Biorthogonality Condition Research Articles

Innovative Peptide Bioconjugation Chemistry with Radionuclides: Beyond Classical Click Chemistry.

Background: The incorporation of radionuclides into peptides and larger biomolecules requires efficient and sometimes biorthogonal reaction conditions, to which click chemistry provides a convenient approach. Methods: Traditionally, click-based radiolabeling techniques have focused on classical click chemistry, such as copper(I)-catalyzed alkyne-azide [3+2] cycloaddition (CuAAC), strain-promoted azide-alkyne [3+2] cycloaddition (SPAAC), traceless Staudinger ligation, and inverse electron demand Diels-Alder (IEDDA). Results: However, newly emerging click-based radiolabeling techniques, including tyrosine-click, sulfo-click, sulfur(VI) fluoride exchange (SuFEx), thiol-ene click, azo coupling, hydrazone formations, oxime formations, and RIKEN click offer valuable alternatives to classical click chemistry. Conclusions: This review will discuss the applications of these techniques in peptide radiochemistry.

DGT-based pulse shaping filter for Generalized Frequency Division Multiplexing system

The future wireless communication systems belonging to the next generation will encounter many diverse demands, like the need for data rates that surpass the capabilities of fifth-generation networks, ultra-low power consumption to cater to battery-operated communication sensors, and extremely short response times essential for control applications. A unified physical layer waveform is envisaged to address these flexible requirements, introduced as Generalized Frequency Division Multiplexing (GFDM) for beyond 5G (B5G) communication systems. One of the important features of GFDM is the utilization of flexible pulse shaping filtering in the time domain, resulting in improved performance. In this paper, a pulse-shaping filter is designed for the GFDM system using discrete Gabor representation, discrete biorthogonality condition and Wigner distribution. An analytical expression for the analysis window is derived using the biorthogonality condition. Further, the performance of the GFDM system is analyzed in terms of out-of-band (OOB) radiation and symbol error rate (SER). The results are presented for the Quadrature Amplitude Modulation (QAM) scheme over Additive White Gaussian Noise (AWGN), Rayleigh, Nakagami-m, two wave with diffuse power (TWDP), and Nakagami-q fading channels. The detailed analysis shows that the OOB radiation and SER performance exhibit strong dependence on the choice of the pulse shaping filter.

Dual Space Latent Representation Learning for Image Representation

Semi-supervised non-negative matrix factorization (NMF) has achieved successful results due to the significant ability of image recognition by a small quantity of labeled information. However, there still exist problems to be solved such as the interconnection information not being fully explored and the inevitable mixed noise in the data, which deteriorates the performance of these methods. To circumvent this problem, we propose a novel semi-supervised method named DLRGNMF. Firstly, dual latent space is characterized by the affinity matrix to explicitly reflect the interrelationship between data instances and feature variables, which can exploit the global interconnection information in dual space and reduce the adverse impacts caused by noise and redundant information. Secondly, we embed the manifold regularization mechanism in the dual graph to steadily retain the local manifold structure of dual space. Moreover, the sparsity and the biorthogonal condition are integrated to constrain matrix factorization, which can greatly improve the algorithm’s accuracy and robustness. Lastly, an effective alternating iterative updating method is proposed, and the model is optimized. Empirical evaluation on nine benchmark datasets demonstrates that DLRGNMF is more effective than competitive methods.

Analytical solution and flow topology in a lid-driven S-shaped cavity

In this study, the Stokes flow problem in an S-shaped double lid-driven cavity filled with fluid was analyzed. Side edges of the cavity were considered as immovable walls. The flow region was divided into two sub-regions, and the streamfunction in each sub-region was considered as an extension of Papkovich–Faddle eigenfunctions. Parameters in the analytical solution were obtained using biorthogonality conditions. The Newton iteration method was used to obtain the eigenvalues of the problem, and integrals were calculated with the Gaussian quadrature method. It was ensured that solutions made separately for the two sub-regions converge on the interface, which is the intersection of these sub-regions. The two parameters controlling the flow structure were determined as the speed ratio of movable lids (S) and the aspect ratio of the cavity (A). The effects of these parameters on flow structures were shown. New eddy formation mechanisms and bifurcations were observed in the cavity by keeping the speed ratio of the lids constant and slowly changing the aspect ratio.

A Design of Spectrally-Efficient Low-Complexity QAM-FBMC Systems With Mismatched Prototype Filters

In this article, we propose a low-complexity quadrature amplitude modulation (QAM) filter-bank multicarrier (FBMC) system with high spectral efficiency and low self-interference. To circumvent the limitations imposed by the Balian-Low theorem on the interference suppression capability of QAM-FBMC systems, the proposed system relaxes time-frequency (TF) product at the transmitter (TX) and time-domain localization at the receiver (RX). The PHYDYAS filter is employed as a TX prototype filter, and a filter mismatched to the TX filter is employed as an RX prototype filter. Since the PHYDYAS filter has excellent spectral confinement, its use well compensates for the loss in TF-product and leads to higher spectral efficiency than the conventional systems in multi-user uplink. The RX has an extended observation window and a separate equalizer followed by a fixed pre-computed filter. To find the RX prototype filter that minimizes the self-interference, an optimization problem is formulated based on a bi-orthogonality condition, subject to the frequency-domain sparsity constraint in terms of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{0}$</tex-math></inline-formula> -norm. To efficiently search for the solution, a modified relaxed LASSO procedure is proposed, where the size of the problem is reduced to make the problem numerically tractable. Numerical results and discussions show that the proposed QAM-FBMC system strikes an excellent balance between performance and complexity.

A contact algorithm for cohesive cracks in the extended finite element method

SummaryCracks with quasibrittle behavior are extremely common in engineering structures. The modeling of cohesive cracks involves strong nonlinearity in the contact, material, and complex transition between contact and cohesive forces. In this article, we propose a novel contact algorithm for cohesive cracks in the framework of the extended finite element method. A cohesive‐contact constitutive model is introduced to characterize the complex mechanical behavior of the fracture process zone. To avoid the stress oscillations and ill‐conditioned system matrix that often occur in the conventional contact approach, the proposed algorithm employs a special dual Lagrange multiplier to impose the contact constraint. This Lagrange multiplier is constructed by means of the area‐weighted average and biorthogonality conditions at the element level. The system matrix can be condensed into a positive definite matrix with an unchanged size at a very low computational cost. In addition, we illustrate solving the cohesive crack contact problem using a novel iteration strategy. Several numerical experiments are performed to illustrate the efficiency and high‐quality results of our method in contact analysis of cohesive cracks.

Interference Cancellation and Iterative Detection for Orthogonal Time Frequency Space Modulation

The recently proposed orthogonal time–frequency–space (OTFS) modulation technique was shown to provide significant error performance advantages over orthogonal frequency division multiplexing (OFDM) over delay-Doppler channels. In this paper, we first derive the explicit input–output relation describing OTFS modulation and demodulation (mod/demod). We then analyze the cases of: 1) ideal pulse-shaping waveforms that satisfy the bi-orthogonality conditions and 2) rectangular waveforms which do not. We show that while only inter-Doppler interference (IDI) is present in the former case, additional inter-carrier interference (ICI) and inter-symbol interference (ISI) occur in the latter case. We next characterize the interferences and develop a novel low-complexity yet efficient message passing (MP) algorithm for joint interference cancellation (IC) and symbol detection. While ICI and ISI are eliminated through appropriate phase shifting, IDI can be mitigated by adapting the MP algorithm to account for only the largest interference terms. The MP algorithm can effectively compensate for a wide range of channel Doppler spreads. Our results indicate that OTFS using practical rectangular waveforms can achieve the performance of OTFS using ideal but non-realizable pulse-shaping waveforms. Finally, simulation results demonstrate the superior error performance gains of the proposed uncoded OTFS schemes over OFDM under various channel conditions.

Non-Hermiticity and conservation of orthogonal relation in dielectric microcavity

Non-Hermitian properties of open quantum systems and their applications have attracted much attention in recent years. While most of the studies focus on the characteristic nature of non-Hermitian systems, here we focus on the following issue: A non-Hermitian system can be a subsystem of a Hermitian system as one can clearly see in Feshbach projective operator (FPO) formalism. In this case, the orthogonality of the eigenvectors of the total (Hermitian) system must be sustained, despite the eigenvectors of the subsystem (non-Hermitian) satisfy the bi-orthogonal condition. Therefore, one can predict that there must exist some remarkable processes that relate the non-Hermitian subsystem and the rest part, and ultimately preserve the Hermiticity of the total system. In this paper, we study such processes in open elliptical microcavities. The inner part of the cavity is a non-Hermitian system, and the outer part is the coupled bath in FPO formalism. We investigate the correlation between the inner- and the outer-part behaviors associated with the avoided resonance crossings (ARCs), and analyze the results in terms of a trade-off between the relative difference of self-energies and collective Lamb shifts. These results come from the conservation of the orthogonality in the total Hermitian quantum system.

Propagation of Natural Waves on Plates of a Variable Cross Section

In this paper, a conjugate spectral problem and biorthogonality conditions for the problem of extended plates of variable thickness are constructed. A technique for solving problems and numerical results on the propagation of waves in infinite extended viscoelastic plates of variable thickness is described. The viscous properties of the material are taken into account using the Voltaire integral operator. The investigation is carried out within the framework of the spatial theory of viscoelasticity. The technique is based on the separation of spatial variables and the formulation of a boundary value problem for Eigen values which are solved by the Godunov orthogonal sweep method and the Muller method. Numerical values of the real and imaginary parts of the phase velocity are obtained depending on the wave numbers. In this case, the coincidence of numerical results with known data is obtained.

A POD-Based Procedure for the Split of Unsteady Losses of an LPT Cascade

A time-resolved particle image velocimetry (TR-PIV) system has been employed to investigate the unsteady propagation of upstream wakes in a low-pressure turbine cascade. Data are obtained in the steady state condition and for two passing wake reduced frequencies. The study is focused on the identification and split of the different dynamics responsible for deterministic and random oscillations, thus loss generation by means of a new procedure based on proper orthogonal decomposition (POD). The paper takes advantage of the properties of POD that reduce the data set to a low number of modes that represent the most energetic dynamics of the system. It is clearly shown that the phase averaged flow field can be represented by a few number of POD modes related to the wake passing event for the unsteady cases. Proper orthogonal decomposition is also able to capture flow features affecting the instantaneous flow field not directly related to the wake passage (i.e., the vortex shedding phenomenon induced by the intermittent separation developing between adjacent wakes), which are smeared out in the phase averaged results. A procedure exploiting the biorthogonality condition of the POD modes, and the related temporal coefficients, has been developed for the quantification of the contribution due to the different POD modes to the overall turbulence kinetic energy production, or, equivalently, the mean flow energy dissipation rate. Results into the paper clearly show that losses due to wake migration, boundary layer and vortex shedding related phenomena can be distinguished and separately quantified for the different tested conditions.

The boundary integral equations method for analysis of high-frequency vibrations of an elastic layer

The boundary integral equations are derived in the framework of the analytical five-mode models for propagation of symmetric and skew-symmetric waves in a straight elastic layer of the constant thickness. The forcing problems for fundamental loading cases are solved with the bi-orthogonality conditions employed. By these means, the Green’s matrices are constructed. The derivation of the Somigliana’s identities for the five-mode models is presented. To exemplify application of the method of boundary integral equations, eigenfrequencies of a layer of the finite length are found for two sets of boundary conditions. In the course of analysis, the essential features and advantages of the method are highlighted. The isogeometric analysis at several approximation levels and the standard finite element software are also used to calculate the eigenfrequencies. The results obtained by alternative methods are shown to be in an excellent agreement with each other.

Lifting‐based design of two‐channel biorthogonal graph filter bank

In this study, the lifting scheme is first employed to design two-channel biorthogonal graph filter bank. The biorthogonal condition is parameterised by imposing a single-level lifting structure on the analysis and synthesis graph kernels. Based on the parametric structure, the two kernels are separately optimised by constrained quadratic programming. The obtained two-channel biorthogonal graph filter banks are of structurally perfect reconstruction. Numerical results and comparison are included to show the proposed algorithm can lead to biorthogonal graph filter banks with improved performance.

Behavior of Gabor frame operators on Wiener amalgam spaces

It is well-known that the Gabor expansions converge to identity operator in weak* sense on the Wiener amalgam spaces as sampling density tends to infinity. In this paper, we prove the convergence of Gabor expansions to identity operator in the operator norm as well as weak* sense on [Formula: see text] as the sampling density tends to infinity. Also we show the validity of the Janssen’s representation and the Wexler–Raz biorthogonality condition for Gabor frame operator on [Formula: see text].

Azidopropylvinylsulfonamide as a New Bifunctional Click Reagent for Bioorthogonal Conjugations: Application for DNA-Protein Cross-Linking.

N-(3-Azidopropyl)vinylsulfonamide was developed as a new bifunctional bioconjugation reagent suitable for the cross-linking of biomolecules through copper(I)-catalyzed azide-alkyne cycloaddition and thiol Michael addition reactions under biorthogonal conditions. The reagent is easily clicked to an acetylene-containing DNA or protein and then reacts with cysteine-containing peptides or proteins to form covalent cross-links. Several examples of bioconjugations of ethynyl- or octadiynyl-modified DNA with peptides, p53 protein, or alkyne-modified human carbonic anhydrase with peptides are given.

Dynamic analysis of a hollow cylinder subject to a dual traveling force imposed on its inner surface

The dynamic behavior of a hollow cylinder under a dual traveling force applied to the inner surface is investigated in this study. The cylinder is constrained at both the top and bottom surfaces not to move in the length direction but free in other directions. And a dual force travels at a constant velocity along the length direction on the inner surface of the hollow cylinder. The resulting governing field equations and the associated boundary conditions are ruled by the general Hooke׳s law. Due to the nature of the field equations, proper adjoint system of equations and biorthogonality conditions were derived in a precise and detailed manner. To solve these field equations in this study, the method of separation of variable is used and the method of Fro¨benius is employed for the differential equations in the radial direction. Using the field equations, the eigenanalyses on both the original and its adjoint system were performed with great care, which results in the eigenfunction sets of both systems. The biorthogonality conditions were applied to the field equations to obtain the discretized equation for each mode. Using the solutions of the discretized equations that account for the boundary forcing terms, the critical speed for a dual traveling force for each mode could be computed.

Generalized Gabor expansion associated with linear canonical transform series

The Gabor expansion (GE), which maps the time domain signal into the joint time and frequency domain, has been recognized as very useful for signal processing. However, sinusoidal analysis used in the traditional GE is not appropriate for a compact representation for chirp-type signals. In this paper, a generalized Gabor expansion (GGE) is proposed in order to rectify the limitations of the GE, the proposed expansion not only inherits the advantage of GE, but also has the capability of signal representations in the linear canonical transform (LCT) domain which is similar to the LCT. Basis functions of the proposed expansion are obtained via LCT basis. Compared with the traditional GE, the GGE can offer signal representations on a general, non-rectangular time–frequency plane tiling. Besides, the completeness and biorthogonality conditions of the GGE are derived.

A hierarchy of high-order theories for symmetric modes in an elastic layer

Abstract A hierarchy of high-order theories for symmetric modes in an infinitely long elastic layer of the constant thickness is derived by means of the inertia-corrected polynomial approximations. For each member of the hierarchy, boundary conditions for layers of the finite length are formulated. The forcing problems at several approximation levels are solved with the use of the bi-orthogonality conditions. Accuracy of these approximations is assessed by comparison of results with the exact solution of the Rayleigh–Lamb problem. Special attention is paid to the power flow analysis in alternative modal excitation cases and to the applicability of the Saint-Venant׳s principle in stationary elasto-dynamics.

Asymptotic zero distribution of biorthogonal polynomials

Let ψ:[0,1]→R be a strictly increasing continuous function. Let Pn be a polynomial of degree n determined by the biorthogonality conditions ∫01Pn(x)ψ(x)jdx=0,j=0,1,…,n−1. We study the distribution of zeros of Pn as n→∞, and related potential theory.

On the bi-orthogonality conditions for multi-modal elastic waveguides

The bi-orthogomality conditions in terms of generalised forces and displacements are derived from the reciprocity relations for a hierarchy of elastic waveguides, which support several travelling and evanescent modes (free waves). In the simple cases of waves in a straight beam and axisymmetric waves in a thin elastic cylindrical shell, these conditions are formulated as identities in an explicit form via wavenumbers. The forced vibrations of these waveguides under localised excitation are also considered with these identities being employed. The bi-orthogonality conditions in more advanced cases, specifically, for non-axisymmetric waves in an elastic cylindrical shell and for waves in an elastic helical spring, are derived, but not presented in an explicit form via wavenumbers. The results obtained for the hierarchy of waveguides are discussed in view of the classical bi-orthogonality conditions for an elastic layer. The grouping of generalised forces and displacements in these conditions is explained by inspection of the response of a given waveguide to the localised excitation.

Dual Quadratic Mortar Finite Element Methods for 3D Finite Deformation Contact

Mortar finite element methods allow for a flexible and efficient coupling of arbitrary nonconforming interface meshes and are by now quite well established in nonlinear contact analysis. In this paper, a mortar method for three-dimensional (3D) finite deformation contact is presented. Our formulation is based on so-called dual Lagrange multipliers, which in contrast to the standard mortar approach generate coupling conditions that are much easier to realize, without impinging upon the optimality of the method. Special focus is set on second-order interpolation and on the construction of novel discrete dual Lagrange multiplier spaces for the resulting quadratic interface elements (8-node and 9-node quadrilaterals, 6-node triangles). Feasible dual shape functions are obtained by combining the classical biorthogonality condition with a simple basis transformation procedure. The finite element discretization is embedded into a primal-dual active set algorithm, which efficiently handles all types of nonlinearities in one single iteration scheme and can be interpreted as a semismooth Newton method. The validity of the proposed method and its efficiency for 3D contact analysis including Coulomb friction are demonstrated with several numerical examples.