Numerical Estimates Research Articles

Optimal Subsampling for Functional Quasi-Mode Regression with Big Data

We propose investigating optimal subsampling for functional regression with massive datasets based on the mode value, which is referred to as functional quasi-mode regression, to reduce data volume and alleviate computational burden. Using data-adaptive weights derived from regression residuals, the suggested regression offers enhanced robustness against nonnormal errors compared to traditional least squares or maximum likelihood estimation methods. To estimate the model, we employ B-spline basis functions to approximate the functional coefficient and include a penalty term in the objective function for enforcing smoothness in the resulting estimator. We adopt a computationally efficient mode-expectation-maximization algorithm, augmented by a Gaussian kernel, for numerical estimation. Under mild regularity conditions, we derive the asymptotic distributions of both full data and subsample quasi-mode estimators. The optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under A- and L-optimality criteria are identified. These optimal probabilities rely on the full data estimate, prompting the development of a two-step algorithm to approximate the optimal subsampling procedure. The resultant algorithm is processing-efficient and can significantly reduce computational time compared to the full data approach. We also establish the asymptotic normality of the quasi-mode estimator obtained through this two-step algorithm. To assess finite sample performance, we conduct Monte Carlo simulations and analyze air quality data, showcasing the effectiveness of the developed estimator. Supplemental materials for this article are available online.

LBM-DEM modeling of particle-fluid interactions on active small solar bodies

Aeolian-like surface features observed on small Solar System bodies have piqued interest in their underlying formation mechanisms. Understanding the evolution of fluid-solid interactions is crucial for elucidating the nature of cometary activity. We established a resolved fluid-particle simulation approach and implemented it into our self-developed DEMBody and LBMCoupler codes to simulate the wind erosion process on comet 67P. We developed this novel framework by applying the lattice Boltzmann method-discrete element method (LBM-DEM) in a low-gravity and rarefied atmosphere environment. The inter-particle forces were modeled using the Hertz contact model, friction, and cohesion. The fluid field was calculated by solving the lattice Boltzmann equations, which use the distribution function as the variable. The fluid-particle forces were modeled using the partially saturated cells method, in which the force is calculated based on the populations of the fluid cells occupied by the solid phase. We conducted 2D and 3D validation simulations and a series of simulations of a regolith layer as a preliminary application to validate the framework. The validation results of the drag coefficient under 2D and 3D conditions are in good agreement with previous theoretical and numerical estimates. Additionally, the wind erosion process on the surface of comet 67P is reproduced using the presented approach. This preliminary application show that the threshold velocity to initiate grain motion on comet 67P is about $25$ $ m/s$, which is consistent with the observations that sediment transport driven by winds frequently occurs near the perihelion of comet 67P. The proposed LBM-DEM framework can be successively applied to simulate the fluid-solid interaction on small solar bodies that have extremely low-gravity and rarefied atmosphere environments. Future works based on this tool and focused on aeolian geologic landforms, such as sand dunes, can help us understand the dynamics of cometary activity.

A Note on Related-Tweakey Impossible Differential Attacks

In this note we review the technique proposed at ToSC 2018 by Sadeghi et al. for attacks built upon several related-tweakey impossible differential trails. We show that the initial encryption queries are improper and lead the authors to misevaluate a filtering value in the key recovery phase. We identified 4 other papers (from Eurocrypt, DCC, and 2 from ToSC) that follow on the results of Sadeghi et al. and in three of them the flawed technique was reused. We thus present a careful analysis of these types of attacks and give generic complexity formulas similar to the ones proposed by Boura et al. at Asiacrypt 2014. We apply these to the aforementioned papers and provide patched versions of their attacks. The main consequence is an increase in the memory complexity. We show that in many cases (a notable exception being quantum impossible differentials) it is possible to recover the numeric time estimates of the flawed analysis, and in all cases we were able to build a correct attack reaching the same number of rounds.

Determination of the density of dark matter in the Solar system

A method based on the Newtonian and relativistic theories of body motion is proposed for calculating the density of dark matter, which, like visible (baryonic) matter, creates a gravitational field. Experimental data obtained by the Pioneer 10 and Pioneer 11 spacecraft and a variety of astronomical observations are used to detect and establish the mass of dark matter in the solar system, which turned out to be approximately equal to the mass of the Sun. Using the equations of motion of test bodies in the Newtonian and post-Newtonian approximations of the general theory of relativity, calculation formulas are obtained for calculating the density of dark matter in three cases: 1) baryonic and dark matter are uniformly distributed in space (their density is constant); 2) they are distributed according to spherically symmetrical laws; 3) baryonic matter is distributed spherically symmetrically, while dark matter is uniformly distributed. In the volume of a sphere with radius of 45 a. u. with the center in the center of gravity of the Sun, on the basis of known experimental data, the average density of the gas-dust and relict matter located in it is calculated, equal to 1,26 · 10–16 g · cm–3. In the same volume, the density of dark matter in all three cases varies according to the derived calculation formulas in the range from 3,38 · 10–16 to 3,34 · 10–16 g · cm–3, which gives the superiority of dark matter over baryonic one from 2.68 to 2.72 times. The given numerical estimates may change when the experimental data used change. The paper also contains a brief discussion of other methods for calculating the density of dark matter in space and a comparison with our results.

Observation-based quantification of aerosol transport using optical flow: A satellite perspective to characterize interregional transport of atmospheric pollution

Interregional transport plays a significant role in haze formation with varying and disputable contribution extent. Current research on quantitatively analyzing interregional atmospheric pollution transport has mainly relied on meteorological and chemical models. However, these models are typically affected by uncertainties due to the assumptions and simplifications inherent in the numerical simulations and source emission estimations. In this study, a comprehensive optical flow framework is developed to offer a new perspective on quantitative characterization of interregional transport of atmospheric pollution based on synergistic observations from geostationary and sun-synchronous satellites. In this framework, the high-frequency continuous aerosol observing images are regarded as video in computer vision, and an aerosol dynamic optical flow algorithm is proposed by incorporating aerosol-specific assumptions and constraints, overcoming the limitation that traditional optical flow methods are typically confined to rigid bodies. Results demonstrate that the developed optical flow framework could distinguish the aerosol transport process from other dynamic processes of aerosol development and accurately capture the fast-changing details of transport processes. Moreover, the satellite-based optical flow framework achieves aerosol transport results comparable to those of widely accepted model-based methods, demonstrating the physical interpretation of pixel-based optical flow results and highlighting its effectiveness in quantitative characterization of the atmospheric pollution transport process via the Aerosol Transport Index (ATI). Furthermore, a case analysis of long-term assessments of interregional transport of atmospheric pollution indicates that Beijing acts as a “sink” of atmospheric pollution, and a downward trend could be found from the annually averaged transported aerosol net loadings due to the emission reduction policy. Compared with model-based methods, the satellite-based optical flow framework is directly grounded in observations and does not rely on emission inventories that take years to update. Therefore, it not only helps improve understanding the patterns of atmospheric pollution interregional transport, but also provides a more efficient and economical way to assess the effectiveness of regional joint control policy.

Forecasting two-dimensional channel flow using machine learning

Over the past decade, the integration of artificial neural networks (ANNs) has garnered significant interest, capitalizing on their ability to discern intricate patterns within data. Focused on enhancing computational efficiency, this article explores the application of ANNs in forecasting fluid-dynamics simulations, particularly for the benchmark problem of fluid flow in a two-dimensional (2D) channel. Leveraging a multilayer perceptron trained on finite volume method numerical data, for both interpolation and extrapolation estimations and various grid resolutions, our findings demonstrate the ANN's prowess as a swift and accurate surrogate for traditional numerical methods. Overall, the results of this work mark a pioneering step toward leveraging machine learning for modeling complex relationships in fluids phenomena, promising transformative advancements in computational fluid dynamics.

Hydrodynamic force coefficients for spherical triangle shell fragments: Dependence on the aspect ratio and flatness

Euler–Lagrange simulations of particle-laden flow require hydrodynamic models of drag and lift forces for individual particles. Our goal is to develop models that can prescribe these forces for arbitrarily orientated shell objects. Here, we use computational fluid dynamics simulations of steady bottom-boundary layer flow over a series of spherical triangle shell fragments to calculate the hydrodynamic forces. The simulations explicitly resolve the wall boundary layers using grid resolution on the order of y+=1 at the shell fragment surface and use the SST k-omega turbulence closure model. These fragments cover a range of aspect ratio and flatness characteristics. The shell fragments are generated as triangular selections of a spherical shell with azimuthal and longitudinal angles proscribed based on elongation and flatness parameters (varying between 1 to 5, and 0.02 to 0.2 respectively), while characteristic length of the fragment is held constant to define the overall fragment size. Fragment orientations are considered with independently varying pitch, roll, and yaw each ranging from 0 to 180 degrees. The numerical estimates for the forces from all simulations were used to develop robust parameterizations of the drag and lift as a function of aspect ratio and flatness characteristics, as well as orientation of the shell fragments.

Characterization of fine geographic scale population genetics in sugar kelp (Saccharina latissima) using genome-wide markers

BackgroundKelps are not only ecologically important, being primary producers and habitat forming species, they also hold substantial economic potential. Expansion of the kelp cultivation industry raises the interest for genetic improvement of kelp for cultivation, as well as concerns about genetic introgression from cultivated to wild populations. Thus, increased understanding of population genetics in natural kelp populations is crucial. Genotyping-by-sequencing (GBS) is a powerful tool for studying population genetics. Here, using Saccharina latissima (sugar kelp) as our study species, we characterize the population genetics at a fine geographic scale, while also investigating the influence of marker type (biallelic SNPs versus multi-allelic short read-backed haplotypes) and minor allele count (MAC) thresholds on estimated population genetic metrics.ResultsWe examined 150 sporophytes from 10 locations within a small area in Mid-Norway. Employing GBS, we detected 20,710 bi-allelic SNPs and 42,264 haplotype alleles at 20,297 high quality GBS loci. We used both marker types as well as two MAC filtering thresholds (3 and 15) in the analyses. Overall, higher genetic diversity, more outbreeding and stronger substructure was estimated using haplotypes compared to SNPs, and with MAC 15 compared to MAC 3. The population displayed high genetic diversity (HE ranging from 0.18–0.37) and significant outbreeding (FIS ≤ − 0.076). Construction of a genomic relationship matrix, however, revealed a few close relatives within sampling locations. The connectivity between sampling locations was high (FST ≤ 0.09), but subtle, yet significant, genetic substructure was detected, even between sampling locations separated by less than 2 km. Isolation-by-distance was significant and explained 15% of the genetic variation, while incorporation of predicted currents in an “isolation-by-oceanography” model explained a larger proportion (~ 27%).ConclusionThe studied population is diverse, significantly outbred and exhibits high connectivity, partly due to local currents. The use of genome-wide markers combined with permutation testing provides high statistical power to detect subtle population substructure and inbreeding or outbreeding. Short haplotypes extracted from GBS data and removal of rare alleles enhances the resolution. Careful consideration of marker type and filtering thresholds is crucial when comparing independent studies, as they profoundly influence numerical estimates of population genetic metrics.

Numerical Simulation and Parameter Estimation of the Space-Fractional Magnetohydrodynamic Flow and Heat Transfer Coupled Model

Numerical Simulation and Parameter Estimation of the Space-Fractional Magnetohydrodynamic Flow and Heat Transfer Coupled Model

On a numerical estimation method with a given accuracy of a quantile criterion in the case of a piece-linear loss function and a gaussian probability density

The solution of many practical problems leads to the calculation of the values of probabilistic criteria, the most common of which are the quantile and probability functionals. It is known that, under fairly general assumptions, methods suitable for solving problems of finding the values of a probabilistic criterion can be used to solve the problem of quantile analysis. The proposed method for solving the problem of quantile analysis is based on the use of the method of numerical multidimensional integration described in the previous works of the author. One of the important properties of this integration method is universality (when using it, we can set an arbitrary number of variables n and an arbitrary number of linear constraints r). The only limitation is the case of an unacceptably long solution time. Thus, the indicated universality is transferred to the solution of the considered problem of quantile analysis.

A combined DFT and finite difference simulation study on hybrid halide perovskite-based solar cells

This work reports the modelling and numerical estimation of the photovoltaic parameters of perovskite solar cells (PSCs) containing formamidinium lead iodide (FAPbI3) and formamidinium tin iodide (FASnI3) in the form of light active materials using SCAPS 1D software. The analysis is done by introducing diverse hole and electron transport materials and back metal contacts to identify the most appropriate device configuration that can deliver optimum photovoltaic output. The optoelectronic properties and the absorption spectra of the two compounds are estimated by DFT calculation using WIEN2k, which incorporates density functional theory (DFT) principles and are provided as input to SCAPS 1D to improve the accuracy of modelling study. For FAPbI3 as absorber material, the configuration FTO/IGZO/FAPbI3/NiO/Au shows the highest photovoltaic parameter exhibiting a power conversion efficiency (PCE) and fill factor (FF) of 19.75 % and 74.29 % respectively. With FASnI3 as the absorber material, FTO/PCBM/FASnI3/P3HT/Au gives a PCE and FF of 21.6 % and 67.74 % respectively. The work also includes the analysis of influence of defect density at the interface layers and series and shunt resistance on performance of above-mentioned device architectures to identify their limitations under real experimental conditions. The influence of various attributes of perovskite on the performance of the device is examined to determine their optimum values.

Competition between transient oscillations and early stochasticity in exponentially growing populations

It has been recently shown that the exponential growth rate of a population of bacterial cells starting from a single cell shows transient oscillations due to early synchronized bursts of division. These oscillations are enhanced by cell size regulation and contain information about single-cell growth statistics. Here, we report a phase transition in these oscillations as a function of growth rate variability. Below the transition point, these oscillations become asymptotically deterministic and can be measured experimentally, while above the transition point, the stochasticity in population growth dominates the oscillations and masks all the information about single cell growth statistics. The analytically calculated transition point, which roughly corresponds to 13% variability in single-cell growth rate, falls within physiologically relevant parameters. Additionally, we show that the oscillations can stochastically emerge even when the initial state contains multiple cells with out-of-phase division cycles. We show that the amplitude and phase of these oscillations are stochastic and vary across repeated measurements with the same initial conditions. We provide analytic expressions as well as numerical estimates for the typical oscillation amplitude and the number of generations before the amplitude falls below a given measurement threshold for in multiple growth conditions. Published by the American Physical Society 2024

Estimation and validation of elastic constants in fused filament fabrication 3D printing: From mesoscale to macroscale

Evaluating the mechanical properties of 3D-printed parts is a cumbersome task. This study poses an approach based on computational homogenization to estimate the elastic constants of fused filament fabrication 3D-printed parts. A whole methodology for characterization and experimental validation is necessary to improve finite element numerical models.Samples are characterized both mechanically and geometrically. To improve the characterization, novel algorithms based on micro-computed tomography images and image segmentation techniques are implemented. Thereafter, elastic constants are estimated, informed by the characterization results. The method’s effectiveness is assessed through a deep comparison, based on the digital image correlation technique, between different experimental samples and finite element models.Results show that the numerical estimation provided in this work is accurate enough to develop realistic finite element models, including anisotropy of the structures. However, defects and voids developed during 3D printing are an important source of error for these numerical models.This work provides an estimation and validation of elastic constants in 3D-printed parts, including geometrical characterization, numerical homogenization and experimental validation. The results of this work provide valuable information encompassing techniques to improve the characterization of 3D-printed parts, tendencies on elastic constants, and main sources of error.

Analysis of The Influence of Models of Individual Physical Processes and Phenomena on the Calculation Time of the Source Term in Severe Accidents

Dependence of the CPU time needs for calculation of the source term during a severe accident at nuclear power plants with WWER reactors from the individual physical processes and phenomena used as part of the calculation tools similar to the SOСRAT/V3 severe accident code is investigated. This analysis allows revealing the most expensive models in terms of runtime. The simplification of these models can ensure the greatest acceleration of the calculation. The relevance of the task draws from the need to develop new or adapt existing calculation tools for assessing the intensity of radioactive emission sources for the tasks of emergency preparedness and response considering the specific requirements for the accuracy of numerical estimates and time to obtain them. The paper demonstrates the possibility of reducing CPU time without significant loss of accuracy of the numerical estimates by simplifying the spectrum of aerosols sizes. The efficiency of the proposed approach is demonstrated by the example of modeling the Phebus FPT1 experiment.

Numerical investigation on secondary injection and thrust vector control in a planar double divergent nozzle

In this work, the performance of secondary injection thrust vector control of an altitude adaptive planar double divergent supersonic nozzle is numerically investigated. The compressible turbulent flow is solved using the kT−kL−ω transition-sensitive eddy-viscosity model. An analytical model to predict the separation distance and penetration height due to secondary fluid injection is developed based on the blunt-body theory, and it shows good agreement with the numerical estimation. The computational results indicate that injection pressure, injector location and injection angle significantly impact the thrust vector control performance. The core flow is disrupted by the momentum injection from the secondary fluid, causing the flow field structure to become asymmetrical. The wall pressure imbalance between the upper and lower nozzle increases as the secondary jet pressure elevates. Further, the thrust vectoring amplification factor is improved when the injector is placed downstream near the outlet since the shock reflection is circumvented. Indeed, that resulted in the generation of a large lateral thrust force. Most importantly, for a high injector slot angle, the primary downstream vortex disappears, and a strong secondary upstream vortex is generated, which shifts the primary upstream vortex opposite to the core flow, subsequently the shock separation is advanced. In addition, a secondary injector fitted near the exit with high inclination angles and injection pressure generated a lateral thrust of 20%.

Unraveling gluon TMDs in J/ψ and pion production at the EIC

We investigate the azimuthal asymmetries such as cos2ϕT and Sivers symmetry for J/ψ and π± production in electron-proton scattering, focusing on scenarios where the J/ψ and the pion are produced in an almost back-to-back configuration. The electron is unpolarized, while the proton can be unpolarized or transversely polarized. For the J/ψ formation, we use nonrelativistic QCD (NRQCD), while π± is formed due to parton fragmentation. In this kinematics, we utilize the transverse momentum-dependent factorization framework to calculate the cross sections and asymmetries. We consider both quark and gluon-initiated processes and show that the gluon contribution dominates. In this work, we used the generalized parton model (GPM) for the transverse momentum distribution (TMD) parametrizations and did not consider the effect of TMD evolution. We provide numerical estimates of the upper bounds on the azimuthal asymmetries, as well as employ a Gaussian parametrization for the gluon TMDs, within the kinematical region accessible by the upcoming Electron-Ion Collider (EIC). Published by the American Physical Society 2024

Investigation of the dynamics of transverse oscillations of a vertical rod under gravity, friction, and thermal expansion

The paper considers the mathematical formulation of the problem of transverse oscillations of a vertical rod under gravity, friction and external pulse effect, leading to thermal expansion of the rod. The dynamics of the system under consideration corresponds to the behavior of a fuel element (FE) in a pulsed reactor and is related to the dynamic stability of the processes occurring in it.The FE dynamics is described by inhomogeneous linear differential equation of the fourth order with non-constant coefficients. Initial boundary conditions are not smooth since they correspond to the instant heating of the part of the FE surface exposed to neutron pulse radiation. The general solution of the homogeneous linear equation can be found using the concept of generalized functions expressed as a series expansion in terms of coordinate eigenfunctions dependent on p parameter. The p parameter is related with the FE mass and at some certain values results in bifurcation points of the boundary value problem for eigenfunctions. The partial solution can be found in several ways: using the Fourier transform, the method of Green's function, and in terms of series expansion by eigenfunctions.Eigenfunction expansion coefficients in an explicit form have been obtained and the numerical solution accuracy has been estimated for some important particular cases. The results of the obtained exact solutions appear to be very close to the results of the ANSYS numerical estimations. In the future the obtained exact solutions will be used as input data to simulate self-consistent system dynamics of more than 400 FE. Therefore, the advantage of the exact solution in practical use is that its calculation is much faster as compared with the finite element method done with ANSYS.

GaAs quantum transport: Scrutinizing the effects of pressure, temperature and Rashba-Dresselhaus spin-orbit interactions for next-generation spintronic devices

This research investigates the spin-dependent transmission attributes and associated Giant Magnetoresistance (GMR) effect emerging from spin-polarized electron tunneling in a GaAs quantum well superlattice (QWS). The influence of Rashba and Dresselhaus spin-orbit interactions (SOIs) on transport properties is analyzed under the framework of the scattering matrix method. Our quantitative findings revealed that these spin-orbit couplings (SOCs) introduce inherent spin-filtering mechanisms, significantly influencing transmission probabilities. Furthermore, numerical estimations proved that external perturbations including pressure, temperature and structural modifications considerably impact the quantum transport characteristics of the scrutinized system. Additionally, major outcomes suggest that precise manipulation of spin-dependent transport in GaAs QWS holds promise for advancing spintronics technology. It is found that with well-tuned parameter values, the SOCs behave as a spin-dependent barrier modifying the band shape and its anisotropy. This study offers novel insights into the fundamental physics governing spin-dependent transport within quantum superlattices with promising implications for the development of advanced spintronic devices.

Point evaluation in Paley–Wiener spaces

We study the norm of point evaluation at the origin in the Paley–Wiener space PWp for 0 < p < ∞, i.e., we search for the smallest positive constant C, called Cp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathscr{C}}_{p}$$\\end{document}, such that the inequality |f(0)|p≤C∥f∥pp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\vert f(0)\\vert ^{p}\\leq C \\Vert f\\Vert _{p}^{p}$$\\end{document} holds for every f in PWp. We present evidence and prove several results supporting the following monotonicity conjecture: The function p↦Cp/p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p \\mapsto {\\mathscr{C}}_{p}/p$$\\end{document} is strictly decreasing on the half-line (0, ∞). Our main result implies that Cp<p/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathscr{C}}_{p} < p/2$$\\end{document} for 2 < p < ∞, and we verify numerically that Cp>p/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathscr{C}}_{p} > p/2$$\\end{document} for 1 ≤ p < 2. We also estimate the asymptotic behavior of Cp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathscr{C}}_{p}$$\\end{document} as p → ∞ and as p → 0+. Our approach is based on expressing Cp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathscr{C}}_{p}$$\\end{document} as the solution of an extremal problem. Extremal functions exist for all 0 < p < ∞; they are real entire functions with only real zeros, and the extremal functions are known to be unique for 1 ≤ p < ∞. Following work of Hörmander and Bernhardsson, we rely on certain orthogonality relations associated with the zeros of extremal functions, along with certain integral formulas representing respectively extremal functions and general functions at the origin. We also use precise numerical estimates for the largest eigenvalue of the Landau–Pollak–Slepian operator of time-frequency concentration. A number of qualitative and quantitative results on the distribution of the zeros of extremal functions are established. In the range 1 < p < ∞, the orthogonality relations associated with the zeros of the extremal function are linked to a de Branges space. We state a number of conjectures and further open problems pertaining to Cp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathscr{C}}_{p}$$\\end{document} and the extremal functions.

Quantifying the performance of bidirectional quantum teleportation

Bidirectional teleportation is a fundamental protocol for exchanging quantum information between two parties by means of a shared resource state and local operations and classical communication (LOCC). In this paper, we develop two seemingly different ways of quantifying the simulation error of unideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity, and we prove that they are equivalent. By relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semi-definite programming lower bounds on the simulation error of unideal bidirectional teleportation. We evaluate these bounds for several key examples: when there is no resource state at all and for isotropic and Werner states, in each case finding an analytical solution. The first aforementioned example establishes a benchmark for classical versus quantum bidirectional teleportation. Another example consists of a resource state resulting from the action of a generalized amplitude damping channel on two Bell states, for which we find an analytical expression for the simulation error that is in agreement with numerical estimates (up to numerical precision). We then evaluate the performance of some schemes for bidirectional teleportation due to (Kiktenko et al., Phys. Rev. A 93, 062305 (2016)) and find that they are suboptimal and do not go beyond the aforementioned classical limit for bidirectional teleportation. We offer a scheme alternative to theirs that is provably optimal. Finally, we generalize the whole development to the setting of bidirectional controlled teleportation, in which there is an additional assisting party who helps with the exchange of quantum information, and we establish semi-definite programming lower bounds on the simulation error for this task. More generally, we provide semi-definite programming lower bounds on the performance of bipartite and multipartite channel simulation using a shared resource state and LOCC.