Network Response Research Articles

Design of a sustainable and reliable hydrogen supply chain network under mixed uncertainties: A case study

In the recent decade, the design of green hydrogen supply chains has been highlighted by researchers. Although, nowadays, responsiveness and social responsibility of networks could also be regarded as important measures that could attract more consumers to use hydrogen. Accordingly, this paper aims to improve the reliability and social responsibility of a hydrogen supply chain along with its economic and environmental aspects. To ensure the network's responsiveness, a new objective function is extended that maximizes the reliability of products' delivery. Also, a novel reliability approach is developed to immune the network against disruptions. As a new sustainability indicator, social factors are considered in the design of the hydrogen supply chain. Finally, a mixed possibilistic flexible programming method is proposed to assure the outputs' reliability. The results illustrate that by 28.4% enhancement in cost objective, the value of environmental, social, and reliability objectives are desirably improved 39.2%, 45.6%, and 24.1%, respectively.

Increasing the energy flexibility of existing district heating networks through flow rate variations

The possibility of recovering waste and renewable heat in urban areas has made district heating networks one of the key infrastructures for decarbonising the heating sector in Europe. The ability to shift the heat production over time is an important asset to improve the competitiveness of both new and existing networks. To this purpose, the present study evaluates the flexibility potential provided by the water volume enclosed in the network pipelines using the district heating network of Verona (Italy) as a case study.Given the users heat demand in two representative weeks, computer simulations were carried out to calculate the network's thermal response to circulating flow rate variations. The latter were designed to cause an early or late shift in the daily peak thermal load. The local temperature drop at the users substations compared to the current situation was used as a relative discomfort indicator. The simulations were carried out using the model NeMo, which has been attached as supplementary material to this publication. The simulation results show that the network pre-charge strategy achieves significant benefits in terms of both peak shaving and load shifting with a limited impact on discomfort for the users. Furthermore, the paper shows that the available storage capacity of the network is significantly influenced by the duration of the flow adjustment, by the average velocity of the heat carrier fluid and by the daily heat demand pattern. Finally, it is shown that the energy flexibility of the network also depends on its topology. In this regard, the article provides preliminary indications on the number and position of the bypass pipes needed to implement the proposed flow rate variations.In conclusion, the article shows that the thermal inertia of the heat carrier fluid is an interesting source of flexibility for existing networks, and the results highlight its potential and limitations.

Self-disclosure on social media: The role of perceived network responsiveness

Social media sites allow users to instantaneously self-disclose to their entire social network. This creates an opportunity to engage in self-expression that is farther-reaching than ever before, but also a new challenge: managing the risk inherent in self-disclosing to a large and diverse set of people. What guides decisions about how openly to self-disclose in such contexts? Building on theoretical and empirical evidence linking perceived partner responsiveness to open self-disclosure in face-to-face dyadic interactions, we hypothesized that perceptions of a Facebook network's responsiveness would shape people's self-disclosure on Facebook. We also examined whether observers can infer people's perceived network responsiveness from thin-slices of self-disclosure. Across two studies, people who perceived their Facebook network as more (vs. less) responsive self-disclosed more openly on Facebook. Furthermore, observers could infer participants' perceived network responsiveness with some accuracy on the basis of disclosure openness. Implications for the self-disclosure and person perception literatures are discussed.

Climatic Controls on Landscape Dissection and Network Structure in the Absence of Vegetation

AbstractDrainage networks emerge due to the movement of sediment driven by climatic and tectonic forcings. Previous observations revealed the dependence of drainage density (Dd) on climatic factors such as mean annual precipitation (MAP). Specifically, it has been observed in intermediate climate (~175 mm < MAP < 700 mm) that Dd decreases with increasing MAP. This declining trend has been argued to be attributed to biotic activity, that is, the dominance of vegetation growth over runoff erosive force. Using high‐resolution topographic data from a physical experiment, we show that increasing rainfall may result in decreasing Dd even in the absence of biotic activity. Increasing rainfall rate results in narrower and less variable bifurcation angle and relatively longer links. The response of the evolving network in terms of bifurcation angle continues beyond the time when Dd has reached a new stable value, indicating that the network's topological response is relatively slower than the geomorphic response.

Bio-ModelChecker: Using Bounded Constraint Satisfaction to Seamlessly Integrate Observed Behavior With Prior Knowledge of Biological Networks.

The in silico study and reverse engineering of regulatory networks has gained in recognition as an insightful tool for the qualitative study of biological mechanisms that underlie a broad range of complex illness. In the creation of reliable network models, the integration of prior mechanistic knowledge with experimentally observed behavior is hampered by the disparate nature and widespread sparsity of such measurements. The former challenges conventional regression-based parameter fitting while the latter leads to large sets of highly variable network models that are equally compliant with the data. In this paper, we propose a bounded Constraint Satisfaction (CS) based model checking framework for parameter set identification that readily accommodates partial records and the exponential complexity of this problem. We introduce specific criteria to describe the biological plausibility of competing multi-valued regulatory networks that satisfy all the constraints and formulate model identification as a multi-objective optimization problem. Optimization is directed at maximizing structural parsimony of the regulatory network by mitigating excessive control action selectivity while also favoring increased state transition efficiency and robustness of the network's dynamic response. The framework's scalability, computational time and validity is demonstrated on several well-established and well-studied biological networks.

Rapid Information Transfer in Swarms Under Update-Rate-Bounds Using Delayed Self-Reinforcement

The effectiveness of a network's response to external stimuli depends on rapid distortion-free information transfer across the network. However, the rate of information transfer, when each agent aligns with information from its network neighbors, is limited by the update rate at which each individual can sense and process information. Moreover, such neighbor-based, diffusion-type information transfer does not predict the superfluid-like information transfer during swarming maneuvers observed in nature. The main contribution of this paper is to propose a novel model that uses self-reinforcement, where each individual augments its neighbor-averaged information update using its previous update to (i) increase the information-transfer rate without requiring an increased, individual update-rate and (ii) enable superfluid-like information transfer. Simulations results of example systems show substantial improvement, more than an order of magnitude increase, in the information transfer rate, without the need to increase the update rate. Moreover, the results show that the delayed self-reinforcement (DSR) approach's ability to enable superfluid-like, distortion-free information transfer results in maneuvers with smaller turn radius and improved cohesiveness. Such faster response rate with limited individual update rate can enable better understanding of cohesiveness of flocking in nature, as well as improve the performance of engineered swarms such as unmanned mobile systems.

Building the neural tube

Neurodevelopment The development of the neural tube is regulated by a pair of morphogens acting in opposing gradients. The mature neural tube is built from a variety of different cell types organized in a consistent dorsal-ventral pattern. Zagorski et al. asked how this pattern is defined in a reproducible way from individual to individual. The morphogens define positions most accurately toward the top of their respective gradients, but things get a bit messy in the middle. Modeling the gene regulatory network's response as a maximum likelihood estimation from the combined input of both morphogens, however, succeeds at defining even the intermediate positions. Thus, the computation of position by the gene regulatory network establishes accurate tissue patterning despite messy inputs. Science , this issue p. [1379][1] [1]: /lookup/doi/10.1126/science.aam5887

Experimental verification of orbital engineering at the atomic scale: Charge transfer and symmetry breaking in nickelate heterostructures

Epitaxial strain, layer confinement and inversion symmetry breaking have emerged as powerful new approaches to control the electronic and atomic-scale structural properties in complex metal oxides. Nickelate heterostructures, based on RENiO$_3$, where RE is a trivalent rare-earth cation, have been shown to be relevant model systems since the orbital occupancy, degeneracy, and, consequently, the electronic/magnetic properties can be altered as a function of epitaxial strain, layer thickness and superlattice structure. One such recent example is the tri-component LaTiO$_3$-LaNiO$_3$-LaAlO$_3$ superlattice, which exhibits charge transfer and orbital polarization as the result of its interfacial dipole electric field. A crucial step towards control of these parameters for future electronic and magnetic device applications is to develop an understanding of both the magnitude and range of the octahedral network's response towards interfacial strain and electric fields. An approach that provides atomic-scale resolution and sensitivity towards the local octahedral distortions and orbital occupancy is therefore required. Here, we employ atomic-resolution imaging coupled with electron spectroscopies and first principles theory to examine the role of interfacial charge transfer and symmetry breaking in a tricomponent nickelate superlattice system. We find that nearly complete charge transfer occurs between the LaTiO$_3$ and LaNiO$_3$ layers, resulting in a Ni$^{2+}$ valence state. We further demonstrate that this charge transfer is highly localized with a range of about 1 unit cell, within the LaNiO$_3$ layers. The results presented here provide important feedback to synthesis efforts aimed at stabilizing new electronic phases that are not accessible by conventional bulk or epitaxial film approaches.

Using guitar learning to probe the Action Observation Network's response to visuomotor familiarity

Watching other people move elicits engagement of a collection of sensorimotor brain regions collectively termed the Action Observation Network (AON). An extensive literature documents more robust AON responses when observing or executing familiar compared to unfamiliar actions, as well as a positive correlation between amplitude of AON response and an observer's familiarity with an observed or executed movement. On the other hand, emerging evidence shows patterns of AON activity counter to these findings, whereby in some circumstances, unfamiliar actions lead to greater AON engagement than familiar actions. In an attempt to reconcile these conflicting findings, some have proposed that the relationship between AON response amplitude and action familiarity is nonlinear in nature. In the present study, we used an elaborate guitar training intervention to probe the relationship between movement familiarity and AON engagement during action execution and action observation tasks. Participants underwent fMRI scanning while executing one set of guitar sequences with a scanner-compatible bass guitar and observing a second set of sequences. Participants then acquired further physical practice or observational experience with half of these stimuli outside the scanner across 3 days. Participants then returned for an identical scanning session, wherein they executed and observed equal numbers of familiar (trained) and unfamiliar (untrained) guitar sequences. Via region of interest analyses, we extracted activity within AON regions engaged during both scanning sessions, and then fit linear, quadratic and cubic regression models to these data. The data best support the cubic regression models, suggesting that the response profile within key sensorimotor brain regions associated with the AON respond to action familiarity in a nonlinear manner. Moreover, by probing the subjective nature of the prediction error signal, we show results consistent with a predictive coding account of AON engagement during action observation and execution that also takes into account effects of changes in neural efficiency.

A Spiking Neurocomputational Model of High-Frequency Oscillatory Brain Responses to Words and Pseudowords.

Experimental evidence indicates that neurophysiological responses to well-known meaningful sensory items and symbols (such as familiar objects, faces, or words) differ from those to matched but novel and senseless materials (unknown objects, scrambled faces, and pseudowords). Spectral responses in the high beta- and gamma-band have been observed to be generally stronger to familiar stimuli than to unfamiliar ones. These differences have been hypothesized to be caused by the activation of distributed neuronal circuits or cell assemblies, which act as long-term memory traces for learned familiar items only. Here, we simulated word learning using a biologically constrained neurocomputational model of the left-hemispheric cortical areas known to be relevant for language and conceptual processing. The 12-area spiking neural-network architecture implemented replicates physiological and connectivity features of primary, secondary, and higher-association cortices in the frontal, temporal, and occipital lobes of the human brain. We simulated elementary aspects of word learning in it, focussing specifically on semantic grounding in action and perception. As a result of spike-driven Hebbian synaptic plasticity mechanisms, distributed, stimulus-specific cell-assembly (CA) circuits spontaneously emerged in the network. After training, presentation of one of the learned “word” forms to the model correlate of primary auditory cortex induced periodic bursts of activity within the corresponding CA, leading to oscillatory phenomena in the entire network and spontaneous across-area neural synchronization. Crucially, Morlet wavelet analysis of the network's responses recorded during presentation of learned meaningful “word” and novel, senseless “pseudoword” patterns revealed stronger induced spectral power in the gamma-band for the former than the latter, closely mirroring differences found in neurophysiological data. Furthermore, coherence analysis of the simulated responses uncovered dissociated category specific patterns of synchronous oscillations in distant cortical areas, including indirectly connected primary sensorimotor areas. Bridging the gap between cellular-level mechanisms, neuronal-population behavior, and cognitive function, the present model constitutes the first spiking, neurobiologically, and anatomically realistic model able to explain high-frequency oscillatory phenomena indexing language processing on the basis of dynamics and competitive interactions of distributed cell-assembly circuits which emerge in the brain as a result of Hebbian learning and sensorimotor experience.

Functional Implications of Cardiac Mitochondria Clustering.

The spatio-temporal organization of mitochondria in cardiac myocytes facilitates myocyte-wide, cluster-bound, mitochondrial inner membrane potential oscillatory depolarizations, commonly triggered by metabolic or oxidative stressors. Local intermitochondrial coupling can be mediated by reactive oxygen species (ROS) that activate inner membrane pores to initiate a ROS-induced-ROS-release process that produces synchronized limit cycle oscillations of mitochondrial clusters within the whole mitochondrial network. The network's dynamic organization, structure and function can be assessed by quantifying dynamic local coupling constants and dynamic functional clustering coefficients, both providing information about the network's response to external stimuli. In addition to its special organization, the mitochondrial network of cardiac myocytes exhibits substrate-sensitive coupling constants and clustering coefficients. The myocyte's ability to form functional clusters of synchronously oscillating mitochondria is sensitive to conditions such as substrate availability (e.g., glucose, pyruvate, β-hydroxybutyrate), antioxidant status, respiratory chain activity, or history of oxidative challenge (e.g., ischemia-reperfusion). This underscores the relevance of quantitative methods to characterize the network's functional status as a way to assess the myocyte's resilience to pathological stressors.

Linking dynamics of the inhibitory network to the input structure.

Networks of inhibitory interneurons are found in many distinct classes of biological systems. Inhibitory interneurons govern the dynamics of principal cells and are likely to be critically involved in the coding of information. In this theoretical study, we describe the dynamics of a generic inhibitory network in terms of low-dimensional, simplified rate models. We study the relationship between the structure of external input applied to the network and the patterns of activity arising in response to that stimulation. We found that even a minimal inhibitory network can generate a great diversity of spatio-temporal patterning including complex bursting regimes with non-trivial ratios of burst firing. Despite the complexity of these dynamics, the network's response patterns can be predicted from the rankings of the magnitudes of external inputs to the inhibitory neurons. This type of invariant dynamics is robust to noise and stable in densely connected networks with strong inhibitory coupling. Our study predicts that the response dynamics generated by an inhibitory network may provide critical insights about the temporal structure of the sensory input it receives.

Structural Plasticity Denoises Responses and Improves Learning Speed.

Despite an abundance of computational models for learning of synaptic weights, there has been relatively little research on structural plasticity, i.e., the creation and elimination of synapses. Especially, it is not clear how structural plasticity works in concert with spike-timing-dependent plasticity (STDP) and what advantages their combination offers. Here we present a fairly large-scale functional model that uses leaky integrate-and-fire neurons, STDP, homeostasis, recurrent connections, and structural plasticity to learn the input encoding, the relation between inputs, and to infer missing inputs. Using this model, we compare the error and the amount of noise in the network's responses with and without structural plasticity and the influence of structural plasticity on the learning speed of the network. Using structural plasticity during learning shows good results for learning the representation of input values, i.e., structural plasticity strongly reduces the noise of the response by preventing spikes with a high error. For inferring missing inputs we see similar results, with responses having less noise if the network was trained using structural plasticity. Additionally, using structural plasticity with pruning significantly decreased the time to learn weights suitable for inference. Presumably, this is due to the clearer signal containing less spikes that misrepresent the desired value. Therefore, this work shows that structural plasticity is not only able to improve upon the performance using STDP without structural plasticity but also speeds up learning. Additionally, it addresses the practical problem of limited resources for connectivity that is not only apparent in the mammalian neocortex but also in computer hardware or neuromorphic (brain-inspired) hardware by efficiently pruning synapses without losing performance.

The cortical modulation of stimulus-specific adaptation in the auditory midbrain and thalamus: a potential neuronal correlate for predictive coding.

To follow an ever-changing auditory scene, the auditory brain is continuously creating a representation of the past to form expectations about the future. Unexpected events will produce an error in the predictions that should “trigger” the network’s response. Indeed, neurons in the auditory midbrain, thalamus and cortex, respond to rarely occurring sounds while adapting to frequently repeated ones, i.e., they exhibit stimulus specific adaptation (SSA). SSA cannot be explained solely by intrinsic membrane properties, but likely involves the participation of the network. Thus, SSA is envisaged as a high order form of adaptation that requires the influence of cortical areas. However, present research supports the hypothesis that SSA, at least in its simplest form (i.e., to frequency deviants), can be transmitted in a bottom-up manner through the auditory pathway. Here, we briefly review the underlying neuroanatomy of the corticofugal projections before discussing state of the art studies which demonstrate that SSA present in the medial geniculate body (MGB) and inferior colliculus (IC) is not inherited from the cortex but can be modulated by the cortex via the corticofugal pathways. By modulating the gain of neurons in the thalamus and midbrain, the auditory cortex (AC) would refine SSA subcortically, preventing irrelevant information from reaching the cortex.

A civil society network's response to regulatory policy in post-neoliberal Ecuador: Figure 1

A civil society network's response to regulatory policy in post-neoliberal Ecuador: Figure 1

A compound memristive synapse model for statistical learning through STDP in spiking neural networks.

Memristors have recently emerged as promising circuit elements to mimic the function of biological synapses in neuromorphic computing. The fabrication of reliable nanoscale memristive synapses, that feature continuous conductance changes based on the timing of pre- and postsynaptic spikes, has however turned out to be challenging. In this article, we propose an alternative approach, the compound memristive synapse, that circumvents this problem by the use of memristors with binary memristive states. A compound memristive synapse employs multiple bistable memristors in parallel to jointly form one synapse, thereby providing a spectrum of synaptic efficacies. We investigate the computational implications of synaptic plasticity in the compound synapse by integrating the recently observed phenomenon of stochastic filament formation into an abstract model of stochastic switching. Using this abstract model, we first show how standard pulsing schemes give rise to spike-timing dependent plasticity (STDP) with a stabilizing weight dependence in compound synapses. In a next step, we study unsupervised learning with compound synapses in networks of spiking neurons organized in a winner-take-all architecture. Our theoretical analysis reveals that compound-synapse STDP implements generalized Expectation-Maximization in the spiking network. Specifically, the emergent synapse configuration represents the most salient features of the input distribution in a Mixture-of-Gaussians generative model. Furthermore, the network's spike response to spiking input streams approximates a well-defined Bayesian posterior distribution. We show in computer simulations how such networks learn to represent high-dimensional distributions over images of handwritten digits with high fidelity even in presence of substantial device variations and under severe noise conditions. Therefore, the compound memristive synapse may provide a synaptic design principle for future neuromorphic architectures.

Networked Enzymatic Logic Gates with Filtering: New Theoretical Modeling Expressions and Their Experimental Application

We report the first study of a network of connected enzyme-catalyzed reactions, with added chemical and enzymatic processes that incorporate the recently developed biochemical filtering steps into the functioning of this biocatalytic cascade. New theoretical expressions are derived to allow simple, few-parameter modeling of network components concatenated in such cascades, both with and without filtering. The derived expressions are tested against experimental data obtained for the realized network's responses, measured optically, to variations of its input chemicals' concentrations with and without filtering processes. We also describe how the present modeling approach captures and explains several observations and features identified in earlier studies of enzymatic processes when they were considered as potential network components for multistep information/signal processing systems.

Meeting Hurricane Sandy Head-On: New York City’s Aging Services Network Delivers in a Crisis

When Hurricane Sandy pummeled New York City on October 29, 2012, it crippled mass transit, devastated whole neighborhoods, and triggered gas shortages and power outages that left thousands of residents without heat, hot water, or electricity. These conditions created formidable challenges for the city's providers of senior center, home-delivered meals, and other vital services to older New Yorkers.At many program sites along shoreline areas, flooding, wind, sand accumulation, and debris damaged windows, doors, walls, ceilings, kitchen equipment, furniture, files, and computers. Widespread electrical failure shut down elevators; heating, ventilation, and air-conditioning (HVAC) systems; hot water heaters; fire alarm; and telephone systems.Staff faced huge hurdles doing their jobs. Like the elders they served, many were themselves victims of the storm, coping without heat and electricity at home, and worrying about their cars that had been washed away, their flooded basements, and disrupted lives. It took hours, sometimes, to get to work by car pool or mass transit, even when mass transit was running. Where gas for their vehicles was not available, staff and volunteers walked to deliver meals to the homebound. Those who could obtain gas waited in long lines at stations and drove through debris-strewn streets without working traffic lights. They climbed flights of stairs flashlight in hand, and groped their way down hallways to knock on doors in darkened apartment buildings that lacked buzzers and elevators. Case managers making home visits underwent the same ordeal of climbing stairs in the dark to get to clients' apartments. When senior centers reopened as warming centers for their communities,1 hundreds of individuals of all ages turned to directors and staff for hot meals and respite, not just their regular members.New York's aging services providers-a network of communitybased organizations in every borough-overcame these obstacles to achieve a remarkable level of service delivery. They not only managed to continue to provide services to their clients during a time of havoc and devastation but also to bring relief to thousands they had not previously served. This article describes the mandated New York City emergency preparation and response procedures that guided these agencies through the crisis. It also describes how the New York City Department for the Aging (DFTA)-the city agency that administers aging services-facilitated the network's response and coordination efforts within the context of the city's overall response, despite a compromised communications system and the absence of a central office. Although recognizing that more programs than can be mentioned here have similar stories, the article's third section tells of exemplary programs that worked tirelessly and selflessly to ensure that elders in stricken communities were safe, fed, cared for, and assisted.NEW YORK'S SERVICE SYSTEM FOR THE ELDERLYAging services in New York City are administered by the city's DFTA, a mayoral agency as well as a Federal Area Agency on Aging under the New York State Office on Aging. Actual service delivery is the province of hundreds of community-based organizations throughout the five boroughs that contract with the department. Eighty-five percent of the federal, state, and city tax levy funds that DFTA receives to serve the elderly under the Older Americans Act and other statutes is channeled by the Department to these contracted community-based organizations for direct service provision. DFTA monitors these community agencies and manages contract compliance.DFTA-funded services provided in the community include senior center services such as congregate meals, information and assistance, exercise programs, and social, creative, recreational, and learning activities. They also include home-delivered meals for older adults who cannot prepare or shop for food on their own and home care services for elders with functional impairments who are not eligible for Medicaid. …

Attractor dynamics in local neuronal networks

A hallmark feature of cortical networks is the presence of synaptic motifs, defined as ensembles of neurons whose synaptic pattern follows a particular configuration [1]. Simulated networks of neurons whose excitatory synapses follow a three-node motif (Figure ​(Figure1A)-the1A)-the most frequent motif in primate visual cortex- exhibit synchronization with zero time lag [2], a form of activity reported in a spectrum of experiments [3]. Here, using simulations of leaky integrate-and-fire networks (LIF) as well as mean-field stability analyses, we show that this relay motif promotes the emergence of a limit cycle whose period is determined by intrinsic properties of the model (Figure ​(Figure1B).1B). While cortical recordings show evidence of limit-cycle oscillations [4], this behavior is typically transient in non-pathological states. The question thus arises, of how to generate transient yet precise synchronization under different forms of motif connectivity. To address this question, we introduce a mechanism of selective gain inhibition by which cortical circuits may disengage from a strict limit cycle behavior. This mechanism works by tuning the gain inhibition [5] of a selective population of neurons in the model. In a first series of simulations, we show that applying selective gain inhibition to one population of a network (Figure ​(Figure1A,1A, shown in black) disengages the network from a limit cycle behaviour (Figure ​(Figure1C).1C). Next, we examine the effect of selective gain inhibition on a network's response to an incoming stimulus and show that transient synchronization arises in response to a time-delimited input current (Figure ​(Figure1D).1D). Selective gain inhibition enables stimulus-induced synchronization under strong stimulation and suppresses zero-lag synchrony under weak stimulation (Figure ​(Figure1E).1E). Transient synchronization would not be possible without selective gain inhibition, given that a network configured with a motif follows a limit cycle attractor (Figure ​(Figure1B).1B). We conclude that a relay' motif of connectivity imposes strict constraints on the types of dynamics produced by a network under both spontaneous and evoked states. Going further, results of simulations suggest that a mechanism of selective gain inhibition breaks the rigid constraints imposed by synaptic connectivity, providing flexible and transient responses to incoming stimuli. Figure 1 Transient synchronization in LIF networks. A. Three groups of neurons with arrows showing the presence of between-group synapses (1,000 neurons/group; gain inhibition set to 1.5 nS). B. Spike raster of spontaneous activity for network in A. C. Raster ...

Perturbations can distinguish underlying dynamics in phase-locked two-neuron networks

Synchronization of neuronal activity is observed in high- and low-level functions of the nervous system. For example, during memory tasks, neural activity in different brain regions phase-locks [1,2], while synchronized cells in the brainstem contribute to respiratory function [3]. In a two-cell system, network phase is a measure of when one neuron spikes with respect to the other neuron, normalized by the network period; phase-locked systems have a constant network phase, and here we define synchronized systems as those with a network phase close to zero. Understanding how and under what conditions neurons synchronize and phase-lock is important for understanding how neuronal populations function. Phase resetting curves (PRCs) describe how a neuron's period changes in response to inputs applied at various times during the interspike interval [4,5]. We use a PRC-based map of stimulus times vs response times [6] to predict if two coupled neurons will phase-lock, as well as how robust this phase-locking is against perturbations; two curves, one per neuron, are plotted against each other on this map, and intersections of the curves correspond to fixed points of the coupled system. Stable fixed points indicate stable phase-locking, while unstable points predict movement around the map. Close, but non-intersecting, curves result in networks that show a preferred phase with some phase slips. The fixed points (or lack thereof) on this map determine the dynamics of the coupled system, but similar statistics of network phases can be obtained from different underlying dynamics. Our goal is to discern underlying dynamic properties of the coupled system when a PRC cannot be measured. Here we explore perturbation-based methods to distinguish between different fixed point cases that result in similar network phase histograms. Because fixed points determine the network's response to perturbations, we use perturbations to uncover if, and where, fixed points exist without actually creating the PRC-based map. Parameters for coupled, conductance-based neuron models are chosen such that different numbers of fixed points produce phase histograms with similar network phases. When a synaptic perturbation or random noise is applied to one simulated neuron, the resulting trajectory of subsequent cycles around the map plane gives clues to the location and presence of underlying fixed points; different trajectories that point to the same location indicate a stable fixed point, while trajectories that point away from a region indicate an unstable point. Trajectories that only traverse the map plane in one direction are indicative of zero fixed points but close curves. Because biological neurons are not perfectly regular oscillators, we also investigate the effects of noise on the network phase histogram and how it affects our ability to resolve fixed point cases. The simulation results presented here will be validated in experimental hybrid circuits of one Aplysia californica neuron and one computational neuron coupled using the dynamic clamp.