Publications

• K. Hikino*, M. Nakayama*, Y. Wu*, V.J. Barranca, A Novel Image-Based Neuronal Network Model Framework for Understanding Visual Multistability and Neurological Disorders, Front. Comp. Neurosci., Volume 20, doi: https://doi.org/10.3389/fncom.2026.1793265 [2026]
• X. Du, J. Crodelle, V.J. Barranca, S. Li, Y. Shi, S. Gao, D. Zhou, Biophysical Modeling and Experimental Analysis of the Dynamics of C. Elegans Body-Wall Muscle Cells, PLOS Comp. Biol., https://doi.org/10.1371/journal.pcbi.1012318 [2025]
• V.J. Barranca, Distance-Dependent Connectivity in the Brain Facilitates High Dynamical and Structural Complexity , Cogn. Neurodyn., Volume 20, Article 23, doi: https://doi.org/10.1007/s11571-025-10398-9 [2025]
• L. Tao, D. Ayambem*, V.J. Barranca, and V. Bhandawat, Neurons Underlying Aggressive Actions that are Shared by Both Males and Females in Drosophila, J. Neurosci.,  doi: 10.1523/jneurosci.0142-24.2024[2024]
• K. Barkdoll*, L. Lu*, and V.J. Barranca, New Insights into Binocular Rivalry from the Reconstruction of Evolving Percepts Using Model Network Dynamics, Front. Comput. Neurosci., Volume 17, doi: 10.3389/fncom.2023.1137015 [2023]
• V.J. Barranca, Reconstruction of Sparse Recurrent Connectivity and Inputs from the Nonlinear Dynamics of Neuronal Networks, J. Comput. Neurosci., doi.org/10.1007/s10827-022-00831 [pdf] [2022]
• V.J. Barranca, A. Bhuiyan*, M. Sundgren*, and F. Xing*, Functional Implications of Dale's Law in Balanced Neuronal Network Dynamics and Decision Making, Front. Neurosci., doi:10.3389/fnins.2022.801847 [2022]
• V.J. Barranca, Y. Hu*, Z. Porterfield*, S. Rothstein*, and A. Xuan*, Data-Driven Reconstruction and Encoding of Sparse Stimuli Across Convergent Sensory Layers from Downstream Neuronal Network Dynamics, SIAM J. Appl. Dyn. Syst. , Volume 20, Issue 4, Pages 2602-2629, doi:10.1137/21M1403114 [pdf] [2021]
• V.J. Barranca, Neural Network Learning of Improved Compressive Sensing Sampling and Receptive Field Structure, Neurocomputing, Volume 455, Sept. 2021, Pages 368-378, doi: 10.1016/j.neucom.2021.05.061 [pdf] [2021]
• T. Borofsky*, V.J. Barranca, R. Zhou*, D. von Trentini*, R.L. Broadrup, and C. Mayack, Hive Minded: Like Neurons, Honey Bees Collectively Integrate Negative Feedback to Regulate Decisions, Anim. Behav., Volume 168, Oct. 2020, Pages 33-44, https://doi.org/10.1016/j.anbehav.2020.07.023 [pdf] [2020]
• V. J. Barranca and D. Zhou, Compressive Sensing Inference of Neuronal Network Connectivity in Balanced Neuronal Dynamics, Front. Neurosci., doi: 10.3389/fnins.2019.01101 [2019]
• V. J. Barranca, H. Huang*, G. Kawakita*, Network Structure and Input Integration in Competing Firing Rate Models for Decision-Making, J. Comput. Neurosci., 46: 145, doi:10.1007/s10827-018-0708-6 [pdf] [2019]
• V. J. Barranca, G. Kovacic, and D. Zhou, The Role of Sparsity in Inverse Problems for Networks with Nonlinear Dynamics, Comm. Math. Sci., Volume 17, Issue 5, Pages 1291-1331, doi:10.4310/CMS.2019.v17.n5.a6 [pdf] [2019]
• V. J. Barranca, H. Huang*, S. Li*, The Impact of Spike-Frequency Adaptation on Balanced Network Dynamics, Cogn. Neurodyn., doi:10.1007/s11571-018-9504-2 [pdf] [2018]
• V. J. Barranca, X.G. Zhu*, A Computational Study of the Role of Spatial Receptive Field Structure in Processing Natural and Non-Natural Scenes, J. Theor. Biol., Volume 454, doi:10.1016/j.jtbi.2018.06.011 [pdf] [2018]
• A. Newton, A. Seidenstein, V.J. Barranca et. al, The Role of Receptive Field Structure in Neuronal Compressive Sensing Signal Processing, BMC Neurosci., doi:18.60.10.1186/s12868-017-0372-1 [2017]
• V. J. Barranca, D. Zhou, and D. Cai, Compressive Sensing Reconstruction of Feed-Forward Connectivity in Pulse-Coupled Nonlinear Networks, Phys. Rev. E Rapid Comm., Volume 93, 060201 [pdf] [2016]
• V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai, Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling, Nature Sci. Rep., doi:10.1038/srep31976, Volume 6, Article 31976 [2016]
• V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai, Efficient Image Processing Via Compressive Sensing of Integrate-And-Fire Neuronal Network Dynamics, Neurocomputing, Volume 171, Page 1313-1322 [pdf] [2016]
• V. J. Barranca, D. Zhou, and D. Cai, Low-Rank Network Decomposition Reveals Structural Characteristics of Small-World Networks, Phys. Rev. E, Volume 92, 062822 [pdf] [2015]
• V. J. Barranca, D. Zhou, and D. Cai, A Novel Characterization of Amalgamated Networks in Natural Systems, Nature Sci. Rep., doi:10.1038/srep10611, Volume 5, Article 10611 [2015]
• V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai, Sparsity and Compressed Coding in Sensory Systems, PLoS Comput. Biol., 10(8): e1003793, doi:10.1371/journal.pcbi.1003793 [2014]
• V. J. Barranca, D. C. Johnson, J. L. Moyher, J. P. Sauppe, M. S. Shkarayev, G. Kovacic, and D. Cai, Dynamics of the Exponential Integrate-and-Fire Model with Slow Currents and Adaptation, J. Comput. Neurosci., doi: 10.1007/s10827-013-0494-0, Volume 37, Issue 1, Page 161-180 [2014]
• V. J. Barranca, G. Kovacic, D. Zhou, and D. Cai, Network Dynamics for Optimal Compressive-Sensing Input-Signal Recovery, Phys. Rev. E, Volume 90, 042908 [pdf] [2014]

Selected Presentations

• SIAM Conference on Applications of Dynamical Systems 2025: A Novel Image-Based Neuronal Network Model Framework for Understanding Visual Multistability and Neurological Disorders
• Neural Computation 2025: A Unifying Neuronal Network Model Framework Addressing Perceptual Multistability and Autism
• SIAM Conference on Nonlinear Waves and Coherent Structures 2024: Reconstruction of Evolving Percepts in Binocular Rivalry from Nonlinear Neuronal Network Dynamics
• Middlebury College Mathematics and Statistics Colloquium 2024: Mathematical Modeling, Sparsity, and Data Compression in Neuroscience
• Math League International Summer Tournament 2024: Why do Mathematics? Answers in History, Applications, and Enjoyment
• Organization for Computational Neuroscience Annual Meeting 2023: Reconstruction of Recurrent Neuronal Network Connectivity from Integrate-And-Fire Model Network Dynamics
• ICIAM 2023: Reconstruction of Evolving Percepts in Binocular Rivalry using Novel Model Network Dynamics
• SIAM Conference on Applications of Dynamical Systems 2023: New Insights into Binocular Rivalry from the Reconstruction of Evolving Percepts using Model Network Dynamics
• RPI Mathematical Sciences Colloquium (SIAM Invited Speaker) 2023: Compressive Sensing Approaches for Reconstructing Neuronal Network Connectivity and Gaining Insights into Binocular Rivalry
• JMM 2023: Recovering Neuronal Network Topology with Compressed Sensing and the Balanced Dynamical Regime
• Northwestern University Engineering Sciences and Applied Math Colloquium 2022: Reconstruction of Neuronal Network Connectivity and Rivalrous Percepts Via Compressive Sensing of Network Dynamics
• MAA MathFest 2022: Compressive Sensing Reconstruction of Structural Neuronal Network Connectivity and the Balanced Dynamical Regime
• SIAM Conference on Applications of Dynamical Systems 2021: Reconstruction of Sparse Recurrent Neuronal Network Connectivity and the Network Dynamical Regime
• Trinity University Mathematics Colloquium 2021: Mathematical Modeling and Data Compression in Neuroscience
• Kenyon College Mathematics Colloquium 2021: Mathematical Modeling and Data Compression in Neuroscience
• MAA MathFest 2021: How Neuroscience Provides an Accessible Context for Undergraduate Research in Mathematics
• SIAM Conference on Life Sciences 2020: Compressive Sensing Inference of Neuronal Network Connectivity in Balanced Neuronal Dynamics
• Swarthmore Faculty Lunch Series 2020: Striking a Balance in Understanding Brain Activity using Applied Mathematics
• Organization for Computational Neuroscience Annual Meeting 2019: Reconstruction of Sparse Neuronal Network Connectivity in the Balanced Operating Regime
• SIAM Conference on Applications of Dynamical Systems 2019: Balanced Neuronal Dynamics Facilitate Reconstruction of Recurrent Network Connectivity
• University of Pennsylvania Computational Neuroscience Initiative Seminar 2019: The Role of Sparsity in Encoding Neuronal Network Stimuli and Connectivity Information
• JMM 2019: The Role of Sparsity in Inverse Problems for Networks with Nonlinear Dynamics
• SIAM Conference on Life Sciences 2018: A Signal Processing Perspective on the Role of Receptive Field Structure in Encoding Natural Scenes and Illusory Images
• International Conference on Applied Mathematics and Computational Neuroscience 2018: Reconstruction of Sparse Connectivity in Neuronal Networks Using Compressive Sensing of Network Dynamics
• AMS Spring Central Sectional Meeting 2018: The Role of Neuronal Network Structure in Encoding Natural and Non-Natural Scenes
• Organization for Computational Neuroscience Annual Meeting 2017: The Role of the Receptive Field Structure in Neuronal Compressive Sensing Signal Processing
• SIAM Conference on Applications of Dynamical Systems 2017: The Role of Localization and Center-Surround Structure in Compressive Sensory Signal Processing
• SIAM Conference on Nonlinear Waves and Coherent Structures 2016: Improved Compressive Sensing Signal Reconstruction via Localized Random Sampling
• SIAM Conference on Applied Mathematics Education 2016: Musings on Mathematical Modeling: Reflections on an Upper-Level Undergraduate Course
• SIAM Conference on Life Sciences 2016: Compressive Sensing Reconstruction of Feed-Forward Connectivity in Pulse-Coupled Nonlinear Neuronal Networks
• Bryn Mawr-Haverford College Colloquium 2016: Compressed Coding in Sensory Systems: From Sparse Stimuli to Network Structure
• SIAM Conference on Applications of Dynamical Systems 2015: Reconstruction of Structural Connectivity in Neuronal Networks Using Compressive Sensing of Network Dynamics
• RPI Mathematical Sciences Colloquium 2015: Sparsity, Compression, and Complexity: Fundamental Organizing Features in the Brain
• IMACS 2015: Efficient Reconstruction of Structural Connectivity From Neuronal Dynamics
• JMM 2015: Reconstruction of Structural Connectivity in Sparsely-Connected Neuronal Networks Using Compressive Sensing
• Courant Computational Biology Colloquium 2014: A Novel Characterization of Amalgamated Networks in Natural Systems Using Sparse and Low-Rank Optimization
• SIAM Conference on Life Sciences 2014: Novel Characterization of Brain Networks Through Low-Rank Network Decomposition
• Sino-French International Workshop on Computational Neuroscience 2014: Compressive Sensing in Sensory Systems
• Peking University Invited Lecture 2014: Input Data Recovery Via Compressive Sensing of Time-Evolving Networks
• RPI Mathematical Sciences Colloquium 2014: A Novel Characterization of Amalgamated Networks in Natural Systems
• NYUAD Annual Research Conference 2014: Sparsity and Compressed Coding in Sensory Systems
• Courant Biomathematics Colloquium 2013: Sparsity and Compressed Coding in Sensory Systems
• IMACS 2013: Data Compression in Sensory Processing
• JMM 2013: Is Our Sensing Compressed?
• SIAM Conference on Life Sciences 2012: Data Compression and Sparsity in the Retina
• AIMS Conference on Dynamical Systems 2012: Compressed Sensing in Retinal Image Processing
• Applied Math Days 2012: Compressed Sensing in Retinal Image Processing
• New York Conference on Applied Mathematics 2011: Neuronal Dynamics Subject to Additional Slow Ionic Currents
• SIAM Annual Meeting 2010: A Comparison of Bifurcations for Neuronal Models with Slow Ionic Currents

 

Organized Conference Sessions

• SIAM Conference on Applications of Dynamical Systems 2025: Exploring the Functional Roles of Neuronal Network Dynamics in Brain Computation
• SIAM Conference on Applications of Dynamical Systems 2023: Novel Insights into the Dynamics and Computation of Neuronal Networks
• SIAM Conference on Applications of Dynamical Systems 2021: New Dynamical Systems Frameworks for Investigating Neuronal Network Computations
• SIAM Conference on Life Sciences 2020: The Organization and Dynamics of Complex Brain Networks
• SIAM Conference on Applications of Dynamical Systems 2019: The Dynamics and Structure of Neuronal Networks
• SIAM Conference on Life Sciences 2018: Information Processing in Neuronal Networks
• SIAM Conference on Applications of Dynamical Systems 2017: The Dynamics and Function of Neuronal Networks
• SIAM Conference on Nonlinear Waves and Coherent Structures 2016: Coherent Structures and Nonlinear Dynamics in Neuronal Networks
• SIAM Conference on Life Sciences 2016: The Dynamics and Structure of Neuronal Networks
• SIAM Conference on Applications of Dynamical Systems 2015: The Dynamics and Computation of Neuronal Networks
• SIAM Conference on Life Sciences 2014: Dynamics and Connectivity of Complex Networks in the Brain

 

About My Research

My research interests in applied mathematics give me the opportunity to study a wide array of fascinating scientific problems. A central thread of my work is characterizing the relationship between the structure of a network and its function, particularly in the context of high dimensional systems with nonlinear dynamics. Currently, I mostly find myself involved in the exciting field of theoretical neuroscience. Though the brain is a fundamental component of human existence, it still remains one of the most mysterious and captivating biological systems. My research uses new mathematical approaches to investigate the neuronal computations underlying sensory processing and the role of neuronal network connectivity in facilitating brain function. While much of my work is motivated by experimental findings, mathematical techniques prove valuable in exploring novel theories currently impossible to verify experimentally and also crucial in the interpretation of neuroscientific data. Interestingly, much of this research has raised important theoretical questions in other fields. So, I also investigate intriguing problems in the realms of network science and signal processing. This flexibility to explore diverse research topics is one of the features uniquely remarkable about being an applied mathematician.

Additional insights regarding my research are highlighted in a two-part interview published in The Phoenix.

This research was funded by NSF DMS-1812478 from May 2018 - June 2022.

 

Research Profiles

• ResearchGate
• ORCiD
• Loop

  
  

 

Undergraduate Research

If you are an undergraduate student at Swarthmore interested in applying mathematics to understand the mechanisms underlying computation in the brain, please feel free to contact me. Preferred prerequisites include a background in differential equations and basic computer science. I am passionate about mentoring student research projects nearly every summer, and undergraduate co-authors in the publications above are denoted with a *. More information about my expectations and commitment to student success in summer research can be found here.