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6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995

作者： Ajtai, Miklos Aspnes, James Naor, Moni Rabani, Yuval Schulman, Leonard J. Waarts, Orli IBM Research Division Almaden Research Center United States Dept. of Computer Science Yale University United States Dept. of Applied Math and Computer Science Weizmann Institute Israel ICSI Berkeley Lab. for Computer Science MIT United States Department of Computer Science University of Toronto TorontoONM5S 1A4 Canada Computer Science Division U.C. Berkeley United States

ISBN: (纸本)0898713498

On-line machine scheduling has been studied extensively, but the fundamental issue of fairness in scheduling is still mostly open. In this paper we explore the issue in settings where there are long living processes which should be repeatedly scheduled for various tasks throughout the lifetime of a system. For any such instance we develop a notion of desired load of a process, which is a function of the tasks it participates in. The unfairness of a system is the maximum, taken over all processes, of the difference between the desired load and the actual load. An example of such a setting is the carpooi problem suggested by Fagin and Williams [17]. In this problem, a set of n people form a carpooi. On each day a subset of the people arrive and one of them is designated as the driver. A scheduling rule is required so that the driver will be determined in a 'fair' way. We investigate this problem under various assumptions on the input distribution. We also show that the carpooi problems can capture several other problems of fairness in scheduling.

关键词： Scheduling

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Private everlasting prediction 23

Private everlasting prediction

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Proceedings of the 37th International Conference on Neural Information Processing Systems

作者： Moni Naor Kobbi Nissim Uri Stemmer Chao Yan Department of Computer Science and Applied Math Weizmann Institute of Science Department of Computer Science Georgetown University Blavatnik School of Computer Science Tel Aviv University and Google Research

A private learner is trained on a sample of labeled points and generates a hypothesis that can be used for predicting the labels of newly sampled points while protecting the privacy of the training set [Kasiviswannathan et al., FOCS 2008]. Past research uncovered that private learners may need to exhibit significantly higher sample complexity than non-private learners as is the case of learning of one-dimensional threshold functions [Bun et al., FOCS 2015, Alon et al., STOC 2019].We explore prediction as an alternative to learning. A predictor answers a stream of classification queries instead of outputting a hypothesis. Earlier work has considered a private prediction model with a single classification query [Dwork and Feldman, COLT 2018]. We observe that when answering a stream of queries, a predictor must modify the hypothesis it uses over time, and in a manner that cannot rely solely on the training *** introduce private everlasting prediction taking into account the privacy of both the training set and the (adaptively chosen) queries made to the predictor. We then present a generic construction of private everlasting predictors in the PAC model. The sample complexity of the initial training sample in our construction is quadratic (up to polylog factors) in the VC dimension of the concept class. Our construction allows prediction for all concept classes with finite VC dimension, and in particular threshold functions over infinite domains, for which (traditional) private learning is known to be impossible.

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On the (In)security of the Fiat-Shamir paradigm

On the (In)security of the Fiat-Shamir paradigm

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Annual IEEE Symposium on Foundations of computer science

作者： S. Goldwasser Y.T. Kalai Department of Computer Science and Electrical Engineering Massachusetts Institute of Technology USA Department of Computer Science and Applied Math Weizmann Institute of Science Rehovot Israel

In 1986, Fiat and Shamir proposed a general method for transforming secure 3-round public-coin identification schemes into digital signature schemes. The idea of the transformation was to replace the random message of the verifier in the identification scheme, with the value of some deterministic hash function evaluated on various quantities in the protocol and on the message to be signed. The Fiat-Shamir methodology for producing digital signature schemes quickly gained popularity as it yields efficient and easy to implement digital signature schemes. The most important question however remained open: are the digital signatures produced by the Fiat-Shamir methodology secure? We answer this question negatively. We show that there exist secure 3-round public-coin identification schemes for which the Fiat-Shamir transformation yields insecure digital signature schemes for any hash function used by the transformation. This is in contrast to the work of Pointcheval and Stern which proved that the Fiat-Shamir methodology always produces digital signatures secure against chosen message attack in the "Random Oracle Model" - when the hash function is modeled by a random oracle. Among other things, we make new usage of Barak's technique for taking advantage of nonblack-box access to a program, this time in the context of digital signatures.

关键词： Digital signatures Protocols computer science Law Legal factors Cryptography Design methodology computer security Forgery Cost function

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Multiple translational containment: approximate and exact algorithms 95

Multiple translational containment: approximate and exact al...

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Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms

作者： Karen Daniels Victor J. Milenkovic Harvard University Division of Applied Sciences University of Miami Department of Math and Computer Science

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The δ- sensitivity and its application to stochastic optimal control of nonlinear diffusions.

The δ- sensitivity and its application to stochastic optima...

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American Control Conference

作者： Evangelos A. Theodorou Emo Todorov the Department of Computer Science and Engineering University of Washington Seattle. Departments of Computer Science and Engineering and Applied Math University of Washington

ISBN: (纸本)9781479901777

We provide optimal control laws by using tools from stochastic calculus of variations and the mathematical concept of δ-sensitivity. The analysis relies on logarithmic transformations of the value functions and the use of linearly solvable Partial Differential Equations(PDEs). We derive the corresponding optimal control as a function of the δ-sensitivity of the logarithmic transformation of the value function for the case of nonlinear diffusion processes affine in control and noise.

关键词： nonlinear diffusions PDEs value functions

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Calcination Temperature-Dependent Structural and Photoluminescence Properties of Hydroxyapatite Derived from Labeo Rohita Fish Scales

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Journal of The Institution of Engineers (India): Series D 2020年第2期101卷 223-232页

作者： Sinha, Arijit Pal, Anindya Santra, A. Murmu, S. Ghorai, U.K. Chowdhury, Amit Roy Banerjee, D. Dr. M.N. Dastur School of Materials Science Engineering Indian Institute of Engineering Science and Technology Botanic Garden Shibpur Howrah711103 India Ramakrishna Mission Vidyamandira Department of Industrial Chemistry & Applied Chemistry Swami Vivekananada Research Centre Belur Math Howrah711202 India Aerospace Engineering and Applied Mechanics Indian Institute of Engineering Science and Technology Botanic Garden Shibpur Howrah711103 India Faculty of Engineering and Computer Science Teerthanker Mahaveer University MoradabadUP244001 India

The nanocrystalline hydroxyapatite was synthesized from Labeo Rohita fish scales by calcination of raw scales at temperatures ranges from 400 to 1000 °C. The synthesized powders were characterized using, X-ray diffraction (XRD), thermogravimetric/differential thermal analyzer (TG–DTA), Fourier transform infrared spectroscopy, scanning and high-resolution transmission electron microscope and energy-dispersive X-ray analysis, respectively. Crystallite size, crystallinity and lattice parameters of HAp were evaluated from XRD, and it is shown that the average crystallite sizes were significantly enhanced with the calcination temperature attending its maximum value at ~ 40 nm. TG–DTA analysis predicts the thermal stability of the samples, and it has been observed that the thermal stability increases with the calcination temperature. Moreover, a detailed photoluminescence study of the as-synthesized samples has been carried out for the first time and an appropriate excitation energy gives rise to several distinct peaks in the emission spectra which has not been reported previously. © 2020, The Institution of Engineers (India).

关键词： Optical properties

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Stochastic Optimal Control for Nonlinear Markov Jump Diffusion Processes

Stochastic Optimal Control for Nonlinear Markov Jump Diffusi...

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American Control Conference

作者： Evangelos A. Theodorou Emmanuel Todorov Department of Computer Science and Engineering University of Washington Seattle USA Department of Computer Science and Engineering and Department of Applied Math University of Washington Seattle USA

ISBN: (纸本)9781457710957

We consider the problem finite horizon stochastic optimal control for nonlinear markov jump diffusion processes. In particular, by using stochastic calculus for markov jump diffusions processes and the logarithmic transformation of the value function we demonstrate the transformation of the corresponding Hamilton-Jacobi-Bellman (HJB) Partial Differential Equation (PDE) to the backward Chapman Kolmogorov PDE for jump diffusions. Furthermore we derive the Feynman-Kac lemma for nonlinear markov jump diffusions processes and apply it to the transformed HJB equation. Application of the Feynman-Kac lemma yields the solution of the transformed HJB equation. The path integral interpretation is derived. Finally, conclusions and future directions are discussed.

关键词： jump Markov stochastic optimal control logarithmic transformation diffusion Diffusion processes Lemma

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Adjoint-Free 4D-Var Methods Via Line Search Optimization For Non-Linear Data Assimilation

arXiv

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arXiv 2023年

作者： Nino-Ruiz, Elias D. Diaz-Rodriguez, Jairo Applied Math and Computer Science Laboratory Department of Computer Science Universidad del Norte Colombia Department of Mathematics and Statistics York University Canada

This paper proposes two practical implementations of Four-Dimensional Variational (4D-Var) Ensemble Kalman Filter (4D-EnKF) methods for non-linear data assimilation. Our formulations' main idea is to avoid the intrinsic need for adjoint models in the context of 4D-Var optimization and, even more, to handle non-linear observation operators during the assimilation of observations. The proposed methods work as follows: snapshots of an ensemble of model realizations are taken at observation times, these snapshots are employed to build control spaces onto which analysis increments can be estimated. Via the linearization of observation operators at observation times, a line-search based optimization method is proposed to estimate optimal analysis increments. The convergence of this method is theoretically proven as long as the dimension of control-spaces equals model one. In the first formulation, control spaces are given by full-rank square root approximations of background error covariance matrices via the Bickel and Levina precision matrix estimator. In this context, we propose an iterative Woodbury matrix formula to perform the optimization steps efficiently. The last formulation can be considered as an extension of the Maximum Likelihood Ensemble Filter to the 4D-Var context. This employs pseudo-square root approximations of prior error covariance matrices to build control spaces. Experimental tests are performed by using the Lorenz 96 model. The results reveal that, in terms of Root-Mean-Square-Error values, both methods can obtain reasonable estimates of posterior error modes in the 4D-Var optimization problem. Moreover, the accuracies of the proposed filter implementations can be improved as the ensemble sizes are increased. © 2023, CC BY.

关键词： Optimization

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A new trigonometric kernel function for support vector machine

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Iran Journal of computer science 2023年第2期6卷 137-145页

作者： Fathi Hafshejani, Sajad Moaberfard, Zahra Department of Applied Mathematics Shiraz University of Technology Modarres Boulevard Fars Shiraz 71557-13876 Iran Department of Math and Computer Science University of Lethbridge 4401 University Dr W Lethbridge T1K 3M4 AB Canada

In the last few years, various types of machine learning algorithms, such as support vector machine (SVM), support vector regression (SVR), and non-negative matrix factorization (NMF) have been introduced. The kernel approach is an effective method for increasing the classification accuracy of machine learning algorithms. This paper introduces a family of one-parameter kernel functions for improving the accuracy of SVM classification. The proposed kernel function consists of a trigonometric term and differs from all existing kernel functions. We show this function is a positive definite kernel function. Finally, we evaluate the SVM method based on the new trigonometric kernel, the Gaussian kernel, the polynomial kernel, and a convex combination of the new kernel function and the Gaussian kernel function on various types of datasets. Empirical results show that the SVM based on the new trigonometric kernel function and the mixed kernel function achieve the best classification accuracy. Moreover, some numerical results of performing the SVR based on the new trigonometric kernel function and the mixed kernel function are presented. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022.

关键词： Kernel method Support vector machine Trigonometric kernel function

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Private Everlasting Prediction

arXiv

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arXiv 2023年

作者： Naor, Moni Nissim, Kobbi Stemmer, Uri Yan, Chao Department of Computer Science and Applied Math Weizmann Institute of Science Blavatnik School of Computer Science Tel Aviv University Google Research Department of Computer Science Georgetown University United States

A private learner is trained on a sample of labeled points and generates a hypothesis that can be used for predicting the labels of newly sampled points while protecting the privacy of the training set [Kasiviswannathan et al., FOCS 2008]. Research uncovered that private learners may need to exhibit significantly higher sample complexity than non-private learners as is the case with, e.g., learning of one-dimensional threshold functions [Bun et al., FOCS 2015, Alon et al., STOC 2019]. We explore prediction as an alternative to learning. Instead of putting forward a hypothesis, a predictor answers a stream of classification queries. Earlier work has considered a private prediction model with just a single classification query [Dwork and Feldman, COLT 2018]. We observe that when answering a stream of queries, a predictor must modify the hypothesis it uses over time, and, furthermore, that it must use the queries for this modification, hence introducing potential privacy risks with respect to the queries themselves. We introduce private everlasting prediction taking into account the privacy of both the training set and the (adaptively chosen) queries made to the predictor. We then present a generic construction of private everlasting predictors in the PAC model. The sample complexity of the initial training sample in our construction is quadratic (up to polylog factors) in the VC dimension of the concept class. Our construction allows prediction for all concept classes with finite VC dimension, and in particular threshold functions with constant size initial training sample, even when considered over infinite domains, whereas it is known that the sample complexity of privately learning threshold functions must grow as a function of the domain size and hence is impossible for infinite domains. Copyright © 2023, The Authors. All rights reserved.

关键词： Forecasting

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