Discrete Ambiguities Research Articles

Ambiguities in a partial-wave analysis of γ p → π 0 p with truncation in total angular momentum

We address some questions related to the discrete ambiguity problem in a truncated partial-wave analysis in the case when the helicity basis together with truncation in total angular momentum j is employed. As a numerical application, we consider the case using as input the MAID2007 and SAID multipoles in the γ p → π 0 p channel.

Using Bs0→Ds∓K± decays as a portal to new physics

The system of $B^0_s\to D_s^\mp K^\pm$ decays offers a theoretically clean determination of the angle $\gamma$ of the Unitarity Triangle. A corresponding LHCb analysis resulted in a surprisingly large result, which is in tension with other determinations and global analyses of the Unitarity Triangle. Paying special attention to discrete ambiguities, we confirm this picture and resolve a final ambiguity. Moreover, we extract the branching ratios of the underlying $\bar{B}^0_s\to D_s^+K^-$ and $\bar{B}^0_s\to D_s^- K^+$ modes. Combining them with information from semileptonic $B_{(s)}$ decays, we arrive at another puzzling situation, which we obtain also for other decays with similar dynamics. These patterns could be footprints of New Physics in the $b\to c \bar{u} s$ and $b \to u \bar{c} s$ processes which govern the dynamics of the $\bar{B}^0_s\to D_s^\mp K^\pm$ channels. Employing a model-independent parametrisation, we present a strategy to reveal such effects. Applying it to the present data, we obtain strongly correlated New-Physics contributions with potentially large CP-violating phases. We find that new contributions sizeably smaller than the Standard Model amplitudes could actually accommodate the current data. This strategy offers an exciting probe for new sources of CP violation at the future high-precision frontier of $B$ physics.

Simplification of the complete-experiment problem for photoproduction of two pseudoscalar mesons on a nucleon in a truncated partial-wave analysis

It is shown that within a truncated partial-wave analysis for photoproduction of two pseudoscalar mesons, it is possible to halve the number of independent partial amplitudes by taking into account parity conservation. In addition, within the framework of the proposed formalism, one can rather easily resolve the double discrete ambiguity arising from the symmetry under complex conjugation of the helicity amplitudes. This leads to essential simplifications of the complete experiment problem, at least, as far as mathematical aspects are concerned.

Sequence Set Design for a New LFM-PC Hybrid Modulated Radar Signal.

In this paper we study the code design problem of a new form of linear frequency modulation phase-coded (LFM-PC) hybrid signal with wide Doppler tolerance based on a range-Doppler discrete ambiguity function (DAF) to get better detection performance and anti-jamming capability. The DAF of the LFM-PC inter pulse signal is derived within the Doppler tolerance. Two optimization models are established. One is single pulse sequence design (SSD) for Doppler tolerance extension based on minimum integral normalized sidelobe level (INSL); the other is multi pulse sequence set design (MSSD) for signal orthogonality based on the minimizing sum of the normalized DAF sidelobe (NDAFSL) and discrete cross ambiguity function (DCAF). Two low-complexity signal optimization methods based on alternating direction method of multiplier (ADMM) are proposed, respectively. The simulation results show that the optimized signals have either wide Doppler tolerance or good orthogonal performance, and the optimization methods (i.e., SSD-ADMM and MSSD-ADMM) have the characteristics of fast convergence speed and low operation amount.

Nature of potential families from elastic 16O + 16O rainbow scattering* *Dedicated to the loving memories of F Bary Malik for inspiring us to use NM potentials; and Devika Basak, who was not only the loving wife of our group leader (AKB), but a source of extraordinary care, affection and inspiration for all his students and colleagues, sadly leaving us

The experimental differential cross-sections of 16O + 16O elastic scattering in the energy range 75 MeV ⩽ E lab ⩽ 1120 MeV are analysed using families of non-monotonic (NM) shallow nucleus–nucleus potential in the framework of the optical model. The experimental data is reproduced successfully using six families of NM potentials. It is found that all families converge at 350 MeV. The clear indication of the convergence of the potential families at 350 MeV conforms to the Goldberg criterion concerning the removal of discrete ambiguities even for the shallow NM potential. The study further suggests that the energy of convergence heralds the occurrence of the primary rainbow at that incident energy.

Non-monotonic shallow nucleus-nucleus potential for heavy-ion elastic scattering2

‘Goldberg criterion’ [Goldberg and Smith, Phys. Rev. Lett. 29 (1972) 500] tells that at sufficiently high energies, where pronounced refractive scattering with nuclear rainbow oscillations are followed by an ‘exponential-type falloff’ in the angular distribution, discrete ambiguities are eliminated for the deep monotonic potential. The criterion is also confirmed in the work of Bartnitzky et al. [Phys. Lett. B 365 (1996) 23] on the 16O+16O elastic scattering in the energy range of 250 - 704 MeV. However, their finding ‘using model-independent potentials’ suggests that heavy-ion elastic scattering data unambiguously favour deep potentials. The Goldberg criterion is examined in our work for non-monotonic shallow potentials using the 16O+16O elastic scattering at energy region up to 350 MeV.

Discrete Phase Coded Sequence Set Design for Waveform-Agile Radar Based on Alternating Direction Method of Multipliers

With increased degrees of freedom of the transmitter, a coherent waveform-agile radar system can change its interpulse waveform to enhance the capability against increasingly sophisticated jamming and spoofing threats. Furthermore, radar agile waveform can provide better detection performance than a single waveform. In this article, we consider discrete phase coded sequence set design (DPCSSD) problem based on range-Doppler discrete ambiguity function for coherent waveform-agile radar system. DPCSSD problem for optimizing discrete phase coded sequence set under constant module constraint with desired minimized sidelobes on range-Doppler plane, is a quartic function and the constraint is nonconvex. To solve this quartic optimization problem, we propose an effective algorithm based on alternating direction method of multipliers (ADMM), which is a powerful mathematical tool of the augmented Lagrangian scheme for dealing with separable objective functions. As the quartic optimization problem is hard to solve, majorization-minimization (MM) is also considered to introduce a quadratic auxiliary function which is the upperbound of the original function. By minimizing the auxiliary function, the original DPCSSD optimization problem can be solved through MM in an iterative way. Meanwhile, the problem of minimizing the quadratic auxiliary function with constraints can be solved through ADMM algorithm. In particular, fast implementation for the most computationally demanding step of matrix inversion is investigated. The effectiveness of the proposed approach is demonstrated via computer simulations.

Revisiting CP violation in D→PP and VP decays

Direct CP violation in the hadronic charm decays provides a good testing ground for the Kobayashi-Maskawa mechanism in the Standard Model. Any significant deviations from the expectation would be indirect evidence of physics beyond the Standard Model. In view of improved measurements from LHCb and BESIII experiments, we re-analyze the Cabibbo-favored $D \to P\!P$ and $V\!P$ decays in the topological diagram approach. By assuming certain SU(3)-breaking effects in the tree-type amplitudes, we make predictions for both branching fractions and CP asymmetries of the singly Cabibbo-suppressed decay modes. While the color-allowed and -suppressed amplitudes are preferred to scale by the factor dictated by factorization in the $P\!P$ modes, no such scaling is required in the $V\!P$ modes. The $W$-exchange amplitudes are found to change by 10\% to 50\% and depend on whether $d\overline{d}$ or $s\overline{s}$ pair directly emerges from $W$-exchange. The predictions of branching fractions are generally improved after these SU(3) symmetry breaking effects are taken into account. We show in detail how the tree-type, QCD-penguin, and weak penguin-annihilation diagrams contribute and modify CP asymmetry predictions. Future measurements of sufficiently many direct CP asymmetries will be very useful in removing a discrete ambiguity in the strong phases as well as discriminating among different theory approaches. In particular, we predict $a_{CP}(K^+K^-)-a_{CP}(\pi^+\pi^-) = (-1.14 \pm 0.26) \times 10^{-3}$ or $(-1.25 \pm 0.25) \times 10^{-3}$, consistent with the latest data, and $a_{CP}(K^+K^{*-})-a_{CP}(\pi^+\rho^-) = (-1.52 \pm 0.43) \times 10^{-3}$, an attractive and measurable observable in the near future. Moreover, we observe that such CP asymmetry differences are dominated by long-distance penguin-exchange through final-state rescattering.

Shape-From-Template with Curves

Shape-from-Template (SfT) is the problem of using a shape template to infer the shape of a deformable object observed in an image. The usual case of SfT is ‘Surface’ SfT, where the shape is a 2D surface embedded in 3D, and the image is a 2D perspective projection. We introduce ‘Curve’ SfT, comprising two new cases of SfT where the shape is a 1D curve. The first new case is when the curve is embedded in 2D and the image a 1D perspective projection. The second new case is when the curve is embedded in 3D and the image a 2D perspective projection. We present a thorough theoretical study of these new cases for isometric deformations, which are a good approximation of ropes, cables and wires. Unlike Surface SfT, we show that Curve SfT is only ever solvable up to discrete ambiguities. We present the necessary and sufficient conditions for solvability with critical point analysis. We further show that unlike Surface SfT, Curve SfT cannot be solved locally using exact non-holonomic Partial Differential Equations. Our main technical contributions are two-fold. First, we give a stable, global reconstruction method that models the problem as a discrete Hidden Markov Model. This can generate all candidate solutions. Second, we give a non-convex refinement method using a novel angle-based deformation parameterization. We present quantitative and qualitative results showing that real curve shaped objects such as a necklace can be successfully reconstructed with Curve SfT.

Costas Array Waveforms for Closely Spaced Target Detection

In this paper, we consider requirement-driven selection of Costas arrays for the detection of closely spaced targets. We review existing order selection strategies in terms of the time–bandwidth product and treat selection of specific Costas arrays separably. Our computational analyses prioritize a clear central region in single-pulse discrete ambiguity functions (DAFs) and also address maximum frequency hops. Using finite field arithmetic, we significantly generalize results about 1s in the central square DAF regions for Welch and Lempel–Golomb arrays, and prove two general results about the nonexistence of such clear regions. We find that order 14 is very beneficial for target detection in which Costas arrays having an almost entirely clear $5 \times 5$ square central region in the single-pulse DAF exist and feature the corresponding time–bandwidth product of 196 within an example. We feature a first-principles system simulation with such an order-14 Costas array to obtain a 3-dB target detection improvement. Since radars commonly use burst waveforms, we also consider three different kinds of bursts and discuss their merits using ambiguity function analyses. We provide supporting computational database surveys on central rectangular $3 \times m$ regions.

Exploring Brightarrow pi pi , pi K decays at the high-precision frontier

The Brightarrow pi pi ,pi K system offers a powerful laboratory to probe strong and weak interactions. Using the isospin symmetry, we determine hadronic Brightarrow pi pi parameters from data where new measurements of direct CP violation in B^0_drightarrow pi ^0pi ^0 resolve a discrete ambiguity. With the help of the SU(3) flavour symmetry, the Brightarrow pi pi parameters can be converted into their Brightarrow pi K counterparts, thereby allowing us to make predictions of observables. A particularly interesting decay is B^0_drightarrow pi ^0 K_mathrm{S} as it exhibits mixing-induced CP violation. Using an isospin relation, complemented with a robust SU(3) input, we calculate correlations between the direct and mixing-induced CP asymmetries of B^0_drightarrow pi ^0 K_mathrm{S}, which are the theoretically cleanest Brightarrow pi K probes. Interestingly, they show tensions with respect to the Standard Model. Should this Brightarrow pi K puzzle originate from New Physics, electroweak penguins offer an attractive scenario for new particles to enter. We present a strategy to determine the parameters characterising these topologies and obtain the state-of-the-art picture from current data. In the future, this method will allow us to reveal the Brightarrow pi K dynamics and to obtain insights into the electroweak penguin sector with unprecedented precision.

P099 Comparison of ssop versus ngs for typing of HLA-A, B, C, DRB1, DRB3/B4/B5, DQA1, DQB1, DPA1, DPB1: Toward single pass high resolution hla typing in support of solid organ and hematopoietic cell transplant programs

Aim Many laboratories use a 2-tier HLA typing process: a first pass intermediate resolution and then high resolution, when clinically necessary. SSP or qPCR provide rapid typing for deceased donor workup; SSOP is widely employed for higher volumes; and Sanger sequencing has been the gold standard for high resolution. However, SSOP and Sanger SBT often yield ambiguous results and resolution is expensive and time consuming. Next generation sequencing offers a single pass technology to achieve unambiguous HLA allele assignments. We compared commercial SSOP and NGS systems with respect to accuracy, turnaround time, effort and resolution level. Methods Five laboratories submitted coded, blinded samples, previously typed by SSOP at each institute, to a separate lab for NGS of HLA-A, B, C at exons 1–7, DRB1, DRB3/4/5, DQA1, DQB1, DPB1 at exons 1–4, and DPA1 at exons 2–4. For up to 24 samples by SSOP or up to 48 samples by NGS, benchwork is completed by one technologist on day 1 with results available for reporting on day 2. Results At the SSOP resolution level, results were concordant except for 11 SSOP assignments in 8 specimens due to false probe reactions at DRB1, DRB5, DQA1, DQB1, and DPB1. NGS identified 21 novel sequences: one with a multi-exon deletion and 20 with SNP polymorphisms in HLA-C, DPA1, DPB1, DQA1, DRB1, DRB3, DRB4, and DRB5 alleles. Across the highly polymorphic HLA-A, B, C, DRB1 loci, only 1% of intermediate resolution, IR, SSOP results were unambiguous. Even higher resolution, HR, SSOP by 1 lab gave only 17% specific allele assignments. In contrast, over 99% of NGS results were specific unambiguous genotypes. Across all loci, NGS typing was specific except for certain discrete diploid ambiguities, also found in SSOP. Conclusions This study provides a compelling rationale for implementing NGS for single pass HLA analysis with accurate, 2 day turnaround, which includes the high resolution, unambiguous genotyping critical for unrelated donor HCT and that may be required for sensitized patients with allele specific antibodies. A.G. Smith: 2. Consultant; Company/Organization; Scisco Genetics Inc. S.E. Pereira: 4. Scientific/Medical Advisor; Company/Organization; Scisco Genetics Inc. C. Pyo: 4. Scientific/Medical Advisor; Company/Organization; Scisco Genetics Inc. W. Nelson: 5. Employee; Company/Organization; Scisco Genetics Inc. M. Bettinotti: 3. Speaker’s Bureau; Company/Organization; One Lambda ThermoFisher. M.Z. Askar: 3. Speaker’s Bureau; Company/Organization; Immucor. 4. Scientific/Medical Advisor; Company/Organization; Illumina. D.E. Geraghty: 6. Stock Shareholder; Company/Organization; Scisco Genetics Inc. Download : Download high-res image (283KB) Download : Download full-size image

Novel Adaptive Filter Design for Filter Bank Multicarrier System Under Doubly Dispersive Channel Conditions

ABSTRACTFilter bank multicarrier (FBMC) has emerged as the favourite multicarrier communication technique since it meets the demands of the next-generation standards, especially for communication under doubly dispersive channels. In order to combat the undesirable channel effects like inter symbol interference and inter carrier interference, the prototype filters used in FBMC systems must satisfy orthogonality conditions and be well localized simultaneously in both time and frequency domains. Even though conventional doubly localized filters are optimum in the absence of channel, they fail to satisfy orthogonality and localization criteria under doubly dispersive channels. In the present study, an adaptive filter design method is proposed in which the prototype filter is designed as the weighted sum of a time-limited Nyquist filter, a band-limited Nyquist filter, and doubly localized Gaussian filter based on the analysis of discrete ambiguity function (DAF). The filter is designed to vary its characteristics according to the maximum time and frequency domain dispersions of the channel, so that signal-to-interference ratio is maximized. In order to ensure distortion-less transmission, the perfect reconstruction criterion for distortion-less transmission is mapped to specific conditions for DAF according to two-dimensional channel scattering function. The superiority in performance of the proposed adaptive filter is analysed in terms of signal-to-interference ratio and bit error rate, and is compared with the conventional filters for various channel scattering conditions.

Toward an understanding of discrete ambiguities in truncated partial-wave analyses

It is well known that the observables in a single-channel scattering problem remain invariant once the amplitude is multiplied by an overall energy- and angle-dependent phase. This invariance is called the continuum ambiguity and acts on the infinite partial wave set. It has also long been known that, in the case of a truncated partial wave set, another invariance exists, originating from the replacement of the roots of partial wave amplitudes with their complex conjugate values. This discrete ambiguity is also known as the Omelaenko-Gersten-type ambiguity. In this paper, we show that for scalar particles, discrete ambiguities are just a subset of continuum ambiguities with a specific phase and thus mix partial waves, as the continuum ambiguity does. We present the main features of both, continuum and discrete ambiguities, and describe a numerical method which establishes the relevant phase connection.

Lepton polarization asymmetries in rare semi-tauonic b rightarrow s exclusive decays at FCC-ee

We consider measurements of exclusive rare semi-tauonic b-hadron decays, mediated by the b rightarrow s tau ^+ tau ^- transition, at a future high-energy circular electron–positron collider (FCC-ee). We argue that the high boosts of b-hadrons originating from on-shell Z boson decays allow for a full reconstruction of the decay kinematics in hadronic tau decay modes (up to discrete ambiguities). This, together with the potentially large statistics of Zrightarrow bbar{b}, opens the door for the experimental determination of tau polarizations in these rare b-hadron decays. In the light of the current experimental situation on lepton flavor universality in rare semileptonic B decays, we discuss the complementary short-distance physics information carried by the tau polarizations and suggest suitable theoretically clean observables in the form of single- and double-tau polarization asymmetries.

Efficient User Identification and Semi-Blind Channel Estimation for MU-MIMO Systems

In this letter, we consider an uncoordinated access to the uplink of MU-MIMO cellular networks. Based on randomly rotated modulation constellations, we propose an efficient approach to blind identification of active users and estimation of all involved channels, up to a discrete phase ambiguity. To eliminate this ambiguity, we use short orthogonal pilot sequences. To improve the obtained channel estimates, we also rely on a combination of pilot-based and blind channel estimates. Moreover, since no coordination is assumed with the base station the problem of pilot contamination can occur when some active users use the same pilot sequence. As a solution for this problem, we propose an efficient semi-blind recovery of all contaminated channel estimates.

Shaping Radar Ambiguity Function by <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math> </inline-formula>-Phase Unimodular Sequence

In this paper, we discuss the ambiguity function (AF) synthesis problem for unimodular sequences, which are widely used in radar/sonar and communication systems. Notions of discrete-time ambiguity function and discrete ambiguity function (DAF) are defined, and the corresponding properties are also discussed for unimodular sequences. Depending on these properties, two algorithms are proposed to synthesize the DAF of the unimodular sequence by minimizing the squared error between a desired complex/real function and a realizable one over $L$ -phase alphabet. To break the volume invariant constraint of a single sequence’s AF, multi-sequences are also considered to be optimized simultaneously to suppress sidelobes of ambiguity surface. Numerical examples show the effectiveness of the proposed algorithms in synthesizing unimodular sequence with a desired AF, and typical polyphase sequences can be well approximated by eight-phase unimodular sequences from the viewpoint of DAF.

Shape-from-Template.

We study a problem that we call Shape-from-Template, which is the problem of reconstructing the shape of a deformable surface from a single image and a 3D template. Current methods in the literature address the case of isometric deformations, and relax the isometry constraint to the convex inextensibility constraint, solved using the so-called maximum depth heuristic. We call these methods zeroth-order since they use image point locations (the zeroth-order differential structure) to solve the shape inference problem from a perspective image. We propose a novel class of methods that we call first-order. The key idea is to use both image point locations and their first-order differential structure. The latter can be easily extracted from a warp between the template and the input image. We give a unified problem formulation as a system of PDEs for isometric and conformal surfaces that we solve analytically. This has important consequences. First, it gives the first analytical algorithms to solve this type of reconstruction problems. Second, it gives the first algorithms to solve for the exact constraints. Third, it allows us to study the well-posedness of this type of reconstruction: we establish that isometric surfaces can be reconstructed unambiguously and that conformal surfaces can be reconstructed up to a few discrete ambiguities and a global scale. In the latter case, the candidate solution surfaces are obtained analytically. Experimental results on simulated and real data show that our isometric methods generally perform as well as or outperform state of the art approaches in terms of reconstruction accuracy, while our conformal methods largely outperform all isometric methods for extensible deformations.

Non-monotonic potential description of alpha–Zr refractive elastic scattering

Experimental differential cross sections of α elastic scattering by 90Zr in the 15.0–141.7 MeV range of the bombarding energies have been analysed within the framework of an optical model using non-monotonic (NM) potentials. These potentials are generated from the energy-density functional theory using a realistic two-nucleon potential coupled with an appropriate consideration of the Pauli principle. The NM nature of the real part of the potential seems to be gradually diminishing at energies beyond 118.0 MeV. The Airy structure of the nuclear rainbow scattering data in the energy range of 79.5–141.7 MeV is for the first time well accounted for by the shallow NM potential. Two potential families, which are located in the real part, bear a linear variation of a volume integral in the energy range 25.0–141.7 MeV with a threshold anomaly at the lower energies. The potential contains an interior repulsive part that, with energy, shifts towards the surface and gradually weakens until it is almost lost in the nuclear surface. The requirement of a deep attractive real part of the nuclear potential seems to be generally non-stringent for describing the nuclear rainbow oscillations. Some discrete ambiguities in the potentials seem to persist even when the ‘exponential falloff’ in the angular distribution following the ‘rainbow angle’ is well reproduced in this investigation using the NM real part of the optical potentials.

Truncated partial-wave analysis of a complete experiment for photoproduction of two pseudoscalar mesons on a nucleon

A truncated partial wave analysis for the photoproduction of two pseudoscalar mesons on a nucleon is discussed with respect to the determination of a complete set of observables. For the selection of such a set we have applied a criterion previously developed for photo- and electrodisintegration of a deuteron, which allows one to find a `minimal' set of observables for determining the partial wave amplitudes up to possible discrete ambiguities. The question of resolving the remaining ambiguities by invoking additional observables is discussed for the simplest case, when the partial wave expansion is truncated at the lowest total angular momentum of the final state ${J}_{\mathrm{max}}=1/2$. The resulting `fully' complete set, allowing an unambiguous determination of the partial wave amplitudes, is presented.