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What distinguishes causation from grounding? One suggestion is that causation, but not grounding, occurs over time. Recently, however, counterexamples to this simple temporal criterion have been offered. In this paper, we situate the temporal criterion within a broader framework that focuses on two aspects: locational overlapping in space and time and the presence of intermediaries in space and time. We consider, and reject, the idea that the difference between grounding and causation is that grounding can occur without intermediaries. We go on to use the fact that grounding and causation both involve intermediaries to develop a better temporal criterion for distinguishing causation from grounding. The criterion is this: when a cause and effect are spatially disjoint, there is always a chain of causal intermediaries between the cause and the effect that are extended in time. By contrast, when the grounds and the grounded are spatially disjoint, there is always a chain of grounding intermediaries, but the chain need not be extended in time, it can be purely spatial. The difference between grounding and causation, then, is that causation requires time for chaining in a way that grounding does not. [ABSTRACT FROM AUTHOR]

One of the challenges in cluster analysis is the evaluation of the obtained clustering results without using auxiliary information. To this end, a common approach is to use internal validity criteria. For mixtures of linear regressions whose parameters are estimated by maximum likelihood, we propose a three-term decomposition of the total sum of squares as a starting point to define some internal validity criteria. In particular, three types of mixtures of regressions are considered: with fixed covariates, with concomitant variables, and with random covariates. A ternary diagram is also suggested for easier joint interpretation of the three terms of the proposed decomposition. Furthermore, local and overall coefficients of determination are respectively defined to judge how well the model fits the data group-by-group but also taken as a whole. Artificial data are considered to find out more about the proposed decomposition, including violations of the model assumptions. Finally, an application to real data illustrates the use and the usefulness of these proposals. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the cross-coupled Camassa-Holm system. First, we prove local well-posedness for the cross-coupled Camassa-Holm equations in $$H^s ({\mathbb {R}})$$ with $$s > 3/2$$ . Then, a blow-up criterion is established. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is one of the most successful and powerful evolutionary algorithms for global optimization problem. The most important operator in this algorithm is mutation operator, in which parents are selected randomly to participate in it. Recently, numerous papers are tried to make this operator more intelligent by selection of parents for mutation intelligently. The intelligent selection for mutation vectors is performed by applying design space (also known as decision space) criterion or fitness space criterion; however, in both cases, half of valuable information of the problem space is disregarded. In this article, a Union Differential Evolution (UDE) is proposed which takes advantage of both design and fitness spaces criteria for intelligent selection of mutation vectors. The experimental analysis on UDE are performed on CEC2005 benchmarks and the results stated that UDE significantly improved the performance of DE in comparison with other methods that only use one criterion for intelligent selection. [ABSTRACT FROM AUTHOR]

This letter studies the tracking performance of a stochastic gradient-based adaptive algorithm, namely the maximum correntropy criterion algorithm, where a random walk is used to model the non-stationarity. In our analysis, we use the energy conservation argument to derive expressions for the steady-state excess mean square error (EMSE). We consider two different cases for measurement of noise distribution including the Gaussian noise and general non-Gaussian noise. For the Gaussian case, we derive a fixed-point equation that can be solved numerically to find steady-state EMSE value. For the general non-Gaussian case, we derive an approximate closed-form expression for EMSE. For both cases, unlike the stationary environment, the EMSE curves are not increasing functions of step size parameter. We use this observation to find the optimum step size learning parameter for general non-Gaussian case. The validity of the theoretical results are justified via simulation results. [ABSTRACT FROM AUTHOR]

The complex behaviours of rocks and rock masses have presented paradoxes to the rock engineer, including the fracturing of seemingly strong rock under low stress conditions, which often occurs near excavation boundaries. The extension strain criterion was presented as a fracture initiation criterion under these conditions (Stacey in Int J Rock Mech Min Sci 18:469-474, 1981). This criterion has been used successfully by some and criticised by others. In this paper, we review the literature on the extension strain criterion and present a case for the correct interpretation of the criterion and the conditions suitable for its use. We argue that the extension strain criterion can also be used to provide an indication of damage level under conditions of relatively low confining stress. We also present an augmentation of the criterion, the ultimate extension strain, which is applicable under extensional loading conditions when σ is similar in magnitude to σ . [ABSTRACT FROM AUTHOR]

We study various single machine scheduling problems with two competing agents, unit processing times and arbitrary integer release dates. The problems differ by the scheduling criterion used by each of the two agents, and by the variant of the bicriteria problem that has to be solved. We prove that when the scheduling criterion of either one of the two agents is of a max-type, then all considered variants of the bicriteria problem are solvable in polynomial time. However, when the two agents have a sum-type of scheduling criterion, several variants of the bicriteria problem become $$\mathcal {NP}$$ -hard. [ABSTRACT FROM AUTHOR]

I propose formulating identity criteria as generic statements of ground, thereby avoiding objections that have been made to the more usual formulations. [ABSTRACT FROM AUTHOR]

Peter van Inwagen proposes a criterion of philosophical success. He takes it to support an extremely pessimistic view about philosophy. He thinks that all philosophical arguments for substantive conclusions fail, including the argument from evil. I'm more optimistic on both counts. I'll identify problems with van Inwagen's criterion and propose an alternative. I'll then explore the differing implications of our criteria. On my view, philosophical arguments can succeed and the argument from evil isn't obviously a failure. [ABSTRACT FROM AUTHOR]

In the first part of my paper I discuss eight arguments in favour of the theory-dependence of observation: (1) realistic content, (2) guidance function of theories, (3) perception as cognitive construction, (4) expectation-dependence of perception, (5) theory-dependence of scientific data, (6) continuity between observational and theoretical concepts, (7) language-dependence, and (8) meaning holism. I argue that although these arguments make correct points, they do not exclude the existence of observations that are weakly theory-neutral in the sense that they don't depend on acquired background knowledge. In the second part I suggest an experimental method, the method of ostensive learning experiments, by which the degree of theory- and language-independence of a concept can be tested. [ABSTRACT FROM AUTHOR]

The uniaxial compressive strength (UCS) of intact rock, which can be estimated using relatively straightforward and cost-effective techniques, is one of the most practical rock properties used in rock engineering. Thus, constitutive laws to represent the strength and behavior of (intact) rock frequently use it, along with additional intrinsic rock properties. Although triaxial tests can be employed to obtain best-fit failure criterion parameters that provide best strength predictions, they are more expensive and require time-consuming procedures; as a consequence, they are often not readily available at early stages of a project. Based on the analysis of an extensive triaxial test database for intact rocks, we propose a simplified empirical failure criterion in which rock strength at failure is expressed in terms of confining stress and UCS, with a new parameter which can be directly estimated from the UCS for a specified rock type in the absence of triaxial test data. Performance of the proposed failure criterion is then tested for validation against experimental data for eight rock types. The results show that strengths of intact rock estimated by the proposed failure criterion are in good agreement with experimental test data, with small discrepancies between estimated and measurements strengths. Therefore, the proposed criterion can be useful for preliminary (triaxial) strength estimation of intact rocks when triaxial tests data are not available. [ABSTRACT FROM AUTHOR]

Strength anisotropy is an important soil behavior which is closely related to the microstructural characteristics in soil. Proper consideration of the microscopic properties of a soil is key to accurate description of its strength anisotropy. This paper presents a failure criterion for cross-anisotropic soils based on the Spatially Mobilized Plane (SMP) criterion. In the new criterion, the shear-normal stress ratio defined in the SMP is related to the relative orientation of the loading direction with respect to the axes of material anisotropy through a microstructure-based tensor. The formulation includes only two parameters which can be easily calibrated by conventional triaixal tests. By comparison with tests data, the criterion is shown to offer good characterization of the strength anisotropy for a variety of geomaterials with cross-anisotropy. [ABSTRACT FROM AUTHOR]

A formula is proposed for practical calculation of the limiting expansion pressure of a spherical and cylindrical cavity in a dilatance-prone soil subject to the Mohr-Coulomb yield criterion, and computed coefficients are cited. [ABSTRACT FROM AUTHOR]

In this paper I argue for a view of groups, things like teams, committees, clubs and courts. I begin by examining features all groups seem to share. I formulate a list of six features of groups that serve as criteria any adequate theory of groups must capture. Next, I examine four of the most prominent views of groups currently on offer-that groups are non-singular pluralities, fusions, aggregates and sets. I argue that each fails to capture one or more of the criteria. Last, I develop a view of groups as realizations of structures. The view has two components. First, groups are entities with structure. Second, since groups are concreta, they exist only when a group structure is realized. A structure is realized when each of its functionally defined nodes or places are occupied. I show how such a view captures the six criteria for groups, which no other view of groups adequately does, while offering a substantive answer to the question, 'What are groups?' [ABSTRACT FROM AUTHOR]

This study describes a general liquefaction flow instability criterion for elastoplastic soils based on the concept of loss of uniqueness. We apply the criterion to the general case of axisymmetric loading and invoke the concepts of effective stresses and loss of controllability to arrive at a general criterion for the onset of liquefaction flow. The criterion is used in conjunction with an elastoplastic model for sands to generate numerical simulations. The numerical results are compared with experimental evidence to give the following insights into predicting liquefaction. (1) The onset of liquefaction flow is a state of instability occurring under both monotonic and cyclic tests, and coincides with loss of controllability. (2) The criterion proposed herein clearly and naturally differentiates between liquefaction flow (instability) and cyclic mobility. (3) Flow liquefaction not only depends on the potential of the material to generate positive excess pore pressures, but more importantly, it also depends on the current state of the material, which is rarely predicted by phenomenology. [ABSTRACT FROM AUTHOR]

A new quadratic strength criterion for an orthotropic material is put forward. It is based on the data of 21 simplest experiments in uniaxial tension, compression, and pure shear. The number of independent tests to failure is shown to be reduced to ten in the case of a unidirectionally reinforced (transtropic) composite. The paper addresses also some of the other types of symmetry of elastic and strength properties, which are frequently encountered in practice. [ABSTRACT FROM AUTHOR]

We establish a new criterion for the dynamical stability of black holes in D ≥ 4 spacetime dimensions in general relativity with respect to axisymmetric perturbations: Dynamical stability is equivalent to the positivity of the canonical energy, $${\mathcal{E}}$$, on a subspace, $${\mathcal{T}}$$, of linearized solutions that have vanishing linearized ADM mass, momentum, and angular momentum at infinity and satisfy certain gauge conditions at the horizon. This is shown by proving that-apart from pure gauge perturbations and perturbations towards other stationary black holes- $${\mathcal{E}}$$ is nondegenerate on $${\mathcal{T}}$$ and that, for axisymmetric perturbations, $${\mathcal{E}}$$ has positive flux properties at both infinity and the horizon. We further show that $${\mathcal{E}}$$ is related to the second order variations of mass, angular momentum, and horizon area by $${\mathcal{E} = \delta^2 M -\sum_A \Omega_A \delta^2 J_A - \frac{\kappa}{8\pi}\delta^2 A}$$, thereby establishing a close connection between dynamical stability and thermodynamic stability. Thermodynamic instability of a family of black holes need not imply dynamical instability because the perturbations towards other members of the family will not, in general, have vanishing linearized ADM mass and/or angular momentum. However, we prove that for any black brane corresponding to a thermodynamically unstable black hole, sufficiently long wavelength perturbations can be found with $${\mathcal{E} < 0}$$ and vanishing linearized ADM quantities. Thus, all black branes corresponding to thermodynmically unstable black holes are dynamically unstable, as conjectured by Gubser and Mitra. We also prove that positivity of $${\mathcal{E}}$$ on $${\mathcal{T}}$$ is equivalent to the satisfaction of a ' local Penrose inequality,' thus showing that satisfaction of this local Penrose inequality is necessary and sufficient for dynamical stability. Although we restrict our considerations in this paper to vacuum general relativity, most of the results of this paper are derived using general Lagrangian and Hamiltonian methods and therefore can be straightforwardly generalized to allow for the presence of matter fields and/or to the case of an arbitrary diffeomorphism covariant gravitational action. [ABSTRACT FROM AUTHOR]

This paper aims at studying the generalized well-posedness in the sense of Bednarczuk for set optimization problems with set-valued maps. Three kinds of B-well-posedness for set optimization problems are introduced. Some relations among the three kinds of B-well-posedness are established. Necessary and sufficient conditions of well-posedness for set optimization problems are obtained. [ABSTRACT FROM AUTHOR]

An argument is usually said to be valid iff it is truth-preserving-iff it cannot be that all its premises are true and its conclusion false. But imperatives (it is normally thought) are not truth-apt. They are not in the business of saying how the world is, and therefore cannot either succeed or fail in doing so. To solve this problem, we need to find a new criterion of validity, and I aim to propose such a criterion. [ABSTRACT FROM AUTHOR]

We consider a double power system with degenerate coefficients. Under certain conditions we obtain a completeness criterion for this system in the Lebesgue function space. [ABSTRACT FROM AUTHOR]

Space-time (ST) trellis coded modulation (TCM) represents a high spectral efficiency technique for multiple antennas transmissions over fading channels. In literature, it was shown that ST-TCM technique offers full diversity when the rank criterion is met. However, 'brute force' methods were used in almost all previous work to search for full diversity ST-TCM codes. In the present paper, we aim to derive an exact expression for the minimum coding gain distance (CGD) in the case of full diversity ST-TCM codes with minimum memory size, for two transmit antennas. Therefore, we transpose the ST-TCM design rules into operations over the set of modulo- M integer numbers ( Z), between the current trellis state and encoder's input information symbol value, in order to derive the transmitted M-levels phase shift keying modulated ( M-PSK) output values. In this context, a new design method is introduced to control the code's minimum CGD value of full diversity ST-TCM schemes. [ABSTRACT FROM AUTHOR]

We propose an ideal experiment enabling the simultaneous assignment of the objective values, 0 or 1, of two incompatible properties of a system made up of two separated, non-interacting spin particles when a strict interpretation of the criterion of reality of Einstein, Podolsky and Rosen is adopted. We compare this experiment with the physical situation involving two-value observables of a system of two correlated spin-1/2 particles envisaged by Bohm; in particular, we show its inadequacy in the dual assignment at issue. Finally, we discuss a number of questions of interpretation of the consistent quantum theory highlighted by our experiment. [ABSTRACT FROM AUTHOR]

We consider the robust tracking problem for a discrete time control object with unknown upper bounds on the perturbations. The transition function in the nominal model of the controllable object is assumed to be known, while upper bounds on the external perturbation, measurement noise, and operator perturbations with respect to both output and control are assumed to be unknown or rough. Current estimates of upper bounds on the perturbations are obtained from measurement data with the quality criterion of the tracking problem as the identification criterion. [ABSTRACT FROM AUTHOR]

Nonsimplicity criteria for groups with systems of Frobenius subgroups are crucial in research on infinite groups with finite elements. Here we prove a criterion for nonsimplicity of a group with a system of F-subgroups whose properties are close to those of Frobenius groups. [ABSTRACT FROM AUTHOR]

The article presents information on the modified Lade criterion (MLC) in context to the failure criterion Lade criterion (LC) and its effective variation. It mentions the strength of isotropic rocks regarding the functions of effective stresses including stress space, and stress field, and highlights the use of failure criterion from Mohr-Coulomb and Hoek-Brown for the geotechnical engineering.

Advocates of extended cognition argue that the boundaries of cognition span brain, body, and environment. Critics maintain that cognitive processes are confined to a boundary centered on the individual. All participants to this debate require a criterion for distinguishing what is internal to cognition from what is external. Yet none of the available proposals are completely successful. I offer a new account, the mutual manipulability account, according to which cognitive boundaries are determined by relationships of mutual manipulability between the properties and activities of putative components and the overall behavior of the cognitive mechanism in which they figure. Among its main advantages, this criterion is capable of (a) distinguishing components of cognition from causal background conditions and lower-level correlates, and (b) showing how the core hypothesis of extended cognition can serve as a legitimate empirical hypothesis amenable to experimental test and confirmation. Conceiving the debate in these terms transforms the current clash over extended cognition into a substantive empirical debate resolvable on the basis of evidence from cognitive science and neuroscience. [ABSTRACT FROM AUTHOR]

We obtain a criterion for manifolds of dimension 4 and greater to be conharmonically para-Kähler and the condition for a manifold to be conharmonically flat. [ABSTRACT FROM AUTHOR]

It is illustrated by a class of counter examples why the Brill-Cantor criterion is not sufficient to ensure the solvability of the Lichnerowicz equation for asymptotically flat, time reflection symmetric-free data. [ABSTRACT FROM AUTHOR]

Siegel, Allan, Hannah, and Crump () demonstrated that cue interaction effects in human contingency judgments reflect processing that occurs after the acquisition of information. This finding is in conflict with a broad class of theories. We present a new postacquisition model, the criterion-calibration model, that describes cue interaction effects as involving shifts in a report criterion. The model accounts for the Siegel et al. data and outperforms the only other postacquisition model of cue interaction, Stout and Miller's () SOCR model. We present new data from an experiment designed to evaluate a prediction of the two models regarding reciprocal cue interaction effects. The new data provide further support for the criterion-calibration model. [ABSTRACT FROM AUTHOR]

An essay is presented regarding the book "Reflective Knowledge," by Ernest Sosa. The author states that Sosa draws various doctrines and distinctions from the early chapter of the book to address the easy knowledge and criterion problem. Furthermore, Sosa sketches a coherence model of justification in the final chapter of the book, in which the author questions how Sosa arrive to the coherentist solution.

The paper revisits the problem of selection of priors for regular one-parameter family of distributions. The goal is to find some 'objective' or 'default' prior by approximate maximization of the distance between the prior and the posterior under a general divergence criterion as introduced by Amari (Ann Stat 10:357-387, 1982) and Cressie and Read (J R Stat Soc Ser B 46:440-464, 1984). The maximization is based on an asymptotic expansion of this distance. The Kullback-Leibler, Bhattacharyya-Hellinger and Chi-square divergence are special cases of this general divergence criterion. It is shown that with the exception of one particular case, namely the Chi-square divergence, the general divergence criterion yields Jeffreys' prior. For the Chi-square divergence, we obtain a prior different from that of Jeffreys and also from that of Clarke and Sun (Sankhya Ser A 59:215-231, 1997). [ABSTRACT FROM AUTHOR]

The paper addresses subcritical growth of a crack in a thin isotropic plate made of an aging viscoelastic material with time-dependent elastic modulus. The behavior of the material is described by Arutyunyan's creep theory. To simulate fracture, a modified Leonov-Panasyuk-Dugdale model and a critical crack opening displacement criterion are used. An equation describing the subcritical growth of the crack is derived assuming that Poisson's ratio is constant. As an example, the critical loads are determined, and curves of subcritical crack growth are plotted for a specific material. The results are compared with the case of constant elastic modulus [ABSTRACT FROM AUTHOR]

For a degenerate equation of the mixed type in a rectangular domain, we pose a nonlocal boundary value problem. By the spectral analysis method, we prove a criterion for the uniqueness of the solution of the problem. [ABSTRACT FROM AUTHOR]

A new cut selection criterion for Benders’ cuts is proposed and computationally analyzed. The results show that the new criterion is more robust—and often considerably faster—than the standard ones. [ABSTRACT FROM AUTHOR]

The ability of bone mineral density (BMD) to discriminate cervical and trochanteric hip fractures was studied. Since the majority of fractures occur among people who are not diagnosed as having osteoporosis, we also examined this population to elucidate whether geometrical risk factors can yield additional information on hip fracture risk beside BMD. The study showed that the T-score criterion was able to discriminate fracture patients from controls in the cases of trochanteric fractures, whereas geometrical measures may discriminate cervical fracture cases in patients with T-score >−2.5. Low bone mineral density (BMD) is a well-established risk factor for hip fracture. However, majority of fractures occur among people not diagnosed as having osteoporosis. We studied the ability of BMD to discriminate cervical and trochanteric hip fractures. Furthermore, we examined whether geometrical measures can yield additional information on the assessment of hip fracture risk in the fracture cases in subjects with T-score >−2.5. Study group consisted of postmenopausal females with non-pathologic cervical ( n = 39) or trochanteric ( n = 18) hip fracture (mean age 74.2 years) and 40 age-matched controls. BMD was measured at femoral neck, and femoral neck axis length, femoral neck and shaft cortex thicknesses (FNC and FSC), and femoral neck-shaft angle (NSA) were measured from radiographs. BMD T-score threshold of −2.5 was able to discriminate trochanteric fractures from controls ( p < 0.001). Seventeen out of 18 trochanteric fractures occurred in individuals with T-score ≤−2.5. However, the T-score criterion was not able to discriminate cervical fractures. Twenty of these fractures (51.3%) occurred in individuals with BMD in osteoporotic range and 19 (48.7%) in individuals with T-score >−2.5. Within these non-osteoporotic cervical fracture patients ( N = 19) and non-osteoporotic controls ( N = 35), 83.3% were classified correctly based on a model including NSA and FNC ( p < 0.001), area under the receiver operating characteristics curve being 0.85 for the model, while it was only 0.56 for BMD alone. The study suggests that the risk of trochanteric fractures could be discriminated based on a BMD T-score <−2.5 criterion, whereas cervical fracture cases would remain under-diagnosed if solely using this criterion. Instead, geometrical risk factors are able to discriminate cervical fracture cases even among individuals with T-score >−2.5. For cervical and trochanteric fractures combined, BMD and geometric measures independently contributed to hip fracture discrimination. Our data support changing from T-score <−2.5 to a more comprehensive assessment of hip fracture etiology, in which fracture type is also taken into account. The findings need to be confirmed with a larger sample, preferably in a prospective study. [ABSTRACT FROM AUTHOR]

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don’t have an a-priori opinion on the relative importance of all these criteria. Roemer (Econ. Bull. 3:1–13, ) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution (see Kalai and Smorodinsky in Econometrica 43:513–518, ). We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered by Roemer (Econ. Bull. 3:1–13, ). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations; in particular, we consider the extension to multicriteria games of the Selten’s trembling hand perfect equilibrium concept (see Selten in Int. J. Game Theory 4:25–55, ) and prove that perfect Kalai-Smorodinsky bargaining solution equilibria exist and properly refine both the perfect equilibria and the Kalai-Smorodinsky bargaining solution equilibria. [ABSTRACT FROM AUTHOR]

We define and axiomatize prudent choices for two criteria. Given two criteria, the alternatives chosen by the prudent choice procedure are the ones maximizing some composition of the criteria. This composition is such that (1) it contains the first criterion and a part of the second one, and (2) the new binary relation is not cyclic and cannot be enlarged with preferences of the second criterion without becoming cyclic. We also make the link between prudent choices, classical rational choices, sequentially rational choices (Manzini and Mariotti in Am Econ Rev 97(5):1824–1839, 2007a) and lexicographic binary choice rational choices (Tadenuma in J Econ Theory 104(2):462–472, 2002). [ABSTRACT FROM AUTHOR]

This paper presents two new methods to optimize the selection of minimum number of thermal sensors for machine tool thermal error compensation. The two methods, namely, direct criterion method and indirect grouping method, are based on the synthetic grey correlation theory. They are applied to analyze the data of an air cutting experiment on a CNC turning center. After optimization, the number of thermal points reduced from 16 to four. Thus, for machine tool thermal error modeling, the number of temperature variables is greatly reduced while coupling problems among temperature variables can be avoided. A real cutting experiment is then conducted to verify the efficiency of the presented optimization methods under practical manufacturing conditions. The comparison of the results between the model with all 16 thermal sensors and the model with four optimized thermal sensors indicates that, after optimization, the model accuracy is greatly improved. [ABSTRACT FROM AUTHOR]

We consider self-similar (pseudo-steady) shock reflection at an oblique wall. There are three parameters: wall corner angle, Mach number, angle of incident shock. Ever since Ernst Mach discovered the irregular reflection named after him, researchers have sought to predict precisely for which parameters the reflection is regular. Three conflicting proposals—the detachment, sonic and von Neumann criteria—have been studied extensively without a clear result. We demonstrate that the sonic criterion is not correct. We consider polytropic potential flow and prove that there is an open nonempty set of parameters that admit a global regular reflection with a reflected shock that is transonic. We also provide a clear physical reason: the flow type (sub- or supersonic) is not decisive; instead the reflected shock type (weak or strong) determines whether structural perturbations decay towards the reflection point. [ABSTRACT FROM AUTHOR]

We give a simple criterion for equivariant harmonic maps into complex projective spaces CP n. As an application of the criterion, we give examples of equivariant harmonic cylinders. We also give examples of non-equivariant harmonic cylinders as perturbations of equivariant harmonic cylinders. [ABSTRACT FROM AUTHOR]

Abstract  Consider the problem of discriminating between two rival response surface models and estimating parameters in the identified model. To construct designs serving for both model discrimination and parameter estimation, the M γ-optimality criterion, which puts weight γ (0≤γ≤1) for model discrimination and 1 − γ for parameter estimation, is adopted. The corresponding M γ-optimal product design is explicitly derived in terms of canonical moments. With the application of the maximin principle on the M γ-efficiency of any M γ'-optimal product design, a criterion-robust optimal product design is proposed. [ABSTRACT FROM AUTHOR]

Foias, Guillopé, & Temam showed in 1985 that for a given weak solution $${u\in L^\infty(0,T;L^2)\cap L^2(0,T;H^1)}$$ of the three-dimensional Navier-Stokes equations on a domain Ω, one can define a ‘trajectory mapping’ $${\Phi:\Omega\times[0,T]\rightarrow\Omega}$$ that gives a consistent choice of trajectory through each initial condition $${a\in\Omega,\,\xi_a(t)=\Phi(a,t)}$$ , and that respects the volume-preserving property one would expect for smooth flows. The uniqueness of this mapping is guaranteed by the theory of renormalised solutions of non-smooth ODEs due to DiPerna & Lions. However, this is a distinct question from the uniqueness of individual particle trajectories. We show here that if one assumes a little more regularity for u than is known to be the case, namely that $${u\in L^{6/5}(0,T;L^\infty(\Omega))}$$ , then the particle trajectories are unique and C1 in time for almost every choice of initial condition in Ω. This degree of regularity is more than can currently be guaranteed for weak solutions ( $${u\in L^1(0,T;L^\infty)}$$) but significantly less than that known to ensure that u is regular ( $${u\in L^2(0,T;L^\infty))}$$ . We rely heavily on partial regularity results due to Caffarelli, Kohn, & Nirenberg and Ladyzhenskaya & Seregin. [ABSTRACT FROM AUTHOR]

This study deals with interoperability testing of protocol implementations. The objective is to define a method for automatic test derivation based on formal definitions. First, the notion of interoperability criteria is introduced. They formally describes the conditions that two implementations must verify in order to be considered interoperable. Then, based on the equivalence of two of the defined interoperability criteria, we propose a method to derive automatically interoperability test cases that avoids the state-space explosion problem. [ABSTRACT FROM AUTHOR]

Neyman-Pearson(NP) criterion is one of the most important ways in hypothesis testing. It is also a criterion for classification. This paper addresses the problem of bounding the estimation error of NP classification, in terms of Rademacher averages. We investigate the behavior of the global and local Rademacher averages, and present new NP classification error bounds which are based on the localized averages, and indicate how the estimation error can be estimated without a priori knowledge of the class at hand. [ABSTRACT FROM AUTHOR]

The article discusses the criterial problem, with reference to the final chapter of the book "A Virtue Epistemology: Apt Belief and Reflective Knowledge" by Ernie Sosa. It states that the problem is not about the criterion, but the skeptical argument related to appearances. It highlights that the book has argued that a certain reliability judgment is required to have knowledge of a certain high quality.

The theory of long-term damage of homogeneous materials, which is based on the equations of the mechanics of stochastically inhomogeneous materials, is generalized to composite materials reinforced with orthotropic ellipsoidal inclusions. The microdamage of the composite components is modeled by randomly dispersed micropores. The failure criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. Given macrostresses or macrostrains, an equation of porosity balance in the composite components at an arbitrary time is formulated. The time dependence of microdamage and macrostresses or macrostrains is established in the case of unlimited stress-rupture microstrength described by an exponential power function [ABSTRACT FROM AUTHOR]

It is shown that under the vector approach, the problem of making decisions by decomposing the properties of alternatives can be represented by a hierarchical system of criteria. At the lower hierarchy level, an alternative is evaluated for separate properties on the basis of a criterion vector and, at the upper level, a composition is used to evaluate the alternative as a whole. The problem is solved by the method of nested scalar convolutions of vector-valued criteria. [ABSTRACT FROM AUTHOR]

How does the causal structure of a problem concept influence judgments of treatment efficacy? We argue that the task of evaluating treatment efficacy involves a combination of causal reasoning and categorization. After an exemplar has been categorized, a treatment task involves judging where to intervene in the causal structure to eradicate the problem, removing the exemplar from category membership. We hypothesized that the processes underlying such category membership removal tasks are not identical to those underlying categorization. Whereas previous experiments have shown that both the root cause (as the most generative feature) and the coherence of the exemplar heavily influence categorization, Experiments 1 and 2 showed that people base category membership removal judgments on the root cause. In Experiment 3, people spontaneously chose to remove an exemplar from category membership when asked to treat the terminal effect. We discuss how our findings are compatible with existing models of categorization. A description of pilot studies for Experiment 1 may be downloaded as supplemental materials from mc.psychonomic-journals.org. [ABSTRACT FROM AUTHOR]

The effects of base rates and payoffs on the shapes of rating receiver operating characteristic curves are inconsistent with the basic assumptions of signal detection theory (SDT), in particular the notion of a shifting decision criterion. Mueller and Weidemann (2008) propose that these unexpected phenomena are not due to problems with the decision-criterion construct but are instead due to two compounded effects: instability of the decision criterion across trials, and even greater instability in the flanking criteria that determine which confidence rating will be reported. There are several problems with the authors' decision-noise hypothesis. First, even if their hypothesis about decision noise were taken for granted, the key feature of the ratings data that rejects the SDT model would remain a mystery. Second, the same violations of SDT that are exhibited in the ratings paradigm are also exhibited in the yes-no detection task when response time is substituted for confidence as a basis for analysis. Finally, the decision-noise hypothesis predicts that sensitivity will increase when one source of this variation-the response on a previous trial-is controlled for. This prediction was consistently violated in both the yes-no and ratings conditions of Mueller and Weidemann's experiment. In an Addendum, we respond to Weidemann and Mueller's (2008) reply to this Comment. [ABSTRACT FROM AUTHOR]

A theoretical substantiation of the acoustic curve of growth of fatigue cracks is presented, including the main assumptions and the dependence of the amplitude of surface acoustic wave oscillations on the number of cycles in cyclic tests. It is shown that this dependence does not qualitatively contradict the classical theory of crack growth from notches. A criterion for previous damage intended for ensuring timely replacement of a fatigue-damaged article is considered. This criterion is implemented using the backscattering (acoustic fatigue curve) and signal-oscillation methods. It is asserted that the signal-oscillation method is an active low-frequency analogue of the acoustic-emission method. [ABSTRACT FROM AUTHOR]