Binary Signals Research Articles

Observability of spin precession in the presence of a black-hole remnant kick

Remnants of binary black-hole mergers can gain significant recoil or kick velocities when the binaries are asymmetric. The kick is the consequence of the anisotropic emission of gravitational waves, which may leave a characteristic imprint in the observed signal. So far, only one gravitational-wave event supports a nonzero kick velocity: GW200129_065458. This signal is also the first to show evidence for spin precession. For most other gravitational-wave observations, spin orientations are poorly constrained as this would require large signal-to-noise ratios, unequal mass ratios, or inclined systems. Here we investigate whether the imprint of the kick can help to extract more information about the spins. We perform an injection and recovery study comparing binary black-hole signals with significantly different kick magnitudes, but the same spin magnitudes and spin tilts. To exclude the impact of higher signal harmonics in parameter estimation, we focus on equal-mass binaries that are oriented face-on. This is also motivated by the fact that equal-mass binaries produce the largest kicks and many observed gravitational-wave events are expected to be close to this configuration. We generate signals with henom4a, which includes mode asymmetries. These asymmetries are the main cause for the kick in precessing binaries. For comparison with an equivalent model without asymmetries, we repeat the same injections with henom. We find that signals with large kicks necessarily include large asymmetries, and these give more structure to the signal, leading to more informative measurements of the spins and mass ratio. Our results also complement previous findings that argued precession in equal-mass, face-on, or face-away binaries is nearly impossible to identify. In contrast, we find that in the presence of a remnant kick, even those signals become more informative and allow determining precession with signal-to-noise ratios observable already by current gravitational-wave detectors. Published by the American Physical Society 2024

Design of modulated signal waveform in fully digital programmable optical frequency comb

AbstractThis paper presents a new design method of digital baseband signal for generating fully digital programmable optical frequency comb (OFC), which solves the problem of how to optimally select the digital baseband signal when OFC is generated by binary digital signal modulation. The inverse Fourier transform is used to study the waveform of binary digital signal which is used to generate OFC. It is found that the number of “0” bits of digital signal determines the flatness of comb lines. Based on this, a tunable ultra‐fine and ultra‐flat OFC was obtained by using a digital signal containing a large number of “0” bits in the experiment. This saves substantial computing time and resources compared to the current method of the k‐means clustering algorithm.

Analysis of Moiré pattern for parallel binary gratings based on AND and OR operators

A method for analyzing the Moiré pattern of a parallel binary grating based on the high-frequency component of the omitted pattern is proposed. The analysis aims to investigate the signal components that influence the dark-light band formation of the Moiré pattern. The analytical technique begins with the consideration that both grating patterns are a set of binary rectangular signals with two signal level values, ‘0’ and ‘1.’ Subsequently, Fourier series expansion of these two sets of signals was performed considering the frequency, initial phase and duty cycle of the signals. The superposition of both input signals relies on algebraic equations equivalent to AND and OR operators. The final step was to eliminate the effect of the high-frequency component, which is analogous to the low-pass filter of the electronic circuit (based on averaging the signal intensity per image length). If the frequencies of the two gratings are equal, the analysis based on both operators provides an output signal depending on the initial phase (placement position) and duty cycle values. If the frequencies of the two gratings are not equal, the analysis results show that the output signal has a frequency equal to the frequency difference between the two signals. Moreover, if the two input gratings had a duty cycle of 0.5, the overlapping resulted in a triangular shape. The results from the computer program to simulate the AND and OR operators were consistently compared to the plots of the analytical equations. In addition, they are compatible with image processing results.

Creation of a Mathematical Model of a Stationary Rail Circuit in the Form of a Finite Discrete Automaton

Purpose. Ensuring the safety of train traffic is a mandatory task in the development of technical equipment of railway transport in Ukraine. To diagnose and verify the performance of such systems, simulation models of overhead devices, in particular, the rail circle, are used. The most commonly used models are in the form of differential equations and in operator form. Unfortunately, they are not fully suitable for solving this problem. In this regard, there is a need to create a mathematical model that is easier to integrate for checking both relay electrical interlocking and microprocessor-based interlocking systems. Methodology. To achieve this goal, the authors proposed to create a mathematical model in the form of a finite discrete automaton. This paper considers the creation of a model of a station rail circuit as a directed graph. During the creation of the model, the input and output values of the model and the states are determined. The tables of inputs and outputs of the automaton are constructed, sequential expressions for the abstract model of the automaton are created, and their minimization is performed. The states of the automaton are coded using trigger circuits. Findings. In the course of the research, a mathematical model of the rail circle in the form of a Moore model finite automaton was created, and its performance was tested in the Proteus software environment. The developed model allows to simulate the operation of a stationary rail circuit at the level of abstraction, which operates with binary signals. This makes it possible to simplify the coordination of the model with microprocessor-based centralization software. In general, it is now possible to more effectively check the performance of microprocessor-based interlocking systems at the design and commissioning stages. Originality. The developed mathematical model makes it possible to determine the response of the microprocessor-based centralization software to the behavior of the rail circuit in various, in particular atypical, operating modes, as well as to determine the response of the station electrical centralization system to individual failures and to the occurrence of several failures simultaneously. Practical value. The proposed mathematical model can be used both to check the operation of microprocessor-based centralization systems at the design and implementation stages and for relay centralization systems when developing diagnostic complexes for monitoring their performance.

Reconstruction of Binary Black Hole Harmonics in LIGO Using Deep Learning

Gravitational-wave signals from coalescing compact binaries in the LIGO and Virgo interferometers are primarily detected by the template-based matched filtering method. While this method is optimal for stationary and Gaussian data scenarios, its sensitivity is often affected by nonstationary noise transients in the detectors. Moreover, most of the current searches do not account for the effects of precession of black hole spins and higher-order waveform harmonics, focusing solely on the leading-order quadrupolar modes. This limitation impacts our search for interesting astrophysical sources, such as intermediate-mass black hole binaries and hierarchical mergers. Here we show, for the first time, that deep learning can be used for accurate waveform reconstruction of precessing binary black hole signals with higher-order modes. This approach can also be adapted into a rapid trigger generation algorithm to enhance online searches. Our model, tested on simulated injections in real LIGO noise from the third observing run (2019–2020) achieved a high degree of overlap with injected signals. This accuracy was consistent across a wide range of black hole masses and spin configurations chosen for this study. When applied to real gravitational-wave events, our model's reconstructions achieved between 85% and 98% overlap with those obtained by Coherent WaveBurst (unmodeled) and LALInference (modeled) analyses. These results suggest that deep learning is a potent tool for analyzing signals from a diverse catalog of compact binaries.

Photo-dynamical Analysis of Circumbinary Multi-planet System TOI-1338: A Fully Coplanar Configuration with a Puffy Planet

TOI-1338 is the first circumbinary planet (CBP) system discovered by TESS. It has one transiting planet at P ∼ 95 days and an outer nontransiting planet at P ∼ 215 days complemented by radial velocity (RV) observation. Here we present a global photodynamical modeling of the TOI-1338 system that self-consistently accounts for the mutual gravitational interactions between all known bodies in the system. As a result, the three-dimensional architecture of the system can be established by comparing the model with additional data from TESS Extended Mission and published HARPS/ESPRESSO RV data. We report an inconsistency of binary RV signal between HARPS and ESPRESSO, which could be due to the contamination of the secondary star. According to stability analysis, the RV data via ESPRESSO are preferred. Our results are summarized as follows: (1) The inner transiting planet is extremely coplanar to the binary plane ΔI b ∼ 0.°12, making it a permanently transiting circumbinary planet at any nodal precession phases; we updated the future transit ephemerides with improved precisions. (2) The outer planet, despite its untransiting nature, is also coplanar with the binary plane by ΔIc=9.°1−4.°8+6.°0 (22° for the 99% upper limit). (3) The inner planet could have an extremely low density of 0.137 ± 0.026 g cm−3. With a TESS magnitude of 11.45, TOI-1338 b is an optimal circumbinary planet CBP for ground-based follow-up and transit spectroscopy.

Calibrating gravitational-wave search algorithms with conformal prediction

In astronomy, we frequently face the decision problem: does this data contain a signal? Typically, a statistical approach is used, which requires a threshold. The choice of threshold presents a common challenge in settings where signals and noise must be delineated, but their distributions overlap. Gravitational-wave astronomy, which has gone from the first discovery to catalogs of hundreds of events in less than a decade, presents a fascinating case study. For signals from colliding compact objects, the field has evolved from a frequentist to a Bayesian methodology. However, the issue of choosing a threshold and validating noise contamination in a catalog persists. Confusion and debate often arise due to the misapplication of statistical concepts, the complicated nature of the detection statistics, and the inclusion of astrophysical background models. We introduce conformal prediction (CP), a framework developed in machine learning to provide distribution-free uncertainty quantification to point predictors. We show that CP can be viewed as an extension of the traditional statistical frameworks whereby thresholds are calibrated such that the uncertainty intervals are statistically rigorous and the error rate can be validated. Moreover, we discuss how CP offers a framework to optimally build a metapipeline combining the outputs from multiple independent searches. We introduce CP with a toy cosmic-ray detector, which captures the salient features of most astrophysical search problems and allows us to demonstrate the features of CP in a simple context. We then apply the approach to a recent gravitational-wave mock data challenge using multiple search algorithms for compact binary coalescence signals in interferometric gravitational-wave data. Finally, we conclude with a discussion on the future potential of the method for gravitational-wave astronomy. Published by the American Physical Society 2024

A High-Speed Multichannel Electrochemical Impedance Spectroscopy System Using Broadband Multi-Sine Binary Perturbation for Retired Li-Ion Batteries of Electric Vehicles

Retired electric vehicle (EV) batteries are reused in second-life energy storage applications. However, the overall performance of repurposed energy storage systems (ESSs) is limited by the variability in the individual batteries used. Therefore, battery grading is required for the optimal performance of ESSs. Electrochemical impedance spectroscopy (EIS)-based evaluation of battery aging is a promising way to grade lithium-ion batteries. However, it is not practical to measure the impedance of mass-retired batteries due to their high complexity and slowness. In this paper, a broadband multi-sine binary signal (MSBS) perturbation integrated with a multichannel EIS system is presented to measure the impedance spectra for the high-speed aging evaluation of lithium-ion batteries or modules. The measurement speed is multiple times higher than that of the conventional EIS. The broadband MSBS is validated with a reference sinusoidal sweep perturbation, and the corresponding root-mean-square error (RMSE) analysis is performed. Moreover, the accuracy of the presented multichannel EIS system is validated by impedance spectra measurements of Samsung INR18650-29E batteries and compared with those measured using a commercial EIS instrument. A chi-squared error under 0.641% is obtained for all channels. The non-linearity of batteries has a significant impact on the quality of impedance spectra. Therefore, Kronig–Kramer (KK) transform validation is also performed.

Correlation properties of complete code of binary spread spectrum phase-shift keyed signals with polarization coding

Problem statement. Investigation of correlation properties of complete code of binary spread spectrum phase-shift keyed signals as the limiting case of large systems is a topical task for building large systems of binary spread spectrum phase-shift keyed signals with polarization coding with optimal correlation properties. Also, this task is of independent academic interest due to the fact that the alphabet of symbols for these signals lacks multicasting properties unlike the familiar cases of complete codes of spread spectrum phase-shift keyed signals. Objective. To accurately define the distribution laws as well as the moments about zero and the mean for the n-th order of presented values of aperiodic and periodic correlation functions of the complete code of binary spread spectrum phase-shift keyed signals with polarization coding. To offer approximations of accurate distribution laws suitable for engineering applications. Results. The accurate distribution laws for presented values of aperiodic and periodic correlation functions of the complete code of binary spread spectrum phase-shift keyed signals with polarization coding were found in the form of the related distribution series. The analytic expressions for the n-th order of presented values of these functions for the complete code of the specified signals were assigned. The calculation example for the distribution series of presented values of aperiodic and periodic correlation functions for the complete code of the specified signals with the length of vector code sequences N=4 was given. The values of the relative frequencies of the correlation functions values for this case were found by the means of direct computing and their exact match with the corresponding predicted probability values was demonstrated. The approximations of the accurate distribution laws were given: for periodic correlation functions case – by Gaussian probability density, and for the aperiodic functions case – by the Pearson curve of VII type. Practical relevance. The found accurate laws for presented values of aperiodic and periodic correlation functions of the complete code of binary spread spectrum phase-shift keyed signals with polarization coding and their approximations allow to assess the correlation properties of large systems of such signals.

Prediction of flame transfer function and combustion instability on a partially premixed swirling combustor by the system identification and CFD methods

Combustion instability can lead to high amplitude oscillations of pressure in the combustion chamber, which would seriously affect the normal operation of the combustion system. In order to reduce the cost and time of combustion chamber design and testing, combustion instability of the partially premixed swirl combustor was predicted, by solving the Helmholtz equation coupled the flame transfer unction (FTF). In the experimental study, by changing the equivalence ratio, the pressure in the combustion chamber appeared to oscillate in different forms including combustion noise, intermittent oscillation and limit cycle oscillation, while the frequency of the self-excited oscillations was obtained to be 165 Hz at the equivalence ratio of 0.7. In Computational Fluid Dynamics (CFD) Simulations, by applying Discrete Random Binary Signal (DRBS) excitation at the inlet, the FTF has been calculated by system identification method, where the excitation results of perturbation signals with different magnitudes were studied. And the result was basically consistent with the FTF calculated by the single-frequency excitation method, which means that the system identification method is suitable for calculating the FTF of the partially premixed swirl combustor. The pulse excitation method has been proposed to determine the selection of the filtering order, and the accuracy of the method has been validated through comparing the FTF results obtained by using different filter orders for discrimination. Moreover, coupling the FTF into the Helmholtz equation, the oscillation frequency of the system was predicted as 159.7 Hz, compared with the experimentally measured oscillation frequency of 165 Hz, which verified that the model could be effectively used for the prediction of oscillation frequency in the partially premixed combustion systems.

Помехоустойчивость когерентного приема двоичных сигналов с огибающей вида приподнятый косинус в гидроакустическом канале связи

Goals: The main purpose of this work is to develop a methodology for determining the parameters of binary signals, at which the signals become relatively invariant to frequency distortions in the marine environment. The frequency distortion of the signals is caused by the uneven frequency response of the attenuation of the marine environment. The main part of this technique is to assess the effect of frequency distortion of signals on the noise immunity of reception. In accordance with this, the error probabilities of signal receivers with various types of manipulation are determined, which are optimal in the absence of distortion. Methods: The provisions of applied hydroacoustics, the theory of random processes and the theory of transmission of discrete messages are used. The main content: The paper considered a model of a single-beam hydroacoustic communication channel, characteristic of the deep sea, when the receiver or transmitter is located in the depths of the sea. The transmission coefficient of the channel is used as a transmission coefficient with a Gaussian amplitude -frequency response and a linear phase-frequency response. The error probabilities of coherent receivers of binary signals with amplitude, frequency and phase manipulation with an envelope of the raised cosine type are determined. Coherent receivers optimal by the criterion of maximum likelihood under the action of white Gaussian noise and the absence of distortion in the marine environment are considered as receivers. A logarithmic measure of increasing the probability of error is introduced, which characterizes the deterioration of noise immunity due to frequency distortions in the channel. For some typical cases, the values of signal parameters that are relatively invariant to frequency distortions in the marine environment are determined. Results: Expressions of the error probability of coherent receivers of binary signals with amplitude, frequency and phase manipulation with an envelope of the raised cosine type are found. A logarithmic measure of the relative increase in the probability of error compared to the case of no distortion is introduced. The functional dependence of this measure on the duration of sending the signal, the carrier frequency and the initial phase of the signal, as well as on the communication range and the signal-to-noise ratio is determined. On the plane of the carrier frequency, signal duration, for each type of signal, the boundary of the region above which the signals are relatively invariant to frequency distortions in the marine environment is constructed, a comparison is made with the case of signals with a sinusoidal envelope. For communication ranges R = 1.5 km and 3 km and typical carrier frequencies, the minimum values of the duration of invariant signals are given. Expressions of the error probability of coherent receivers of binary signals with amplitude, frequency and phase manipulation with an envelope of the raised cosine type are found. A logarithmic measure of the relative increase in the probability of error compared to the case of no distortion is introduced. The functional dependence of this measure on the duration of sending the signal, the carrier frequency and the initial phase of the signal, as well as on the communication range and the signal-to-noise ratio is determined. On the plane of the carrier frequency, signal duration, for each type of signal, the boundary of the region above which the signals are relatively invariant to frequency distortions in the marine environment is constructed, a comparison is made with the case of signals with a sinusoidal envelope. For communication ranges R = 1.5 km and 3 km and typical carrier frequencies, the minimum values of the duration of invariant signals are given.

Simulation and Controller Design for a Fish Robot with Control Fins.

In this paper, a nonlinear simulation block for a fish robot was designed using MATLAB Simulink. The simulation block incorporated added masses, hydrodynamic damping forces, restoring forces, and forces and moments due to dorsal fins, pectoral fins, and caudal fins into six-degree-of-freedom equations of motion. To obtain a linearized model, we used three different nominal surge velocities (i.e., 0.2 m/s, 0.4 m/s, and 0.6 m/s). After obtaining output responses by applying pseudo-random binary signal inputs to a nonlinear model, an identification tool was used to obtain approximated linear models between inputs and outputs. Utilizing the obtained linearized models, two-degree-of-freedom proportional, integral, and derivative controllers were designed, and their characteristics were analyzed. For the 0.4 m/s nominal surge velocity models, the gain margins and phase margins of the surge, pitch, and yaw controllers were infinity and 69 degrees, 26.3 dB and 85 degrees, and infinity and 69 degrees, respectively. The bandwidths of surge, pitch, and yaw control loops were determined to be 2.3 rad/s, 0.17 rad/s, and 2.0 rad/s, respectively. Similar characteristics were observed when controllers designed for linear models were applied to the nonlinear model. When step inputs were applied to the nonlinear model, the maximum overshoot and steady-state errors were very small. It was also found that the nonlinear plant with three different nominal surge velocities could be controlled by a single controller designed for a linear model with a nominal surge velocity of 0.4 m/s. Therefore, controllers designed using linear approximation models are expected to work well with an actual nonlinear model.

A low-latency and energy-efficient 4-bit absolute value detector for brain-machine interface applications

This research article aims to develop a 4-bit absolute value detector, balancing speed and power efficiency, with potential applications in Brain-Machine Interface (BMI) systems. The detector outputs a binary signal, indicating whether the absolute value of the input surpasses a predefined threshold. The design integrates two primary modules: an absolute value calculator and a comparator. Initially, the study focuses on enhancing the architecture of a multiplexer-based adder for absolute value calculation and selecting an efficient comparator structure, emphasizing least significant bit comparison. Further, the implementation of logic gates using Complementary Metal-Oxide-Semiconductor (CMOS) technology is elaborated. The research concludes by assessing the minimum delay achievable in the critical path, quantified at 74.22 units, and investigating strategies to minimize energy consumption. This is achieved by adjusting gate dimensions and supply voltage, aiming for a delay 1.5 times the minimum. The energy expenditure of the critical path is extrapolated to estimate the overall circuit consumption. The findings demonstrate that, at 1.5 times the minimal delay, the circuit achieves a maximum energy savings of 62.8% with a supply voltage of 0.815V.

Noise Immunity of Binary Chirp Signals

The results of a study of the noise immunity of receiving signals with linear frequency modulation in telecommunication information transmission systems are considered. Analytical expressions for the synthesis of binary signals by linear frequency modulation with control parameters are obtained. The dependence of the structure of linear frequency modulation signals on the shaping parameters has been studied. The optimization problem of finding the maximum value of the Euclidean distance for linear frequency modulation signals of a binary structure has been solved by modeling. Differences have been established in the noise immunity of receiving linear frequency modulation signals in relation to the binary structures of opposite and orthogonal signals. Diagrams of time and spectral fragments of linear frequency modulation signals are presented, explaining the essence of the research results. Graphs are presented for comparative assessment of the noise immunity of receiving binary signals of various structures in terms of the bit error probability as a function of the signal-to-noise ratio in the channel. The essence of correlation processing of signals with a large base is revealed.

Wideband Measurement Approach for EIS of Lithium-Ion Batteries Using Low-Frequency Concentrated Disturbance

Precise and rapid measurement for electrochemical impedance spectroscopy (EIS) is conducive to the working state monitoring and fault diagnosis of lithium-ion batteries (LIBs). Although using a wideband signal can effectively reduce measurement time, it will deteriorate the measurement precision due to the insufficient Signal-to-Noise Ratio. Considering this issue, this paper proposes a wideband measurement approach using low-frequency concentrated disturbance for the EIS of LIBs. This approach can obtain high measurement accuracy and a wide measurement bandwidth under a small current disturbance. Besides, it effectively reduces the measurement time. First, LIBs are stimulated by a low-frequency concentrated binary sequence signal to enhance measurement precision in a low-frequency region. Then, in the entire frequency region, an accurate EIS can be obtained by a fast Morlet wavelet transform and covariance-based impedance calculation. Finally, the effectiveness of the proposed approach is verified on a buck-boost converter-based EIS measurement platform, and comparative analyses with literature methods are conducted. The experimental results illustrate that the maximum Normalized Root Square Error of the two types of LIBs at different state-of-charge is 0.37% under the response voltage amplitude of less than 10mV. Moreover, this approach is approximately 20 times faster than commercial electrochemical workstations in measurement time.

Binary multi-frequency signal for accurate and rapid electrochemical impedance spectroscopy acquisition in lithium-ion batteries

Electrochemical Impedance Spectroscopy (EIS) plays a crucial role in characterizing the internal electrochemical states of lithium-ion batteries and proves to be effective for estimating battery states. Traditional EIS measurement, however, requires expensive electrochemical workstations with time-consuming signal injection, especially in low-frequency regions, thus limiting its practical applications. Here we show that applying our proposed pulse-like Binary Multi-Frequency Signals (BMFS) as the excitation signal in the EIS measurement, which simultaneously possesses numerous frequency components and maintains high energy at each frequency component, will significantly improve test speed while retaining accuracy. The applicability of the BMFS under various cathode material types, including nickel cobalt manganese (NCM), lithium cobalt oxide (LCO), and lithium iron phosphate (LFP) is demonstrated. The robustness of the signal is experimentally verified through varying C-rates and measurement window lengths. The BMFS, requiring only 30 s per test, can achieve test results with an amplitude error of 1% and a phase error of 1° as compared with those obtained from traditional EIS tests. Moreover, BMFS can also be applied in online EIS measurement scenarios, favorable for real-world applications. This work enables accurate and rapid acquisition of EIS results, which is currently expensive and time-consuming to obtain, ensuring a faster and more nuanced characterization of the internal states of many battery systems in an affordable and accessible manner, especially in data-driven and machine-learning approaches.

DAC-less PAM4 signal generation using a silicon dual-drive push-pull MZI modulator.

In this study, we demonstrate DAC-less PAM-4 signal generation by driving a silicon MZI modulator based on a series push-pull configuration with two independent binary signals of varying amplitudes. Such configuration boosts transfer speed between PAM4 levels, leading to enhanced performance metrics compared to the differential driving scheme. Experimentally, our scheme demonstrated a lower bit-error rate compared to the differential scheme, proving its cost-efficiency and feasibility for PAM4 generation.

Reliable Identification of Binary Supermassive Black Holes from Rubin Observatory Time-domain Monitoring

Periodic signatures in time-domain observations of quasars have been used to search for binary supermassive black holes (SMBHs). These searches, across existing time-domain surveys, have produced several hundred candidates. The general stochastic variability of quasars, however, can masquerade as a false-positive periodic signal, especially when monitoring cadence and duration are limited. In this work, we predict the detectability of binary SMBHs in the upcoming Rubin Observatory Legacy Survey of Space and Time (LSST). We apply computationally inexpensive sinusoidal curve fits to millions of simulated LSST Deep Drilling Field light curves of both single, isolated quasars and binary quasars. The period and phase of simulated binary signals can generally be disentangled from quasar variability. Binary amplitude is overestimated and poorly recovered for two-thirds of potential binaries due to quasar accretion variability. Quasars with strong intrinsic variability can obscure a binary signal too much for recovery. We also find that the most luminous quasars mimic current binary candidate light curves and their properties: The false-positive rates are 60% for these quasars. The reliable recovery of binary period and phase for a wide range of input binary LSST light curves is promising for multi-messenger characterization of binary SMBHs. However, pure electromagnetic detections of binaries using photometric periodicity with amplitude greater than 0.1 mag will result in samples that are overwhelmed by false positives. This paper represents an important and computationally inexpensive way forward for understanding the true and false-positive rates for binary candidates identified by Rubin.

Equilibrium information in credence goods

We study credence goods in a general model. A consumer may suffer a loss which is a continuous random variable. Privately observing the loss value, an expert can provide a repair at a price to eliminate the consumer's loss. All perfect-Bayesian equilibria are inefficient, in that some losses are not repaired. In closed form, we derive a pooling equilibrium (where losses are inferred to be in an interval), and a separating equilibrium (where losses are precisely inferred). If the expert can acquire an information structure on losses, the first best is achieved by a binary signal. Results are robust when cost and loss are random and correlated, and when there are multiple experts.

A binary acceleration signal reduces overestimation in pedestrians’ visual time-to-collision estimation for accelerating vehicles

When a pedestrian intends to cross the street, it is essential for safe mobility to correctly estimate the arrival time (time-to-collision, TTC) of an approaching vehicle. However, visual perception of acceleration is rather imprecise. Previous studies consistently showed that humans (mostly) disregard acceleration, but judge the TTC for an object as if it were traveling at constant speed (first-order estimation), which is associated with overestimated TTCs for positively accelerating objects. In a traffic context, such TTC overestimation could motivate pedestrians to cross in front of an approaching vehicle, although the time remaining is not sufficiently long. Can a simple acceleration signal help improve visual TTC estimation for accelerating objects? The present study investigated whether a signal that only indicates whether a vehicle is accelerating or not can remove the first-order pattern of overestimated TTCs. In a virtual reality simulation, 26 participants estimated the TTC of vehicles that approached with constant velocity or accelerated, from the perspective of a pedestrian at the curb. In half of the experimental blocks, a light band on the windshield illuminated whenever the vehicle accelerated but remained deactivated when the vehicle travelled at a constant speed. In the other blocks, the light band never illuminated, regardless of whether or not the vehicle accelerated. Participants were informed about the light band function in each block. Without acceleration signal, the estimated TTCs for the accelerating vehicles were consistent with an erroneous first-order approximation. In blocks with acceleration signal, participants substantially changed their estimation strategy, so that TTC overestimations for accelerating vehicles were reduced. Our data suggest that a binary acceleration signal helps pedestrians to effectively reduce the TTC overestimation for accelerating vehicles and could therefore increase pedestrian safety.