Non-standard Setting Research Articles

Adaptive and efficient isotonic estimation in Wicksell's problem

We consider nonparametric estimation in Wicksell's problem, which has applications in astronomy for estimating the distribution of star positions in a galaxy and in material sciences for determining a material's 3D microstructure from 2D cross sections. We focus on the isotonised version of the plug-in estimator (IIE) for the cdf F of the spheres' squared radii. This estimator is fully automatic, requiring no tuning parameters, and we show it is adaptive to local smoothness properties of the distribution function F to be estimated. We also prove a local asymptotic minimax lower bound in this non-standard setting, with log ⁡ n / n -asymptotics and where the functional F to be estimated is not regular. Combined, our results prove that the isotonic estimator (IIE) is an adaptive, easy-to-compute, and efficient estimator.

On generalized definitions of ultradifferentiable classes

We show that the ultradifferentiable-like classes of smooth functions introduced and studied by S. Pilipović, N. Teofanov and F. Tomić are special cases of the general framework of spaces of ultradifferentiable functions defined in terms of weight matrices in the sense of A. Rainer and the third author. We study classes “beyond geometric growth factors” defined in terms of a weight sequence and an exponent sequence, prove that these new types admit a weight matrix representation and transfer known results from the matrix-type to such a non-standard ultradifferentiable setting.

Vector-valued nonuniform multiresolution analysis associated with linear canonical transform domain

A generalization of Mallat?s classical multiresolution analysis, based on the theory of spectral pairs, was considered in two articles by Gabardo and Nashed. In this setting, the associated translation set is no longer a discrete subgroup of R but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we continue the study based on this nonstandard setting and introduce vector-valued nonuniform multiresolution analysis associated with linear canonical transform (LCT-VNUMRA) where the associated subspace V?0 of the function space L2 (R,CM) has an orthonormal basis of the form {?(x ? ?)e? ??A B (t2??2)} ??? where ? = {0, r/N} + 2Z,N ? 1 is an integer and r is an odd integer such that r and N are relatively prime. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of vector-valued nonuniform multiresolution analysis starting from a vector refinement mask with appropriate conditions

Generalized inequalities for nonuniform wavelet frames in linear canonical transform domain

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in L2(R) was considered by Gabardo and Nashed. In this setting, the associated translation set is a spectrum ? which is not necessarily a group nor a uniform discrete set, given ? = {0, r/N} + 2Z, where N ? 1 (an integer) and r is an odd integer with 1 ? r ? 2N?1 such that r and N are relatively prime and Z is the set of all integers. In this article, we continue this study based on non-standard setting and obtain some inequalities for the nonuniform wavelet system {f?j,?(x) = (2N)j/2f((2N)jx??)e???A/B (t2??2), j ? Z, ? ? ?}to be a frame associated with linear canonical transform in L2(R). We use the concept of linear canonical transform so that our results generalise and sharpen some well-known wavelet inequalities.

Statistical process control for the analysis of quality control in urodynamics: A potential new approach for quality review of urodynamics.

To analyze quality control in urodynamic studies, using a proportion control chart (p-chart) for statistical process control. This single-center study was conducted at the Urodynamic Center of West China Hospital, Sichuan University. We randomly selected 15 samples from each month in 2020, and 180 urodynamic traces were finally enrolled. We used the p-chart of statistical process control for analysis. We calculated the proportion of the incidence of a selected set of artefacts in the monthly urodynamic study process, including non-standard zero setting, no cough test, incomplete records of all measurements by urodynamicists, catheter displacement, and baseline drift. Through the specific calculation formula of statistical process control, we obtained the values of the center line, lower control limit, and upper control limit. All data points of each artefact were within zone A. However, one outlier was found in the p-chart of all artefacts in October, which might have been caused by inexperienced operators. Statistical process control may play an important role in the process control of urodynamic studies and guide us in identifying the cause of poor quality in process management.

Fractional vector-valued nonuniform MRA and associated wavelet packets on $$L^2\big ({\mathbb {R}},{\mathbb {C}}^M\big )$$

A generalization of Mallat’s classical multiresolution analysis, based on the theory of spectral pairs, was considered in two articles by Gabardo and Nashed. In this setting, the associated translation set is no longer a discrete subgroup of \({\mathbb {R}}\) but a spectrum associated with a certain one-dimensional spectral pair and the associated dilation is an even positive integer related to the given spectral pair. In this paper, we continue the study based on this nonstandard setting and introduce fractional vector-valued nonuniform multiresolution analysis (Fr-VNUMRA) where the associated subspace of the function space has an orthonormal basis. We establish a necessary and sufficient condition for the existence of associated wavelets and derive an algorithm for the construction of fractional vector-valued nonuniform multiresolution analysis starting from a vector refinement mask with appropriate conditions. Nevertheless, to extend the scope of the present study, we worked to construct the associated wavelet packets for such an MRA and investigate their properties by means of fractional Fourier transform.

Regularity of nonlinear generalized functions: A counterexample in the nonstandard setting

Regularity theory in generalized function algebras of Colombeau type is largely based on the notion of G∞-regularity, which reduces to C∞-regularity when restricted to Schwartz distributions. Surprisingly, in the nonstandard version of the Colombeau algebras, this basic property of G∞-regularity does not hold.

Firm dynamics and employee performance management in duopoly markets

The effects of the Peter Principle (PP) on a hierarchical firm have been extensively studied, but existing firm models fail to capture real-world firm dynamics such as employee motivation and CEO characteristics. We thus extend an existing firm model to introduce the notion of employee motivation and a CEO agent with parameters for leadership and managerial qualities, and incorporate the vitality curve. Through our experiments, we show that a firm’s performance depends on the characteristics of the CEO agent, as observed in reality. We run simulations for a firm model under two hypotheses: when a firm is subject to PP and when it is not. We find that a non-standard vitality curve setting leads to an efficiency gain over the standard one. We also study the effects of PP on firms competing in Stackelberg and Cournot games. We find that there exists a possibility for a follower firm to overtake a leader firm in a Stackelberg game when the leader is subject to PP. In a Cournot game, we find that a firm that is not subject to PP produces more quantity and makes more profit compared to a firm that is.

Kernowite, Cu2Fe(AsO4)(OH)4⋅4H2O, the Fe3+-analogue of liroconite from Cornwall, UK

Abstract The occurrence, chemical composition and structural characterisation of the new mineral kernowite, ideally Cu2Fe(AsO4)(OH)4⋅4H2O, the Fe3+-analogue of liroconite, Cu2Al(AsO4)(OH)4⋅4H2O, are described. Kernowite (IMA2020-053) occurs on specimens probably sourced from the Wheal Gorland mine, St Day, Cornwall, UK, in the cavities of a quartz-gossan rich in undifferentiated micro-crystalline grey sulfides and poorly crystalline arsenic phases including both pharmacosiderite and olivenite-group minerals. The average composition of kernowite determined from several holotype fragments by electron microprobe analysis is Cu1.88(Fe0.79Al0.09)Σ0.88(As1.12O4)(OH)4⋅3.65H2O. The structure of kernowite has been determined in monoclinic space group I2/a (a non-standard setting of C2/c) by single-crystal X-ray diffraction (SCXRD) to R1 = 0.025, wR2 = 0.051 and Goodness-of-fit = 1.112. Unit-cell parameters from SCXRD are a = 12.9243(4) Å, b = 7.5401(3) Å, c = 10.0271(3) Å, β = 91.267(3)°, V = 976.91(6) Å3 and Z = 4. The chemical formula of this crystal indicated by SCXRD from refined site-scattering is Cu2(Fe3+0.84(1)Al0.16)AsO4(OH)4⋅4H2O. The network of hydrogen bonding has been determined and is similar to that reported for liroconite from Wheal Gorland by Plumhoff et al. (2020).

Non-Invasive Ventilation in a Non-Standard Setting – Is it Safe to Ventilate Outside the ICU?

Abstract Non-invasive ventilation (NIV) is considered a fundamental method in treating patients with various disorders, requiring respiratory support. Often the lack of beds in the intensive care unit (ICU) and the concomitant medical conditions, which refer patients as unsuitable for aggressive treatment in the ICU, highlight the need of NIV application in general non-monitored wards and unusual settings – most commonly emergency departments, high-dependency units, pulmonary wards, and even ambulances. Recent studies suggest faster improvement of all physiological variables, reduced intubation rates, postoperative pulmonary complications and hospital mortality with better outcome and quality of life by early well-monitored ward-based NIV compared to standard medical therapy in patients with exacerbation of a chronic obstructive pulmonary disease, after a surgical procedure or acute hypoxemic respiratory failure in hematologic malignancies. NIV is a ceiling of treatment and a comfort measure in many patients with do-not-intubate orders due to terminal illnesses. NIV is beneficial only by proper administration with appropriate monitoring and screening for early NIV failure. Successful NIV application in a ward requires a well-equipped area and adequately trained multidisciplinary team. It could be initiated not only by attending physicians, respiratory technicians, and nurses but also by medical emergency teams. Ward-based NIV is supposed to be more cost-effective than NIV in the ICU, but further investigation is required to establish the safety and efficacy in hospital wards with a low nurse to patient ratio.

EFFICIENT ESTIMATION OF INTEGRATED VOLATILITY FUNCTIONALS UNDER GENERAL VOLATILITY DYNAMICS

We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.

Evolution of Rotations of a Spheroid with a Cavity Filled with a Fluid of High Viscosity

In a non-standard setting, motion with respect to the center of mass of a spheroid with a cavity filled with a fluid of high viscosity is considered. The moment of forces acting on the body from the side of a viscous fluid in the cavity is determined by the technique developed in the works of F.L. Chernousko. As a result of original asymptotic and numerical calculations, solutions are obtained that describe the evolution of body motion over an infinite time interval with an asymptotically small error.

Dense enough non-standard reals

Non-standard analysis is a branch of Mathematics introduced by Abraham Robinson in 1966[1]. In 1977, Edward Nelson gave an axiomatic approach to Non-standard analysis [2]. One of the main features of these approaches is the reduction of infiniteness to finiteness. In this paper we have come up with functions in the nonstandard setting, especially in the extended Real number system consisting of infinitesimals and infinite numbers, that are analogous with functions in classical analysis and show that non-standard numbers are dense enough to facilitate continuity of functions

Challenges for a second decade of ubimus research: knowledge transfer in ubimus activities


 
 
 This is the second part of a discussion on the challenges of a second decade of ubimus research. I discuss the issues involved in supporting knowledge transfer in musical activities. I lay out and exemplify the concept of metaphor for creative action. I summarize the results of three studies employing the time tagging metaphor, configuring an effective strategy for supporting everyday musical creativity. Then I report results of a study employing the stripe meta- phor – an extension of time tagging devised for usage of a large number of resources. Twelve subjects, encompassing musicians and casual participants, realized improvisatory sessions in a non-standard setting – an audio and musical equipment store. The results indicated a promising new avenue of research targeting lay-musician interaction. The results also raised new questions regarding the strategies adopted for knowledge transfer support. The last section of the paper places these results within the context of the ongoing ubimus efforts, highlighting four issues that have emerged as viable research avenues: everyday musical creativity, lay-musician interaction, design for sustainability and design for distributed creativity. 
 
 

STRICT FINITISM, FEASIBILITY, AND THE SORITES

AbstractThis article bears on four topics: observational predicates and phenomenal properties, vagueness, strict finitism as a philosophy of mathematics, and the analysis of feasible computability. It is argued that reactions to strict finitism point towards a semantics for vague predicates in the form of nonstandard models of weak arithmetical theories of the sort originally introduced to characterize the notion of feasibility as understood in computational complexity theory. The approach described eschews the use of nonclassical logic and related devices like degrees of truth or supervaluation. Like epistemic approaches to vagueness, it may thus be smoothly integrated with the use of classical model theory as widely employed in natural language semantics. But unlike epistemicism, the described approach fails to imply either the existence of sharp boundaries or the failure of tolerance for soritical predicates. Applications ofmeasurement theory(in the sense of Krantz, Luce, Suppes, & Tversky (1971)) to vagueness in the nonstandard setting are also explored.

Adjustments for a class of tests under nonstandard conditions

Generally, the likelihood ratio statistic \(\varLambda \) for standard hypotheses is asymptotically \(\chi ^2\) distributed, and the Bartlett adjustment improves the \(\chi ^2\) approximation to its asymptotic distribution in the sense of third-order asymptotics. However, if the parameter of interest is on the boundary of the parameter space, Self and Liang (1987) show that the limiting distribution of \(\varLambda \) is a mixture of \(\chi ^2\) distributions. For such “nonstandard setting of hypotheses”, the current chapter develops the third-order asymptotic theory for a class \(\mathcal {S}\) of test statistics, which includes the Likelihood Ratio, the Wald and the Score statistic, in the case of observations generated from a general stochastic process, providing widely applicable results. In particular, it is shown that \(\varLambda \) is Bartlett adjustable despite its nonstandard asymptotic distribution. Although the other statistics are not Bartlett adjustable, a nonlinear adjustment is provided for them which greatly improves the \(\chi ^2\) approximation to their distribution and allows a subsequent Bartlett type adjustment. Numerical studies confirm the benefits of the adjustments on the accuracy and on the power of tests whose statistics belong to \(\mathcal {S}\).

Effect of the M3+ cation size on the structural and high temperature phase transitions in Sr2 MSbO6 (M = Ln, Y) double perovskites

In the present work, synchrotron X-ray powder-diffraction measurements at room temperature and laboratory X-ray powder-diffraction measurements at high temperatures of nine members of the antimony family Sr2MSbO6 M = Ln (Nd, Eu, Gd, Dy, Ho, Er, Tm, Yb) and Y ; are reported. Six of them are synthesized for the first time in this work. The crystal structures at room temperature of these compounds are determined and their symmetries are described in the P21/n (a-a-b+) space group (No. 14, non-standard setting). The materials have double perovskite structure with 1:1 ordered arrangement of the B sites. The high-temperature measurements show the existence of two temperature driven phase-transitions: a discontinuous one, from the RT symmetry to R3¯ (a-a-a-) and a continuous one from the latter symmetry to the highest one, the cubic Fm3¯m (a0a0a0). The phase transition temperatures are correlated to the M3+ cation size. The analysis of the phase transitions and the structural refinements have done using the symmetry-adapted modes. A step forward in these analysis is performed: parametrization of the refinements by fixing a selected common direction in the sub-space spanned by X5+ , tri-linearly coupled to the order parameters of the cubic to monoclinic first order phase transition.

MAGNDATA: towards a database of magnetic structures. I. The commensurate case

A free web page under the nameMAGNDATA, which provides detailed quantitative information on more than 400 published magnetic structures, has been developed and is available at the Bilbao Crystallographic Server (http://www.cryst.ehu.es). It includes both commensurate and incommensurate structures. This first article is devoted to explaining the information available on commensurate magnetic structures. Each magnetic structure is described using magnetic symmetry,i.e.a magnetic space group (or Shubnikov group). This ensures a robust and unambiguous description of both atomic positions and magnetic moments within a common unique formalism. A non-standard setting of the magnetic space group is often used in order to keep the origin and unit-cell orientation of the paramagnetic phase, but a description in any desired setting is possible. Domain-related equivalent structures can also be downloaded. For each structure its magnetic point group is given, and the resulting constraints on any macroscopic tensor property of interest can be consulted. Any entry can be retrieved as a magCIF file, a file format under development by the International Union of Crystallography. An online visualization tool usingJmolis available, and the latest versions ofVESTAandJmolsupport the magCIF format, such that these programs can be used locally for visualization and analysis of any of the entries in the collection. The fact that magnetic structures are often reported without identifying their symmetry and/or with ambiguous information has in many cases forced a reinterpretation and transformation of the published data. Most of the structures in the collection possess a maximal magnetic symmetry within the constraints imposed by the magnetic propagation vector(s). When a lower symmetry is realized, it usually corresponds to an epikernel (isotropy subgroup) of one irreducible representation of the space group of the parent phase. Various examples of the structures present in this collection are discussed.

Regularity and infinitely tossed coins

Timothy Williamson has claimed to prove that regularity must fail even in a nonstandard setting, with a counterexample based on tossing a fair coin infinitely many times. I argue that Williamson’s argument is mistaken, and that a corrected version shows that it is not regularity which fails in the non-standard setting but a fundamental property of shifts in Bernoulli processes.

Measuring Device for the Cutting Parameters Monitoring during Drilling

A drilling process quality and a drill life depend on the cutting conditions optimal setting. Research in the area of cutting fluid composition and drilling tools parameters for nonstandard material setting is performed at Technical university of Liberec. Real drilling parameters monitoring is essential during this research. Axial force and torque are two basic parameters describing this process. The measuring device for these parameters monitoring which was built at Technical university of Liberec is described in this paper.