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We describe the shrinking neighborhood approach of Robust Statistics, which applies to general smoothly parametrized models, especially, exponential families. Equal generality is achieved by object oriented implementation of the optimally…

Methodology · Statistics 2010-08-04 Matthias Kohl , Peter Ruckdeschel , Helmut Rieder

In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…

Logic in Computer Science · Computer Science 2023-06-22 Arnon Avron , Liron Cohen

The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…

Logic in Computer Science · Computer Science 2023-06-23 Eben Blaisdell

The paper proposes some robust estimators of the finite population mean. Such estimators are particularly suitable in the presence of some outlying observations. Included as special cases of our general result are robust versions of the…

Statistics Theory · Mathematics 2008-12-18 Malay Ghosh

Many interesting questions in arithmetic dynamics revolve, in one way or another, around the (local and/or global) reducibility behavior of iterates of a polynomial. We show that for very general families of integer polynomials $f$ (and,…

Number Theory · Mathematics 2025-10-16 Joachim König

Randomized block factorial experiments are widely used in industrial engineering, clinical trials, and social science. Researchers often use a linear model and analysis of covariance to analyze experimental results; however, limited studies…

Methodology · Statistics 2022-08-04 Hanzhong Liu , Jiyang Ren , Yuehan Yang

In generic realizability for set theories, realizers treat unbounded quantifiers generically. To this form of realizability, we add another layer of extensionality by requiring that realizers ought to act extensionally on realizers, giving…

Logic · Mathematics 2020-12-22 Emanuele Frittaion , Michael Rathjen

Assuming the obvious definitions (see paper) we show the a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to…

Logic · Mathematics 2017-01-31 Peter Cholak , Charlie McCoy

In what follows, essentially two things will be accomplished: Firstly, it will be proven that a version of the Arzel\`a--Ascoli theorem and the Fr\'echet--Kolmogorov theorem are equivalent to the axiom of countable choice for subsets of…

Logic · Mathematics 2018-03-23 Adrian Fellhauer

There are three types of results in this paper. The first, extending a representation theorem on a conformal mapping that omits two values of equal modulus. This was due to Brickman and Wilken. They constructed a representation as a convex…

Complex Variables · Mathematics 2019-01-30 Ronen Peretz

In this note we show that if a continuous-time, nonlinear, time-invariant, finite-dimensional system evolves on a compact subset of Rn and if the Jacobian of the vector field is Hurwitz at each point of the compact set, then there is a…

Optimization and Control · Mathematics 2016-09-06 Ravi Mazumdar , Christopher Nielsen , Arpan Mukhopadhyay

For each $\alpha \in (0, 1)$, we construct a bounded monotone deterministic sequence $(c_k)_{k \geq 0}$ of real numbers so that the number of real roots of the random polynomial $f_n(z) = \sum_{k=0}^n c_k \varepsilon_k z^k$ is $n^{\alpha +…

Probability · Mathematics 2024-04-08 Marcus Michelen , Sean O'Rourke

Much like admissibility is the key concept underlying preferred semantics, strong admissibility is the key concept underlying grounded semantics, as membership of a strongly admissible set is sufficient to show membership of the grounded…

Artificial Intelligence · Computer Science 2022-04-08 Martin Caminada , Sri Harikrishnan

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

Optimization and Control · Mathematics 2015-08-21 Bram L. Gorissen

Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of G\"odel logic. The calculi are used to establish…

Logic · Mathematics 2015-07-01 George Metcalfe , Nicola Olivetti

The main aim of this work is to show, in the absence of the Axiom of Choice, fundamental results on $\mathbf{E}$-compact extensions of $\mathbf{E}$-completely regular spaces, in particular, on Hewitt realcompactifications and Banaschewski…

General Topology · Mathematics 2023-10-16 AliReza Olfati , Eliza Wajch

In this paper we calibrate the strength of the soundness of a Kripke-Platek set theory with the axioms of Infinity and \Pi_{1}-Collection with the assumption that`there exists an uncountable regular ordinal' in terms of the existence of…

Logic · Mathematics 2018-01-31 Toshiyasu Arai

Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…

Systems and Control · Electrical Eng. & Systems 2025-08-11 Akash Harapanahalli , Samuel Coogan

We present a novel treatment of set theory in a four-valued paraconsistent and paracomplete logic, i.e., a logic in which propositions can be both true and false, and neither true nor false. Our approach is a significant departure from…

Logic · Mathematics 2023-10-18 Yurii Khomskii , Hrafn Valtýr Oddsson

We treat uncertain linear programming problems by utilizing the notion of weighted analytic centers and notions from the area of multi-criteria decision making. After introducing our approach, we develop interactive cutting-plane algorithms…

Optimization and Control · Mathematics 2018-05-21 Mehdi Karimi , Somayeh Moazeni , Levent Tuncel