Unifying different theories of conformal prediction

A unified theory for predicting the compressive stress–strain curve of concrete block masonry

We investigated the capability of honeybees to discriminate between single odorants, binary olfactory mixtures, and ternary olfactory mixtures in olfactory conditioning of the proboscis extension reflex. In Experiment 1, three single odorants (A+, B+, and C+) and three binary mixtures of these odors (AB+, AC+, and BC+) were reinforced while the ternary compound, consisting of all three odors (ABC-), was nonreinforced. In Experiment 2, only one single odorant (A+) and one binary olfactory compound (BC+) were reinforced while the ternary compound (ABC-) consisting of the single odor and the binary compound was nonreinforced. We studied whether bees can solve these problems and whether the course of differentiation can be predicted by the unique cue theory, a modified unique cue theory, or Pearce's configural theory. Honeybees were not able to differentiate reinforced from nonreinforced stimuli in Experiment 1. However, summation to ABC observed at the beginning of training contradicts the predictions of Pearce's configural theory. In Experiment 2, differentiation between the single odorant A and the ternary compound developed more easily than between the binary compound BC and ABC. This pattern of differentiation is in line with a modified unique cue theory and Pearce's configural theory. Summation to ABC at the beginning of training, however, again was at odds with Pearce's configural theory. Thus, olfactory compound processing in honeybees can best be explained by a modified unique cue theory.

Grand unified theories, despite their obvious aesthetic appeal, leave few experimentally accessible remnants at present energies. It is important that each of these testable predictions of unified theories be reviewed periodically in light of recent advances in the measurement of low energy parameters pertinent to these predictions and advances in the calculational techniques necessary to extrapolate them to unification energies. Let us, therefore, take another look at one of the famous, although perhaps least understood, predictions of unified theories, the prediction of fermion masses and mass ratios.

Yield and failure theory for unidirectional polymer-matrix composites

A review is given of the theoretical and experimental situation concerning the problem of superconductivity in the presence of pair-breaking perturbations. The problem was first considered by Abrikosov and Gorkov, who advanced a theory which explained the results of the experiments by Matthias and co-workers on the lowering of Tc of superconductors containing small concentrations of magnetic impurities. The theory predicted further that the presence of magnetic scattering centers severely distorts the excitation spectrum of a superconductor and that for sufficiently large spin concentrations the energy gap disappears from the spectrum, even at T=0°K. It has since been found that the AG theory can be extended to treat other pair-breaking situations which lead to second-order superconducting-normal phase transitions. Examples of these are the vortex state, the surface sheath state, the proximity effect, small superconductors in large magnetic fields, superconductivity in the presence of high currents, and superconductivity in the presence of strong Pauli paramagnetism. In the dirty limit (where the mean free path is much smaller than the zero-temperature coherence length) the different pair-breaking regimes are equivalent in that their behavior is specified by a unified single parameter theory. In transforming from one pair-breaking regime to another, one needs only to change the pair-breaking parameter. Experimental results from the different depairing regimes are presented and compared with the predictions of the unified theory.

We propose a unifying, analytical theory accounting for the self-organization of colloidal systems in nanocluster or microcluster phases. We predict the distribution of cluster sizes with respect to interaction parameters and colloid concentration. In particular, we anticipate a proportionality regime where the mean cluster size grows proportionally to the concentration, as observed in several experiments. We emphasize the interest in a predictive theory in soft matter, nanotechnologies, and biophysics.

Traditionally, community ecologists assumed that spe-cies differ in some aspects of their traits or responsesto the environment (i.e. their niches), which allow themto coexist in the same habitat (Hutchinson 1957, 1959).Recently, Hubbell (2001) and others (e.g. Bell 2001,2003) have suggested that this view is inadequate toexplain the diversity often observed in speciose systems.For example, hundreds to thousands of tree species livein tropical forests, which only have a handful of limitingresources such as water, light, and a variety of macro- andmicronutrients. Such high diversity, with so few resources,they argue, cannot be explained by niche theory.As an alternative to the traditional niche theory,Hubbell (2001) developed a neutral theory of commu-nity structure (see also Caswell 1976; Hubbell 1979;Hubbell & Foster 1986; Bell 2000, 2001, 2003; Chave L Chave 2004). In the neutral theory, pat-terns of species diversity, relative abundance, andcomposition are primarily a function of the size of themetacommunity, the dispersal rate of organisms withinthe metacommunity, and the rates of generation (spe-ciation) of new species (Bell 2001; Hubbell 2001; Chave2004). Because species are assumed to be identicalecologically, Hubbell termed his a ‘neutral theory’, bydirect analogy to neutral genes in population genetics.Hubbell further termed his theory ‘unified’ in that it issimultaneously able to predict diversity and relativeabundance of organisms in a locality, as well as bioge-ographic patterns of species composition.In this essay, I overview the key assumptions (inputs)required and the insights (outputs) that can be gainedfrom each framework. While a complete discussion ofall of the assumptions and predictions of these modelsis beyond the scope of this essay (but see Chase

The idea that the Newtonian gravitational constant may vary on cosmic time scales, originally suggested by P.A.M. Dirac, has become a generic prediction of several unified field theories that include gravitation along with the other quantum fields. Experiments looking for the effects of such theories have limited the variation to be less than 10−11yr−1. In the next few years, that limit may be reduced as a result of the Soviet-Franco-American dynamics experiment on the Soviet mission to Phobos in 1990.

On the application of a unified adaptive filter theory in the performance prediction of adaptive filter algorithms

The paper presents a unified jackknife theory for a fairly general class of mixed models which includes some of the widely used mixed linear models and generalized linear mixed models as special cases. The paper develops jackknife theory for the important, but so far neglected, prediction problem for the general mixed model. For estimation of fixed parameters, a jackknife method is considered for a general class of M-estimators which includes the maximum likelihood, residual maximum likelihood and ANOVA estimators for mixed linear models and the recently developed method of simulated moments estimators for generalized linear mixed models. For both the prediction and estimation problems, a jackknife method is used to obtain estimators of the mean squared errors (MSE). Asymptotic unbiasedness of the MSE estimators is shown to hold essentially under certain moment conditions. Simulation studies undertaken support our theoretical results.

Research Question/IssueAlthough there is no unified theory that can explain the relationship between CEO power and corporate risk, the empirical evidence generally finds a positive association. This study argues that market competition and corporate governance play critical roles in influencing this relationship.Research Findings/InsightsUsing a large panel of nonfinancial U.S. corporations for the period 1992–2015, I find that CEO power is positively associated with total and idiosyncratic measures of risk. However, this positive association remains significant only when market competition is high or corporate governance is strong.Theoretical/Academic ImplicationsThe research design of this study combines the predictions of agency theory, the behavioral agency model, and prospect theory to further our understanding of the relationship between CEO power and corporate risk, including consideration of how competition and corporate governance influence this relationship.Practitioner/Policy ImplicationsThe empirical evidence presented in this study can help boards to more accurately gauge when CEO power is most beneficial in terms of optimal levels of corporate risk and to better understand the relationship between power and risk. The results suggest that boards should grant more power to their CEOs when their firms operate in high‐competition markets or have strong corporate governance in place.

Proton decay: Numerical simulations confront grand unification

The discovery of the Z boson 7 years ago verified a key prediction of the unified theory of electromagnetic and weak forces. Today an experimental program is beginning at two electron-positron colliders to study the properties of the Z particle in great detail. The data accumulated will subject the unified theory to more rigorous tests and will probe with great sensitivity for new physics not encompassed by the existing standard model of the elementary particles and forces. Questions under study include the number of quark and lepton families, the mass of the still undiscovered top quark, and the search for the still unknown fifth force of nature required by the theory to generate the masses of the elementary particles.

One of the complex inelastic behavioural phenomena that structural materials may exhibit when subjected to specific thermomechanical loading histories is Dynamic Strain Ageing (DSA). The modeling of DSA within the context of unified theories of viscoplasticity is studied in this paper. In particular, an algorithm is proposed to include DSA modeling capability in Chaboche’s theory. In doing so, use is made of the so-called “correction function” proposed by other investigators. A rather general form of such a function is adopted, and included in the theory in three different ways. It is found that the simplest and most appropriate way to model DSA is to introduce the correction function into the initial value of the isotropic hardening stress, Do. As such, Do is made to change with the imposed strain rate within the range of negative strain-rate sensitivity, and is held constant otherwise.The material parameters of the modified Chaboche theory are evaluated and revised for superalloy Inconel 718 at 1100 °F (593 °C). Predictive capabilities of the theory are examined in monotonic tension, creep and cyclic loading. Predicted responses are also compared with experimental data and found to agree fairly well. Comparisons with predictions of other theories are also performed, and are in favour of Chaboche’s.KeywordsCorrection FunctionDynamic Strain AgeingKinematic HardeningInelastic StrainBack StressThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Over the past 15 years a new class of unified theories has been developed to describe the forces acting between elementary particles. The most successful of the new theories establishes a link between electromagnetism and the weak force. A crucial prediction of this unified electroweak theory is the existence of three massive particles called intermediate vector bosons. If these intermediate vector bosons exist and if they have properties attributed to them by electroweak theory, they should soon be detected, as the world's first particle accelerator with enough energy to create such particles has recently been completed at the European Organization for Nuclear Research (CERN) in Geneva. The accelerator has been converted to a colliding beam machine in which protons and antiprotons collide head on. According to electroweak theory, intermediate vector bosons can be created in proton-antiproton collisions. (SC)