept obtained from the calibration curve) and slope, the Limit of detection (LOD) and Limit of Quantitation (LOQ) were calculated for DPD and IPZ. The Limit of detection (LOD) of DPD and IPZ were found 0.006mg/ml and 0.001mg/ml respectively. And the Limit of Quantitation (LOQ) of DPD and IPZ were found 0.018mg/ml and 0.004mg/ml respectively. Robustness of the method was checked by small deliberate changes in the method parameters such as wavelength (±2nm) and flow rate (±0.2ml) but these changes did not affect the chromatographic parameter and the method results which indicate that the method is robust.CONCLUSION: Thus the proposed method was found to be simple, accurate, precise and rapid for simultaneous estimation of Domperidone and Ilaprazole in pharmaceutical capsule dosage form and could be used for routine analysis. All the parameters meet the criteria of ICH guidelines for method validation and found to be simple, sensitive, accurate and precise. It can therefore be concluded that the reported method is more economical and can find practical application for simultaneous analysis of the Domperidone (DPD) and Ilaprazole (IPZ) in their combined dosage forms both in research and quality control laboratorie

On Reconstructing a Hidden Permutation

The Mallows model is a classical model for generating noisy perturbations of a hidden permutation, where the magnitude of the perturbations is determined by a single parameter. In this work we consider the following reconstruction problem: given several perturbations of a hidden permutation that are generated according to the Mallows model, each with its own parameter, how to recover the hidden permutation? When the parameters are approximately known and satisfy certain conditions, we obtain a simple algorithm for reconstructing the hidden permutation; we also show that these conditions are nearly inevitable for reconstruction. We then provide an algorithm to estimate the parameters themselves. En route we obtain a precise characterization of the swapping probability in the Mallows model