Circulant Research Articles

DIVERSITY AES IN MIXCOLUMNS STEP WITH 8X8 CIRCULANT MATRIX

In AES MixColumns operation, the branch number of circulant matrix is raised from 5 to 9 with 8´8 circulant matrices that can be enhancing the diffusion power. An efficient method to compute the circulant matrices in AES MixColumns transformation for speeding encryption is presented. Utilizing 8´8 involutory matrix multiplication is required 64 multiplications and 56 additions in in AES Mix-Columns transformation. We proposed the method with diversity 8´8 circulant matrices is only needed 19 multiplications and 57 additions. It is not only to encryption operations but also to decryption operations. Therefore, 8´8 circlant matrix operation with AES key sizes of 128bits, 192bits, and 256 bits are above 29.1%, 29.3%, and 29.8% faster than using 4´4 involutory matrix operation (16 multiplications, 12 additions), respectively. 8´8 circulant matrix encryption/decryption speed is above 78% faster than 8´8 involutory matrix operation. Ultimately, the proposed method for evaluating matrix multiplication can be made regular, simple and suitable for software implementations on embedded systems.

Cluster solutions in networks of weakly coupled oscillators on a 2D square torus


 
 
 We consider a model for an N × N lattice network of weakly coupled neural oscilla- tors with periodic boundary conditions (2D square torus), where the coupling between neurons is assumed to be within a von Neumann neighborhood of size r, denoted as von Neumann r-neighborhood. Using the phase model reduction technique, we study the existence of cluster solutions with constant phase differences (Ψh, Ψv) between adjacent oscillators along the horizontal and vertical directions in our network, where Ψh and Ψv are not necessarily to be identical. Applying the Kronecker production representation and the circulant matrix theory, we develop a novel approach to analyze the stability of cluster solutions with constant phase difference (i.e., Ψh,Ψv are equal). We begin our analysis by deriving the precise conditions for stability of such cluster solutions with von Neumann 1-neighborhood and 2 neighborhood couplings, and then we generalize our result to von Neumann r-neighborhood coupling for arbitrary neighborhood size r ≥ 1. This developed approach for the stability analysis indeed can be extended to an arbitrary coupling in our network. Finally, numerical simulations are used to validate the above analytical results for various values of N and r by considering an inhibitory network of Morris-Lecar neurons.
 
 

Quantum graphs: Self-adjoint, and yet exhibiting a nontrivial [formula omitted]-symmetry

We demonstrate that a quantum graph exhibits a PT-symmetry provided the coefficients in the condition describing the wave function matching at the vertices are circulant matrices; this symmetry is nontrivial if they are not invariant with respect to transposition. We also illustrate how the transport properties of such graphs are significantly influenced by the presence or absence of the non-Robin component of the coupling.

Subsampled Circulant Matrix Based Wideband Spectrum Sensing Using Fusion Based Recovery Algorithm

This paper reflects the problem of wideband spectrum recovery. The demand for spectrum usage is increasing exponentially as the wireless technologies rules the world. To meet these needs, Cognitive Radio is one of the emerging technologies, which intelligently allots the spectrum to the secondary users. Since the spectrum is wideband, the capability of spectrum sensing is improved by introducing sub-nyquist sampling under compressive sensing framework. In this paper, a sub-nyquist sampling technique of Modulated Wideband Converter (MWC) is used as it possesses m-parallel channels providing fast sensing and robust structure. A circulant matrix method is used to improve the hardware complexity of MWC. Also at the reconstruction of MWC, a fusion based recovery algorithm is proposed which became an added benefit for perfect recovery of the support. The results are compared with conventional MWC in terms of support recovery, mean square error and SNR gain. Simulations proved that the proposed algorithm performs superior at low as well as high SNR with increased gain.

New extremal binary self-dual codes from block circulant matrices and block quadratic residue circulant matrices

In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2 and F2+uF2. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.

Matrices in companion rings, Smith forms, and the homology of 3-dimensional Brieskorn manifolds

We study the Smith forms of matrices of the form f(Cg) where f(t),g(t)∈R[t], where R is an elementary divisor domain and Cg is the companion matrix of the (monic) polynomial g(t). Prominent examples of such matrices are circulant matrices, skew-circulant matrices, and triangular Toeplitz matrices. In particular, we reduce the calculation of the Smith form of the matrix f(Cg) to that of the matrix F(CG), where F,G are quotients of f(t),g(t) by some common divisor. This allows us to express the last non-zero determinantal divisor of f(Cg) as a resultant. A key tool is the observation that a matrix ring generated by Cg – the companion ring of g(t) – is isomorphic to the polynomial ring Qg=R[t]/<g(t)>. We relate several features of the Smith form of f(Cg) to the properties of the polynomial g(t) and the equivalence classes [f(t)]∈Qg. As an application we let f(t) be the Alexander polynomial of a torus knot and g(t)=tn−1, and calculate the Smith form of the circulant matrix f(Cg). By appealing to results concerning cyclic branched covers of knots and cyclically presented groups, this provides the homology of all Brieskorn manifolds M(r,s,n) where r,s are coprime.

On $${\mathbb {A}}$$-numerical radius equalities and inequalities for certain operator matrices

The main goal of this article is to establish several new {mathbb {A}}-numerical radius equalities for ntimes n circulant, skew circulant, imaginary circulant, imaginary skew circulant, tridiagonal, and anti-tridiagonal operator matrices, where {mathbb {A}} is the ntimes n diagonal operator matrix whose diagonal entries are positive bounded operator A. Some special cases of our results lead to the results of earlier works in the literature, which shows that our results are more general. Further, some pinching type {mathbb {A}}-numerical radius inequalities for ntimes n block operator matrices are given. Some equality conditions are also given. We also provide a concluding section, which may lead to several new problems in this area.

Digital interpolation-based SFO compensation in OCT precoding-enabled NHS-OFDM transmission systems

The non-Hermitian symmetric optical orthogonal frequency division multiplexing (NHS-OFDM) system exhibits lower hardware implementation complexity and power consumption as maintaining the same bandwidth granularity, compared to the conventional Hermitian symmetric optical OFDM (HS-OFDM) system. Also, NHS-OFDM can obtain a similar peak-to-average power ratio as well as bit error rate (BER) performance. It is expected to be a new candidate for the next-generation passive optical network. In the asynchronous NHS-OFDM system, the sampling clocks for the analog to digital converter in the receiver and the digital to analog converter in the transmitter generated from different sources and their frequencies always have a certain degree of deviation, i.e., sampling frequency offset (SFO). It may significantly deteriorate the receiver performance. Besides, the imperfect frequency response of the optical/electrical devices is another factor for the degraded BER performance. In this work, we experimentally investigate the digital interpolation (DI)-based SFO compensation in a short-reach NHS-OFDM transmission system. The orthogonal circulant matrix transform (OCT) precoding technique is employed to equalize the signal-to-noise ratio over data-carrying subcarriers and then improve the BER performance. The experimental results indicate that, with the help of the 4-th order DI, the SFO up to 200 ppm can be well compensated without power penalties in comparison with the SFO-free case. Furthermore, the receiver sensitivity of the NHS-OFDM enabled by OCT precoding can be improved by more than 2 dB at the BER of 1e-3 after 20 km standard single-mode fiber transmission.

The New FA₂ST Stroke Screening Score: An Expanding Recognition to Posterior Circulation Stroke

Background: Rapid screening and intervention are the keys to successful early treatment of stroke. Generally, the conventional FAST stroke screening score has been used by triage nurses to promptly detect acute stroke. However, the conventional FAST score has a limitation in detecting posterior circulation stroke, which results in high mortality rates. Previous studies have shown that adding ataxia could increase the sensitivity of posterior circulation stroke detection. Objective: To introduce and evaluate the diagnostic performance of a new stroke screening score, FA₂ST score, by adding ataxia to the conventional FAST score. Materials and Methods: The present study was a cross-sectional study. The new FA₂ST and conventional FAST scores were used by triage nurses in patients presented with acute neurological symptoms within seven days at the emergency department of three different types of hospitals in Thailand. Patients with Glasgow Coma Score less than 9 and those having unstable vital signs were excluded. Final diagnosis was made by a neurologist using clinical and neuroimaging information. The diagnostic performance of the new FA₂ST score was calculated using ROC curve in comparison to the conventional FAST score. The rate of posterior circulation stroke detection was calculated as percentage. Results: One hundred forty-six patients were studied. Of these, 127 (86%) had acute ischemic stroke and 19 (14%) had other diagnoses. The overall diagnostic performance of the new FA₂ST score was not statistically different with conventional FAST score in terms of area under the curve (0.642 versus 0.684, p=0.221). However, after in-depth analysis, the rate of posterior circulation stroke detection of the new FA₂ST score was higher compared with the conventional FAST score (94.12% versus 82.35%). Conclusion: The present study introduces the new FA₂ST stroke screening score and emphasizes the importance of posterior circulation stroke detection in acute stroke screening. Future studies should be considered before implementation of this score. Keywords: Screening score; Acute stroke treatment; Stroke; Emergency neurology

STRUCTURED SINGULAR VALUES OF SOME GENERALISED STOCHASTIC MATRICES

AbstractWe investigate a class of generalised stochastic complex matrices constructed from the class of all doubly stochastic matrices and a special class of circulant matrices. We determine the exact values of the structured singular values of all matrices in the class in terms of the constant row (column) sum.

Description of beam instabilities in synchrotrons with wakefields and space charge forces using the circulant matrix model

A new model for the description of beam instabilities in synchrotrons featuring wakefields and space charge forces is proposed, using the circulant matrix approach. The predictions of this model are discussed in light of past ones, with a particular emphasis on the possible mitigation of the transverse mode coupling instability by space charge forces. The existence of transient amplification in spite of the absence of unstable eigenvalues in configuration featuring strong space charge forces is also addressed. It is shown that this behavior can be recovered when considering an airbag distribution. Yet when considering a more realistic Gaussian distribution, the radial modes lead to other types of mode coupling instabilities. The predictions of the new model are then compared to results of an experiment conducted at the CERN Super Proton Synchrotron, showing a reasonable agreement.

Highlights From the Circulation Family of Journals.

Highlights From the Circulation Family of Journals.

Magnetic-Free Traveling-Wave Nonreciprocal Superconducting Microwave Components

We propose a design to realize integrated broadband nonreciprocal microwave isolators and circulators using superconducting circuit elements without any magnetic materials. To obtain a broadband response, we develop a waveguide-based design by temporal modulations. The corresponding compact traveling-wave structure is implemented with integrated superconducting composite right-/left-handed transmission lines. The calculations show that the bandwidth of 580 MHz can be realized over a nonreciprocal isolation of 20 dB in reflections. Such on-chip isolators and circulators are useful for cryogenic integrated microwave connections and measurements, such as protecting qubits from the amplified reflected signal in multiplexed readout.

Spectral distribution of symmetrized circulant matrices

AbstractWe provide a description of the spectrum and compute the eigenvalues distribution of circulant Hankel matrices obtained as symmetrization of classical Toeplitz circulant matrices. Other types of circulant matrices such as simple and Cesàro circulant matrices are also considered.

Front Cover: A CRET‐Based Multicolor Sensing Nanoplatform for Simultaneously and Sensitively Visualizing Multiple Circulating MicroRNAs (Analysis &amp; Sensing 3/2021)

Front Cover: A CRET‐Based Multicolor Sensing Nanoplatform for Simultaneously and Sensitively Visualizing Multiple Circulating MicroRNAs (Analysis &amp; Sensing 3/2021)

Laboratory tests for the detection of SARS-CoV-2 infection: basic principles and examples.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has circulated throughout the world causing the worst pandemic since 1918. All efforts have been marshalled towards testing different treatment approaches, obtaining clinical and epidemiological information, developing suitable diagnostic tests, and developing new vaccines. New ribonucleic acid (RNA)-based and viral vector-based vaccines have been developed and licensed under emergency use in many countries; however, there is a huge demand for vaccines, and it will take some time before a sufficient number of people are vaccinated to stop the circulation of the virus. Therefore, the proper diagnosis and identification of infected individuals are crucial for the isolation and treatment of these patients and tracing of their contacts. Many diagnostic tests and diag-nostic kits have been developed in a relatively short time. This review summarizes the principles of the available laboratory assays that are in use for the detection of SARS-CoV-2 RNA, antigens, or antibodies.

Highlights From the Circulation Family of Journals.

Highlights From the Circulation Family of Journals.

Statement of Ownership, Management and Circulation

Statement of Ownership, Management and Circulation

Osteoradionecrosis and bisphosphonate-related osteonecrosis of the jaw: a review of the pathogenesis and treatment

Osteoradionecrosis of the jaw (ORNJ) and bisphosphonate-related osteonecrosis of the jaw (BRONJ) are usually caused by head and neck radio-therapy and by the usage of bisphosphonate, respectively. These diseases can lead to facial deformity and dysfunction of the mandible, and may cause severe chronic facial pain. The pathogenesis of ORNJ and BRONJ are complex, and the therapy of which is still challenged. The present article reviewed the latest literature about the pathogenesis and treatment of ORNJ and BRONJ were reviewed for update. The irradiation may damage the endothelia cells and microvessels in jaw bone, which leads to the termination of the bone remodeling 15 days after irradiation. Mesenchymal stem cells based bio-therapy can assist the recovery of mandibular circulation and the reconstruction of the bone, showing therapeutic potential for ORNJ clinical treatment. Bisphosphonate can induce the dysfunction of bone marrow mesenchymal stem cells and the immune imbalance of the body. Allogeneic mesenchymal stem cells transplantation can rebuild the jaw bone and rebalance the immune of the recipient, demonstrating the ideally potential for the treatment of BRONJ. Taking together, although it would be complicated and winding, the improvement of biotech and the usage of mesenchymal stem cells shed a light on the way of ORNJ and BRONJ treatments.

Detection of circulating tumor cells with chromosomes 7 and 8 polysomy in non-small cell lung cancer and its correlation with epidermal growth factor receptor mutations in cancer tissue

Objective: To investigate the value of chromosomes 7 and 8 polysomy in circulating tumor cells (CTCs) for the diagnosis of non-small cell lung cancer, and the correlation of CTCs with clinical pathological characteristics and epidermal growth factor receptor (EGFR) mutations in cancer tissue. Methods: Fifty-seven patients with non-small cell lung cancer and 21 patients with benign lung diseases were enrolled at Beijing Chaoyang Hospital, Capital Medical University, Beijing, China from November 2017 to October 2020. Negative enrichment combined with immunofluorescence in situ hybridization (imFISH) was used to identify CTCs polysomy on chromosomes 7 and 8. EGFR mutations in 56 lung cancer patients was detected using ARMS-PCR. Results: CTCs were detected in 93.0% (53/57) of non-small cell lung cancers and 28.6% (6/21) benign lung lesions. The difference between lung cancer patients and the control cohort was statistically significant (P<0.01). Receive operator curve (ROC) analyses showed that, when the cut-off value was 1 cell/3.2 mL, Youden index had the highest sensitivity of 93.0% and specificity of 71.4% (AUC=0.906, 95%CI:0.833-0.980, P<0.01). The positive rate of CTCs in stage Ⅲ-Ⅳ cancers was significantly higher than that in stage Ⅰ-Ⅱ (P=0.023). No significant correlation was observed between positive rate of CTCs or chromosome polysomy and age, gender, smoking status, pathologic types and EGFR mutation status. The number of CTCs in EGFR mutated group was higher than that in the non-mutated group (6.5±1.1 vs. 3.7±0.7, P=0.045). The detection rate for CTCs ≥5 in the EGFR mutated group was also higher than the EGFR non-mutated group (52.0% vs. 19.4%,P=0.010). Conclusion: Detection of CTCs with chromosomes 7 and 8 polysomy has potential value in auxiliary diagnosis of non-small cell lung cancer, and the number of CTCs is correlated to TNM stage and EGFR gene mutation status.