Covariant Pairs Research Articles

Matching points: Supplementing instruments with covariates in triangular models

Models with a discrete endogenous variable and an instrument that takes on fewer values are common in economics. This paper presents a new method that matches pairs of covariates and instruments to restore the order condition in this scenario and to achieve point-identification of the outcome function. The outcome function must be monotonic in a scalar disturbance, but it can be nonseparable. The first stage for the discrete endogenous variable needs to have a multi-index structure but allows for multidimensional heterogeneity. This paper also provides estimators of the outcome function. Two empirical examples of the return to education and of selection into Head Start illustrate the usefulness and limitations of the method.

Selection and integration of generalized instrumental variables for estimating total effects

We consider a situation where cause–effect relationships between variables can be described as a directed acyclic graph (DAG) and the corresponding linear structural equation model (linear SEM). When several pairs of instrumental variables (IVs) and covariates (IV-pairs; Pearl in: Proceedings of the 20th conference on uncertainty in artificial intelligence, AUAI Press, Arlington, Virginia, United States, UAI’04, 2004) are available, we propose (i) the graphical selection criteria of IV-pairs for total effects and (ii) an integrated estimator that combines them to estimate total effects with better accuracy. In this paper, in accordance with the paper by Brito and Pearl (in: Proceedings of the 18th conference on uncertainty in artificial intelligence, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, UAI’02, 2002), the proposed estimator is called an integrated generalized instrumental variable (iGIV) estimator. The proposed graphical selection criteria imply that (a) the back-door criterion achieves better estimation accuracy than the traditional instrumental variable (IV) method of estimating total effects even when the treatment and covariates are highly correlated and (b) the conditional IV method can be superior to the back-door criterion in some situations. The iGIV estimator provides a general class that includes both the ordinary least squares (OLS) estimator based on the back-door criterion and the two-stage least squares (2SLS) estimator based on the (conditional) IV method. We clarify the properties of the iGIV estimator, some of which can be read off from the DAG structure. Furthermore, through numerical experiments and an application to a case study, we show that the performance of the iGIV estimator is superior to those of the OLS and IV estimators. The iGIV estimator can be a powerful tool to estimate the total effect when the proposed graphical selection criteria of the IV-pairs are not satisfied.

Deep Analysis of Residue Constraints (DARC): identifying determinants of protein functional specificity

Protein functional constraints are manifest as superfamily and functional-subgroup conserved residues, and as pairwise correlations. Deep Analysis of Residue Constraints (DARC) aids the visualization of these constraints, characterizes how they correlate with each other and with structure, and estimates statistical significance. This can identify determinants of protein functional specificity, as we illustrate for bacterial DNA clamp loader ATPases. These load ring-shaped sliding clamps onto DNA to keep polymerase attached during replication and contain one δ, three γ, and one δ’ AAA+ subunits semi-circularly arranged in the order δ-γ1-γ2-γ3-δ’. Only γ is active, though both γ and δ’ functionally influence an adjacent γ subunit. DARC identifies, as functionally-congruent features linking allosterically the ATP, DNA, and clamp binding sites: residues distinctive of γ and of γ/δ’ that mutually interact in trans, centered on the catalytic base; several γ/δ’-residues and six γ/δ’-covariant residue pairs within the DNA binding N-termini of helices α2 and α3; and γ/δ’-residues associated with the α2 C-terminus and the clamp-binding loop. Most notable is a trans-acting γ/δ’ hydroxyl group that 99% of other AAA+ proteins lack. Mutation of this hydroxyl to a methyl group impedes clamp binding and opening, DNA binding, and ATP hydrolysis—implying a remarkably clamp-loader-specific function.

Interaction Analysis of Risk Factors for Long-Term Skeletal Relapse Following Mandibular Advancement with Bilateral Sagittal Split Osteotomy

The aim of this study was to identify interaction effects among risk factors for long-term skeletal relapse. The study sample consisted of 96 patients who underwent mandibular advancement with bilateral sagittal split osteotomy. Ten predictor variables were analyzed for an interaction effect: sex, age, preoperative temporomandibular joint symptoms, mandibular plane angle (MPA), single or double jaw surgery, clockwise or counterclockwise mandibular rotation, magnitude of mandibular advancement, concomitant genioplasty, type of fixation, and follow-up duration. Modeling interactions between pairs of covariates were applied to detect a significant interaction among these risk factors on horizontal and vertical long-term skeletal relapse, respectively. Stratification analyses and two-way full factorial interaction analyses were performed to demonstrate how the interaction influenced the associations between covariates and relapse. The interactions between sex and mandibular rotation (P=0.006) and between MPA and mandibular rotation (P=0.002) were statistically significant for horizontal long-term skeletal relapse. No significant interaction was identified for vertical relapse. This study showed that female patients and those with an MPA ≥30° undergoing counterclockwise mandibular rotation are predisposed to greater horizontal long-term skeletal relapse. Therefore, the judicious use of counterclockwise rotation is recommended in order to minimize the relapse, especially in female patients and those with a high MPA.

Interaction analysis of risk factors for long-term skeletal relapse following mandibular advancement with bilateral sagittal split osteotomy

The aim of this study was to identify interaction effects among risk factors for long-term skeletal relapse. The study sample consisted of 96 patients who underwent mandibular advancement with bilateral sagittal split osteotomy. Ten predictor variables were analyzed for an interaction effect: sex, age, preoperative temporomandibular joint symptoms, mandibular plane angle (MPA), single or double jaw surgery, clockwise or counterclockwise mandibular rotation, magnitude of mandibular advancement, concomitant genioplasty, type of fixation, and follow-up duration. Modeling interactions between pairs of covariates were applied to detect a significant interaction among these risk factors on horizontal and vertical long-term skeletal relapse, respectively. Stratification analyses and two-way full factorial interaction analyses were performed to demonstrate how the interaction influenced the associations between covariates and relapse. The interactions between sex and mandibular rotation (P=0.006) and between MPA and mandibular rotation (P=0.002) were statistically significant for horizontal long-term skeletal relapse. No significant interaction was identified for vertical relapse. This study showed that female patients and those with an MPA ≥30° undergoing counterclockwise mandibular rotation are predisposed to greater horizontal long-term skeletal relapse. Therefore, the judicious use of counterclockwise rotation is recommended in order to minimize the relapse, especially in female patients and those with a high MPA.

Admissible Vectors of a Covariant Representation of a Dynamical System

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system. In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to a uniform lattice of $G$.

Semicrossed products of operator algebras by semigroups

We examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. We seek quite general conditions which will allow us to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Our analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups. In particular, we show that the C*-envelope of the semicrossed product of C*-dynamical systems by doubly commuting representations of $\mathbb{Z}^n_+$ (by generally non-injective endomorphisms) is the full corner of a C*-crossed product. In consequence we connect the ideal structure of C*-covers to properties of the actions. In particular, when the system is classical, we show that the C*-envelope is simple if and only if the action is injective and minimal. The dilation methods that we use may be applied to non-abelian semigroups. We identify the C*-envelope for actions of the free semigroup $\mathbb{F}_+^n$ by automorphisms in a concrete way, and for injective systems in a more abstract manner. We also deal with C*-dynamical systems over Ore semigroups when the appropriate covariance relation is considered.

A novel algorithm for detecting multiple covariance and clustering of biological sequences.

Single genetic mutations are always followed by a set of compensatory mutations. Thus, multiple changes commonly occur in biological sequences and play crucial roles in maintaining conformational and functional stability. Although many methods are available to detect single mutations or covariant pairs, detecting non-synchronous multiple changes at different sites in sequences remains challenging. Here, we develop a novel algorithm, named Fastcov, to identify multiple correlated changes in biological sequences using an independent pair model followed by a tandem model of site-residue elements based on inter-restriction thinking. Fastcov performed exceptionally well at harvesting co-pairs and detecting multiple covariant patterns. By 10-fold cross-validation using datasets of different scales, the characteristic patterns successfully classified the sequences into target groups with an accuracy of greater than 98%. Moreover, we demonstrated that the multiple covariant patterns represent co-evolutionary modes corresponding to the phylogenetic tree, and provide a new understanding of protein structural stability. In contrast to other methods, Fastcov provides not only a reliable and effective approach to identify covariant pairs but also more powerful functions, including multiple covariance detection and sequence classification, that are most useful for studying the point and compensatory mutations caused by natural selection, drug induction, environmental pressure, etc.

Bell polynomials approach for two higher-order KdV-type equations in fluids

The present paper investigates the higher-order Sawada–Kotera-type equation and the higher-order Lax-type equation in fluids. The Bell polynomials approach is employed to directly bilinearize the two equations. For the Lax-type equation, bilinear Bäcklund transformation, Lax pair, Darboux covariant Lax pair and infinitely many conservation laws are obtained by means of binary Bell polynomials. Moreover, based on its bilinear form, N-soliton solutions are also obtained. For the Sawada–Kotera-type equation, with the help of the Riemann theta function and Hirota bilinear method, its one periodic wave solution is obtained. A limiting procedure is presented to analyze in detail the relations between the one periodic wave solution and one soliton solution.

Coherent state transforms and the Mackey-Stone-Von Neumann theorem

Mackey showed that for a compact Lie group K, the pair (K, C 0(K)) has a unique non-trivial irreducible covariant pair of representations. We study the relevance of this result to the unitary equivalence of quantizations for an infinite-dimensional family of K × K invariant polarizations on T*K. The Kähler polarizations in the family are generated by (complex) time-τ Hamiltonian flows applied to the (Schrödinger) vertical real polarization. The unitary equivalence of the corresponding quantizations of T*K is then studied by considering covariant pairs of representations of K defined by geometric prequantization and of representations of C 0(K) defined via Heisenberg time-(−τ) evolution followed by time-(+τ) geometric-quantization-induced evolution. We show that in the semiclassical and large imaginary time limits, the unitary transform whose existence is guaranteed by Mackey's theorem can be approximated by composition of the time-(+τ) geometric-quantization-induced evolution with the time-(−τ) evolution associated with the momentum space [W. D. Kirwin and S. Wu, “Momentum space for compact Lie groups and the Peter-Weyl theorem” (unpublished)] quantization of the Hamiltonian function generating the flow. In the case of quadratic Hamiltonians, this asymptotic result is exact and unitary equivalence between quantizations is achieved by identifying the Heisenberg imaginary time evolution with heat operator evolution, in accordance with the coherent state transform of Hall.

MCA: Multiresolution Correlation Analysis, a graphical tool for subpopulation identification in single-cell gene expression data.

BackgroundBiological data often originate from samples containing mixtures of subpopulations, corresponding e.g. to distinct cellular phenotypes. However, identification of distinct subpopulations may be difficult if biological measurements yield distributions that are not easily separable.ResultsWe present Multiresolution Correlation Analysis (MCA), a method for visually identifying subpopulations based on the local pairwise correlation between covariates, without needing to define an a priori interaction scale. We demonstrate that MCA facilitates the identification of differentially regulated subpopulations in simulated data from a small gene regulatory network, followed by application to previously published single-cell qPCR data from mouse embryonic stem cells. We show that MCA recovers previously identified subpopulations, provides additional insight into the underlying correlation structure, reveals potentially spurious compartmentalizations, and provides insight into novel subpopulations.ConclusionsMCA is a useful method for the identification of subpopulations in low-dimensional expression data, as emerging from qPCR or FACS measurements. With MCA it is possible to investigate the robustness of covariate correlations with respect subpopulations, graphically identify outliers, and identify factors contributing to differential regulation between pairs of covariates. MCA thus provides a framework for investigation of expression correlations for genes of interests and biological hypothesis generation.

Helminth communities in the burrowing toad, Rhinella fernandezae, from Northeastern Argentina

The main goals of this study were to determine the richness and diversity of helminth parasites of Rhinella fernandezae at the component and infracommunity levels and determine the ecological implications of different biotic and abiotic factors. Specimens were collected near the city of Corrientes, Corrientes Province, Argentina. Prevalence of infection was 94% in the specimens examined (n = 65). The helminth component community in R. fernandezae in this area was comprised a total of 22 species. Of all helminth species, only three (Catadiscus inopinatus, Cosmocerca podicipinus and C. parva) were dominant (importance value: I > 1.0) in the community. The most abundant species were B. tetracotyloides (d = 0.43) among the larvae and C. podicipinus (d = 0.09) among adult worms. At the infracommunity level, the mean individual species richness (2.28 ± 1.48) (mean ± SD) was no more than 3 helminth species per infected host; the diversity and equitability of helminths were 0.23 ± 0.21 and 0.48 ± 0.38, respectively. The host body size was the main factor in determining the parasite abundance. Species richness was significantly and positively correlated with host body size. The parasite helminth species predominantly showed an overdispersed pattern of distribution. Helminth species showed two negative and significant pairs of covariation and one significant pair of association (P < 0.05). R. fernandezae has a wide variety of parasites relating to the host microhabitat, mobility and feeding habits.

On the Integrability of a Generalized Variable‐Coefficient Forced Korteweg‐de Vries Equation in Fluids

With the inhomogeneities of media taken into account, under investigation is hereby a generalized variable‐coefficient forced Korteweg‐de Vries (vc‐fKdV) equation, which describes shallow‐water waves, internal gravity waves, etc. Under an integrable constraint condition on the variable coefficients, in this paper, the complete integrability of the generalized vc‐fKdV equation is proposed. By virtue of a generalization of Bells polynomials, we systematically present its bilinear representations, Bäcklund transformations, Lax pairs and Darboux covariant Lax pairs, which can be reduced to the ones of some integrable models, such as vcKdV model, cylindrical KdV equation, and an analytical model of tsunami generation. It is very interesting that its bilinear formulism is free for the integrable constraint condition. Besides, researching the Lax equations yield its infinitely conservation laws, all conserved densities and fluxes of them are obtained by explicit recursion formulas. Furthermore, by considering its bilinear formulism with an extra auxiliary variable, we present the soliton solutions and Riemann theta function periodic wave solutions of the equation. According to the constraint among the nonlinear, dispersive, and line‐damping coefficients, we further discuss the solitonic structures and interaction properties by some graphic analysis. Finally, the relationships between the periodic wave solutions and soliton solutions are presented in detail by a limiting procedure.

Bell polynomial approach to an extended Korteweg–de Vries equation

Under investigation in this paper is an extended Korteweg–de Vries equation. Via Bell polynomial approach and symbolic computation, this equation is transformed into two kinds of bilinear equations by choosing different coefficients, namely KdV–SK‐type equation and KdV–Lax‐type equation. On the one hand, N‐soliton solutions, bilinear Bäcklund transformation, Lax pair, Darboux covariant Lax pair, and infinite conservation laws of the KdV–Lax‐type equation are constructed. On the other hand, on the basis of Hirota bilinear method and Riemann theta function, quasiperiodic wave solution of the KdV–SK‐type equation is also presented, and the exact relation between the one periodic wave solution and the one soliton solution is established. It is rigorously shown that the one periodic wave solution tend to the one soliton solution under a small amplitude limit. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Integrability of an extended (2+1)-dimensional shallow water wave equation with Bell polynomials

We investigate the extended (2+1)-dimensional shallow water wave equation. The binary Bell polynomials are used to construct bilinear equation, bilinear Bäcklund transformation, Lax pair, and Darboux covariant Lax pair for this equation. Moreover, the infinite conservation laws of this equation are found by using its Lax pair. All conserved densities and fluxes are given with explicit recursion formulas. The N-soliton solutions are also presented by means of the Hirota bilinear method.

Binary Bell polynomial manipulations on the integrability of a generalized (2+1) -dimensional Korteweg–de Vries equation

This paper investigates the integrability of a generalized (2+1)-dimensional Korteweg–de Vries equation. With the aid of binary Bell polynomials, its bilinear formalism, bilinear Bäcklund transformation, Lax pair and Darboux covariant Lax pair are succinctly constructed, which can be reduced to the ones of several integrable equations such as the Korteweg–de Vries equation and the Calogero–Bogoyavlenskii–Schiff equation. Moreover, the infinite conservation laws of the generalized (2+1)-dimensional Korteweg–de Vries equation are found by virtue of binary Bell polynomials. All conserved densities and fluxes are given with explicit recursion formulas.

On the integrability of a generalized variable-coefficient Kadomtsev–Petviashvili equation

By considering the inhomogeneities of media, a generalized variable-coefficient Kadomtsev–Petviashvili (vc-KP) equation is investigated, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. In this paper, we systematically investigate the complete integrability of the generalized vc-KP equation under an integrable constraint condition. With the aid of generalized Bell’s polynomials, its bilinear formalism, bilinear Bäcklund transformations, Lax pairs and Darboux covariant Lax pairs are succinctly constructed, which can be reduced to the ones of several integrable equations such as KdV, cylindrical KdV, KP, cylindrical KP, generalized cylindrical KP, non-isospectral KP equations, etc. Moreover, the infinite conservation laws of the equation are found by using its Lax equations. All conserved densities and fluxes are given with explicit recursion formulas. Furthermore, an extra auxiliary variable is introduced to obtain the bilinear formalism, based on which, the soliton solutions and Riemann theta function periodic wave solutions are presented. The influence of inhomogeneity coefficients on solitonic structures and interaction properties are discussed for physical interest and possible applications by some graphic analysis. Finally, a limiting procedure is presented to analyze in detail the asymptotic behavior of the periodic waves and the relations between the periodic wave solutions and soliton solutions.

Novel Nucleotide and Amino Acid Covariation between the 5′UTR and the NS2/NS3 Proteins of Hepatitis C Virus: Bioinformatic and Functional Analyses

Molecular covariation of highly polymorphic viruses is thought to have crucial effects on viral replication and fitness. This study employs association rule data mining of hepatitis C virus (HCV) sequences to search for specific evolutionary covariation and then tests functional relevance on HCV replication. Data mining is performed between nucleotides in the untranslated regions 5′ and 3′UTR, and the amino acid residues in the non-structural proteins NS2, NS3 and NS5B. Results indicate covariance of the 243rd nucleotide of the 5′UTR with the 14th, 41st, 76th, 110th, 211th and 212th residues of NS2 and with the 71st, 175th and 621st residues of NS3. Real-time experiments using an HCV subgenomic system to quantify viral replication confirm replication regulation for each covariant pair between 5′UTR243 and NS2-41, -76, -110, -211, and NS3-71, -175. The HCV subgenomic system with/without the NS2 region shows that regulatory effects vanish without NS2, so replicative modulation mediated by HCV 5′UTR243 depends on NS2. Strong binding of the NS2 variants to HCV RNA correlates with reduced HCV replication whereas weak binding correlates with restoration of HCV replication efficiency, as determined by RNA-protein immunoprecipitation assay band intensity. The dominant haplotype 5′UTR243-NS2-41-76-110-211-NS3-71-175 differs according to the HCV genotype: G-Ile-Ile-Ile-Gly-Ile-Met for genotype 1b and A-Leu-Val-Leu-Ser-Val-Leu for genotypes 1a, 2a and 2b. In conclusion, 5′UTR243 co-varies with specific NS2/3 protein amino acid residues, which may have significant structural and functional consequences for HCV replication. This unreported mechanism involving HCV replication possibly can be exploited in the development of advanced anti-HCV medication.

C*-algebras of generalized Hecke pairs

Abstract We generalize the concept of Hecke pairs and study representations of the corresponding C*-algebra. We introduce the notions of covariant pairs and matrix unit pairs of representations in this general setting and show that covariant pairs are exactly faithful matrix unit pairs.

Darboux covariant Lax pairs and infinite conservation laws of the (2+1)-dimensional breaking soliton equation

In this paper, the binary Bell polynomials are applied to succinctly construct bilinear formulism, bilinear Bäcklund transformations, Lax pairs, and Darboux covariant Lax pairs for the (2+1)-dimensional breaking soliton equation. An extra auxiliary variable is introduced to get the bilinear formulism. The infinitely local conservation laws of the equation are found by virtue of its Lax equation and a generalized Miura transformation. All conserved densities and fluxes are given with explicit recursion formulas.