The Limiting Density of Unit Root Test Statistics: A Unifying Technique

In this note we introduce a simple principle to derive a constructive expression for the density of the limiting distribution, under the null hypothesis, of unit root statistics for an AR(1)-process in a variety of situations. We consider the case of unknown mean and reconsider the well-known situation where the mean is zero. For long-range dependent errors we indicate how the principle might apply again. We also show that in principle the method also works for a near unit root case. Weak convergence and subsequent Karhunen-Loeve expansion of the weak limit of the partial sum process of the errors plays an important role, along with the evaluation of a certain normal type integral with complex mean and variance. For independent and long range dependent errors this weak limit is ordinary and fractional Brownian motion respectively.
AMS 1991 subject classification. Primary 62M10; secondary 62E20.     

A smart process controller framework for Industry 4.0 settings

This paper presents a smart supervisory framework for a single process controller, designed for Industry 4.0 shop floors. This digitization of a full supervisory suite for a single process controller enables self-awareness, self-diagnosis, self-prognosis, and self-healing (by definition, these "self" elements are missing from other supervisory frameworks diagnosing numerous controllers in parallel). The proposed framework is aligned with the concept of a Cyber Physical System (CPS), since its implementation generates a rich cyber physical entity of the controlled process. This CPS entity can either be considered as the process digital twin, or can provide a solid basis for generating it. Finally, the framework includes the main characteristics of Industry 4.0, such as advanced use of Artificial Intelligence (AI) and big data analysis. The framework is based on four modules: (1) Control and Awareness module—performing both continuous process control and adjustments, as well as machine learning (ML) and statistical process control (SPC) for identifying abnormalities that require further diagnosis; (2) Process -diagnosis module—performing continual (recurrent) analysis of the process state and trends; (3) Prognosis and Healing module—performing prognosis and automated intervention via parameter changes, re-configurations, and automated maintenance; (4) External Interaction Platform—an interactive module for interfacing with experts, presenting them with the process analysis information and obtaining feedback from them as part of a learning process. Using an implementation showcase to illustrate the methodological framework’s applicability, we demonstrate its real-world potential. The proposed framework could serve as a guide for implementing smart process control and maintenance systems in Industry 4.0 shop floors. It could also provide a firm basis for comparison with future suggested frameworks. Future research directions could include pursuing improvements to the proposed process control framework and validating the framework by case studies of its implementation.

     

Topology‐based Smoothing of 2D Scalar Fields with C1‐Continuity

Data sets coming from simulations or sampling of real‐world phenomena often contain noise that hinders their processing and analysis. Automatic filtering and denoising can be challenging: when the nature of the noise is unknown, it is difficult to distinguish between noise and actual data features; in addition, the filtering process itself may introduce “artificial” features into the data set that were not originally present. In this paper, we propose a smoothing method for 2D scalar fields that gives the user explicit control over the data features. We define features as critical points of the given scalar function, and the topological structure they induce (i.e., the Morse‐Smale complex). Feature significance is rated according to topological persistence. Our method allows filtering out spurious features that arise due to noise by means of topological simplification, providing the user with a simple interface that defines the significance threshold, coupled with immediate visual feedback of the remaining data features. In contrast to previous work, our smoothing method guarantees a C¹‐continuous output scalar field with the exact specified features and topological structures.     

Gaming Prediction Markets: Equilibrium Strategies with a Market Maker

We study the equilibrium behavior of informed traders interacting with market scoring rule (MSR) market makers. One attractive feature of MSR is that it is myopically incentive compatible: it is optimal for traders to report their true beliefs about the likelihood of an event outcome provided that they ignore the impact of their reports on the profit they might garner from future trades. In this paper, we analyze non-myopic strategies and examine what information structures lead to truthful betting by traders. Specifically, we analyze the behavior of risk-neutral traders with incomplete information playing in a dynamic game. We consider finite-stage and infinite-stage game models. For each model, we study the logarithmic market scoring rule (LMSR) with two different information structures: conditionally independent signals and (unconditionally) independent signals. In the finite-stage model, when signals of traders are independent conditional on the state of the world, truthful betting is a Perfect Bayesian Equilibrium (PBE). Moreover, it is the unique Weak Perfect Bayesian Equilibrium (WPBE) of the game. In contrast, when signals of traders are unconditionally independent, truthful betting is not a WPBE. In the infinite-stage model with unconditionally independent signals, there does not exist an equilibrium in which all information is revealed in a finite amount of time. We propose a simple discounted market scoring rule that reduces the opportunity for bluffing strategies. We show that in any WPBE for the infinite-stage market with discounting, the market price converges to the fully-revealing price, and the rate of convergence can be bounded in terms of the discounting parameter. When signals are conditionally independent, truthful betting is the unique WPBE for the infinite-stage market with and without discounting.     

How Catalytic Order Drives the Complexification of Molecular Replication Networks

Catalytic replication networks have frequently served to study emergent phenomena in complex mixtures. In a series of recent research papers, we have analyzed the effects of the autocatalytic reaction order on various behaviors of these networks, and in particular, on their possibility to evolve and mimic functions often observed in cell biochemistry. In this review, we first discuss and derive properties of minimal self-replication, with an emphasis on catalytic order, reaction order, and properties directly affected by the order. We then expand our discussion to include catalytic networks, and review some of the implications of symmetry and order in these networks. Consequently, we look at open catalytic networks and their oscillations in replication product formation, again emphasizing the critical role played by the catalytic order. Finally, we describe an extension of the catalytic networks research using the quasispecies model, where we note the implications of the order on the phase transitions observed in these systems. Further implications of these results for emergence and evolution are discussed.     

The effect of surface treatments on the adhesion of electrochemically deposited hydroxyapatite coating to titanium and on its interaction with cells and bacteria

The effect of different mechanical and chemical pre-treatments on the adhesion strength of hydroxyapatite (HAp) coating on a commercially pure titanium (CP-Ti) substrate was studied by means of a standard tensile test followed by microscopic and chemical analysis to determine the locus of fracture. In addition, the effects of either these pre-treatments or post-treatment by low-energy electron irradiation, which allowed tuning the wettability of the surface, on both osteoblast progenitor attachment and S. aureus bacteria attachment were investigated. A dedicated program was developed for unambiguous identification and count of stained cells. A single-phase HAp coating was formed by electrodeposition. A series of surface pre-treatments consisted of grinding down to P1000, etching in HNO₃/HF solution, grit blast, soaking in NaOH and subsequent heat treatment provided the highest adhesion strength to the HAp coating. Osteoblast progenitors derived from rats may be attached preferentially to a hydrophilic surface (post-treatment to θ = 30°), while the bacteria seemed to be less attached to hydrophobic surfaces (post-treatment to θ = 105°). However, the results were not statistically different. The bacteria seemed to be less attached to the smoother, uncoated surfaces.     

Nephelometric Measurements by Use of a Spectrofluorometer. Part I: (A) Determination of Sulphate; and (B) Determination of Calcium

An approach to quantitative nephelometric measurements using a spectrofluorometer is presented. The measurements are performed with the aid of a monochromatic filter, which is transparent for the line 546 nm and by adjusting the monochromator for the same wavelength. The method was applied for the determination of micro amounts of: (1) sulphate as barium sulphate in colorless or colored aqueous solutions, in phosphoric acid, in the presence of large amounts of iron and in ores; is also suitable for determination of total inorganic sulfur after oxidation to sulphate and in organics after combustion; (2) calcium as calcium naphthalhydroxamate in aqueous and phosphoric acid solutions; and (3) calcium in the presence of large amounts of magnesium. The proposed technique has proved useful for quantitative nephelometric determinations in colored solutions. The high sensitivity also permits the use of micro samples.