Sign Ambiguity Research Articles

Subspace-Based Blind Channel Estimation by Separating Real and Imaginary Symbols for Cyclic-Prefixed Single-Carrier Systems

Blind channel estimation based on a subspace-based algorithm for single-input single-output cyclic-prefixed single-carrier systems is proposed in this brief. The proposed method is different from conventional subspace-based approaches, which exploit the original complex structure of the received data symbols. In contrast, we separate the real part and the imaginary part of the received complex symbols and then exploit these two kinds of symbols to construct the signal model. The noise subspace can then be established to estimate the channel impulse response (CIR) using a subspace algorithm when real symbols, such as binary phase shift keying or pulse amplitude modulation symbols, are applied. The real part and the imaginary part of the CIR can be estimated individually and simultaneously with only a sign ambiguity. With the aid of repetition index, the proposed method is workable even if few data blocks are available. Simulation results demonstrate that the proposed approach outperforms conventional methods in normalized mean-squared error under static channel environments.

On the ambiguities in the tri-bimaximal mixing matrix and corresponding charged lepton corrections

Two negative signs naturally appear in the Uμ1 and Uτ2 elements of the tri-bimaximal (TBM) matrix for positive values of the mixing angles θ12 and θ23. Apart from this, in other TBM matrices negative signs are shifted to other elements in each case. They account for positive as well as negative values of θ12 and θ23. We discuss the sign ambiguity in the TBM matrix and find that the TBM matrices, in fact, can be divided into two groups under certain circumstances. Interestingly, this classification of the TBM matrices is accompanied by two different μ − τ symmetric mass matrices which can separately be related to the groups. To accommodate the non-zero value of θ13 and deviate θ23 toward the first octant, we then perturb the TBM mixing ansatz with the help of charged lepton correction. The diagonalizing matrices for the charged lepton mass matrices also possess sign ambiguity and respect the grouping of the TBM matrices. They are parameterized in terms of the Wolfenstein parameter λ and satisfy the unitarity condition up to the second order in λ.

Signatures of hermitian forms and the Knebusch trace formula

Signatures of quadratic forms have been generalized to hermitian forms over algebras with involution. In the literature this is done via Morita theory, which causes sign ambiguities in certain cases. In this paper, a hermitian version of the Knebusch Trace Formula is established and used as a main tool to resolve these ambiguities. The last page is an erratum for the published version. We inadvertently (I) gave an incorrect definition of adjoint involutions; (II) omitted dealing with the case $(H\times H, \widehat{\phantom{m}}\,)$. As $W(H\times H, \widehat{\phantom{m}}\,)= W(R\times R, \widehat{\phantom{m}}\,)=0$, the omission does not affect our reasoning or our results. For the sake of completeness we point out where some small changes should be made in the published version.

Computing modular Galois representations

We compute modular Galois representations associated with a newform \(f\), and study the related problem of computing the coefficients of \(f\) modulo a small prime \(\ell \). To this end, we design a practical variant of the complex approximations method presented in Edixhoven and Couveignes (Ann. of Math. Stud., vol. 176, Princeton University Press, Princeton, 2011). Its efficiency stems from several new ingredients. For instance, we use fast exponentiation in the modular jacobian instead of analytic continuation, which greatly reduces the need to compute abelian integrals, since most of the computation handles divisors. Also, we introduce an efficient way to compute arithmetically well-behaved functions on jacobians, a method to expand cuspforms in quasi-linear time, and a trick making the computation of the image of a Frobenius element by a modular Galois representation more effective. We illustrate our method on the newforms \(\Delta \) and \(E_4 \cdot \Delta \), and manage to compute for the first time the associated faithful representations modulo \(\ell \) and the values modulo \(\ell \) of Ramanujan’s \(\tau \) function at huge primes for \(\ell \in \{ 11,13,17,19,29\}\). In particular, we get rid of the sign ambiguity stemming from the use of a projective representation as in Bosman (On the computation of Galois representations associated to level one modular forms. arxiv.org/abs/0710.1237, 2007). As a consequence, we can compute the values of \(\tau (p)~\mathrm{mod}~2^{11} \times 3^6 \times 5^3 \times 7 \times 11 \times 13 \times 17 \times 19 \times 23 \times 29 \times 691 \approx 2.8 \times 10^{19}\) for huge primes \(p\). The representations we computed lie in the jacobian of modular curves of genus up to \(22\).

Radial Hilbert transform phase retrieval algorithm for circular carrier interferogram

In this paper, we introduce an easy method called radial Hilbert transform phase retrieval algorithm in order to extract phase distribution from single circular carrier interferogram. This new method overcomes the drawbacks of sign ambiguity via some traditional phase retrieval algorithms and simplifies the phase unwrapping method as only one dimensional phase unwrapping is needed. It also remains the advantages of Hilbert transform method such as it could realize automatically calculation without choosing specific information as fast Fourier transform method and obtain more details since it remains more high order information in frequency domain. The approach could be applied to calculate the wavefront from circular carrier interferograms.

CP violation and mass hierarchy at medium baselines in the large θ 13 era

The large value of theta(13) recently measured by rector and accelerator experiments opens unprecedented opportunities for precision oscillation physics. In this paper, we reconsider the physics reach of medium baseline superbeams. For theta(13) ~ 9 degree we show that facilities at medium baselines -- i.e. L ~ O(1000 km) -- remain optimal for the study of CP violation in the leptonic sector, although their ultimate precision strongly depends on experimental systematics. This is demonstrated in particular for facilities of practical interest in Europe: a CERN to Gran Sasso and CERN to Phyasalmi nu_mu beam based on the present SPS and on new high power 50 GeV proton driver. Due to the large value of theta(13), spectral information can be employed at medium baselines to resolve the sign ambiguity and determine the neutrino mass hierarchy. However, longer baselines, where matter effects dominate the nu_mu->nu_e transition, can achieve much stronger sensitivity to sign(Delta m^2) even at moderate exposures.

Study of Segment Training Based Individual Channel Estimation for Two-Way Relay Network

In this letter, we design a segment training based individual channel estimation (STICE) scheme in the classical three-node it amplify-and-forward two-way relay network (TWRN). We resort to linear minimum-mean-square-error (LMMSE) estimators to achieve the in-channel estimation without sign ambiguity through two consecutive segments. We derive the mean-square-error (MSE) of the individual channel estimation, from which the optimal training and the optimal relay's power allocation are obtained. Numerical results are provided to corroborate the provided studies.

Polarimetric Measurement of Jones Matrix of a Twisted Nematic Liquid Crystal Spatial Light Modulator

A polarimetric experimental method was developed to determine the Jones matrix elements of transparent optical materials without sign ambiguity. A set of polarization dependent transmittance data of the samples was measured with polarizer - sample - analyzer system and another set of data was measured with polarizer - sample - quarter-wave plate - analyzer. Two data sets were compared and mathematically analyzed to obtain the correct signs of the elements of the matrix. The Jones matrix elements of a quarter-wave plate were determined to check the validity of the method. The experimentally obtained matrix elements of the quarter-wave plate were consistent with the theoretical expectations. The same method was applied to obtain the Jones matrix elements of a twisted nematic liquid crystal panel.

UNCOVER CONTEXT-SPECIFIC GENE REGULATION BY TRANSCRIPTION FACTORS AND microRNAs USING BAYESIAN SPARSE NONNEGATIVE FACTOR REGRESSION

In multicellular organisms, transcription factors (TFs) and microRNAs (miRNA) embody two largest families of molecules that modulate messenger RNA (mRNA) expressions through transcriptional and post-transcriptional regulations. While mRNA and microRNA expressions can be measured by microarray technique, the activities of transcription factors manifested by their protein expression are still difficult to observe, making it usually a complex problem to reconstruct a collaborative gene regulatory network (GRN) by TFs and miRNAs from expression data. In this paper, a novel Bayesian sparse non-negative factor regression (BSNFR) model is proposed for modeling the joint regulations of mRNAs by TFs and miRNAs and integration of multiple data types including gene expressions, microRNA expressions, TF targeted genes, and microRNA targets. Powered by a Gibbs sampling solution, BSNFR can infer both the TF/microRNA-mediated mRNA regulations and the unknown TF activities. Additionally, since BSNFR directly models the non-negative activities of TFs, it avoids the common problem of sign ambiguity with factor models and is capable of accurate prediction of the types (up or down) of regulations as well. BSNFR also includes a nonparametric Bayesian model for the latent factor activities, which enables the discovery of the clustering effects among samples due to (disease) subtypes. The proposed BSNFR model and the developed Gibbs sampling solution were validated on simulated systems and applied to real data of glioblastoma multiforme (GBM) patients from The Cancer Genome Atlas (TCGA). A GBM specific gene regulatory network by TFs and miRNAs was reconstructed. This GBM network includes 107 regulations recorded in the existing databases and 16 new regulations. Functional analysis suggests that the regulated genes are enriched in cell cycle and P53 pathways. In addition, BSNFR also identified 3 clusters among GBM patient samples, two of which demonstrates significant survival differences (p=0.004). Finally, the estimated TF activities imply that EGR-1 is significantly correlated with patient survivals (p=0.004) and may be used as a prognostic biomarker. The data and matlab code are available at: http://compgenomics.cbi.utsa.edu/BSNFR .

Direct ESPI phase estimating from only two interferograms

One step phase shifting method for Electronic speckle pattern interferometry (ESPI) is an effective way for dynamic phenomenon analysis. But all the present methods need prior processes to get the reference phase field either by the traditional phase shifting method or by the image-sequence analyzing method. This paper presents a direct phase estimating method using only two interferograms, with no need of any prior information. By reasonably assuming that the background, the modulation and the phase changes are constant in local areas, the whole phase change field modulated by π with sign ambiguity can be estimated. Then through analyzing the phase change values, the whole sign field can be determined. With the help of the sign field, the modulation of the phase changes can be removed by phase unwrapping methods. The effectiveness of this method has been proved by real experimental tests.

Language Assessments as Shibboleths: A Poststructuralist Perspective

The biblical story of the shibboleth is widely cited in language testing as emblematic of the social and political function of language tests. But the meaning of the shibboleth has also been explored within poststructuralism, specifically within Derrida’s discussion of the dilemmas of identity in the work of the German Jewish poet Paul Celan. Derrida discusses language itself as shibboleth, and emphasizes the ambiguity and indeterminacy of the linguistic sign, its ‘undecidability’. This article considers the implications of Derrida’s argument for the area of language testing in order to see what his interpretation of the shibboleth might mean for understanding its practices, typically framed as they are within a modernist paradigm. Examples are drawn from various areas of language assessment, including the use of language analysis in the determination of the claims of asylum seekers. What implications for understanding such assessment practices does a poststructuralist perspective offer?

Holographic imaging and interferometry with non-Bragg diffraction orders on volume and surface-relief gratings in lithium niobate and photo-thermoplastic materials

The recording of holographic volume and surface-relief gratings in a photorefractive crystal using a photo-thermoplastic (PTP) holographic camera with an image-bearing signal beam leads to the appearance of two Bragg and two or more non-Bragg diffracted beams that show the transformed images in each beam (rotation and angular amplification of images). Using this real-time mode of interferometry, the hologram is retrieved with a deformed object beam, resulting in the appearance of fringes with a proper phase shift in each of four diffracted beams. This one-shot (one-exposure) phase-shifting interferometry results in clarification of the object wave-front information (for example, from surface deformation) and solution of the sign ambiguity problem. This procedure demonstrates that high-resolution holographic imaging of the PTP holographic camera static deformations in the order of ∼0.1 mm can be revealed on the diffusion reflection surface. In addition, it was demonstrated that using the PTP materials could achieve holographic recording and imaging through phase aberration, with the image appearing in the non-Bragg diffraction order.

Bs0(B¯s0)→DCP0KK¯: Detecting and discriminating new physics inBs0−B¯s0mixing

If the weak phase of B_s-anti B_s mixing (2 beta_s) is found to be significantly different from zero, this is a clear signal of new physics (NP). However, if such a signal is found, we would like an unambiguous determination of 2 beta_s in order to ascertain which NP models could be responsible. In addition, in the presence of NP, the width difference \Delta\Gamma_s between the two B_s mass eigenstates can be positive or negative, and ideally this sign ambiguity should be resolved experimentally. Finally, in order to see if the NP is contributing to \Gamma^s_{12} in addition to M^s_{12}, the precise measurement of |\Gamma^s_{12}| is crucial. In this paper, we consider several different methods of measuring B_s-anti B_s mixing using two- and three-body decays with ${\bar b} \to {\bar c} u {\bar s}$ and ${\bar b} \to {\bar u} c {\bar s}$ transitions. We find that the most promising of these is a time-dependent Dalitz-plot analysis of $B_s (\bar B_s) \to D^0_{CP} K {\bar K}$. With these decays, all of the above issues can be addressed, and the measurement of the weak phase gamma is also possible. We also note that, with all three-body decays it is possible to resolve the sign ambiguity of \Delta\Gamma_s even without determining the CP phase phi_s.

Molecular structure of the argon-(Z)-1-chloro-2-fluoroethylene complex from chirped-pulse and narrow-band Fourier transform microwave spectroscopy

Broadband chirped pulse, Fourier transform microwave spectra in the 6–18GHz region are obtained for the 35Cl and 37Cl isotopomers of the complex formed between argon and (Z)-1-chloro-2-fluoroethylene. Analysis of the spectra provides predictions of rotational transition frequencies for the two singly substituted 13C isotopomers of Ar-35ClHCCHF sufficient to narrow the search range required for observation in a more sensitive, narrow band cavity Fourier transform instrument. Only a non-planar structure with the argon atom maximizing the number of its contacts with preferably heavy atoms is consistent with the rotational constants for all four isotopomers, and no evidence of tunneling between the two equivalent minima on either side of the ethylene plane is found. Rotational transitions for four isotopomers of (Z)-1-chloro-2-fluoroethylene itself, appearing in the broadband spectrum, are analyzed to determine the complete chlorine nuclear quadrupole coupling tensor for this molecule, and when these are combined with the hyperfine constants determined for the complex with argon, the sign ambiguity of the measured off-diagonal tensor components is removed.

Spin-3 quasinormal modes of the BTZ black hole

Using the operator approach, we obtain quasinormal modes (QNMs) of BTZ black hole in spin-3 topologically massive gravity by solving the first-order equation of motion with the transverse-traceless condition. We find that these are different from those obtained when solving the second-order differential equation for the third-rank tensor of spin-3 field subject to suitable boundary conditions and having the sign ambiguity of mass. However, it is shown clearly that two approaches to the left-moving QNMs are identical, while the right-moving QNMs of solving the second-order equation are given by descendants of the operator approach.

On the Dual of Certain Ternary Weakly Regular Bent Functions

In 2006, Helleseth and Kholosha conjectured and partially proved the existence of a class of ternary weakly regular monomial bent functions and also the expression for the dual bent function up to the sign value. The bentness was finally proved later in 2009 using a complicated technique that employs Stickelberger's theorem. Extensively using the previously found results and approaches, in this paper, a surprisingly short proof for the conjectured expression of the dual is given but without resolving the sign ambiguity. Furthermore, we resolve the sign by finding the trace representation of the dual function.

Single closed fringe pattern phase demodulation in alignment of nanolithography

The single closed fringe pattern that occurs in two superposed grating marks applied in the previously designed moiré alignment scheme based on dual-grating for lithography is processed and analyzed using a frequency domain method based on two-dimensional (2-D) analytic wavelet transform (AWT) and 2-D wavelet ridge algorithm. The sign ambiguities, which always occur in the process of single closed fringe pattern analysis, are removed through the discontinuities of the angle in the 2-D wavelet ridge. Theoretical analysis regarding application of 2-D AWT and 2-D wavelet ridge to the interference fringe in alignment is performed. Verification of this process is carried out through numerical simulation and experiment. Results indicate that the background and noise in the fringes can be filtered effectively through our method, and the phase information can be obtained successfully.

Symmetry Restoration in Hartree-Fock-Bogoliubov Based Theories

We present a Pfaffian formula for projection and symmetry restoration for wave functions of the general Bogoliubov form, including quasiparticle excited states and linear combinations of them. This solves a long-standing problem in calculating states of good symmetry, arising from the sign ambiguity of the commonly used determinant formula. A simple example is given of projecting a good particle number and angular momentum from a Bogoliubov wave function in the Fock space of a single j-shell.

Frequency offset and I/Q imbalance estimation for orthogonal frequency division multiplexing based wireless local area networks

The paper proposes a novel joint estimation of the frequency offset, frequency-independent I/Q imbalance, and frequency-dependent I/Q imbalance, using periodic pilots in orthogonal frequency division multiplexing (OFDM) based wireless local area networks (LANs). Although a low-complexity frequency offset estimation in the presence of I/Q imbalance can be obtained via a periodic pilot, the corresponding closed-form solution encounters a sign ambiguity. A method based on a power comparison between the signal and image interference is then proposed to detect the sign. Meanwhile, since one periodic pilot only is unable to estimate I/Q imbalance in the absence of a frequency offset, we also propose an estimation method based on two different periodic pilots available in the preamble. The validity and superiority of the proposed method are demonstrated by computer simulations.

Energy conversion at the Earth's magnetopause using single and multispacecraft methods

[1] We present a small statistical data set, where we investigate energy conversion at the magnetopause using Cluster measurements of magnetopause crossings. The Cluster observations of magnetic field, plasma velocity, current density and magnetopause orientation are needed to infer the energy conversion at the magnetopause. These parameters can be inferred either from accurate multispacecraft methods, or by using single-spacecraft methods. Our final aim is a large statistical study, for which only single-spacecraft methods can be applied. The Cluster mission provides an opportunity to examine and validate single-spacecraft methods against the multispacecraft methods. For single-spacecraft methods, we use the Generic Residue Analysis (GRA) and a standard one-dimensional current density method using magnetic field measurements. For multispacecraft methods, we use triangulation (Constant Velocity Approach - CVA) and the curlometer technique. We find that in some cases the single-spacecraft methods yield a different sign for the energy conversion than compared to the multispacecraft methods. These sign ambiguities arise from the orientation of the magnetopause, choosing the interval to be analyzed, large normal current and time offset of the current density inferred from the two methods. By using the Finnish Meteorological Institute global MHD simulation GUMICS-4, we are able to determine which sign is likely to be correct, introducing an opportunity to correct the ambiguous energy conversion values. After correcting the few ambiguous cases, we find that the energy conversion estimated from single-spacecraft methods is generally lower by 70% compared to the multispacecraft methods.