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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

The expression and function of the achaete-scute genes in Tribolium castaneum reveals conservation and variation in neural pattern formation and cell fate specification

The study of achaete-scute (ac/sc) genes has recently become a paradigm to understand the evolution and development of the arthropod nervous system. We describe the identification and characterization of the ac/sc genes in the coleopteran insect species Tribolium castaneum. We have identified two Tribolium ac/sc genes - achaete-scute homolog (Tc-ASH) a proneural gene and asense (Tc-ase) a neural precursor gene that reside in a gene complex. Focusing on the embryonic central nervous system we find that Tc-ASH is expressed in all neural precursors and the proneural clusters from which they segregate. Through RNAi and misexpression studies we show that Tc-ASH is necessary for neural precursor formation in Tribolium and sufficient for neural precursor formation in Drosophila. Comparison of the function of the Drosophila and Tribolium proneural ac/sc genes suggests that in the Drosophila lineage these genes have maintained their ancestral function in neural precursor formation and have acquired a new role in the fate specification of individual neural precursors. Furthermore, we find that Tc-ase is expressed in all neural precursors suggesting an important and conserved role for asense genes in insect nervous system development. Our analysis of the Tribolium ac/sc genes indicates significant plasticity in gene number, expression and function, and implicates these modifications in the evolution of arthropod neural development.

Non-NASA Center↗
NASA NTRS1998

Model-Trained Neural Networks and Electronic Holography Demonstrated to Detect Damage in Blades

Detect Damage in Blades Electronic holography can show damaged regions in fan blades at 30 frames/sec. The electronic holograms are transformed by finite-element-model-trained artificial neural networks to visualize the damage. The trained neural networks are linked with video and graphics to visualize the bending-induced strain distribution, which is very sensitive to damage. By contrast, it is very difficult to detect damage by viewing the raw, speckled, characteristic fringe patterns. For neural-network visualization of damage, 2 frames or 2 fields are used, rather than the 12 frames normally used to compute the displacement distribution from electronic holograms. At the NASA Lewis Research Center, finite element models are used to compute displacement and strain distributions for the vibration modes of undamaged and cracked blades. A model of electronic time-averaged holography is used to transform the displacement distributions into finite-element-resolution characteristic fringe patterns. Then, a feedforward neural network is trained with the fringe-pattern/strain-pattern pairs, and the neural network, electronic holography, and video are implemented on a workstation. Now that the neural networks have been tested successfully at 30 frames/sec on undamaged and cracked cantilevers, the electronic holography and neural-network processing are being adapted for onsite damage inspection of twisted fan blades and rotormounted blades. Our conclusion is that model-trained neural nets are effective when they are trained with good models whose application is well understood. This work supports the aeromechanical testing portion of the Advanced Subsonic Technology Project.

Decker, Arthur J.↗
NASA NTRS2004

Optical Calibration Process Developed for Neural-Network-Based Optical Nondestructive Evaluation Method

A completely optical calibration process has been developed at Glenn for calibrating a neural-network-based nondestructive evaluation (NDE) method. The NDE method itself detects very small changes in the characteristic patterns or vibration mode shapes of vibrating structures as discussed in many references. The mode shapes or characteristic patterns are recorded using television or electronic holography and change when a structure experiences, for example, cracking, debonds, or variations in fastener properties. An artificial neural network can be trained to be very sensitive to changes in the mode shapes, but quantifying or calibrating that sensitivity in a consistent, meaningful, and deliverable manner has been challenging. The standard calibration approach has been difficult to implement, where the response to damage of the trained neural network is compared with the responses of vibration-measurement sensors. In particular, the vibration-measurement sensors are intrusive, insufficiently sensitive, and not numerous enough. In response to these difficulties, a completely optical alternative to the standard calibration approach was proposed and tested successfully. Specifically, the vibration mode to be monitored for structural damage was intentionally contaminated with known amounts of another mode, and the response of the trained neural network was measured as a function of the peak-to-peak amplitude of the contaminating mode. The neural network calibration technique essentially uses the vibration mode shapes of the undamaged structure as standards against which the changed mode shapes are compared. The published response of the network can be made nearly independent of the contaminating mode, if enough vibration modes are used to train the net. The sensitivity of the neural network can be adjusted for the environment in which the test is to be conducted. The response of a neural network trained with measured vibration patterns for use on a vibration isolation table in the presence of various sources of laboratory noise is shown. The output of the neural network is called the degradable classification index. The curve was generated by a simultaneous comparison of means, and it shows a peak-to-peak sensitivity of about 100 nm. The following graph uses model generated data from a compressor blade to show that much higher sensitivities are possible when the environment can be controlled better. The peak-to-peak sensitivity here is about 20 nm. The training procedure was modified for the second graph, and the data were subjected to an intensity-dependent transformation called folding. All the measurements for this approach to calibration were optical. The peak-to-peak amplitudes of the vibration modes were measured using heterodyne interferometry, and the modes themselves were recorded using television (electronic) holography.

Decker, Arthur J.↗
NASA NTRS2003

The Expression and Function of the Achaete-Scute Genes in Tribolium castaneum Reveals Conservation and Variation in Neural Pattern Formation and Cell Fate Specification

SUMMARY The study of achaete-scute (ac/sc) genes has recently become a paradigm to understand the evolution and development of the arthropod nervous system. We describe the identification and characterization of the ache genes in the coleopteran insect species Tribolium castaneum. We have identified two Tribolium ache genes - achaete-scute homolog (Tc-ASH) a proneural gene and asense (Tc-ase) a neural precursor gene that reside in a gene complex. Focusing on the embryonic central nervous system we fmd that Tc-ASH is expressed in all neural precursors and the proneural clusters from which they segregate. Through RNAi and misexpression studies we show that Tc-ASH is necessary for neural precursor formation in Triboliurn and sufficient for neural precursor formation in Drosophila. Comparison of the function of the Drosophila and Triboliurn proneural ac/sc genes suggests that in the Drosophila lineage these genes have maintained their ancestral function in neural precursor formation and have acquired a new role in the fate specification of individual neural precursors. Furthermore, we find that Tc-use is expressed in all neural precursors suggesting an important and conserved role for asense genes in insect nervous system development. Our analysis of the Triboliurn ache genes indicates significant plasticity in gene number, expression and function, and implicates these modifications in the evolution of arthropod neural development.

Wheeler, Scott R.↗
DOE OSTI2024

GAINN: The Galaxy Assembly and Interaction Neural Networks for High-redshift JWST Observations

We present the Galaxy Assembly and Interaction Neural Networks (Gainn), a series of artificial neural networks for predicting the redshift, stellar mass, halo mass, and mass-weighted age of simulated galaxies based on James Webb Space Telescope (JWST) photometry. Our goal is to determine the best neural network for predicting these variables at 11 < z < 15. The parameters of the optimal neural network can then be used to estimate these variables for real, observed galaxies. The inputs of the neural networks are JWST filter magnitudes of a subset of five broadband filters (F150W, F200W, F277W, F356W, and F444W) and two medium-band filters (F162M and F182M). We compare the performance of the neural networks using different combinations of these filters, as well as different activation functions and numbers of layers. The best neural network predicted redshift with a normalized rms error of $0.010^{+0.003}_{-0.001}$, stellar mass with rms = $0.089^{+0.044}_{-0.022}$, halo mass with a mean-squared error of $0.022^{+0.014}_{-0.008}$, and mass-weighted age with rms = $12.466^{+5.065}_{-2.408}$. We also test the performance of Gainn on real data from MACS0647JD, an object observed by JWST. Predictions from Gainn for the first projection of the object (JD1) have normalized bias $\langle$Δz$\rangle$ < 0.00228, which is significantly smaller than found with template-fitting methods. We find that the optimal filter combination is F277W, F356W, F162M, and F200W when considering both theoretical accuracy and observational resources from JWST.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Experiments in Neural-Network Control of a Free-Flying Space Robot

Four important generic issues are identified and addressed in some depth in this thesis as part of the development of an adaptive neural network based control system for an experimental free flying space robot prototype. The first issue concerns the importance of true system level design of the control system. A new hybrid strategy is developed here, in depth, for the beneficial integration of neural networks into the total control system. A second important issue in neural network control concerns incorporating a priori knowledge into the neural network. In many applications, it is possible to get a reasonably accurate controller using conventional means. If this prior information is used purposefully to provide a starting point for the optimizing capabilities of the neural network, it can provide much faster initial learning. In a step towards addressing this issue, a new generic Fully Connected Architecture (FCA) is developed for use with backpropagation. A third issue is that neural networks are commonly trained using a gradient based optimization method such as backpropagation; but many real world systems have Discrete Valued Functions (DVFs) that do not permit gradient based optimization. One example is the on-off thrusters that are common on spacecraft. A new technique is developed here that now extends backpropagation learning for use with DVFs. The fourth issue is that the speed of adaptation is often a limiting factor in the implementation of a neural network control system. This issue has been strongly resolved in the research by drawing on the above new contributions.

NEURAL NETS↗
NASA NTRSDate not supplied

Validation of Image-Based Neural Network Controllersthrough Adaptive Stress Testing

Neural networks have become state-of-the-art for computer vision problems because of their ability to efficiently model complex functions from large amounts of data. While neural networks can be shown to perform well empirically fora variety of tasks, their performance is difficult to guarantee.Neural network verification tools have been developed that can certify robustness with respect to a given input image; however,for neural network systems used in closed-loop controllers,robustness with respect to individual images does not address multi-step properties of the neural network controller and itsenvironment. Furthermore, neural network systems interacting in the physical world and using natural images are operating in a black-box environment, making formal verification in-tractable. This work combines the adaptive stress testing (AST)framework with neural network verification tools to search for the most likely sequence of image disturbances that cause the neural network controlled system to reach a failure. Anautonomous aircraft taxi application is presented, and results show that the AST method finds failures with more likely image disturbances than baseline methods. Further analysis of AST results revealed an explainable cause of the failure, giving insight into the problematic scenarios that should be addressed.

Adaptive Stress Testing, Marabou, Deep Neural Netw↗
DOE OSTI2026

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue↗
DOE OSTI2025

On the Effectiveness of Neural Operators at Zero-Shot Weather Downscaling [SWR-25-20]

Code repository for the experiments performed in the paper: On the Effectiveness of Neural Operators at Zero-Shot Weather Downscaling (https://doi.org/10.1017/eds.2025.11) Overall, our work investigates the zero-shot downscaling potential of neural operators. To summarize, our contributions are: 1. We provide a comparative analysis based on two challenging weather downscaling problems, between various neural operator and non-neural-operator methods with large upsampling factors (e.g., 8x and 15x) and fine grid resolutions (e.g., 2 km × 2 km wind speed). 2. We examine whether neural operator layers provide unique advantages when testing downscaling models on upsampling factors higher than those seen during training, i.e., zero-shot downscaling. Our results instead show the surprising success of an approach that combines a powerful transformer-based model with a parameter-free interpolation step at zero-shot weather downscaling. 3. We find that this Swin-Transformer-based approach mostly outperforms all neural operator models in terms of average error metrics, whereas an enhanced super-resolution generative adversarial network (ESRGAN)-based approach is better than most models in capturing the physics of the system, and suggests their use in future work as strong baselines. However, these approaches still do not capture variations at smaller spatial scales well, including the physical characteristics of turbulence in the HR data. This suggests a potential for improvement in transformer or GAN-based methods and neural-operator-based methods for zero-shot weather downscaling.

Sinha, Saumya [National Renewable Energy Laborator↗
NASA NTRS1993

Genetic learning in rule-based and neural systems

The design of neural networks and fuzzy systems can involve complex, nonlinear, and ill-conditioned optimization problems. Often, traditional optimization schemes are inadequate or inapplicable for such tasks. Genetic Algorithms (GA's) are a class of optimization procedures whose mechanics are based on those of natural genetics. Mathematical arguments show how GAs bring substantial computational leverage to search problems, without requiring the mathematical characteristics often necessary for traditional optimization schemes (e.g., modality, continuity, availability of derivative information, etc.). GA's have proven effective in a variety of search tasks that arise in neural networks and fuzzy systems. This presentation begins by introducing the mechanism and theoretical underpinnings of GA's. GA's are then related to a class of rule-based machine learning systems called learning classifier systems (LCS's). An LCS implements a low-level production-system that uses a GA as its primary rule discovery mechanism. This presentation illustrates how, despite its rule-based framework, an LCS can be thought of as a competitive neural network. Neural network simulator code for an LCS is presented. In this context, the GA is doing more than optimizing and objective function. It is searching for an ecology of hidden nodes with limited connectivity. The GA attempts to evolve this ecology such that effective neural network performance results. The GA is particularly well adapted to this task, given its naturally-inspired basis. The LCS/neural network analogy extends itself to other, more traditional neural networks. Conclusions to the presentation discuss the implications of using GA's in ecological search problems that arise in neural and fuzzy systems.

Smith, Robert E.↗
NASA NTRS1997

Vibrational Analysis of Engine Components Using Neural-Net Processing and Electronic Holography

The use of computational-model trained artificial neural networks to acquire damage specific information from electronic holograms is discussed. A neural network is trained to transform two time-average holograms into a pattern related to the bending-induced-strain distribution of the vibrating component. The bending distribution is very sensitive to component damage unlike the characteristic fringe pattern or the displacement amplitude distribution. The neural network processor is fast for real-time visualization of damage. The two-hologram limit makes the processor more robust to speckle pattern decorrelation. Undamaged and cracked cantilever plates serve as effective objects for testing the combination of electronic holography and neural-net processing. The requirements are discussed for using finite-element-model trained neural networks for field inspections of engine components. The paper specifically discusses neural-network fringe pattern analysis in the presence of the laser speckle effect and the performances of two limiting cases of the neural-net architecture.

Decker, Arthur J.↗
NASA NTRS1998

Vibrational Analysis of Engine Components Using Neural-Net Processing and Electronic Holography

The use of computational-model trained artificial neural networks to acquire damage specific information from electronic holograms is discussed. A neural network is trained to transform two time-average holograms into a pattern related to the bending-induced-strain distribution of the vibrating component. The bending distribution is very sensitive to component damage unlike the characteristic fringe pattern or the displacement amplitude distribution. The neural network processor is fast for real-time visualization of damage. The two-hologram limit makes the processor more robust to speckle pattern decorrelation. Undamaged and cracked cantilever plates serve as effective objects for testing the combination of electronic holography and neural-net processing. The requirements are discussed for using finite-element-model trained neural networks for field inspections of engine components. The paper specifically discusses neural-network fringe pattern analysis in the presence of the laser speckle effect and the performances of two limiting cases of the neural-net architecture.

Decker, Arthur J.↗
NASA NTRS2000

A New Neural Network Approach Including First-Guess for Retrieval of Atmospheric Water Vapor, Cloud Liquid Water Path, Surface Temperature and Emissivities Over Land From Satellite Microwave Observations

The analysis of microwave observations over land to determine atmospheric and surface parameters is still limited due to the complexity of the inverse problem. Neural network techniques have already proved successful as the basis of efficient retrieval methods for non-linear cases, however, first-guess estimates, which are used in variational methods to avoid problems of solution non-uniqueness or other forms of solution irregularity, have up to now not been used with neural network methods. In this study, a neural network approach is developed that uses a first-guess. Conceptual bridges are established between the neural network and variational methods. The new neural method retrieves the surface skin temperature, the integrated water vapor content, the cloud liquid water path and the microwave surface emissivities between 19 and 85 GHz over land from SSM/I observations. The retrieval, in parallel, of all these quantities improves the results for consistency reasons. A data base to train the neural network is calculated with a radiative transfer model and a a global collection of coincident surface and atmospheric parameters extracted from the National Center for Environmental Prediction reanalysis, from the International Satellite Cloud Climatology Project data and from microwave emissivity atlases previously calculated. The results of the neural network inversion are very encouraging. The r.m.s. error of the surface temperature retrieval over the globe is 1.3 K in clear sky conditions and 1.6 K in cloudy scenes. Water vapor is retrieved with a r.m.s. error of 3.8 kg/sq m in clear conditions and 4.9 kg/sq m in cloudy situations. The r.m.s. error in cloud liquid water path is 0.08 kg/sq m . The surface emissivities are retrieved with an accuracy of better than 0.008 in clear conditions and 0.010 in cloudy conditions. Microwave land surface temperature retrieval presents a very attractive complement to the infrared estimates in cloudy areas: time record of land surface temperature will be produced.

Aires, F.↗
NASA NTRS2003

Modeling Aircraft Wing Loads from Flight Data Using Neural Networks

Neural networks were used to model wing bending-moment loads, torsion loads, and control surface hinge-moments of the Active Aeroelastic Wing (AAW) aircraft. Accurate loads models are required for the development of control laws designed to increase roll performance through wing twist while not exceeding load limits. Inputs to the model include aircraft rates, accelerations, and control surface positions. Neural networks were chosen to model aircraft loads because they can account for uncharacterized nonlinear effects while retaining the capability to generalize. The accuracy of the neural network models was improved by first developing linear loads models to use as starting points for network training. Neural networks were then trained with flight data for rolls, loaded reversals, wind-up-turns, and individual control surface doublets for load excitation. Generalization was improved by using gain weighting and early stopping. Results are presented for neural network loads models of four wing loads and four control surface hinge moments at Mach 0.90 and an altitude of 15,000 ft. An average model prediction error reduction of 18.6 percent was calculated for the neural network models when compared to the linear models. This paper documents the input data conditioning, input parameter selection, structure, training, and validation of the neural network models.

Allen, Michael J.↗
NASA NTRS2004

Subsonic Aircraft With Regression and Neural-Network Approximators Designed

At the NASA Glenn Research Center, NASA Langley Research Center's Flight Optimization System (FLOPS) and the design optimization testbed COMETBOARDS with regression and neural-network-analysis approximators have been coupled to obtain a preliminary aircraft design methodology. For a subsonic aircraft, the optimal design, that is the airframe-engine combination, is obtained by the simulation. The aircraft is powered by two high-bypass-ratio engines with a nominal thrust of about 35,000 lbf. It is to carry 150 passengers at a cruise speed of Mach 0.8 over a range of 3000 n mi and to operate on a 6000-ft runway. The aircraft design utilized a neural network and a regression-approximations-based analysis tool, along with a multioptimizer cascade algorithm that uses sequential linear programming, sequential quadratic programming, the method of feasible directions, and then sequential quadratic programming again. Optimal aircraft weight versus the number of design iterations is shown. The central processing unit (CPU) time to solution is given. It is shown that the regression-method-based analyzer exhibited a smoother convergence pattern than the FLOPS code. The optimum weight obtained by the approximation technique and the FLOPS code differed by 1.3 percent. Prediction by the approximation technique exhibited no error for the aircraft wing area and turbine entry temperature, whereas it was within 2 percent for most other parameters. Cascade strategy was required by FLOPS as well as the approximators. The regression method had a tendency to hug the data points, whereas the neural network exhibited a propensity to follow a mean path. The performance of the neural network and regression methods was considered adequate. It was at about the same level for small, standard, and large models with redundancy ratios (defined as the number of input-output pairs to the number of unknown coefficients) of 14, 28, and 57, respectively. In an SGI octane workstation (Silicon Graphics, Inc., Mountainview, CA), the regression training required a fraction of a CPU second, whereas neural network training was between 1 and 9 min, as given. For a single analysis cycle, the 3-sec CPU time required by the FLOPS code was reduced to milliseconds by the approximators. For design calculations, the time with the FLOPS code was 34 min. It was reduced to 2 sec with the regression method and to 4 min by the neural network technique. The performance of the regression and neural network methods was found to be satisfactory for the analysis and design optimization of the subsonic aircraft.

Patnaik, Surya N.↗
NASA NTRS2015

A Wirelessly Powered Micro-Spectrometer for Neural Probe-Pin Device

Treatment of neurological anomalies, places stringent demands on device functionality and size. A micro-spectrometer has been developed for use as an implantable neural probe to monitor neuro-chemistry in synapses. The microspectrometer, based on a NASA-invented miniature Fresnel grating, is capable of differentiating the emission spectra from various brain tissues. The micro-spectrometer meets the size requirements, and is able to probe the neuro-chemistry and suppression voltage typically associated with a neural anomaly. This neural probe-pin device (PPD) is equipped with wireless power technology (WPT) enabling operation in a continuous manner without requiring an implanted battery. The implanted neural PPD, together with a neural electronics interface and WPT, allow real-time measurement and control/feedback for remediation of neural anomalies. The design and performance of the combined PPD/WPT device for monitoring dopamine in a rat brain will be presented to demonstrate the current level of development. Future work on this device will involve the addition of an embedded expert system capable of performing semi-autonomous management of neural functions through a routine of sensing, processing, and control.

Choi, Sang H.↗
NASA NTRS2016

Neural Mechanisms to the Space Environment

Highly conserved neural systems have evolved to sense the inertial forces due to head translation and head tilt relative to gravitational vertical. These structures consist of ciliated mechanosensitive receptor cells inserted into a neuroepithelium surmounted by biomineral grains of calcium carbonate (CaCO3) called oto- (vertebrates) or stato-conia (invertebrates). Detection of these forces by receptor cells relies on the CaCO3 mass being weighted in Earths 1G. A change in gravity or orientation with respect to gravity has a profound effect on how an organism interacts with its environment, and it is evident that the nervous system responds to the new gravity state. This response might involve the peripheral receptors, the CaCO3 mass, the brain or any combination of these mechanisms based on the intensity and duration of the gravity change. Here, we examine the arguments supporting the different mechanisms of adaptation to the space environment. First, a pre- or post-synaptic alteration in the strength of synaptic transmission between the receptor cell and nerve afferent can adjust the system output. The number of synaptic ribbons in certain type II hair cells in rodent is labile, increasing following exposure to microgravity. An increase in number of synaptic ribbons in toadfish otolith hair cells following exposure to microgravity could potentially explain the observed afferent hypersensitivity to acceleration postflight. The physiological findings in the isolated statocyst in snails are in line with the vertebrate data, and conform to the proposition that G exposure leads to changes in gravireceptor function. At the same time this similarity in neural response to G exposure between the vertebrates and invertebrates is intriguing: the increased neural sensitivity in the vertebrate was detected in the nerve afferents, one synapse away from the receptor cell, whereas the increased neural sensitivity observed in the snail was detected directly at the receptor level. Second, the CaCO3 mass provides mechanical loading of receptor cell cilia, and their density alters sensitivity. A widely considered mechanism by which the animal responds to a chronic change in amplitude of gravity is a change in weight-lending CaCO3 mass. In G, it is argued, the organism counters the loss of gravity by increasing CaCO3 production, thereby increasing its mass, as a means to increase system gain. In hypergravity, the converse is argued. Earlier evidence in mollusks and recent results in mice suggest a remodeling might occur, especially after long-term space exposure. Lastly, we have to distinguish at least two kinds of neural feedbacks. One is connected with local mechanisms of self-regulation and specific for initial period of organ development when the neural connections are still absent. And the other feedback is related to neural self-regulation and specific for later stages of the organ development, and includes an efferent vestibular feedback. Complexity of the problem is enhanced by incompleteness of experiments, and consequently the experimental results have not led to a clear interpretation despite the numerous studies.

Boyle, Richard D.↗
DOE OSTI2024

Tracking the topology of neural manifolds across populations

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

97 MATHEMATICS AND COMPUTING↗