Non-monotonic Ones Research Articles

ON THE MEANING OF THE TERM «HORMESIS» AND ITS PLACE IN THE GENERAL THEORY OF THE DEPENDENCE OF THE BODY’S RESPONSE TO POTENTIALLY HARMFUL EFFECTS ON ITS STRENGTH

Spherical nanoparticles (NP) of cadmium and lead sulfides (dia.37 ± 5 nm and 24 ± 4 nm, respectively) turned to be cytotoxic for HL-1 cardiomyocytes as illustrated by ATP-dependent luminescence reduction. It was revealed, that CdS-NP affect in a greater degree than PbS-NP. In view of the same dose range, CdS-NP decreased the amount of calcium spikes. Small PbS-NP doses showed the same effect. Besides cell hypertrophy due to certain CdS-NP and PbS-NP impact, doses leading to cardiomyocyte decrease were revealed. In order to correspond with the following three results, both monotonic «dose-response» functions (properly approximated by the hyperbolic function) as well as different variants of non-monotonic ones were deduced by us, for which adequate mathematical expressions through modifying certain hormesis models are to be had in literature. Evidence-based analysis involving response surface linear model as well as a cross term, acknowledged a new support to the formerly inflexible rule stating that the diversity kinds of combined action, typical for the same damaging agents’ pair is of the fundamental propositions in the general theory of combined toxicity.

Novel Non-monotonic Lyapunov-Krasovskii Based Stability Analysis and Stabilization of Discrete State-delay System

This paper proposes a novel less-conservative non-monotonic Lyapunov-Krasovskii stability approach for stability analysis of discrete time-delay systems. In this method, monotonically decreasing requirements of the Lyapunov-Krasovskii method are replaced with non-monotonic ones. The Lyapunov-Krasovskii functional is allowed to increase in some steps, but the overall trend should be decreasing. The model of practical systems used for stability analysis usually contain uncertainty. Therefore, firstly a non-monotonic stability condition is derived for certain discrete time-delay systems, then robust non-monotonic stability conditions are proposed for uncertain systems. Finally, a novel stabilization algorithm is derived based on the introduced non-monotonic stability condition. The Lyapunov-Krasovskii functional and the controller are obtained by solving a set of linear matrix inequalities (LMI) or iterative LMI based nonlinear minimization. The proposed theorems are first evaluated by some numerical examples, and then by simulation and implementation on the pH neutralizing process plant.

Some Peculiarities in the Dose Dependence of Separate and Combined In Vitro Cardiotoxicity Effects Induced by CdS and PbS Nanoparticles With Special Attention to Hormesis Manifestations.

Spherical nanoparticles (NPs) of cadmium and lead sulfides (diameter 37 ± 5 and 24 ± 4 nm, respectively) have been found to be cytotoxic for HL-1 cardiomyocytes as evidenced by decrease in adenosine triphosphate–dependent luminescence. Cadmium sulfide (CdS)-NPs were discovered to produce a much greater cytotoxic impact than lead sulphide (PbS)-NP. Given the same dose range, CdS-NP reduced the number of calcium spikes. A similar effect was observed for small doses of PbS-NP. In addition to cell hypertrophy under the impact of certain doses of CdS-NP and PbS-NP, doses causing cardiomyocyte size reduction were identified. For these 3 outcomes, we obtained both monotonic “dose–response” functions (well approximated by the hyperbolic function) and different variants of non-monotonic ones for which we found adequate mathematical expressions by modifying certain models of hormesis available in the literature. Data analysis using a response surface linear model with a cross-term provided new support to the previously established postulate that a diversity of types of joint action characteristic of one and the same pair of damaging agents is one of the important assertions of the general theory of combined toxicity.

In All But Finitely Many Possible Worlds: Model-Theoretic Investigations on ‘Overwhelming Majority’ Default Conditionals

Defeasible conditionals are statements of the form `ifAthen normallyB'. One plausible interpretation introduced in nonmonotonic reasoning dictates that ($$A\Rightarrow B$$AźB) is true iff B is true in `most' A-worlds. In this paper, we investigate defeasible conditionals constructed upon a notion of `overwhelming majority', defined as `truth in a cofinite subset of$$\omega $$ź', the first infinite ordinal. One approach employs the modal logic of the frame $$(\omega , <)$$(ź,<), used in the temporal logic of discrete linear time. We introduce and investigate conditionals, defined modally over $$(\omega , <)$$(ź,<); several modal definitions of the conditional connective are examined, with an emphasis on the nonmonotonic ones. An alternative interpretation of `majority' as sets cofinal (in $$\omega $$ź) rather than cofinite (subsets of $$\omega $$ź) is examined. For these modal approaches over $$(\omega , <)$$(ź,<), a decision procedure readily emerges, as the modal logic $${\mathbf {K4DLZ}}$$K4DLZ of this frame is well-known and a translation of the conditional sentences can be mechanically checked for validity; this allows also for a quick proof of $$\mathsf {NP}$$NP-completeness of the satisfiability problem for these logics. A second approach employs the conditional version of Scott-Montague semantics, in the form of $$\omega $$ź-many possible worlds, endowed with neighborhoods populated by collections of cofinite subsets of $$\omega $$ź. This approach gives rise to weak conditional logics, as expected. The relative strength of the conditionals introduced is compared to (the conditional logic `equivalent' of) KLM logics and other conditional logics in the literature.

Defining Cognitive Logics by Non-Classical Tableau Rules

Abstract In the paper we propose a new approach to formalization of cognitive logics. By cognitive logics we understand supraclassical, but non-trivial consequence operations, defined in a propositional language. We extend some paradigm of tableau methods, in which classical consequence Cn is defined, to stronger logics - monotonic, as well as non-monotonic ones - by specific use of non-classical tableau rules. So far, in that context tableaus have been treated as a way of formalizing other approaches to supraclassical logics, but we use them autonomically to generate various consequence operations. It requires a description of the hierarchy of non-classical tableau rules that result in different supraclassical consequence operations, so we give it.

Non-monotone traveling waves and entire solutions for a delayed nonlocal dispersal equation

This paper is concerned with the traveling waves and entire solutions for a delayed nonlocal dispersal equation with convolution- type crossing-monostable nonlinearity. We first establish the existence of non-monotone traveling waves. By Ikehara’s Tauberian theorem, we further prove the asymptotic behavior of traveling waves, including monotone and non-monotone ones. Then, based on the obtained asymptotic behavior, the uniqueness of the traveling waves is proved. Finally, the entire solutions are considered. By introducing two auxiliary monostable equations and establishing some comparison arguments for the three equations, some new types of entire solutions are constructed via the traveling wavefronts and spatially independent solutions of the auxiliary equations.

A Cochran-Armitage-type and a score-free global test for multivariate ordinal data.

We propose a Cochran-Armitage-type and a score-free global test that can be used to assess the presence of an association between a set of ordinally scaled covariates and an outcome variable within the range of generalized linear models. Both tests are developed within the framework of the well-established 'global test' methodology and as such are feasible in high-dimensional data situations under any correlation and enable adjustment for covariates. The Cochran-Armitage-type test, for which an intimate connection with the traditional score-based Cochran-Armitage test is shown, rests upon explicit assumptions on the distances between the covariates' ordered categories. The score-free test, in contrast, parametrizes these distances and thus keeps them flexible, rendering it ideally suited for covariates measured on an ordinal scale. As confirmed by means of simulations, the Cochran-Armitage-type test focuses its power on set-outcome relationships where the distances between the covariates' categories are equal or close to those assumed, whereas the score-free test spreads its power over a wide range of possible set-outcome relationships, putting more emphasis on monotonic than on non-monotonic ones. Based on the tests' power properties, it is discussed when to favour one or the other, and the practical merits of both of them are illustrated by an application in the field of rehabilitation medicine. Our proposed tests are implemented in the R package globaltest. Copyright © 2016 John Wiley & Sons, Ltd.

Compressible Poiseuille flows with exponential type pressure-dependent mass density

The effect of fluid compressibility in steady, Newtonian and viscoelastic, isothermal, laminar flows is studied. The mass density of the fluid is assumed to vary exponentially with pressure, and viscoelasticity is taken into account by employing the Oldroyd-B constitutive model. The flow problems are solved using a regular perturbation scheme in terms of the dimensionless isothermal compressibility parameter, ε. The sequence of partial differential equations resulting from the perturbation procedure is solved analytically up to third-order in ε. So far, this is the highest order analytical solution derived for Newtonian and viscoelastic compressible flows. Special emphasis on the validity and convergence of the perturbation series is given. It is shown that the inclusion of the third-order term in the perturbation series has important consequences for the preservation of the physical properties of the solution, which is composed up to third order, as well as its convergence. Furthermore, the high accuracy of the perturbation solution in conjunction with the requirement for a positive definite conformation tensor results in monotonic flow curves, as opposed to non-monotonic ones derived in previous works. Cross-sectional averaged expressions for the pressure drop, volumetric flow rate, skin friction factor, and the first- and second-normal stress differences are derived and discussed. For the Newtonian case, the theoretical results for the pressure drop versus the Reynolds number follow the same trend with experimental data from the literature for a much wider range of the dimensionless numbers and parameters to those reported in previous works, which is mainly due to the fact that a more realistic (exponentially, pressure-dependent) equation of state has been utilized.

Choquet integral with respect to a symmetric fuzzy measure of a function on the real line

Some results about the calculation of the Choquet integral of a monotone function are presented. The construction of monotone functions from non-monotone ones that lead to the same Choquet integral is studied.

Bipolarity in bilattice logics

This paper is centered on a family of propositional multivalued logics, based on bilattices. The semantics of such logics relies on a set of “truth values,” with two orderings that give the set a bilattice structure. Many interesting inference relations can be defined on these grounds, especially paraconsistent ones and/or nonmonotonic ones. The focus is laid on Belnap's fundamental bilattice logic FOUR, with four “epistemic truth values,” which proves sufficient for the purpose of inference. We show how the bilattice can be associated with a second biordinal structure, which no longer is bilatticial but bipolar. We show how additional inference relations in the logic FOUR can be obtained by exploiting the two preorders associated with this structure. © 2008 Wiley Periodicals, Inc.

Characterization of T-measures

As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They made the first steps towards a characterization of monotonic real-valued T-measures for a Frank triangular norm T. Later on, Mesiar and the authors of this paper found independently two generalizations, one for vector-valued T-measures with respect to Frank t-norms (in particular for nonmonotonic ones) [3], the other for monotonic real-valued T-measures with respect to general strict t-norms [15]. Here we present a common generalization --- a characterization of nonmonotonic T-measures with respect to an arbitrary strict t-norm. Moreover, we prove this for vector-valued T-measures. Using this characterization, we generalize Ljapunov Theorem to this context.

Breakdown in Burgers-type equations with saturating dissipation fluxes

We study the recently proposed convection-diffusion model equation , with a bounded function . We consider both strictly monotone dissipation fluxes with , and nonmonotone ones such that . The novel feature of these equations is that large amplitude solutions develop spontaneous discontinuities, while small solutions remain smooth at all times. Indeed, small amplitude kink solutions are smooth, while large amplitude kinks have discontinuities ( subshocks). It is demonstrated numerically that both continuous and discontinuous travelling waves are strong attractors of a wide classes of initial data. We prove that solutions with a sufficiently large initial data blow up in finite time. It is also shown that if is monotone and unbounded, then ux is uniformly bounded for all times. In addition, we present more accurate numerical experiments than previously presented, which demonstrate that solutions to a Cauchy problem with periodic initial data may also break down in a finite time if the initial amplitude is sufficiently large.

Grain-structure refinement in titanium alloy under different loading schedules

The dependence of the kinetics of globularization of the lamellar structure in titanium alloy VT9 (Ti-6.6%Al-3.5%Mo-1.7%Zr-0.27%Si) on the character of high-temperature loading was investigated. It was found that monotonic methods of loading (tension, torsion, tension with simultaneous torsion) were more effective means of refining the structure than non-monotonic ones (reverse torsion, torsion alternate with tension, multiaxial forging).

Stability of viscous shock waves associated with a system of nonstrictly hyperbolic conservations laws

AbstractWe introduce a simple model of two conservation laws which is strictly hyperbolic except for a degenerate parabolic line in the state space. Besides classical shock waves, it also exhibits overcompressive, marginal overcompressive, and marginal undercompressive shock waves. Our purpose is to study the behavior of the corresponding viscous waves, in particular the manner in which these waves are stable. There are several basic differences between classical shock waves and other types of shock waves. A perturbation of an overcompressive shock wave gives rise to a new wave. Monotone marginal overcompressive waves behave distinctly from the nonmonotone ones. Analytical techniques used in our study include characteristic‐energy and weighted‐energy methods, and nonlinear superposition through time‐invariants. Although we carry out our analysis for a simple model, the general phenomena would hold for overcompressive waves which occur in other physical models.

Intensity functions of single unit responses to tone in the medial geniculate body of cat.

Extracellular spike activity was recorded from single units in the medial geniculate body (MGB) of nitrous oxide anaesthetized cats. The responses of 291 units to tone bursts at the characteristic frequency (CF) were studied as a function of stimulus intensity, covering a range from 10 to 100 dB SPL. The proportion of MGB units characterized by a monotonic or a non-monotonic discharge rate--intensity function was 26% and 74%, respectively. In addition, changes of response latency as a function of tone levels were demonstrated to be either monotonic (38% of units) or non-monotonic (62% of units). One third Of MGB units showed a change of response pattern with increasing intensities, in similar proportion towards either prevailing excitatory or inhibitory components. The monotonic units tended to differ from non-monotonic ones in addition to their intensity function by showing shorter response latencies, a higher response probability to broad-band stimuli and simpler response patterns. The mean dynamic range of the monotonic unit population was 60 dB, with thresholds ranging from 10 to 90 dB SPL; most discharge rate--intensity functions did not saturate at sound levels of 100 dB SPL. In the population of non-monotonic units, the 'best' intensity, defined as th intensity giving the strongest response, ranged between 10 and 100 dB SPL. The present results suggest that the intensity could be signaled by the mean firing rate of a restricted population of monotonic units or place coded by the distribution of maximally activated non-monotonic units which are broadly tuned to different intensities.