Orthogonal Counterparts Research Articles

Eigenphase distributions of unimodular circular ensembles

Abstract Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices (β = 2), supported by explicit examples at small N and by numerical samplings at larger N. In this letter, I spell out a concise proof of their formula, and present its orthogonal and symplectic counterparts, i.e. the eigenphase distributions of Haar-random unimodular symmetric (β = 1) and selfdual (β = 4) unitary matrices parametrizing SU(N)/SO(N) and SU(2N)/Sp(2N), respectively.

A Survey of NOMA-Aided Cell-Free Massive MIMO Systems

The Internet of Everything is leading to an increasingly connected intelligent digital world. Envisaged sixth-generation wireless networks require new solutions and technologies due to stringent network requirements. The benefits of cell-free massive MIMO (CF-mMIMO) and non-orthogonal multiple access (NOMA) have brought substantial attention to these approaches as potential technologies for future networks. In CF-mMIMO, numerous distributed access points are linked to a central processing unit, which allocates the same time-frequency resources to a smaller group of users. On the other hand, NOMA can support more users than its orthogonal counterparts by utilizing non-orthogonal resource allocation. This paper provides a comprehensive review and survey of NOMA-aided CF-mMIMO (CF-mMIMO-NOMA). Specifically, we present a comprehensive review of massive MIMO, CF-mMIMO, and NOMA. We then present a state-of-the-art research review of CF-mMIMO-NOMA. Finally, we discuss the challenges and potential of combining CF-mMIMO-NOMA with other enabling technologies to enhance performance.

Intelligent Trajectory Design for RIS-NOMA Aided Multi-Robot Communications

A novel reconfigurable intelligent surface-aided multi-robot network is proposed, where multiple mobile robots are served by an access point (AP) through non-orthogonal multiple access (NOMA). The goal is to maximize the sum-rate of whole trajectories for the multi-robot system by jointly optimizing trajectories and NOMA decoding orders of robots, phase-shift coefficients of the RIS, and the power allocation of the AP, subject to predicted initial and final positions of robots and the quality of service (QoS) of each robot. To tackle this problem, an integrated machine learning (ML) scheme is proposed, which combines long short-term memory (LSTM)-autoregressive integrated moving average (ARIMA) model and dueling double deep Q-network (D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> QN) algorithm. For initial and final position prediction for robots, the LSTM-ARIMA is able to overcome the problem of gradient vanishment of non-stationary and non-linear sequences of data. For jointly determining the phase shift matrix and robots’ trajectories, D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> QN is invoked for solving the problem of action value overestimation. Based on the proposed scheme, each robot holds an optimal trajectory based on the maximum sum-rate of a whole trajectory, which reveals that robots pursue long-term benefits for whole trajectory design. Numerical results demonstrated that: 1) LSTM-ARIMA model provides high accuracy predicting model; 2) The proposed D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> QN algorithm can achieve fast average convergence; and 3) RIS-NOMA networks have superior network performance compared to RIS-aided orthogonal counterparts.

Nonorthogonal multiple access multiple input multiple output communications with harvested energy: Performance evaluation

AbstractThis paper demonstrates improved throughput and energy efficiency of wireless communications by exploiting nonorthogonal multiple access (NOMA), multiple input–multiple output (MIMO), and radio frequency energy harvesting (EH) technologies. To assess the performance of NOMA MIMO communications with EH (MMe), we consider the nonlinear characteristics of EH devices and propose explicit expressions for throughput and outage probability. Based on our results, the system performance is significantly mitigated by EH nonlinearity and is considerably improved by increasing the number of antennas. Additionally, by appropriately adjusting the system parameters, our NOMA MMe innovation can avert complete outages while optimizing system performance. Moreover, the results demonstrate the superiority of the NOMA MMe over its orthogonal multiple access MMe counterparts.

Wide-angle chiral polarization converter for reflection and transmission modes

Metamaterials provide high degrees of freedom for the design and manipulation of electromagnetic (EM) waves such as polarization conversion due to their unique controllable capabilities. In this paper, we propose a tunable wide-angle chiral metamaterial incorporating with vanadium dioxide (VO2), which can realize different operating modes and polarization conversions. When working in reflection mode, it can achieve circular polarization conversion at 3.35 THz and 3.07 THz for two different incident directions, the corresponding polarization conversion rate (PCR) can reach 93.5% and 97.1%, respectively. When operating in transmission mode, the incident x (y)-polarized waves can be converted to the orthogonal counterparts in the range of 2.24–2.88 THz, the asymmetric transmission (AT) parameter is over 0.6. Moreover, the good PCR and large AT effect can still be maintained in wide angle range. The proposed structure has potential application prospects in controllable switch, isolation device, communication system and so on.

Generalized nonorthogonal matrix elements. II: Extension to arbitrary excitations

Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication [H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021)], I introduced a generalized extension to the nonorthogonal Wick's theorem that allows matrix elements to be derived between excited configurations from a pair of reference determinants with a singular nonorthogonal orbital overlap matrix. However, that work only provided explicit expressions for one- and two-body matrix elements between singly- or doubly-excited configurations. Here, this framework is extended to compute generalized nonorthogonal matrix elements between higher-order excitations. Pre-computing and storing intermediate values allows one- and two-body matrix elements to be evaluated with an O(1) scaling relative to the system size, and the LIBGNME computational library is introduced to achieve this in practice. These advances make the evaluation of all nonorthogonal matrix elements almost as easy as their orthogonal counterparts, facilitating a new phase of development in nonorthogonal electronic structure theory.

Partial Non-Orthogonal Multiple Access: A New Perspective for RIS-Aided Downlink

In this letter, a novel reconfigurable intelligent surface (RIS) aided partial non-orthogonal multiple access (P-NOMA) downlink is investigated, where the passive beamforming on the RIS is designed for serving paired user equipments (UEs), with their signal frequencies partially overlapped. We consider the general case that all UEs have both direct and reflection links undergoing Rayleigh and Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> fadings. By approximating the effective channel gains of the P-NOMA UEs as Gamma random variables, we derive the closed-form expressions of the lower and upper bounds on the achievable rates. The accuracy of the derived close-form expressions are verified through simulation and numerical results, where the proposed RIS-aided P-NOMA downlink considerably outperforms the conventional NOMA and orthogonal counterparts.

Variable-Metric Localization of Occupied and Virtual Orbitals.

The key idea of the variable-metric approach to orbital localization is to allow nonorthogonality between orbitals while, at the same time, preventing them from becoming linearly dependent. The variable-metric localization has been shown to improve the locality of occupied nonorthogonal orbitals relative to their orthogonal counterparts. In this work, numerous localization algorithms are designed and tested to exploit the conceptual simplicity of the variable-metric approach with the goal of creating a straightforward and reliable localization procedure for virtual orbitals. The implemented algorithms include the steepest descent, conjugate gradient (CG), limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), and hybrid procedures as well as trust-region (TR) methods based on the CG and Cauchy-point subproblem solvers. Comparative analysis shows that the CG-based TR algorithm is the best overall method to obtain nonorthogonal localized molecular orbitals (NLMOs), occupied or virtual. The L-BFGS and CG algorithms can also be used to obtain NLMOs reliably but often at higher computational cost. Extensive tests demonstrate that the implemented methods allow us to obtain well-localized Boys-Foster (i.e., maximally localized Wannier functions) and Pipek-Mezey, orthogonal and nonorthogonal, and occupied and virtual orbitals for a variety of gas-phase molecules and periodic materials. The tests also show that virtual NLMOs, which have not been described before, are, on average, 13% (Boys-Foster) and 18% (Pipek-Mezey) more localized than their orthogonal counterparts.

Generalized nonorthogonal matrix elements: Unifying Wick’s theorem and the Slater–Condon rules

Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder than their orthogonal counterparts. While several different approaches have been developed, these are predominantly derived from the first-quantized generalized Slater-Condon rules and usually require biorthogonal occupied orbitals to be computed for each matrix element. For coupling terms between nonorthogonal excited configurations, a second-quantized approach such as the nonorthogonal Wick's theorem is more desirable, but this fails when the two reference determinants have a zero many-body overlap. In this contribution, we derive an entirely generalized extension to the nonorthogonal Wick's theorem that is applicable to all pairs of determinants with nonorthogonal orbitals. Our approach creates a universal methodology for evaluating any nonorthogonal matrix element and allows Wick's theorem and the generalized Slater-Condon rules to be unified for the first time. Furthermore, we present a simple well-defined protocol for deriving arbitrary coupling terms between nonorthogonal excited configurations. In the case of overlap and one-body operators, this protocol recovers efficient formulas with reduced scaling, promising significant computational acceleration for methods that rely on such terms.

Weakly correlated synapses promote dimension reduction in deep neural networks.

By controlling synaptic and neural correlations, deep learning has achieved empirical successes in improving classification performances. How synaptic correlations affect neural correlations to produce disentangled hidden representations remains elusive. Here we propose a simplified model of dimension reduction, taking into account pairwise correlations among synapses, to reveal the mechanism underlying how the synaptic correlations affect dimension reduction. Our theory determines the scaling of synaptic correlations requiring only mathematical self-consistency for both binary and continuous synapses. The theory also predicts that weakly correlated synapses encourage dimension reduction compared to their orthogonal counterparts. In addition, these synapses attenuate the decorrelation process along the network depth. These two computational roles are explained by a proposed mean-field equation. The theoretical predictions are in excellent agreement with numerical simulations, and the key features are also captured by deep learning with Hebbian rules.

Deep Energy Autoencoder for Noncoherent Multicarrier MU-SIMO Systems

We propose a novel deep energy autoencoder (EA) for noncoherent multicarrier multiuser single-input multiple-output (MU-SIMO) systems under fading channels. In particular, a single-user noncoherent EA-based (NC-EA) system, based on the multicarrier SIMO framework, is first proposed, where both the transmitter and receiver are represented by deep neural networks (DNNs), known as the encoder and decoder of an EA. Unlike existing systems, the decoder of the NC-EA is fed only with the energy combined from all receive antennas, while its encoder outputs a real-valued vector whose elements stand for the sub-carrier power levels. Using the NC-EA, we then develop two novel DNN structures for both uplink and downlink NC-EA multiple access (NC-EAMA) schemes, based on the multicarrier MU-SIMO framework. Note that NC-EAMA allows multiple users to share the same sub-carriers, thus enables to achieve higher performance gains than noncoherent orthogonal counterparts. By properly training, the proposed NC-EA and NC-EAMA can efficiently recover the transmitted data without any channel state information estimation. Simulation results clearly show the superiority of our schemes in terms of reliability, flexibility and complexity over baseline schemes.

Some monotonicity properties in F-normed Musielak\u2013Orlicz spaces

Strict monotonicity, lower local uniform monotonicity, upper local uniform monotonicity and their orthogonal counterparts are considered in the case of Musielak–Orlicz function spaces L^Phi (mu ) endowed with the Mazur–Orlicz F-norm as well as in the case of their subspaces E^Phi (mu ) with the F-norm induced from L^Phi (mu ). The presented results generalize some of the results from Cui et al. (Aequ Math 93:311–343, 2019) and Hudzik et al. (J Nonlinear Convex Anal 17(10):1985–2011, 2016), obtained only for Orlicz spaces as well as their subspaces of order continuous elements equipped with the Mazur–Orlicz F-norm.

Spectrally Efficient Frequency Division Multiplexing With Index-Modulated Non-Orthogonal Subcarriers

In this letter, we propose a novel index-modulated non-orthogonal spectrally efficient frequency-division multiplexing (SEFDM) scheme, in order to attain a higher bandwidth efficiency than the conventional orthogonal frequency-division multiplexing (OFDM) and SEFDM counterparts. More specifically, the recent index modulation concept is amalgamated with SEFDM, for the sake of reducing the effects of intercarrier interference while benefiting from SEFDM's increased spectral efficiency. We also formulate a low-complexity log-likelihood ratio-based detection algorithm, which allows the proposed SEFDM to operate in the configuration of an arbitrarily high number of subcarriers. Our simulation results demonstrate that the proposed SEFDM scheme outperforms the conventional SEFDM and OFDM, especially in a low-rate scenario.

An Improved Propagator Estimator for DOA Estimation in Monostatic MIMO Radar in the Presence of Imperfect Waveforms

This paper discusses the direction-of-arrival (DOA) estimation problem in multiple-input multiple-output (MIMO) radar with non-orthogonal waveforms. Unlike the traditional orthogonal waveforms-based counterparts, spatially colored noise as well as corrupted virtual direction matrix would appear due to the correlated waveforms in DOA estimation. To tackle these issues, an improved propagator estimator is developed. The spatially colored noise caused by waveform imperfectly is eliminated via cross-correlation technique. Thereafter, DOA is obtained by exploiting the propagator and invariant techniques. The proposed estimator does not involve eigendecomposition of the high dimensional matrix, and it provides closed-form solution for DOA estimation. Compared with the existing frameworks, it is computationally much more economic. Moreover, it offers very close DOA estimation accuracy to the matrix-based methods. Numerical simulations are carried out to show the improvement of the proposed estimator.

Non-orthogonal determinants in multi-Slater-Jastrow trial wave functions for fixed-node diffusion Monte Carlo.

The accuracy and efficiency of ab initio Quantum Monte Carlo (QMC) algorithms benefit greatly from compact variational trial wave functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial wave functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C2 molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. In some cases, fewer non-orthogonal determinants are required compared to orthogonal ones in order to achieve similar accuracy in FN-DMC. Our calculations indicate that trial wave functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts.

Geometric properties of F-normed Orlicz spaces

The paper deals with F-normed functions and sequence spaces. First, some general results on such spaces are presented. But most of the results in this paper concern various monotonicity properties and various Kadec–Klee properties of F-normed Orlicz functions and sequence spaces and their subspaces of elements with order continuous norm, when they are generated by monotone Orlicz functions on {mathbb {R}}_{+} and equipped with the classical Mazur–Orlicz F-norm. Strict monotonicity, lower (and upper) local uniform monotonicity and uniform monotonicity in the classical sense as well as their orthogonal counterparts are considered. It follows from the criteria that are presented for these properties that all the above classical monotonicity properties except for uniform monotonicity differ from their orthogonal counterparts [in contrast to Köthe spaces (see Hudzik et al. in Rocky Mt J Math 30(3):933–950, 2000)]. The Kadec–Klee properties that are considered in this paper correspond to various kinds of convergence: convergence locally in measure and convergence globally in measure for function spaces, uniform convergence and coordinatewise convergence in the case of sequence spaces.

Design of a Dual-Polarized Wideband Conformal Loop Antenna for Capsule Endoscopy Systems

This paper presents a dual-polarized conformal loop antenna for capsule endoscopy systems. The antenna is designed on the capsule shell, with two orthogonal counterparts to generate dual-polarized radiation. This design exhibits broad impedance bandwidths of 271 and 247 MHz for each port, covering the entire Medical Device Radiocommunications Service band as well as the 433.05–434.79 MHz Industrial Scientific Medical band. Due to the highly orthogonal current distributions of the proposed structure, an isolation of higher than 33 dB is achieved among the operating frequency bands in measurement. The dual-polarized antenna also shows an omnidirectional radiation property and a low cross-polarization level of around −40 dB, which helps to enhance communication quality, regardless of position and orientation. Whether other electronics and biocompatible coatings are included or an electromagnetic interference shielding is considered, the antenna still presents a robust performance. The cubic tissue phantom model is utilized for the initial design and optimization of the antenna structure. Moreover, the CST voxel human model is applied to study the conformal antenna in a realistic environment. Measurements are implemented using a solid tissue-mimicking phantom, and performances consistent with theoretical predictions are achieved. Finally, the wireless biotelemetry property is evaluated via the calculation of the communication link budget with an external antenna.

Efficient experimental identification of three-dimensional tyre structural properties

Modal testing is routinely applied to tyres for the identification of structural parameters and prediction of their vibration response to excitations. The present work focuses on the more demanding case of modal testing with the aim of constructing a full mathematical model of a tyre, appropriate for use in a generic time-based simulation. For this purpose, the less common free–free boundary condition is employed for the wheel, while the tyre belt is excited in all three directions, namely radial tangential and lateral. To improve efficiency, a novel partial identification method is developed for the mode shapes, whereby measured and predicted frequency responses are matched around distinct resonance peaks, while eliminating the effect of out-of-band modes. Axial symmetry of the tyre requires high purity mode shapes to avoid angular dependency of the tyre’s response. For this reason, experimental mode shapes are digitally filtered and combined with their orthogonal counterparts. Processed data reveal apparent repetition of selected mode shapes, and this is attributed to rim deflection.

Interlacing of zeros of quasi-orthogonal Meixner polynomials

We consider the interlacing of zeros of polynomials within the sequences of quasi-orthogonal order one Meixner polynomials characterised by −β, c ∈ (0, 1). The interlacing of zeros of quasi-orthogonal Meixner polynomials Mn(x; β, c) with the zeros of their nearest orthogonal counterparts Ml(x; β + k, c), l, n ∈ ℕ, k ∈ {1, 2}, is also discussed.

Cpf1 nucleases demonstrate robust activity to induce DNA modification by exploiting homology directed repair pathways in mammalian cells.

BackgroundCpf1 nucleases have recently been repurposed for site-specific genome modification. Two members of the Cpf1 family, the AsCpf1 from Acidaminococcus sp. and the LbCpf1 from Lachnospiraceae bacterium were shown to induce higher indel frequencies than SpCas9 when examining four randomly-selected target sequences for each type of nuclease. Whether they are a real match for Cas9 nucleases, however, remains to be verified.ResultsHere, we used AsCpf1 and LbCpf1 to induce homology directed repair, either single strand annealing (SSA) or homologous recombination (HR), in N2a mouse neuroblastoma cells. Exploiting a plasmid that contains two GFP halves with overlapping sequences and exploring 20 targets, on all but one both nucleases consistently performed with above 10 % efficiency. Several Cas9 nucleases have been previously characterised in order to find an orthogonal counterpart for the most widely used promiscuous SpCas9. Here, we found that AsCpf1 and LbCpf1 might be better candidates than three of the best such counterparts: Cas9 from Staphylococcus aureus, from Streptococcus thermophilus and from Neisseria meningitidis, when assessed for inducing efficient SSA mediated repair in N2a cells. When tested on genomic targets exploiting HR, both nucleases were able to induce the integration of a donor cassette with 1000 bp-long homologous arms. We also generated plasmids that express these Cpf1 nucleases together with their cognate crRNAs and that are equipped with type IIS restriction enzyme sites to facilitate spacer cloning.ConclusionsOur results suggest that employing As- or LbCpf1 nuclease to induce homology directed repair in N2a cells, although is less effective at present than employing SpCas9, it is an equally or more effective tool than the most frequently used orthogonal Cas9 counterparts of SpCas9. These findings support the position of Cpf1 nucleases on the side of SpCas9 on the palette of effective genome engineering tools.ReviewersThis article was reviewed by Eugene Koonin, Haruhiko Siomi and Jean-Yves Masson.Electronic supplementary materialThe online version of this article (doi:10.1186/s13062-016-0147-0) contains supplementary material, which is available to authorized users.