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Proceedings of the 31st International Conference on Neural Information Processing Systems

作者： Emmanuel Abbe Sanjeev Kulkarni Eun Jee Lee Program in Applied and Computational Mathematics and The Department of Electrical Engineering Princeton University The Department of Electrical Engineering Princeton University Program in Applied and Computational Mathematics

ISBN: (纸本)9781510860964

This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin-Kasteleyn-Ginibre type inequalities, and are computed by message passing algorithms. Nonbacktracking walks have recently allowed for headways in community detection, and this paper shows that their use can also impact the influence computation. Further, we provide parameterized versions of the bounds that control the trade-off between the efficiency and the accuracy. Finally, the tightness of the bounds is illustrated with simulations on various network models.

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Simultaneous confidence bands for Abbott-adjusted quantal response models in benchmark analysis

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Statistical Methodology 2008年第3期5卷 209-219页

作者： Buckley, Brooke E. Piegorsch, Walter W. Department of Mathematics Northern Kentucky University Highland Heights KY 41099 United States Interdisciplinary Program in Statistics BIO5 Institute University of Arizona Tucson AZ 85721 United States

We study the use of a Scheffé-style simultaneous confidence band as applied to low-dose risk estimation with quantal response data. We consider two formulations for the dose-response risk function, an Abbott-adjusted Weibull model and an Abbott-adjusted log-logistic model. Using the simultaneous construction, we derive methods for estimating upper confidence limits on predicted extra risk and, by inverting the upper bands on risk, lower bounds on the benchmark dose, or BMD, at a specific level of 'benchmark risk'. Monte Carlo evaluations explore the operating characteristics of the simultaneous limits. © 2007 Elsevier B.V. All rights reserved.

关键词： Benchmark dose Carcinogenic risk assessment Log-logistic dose-response model Quantitative risk analysis Weibull dose-response model

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Generalized nonbacktracking bounds on the influence in independent cascade models

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2020年第1期21卷 1112-1147页

作者： Emmanuel Abbe Sanjeev Kulkarni Eun Jee Lee Program in Applied and Computational Mathematics and Department of Electrical Engineering Princeton University Princeton NJ Department of Electrical Engineering Princeton University Princeton NJ Program in Applied and Computational Mathematics Princeton University Princeton NJ

This paper develops deterministic upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit r-nonbacktracking walks and Fortuin--Kasteleyn--Ginibre (FKG) type inequalities, and are computed by message passing algorithms. Further, we provide parameterized versions of the bounds that control the trade-off between efficiency and accuracy. Finally, the tightness of the bounds is illustrated on various network models.

关键词： influence estimation nonbacktracking walk message passing social networks independent cascade model

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Classification of Nonlinear Confusion Component Using Hybrid Multi-Criteria Decision Making

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Intelligent Automation & Soft Computing 2023年第5期36卷 1451-1463页

作者： Nabilah Abughazalah Iqra Ishaque Majid Khan Ammar S.Alanazi Iqtadar Hussain Department of Mathematical Sciences College of SciencePrincess Nourah bint Abdulrahman UniversityP.O.Box 84428Riyadh 11671Saudi Arabia Department of Applied Mathematics and Statistics Institute of Space TechnologyIslamabadPakistan Department of Mathematics King Abdulaziz UniversityFaculty of ScienceJeddahSaudi Arabia Mathematics Program Department of MathematicsStatistics and PhysicsCollege of Arts and SciencesQatar University2713DohaQatar Statistical Consulting Unit College of Arts and ScienceQatar UniversityDohaQatar

In today’s digital world,the most inevitable challenge is the protection of digital *** to the weak conﬁdentiality preserving techniques,the existing world is facing several digital information *** make our digital data indecipherable to the unauthorized person,a technique forﬁnding a crypto-graphically strong Substitution box(S-box)have *** S-box with sound cryptographic assets such as nonlinearity(NL),strict avalanche criterion(SAC),bit independence criteria(BIC),bit independence criteria of nonlinearity(BIC-NL),Bit independence criteria of Strict avalanche criteria(BIC-SAC),and Input/output XOR is considered as the robust *** Decision-Making Trial and Evaluation Laboratory(DEMATEL)approach of multi-criteria decision making(MCDM)is proposed forﬁnding the interrelation among cryptographic properties.A combination of two MCDM methods namely Entropy and multi-objective optimization based on ratio analysis(MOORA)is applied for the best S-box selection.A robust substitution box is selected for secure communications in cryptography by using the combination of DEMETAL selection criteria,entro-py weight assigning,and MOORA ranking *** combination of these three methods provides a fast selection procedure for the secure confusion *** offered selection method can also be utilized for the choice of the best cryptosystem with highly secure properties and resistive against all possible linear and differential attacks in the cryptanalysis.

关键词： DEMATEL MCDM MOORA nonlinearity S-box

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Prediction of methylene blue dye sorption to sulfonated date palm kernel biochar using statistical regression and machine learning methods and DFT studies

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Journal of Molecular Liquids 2025年 429卷

作者： Aigbe, Uyiosa Osagie Ukhurebor, Kingsley Eghonghon Onyancha, Robert Birundu Osibote, Adelaja Otolorin Hassaan, Mohamed A. ElKatory, Marwa R. Nemr, Ahmed El Center for Space Research North-West University Private Bag X6001 Potchefstroom2531 South Africa National Institute of Theoretical and Computational Science Johannesburg2000 South Africa School of Chemistry & Physics University of KwaZulu-Natal Pietermaritzburg Campus Private Bag X01 Scottsville3209 South Africa Department of Physics Faculty of Science Edo State University Uzairue Edo State Nigeria School of Physics and Earth Science Faculty of Applied Science and Technology Technical University of Kenya Nairobi Kenya College of Graduate Studies School of Interdisciplinary Research and Graduate Studies Muckleneuk Campus University of South Africa Pretoria0003 South Africa Department of Mathematics and Physics Cape Peninsula University of Technology Cape Town South Africa Kayet Bey Alexandria Elanfoushy Egypt Advanced Technology and New Materials Research Institute SRTA-City New Borg El-Arab City 21934 Alexandria Egypt

In this study, methylene blue (MB) dye adsorption to synthesised sulfonated date palm kernel biochar (SDPKB) was predicted and optimized using statistical-based regression approach (response surface methodology (RSM), machine-learning algorithms (artificial-neural-network (ANN), and adaptive-neuro-fuzzy-inference-system (ANFIS) models), and quantum chemistry calculations performed using density function theory (DFT) to link the electrical properties of the MB dye with the experimental findings. The percentage (%) of MB dye removed using SDPKB was found to be proportional to the biosorbent dosage and interaction time and inversely proportional to the solution pH and initial concentrations based on different used models results. It was observed that these models were accurate and comparable for the prediction of the removal of MB with coefficient of regression (R2) values of 0.9174, 0.9742, and 0.9999, mean square error (MSE) values of 181.71, 94.50, and 0.00000049, and root MSE (RMSE) values of 13.48, 9.72, and 0.0007 for the RSM, ANN, and ANFIS, respectively. The ANFIS model was found to be more effective in the prediction of MB sorption to SDPKB than the other models (ANFIS > ANN > RSM), and it was highly applicable in the sorption process. This study has revealed that the SDPKB can serve as a better biosorbent for MB adsorption. Therefore, this study will serve as a first reference point data that will be of great assistance in industrial effluent management as well as decision-making on the adoption of statistical and machine learning models for adsorption study. © 2025 Elsevier B.V.

关键词： Adversarial machine learning

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The quadratic-quadratic regulator problem: Approximating feedback controls for quadratic-in-state nonlinear systems

arXiv

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arXiv 2019年

作者： Borggaard, Jeff Zietsman, Lizette Interdisciplinary Center for Applied Mathematics Department of Mathematics Virginia Tech BlacksburgVA24061 United States

Feedback control problems involving autonomous quadratic systems are prevalent, yet there are only a limited number of software tools available for approximating their solution due to the complexity of the problem. This paper represents a step forward in the special case where both the state equation and the control costs are quadratic. As it represents the natural extension of the linear-quadratic regulator (LQR) problem, we describe this setting as the quadratic-quadratic regulator (QQR) problem. This is significantly more challenging and holds the LQR as special case that must be solved along the way. We describe an algorithm that exploits the structure of the QQR problem that arises when implementing Al’Brekht’s method. This approach is amenable to feedback laws with low degree polynomials but have a relatively modest model dimension that could be achieved by modern model reduction methods. This problem has an elegant formulation and a solution that introduces several linear systems where the structure suggests modern tensor-based linear solvers. We demonstrate this algorithm on a suite of random test problems then apply it to a distributed parameter control problem that fits the QQR framework. Comparisons to linear feedback control laws show a modest benefit using the QQR formulation.49Mxx, 49L99, 65Y20 Copyright © 2019, The Authors. All rights reserved.

关键词： Feedback control

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The Picone identity: A device to get optimal uniqueness results and global dynamics in Population DynamicsI

arXiv

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arXiv 2019年

作者： Fernández-Rincón, Sergio López-Gómez, Julián Institute of Interdisciplinary Mathematics Department of Mathematical Analysis and Applied Mathematics Complutense University Madrid28040 Spain

This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone *** Codes 35M12, 35J61, 35J57 (Primary) 35K57, 35B09, 35Q92 (Secondary) Copyright © 2019, The Authors. All rights reserved.

关键词： Dynamics

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Fuzzy cyclic modeling of a periodically perturbed pendulum

Fuzzy cyclic modeling of a periodically perturbed pendulum

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Conference of the North American Fuzzy Information Processing Society - NAFIPS

作者： E. Applebaum Graduate Program in Applied Mathematics Department of Mathematics University of Colorado Denver CO USA

This paper extends a product-space clustering method, the bisection and homogeneity algorithm, to the cyclic modeling of a periodically perturbed pendulum. The algorithm creates a structural decomposition of the state space for each drive cycle of the vertical support. Smooth trajectory approximations of chaotic behavior are the result of combining multiple SAM/COG systems with a one-step Euler's method. Experimental results suggest that a finer phase partitioning is necessary and sufficient for the fuzzy model to preserve the periodicity of the vertical drive.

关键词： Chaos Cranes State-space methods Marine vehicles Fuzzy systems mathematics Clustering algorithms Round robin Inference algorithms programmable control

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Randomized near neighbor graphs, giant components and applications in data science

arXiv

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arXiv 2017年

作者： Linderman, George C. Mishne, Gal Kluger, Yuval Steinerberger, Stefan Department of Pathology Program in Applied Mathematics Yale University

If we pick n random points uniformly in [0;1]dand connect each point to its k-nearest neighbors, then it is well known that there exists a giant connected component with high probability. We prove that in [0;1]dit suffices to connect every point to cd,1log log n points chosen randomly among its cd,2log n-nearest neighbors to ensure a giant component of size n-o(n) with high probability. This construction yields a much sparser random graph with ∼ n log log n instead of ∼ n log n edges that has comparable connectivity properties. This result has nontrivial implications for problems in data science where an affinity matrix is constructed: instead of picking the k-nearest neighbors, one can often pick′ k random points out of the k-nearest neighbors without sacrificing efficiency. This can massively simplify and accelerate computation, we illustrate this with several numerical examples. Copyright © 2017, The Authors. All rights reserved.

关键词： k-nearest neighbors

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State estimation in hybrid systems with a bounded number of mode transitions

State estimation in hybrid systems with a bounded number of ...

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作者： Sigalov, Daniel Oshman, Yaakov Technion Israel Institute of Technology Program for Applied Mathematics Haifa 32000 Israel Technion Israel Institute of Technology Department of Aerospace Engineering Haifa 32000 Israel

ISBN: (纸本)9780982443811

We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode switches. The system is assumed to follow either a nominal or an anomalous model, where the nominal model may stand for, e.g., the non-maneuvering motion regime of a target or the fault-free operation mode of a sensor, and the anomalous model may stand for, e.g., the abrupt evasive maneuvers of a target or the faulty operation of a sensor. As is well known, the optimal algorithm requires implementation of an exponentially growing number of primitive Kalman filters. On the other hand, the system's switching dynamics is not Markov because of the a priori bounded number of model switches, thus ruling out the use of popular estimation schemes such as the interacting multiple model (IMM) and generalized pseudo-Bayesian (GPB) filters. We derive an efficient scheme that uses a number of primitive Kalman filters that is linear in the number of possible maneuvers. The scheme resembles the IMM algorithm in that it uses interaction between some of the primitive filters before every estimation cycle, thus reducing the number of such filters. The algorithm's performance is evaluated via a simulation study, and shown to outperform the state-of-the-art IMM filter in a typical example.

关键词： Hybrid systems

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