Open Access. Powered by Scholars. Published by Universities.®
- Discipline
-
- Physical Sciences and Mathematics (11)
- Systems Neuroscience (10)
- Social and Behavioral Sciences (8)
- Psychology (7)
- Cognition and Perception (6)
-
- Cognitive Neuroscience (6)
- Applied Mathematics (5)
- Computer Sciences (4)
- Artificial Intelligence and Robotics (3)
- Cognitive Psychology (3)
- Non-linear Dynamics (3)
- Statistics and Probability (3)
- Applied Statistics (2)
- Behavioral Neurobiology (2)
- Computer Engineering (2)
- Dynamic Systems (2)
- Engineering (2)
- Numerical Analysis and Computation (2)
- Advertising and Promotion Management (1)
- Anatomy (1)
- Animal Structures (1)
- Animal Studies (1)
- Anthropology (1)
- Art Practice (1)
- Art and Design (1)
- Arts Management (1)
- Arts and Humanities (1)
- Institution
- Keyword
-
- Computer Science (2)
- Object recognition (2)
- Rat (2)
- Visual cortex (2)
- Aperture problem (1)
-
- Area V4 (1)
- Assimilation (1)
- Astrocyte (1)
- Attention (1)
- Attentional capture (1)
- Bayesian model (1)
- Biased competition (1)
- Binocular disparity (1)
- Binocular vision (1)
- Biological motion recognition (1)
- Bootstrap (1)
- CA1 (1)
- CNN (1)
- CSS3 (1)
- Calcium Signaling (1)
- Calmodulin (1)
- Cerebrovascular circulation (1)
- Classification (1)
- Closed-loop (1)
- Coherence (1)
- Color constancy (1)
- Competition (1)
- Computational Model (1)
- Computational Neuroscience (1)
- Computational biology (1)
- Publication
-
- MODVIS Workshop (16)
- Honors Scholar Theses (3)
- Georgia State Undergraduate Research Conference (2)
- Publications and Research (2)
- Dartmouth Scholarship (1)
-
- Department of Mathematics: Dissertations, Theses, and Student Research (1)
- Electronic Theses and Dissertations (1)
- Electronic Thesis and Dissertation Repository (1)
- Journal of the South Carolina Academy of Science (1)
- Scripps Senior Theses (1)
- Senior Independent Study Theses (1)
- Statistical Sciences and Operations Research Publications (1)
- The Summer Undergraduate Research Fellowship (SURF) Symposium (1)
- Publication Type
Articles 1 - 30 of 32
Full-Text Articles in Computational Neuroscience
Analysis Of Neuronal Sequences Using Pairwise Biases, Zachary Roth
Analysis Of Neuronal Sequences Using Pairwise Biases, Zachary Roth
Department of Mathematics: Dissertations, Theses, and Student Research
Sequences of neuronal activation have long been implicated in a variety of brain functions. In particular, these sequences have been tied to memory formation and spatial navigation in the hippocampus, a region of mammalian brains. Traditionally, neuronal sequences have been interpreted as noisy manifestations of neuronal templates (i.e., orderings), ignoring much richer structure contained in the sequences. This paper introduces a new tool for understanding neuronal sequences: the bias matrix. The bias matrix captures the probabilistic tendency of each neuron to fire before or after each other neuron. Despite considering only pairs of neurons, the bias matrix captures the best …
The New York Head—A Precise Standardized Volume Conductor Model For Eeg Source Localization And Tes Targeting, Yu Huang, Lucas C. Parra, Stefan Haufe
The New York Head—A Precise Standardized Volume Conductor Model For Eeg Source Localization And Tes Targeting, Yu Huang, Lucas C. Parra, Stefan Haufe
Publications and Research
In source localization of electroencephalograpic (EEG) signals, as well as in targeted transcranial electric current stimulation (tES), a volume conductor model is required to describe the flow of electric currents in the head. Boundary element models (BEM) can be readily computed to representmajor tissue compartments, but cannot encode detailed anatomical information within compartments. Finite element models (FEM) can capture more tissue types and intricate anatomical structures, but with the higher precision also comes the need for semiautomated segmentation, and a higher computational cost. In either case, adjusting to the individual human anatomy requires costlymagnetic resonance imaging (MRI), and thus head …
Predicting Phase Resetting Due To Multiple Stimuli, Kelsey M. Vollmer, Davy C. Vanderweyen, Derek R. Tuck, Sorinel A. Oprisan
Predicting Phase Resetting Due To Multiple Stimuli, Kelsey M. Vollmer, Davy C. Vanderweyen, Derek R. Tuck, Sorinel A. Oprisan
Journal of the South Carolina Academy of Science
We generalized the phase resetting curve (PRC) to a more realistic case of neural oscillators receiving two or more inputs per cycle. The PRC tabulates the transient change in the firing period of a neuron due to an external perturbation, such as a presynaptic stimulus. We used a conductance-based model neuron to estimate experimentally the two-stimulus PRC and compared the results against our mathematical prediction based on the assumption of instantaneous recurrent stimulation. Within the limits of the recurrent stimulation assumptions, we found that the newly introduced prediction for the two-stimulus PRC matched experimental measurements. Our new results open the …
Structure-Function Relationship Of The Brain: A Comparison Between The 2d Classical Ising Model And The Generalized Ising Model, Pubuditha M. Abeyasinghe
Structure-Function Relationship Of The Brain: A Comparison Between The 2d Classical Ising Model And The Generalized Ising Model, Pubuditha M. Abeyasinghe
Electronic Thesis and Dissertation Repository
There is evidence that the functional patterns of the brain observed at rest using fMRI are sustained by a structural architecture of axonal fiber bundles. As neuroimaging techniques advance with time, the relationship between structure and function has become the object of many studies in neuroscience. As recently suggested, the well defined connectivity structure found in the brain can be used to understand the self organization of the brain at rest, as well as to infer the functional connectivity patterns of the brain using different models, such as the Kuramoto model which studies synchronization, and the 2-dimensional classical Ising model, …
Competitive Tuning Of Calmodulin Target Protein Activation Drives E-Ltp Induction In Ca1 Hippocampal Neurons, Daniel R. Romano, Tamara L. Kinzer-Ursem
Competitive Tuning Of Calmodulin Target Protein Activation Drives E-Ltp Induction In Ca1 Hippocampal Neurons, Daniel R. Romano, Tamara L. Kinzer-Ursem
The Summer Undergraduate Research Fellowship (SURF) Symposium
A number of neurological disorders are caused by disruptions in dynamic neuronal connections called synapses. Normally, electrical activity between neurons activates protein cascades that cause long-lasting, localized changes in the structure and molecular composition of synapses. These changes either increase or decrease the strength of synaptic connections, leading to long-term-potentiation (LTP) or long-term-depression (LTD), respectively. The protein cascades responsible for this synaptic plasticity are initiated in a stimulus-dependent manner by the Ca2+ sensor calmodulin (CaM). Ultimately, it is disruptions within these signaling pathways that cause disease. Traditionally, these protein networks are studied in the laboratory, but limitations in existing …
Characterizing Receptive Field Selectivity In Area V2, Corey M. Ziemba, Robbe Lt Goris, J Anthony Movshon, Eero P. Simoncelli
Characterizing Receptive Field Selectivity In Area V2, Corey M. Ziemba, Robbe Lt Goris, J Anthony Movshon, Eero P. Simoncelli
MODVIS Workshop
The computations performed by neurons in area V1 are reasonably well understood, but computation in subsequent areas such as V2 have been more difficult to characterize. When stimulated with visual stimuli traditionally used to investigate V1, such as sinusoidal gratings, V2 neurons exhibit similar selectivity (but with larger receptive fields, and weaker responses) relative to V1 neurons. However, we find that V2 responses to synthetic stimuli designed to produce naturalistic patterns of joint activity in a model V1 population are more vigorous than responses to control stimuli that lacked this naturalistic structure (Freeman, et. al. 2013). Armed with this signature …
‘Edge’ Integration Explains Contrast And Assimilation In A Gradient Lightness Illusion, Michael E. Rudd
‘Edge’ Integration Explains Contrast And Assimilation In A Gradient Lightness Illusion, Michael E. Rudd
MODVIS Workshop
In the ‘phantom’ illusion (Galmonte, Soranzo, Rudd, & Agostini, submitted), either an incremental or a decremental target, when surrounded by a luminance gradient, can to be made to appear as an increment or a decrement, depending on the gradient width. For wide gradients, incremental targets appear as increments and decremental targets appear as decrements. For narrow gradients, the reverse is true. Here, I model these phenomena with a two-stage neural lightness theory (Rudd, 2013, 2014) in which local steps in log luminance are first encoded by oriented spatial filters operating on a log-transformed version of the image; then the filter …
Time-Lapse Statistics Of Cone Signals From Natural Scenes, David H. Foster, Kinjiro Amano, Sérgio M C Nascimento
Time-Lapse Statistics Of Cone Signals From Natural Scenes, David H. Foster, Kinjiro Amano, Sérgio M C Nascimento
MODVIS Workshop
In the natural world, the spectrum and geometry of the illumination from the sun and sky vary over the day. These geometric changes make it especially difficult to extract from the reflected light invariant signals for surface color perception. The aim of this study was to test the utility of certain combinations of retinal cone excitations, in particular, spatial cone-excitation ratios, known to be approximately invariant under non-geometric changes in illumination. Hyperspectral radiance images were acquired at roughly hourly intervals in four outdoor scenes in the Minho region of Portugal. Spatial resolution of the camera was 1344×1024 pixels. Peak-transmission wavelength …
The Bounded Log-Odds Model Of Frequency And Probability Distortion, Hang Zhang, Laurence T. Maloney
The Bounded Log-Odds Model Of Frequency And Probability Distortion, Hang Zhang, Laurence T. Maloney
MODVIS Workshop
No abstract provided.
Putting Saliency In Its Place, John K. Tsotsos
Putting Saliency In Its Place, John K. Tsotsos
MODVIS Workshop
The role of attention and the place within the visual processing stream where the concept of saliency has been situated is critically examined by considering the experimental evidence and performing tests that link experiment to computation.
Towards A Unified Computational Model Of Contextual Interactions Across Visual Modalities, David A. Mély, Thomas Serre
Towards A Unified Computational Model Of Contextual Interactions Across Visual Modalities, David A. Mély, Thomas Serre
MODVIS Workshop
The perception of a stimulus is largely determined by its surrounding. Examples abound from color (Land and McCann, 1971), disparity (Westheimer, 1986) and motion induction (Anstis and Casco, 2006) to orientation tilt effects (O’Toole and Wenderoth, 1976). Some of these phenomena have been studied individually using monkey neurophysiology techniques. In these experiments, a center stimulus is typically used to probe a cell’s classical “center” receptive field (cRF), whose activity is then modulated by an annular “surround” (extra-cRF) stimulus. While this center-surround integration (CSI) has been well characterized, a theoretical framework which unifies these different phenomena across visual modalities is lacking. …
A Conceptual Framework Of Computations In Mid-Level Vision, Jonas Kubilius, Johan Wagemans, Hans P. Op De Beeck
A Conceptual Framework Of Computations In Mid-Level Vision, Jonas Kubilius, Johan Wagemans, Hans P. Op De Beeck
MODVIS Workshop
The goal of visual processing is to extract information necessary for a variety of tasks, such as grasping objects, navigating in scenes, and recognizing them. While ultimately these tasks might be carried out by separate processing pathways, they nonetheless share a common root in the early and intermediate visual areas. What representations should these areas develop in order to facilitate all of these higher-level tasks? Several distinct ideas have received empirical support in the literature so far: (i) boundary feature detection, such as edge, corner, and curved segment extraction; (ii) second-order feature detection, such as the difference in orientation or …
Binocular 3d Motion Perception As Bayesian Inference, Martin Lages, Suzanne Heron
Binocular 3d Motion Perception As Bayesian Inference, Martin Lages, Suzanne Heron
MODVIS Workshop
The human visual system encodes monocular motion and binocular disparity input before it is integrated into a single 3D percept. Here we propose a geometric-statistical model of human 3D motion perception that solves the aperture problem in 3D by assuming that (i) velocity constraints arise from inverse projection of local 2D velocity constraints in a binocular viewing geometry, (ii) noise from monocular motion and binocular disparity processing is independent, and (iii) slower motions are more likely to occur than faster ones. In two experiments we found that instantiation of this Bayesian model can explain perceived 3D line motion direction under …
A Binocular Model For Motion Integration In Mt Neurons, Pamela M. Baker, Wyeth Bair
A Binocular Model For Motion Integration In Mt Neurons, Pamela M. Baker, Wyeth Bair
MODVIS Workshop
Processing of visual motion by neurons in MT has long been an active area of study, however circuit models detailing the computations underlying binocular integration of motion signals remains elusive. Such models are important for studying the visual perception of motion in depth (MID), which involves both frontoparallel (FP) visual motion and binocular signal integration. Recent studies (Czuba et al. 2014, Sanada and DeAngelis 2014) have shown that many MT neurons are MID sensitive, contrary to the prevailing view (Maunsell and van Essen, 1983). These novel data are ideal for constraining models of binocular motion integration in MT. We have …
A Critical Evaluation Of Computational Mechanisms Of Binocular Disparity Processing, Junkyung Kim, David A. Mély, Thomas Serre
A Critical Evaluation Of Computational Mechanisms Of Binocular Disparity Processing, Junkyung Kim, David A. Mély, Thomas Serre
MODVIS Workshop
The past decades of research in visual neuroscience have generated a large and disparate body of literature on the computation of binocular disparity in the primary visual cortex. Models have been proposed to describe specific phenomena, yet we lack a theoretical framework which is grounded in neurophysiology and also explains the effectiveness of disparity computation. Here, we examine neural circuits that are thought to play an important role in the computation of binocular disparity. Starting with the binocular energy model (Ohzawa et al. 1990), we consider plausible extensions which include suppressive mechanisms from units tuned to different phase disparities (Tanabe …
Modeling Shape Representation In Area V4, Wyeth Bair, Dina Popovkina, Abhishek De, Anitha Pasupathy
Modeling Shape Representation In Area V4, Wyeth Bair, Dina Popovkina, Abhishek De, Anitha Pasupathy
MODVIS Workshop
Our model builds on a convolutional-style neural network with hierarchical stages representing processing steps in the ventral visual pathway. It was designed to capture the translation-invariance and shape-selectivity of neurons in area V4. The model uses biologically plausible linear filters at the front end, normalization and sigmoidal nonlinear activation functions. The max() function is used to generate translation invariance.
A Recurrent Multilayer Model With Hebbian Learning And Intrinsic Plasticity Leads To Invariant Object Recognition And Biologically Plausible Receptive Fields, Michael Teichmann, Fred H. Hamker
A Recurrent Multilayer Model With Hebbian Learning And Intrinsic Plasticity Leads To Invariant Object Recognition And Biologically Plausible Receptive Fields, Michael Teichmann, Fred H. Hamker
MODVIS Workshop
Much effort has been spent to develop biologically plausible models for different aspects of the processing in the visual cortex. However, most of these models are not investigated with respect to the functionality of the neural code for the purpose of object recognition comparable to the framework of deep learning in the machine learning community.
We developed a model of V1 and V2 based on anatomical evidence of the layered architecture, using excitatory and inhibitory neurons where the connectivity to each neuron is learned in parallel. We address learning by three different mechanisms of plasticity: intrinsic plasticity, Hebbian learning with …
A Computational Model To Account For Dynamics Of Spatial Updating Of Remembered Visual Targets Across Slow And Rapid Eye Movements, Yalda Mohsenzadeh, J. Douglas Crawford
A Computational Model To Account For Dynamics Of Spatial Updating Of Remembered Visual Targets Across Slow And Rapid Eye Movements, Yalda Mohsenzadeh, J. Douglas Crawford
MODVIS Workshop
Despite the ever-changing visual scene on the retina between eye movements, our perception of the visual world is constant and unified. It is generally believed that this space constancy is due to the brain’s ability of spatial updating. Although many efforts have been made to discover the mechanism underlying spatial updating across eye movements, still there are many unanswered questions about the neuronal mechanism of this phenomenon.
We developed a state space model for updating gaze-centered spatial information. To explore spatial updating, we considered two kinds of eye movements, saccade and smooth pursuit. The inputs to our proposed model are: …
A Model Of Repetitive Microsaccades, Coupled With Pre-Microsaccadic Changes In Vision, Is Sufficient To Account For Both Attentional Capture And Inhibition Of Return In Posner Cueing, Ziad M. Hafed, Xiaoguang Tian
A Model Of Repetitive Microsaccades, Coupled With Pre-Microsaccadic Changes In Vision, Is Sufficient To Account For Both Attentional Capture And Inhibition Of Return In Posner Cueing, Ziad M. Hafed, Xiaoguang Tian
MODVIS Workshop
When a cue is presented at a location, orienting efficacy towards that location is improved relative to other locations (“attentional capture”), but only briefly; a mere few hundred milliseconds later, orienting incurs large costs. These costs have been classically termed “inhibition of return” (IOR), alluding to voluntary, cognitive strategies avoiding perseverance at one location. However, despite this popular hypothesis, the origins of both attentional capture and IOR remain elusive. Here we show that both of these phenomena can be accounted for by a single concept of oculomotor rhythmicity, and one that involves the entire gamut of saccadic activity including microsaccades. …
Object Recognition And Visual Search With A Physiologically Grounded Model Of Visual Attention, Frederik Beuth, Fred H. Hamker
Object Recognition And Visual Search With A Physiologically Grounded Model Of Visual Attention, Frederik Beuth, Fred H. Hamker
MODVIS Workshop
Visual attention models can explain a rich set of physiological data (Reynolds & Heeger, 2009, Neuron), but can rarely link these findings to real-world tasks. Here, we would like to narrow this gap with a novel, physiologically grounded model of visual attention by demonstrating its objects recognition abilities in noisy scenes.
To base the model on physiological data, we used a recently developed microcircuit model of visual attention (Beuth & Hamker, in revision, Vision Res) which explains a large set of attention experiments, e.g. biased competition, modulation of contrast response functions, tuning curves, and surround suppression. Objects are represented by …
Modeling Visual Features To Recognize Biological Motion: A Developmental Approach, Giulio Sandini, Nicoletta Noceti, Alessia Vignolo, Alessandra Sciutti, Francesco Rea, Alessandro Verri, Francesca Odone
Modeling Visual Features To Recognize Biological Motion: A Developmental Approach, Giulio Sandini, Nicoletta Noceti, Alessia Vignolo, Alessandra Sciutti, Francesco Rea, Alessandro Verri, Francesca Odone
MODVIS Workshop
In this work we deal with the problem of designing and developing computational vision models – comparable to the early stages of the human development – using coarse low-level information.
More specifically, we consider a binary classification setting to characterize biological movements with respect to non-biological dynamic events. To this purpose, our model builds on top of the optical flow estimation, and abstract the representation to simulate the limited amount of visual information available at birth. We take inspiration from known biological motion regularities explained by the Two-Thirds Power Law, and design a motion representation that includes different low-level features, …
Pathological Effects Of Repeated Concussive Tbi In Mouse Models: Periventricular Damage And Ventriculomegaly, Richard H. Wolferz Jr.
Pathological Effects Of Repeated Concussive Tbi In Mouse Models: Periventricular Damage And Ventriculomegaly, Richard H. Wolferz Jr.
Honors Scholar Theses
Repeated concussive traumatic brain injury (rcTBI) is the most prominent form of head injury affecting the brain, with an estimated 1.7 million Americans affected each year (Kuhn 2012). Neurologists have been concerned about the danger of repeated head impacts since the 1920’s, but researchers have only begun to understand the long-term effects of rcTBI (McKee 2009). Although symptoms can be as mild as dizziness, current research suggests that multiple concussions can lead to a progressive degenerative brain disease known as chronic traumatic encephalopathy (CTE) (Luo 2008, McKee 2009, Kane 2013). Research on the brain is just beginning to scratch the …
Spike Field Coherence (Sfc) For Ripples In Rat Hippocampus, Pranav Singla
Spike Field Coherence (Sfc) For Ripples In Rat Hippocampus, Pranav Singla
Honors Scholar Theses
The aim of this project was to determine coherence between two types of neural recordings which can be obtained from the rat hippocampus: spikes and local field potentials. Extracellular recording makes it possible to determine spiking activity from individual neurons in the vicinity of the recording electrode. Local field potential recording gives a combined activity of many neurons (thousands) at once to determine an overall picture of the coordination of the cells in real time. Here we examine the relationship between these two signals, focusing on place cells which spike at their maximal rate only at certain positions in physical …
Design, Programming, And User-Experience, Kaila G. Manca
Design, Programming, And User-Experience, Kaila G. Manca
Honors Scholar Theses
This thesis is a culmination of my individualized major in Human-Computer Interaction. As such, it showcases my knowledge of design, computer engineering, user-experience research, and puts into practice my background in psychology, com- munications, and neuroscience.
I provided full-service design and development for a web application to be used by the Digital Media and Design Department and their students.This process involved several iterations of user-experience research, testing, concepting, branding and strategy, ideation, and design. It lead to two products.
The first product is full-scale development and optimization of the web appli- cation.The web application adheres to best practices. It was …
Complementary Effect Of Electrical And Inhibitory Coupling In Bursting Synchronization, Kevin Daley
Complementary Effect Of Electrical And Inhibitory Coupling In Bursting Synchronization, Kevin Daley
Georgia State Undergraduate Research Conference
gsurc 2015
Quantitative And Qualitative Stability Analysis Of Polyrhythmic Circuits, Drake Knapper
Quantitative And Qualitative Stability Analysis Of Polyrhythmic Circuits, Drake Knapper
Georgia State Undergraduate Research Conference
No abstract provided.
Modeling Neurovascular Coupling From Clustered Parameter Sets For Multimodal Eeg-Nirs, M. Tanveer Talukdar, H. Robert Frost, Solomon G. G. Diamond
Modeling Neurovascular Coupling From Clustered Parameter Sets For Multimodal Eeg-Nirs, M. Tanveer Talukdar, H. Robert Frost, Solomon G. G. Diamond
Dartmouth Scholarship
Despite significant improvements in neuroimaging technologies and analysis methods, the fundamental relationship between local changes in cerebral hemodynamics and the underlying neural activity remains largely unknown. In this study, a data driven approach is proposed for modeling this neurovascular coupling relationship from simultaneously acquired electroencephalographic (EEG) and near-infrared spectroscopic (NIRS) data. The approach uses gamma transfer functions to map EEG spectral envelopes that reflect time-varying power variations in neural rhythms to hemodynamics measured with NIRS during median nerve stimulation. The approach is evaluated first with simulated EEG-NIRS data and then by applying the method to experimental EEG-NIRS data measured from …
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly
Statistical Sciences and Operations Research Publications
Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model, …
Towards Closed-Loop Deep Brain Stimulation: Behavior Recognition From Human Stn, Soroush Niketeghad
Towards Closed-Loop Deep Brain Stimulation: Behavior Recognition From Human Stn, Soroush Niketeghad
Electronic Theses and Dissertations
Deep brain stimulation (DBS) provides significant therapeutic benefit for movement disorders such as Parkinson’s disease (PD). Current DBS devices lack real-time feedback (thus are open loop) and stimulation parameters are adjusted during scheduled visits with a clinician. A closed-loop DBS system may reduce power consumption and side effects by adjusting stimulation parameters based on patient’s behavior. Thus behavior detection is a major step in designing such systems. Various physiological signals can be used to recognize the behaviors. Subthalamic Nucleus (STN) Local field Potential (LFP) is a great candidate signal for the neural feedback, because it can be recorded from the …
A Principle Of Economy Predicts The Functional Architecture Of Grid Cells, Xue-Xin Wei, Jason Prentice, Vijay Balasubramanian
A Principle Of Economy Predicts The Functional Architecture Of Grid Cells, Xue-Xin Wei, Jason Prentice, Vijay Balasubramanian
Publications and Research
Grid cells in the brain respond when an animal occupies a periodic lattice of ‘grid fields’ during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts that (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be √e for idealized neurons, and lie between 1.4 and 1.7 …