First-order Property Research Articles

The dynamic complexity of formal languages

The article investigates the power of the dynamic complexity classes D yn FO, D yn QF, and D yn PROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in D yn PROP are exactly the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for D yn PROP and separates D yn PROP from D yn QF and D yn FO. Further, it is shown that any context-free language can be maintained in D yn FO and a number of specific context-free languages, for example all Dyck-languages, are maintainable in D yn QF. Furthermore, the dynamic complexity of regular tree languages is investigated and some results concerning arbitrary structures are obtained: There exist first-order definable properties which are not maintainable in D yn PROP. On the other hand, any existential first-order property can be maintained in D yn QF when allowing precomputation.

All the existences that there are

Abstract In this paper, I will defend the claim that there are three existence properties: the second-order property of being instantiated, a substantive first-order property (or better a group of such properties) and a formal, hence universal, first-order property. I will first try to show what these properties are and why we need all of them for ontological purposes. Moreover, I will try to show why a Meinong-like option that positively endorses both the former and the latter first-order property is the correct view in ontology. Finally, I will add some methodological remarks as to why this debate has to be articulated from the point of view of reality, i.e., by speaking of properties, rather than from the point of view of language, i.e., by speaking of predicates (for such properties).

Recursive Bayesian Control of Multichannel Acoustic Echo Cancellation

We present a novel recursive Bayesian method in the DFT-domain to address the multichannel acoustic echo cancellation problem. We model the echo paths between the loudspeakers and the near-end microphone as a multichannel random variable with a first-order Markov property. The incorporation of the near-end observation noise, in conjunction with the multichannel Markov model, leads to a multichannel state-space model. We derive a recursive Bayesian solution to the multichannel state-space model, which turns out to be well suited for input signals that are not only auto-correlated but also cross-correlated. We show that the resulting multichannel state-space frequency-domain adaptive filter (MCSSFDAF) can be efficiently implemented due to the submatrix-diagonality of the state-error covariance. The filter offers optimal tracking and robust adaptation in the presence of near-end noise and echo path variability.

Plug-In Sequential Normal Density Estimation Under Unknown Variance: Mise Loss

Consider independent observations X1, X2,… having a common normal probability density function [Formula: see text] and unknown variance σ2(> 0). We propose estimating f( x; σ2) with a purely sequential methodology under the mean integrated squared error (MISE) loss function. Our goal is to make the associated risk not to exceed a preassigned positive number c, referred to as the risk-bound. Since no fixed-sample-size methodology would be able to handle this estimation problem, Mukhopadhyay and Pepe (2009) first gave a two-stage sampling method. We show that our purely sequential density estimation methodology satisfies asymptotic (i) first-order efficiency property (Theorem 2.1) and (ii) first-order risk-efficiency property (Theorem 2.2) just like the Mukhopadhyay and Pepe two-stage methodology did. But, the present purely sequential density estimation methodology has better second-order efficiency property (Theorems 2.3 and 3.1) than those associated with the Mukhopadhyay and Pepe two-stage methodology. Small, moderate, and large sample performances are investigated with the help of simulations. Illustrations are included with the help of a real dataset.

Apparent transverse compressive material properties of the digital flexor tendons and the median nerve in the carpal tunnel

Carpal tunnel syndrome is a frequently encountered peripheral nerve disorder caused by mechanical insult to the median nerve, which may in part be a result of impingement by the adjacent digital flexor tendons. Realistic finite element (FE) analysis to determine contact stresses between the flexor tendons and median nerve depends upon the use of physiologically accurate material properties. To assess the transverse compressive properties of the digital flexor tendons and median nerve, these tissues from ten cadaveric forearm specimens were compressed transversely while under axial load. The experimental compression data were used in conjunction with an FE-based optimization routine to determine apparent hyperelastic coefficients (μ and α) for a first-order Ogden material property definition. The mean coefficient pairs were μ=35.3kPa, α=8.5 for the superficial tendons, μ=39.4kPa, α=9.2 for the deep tendons, μ=24.9kPa, α=10.9 for the flexor pollicis longus (FPL) tendon, and μ=12.9kPa, α=6.5 for the median nerve. These mean Ogden coefficients indicate that the FPL tendon was more compliant at low strains than either the deep or superficial flexor tendons, and that there was no significant difference between superficial and deep flexor tendon compressive behavior. The median nerve was significantly more compliant than any of the flexor tendons. The material properties determined in this study can be used to better understand the functional mechanics of the carpal tunnel soft tissues and possible mechanisms of median nerve compressive insult, which may lead to the onset of carpal tunnel syndrome.

The effect of local approximations on first-order properties from expectation-value coupled cluster theory

The accuracy of local approximations has been studied for expectation-value coupled cluster theory restricted to single and double excitations (XCCSD), applied to first-order one-electron molecular properties, such as dipole and quadrupole moments. The analysis has been performed separately for each component of the XCCSD expression, which allows to gauge the sensitivity of various parts of the formula to the localization conditions. The varying impact of local approximations is explained by examining the most important terms in the Moller-Plesset expansion of the first-order XCCSD property formula. It has been found that the contribution from the singly excited cluster operator plays a dominant role in the correlation part of the property, and that the common local settings, which consist in including only strong orbital pairs in the CCSD residual equations, lead to significant errors in the local multipole moments. Fortunately, the Moller-Plesset analysis of the XCCSD method allows to formulate a modified set of local approximations, which is better suited for a description of first-order properties. The new options involve the inclusion of close pairs into the CCSD residual equations and the extension of the strong-pair domains, which considerably improves the agreement of the singles-dependent part of the property with the nonlocal reference value. Additionally, for an accurate description of the part of the XCCSD expression containing the doubly excited cluster operator, it is necessary to include close and weak pairs from local MP2 theory. The mean absolute percent error of the correlation part of the dipole moment for the test set of 31 molecules in the cc-pVDZ basis amounts to 16% with the standard local settings, but can be reduced to only 5%, if the new set of local approximations is utilized instead. The existence of local approximations that are appropriate for local XCCSD opens a possibility to calculate first-order properties for large molecules on the coupled cluster level, without a need to solve an additional expensive set of equations for the zeroth-order Lagrangian multipliers from response coupled cluster theory.

A Graphical Approach to Evaluating Equating Using Test Characteristic Curves

An essential concern in the application of any equating procedure is determining whether tests can be considered equated after the tests have been placed onto a common scale. This article clarifies one equating criterion, the first-order equity property of equating, and develops a new method for evaluating equating that is linked to this criterion. The new approach involves graphically examining the difference in test characteristic curves (TCCs), calculating the maximum absolute difference between the TCCs, and comparing the differences in TCCs to the difference that matters (DTM). The new approach is applied to evaluate the equating of the Multistate Bar Exam (MBE) for six different item response theory (IRT) scaling approaches in the common item nonequivalent groups design. The new approach is also contrasted with Tong and Kolen’s (2005) index for assessing first-order equity. The empirical investigations indicated that the Stocking-Lord and fixed-parameter equating methods appear to perform the best for equating the MBE and that the use of concurrent calibration is not desirable.

A/D Conversion Using Asynchronous Delta-Sigma Modulation and Time-to-Digital Conversion

An analog-to-digital conversion (ADC) scheme based on asynchronous ΔΣ modulation and time-to-digital conversion is presented. An asynchronous ΔΣ modulator translates the analog input to an asynchronous duty-cycle modulated signal. Next, the edge locations are digitally measured using a time-to-digital converter (TDC). This information is then digitally processed into a conventional digital signal. The performance of this novel ADC scheme is theoretically analyzed and verified with simulations. With the proposed digital demodulation algorithm, 11-bit resolution can be obtained with an overcycling ratio (OCR) of only four, which is suitable for high bandwidth applications such as very high bit-rate digital subscriber line (VDSL). When a higher OCR can be tolerated, a gated ring-oscillator (GRO) TDC with an inherent first-order noise shaping property is suggested in combination with a digital continuous-time moving-average (CTMA) filter. This allows for resolutions in excess of 13 bits, which is suitable for ADSL2+. The proposed technique shifts the complexity toward the digital domain, leading to more compact ADC and reduced power consumption, and is, therefore, particularly suited for ADC in ultralow-voltage nanometer technologies that are used for high-speed data communication applications.

Structure Theorem and Strict Alternation Hierarchy for FO^2 on Words

It is well-known that every first-order property on words is expressible using at most three variables. The subclass of properties expressible with only two variables is also quite interesting and well-studied. We prove precise structure theorems that characterize the exact expressive power of first-order logic with two variables on words. Our results apply to both the case with and without a successor relation. For both languages, our structure theorems show exactly what is expressible using a given quantifier depth, n, and using m blocks of alternating quantifiers, for any m \leq n. Using these characterizations, we prove, among other results, that there is a strict hierarchy of alternating quantifiers for both languages. The question whether there was such a hierarchy had been completely open. As another consequence of our structural results, we show that satisfiability for first-order logic with two variables without successor, which is NEXP-complete in general, becomes NP-complete once we only consider alphabets of a bounded size.

Representation of the orientation distribution function and computation of first-order elastic properties closures using discrete Fourier transforms

The orientation distribution function (ODF) is most commonly described in the Bunge–Euler space using generalized spherical harmonics (GSH) as a Fourier basis. In this paper, we explore critically the relative advantages and disadvantages of using an alternate description of the ODF using the much more readily accessible discrete Fourier transforms (DFTs). Appropriate protocols to address the consideration of crystal and sample symmetries in the DFT representations of ODFs have been developed and validated in this paper. It was also observed that the representation of first-order texture-elastic property linkages using DFTs needed a higher number of terms compared to the GSH representations. However, the use of DFT representations resulted in major computational economy in producing the ODF plots as well as the delineation of the property closures. It is shown that the improved computational efficiency facilitated the delineation of the first-order elastic property closures involving the normal–shear coupling stiffness coefficients.

On expansions and extensions of powerful digraphs

We study the problem of expanding and extending the structure of a stable powerful digraph to the structure of a stable Ehrenfeucht theory. We define the concepts of type unstability and type strict order property. We establish the presence of the type strict order property for every acyclic graph structure with an infinite chain. The simplest form of expansion of a powerful digraph to the structure of an Ehrenfeucht theory is the expansion with a 1-inessential ordered coloring and locally graph ∃-definable many-placed relations, which enable us to mutually realize nonprincipal types; we prove that this expansion is incapable of keeping the structure in the class of stable structures, and moreover, by the type strict order property it generates the first-order definable strict order property. We define the concept of a locally countably categorical theory (LCC theory) and prove that given the list p1(x), ..., pn(x) of all nonprincipal 1-types in an LCC theory, if all types r(x1, ..., xm) containing \( p_{i_1 } \) (x1) ∪ ... ∪ \( p_{i_m } \)(xm) are dominated by some type q then q is a powerful type.

Plug-In Two-Stage Normal Density Estimation Under MISE Loss: Unknown Variance

Consider independent observations X 1, X 2,… having a common normal probability density function with − ∞ < x < ∞ and unknown variance σ2 ( > 0). We propose to estimate f(x;σ2) by a plug-in maximum likelihood (ML) two-stage estimator under the mean integrated squared error (MISE) loss function. Our goal is to make the associated risk not to exceed a preassigned positive number c, referred to as the risk-bound. Because no fixed-sample-size methodology would handle this estimation problem, we design an appropriate two-stage estimation methodology that is shown to satisfy the asymptotic (i) first-order efficiency property (Theorem 2.1), (ii) first-order risk-efficiency property (Theorem 2.2), as well as (iii) second-order efficiency property (Theorem 2.3). The performances of the proposed methodology for small, moderate, and large sample sizes are examined with the help of simulations. We have noticed some limited robustness of the proposed methodology under mixture-normal population densities, in which case the asymptotic second-order efficiency property (Theorem 3.1) is shown. Illustrations are included with real data and analysis. Overall, we feel that the proposed two-stage plug-in density estimation methodology performs remarkably well.

A study on the mapping of quantitative trait loci in advanced populations derived from two inbred lines

In genetic and biological studies, the F2 population is one of the most popular and commonly used experimental populations mainly because it can be readily produced and its genome structure possesses several niceties that allow for productive investigation. These niceties include the equivalence between the proportion of recombinants and recombination rates, the capability of providing a complete set of three genotypes for every locus and an analytically attractive first-order Markovian property. Recently, there has been growing interest in using the progeny populations from F2 (advanced populations) because their genomes can be managed to meet specific purposes or can be used to enhance investigative studies. These advanced populations include recombinant inbred populations, advanced intercrossed populations, intermated recombinant inbred populations and immortalized F2 populations. Due to an increased number of meiosis cycles, the genomes of these advanced populations no longer possess the Markovian property and are relatively more complicated and different from the F2 genomes. Although issues related to quantitative trait locus (QTL) mapping using advanced populations have been well documented, still these advanced populations are often investigated in a manner similar to the way F2 populations are studied using a first-order Markovian assumption. Therefore, more efforts are needed to address the complexities of these advanced populations in more details. In this article, we attempt to tackle these issues by first modifying current methods developed under this Markovian assumption to propose an ad hoc method (the Markovian method) and explore its possible problems. We then consider the specific genome structures present in the advanced populations without invoking this assumption to propose a more adequate method (the non-Markovian method) for QTL mapping. Further, some QTL mapping properties related to the confounding problems that result from ignoring epistasis and to mapping closely linked QTL are derived and investigated across the different populations. Simulations show that the non-Markovian method outperforms the Markovian method, especially in the advanced populations subject to selfing. The results presented here may give some clues to the use of advanced populations for more powerful and precise QTL mapping.

Analysis and Design of Voltage-Controlled Oscillator Based Analog-to-Digital Converter

A voltage-controlled oscillator (VCO) based analog-to-digital converter (ADC) is a time-based architecture with a first-order noise-shaping property, which can be implemented using a VCO and digital circuits. This paper analyzes the performance of VCO-based ADCs in the presence of nonidealities such as jitter, nonlinearity, mismatch, and the metastability of D flip-flops. Based on this analysis, design criteria for determining parameters for VCO-based ADCs are described. In addition, a digital calibration technique to enhance the spurious-free dynamic range degraded by the nonlinearity is also introduced. To verify the theoretical analysis, a prototype chip is implemented in a 0.13-?m CMOS process. With a 500-MHz sampling frequency, the prototype achieves a signal-to-noise ratio ranging from 71.8 to 21.3 dB for an input bandwidth of 100 kHz-247 MHz, while dissipating 12.6 mW and occupying an area of 0.078 mm2.

Interpreting the phosphocreatine time constant in aerobically exercising skeletal muscle

to the editor: Francescato et al. ([1][1]) contrast the lack of interindividual correlation between the phosphocreatine (PCr) time constant (τPCr) and the ADP concentration ([ADP]) change from rest to steady state (Δ[ADP]S) during moderate aerobic exercise with the fact that “…ADP

On texture and image interpolation using Markov models

Markov-type models characterize the correlation among neighboring pixels in an image in many image processing applications. Specifically, a wide-sense Markov model, which is defined in terms of minimum linear mean-square error estimates, is applicable to image restoration, image compression, and texture classification and segmentation. In this work, we address first-order (auto-regressive) wide-sense Markov images with a separable autocorrelation function. We explore the effect of sampling in such images on their statistical features, such as histogram and the autocorrelation function. We show that the first-order wide-sense Markov property is preserved, and use this result to prove that, under mild conditions, the histogram of images that obey this model is invariant under sampling. Furthermore, we develop relations between the statistics of the image and its sampled version, in terms of moments and generating model noise characteristics. Motivated by these results, we propose a new method for texture interpolation, based on an orthogonal decomposition model for textures. In addition, we develop a novel fidelity criterion for texture reconstruction, which is based on the decomposition of an image texture into its deterministic and stochastic components. Experiments with natural texture images, as well as a subjective forced-choice test, demonstrate the advantages of the proposed interpolation method over presently available interpolation methods, both in terms of visual appearance and in terms of our novel fidelity criterion.

Accountable internet protocol (aip)

This paper presents AIP (Accountable Internet Protocol), a network architecture that provides accountability as a first-order property. AIP uses a hierarchy of self-certifying addresses, in which each component is derived from the public key of the corresponding entity. We discuss how AIP enables simple solutions to source spoofing, denial-of-service, route hijacking, and route forgery. We also discuss how AIP's design meets the challenges of scaling, key management, and traffic engineering.

Run-Time Checking of Dynamic Properties

We consider a first-order property specification language for run-time monitoring of dynamic systems. The language is based on a linear-time temporal logic and offers two kinds of quantifiers to bind free variables in a formula. One kind contains the usual first-order quantifiers that provide for replication of properties for dynamically created and destroyed objects in the system. The other kind, called attribute quantifiers, is used to check dynamically changing values within the same object. We show that expressions in this language can be efficiently checked over an execution trace of a system.

A generalized temporal context model for classifying image collections

Semantic scene classification is an open problem in computer vision, especially when information from only a single image is employed. In applications involving image collections, however, images are clustered sequentially, allowing surrounding images to be used as temporal context. We present a general probabilistic temporal context model in which the first-order Markov property is used to integrate content-based and temporal context cues. The model uses elapsed time-dependent transition probabilities between images to enforce the fact that images captured within a shorter period of time are more likely to be related. This model is generalized in that it allows arbitrary elapsed time between images, making it suitable for classifying image collections. In addition, we derived a variant of this model to use in ordered image collections for which no timestamp information is available, such as film scans. We applied the proposed context models to two problems, achieving significant gains in accuracy in both cases. The two algorithms used to implement inference within the context model, Viterbi and belief propagation, yielded similar results with a slight edge to belief propagation.

Assessing Equating Results on Different Equating Criteria

The performance of three equating methods— the presmoothed equipercentile method, the item response theory (IRT) true score method, and the IRT observed score method—were examined based on three equating criteria: the same distributions property, the first-order equity property, and the second-order equity property. The magnitude of the difficulty differences in the alternate forms was found to affect the extent to which the three equating properties hold. The Iowa Tests of Basic Skills (ITBS) standardization data and simulated data were analyzed in the study. The results showed that when the raw score distributions of alternate forms are similar, all three methods lead to adequate equating regardless of the criterion used. When the raw score distributions are dissimilar, to preserve the first order equity property, the IRT true score method performs best; to preserve the same distributions and second order equity properties, the equipercentile method and the IRT observed score method both perform well. The greater the difficulty difference between alternate forms, the less likely the first and second order equity properties hold. These results are intended to inform equating practice by suggesting, for actual equatings, the size of form-to-form differences that can lead each equating method to perform well and poorly relative to the various criteria.