Rejoinder on “Statistical reasoning with set-valued information: Ontic vs. epistemic views”

This note replies to comments made on our contribution to the Low Quality Data debate.     

An even earlier (1717) usage of the expression “golden section”

In a previous article in this journal, Roger Herz-Fischler has pointed out an early usage of the expression “golden section” from 1789. In this note an even earlier usage from 1717 is discussed.     

An Introduction to Influence Theory: Kinematics and Dynamics

Influence theory is a foundational theory of physics that is not based on traditional empirically defined concepts, such as positions in space and time, mass, energy, or momentum. Instead, the aim is to derive these concepts, and their empirically determined relationships, from a more primitive model. It is postulated that there exist things, which are call particles, that influence one another in a discrete and directed fashion resulting in a partially ordered set of influence events. The problem of consistent quantification of the influence events is considered. Observers are modeled as particle chains (observer chains) as if an observer were able to track a particle and quantify the influence events that the particle experiences. From these quantified influence events, consistent quantification of the universe of events based on the observer chains is studied. Herein, the kinematics and dynamics of particles from the perspective of influence theory are both reviewed and further developed.     

Computational modelling of multi-material energetic materials and systems

ABSTRACT

In this paper, we present a systematic roadmap for developing a robust and parallel multi-material reactive hydrodynamic solver that integrates historically stable algorithms with new and current modern methods to solve explosive system design problems. The Ghost Fluid Method and Riemann solvers were used to enforce appropriate interface boundary conditions. Improved performance in terms of computational work and convergence properties was achieved by modifying a local node sorting strategy that decouples ghost nodes, allowing us to set material boundary conditions via an explicit procedure, removing the need to solve a coupled system of equations numerically. The locality and explicit nature of the node sorting concept allows for greater levels of parallelism and lower computational cost when populating ghost nodes. Non-linear numerical issues endemic to the use of real Equations of State in hydro-codes were resolved by using more thermodynamically consistent forms allowing us to accurately resolve large density gradients associated with high energy detonation problems at material interfaces. Pre-computed volume tables were implemented adding to the robustness of the solver base.     

Micro-pinch formation and extreme ultraviolet emission of laser-induced discharge plasma

Extreme ultraviolet(EUV) source produced by laser-induced discharge plasma(LDP) is a potential technical means in inspection and metrology. A pulsed Nd:YAG laser is focused on a tin plate to produce an initial plasma thereby triggering a discharge between high-voltage electrodes in a vacuum system. The process of micro-pinch formation during the current rising is recorded by a time-resolved intensified charge couple device camera. The evolution of electron temperature and density of LDP are obtained by optical emission spectrometry. An extreme ultraviolet spectrometer is built up to investigate the EUV spectrum of Sn LDP at 13.5 nm. The laser and discharge parameters such as laser energy, voltage, gap distance,and anode shape can influence the EUV emission.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Crystal structure and DFT calculations of methanol {E-N′-(2-hydroxybenzlidene)benzohydrazido}dioxidomolybdenum (VI) complex

The crystal and molecular structure of methanol {E-N′-(2-hydroxybenzlidene)benzohydrazido}dioxidomolybdenum (VI) was determined by single crystal X-ray diffraction. B3LYP/DZP basis set theoretical calculations nicely reproduce the X-ray experimental geometry. The obtained results are discussed in connection with the electronic and structural properties of the compound.     

Extremal A-statistical limit points via ideals

In this paper, following the line of recent work of Savaş et al. [20] we apply the notion of ideals to A-statistical limit superior and inferior for a sequence of real numbers.     

QSAR Modeling of Large Heterogeneous Sets of Molecules

Abstract

In aquatic toxicology, QSAR models are generally designed for chemicals presenting the same mode of toxic action. Their proper use provides good simulation results. Problems arise when the mechanism of toxicity of a chemical is not clearly identified. Indeed, in that case, the inappropriate application of a specific QSAR model can lead to a dramatic error in the toxicity estimation. With the advent of powerful computers and easy access to them, and the introduction of soft modeling and artificial intelligence in SAR and QSAR, radically different models, designed from large non-congeneric sets of chemicals have been proposed. Some of these new QSAR models are reviewed and their originality, advantages, and limitations are stressed.