CCM’s mission is to create new mathematical approaches, algorithms and software to advance scientific research in multiple disciplines, often in collaboration with other Flatiron Centers.
Applied and computational mathematics play a critical role in many aspects of modern science and engineering, with new opportunities for discovery in virtually every discipline. CCM will focus on developing new tools and software libraries that bring large-scale modeling, simulation and data analysis within practical reach.
Research
Collaborative Work
Machine Learning at the Flatiron Institute
Machine learning has become an indispensable tool for computational science, and it is an active and growing area of research throughout the Flatiron Institute.
- CCM
- CCN
- CCA
- CCB
- CCQ
Structural and Molecular Biophysics
Underlying all biological processes are molecules and their interactions with each other. However, our ability to understand how these molecules function over biologically relevant scales remains very limited.
- CCB
- CCM
Publications
A new version of the adaptive fast Gauss transform for discrete and continuous sources
L. Greengard, S. Jiang, M. Rachh, J. Wang
We present a new version of the fast Gauss transform (FGT) for discrete and continuous sources. Classical Hermite expansions are…
arXiv:2305.07165A Dual-space Multilevel Kernel-splitting Framework for Discrete and Continuous Convolution
We introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. These methods can be applied…
arXiv:2308.00292Microscopic Theory, Analysis, and Interpretation of Conductance Histograms in Molecular Junctions
Leopoldo Mejía, P. Cossio, Ignacio Franco
Molecular electronics break-junction experiments are widely used to investigate fundamental physics and chemistry at the nanoscale. Reproducibility in these experiments…
Nature CommunicationsDirector
Software
SpikeForest
SpikeForest is a continuously-updating web-facing performance comparison of popular neural spike sorting codes, using a massive (1.3 TB) database of ground-truth recordings collected from over a dozen participating laboratories.
Figurl
Figurl lets you use Python to generate shareable figURLs (permalinks) to interactive visualizations. With minimal configuration, these can be generated from any computer with access to the internet.
FMM3D
FMM3D is a set of libraries to compute N-body interactions governed by the Laplace and Helmholtz equations, to a specified precision, in three dimensions, on a multi-core shared-memory machine.
IronClust
IronClust is a fast and drift-resistant spike sorting pipeline. The accuracy of spike sorting is validated by multiple ground-truth datasets from a number of contributing labs.
MountainSort/MountainLab
MountainSort is a plugin package to MountainLab, a general framework for scientific data analysis, sharing, and visualization.
FINUFFT
FINUFFT is a set of libraries to compute efficiently three types of nonuniform fast Fourier transform (NUFFT) to a specified precision, in one, two, or three dimensions, on a multi-core shared-memory machine.
ISO-SPLIT
ISO-SPLIT is an efficient clustering algorithm that handles an unknown number of unimodal clusters in low to moderate dimension, without any user-adjustable parameters.
Fast sinc transform library
Fast sinc transform libraries which compute sums of the sinc and sinc2 kernels between N arbitrary points in 1, 2, or 3 dimensions.
FFT-accelerated Interpolation-based t-SNE
FFT-accelerated interpolation-based t-SNE (FIt-SNE) is an efficient implementation of t-SNE (stochastic neighborhood embedding) for dimensionality reduction and visualization of high dimensional datasets.
CaImAn Python
Computational toolbox for large scale Calcium Imaging Analysis, including movie handling, motion correction, source extraction, spike deconvolution and result visualization.
CaImAn-MATLAB
Complete Matlab pipeline for large scale calcium imaging data analysis.
Kachery-cloud
Kachery-cloud is a network for sharing scientific data files, live feeds, mutable data and calculation results between lab computers and browser-based user interfaces.
Riccati
Riccati is an efficient numerical solver developed for a class of ordinary differential equations whose solution may exhibit extremely quick oscillations.
SCTL
SCTL (Scientific Computing Template Library) is header-only C++ library that serves as a versatile toolkit for developing efficient scientific computing applications.
Stan
Stan is an open-source platform for statistical modeling and high-performance statistical computation.