Mutual Orthogonality Research Articles

Binary pattern retrieval with Kuramoto-type oscillators via a least orthogonal lift of three patterns

Abstract Given a set of standard binary patterns and a defective pattern, the pattern retrieval task is to find the closest pattern to the defective one among these standard patterns. The Hebbian network of Kuramoto oscillators with second-order coupling provides a dynamical model for this task, and the mutual orthogonality in memorised patterns enables us to distinguish these memorised patterns from most others in terms of stability. For the sake of error-free retrieval for general problems lacking orthogonality, a unified approach was proposed which transforms the problem into a series of subproblems with orthogonality using the orthogonal lift for two patterns. In this work, we propose the least orthogonal lift for three patterns, which evidently reduces the time of solving subproblems and even the dimensions of subproblems. Furthermore, we provide an estimate for the critical strength for stability/instability of binary patterns, which is convenient in practical use. Simulation results are presented to illustrate the effectiveness of the proposed approach.

Sensitivity volume as figure-of-merit for maximizing data importance in electrical impedance tomography

Objective. Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the periphery of a heterogeneous conductor are inverted to map its internal conductivity. The EIT method proposed here aims to improve computational speed and noise tolerance by introducing sensitivity volume as a figure-of-merit for comparing EIT measurement protocols. Approach. Each measurement is shown to correspond to a sensitivity vector in model space, such that the set of measurements, in turn, corresponds to a set of vectors that subtend a sensitivity volume in model space. A maximal sensitivity volume identifies the measurement protocol with the greatest sensitivity and greatest mutual orthogonality. A distinguishability criterion is generalized to quantify the increased noise tolerance of high sensitivity measurements. Main result. The sensitivity volume method allows the model space dimension to be minimized to match that of the data space, and the data importance to be increased within an expanded space of measurements defined by an increased number of contacts. Significance. The reduction in model space dimension is shown to increase computational efficiency, accelerating tomographic inversion by several orders of magnitude, while the enhanced sensitivity tolerates higher noise levels up to several orders of magnitude larger than standard methods.

On the complementary nature of ANOVA simultaneous component analysis (ASCA+) and Tucker3 tensor decompositions on designed multi‐way datasets

AbstractThe complementary nature of analysis of variance (ANOVA) Simultaneous Component Analysis (ASCA+) and Tucker3 tensor decompositions is demonstrated on designed datasets. We show how ASCA+ can be used to (a) identify statistically sufficient Tucker3 models; (b) identify statistically important triads making their interpretation easier; and (c) eliminate non‐significant triads making visualization and interpretation simpler. For multivariate datasets with an experimental design of at least two factors, the data matrix can be folded into a multi‐way tensor. ASCA+ can be used on the unfolded matrix, and Tucker3 modeling can be used on the folded matrix (tensor). Two novel strategies are reported to determine the statistical significance of Tucker3 models using a previously published dataset. A statistically sufficient model was created by adding factors to the Tucker3 model in a stepwise manner until no ASCA+ detectable structure was observed in the residuals. Bootstrap analysis of the Tucker3 model residuals was used to determine confidence intervals for the loadings and the individual elements of the core matrix and showed that 21 out of 63 core values of the 3 × 7 × 3 model were not significant at the 95% confidence level. Exploiting the mutual orthogonality of the 63 triads of the Tucker3 model, these 21 factors (triads) were removed from the model. An ASCA+ backward elimination strategy is reported to further simplify the Tucker3 3 × 7 × 3 model to 36 core values and associated triads. ASCA+ was also used to identify individual factors (triads) with selective responses on experimental factors A, B, or interactions, A × B, for improved model visualization and interpretation.

Resisting Turbulence by Equalizing Frequency-Domain for Multiplexing Orbital Angular Momentum Modes Over a Free Space

Owing to the mutual orthogonality among different orbital angular momentums (OAM), OAM mode has been considered as a promising candidate for improving channel capacity and spectrum efficiency. However, the spiral phase-front of OAM mode is susceptible to atmosphere turbulence (AT) in free pace. The distorted spiral phase induces random noise and signal shake (fluctuation) among symbols and then degrades system performance. In order to overcome the issues, an equalization method in frequency-domain is proposed for mitigating the signal shake induced by the AT. For verifying the feasibility and validity of the proposed concept, the corresponding theoretical analysis and experiments are derived and implanted, respectively. The calculated results demonstrate that the signal shake induced by AT can be effectively mitigated when an optimized estimation response matrix is achieved by using a least squares (LS) algorithm. The bit error rate (BER) and constellation plot (CP) of quadrature amplitude modulation (QAM) signal are also investigated to evaluate the system performance, which demonstrate that the proposed concept can effectively resist the AT in an OAM-based free space optical communication system.

Quintuply orthogonal pyrrolysyl-tRNA synthetase/tRNAPyl pairs.

Mutually orthogonal aminoacyl transfer RNA synthetase/transfer RNA pairs provide a foundation for encoding non-canonical amino acids into proteins, and encoded non-canonical polymer and macrocycle synthesis. Here we discover quintuply orthogonal pyrrolysyl-tRNA synthetase (PylRS)/pyrrolysyl-tRNA (tRNAPyl) pairs. We discover empirical sequence identity thresholds for mutual orthogonality and use these for agglomerative clustering of PylRS and tRNAPyl sequences; this defines numerous sequence clusters, spanning five classes of PylRS/tRNAPyl pairs (the existing classes +N, A and B, and newly defined classes C and S). Most of the PylRS clusters belong to classes that were unexplored for orthogonal pair generation. By testing pairs from distinct clusters and classes, and pyrrolysyl-tRNAs with unusual structures, we resolve 80% of the pairwise specificities required to make quintuply orthogonal PylRS/tRNAPyl pairs; we control the remaining specificities by engineering and directed evolution. Overall, we create 924 mutually orthogonal PylRS/tRNAPyl pairs, 1,324 triply orthogonal pairs, 128 quadruply orthogonal pairs and 8 quintuply orthogonal pairs. These advances may provide a key foundation for encoded polymer synthesis.

Isolated vertices and diameter of the BJ-orthograph in C⁎-algebras

We give necessary and sufficient condition that an element of an arbitrary C⁎-algebra is an isolated vertex of the orthograph related to the mutual strong Birkhoff-James orthogonality. Also, we prove that for all C⁎-algebras except C,C⊕C and M2(C) all non isolated points make a single connected component of the orthograph which diameter is less than or equal to 4, i.e. any two non isolated points can be connected by a path with at most 4 edges. Some related results are given.

Structural, opto-electrical, and band-edge properties of full-series multilayer SnS1-xSex (0≤x≤1) compounds with strong in-plane anisotropy

Two-dimensional (2D) semiconductors with black phosphorus (BP) structure have recently received considerable attention on the realization of polarized optoelectronic device, axial-dependent carrier transport, and asymmetric 2D electronic and energy device owing to the strong in-plane anisotropy presented in the van der Waal plane. In this work, multilayered SnS1-xSex chalcogenides of x = 0, 0.2, 0.4, 0.5, 0.6, 0.8 and x = 1 were grown by chemical vapor transport and then exfoliated on a SiO2/Si substrate for further optical characterization. Polarized micro-Raman experiment and theoretical Raman-mode calculation simultaneously demonstrate strong in-plane anisotropy with the maximum Raman intensity of the armchair (AM) chain vibration mode (Ag) shows mutual orthogonality to the zigzag (ZZ) chain-oriented mode (B1g) in the full-series multilayer SnS1-xSex (0 ≤ x ≤ 1). For the intermediate compositions between x = 0.2 and x = 0.8, a crucial physical mechanism as “symmetry breaking” has been proposed to account for the increased number of separated Ag and B1g modes with different energies as compared to those detected for the binary compounds of orthorhombic SnS and SnSe. For the band-edge anisotropy, the bandgap value of ZZ polarized direction is shown to be lower than that of the AM direction for each of the SnS1-xSex compounds evidenced by polarized-thermoreflectance experiments and first-principles calculations.

Hybrid opto-electronic deep neural network based orbital angular momentum mode recognition scheme in oceanic turbulence

Orbital angular momentum (OAM) has been widely used in underwater wireless optical communication (UWOC) systems due to the mutual orthogonality between modes. However, wavefront distortion caused by oceanic turbulence (OT) on the OAM mode seriously affects its mode recognition and communication quality. In this work, we propose a hybrid opto-electronic deep neural network (HOEDNN) based OAM mode recognition scheme. The HOEDNN model consists of a diffractive DNN (DDNN) and convolutional neural network (CNN), where the DDNN is trained to obtain the mapping between intensity patterns of a distorted OAM mode and intensity distributions without OT interference, and the CNN is used to recognize the output of the DDNN. The diffractive layers of the trained DDNN model are solidified, fabricated, and loaded into a spatial light modulator, and the results recorded by a charge-coupled device camera are processed and fed into the trained CNN model. The results show that the proposed scheme can overcome the interference of OT to OAM modes and recognize accurately azimuthal and radial indices. The OAM mode recognition scheme based on HOEDNN has potential application value in UWOC systems.

Intrinsic anomalous spin Hall effect

Charge-spin interconversion in magnetic materials is investigated by using the first-principles calculations. In addition to the conventional spin Hall effect (SHE) that requires mutual orthogonality of the charge current, spin-flow direction, and spin polarization, the recently proposed anomalous SHE (ASHE) is confirmed in Mn2Au and WTe2. The interaction of the order parameter with conduction electrons leads to sizeable non-zero spin Berry curvatures that give rise to anomalous spin Hall conductivity (ASHC). Our calculations show that the ASHE is intrinsic and originates from the order-parameter-controlled spin-orbit interaction, which generates an extra anomalous effective field. A useful relationship among the order parameter, the spin Berry curvature, and the ASHC is revealed. Our findings provide a new avenue for generating and detecting arbitrary types of spin currents.

Diffraction deep neural network based orbital angular momentum mode recognition scheme in oceanic turbulence

Orbital angular momentum (OAM) has the characteristics of mutual orthogonality between modes, and has been applied to underwater wireless optical communication (UWOC) systems to increase the channel capacity. In this work, we propose a diffractive deep neural network (DDNN) based OAM mode recognition scheme, where the DDNN is trained to capture the features of the intensity distribution of the OAM modes and output the corresponding azimuthal indices and radial indices. The results show that the proposed scheme can recognize the azimuthal indices and radial indices of the OAM modes accurately and quickly. In addition, the proposed scheme can resist weak oceanic turbulence (OT), and exhibit excellent ability to recognize OAM modes in a strong OT environment. The DDNN-based OAM mode recognition scheme has potential applications in UWOC systems.

A Theoretical Analysis of Favorable Propagation on Massive MIMO Channels with Generalized Angle Distributions

Massive MIMO obtains the multiuser performance gain based on the favorable propagation (FP) assumption, defined as the mutual orthogonality of different users’ channel vectors. Until now, most of the theoretical analyses of FP are based on uniform angular distributions and only consider the horizontal dimension. However, the real propagation channel contains full dimensions, and the spatial angle varies with the environment. Thus, it remains unknown whether the FP condition holds in real deployment scenarios and how it impacts the massive MIMO system performance. In this paper, we analyze the FP condition theoretically based on a cluster-based three-dimensional (3D) MIMO channel with generalized angle distributions. Firstly, the FP condition’s unified mathematical expectation and variance expressions with full-dimensional angular integral are given. Since the closed-form expressions are hard to derive, we decompose generalized angle distributions, i.e., wrapped Gaussian (WG), Von Mises (VM), and truncated Laplacian (TL) into the functions of Bessel and Cosine basis by introducing Jacobi-Anger expansions and Fourier series. Thus the closed-form expressions of the FP condition are derived. Based on the above, we theoretically analyze the asymptotically FP condition under generalized angle distributions and then compare the impact of angular spreads on the FP performance. Furtherly, the FP condition is also investigated by numerical simulations and practical measurements. It is observed that environments with larger angle spreads and larger antenna spacing are more likely to realize FP. This paper provides valuable insights for the theoretical analysis of the practical application of massive MIMO systems.

The tRNA discriminator base defines the mutual orthogonality of two distinct pyrrolysyl-tRNA synthetase/tRNAPyl pairs in the same organism.

Site-specific incorporation of distinct non-canonical amino acids into proteins via genetic code expansion requires mutually orthogonal aminoacyl-tRNA synthetase/tRNA pairs. Pyrrolysyl-tRNA synthetase (PylRS)/tRNAPyl pairs are ideal for genetic code expansion and have been extensively engineered for developing mutually orthogonal pairs. Here, we identify two novel wild-type PylRS/tRNAPyl pairs simultaneously present in the deep-rooted extremely halophilic euryarchaeal methanogen Candidatus Methanohalarchaeum thermophilum HMET1, and show that both pairs are functional in the model halophilic archaeon Haloferax volcanii. These pairs consist of two different PylRS enzymes and two distinct tRNAs with dissimilar discriminator bases. Surprisingly, these two PylRS/tRNAPyl pairs display mutual orthogonality enabled by two unique features, the A73 discriminator base of tRNAPyl2 and a shorter motif 2 loop in PylRS2. In vivo translation experiments show that tRNAPyl2 charging by PylRS2 is defined by the enzyme's shortened motif 2 loop. Finally, we demonstrate that the two HMET1 PylRS/tRNAPyl pairs can simultaneously decode UAG and UAA codons for incorporation of two distinct noncanonical amino acids into protein. This example of a single base change in a tRNA leading to additional coding capacity suggests that the growth of the genetic code is not yet limited by the number of identity elements fitting into the tRNA structure.

Beyond the Bioorthogonal Inverse-Electron-Demand Diels–Alder Reactions of Tetrazines: 2-Pyrone-Functionalized Fluorogenic Probes

AbstractThe applicability of pyrones as a bioorthogonal platform was explored in inverse-electron-demand Diels–Alder (IEDDA) reactions with a strained cyclooctyne. Studies showed that the pyrones are indeed suitable for IEDDA reactions under physiological conditions. Furthermore, the stable pyrone moiety could be utilized to construct easily accessible fluorogenic probes. Mutual orthogonality of the IEDDA reaction of 2-pyrones with SPAAC reactions of azides was also explored.

Metal- and Strain-Free Bioorthogonal Cycloaddition of o-Diones with Furan-2(3H)-one as Anionic Cycloaddend.

The development of new bioorthogonal reactions with mutual orthogonality to classic bioorthogonal reactions such as the strain-promoted azide-alkyne click reaction and the inverse-electron-demand Diels-Alder reaction is of great importance in providing chemical tools for multiplex labelling of live cells. Here we report the first anionic cycloaddend-promoted bioorthogonal cycloaddition reaction between phenanthrene-9,10-dione and furan-2(3H)-one derivatives, where the high polarity of water is exploited to stabilize the highly electron-rich anionic cycloaddend. The reaction is metal- and strain-free, which proceeds rapidly in aqueous solution and on live cells with a second-order rate constant up to 119 M-1 s-1 . The combined utilization of this reaction together with the two other widely used bioorthogonal reactions allows for mutually orthogonal labelling of three types of proteins or three groups of living cells in one batch without cross-talking. Such results highlight the great potential for multiplex labelling of different biomolecules in live cells.

Metal‐ and Strain‐Free Bioorthogonal Cycloaddition of o‐Diones with Furan‐2(3H)‐one as Anionic Cycloaddend

AbstractThe development of new bioorthogonal reactions with mutual orthogonality to classic bioorthogonal reactions such as the strain‐promoted azide–alkyne click reaction and the inverse‐electron‐demand Diels–Alder reaction is of great importance in providing chemical tools for multiplex labelling of live cells. Here we report the first anionic cycloaddend‐promoted bioorthogonal cycloaddition reaction between phenanthrene‐9,10‐dione and furan‐2(3H)‐one derivatives, where the high polarity of water is exploited to stabilize the highly electron‐rich anionic cycloaddend. The reaction is metal‐ and strain‐free, which proceeds rapidly in aqueous solution and on live cells with a second‐order rate constant up to 119 M−1 s−1. The combined utilization of this reaction together with the two other widely used bioorthogonal reactions allows for mutually orthogonal labelling of three types of proteins or three groups of living cells in one batch without cross‐talking. Such results highlight the great potential for multiplex labelling of different biomolecules in live cells.

120 km low-loss propagating OAM beams enabled by OAM-mode group multiplexing and a ring-core fiber

Due to the mutual orthogonality among different orbital angular momentums (OAMs), vortex beams (VB) carrying OAMs have been widely employed in the form of encoding/decoding or mode-/space-division multiplexing (M/SDM) for further promoting the channel capacity and spectrum effectiveness in a free-space optical communication (FSOC) and an optical fiber communication (OFC), respectively. For improving the propagation distance and loss in the OFC, a propagation concept of VB is proposed by multiplexing OAM-mode groups (OMGs) over a homemade ring-core fiber (RCF). The step-index RCF is proposed and fabricated in our Lab for supporting OMGs propagation and multiplexing with lower loss, which can support 6 OMGs. A proof-of-concept experimental setup is also proposed and performed for verifying the feasibility and validity of the proposed concept, where 16-quadrature amplitude modulation (16-QAM) signal is employed. The detected intensity profiles and interference graphs demonstrate that 5 OMGs can be successfully propagated over the RCF and received at the receiver. For evaluating the performance of the proposed scheme, bit-error rates (BER) and constellation graph (CG) are utilized. The measured BERs and CGs show that the system performance degrades as the order of OMGs or data rate increases and the influence of carrier wavelength on the performance of system is relatively weak in C band. In addition, the measured crosstalk inter-OMGs is much lower than the crosstalk intra-OMGs. The aforementioned results demonstrate that the proposed approach is correct and reliable and can enhance propagation distance and reduce the loss for a long-haul OFC.

De novo design and directed folding of disulfide-bridged peptide heterodimers

Peptide heterodimers are prevalent in nature, which are not only functional macromolecules but molecular tools for chemical and synthetic biology. Computational methods have also been developed to design heterodimers of advanced functions. However, these peptide heterodimers are usually formed through noncovalent interactions, which are prone to dissociate and subject to concentration-dependent nonspecific aggregation. Heterodimers crosslinked with interchain disulfide bonds are more stable, but it represents a formidable challenge for both the computational design of heterodimers and the manipulation of disulfide pairing for heterodimer synthesis and applications. Here, we report the design, synthesis and application of interchain disulfide-bridged peptide heterodimers with mutual orthogonality by combining computational de novo designs with a directed disulfide pairing strategy. These heterodimers can be used as not only scaffolds for generating functional molecules but chemical tools or building blocks for protein labeling and construction of crosslinking hybrids. This study thus opens the door for using this unexplored dimeric structure space for many biological applications.

Orthogonality of Redesigned tRNA Molecules with Three Stop Codons

Comprehensive SummaryThe ability to expand genetic code in living cells has emerged as a powerful method with diverse applications. Here, we design replacement of the anticodons of E. coli tRNAs that recognize codons for 20 natural amino acids, with three anti‐stop codons, resulting in a total of 60 engineered tRNA constructs. We test these constructs one by one in E. coli, and found that six tRNAsCUA (tyrV, serX, hisR, trpT, glnV and leuX), two tRNAsUCA (trpT and leuX) and one tRNAUUA (tyrV) allowed efficient expression of Red Fluorescence Protein (RFP) with the presence of a corresponding stop codon in frame. Furthermore, we exploit the mutual orthogonality of tRNASerCUA, tRNATrpUCA and tRNATyrUUA with corresponding stop codons and demonstrated that the tRNASerCUA and the tRNATrpUCA can provide dynamic range and low crosstalk. Finally, we show the TAG and TGA can not only be used as an “AND gate” circuit to control the translation of target gene, but also be used to control the translation of a prodeoxyviolacein (PDV) pathway and a reporter in parallel. Overall, this work provides flexible tools for translational control and holds great potential to promote synthetic biology studies.

A Genetically Encoded Isonitrile Lysine for Orthogonal Bioorthogonal Labeling Schemes.

Bioorthogonal click-reactions represent ideal means for labeling biomolecules selectively and specifically with suitable small synthetic dyes. Genetic code expansion (GCE) technology enables efficient site-selective installation of bioorthogonal handles onto proteins of interest (POIs). Incorporation of bioorthogonalized non-canonical amino acids is a minimally perturbing means of enabling the study of proteins in their native environment. The growing demand for the multiple modification of POIs has triggered the quest for developing orthogonal bioorthogonal reactions that allow simultaneous modification of biomolecules. The recently reported bioorthogonal [4 + 1] cycloaddition reaction of bulky tetrazines and sterically demanding isonitriles has prompted us to develop a non-canonical amino acid (ncAA) bearing a suitable isonitrile function. Herein we disclose the synthesis and genetic incorporation of this ncAA together with studies aiming at assessing the mutual orthogonality between its reaction with bulky tetrazines and the inverse electron demand Diels–Alder (IEDDA) reaction of bicyclononyne (BCN) and tetrazine. Results showed that the new ncAA, bulky-isonitrile-carbamate-lysine (BICK) is efficiently and specifically incorporated into proteins by genetic code expansion, and despite the slow [4 + 1] cycloaddition, enables the labeling of outer membrane receptors such as insulin receptor (IR) with a membrane-impermeable dye. Furthermore, double labeling of protein structures in live and fixed mammalian cells was achieved using the mutually orthogonal bioorthogonal IEDDA and [4 + 1] cycloaddition reaction pair, by introducing BICK through GCE and BCN through a HaloTag technique.

The joint bidiagonalization process with partial reorthogonalization

The joint bidiagonalization(JBD) process is a useful algorithm for the computation of the generalized singular value decomposition(GSVD) of a matrix pair. However, it always suffers from rounding errors, which causes the Lanczos vectors to loss their mutual orthogonality. In order to maintain some level of orthongonality, we present a semiorthogonalization strategy. Our rounding error analysis shows that the JBD process with the semiorthogonalization strategy can ensure that the convergence of the computed quantities is not affected by rounding errors and the final accuracy is high enough. Based on the semiorthogonalization strategy, we develop the joint bidiagonalization process with partial reorthogonalization(JBDPRO). In the JBDPRO algorithm, reorthogonalizations occur only when necessary, which saves a big amount of reorthogonalization work compared with the full reorthogonalization strategy. Numerical experiments illustrate our theory and algorithm.