Time-dependent Signal Research Articles

Ultrabroadband THz probing of anisotropic optical conductivity and plasmonic damping in graphene nanostructures

Abstract Graphene nanostructures have garnered significant attention in the terahertz (THz) range due to their exceptional plasmonic properties. Exploring the THz conductivity of graphene nanostructures is crucial for optimizing their performance in advanced devices, necessitating comprehensive research into their optical responses across a broad frequency spectrum. In this study, we experimentally investigate the optical conductivity of graphene nanostructures using ultra-broadband THz time-domain spectroscopy. Extracted from the time-dependent THz echo signals, an order-of-magnitude enhancement of localized surface plasmon resonances (LSPRs) in graphene nanostructures was observed. This led to the anisotropic behavior in optical conductivity over the broadband THz range. In addition, the analyzed results show that LSPRs in graphene nanostructures experience damping loss from the intraband transition, resulting in energy dissipation into the substrate through the dielectric space layer. The induced redshift of the LSPR and linewidth broadening, in turn, modifies the optical conductivity of the graphene nanostructures. These findings provide valuable insights for developing advanced tunable THz devices based on graphene nanostructures.

Out-of-Equilibrium ceRNA Crosstalk.

Among non-coding RNAs, microRNAs are pivotal post-transcriptional regulators of gene expression in higher eukaryotes. Through a titration-based mechanism of interaction with their target RNAs, microRNAs can mediate a weak but pervasive form of RNA cross-regulation, as different endogenous RNAs can be effectively coupled by competing for microRNA binding (a phenomenon now known as "crosstalk"). Mathematical modeling has been proven of great help in unraveling many features of these competing endogenous RNA (ceRNA) interactions. However, although many studies have been devoted to the steady-state properties of this indirect regulatory layer, little is known about how the information encoded in frequency, amplitude, duration, and other features of regulatory signals can affect the resulting ceRNA crosstalk picture and hence the overall patterns of gene expression. Here, we focus on such dynamical aspects, with a special emphasis on the encoding and decoding of time-dependent signals.

Intrauterine blood transfusion causes dose- and time-dependent signal alterations in the liver and the spleen on fetal magnetic resonance imaging.

Intrauterine transfusions (IUTs) are a life-saving treatment for fetal anemia. However, with each transfusion, iron bypasses uptake regulation through the placenta and accumulates in fetal organs. Unlike other imaging modalities, fetal magnetic resonance imaging (MRI) is capable of non-invasively assessing fetal liver disease and/or organ iron overload. This study aimed to investigate the effects of IUTs on MRI findings in the fetal liver and spleen. For this retrospective study, we included eight fetuses undergoing IUT and prenatal MRI from 2014 to 2023. The fetuses were gestational age-matched with a cohort that received fetal MRI for other indications, but no IUTs. Signal intensity (SI) and volumetric analyses of the liver and the spleen were performed. Fetuses receiving transfusions had significantly larger volumes of both liver (p = 0.003) and spleen (p = 0.029). T1 SI inversely correlated with the number of IUTs (Pearson's r = -0.43, p = 0.099). This effect regressed over time (r = 0.69, p = 0.057). T2 SI did not correlate significantly with transfusion frequency but showed a strong positive correlation with the number of days between IUT and MRI (r = 0.91, p = 0.002). For splenic SI measures, similar effects were observed regarding T1 SI reduction per received transfusion (r = -0.36, p = 0.167) and recovery of T2 SI after IUT (r = 0.88, p = 0.004). This is the first study to report the effects of IUTs on MRI data of fetal livers and spleens. We observed considerable dose- and time-dependent SI alterations of the liver and spleen following IUT. Furthermore, fetal hepatosplenomegaly can be expected following IUT. Question What fetal changes are found by MRI after life-saving intrauterine transfusion (IUT)? Findings Dose- and time-dependent reductions in signal intensity of the fetal liver and spleen, as well as hepatosplenomegaly, were found after intrauterine transfusion. Clinical relevance Intrauterine transfusions cause transient iron overload with consequential changes in MRI signal intensity of fetal livers and spleens. Fetal hepatosplenomegaly can be expected following transfusions. Radiologists' awareness of changes following IUT may improve report quality.

Exploring the potential of self-pulsing optical microresonators for spiking neural networks and sensing

Photonic platforms are promising for implementing neuromorphic hardware due to their high processing speed, low power consumption, and ability to perform parallel processing. A ubiquitous device in integrated photonics, which has been extensively employed for the realization of optical neuromorphic hardware, is the microresonator. The ability of CMOS-compatible silicon microring resonators to store energy enhances the nonlinear interaction between light and matter, enabling energy efficient nonlinearity, fading memory and the generation of spikes via self-pulsing. In the self-pulsing regime, a constant input signal can be transformed into a time-dependent signal based on pulse sequences. Previous research has shown that self-pulsing enables the microresonator to function as an energy-efficient artificial spiking neuron. Here, we extend the experimental study of single and coupled microresonators in the self-pulsing regime to confirm their potential as building blocks for scalable photonic spiking neural networks. Furthermore, we demonstrate their potential for introducing all-optical long-term memory and event detection capabilities into integrated photonic neural networks. In particular, we show all-optical long-term memory up to at least 10 μs and detection of input spike rates, which is encoded into different stable self-pulsing dynamics.

Nanopore Identification of Polyglutamine Length via Cross-Slit Sensing.

Nanopore sensing is now reshaping analytical proteomics with its simplicity, convenience, and high sensitivity. Determining the length of polyglutamine (polyQ) is crucial for the rapid screening of Huntington's disease. In this computational study, we present a cross-nanoslit detection approach to determine the polyQ length, where the nanoslit is carved within a two-dimensional (2D) in-plane heterostructure of graphene (GRA) and hexagonal boron nitride (hBN). We designed a heterostructure with an hBN strip embedded in the graphene sheet. With such a design, polyQ peptides can spontaneously and linearly stretch out on the hBN stripe. By tuning the strength of an external in-plane electric field, molecular transportation of polyQ peptides along the hBN stripe can be effectively regulated. Subsequent cross-nanoslit motion can be applied to record time-dependent electric signals. The signal features are then utilized to train the machine learning classification models. The machine-learning-assisted recognition enables accurate determination of the protein's length. This nanoslit-sensing method may offer theoretical guidance on 2D heterostructure design for the detection of polyQ peptide lengths and rapid screening of protein-related diseases.

Light-Operated Diverse Logic Gates Enabled by Modulating Time-Dependent Fluorescence of Dissipative Self-Assemblies.

Light-fueled dissipative self-assembly possesses enormous potential in the field of optical information due to controllable time-dependent optical signals, but remains a great challenge for constructing intelligent light-operated logic circuits due to the limited availability of optical signal inputs and outputs. Herein, a series of light-fueled dissipative self-assembly systems with variable optical signals are reported to realize diverse logic gates by modulating time-dependent fluorescence variations of the loaded fluorophores. Three kinds of alkyl trimethylammonium homologs are employed to co-assemble with a merocyanine-based photoinduced amphiphile separately to construct a series of dissipative self-assemblies, showing unexpectedly different fluorescence control behaviors of loaded fluorophores during light irradiation and thermal relaxation processes. The opposite monotonicity of time-dependent emission intensity is achieved just by changing the excitation wavelength. Furthermore, by varying the types of trimethylammoniums and excitation wavelengths, a robust logic system is accomplished, integrating AND, XNOR, and XOR functions, which provides an effective pathway for advancing information transmission applications.

Hyperspectral acquisition with ScanImage at the single pixel level: application to time domain coherent Raman imaging.

We present a comprehensive strategy and its practical implementation using the commercial ScanImage software platform to perform hyperspectral point scanning microscopy when a fast time-dependent signal varies at each pixel level. In the proposed acquisition scheme, the scan along the X-axis is slowed down while the data acquisition is maintained at a high pace to enable the rapid acquisition of the time-dependent signal at each pixel level. The ScanImage generated raw 2D images have a very asymmetric aspect ratio between X and Y, the X axis encoding both for space and time acquisition. The results are X-axis macro-pixel where the associated time-dependent signal is sampled to provide hyperspectral information. We exemplified the proposed hyperspectral scheme in the context of time-domain coherent Raman imaging, where a pump pulse impulsively excites molecular vibrations that are subsequently probed by a time-delayed probe pulse. In this case, the time-dependent signal is a fast acousto-optics delay line that can scan a delay of 4.5ps in 25μs at each pixel level. With this acquisition scheme, we demonstrate ultra-fast hyperspectral vibrational imaging in the low frequency range [10cm-1, 150 cm-1] over a 500 μm field of view (64 x 64 pixels) in 130ms (∼ 7.5 frames/s). The proposed acquisition scheme can be readily extended to other applications requiring the acquisition of a fast-evolving signal at each pixel level.

Experimental study on the formation and evolution of unconfined counter-helicity spheromaks merging using magnetized coaxial plasma gun

The formation and evolution of unconfined counter-helicity spheromaks merging have been experimentally investigated by using a magnetized coaxial plasma gun. By comparing the time-dependent photodiode signals and plasma radiation images of counter-helicity spheromaks merging and plasma jets merging, it is found that the field-reversed configuration (FRC) plasma formed by counter-helicity spheromaks merging has a distinct contour and a long maintenance time. For plasma jets merging, the resulting plasma has no discernible contours and a shorter lifetime. In addition, it is inferred from these data that stagnation heating and magnetic reconnection events occur during the counter-helicity spheromaks merging, causing a rapid rise in plasma pressure at the merging midplane and sharp kinks in the field lines near the merger region. By changing different operating parameters and observing the impact on the merger characteristics, it is suggested that the qualitative dynamics of the FRC plasma depends on the balance between the plasma pressure and the magnetic pressure. The high discharge voltage breaks the equilibrium in the merged body, while the large gas-puffed mass just weakens the compression effect of the merged body. These results give us an intuitive understanding of the counter-helicity spheromak merger process and its dependence on discharge parameters, and also provide a distinct perspective for the optimal design of FRC.

Noise-induced transport in a periodic square-well potential

We investigate a thermal ratchet based on a Brownian particle in a spatially periodic square-well potential driven by a time-dependent square-wave signal. In this model, we rock the Brownian particle between two square-well potentials tilted in opposite directions to induce a net current. Employing the Stratonovich formula and an independent approach using suitable boundary conditions and a normalization condition, we obtain an exact expression for the current in the adiabatic limit, and we observe that there are optimal values of various parameters at which the current can be maximized. In several parameter regimes, our simple non-linear model displays a behavior distinct from some other models of a rocked ratchet. For example, a reversal in the current direction is observed as the square-wave signal’s amplitude or the thermal bath’s temperature is varied. However, under similar conditions, no such current reversal was seen in the case of a periodically rocked Brownian motor in a sawtooth or a smooth potential. Furthermore, unlike the latter type of rocked Brownian motors, the square-well model yields zero current in the deterministic limit, as thermal energy is indispensable for the functioning of the motor.

Nonequilibrium Antigen Recognition during Infections and Vaccinations

The initial immune response to an acute primary infection is a coupled process of antigen proliferation, molecular recognition by naive B cells, and their subsequent clonal expansion. This process contains a fundamental problem: the recognition of an exponentially time-dependent antigen signal. Here, we show that an efficient immune response must be stringently constrained to B-cell lineages with high antigen binding affinity. We propose a tuned proofreading mechanism for primary recognition of new antigens, where the molecular recognition machinery is adapted to the complexity of the immune repertoire. We show that this process produces potent, specific, and fast recognition of antigens, maintaining a spectrum of genetically distinct B-cell lineages as input for affinity maturation. Our analysis maps the proliferation-recognition dynamics of a primary infection to a generalized Luria-Delbrück process, akin to the dynamics of the classic fluctuation experiment. This map establishes a link between signal recognition dynamics and evolution. We derive the resulting statistics of the activated immune repertoire: Antigen binding affinity, expected size, and frequency of active B-cell clones are related by power laws, which define the class of generalized Luria-Delbrück processes. Their exponents depend on the antigen and B-cell proliferation rate, the number of proofreading steps, and the lineage density of the naive repertoire. We extend the model to include spatiotemporal processes, including the diffusion-recognition dynamics of a vaccination. Empirical data of activated mouse immune repertoires are found to be consistent with activation involving about three proofreading steps. The model predicts key clinical characteristics of acute infections and vaccinations, including the emergence of elite neutralizers and the effects of immune aging. More broadly, our results establish infections and vaccinations as a new probe into the global architecture and functional principles of immune repertoires. Published by the American Physical Society 2024

Piezoelectric Behaviour in Biodegradable Carrageenan and Iron (III) Oxide Based Sensor.

This paper is dedicated to the research of phenomena noticed during tests of biodegradable carrageenan-based force and pressure sensors. Peculiar voltage characteristics were noticed during the impact tests. Therefore, the sensors' responses to impact were researched more thoroughly, defining time-dependent sensor output signals from calibrated energy impact. The research was performed using experimental methods when a free-falling steel ball impacted the sensor material to create relatively definable impact energy. The sensor's output signal, which is analogue voltage, was registered using an oscilloscope and transmitted to the PC for further analysis. The obtained results showed a very interesting outcome, where the sensor, which was intended to be piezoresistive, demonstrated a combination of behaviour typical for galvanic cells and piezoelectric material. It provides a stable DC output that is sensitive to the applied statical pressure, and in case of a sudden impact, like a hit, it demonstrates piezoelectric behaviour with some particular effects, which are described in the paper as proton transfer in the sensor-sensitive material. Such phenomena and sensor design are a matter of further development and research.

Time-dependent diffusion MRI-based microstructural mapping for differentiating high-grade serous ovarian cancer from serous borderline ovarian tumor

PurposeTo investigate the value of microstructural characteristics derived from time-dependent diffusion MRI in distinguishing high-grade serous ovarian cancer (HGSOC) from serous borderline ovarian tumor (SBOT) and the associations of immunohistochemical markers with microstructural features. MethodsTotally 34 HGSOC and 12 SBOT cases who received preoperative pelvic MRI were retrospectively included in this study. Two radiologists delineated the tumors to obtain the regions of interest (ROIs). Time-dependent diffusion MRI signals were fitted by the IMPULSED (imaging microstructural parameters using limited spectrally edited diffusion) model, to extract microstructural parameters, including fraction of the intracellular component (fin), cell diameter (d), cellularity and extracellular diffusivity (Dex). Apparent diffusion coefficient (ADC) values were obtained from standard diffusion-weighted imaging (DWI). The parameters of HGSOCs and SBOTs were compared, and the diagnostic performance was evaluated. The associations of microstructural indexes with immunopathological parameters were assessed, including Ki-67, P53, Pax-8, ER and PR. ResultsIn this study, fin, cellularity, Dex and ADC had good diagnostic performance levels in differentiating HGSOC from SBOT, with AUCs of 0.936, 0.909, 0.902 and 0.914, respectively. There were no significant differences in diagnostic performance among these parameters. Spearman analysis revealed in the HGSOC group, cellularity had a significant positive correlation with P53 expression (P = 0.028, r = 0.389) and Dex had a significant positive correlation with Pax-8 expression (P = 0.018, r = 0.415). ICC showed excellent agreement for all parameters. ConclusionTime-dependent diffusion MRI had value in evaluating the microstructures of HGSOC and SBOT and could discriminate between these tumors.

Data-driven Parameterizable Generative Adversarial Networks for Synthetic Data Augmentation of Guided Ultrasonic Wave Sensor Signals

Detecting and characterizing hidden damages in composite materials like Fibre-Metal Laminates (FML) remains a challenge. Guided Ultrasonic Waves (GUW) or X-ray imaging are commonly used to detect these damages, but their interpretation remains limited. Data-driven predictor models can detect damages in structures using GUW time-dependent signals, but the training data lacks variance, quality, and sufficient coverage of the hyper-parameter space. Synthetic data augmentation is often the only solution to create robust and generalized damage predictor models. Synthetic sensor data can be generated using model-based, model-assisted, or model-free methods. However, computed GUW signals show poor reality conformance due to too much constraints and simplifications. Recent developments in Generative Adversarial (Neural) Networks (GAN), commonly driven by a random generation process [1], include deterministic style vectors to generate specific signal data, determining constraints such as damage size, position, transducer positions, material and environmental properties. These new architectures aim to reduce the impact of environmental changes on data-driven damage predictor models by using parameterizable synthetic data generation. We will elaborate these new architectures and discuss the possibilities and challenges of using such GAN models for data generation of US signals in GUW-based SHM applications, as originally proposed in [2]. We will have a focus on low-quality real measuring data used for training and composite materials (e.g., FML) with hidden damages, and show some preliminary results. [1] Karras et al. "A style-based generator architecture for generative adversarial networks." Proceedings of the IEEE/CVF 2019 [2] Virupakshappa et al. "Using Generative Adversarial Networks to Generate Ultrasonic Signals." 2020 IEEE International Ultrasonics Symposium (IUS). IEEE, 2020

Line-field dynamic optical coherence tomography platform for volumetric assessment of biological tissues.

Dynamic optical coherence tomography (dOCT) utilizes time-dependent signal intensity fluctuations to enhance contrast in OCT images and indirectly probe physiological processes in cells. Majority of the dOCT studies published so far are based on acquisition of 2D images (B-scans or C-scans) by utilizing point-scanning Fourier domain (spectral or swept-source) OCT or full-field OCT respectively, primarily due to limitations in the image acquisition rate. Here we introduce a novel, high-speed spectral domain line-field dOCT (SD-LF-dOCT) system and image acquisition protocols designed for fast, volumetric dOCT imaging of biological tissues. The imaging probe is based on an exchangeable afocal lens pair that enables selection of combinations of transverse resolution (from 1.1 µm to 6.4 µm) and FOV (from 250 × 250 µm2 to 1.4 × 1.4 mm2), suitable for different biomedical applications. The system offers axial resolution of ∼ 1.9 µm in biological tissue, assuming an average refractive index of 1.38. Maximum sensitivity of 90.5 dB is achieved for 3.5 mW optical imaging power at the tissue surface and maximum camera acquisition rate of 2,000 fps. Volumetric dOCT images acquired with the SD-LF-dOCT system from plant tissue (cucumber), animal tissue (mouse liver) and human prostate carcinoma spheroids allow for volumetric visualization of the tissues' cellular and sub-cellular structures and assessment of cellular motility.

Oligomeric amyloid-β targeted contrast agent for MRI evaluation of Alzheimer's disease mouse models.

Oligomeric amyloid beta (oAβ) is a toxic factor that acts in the early stage of Alzheimer's disease (AD) and may initiate the pathologic cascade. Therefore, detecting oAβ has a crucial role in the early diagnosis, monitoring, and treatment of AD. The purpose of this study was to evaluate MRI signal changes in different mouse models and the time-dependent signal changes using our novel gadolinium (Gd)-dodecane tetraacetic acid (DOTA)- ob5 aptamer contrast agent. We developed an MRI contrast agent by conjugating Gd-DOTA-DNA aptamer called ob5 to evaluate its ability to detect oAβ deposits in the brain using MRI. A total of 10 control mice, 9 3xTg AD mice, and 11 APP/PS/Tau AD mice were included in this study, with the age of each model being 16 or 36 weeks. A T1-weighted image was acquired at the time points before (0min) and after injection of the contrast agent at 5, 10, 15, 20, and 25min. The analyses were performed to compare MRI signal differences among the three groups and the time-dependent signal differences in different mouse models. Both 3xTg AD and APP/PS/Tau AD mouse models had higher signal enhancement than control mice at all scan-time points after injection of our contrast media, especially in bilateral hippocampal areas. In particular, all Tg AD mouse models aged 16 weeks showed a higher contrast enhancement than those aged 36 weeks. For 3xTg AD and APP/PS/Tau AD groups, the signal enhancement was significantly different among the five time points (0min, 5min, 10min, 15min, 20min, and 25min) in multiple ROI areas, typically in the bilateral hippocampus, left thalamus, and left amygdala. The findings of this study suggest that the expression of the contrast agent in different AD models demonstrates its translational flexibility across different species. The signal enhancement peaked around 15-20min after injection of the contrast agent. Therefore, our novel contrast agent targeting oAβ has the potential ability to diagnose early AD and monitor the progression of AD.

WED-175 Intrauterine blood transfusion causes dose- and time-dependent signal alterations in the liver and the spleen on fetal magnetic resonance imaging

WED-175 Intrauterine blood transfusion causes dose- and time-dependent signal alterations in the liver and the spleen on fetal magnetic resonance imaging

Temporally resolved relative krypton neutral density during breathing mode of a hall effect thruster recorded by TALIF

A key issue in the development of theory and models for plasma propulsion devices is to describe the instabilities and fluctuations of the devices. It has been widely recognized that many Hall effect thrusters (HETs) exhibit oscillations at frequencies in the range of ∼ 20 kHz. These ionization-related oscillations are generally referred to as Breathing Mode oscillations and have been the subject of considerable research. Here, for the first time, we report direct temporally resolved measurements of the ground state neutral density variation during the period of the oscillation. We used the laser-based Two-Photon Absorption Laser Induced Fluorescence (TALIF) technique to measure neutrals within the plume of a 1.5 kW HET operating on krypton (Kr). Our TALIF scheme employs a frequency-doubled, pulsed dye laser operating at ∼ 212 nm to probe ground state Kr atoms. A novel phase-binning approach is used to recover the time-dependent signal by assigning the timing of each collected TALIF signal (laser shot) relative to the phase of the discharge current. We find that the neutral density fluctuates quite strongly over the period of the oscillation, and that this fluctuation leads the current fluctuation as expected.

Real-time nearfield acoustic holography using particle velocity.

In this paper, a series of impulse response functions between acoustic quantities on the source plane and particle velocity on the hologram plane are derived. In virtue of these functions, real-time nearfield acoustic holography (RT-NAH) is extended from pressure-based to particle velocity. Pressure, normal velocity, acceleration, and displacement radiated from planar sources can be reconstructed by measuring time-dependent particle velocity signals on the hologram plane. A simulation of an excited aluminum plate is performed to evaluate the difference in accuracy between RT-NAHs based on pressure and based on particle velocity. This study also examines the impact of impulse response functions on the reconstruction results, allowing for detailed analysis of the reconstruction accuracy based on these functions. The simulation results demonstrate that using RT-NAH based on particle velocity obtains significantly higher-accuracy reconstruction results when reconstructing normal velocity and displacement and slightly more accurate reconstructed pressure and normal acceleration.

Advancing 2D reaction rate measurements in BNCT: Validation of the indirect neutron radiography method

The precise characterization of neutron beams is a cornerstone of Boron Neutron Capture Therapy (BNCT). While Instrumental Neutron Activation Analysis (INAA) is the standard technique for neutron flux measurement, it is limited in its ability to capture two-dimensional (2D) reaction rate distributions. This study aims to validate the Indirect Neutron Radiography (INR) method for 2D reaction rate quantification, addressing critical variables such as temperature sensitivity and signal fading. We designed and constructed an optimized INR platform comprising an Imaging Plate (IP), readout device, activation detectors (copper foils), and real-time temperature monitoring. Comprehensive experiments were conducted to investigate the impact of ambient temperature and fading time on IP signal reliability. A robust calibration curve was formulated, linking IP signals to dose deposition metrics, thereby enabling precise reaction rate assessments. The study found that IP signals are minimally sensitive to temperature variations (less than 0.1% change per 1 °C), but are subjected to linear fading over time, necessitating stringent temperature control and time-dependent signal corrections. A mathematical relationship between IP signals and dose deposition was established, represented by Y = 20,500 × x0.01803-21103. Application of the INR method revealed that the depth-dependent reaction rates in copper strips closely aligned with those acquired through INAA, exhibiting a relative deviation of less than 5% within a 4cm depth range inside the phantom. Our findings demonstrate that the INR method offers a robust alternative to traditional INAA for capturing 2D reaction rates, effectively addressing complexities like temperature sensitivity and signal fading. While challenges persist, particularly in the realm of measurement errors, this study lays the groundwork for further methodological refinements and broadens the scope for future research in BNCT neutron beam characterization.

A geometrical model of cell fate specification in the mouse blastocyst.

The lineage decision that generates the epiblast and primitive endoderm from the inner cell mass (ICM) is a paradigm for cell fate specification. Recent mathematics has formalized Waddington's landscape metaphor and proven that lineage decisions in detailed gene network models must conform to a small list of low-dimensional stereotypic changes called bifurcations. The most plausible bifurcation for the ICM is the so-called heteroclinic flip that we define and elaborate here. Our re-analysis of recent data suggests that there is sufficient cell movement in the ICM so the FGF signal, which drives the lineage decision, can be treated as spatially uniform. We thus extend the bifurcation model for a single cell to the entire ICM by means of a self-consistently defined time-dependent FGF signal. This model is consistent with available data and we propose additional dynamic experiments to test it further. This demonstrates that simplified, quantitative and intuitively transparent descriptions are possible when attention is shifted from specific genes to lineages. The flip bifurcation is a very plausible model for any situation where the embryo needs control over the relative proportions of two fates by a morphogen feedback.