Equivalent Pairs Research Articles

Composite and shaped pulses for efficient and robust pumping of disconnected eigenstates in magnetic resonance

Hyperpolarization methods, which can enhance nuclear spin signals by orders of magnitude, open up important new opportunities in magnetic resonance. However, many of these applications are limited by spin lattice relaxation, which typically destroys the hyperpolarization in seconds. Significant lifetime enhancements have been found with "disconnected eigenstates" such as the singlet state between a pair of nearly equivalent spins, or the "singlet-singlet" state involving two pairs of chemically equivalent spins; the challenge is to populate these states (for example, from thermal equilibrium magnetization or hyperpolarization) and to later recall the population into observable signal. Existing methods for populating these states are limited by either excess energy dissipation or high sensitivity to inhomogeneities. Here we overcome the limitations by extending recent work using continuous-wave irradiation to include composite and adiabatic pulse excitations. Traditional composite and adiabatic pulses fail completely in this problem because the interactions driving the transitions are fundamentally different, but the new shapes we introduce can move population between accessible and disconnected eigenstates over a wide range of radio-frequency (RF) amplitudes and offsets while depositing insignificant amounts of power.

Electrophysiological investigation of the functional overlap between semantic and equivalence relations.

research using the event-related potential (ERP) technique has shown that equivalence relations have properties similar to genuine semantic relations. This study aimed to advance electrophysiological investigations of the functional overlap between semantic and equivalence relations. The N400 component, an index of semantic processing, was used to measure whether semantic relations were experimentally established between arbitrary stimuli. The stimuli became equivalent via a matching-to-sample training designed to maximize the establishment of equivalence relations and the strength of the classes. Non-equivalent pairs of stimuli elicited larger N400 responses than equivalent pairs in electrodes placed over the central and parietal scalp regions, providing additional support for the assumption that stimulus equivalence is an appropriate model of semantic relations. Latency of the N400 component was shorter than in previous studies, probably due to experimental parameters that maximized relational strength. These data raise the possibility that N400 latency may provide a continuous measure of relational strength, thus supplementing the all-or-none character of equivalence tests based on matching to sample.

Equivalent pairs of words and points of connection.

Higman has defined coset diagrams for PGL(2, ℤ). The coset diagrams are composed of fragments, and the fragments are further composed of two or more circuits. A condition for the existence of a certain fragment γ in a coset diagram is a polynomial f in ℤ[𝔃], obtained by choosing a pair of words F[w i, w j] such that both w i and w j fix a vertex v in γ. Two pairs of words are equivalent if and only if they have the same polynomial. In this paper, we find distinct pairs of words that are equivalent. We also show there are certain fragments, which have the same orientations as those of their mirror images.

Biphoton manipulation with a fiber-based pulse shaper

We demonstrate spectral shaping of entangled photons in the telecom band with a programmable, fiber-based optical filter. The fine-resolution spectral control permits implementation of length-40 Hadamard codes, through which we are able to verify frequency anticorrelation with a 20-fold increase in total counts over that permitted by the equivalent pair of monochromators at the same input flux. By programming the complex spectral transmission function corresponding to a Mach-Zehnder interferometer, we also construct variations on Franson interferometers that are free from mechanical instabilities, demonstrating spectral phase independence in the slow-detector limit, in which all temporal features are unobservable. Our configuration furnishes a single, compact arrangement for manipulating telecom biphotons and characterizing their quality.

Tetranomial Thue equations

Let F ( x , y ) be an irreducible binary form of degree n ⩾ 6 with exactly four nonzero terms. Assuming certain conditions relating the coefficients and the degrees of the different terms are satisfied, we prove upper bounds on the number of equivalent pairs of nontrivial solutions of the Thue equation | F ( x , y ) | = 1 . Improved bounds are provided for a variety of cases, where more information about the form is known.

2,6-Dinitrobenzoic acid and its 2 : 1 salts formed with isomeric n-({[(pyridin-1-ium-n-ylmethyl)carbamoyl]formamido}methyl) pyridin-1-ium, n = 2, 3 and 4

Abstract The co-crystallisation of two equivalents of 2,6-dinitrobenzoic acid (1) with one equivalent of a member of the isomeric N,N′-bis(pyridin-n-ylmethyl)ethanediamides, n = 2, 3 and 4, resulted in the anticipated 2 : 1 salts, 2–4. The central core, i.e. CH2N(H)C(=O)C(=O)N(H)CH2, of the isomeric di-cations are superimposable and chemically equivalent pairs of carbonyl, amide and pyridinium groups have an anti conformation. By contrast, the relative orientations of the terminal pyridinium rings from the central core vary significantly across the series as do the relative disposition of the acidic-H atoms. This feature of the structure influences the nature of N—H…O hydrogen bonding and, therefore, the observed supramolecular aggregation patterns. Thus, in 2, the syn-disposition of the nitrogen-bound hydrogen atoms enables the benzoate residue to interact via the two oxygen atoms with both pyridinium- and amine-H atoms to yield a zero-dimensional aggregate. By contrast, in each of 3 and 4, having further distance between the acidic-H atoms, the benzoate residues still interact (either through one both or both oxygen atoms) with pyridinium- and amine-H atoms but those derived from symmetry related molecules to generate one-dimensional aggregates. The three-dimensional architectures of 1–3 are consolidated, in the main, by C—H…O interactions. The structure of 1 revealed the benzoic acid residue to be perpendicular in contrast to the co-planar conforämations of the nitro groups. In the crystal packing, O–H…O hydrogen bonding lead to a helical supramolecular chain.

New de-embedding structures for extracting the electrical parameters of a through-silicon-via pair

Two innovative de-embedding methods are proposed for extracting an electrical model for a through-silicon-via (TSV) pair consisting of a ground-signal (GS) structure. In addition, based on microwave network theory, a new solution scheme is developed for dealing with multiple solutions of the transfer matrix during the process of de-embedding. A unique solution is determined based on the amplitude and the phase characteristic of S parameters. In the first de-embedding method, a typical “π“ type model of the TSV pair is developed, which illustrates the need to allow for frequency dependence in the equivalent TSV pair Spice model. This de-embedding method is shown to be effective for extracting the electrical properties of the TSVs. The feasibility of a second de-embedding method is also investigated.

A simplified regimen for focal radiofrequency ablation of Barrett's mucosa: a randomized multicenter trial comparing two ablation regimens

The currently recommended regimen for focal radiofrequency ablation (RFA) of Barrett's esophagus (BE) comprises 2 applications of energy, cleaning of the device and ablation zone, and 2 additional applications of energy. A simplified regimen may be of clinical utility if it is faster, easier, and equally safe and effective. To compare the efficacy of 2 focal RFA regimens. Three tertiary referral centers. Consecutive patients scheduled for focal RFA of BE with flat type BE with at least 2 BE islands or mosaic groups of islands were enrolled. BE areas were paired: 1 area was randomized to the "standard" regimen (2 × 15 J/cm(2)-clean-2 × 15 J/cm(2)) or to the "simplified" regimen (3 × 15 J/cm(2)-no clean), allocating the second area automatically to the other regimen. The percentage of surface area regression of each area was scored at 2 months by the endoscopist (blinded). Proportion of completely removed BE areas at 2 months. Calculated sample size was 46 pairs of BE areas using a noninferiority design. Noninferiority was defined as <20% difference in the paired proportions. Forty-five equivalent pairs of BE areas were included in 41 patients. The proportion of completely removed BE areas at 2 months after focal RFA was 30 (67%) for standard and 33 (73%) for simplified. Noninferiority was demonstrated by a 7% difference (95% CI, -10.6 to +20.9). Tertiary referral centers. The results of this multicenter randomized trial suggest that a simplified 3 × 15 J/cm(2) focal ablation regimen is not inferior to the standard regimen, regarding the endoscopic removal of residual Barrett islands.

Quantification of local geometry and local symmetry in models of disordered materials

Abstractmagnified imageWe suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first metric is that of geometric invariance: i.e., the extent to which the neighbour arrangements are as similar as possible for different atoms, allowing for variations in frame of reference. The second metric concerns the degree of local symmetry. We propose that for a set of configurations with equivalent pair correlations, ranking highly those configurations with low geometric invariance but with high local symmetry selects for structural simplicity in a way that does not rely on formal group theoretical language (and hence long‐range periodic order). We show that these metrics rank a range of SiO2 and a‐Si configurations in an intuitive manner, and are also significantly more sensitive to unphysical features of those configurations in a way that metrics based on pair correlations are not. We also report that implementation of the metrics within a reverse Monte Carlo (RMC) algorithm gives rise to an energy landscape that is too coarse (at least in this initial implementation) for amorphous structure ‘solution’.

Coarse-Graining Provides Insights on the Essential Nature of Heterogeneity in Actin Filaments

Experiments have shown that actin is structurally polymorphic, but knowledge of the details of molecular level heterogeneity in both the dynamics of a single subunit and the interactions between subunits is still lacking. Here, using atomistic molecular dynamics simulations of the actin filament, we identify domains of atoms that move in a correlated fashion, quantify interactions between these domains using coarse-grained (CG) analysis methods, and perform CG simulations to explore the importance of filament heterogeneity. The persistence length and torsional stiffness calculated from molecular dynamics simulation data agree with experimental values. We additionally observe that distinct actin conformations coexist in actin filaments. The filaments also exhibit random twist angles that are broadly distributed. CG analysis reveals that interactions between equivalent CG pairs vary from one subunit to another. To explore the importance of heterogeneity on filament dynamics, we perform CG simulations using different methods of parameterization to show that only by including heterogeneous interactions can we reproduce the twist angles and related properties. Free energy calculations further suggest that in general the actin filament is best represented as a set of subunits with differing CG sites and interactions, and the incorporating heterogeneity into the CG interactions is more important than including that in the CG sites. Our work therefore presents a systematic method to explore molecular level detail in this large and complex biopolymer.

Orthorhombic polymorph of (2E)-2-(2,3-dihydro-1H-inden-1-ylidene)-2,3-dihydro-1H-inden-1-one

The title compound, C18H14O, is polymorphic at 123 K. The ortho­rhom­bic form reported herein has two independent mol­ecules in the asymmetric unit, with mol­ecular volume 313.5 Å3. The previously reported triclinic (P-1) form [Raston & Scott (2000 ▶). Green Chem., 2, 49–52] has mol­ecular volume 309.6 Å3 at the same temperature. All three mol­ecules deviate significantly and systematically from the putative Cs symmetry (δr.m.s. = 0.0265, 0.0256, 0.0497 Å). Comparison of the two molecules in the orthorhombic polymorph shows that 16 of the 19 equivalent pairs of framework atoms have a mirror-image pattern of deviations (above/below plane), suggesting that the two are quasi-enanti­omorphs. The pattern of deviations in the triclinic form is nearly the same (13 of 19 atom pairs) as the ortho­rhom­bic form.

The Chirality of a Twist–Bend Nematic Phase Identified by NMR Spectroscopy

One of the defining characteristics of the twist-bend nematic phase, formed by the methylene-linked liquid crystal dimer 1″,7″-bis(4-cyanobiphenyl-4'-yl) heptane (CB7CB), is its chirality. This new nematic phase, predicted by Dozov, is of particular interest because although the constituent molecules are achiral the phase itself is chiral. Here, we describe the use of NMR spectroscopy to determine experimentally whether in reality the phase is chiral or not. The basis of this novel procedure is that the equivalence of the protons or deuterons in a prochiral methylene group in a nematic phase with D∞h symmetry is lost in a chiral phase because its symmetry is reduced to D∞ on removal of the mirror plane. Recording proton-enhanced local field (PELF) NMR experiments shows that in the standard nematic phase all of the methylene groups in the heptane spacer have equivalent pairs of C-H groups but this equivalence is lost for the six prochiral methylene groups with their enantiotopic protons on passing to the twist-bend nematic. Strikingly, this equivalence is not lost for the central methylene group where the two protons are homotopic. We also show how the phase chirality can be demonstrated with probe molecules which contain deuteriated prochiral methylene groups, using 4-octyl-4'-cyanobiphenyl-d2, perdeuteroacenaphthene-d10, and acenaphthene-d4 as examples. For the standard nematic phase deuterium, NMR shows that the deuterons in these methylene groups are equivalent but, as expected, in the twist-bend nematic phase this equivalence is lost. The deuterium NMR spectra of these probe molecules dissolved in CB7CB have been recorded from the isotropic phase, through the nematic and deep into the supercooled twist-bend nematic.

Reformulation of strain invariants at incompressibility

The description of (quasi-)incompressible materials such as elastomers is well established in modern continuum mechanics for many years now as well as from a theoretical background as in the numerical implementation in commercial software packages in the context of finite elements. Nevertheless, some questions arise in the practical application of that matter describing technical components, e.g., in the discussion What are valid equivalent measures in order to compare different deformations? Here, one could request for expressions that arise in a deformation intensity and an indication of the deformation mode locally at each material point. We propose an extension of the well-known description of incompressible kinematics. We reformulate the strain invariants at incompressibility in terms of (I 1, I 2) leading to an equivalent pair (λ, m) in order to determine a distance of an arbitrary deformation state, e.g., to its equivalent shearing state. Therefore, we postulate and define an associated deformation state and give the mathematical derivation of quite nice relationships, which we demonstrate on a shear example using the finite elements method to visualize the “new” measure quantity.

Enhancement of Initial Equivalency for Protein Structure Alignment Based on Encoded Local Structures

Most alignment algorithms find an initial equivalent residue pair followed by an iterative optimization process to explore better near-optimal alignments in the surrounding solution space of the initial alignment. It plays a decisive role in determining the alignment quality since a poor initial alignment may make the final alignment trapped in an undesirable local optimum even with an iterative optimization. We proposed a vector-based alignment algorithm with a new initial alignment approach accounting for local structure features called MIRAGE-align. The new idea is to enhance the quality of the initial alignment based on encoded local structural alphabets to identify the protein structure pair whose sequence identity falls in or below twilight zone. The statistical analysis of alignment quality based on Match Index (MI) and computation time demonstrated that MIRAGE-align algorithm outperformed four previously published algorithms, i.e., the residue-based algorithm (CE), the vector-based algorithm (SSM), TM-align, and Fr-TM-align. MIRAGE-align yields a better estimate of initial solution to enhance the quality of initial alignment and enable the employment of a non-iterative optimization process to achieve a better alignment.

Topology of septics with the set of singularities [formula omitted] and [formula omitted]-equivalent weak Zariski pairs

We study the topology of the moduli space of septics with the set of singularities B4,4⊕2A3⊕5A1. In particular, we construct a new π1-equivalent weak Zariski pair.

Volovik effect on NMR measurements of unconventional superconductors

We studied the Volovik effect on the NMR measurements of the two unconventional superconducting (SC) states, the d-wave and $\pm$s-wave states. We showed the generic field dependencies of the spin-lattice relaxation rate $1/T_1$ and Knight shift $K$ at low temperature limit in the pure cases as: $1/T_1 \propto H \log H$, $K \propto \sqrt{H}$ for the d-wave, and $1/T_1 \propto H$, $K \propto H$ for the $\pm$s-wave state, respectively. Performing numerical calculations we showed that these generic power laws survive for the good part of low field region with the realistic amount of impurities. We also found that the Volovik effect acts as an equivalent pair breaker as the unitary impurity scattering, hence induces the same temperature evolutions on $1/T_1$ and $K$, respectively, as the unitary impurities in both SC states. This finding implies that the Volovik effect should always be taken into account for the analysis of the NMR measurements in the mixed state.

Nonlinear damping calculation in cylindrical gear dynamic modeling

The nonlinear dynamic problem posed by cylindrical gear systems has been extensively covered in the literature. Nonetheless, a significant proportion of the mechanisms involved in damping generation remains to be investigated and described. The main objective of this study is to contribute to this task. Overall, damping is assumed to consist of three sources: surrounding element contribution, hysteresis of the teeth, and oil squeeze damping. The first two contributions are considered to be commensurate with the supported load; for its part however, squeeze damping is formulated using expressions developed from the Reynolds equation. A lubricated impact analysis between the teeth is introduced in this study for the minimum film thickness calculation during contact losses. The dynamic transmission error (DTE) obtained from the final model showed close agreement with experimental measurements available in the literature. The nonlinear damping ratio calculated at different mesh frequencies and torque amplitudes presented average values between 5.3 percent and 8 percent, which is comparable to the constant 8 percent ratio used in published numerical simulations of an equivalent gear pair. A close analysis of the oil squeeze damping evidenced the inverse relationship between this damping effect and the applied load.

Technical importance ratings in fuzzy QFD by integrating fuzzy normalization and fuzzy weighted average

Fuzzy quality function deployment (QFD) has been extensively used for translating customer requirements (CRs) into product design requirements (DRs) in fuzzy environments. Existing approaches, however, for rating technical importance of DRs in fuzzy environments are found problematic, either incorrect or inappropriate. This paper investigates how the technical importance of DRs can be correctly rated in fuzzy environments. A pair of nonlinear programming models and two equivalent pairs of linear programming models are developed, respectively, to rate the technical importance of DRs. The developed models are examined and illustrated with two numerical examples.

Pathological Element-Based Active Device Models and Their Application to Symbolic Analysis

This paper proposes new pathological element-based active device models which can be used in analysis tasks of linear(ized) analog circuits. Nullators and norators along with the voltage mirror-current mirror (VM-CM) pair (collectively known as pathological elements) are used to model the behavior of active devices in voltage-, current-, and mixed-mode, also considering parasitic elements. Since analog circuits are transformed to nullor-based equivalent circuits or VM-CM pairs or as a combination of both, standard nodal analysis can be used to formulate the admittance matrix. We present a formulation method in order to build the nodal admittance (NA) matrix of nullor-equivalent circuits, where the order of the matrix is given by the number of nodes minus the number of nullors. Since pathological elements are used to model the behavior of active devices, we introduce a more efficient formulation method in order to compute small-signal characteristics of pathological element-based equivalent circuits, where the order of the NA matrix is given by the number of nodes minus the number of pathological elements. Examples are discussed in order to illustrate the potential of the proposed pathological element-based active device models and the new formulation method in performing symbolic analysis of analog circuits. The improved formulation method is compared with traditional formulation methods, showing that the NA matrix is more compact and the generation of nonzero coefficients is reduced. As a consequence, the proposed formulation method is the most efficient one reported so far, since the CPU time and memory consumption is reduced when recursive determinant-expansion techniques are used to solve the NA matrix.

Identifying Bilingual Synonymous Technical Terms from Phrase Tables and Parallel Patent Sentences

In the task of acquiring technical term translation equivalent pairs, we consider situations where a technical term is observed in many parallel patent sentences and is translated into many translation equivalents. This paper especially studies the issue of identifying synonymous translation equivalent pairs of technical terms. First, we collect candidates of synonymous translation equivalent pairs from parallel patent sentences. Then, we analyze features for identifying synonymous translation equivalent pairs. Finally, we apply the Support Vector Machines (SVMs) to the task of identifying bilingual synonymous technical terms, and achieve the performance of almost 98% precision and over 40% F-measure.