Welcome to Roy R. Lederman’s homepage.
I am a postdoc in the Program in Applied and Computational Mathematics at Princeton University, working with Amit Singer.
Between 1/2016 and 3/2016 I will be at the Hausdorff Research Institute for Mathematics (HIM) in Bonn for the Mathematics of Signal Processing trimester program.
In 20142015 I was a Gibbs Assistant Professor in the Applied Mathematics Program at Yale University, working with Vladimir Rokhlin and Raphy Coifman.
I organize the IDeAS seminar at Princeton, please email me if you would like to give a talk.
Research
Some Recent work:
 Numerical analysis: signal processing, the Laplace transform, decaying signals
 Empirical geometry of data: manifold learning, diffusion maps, multisensor problems, unordered datasets
 CryoEM: application of representation theory, numerical analysis, and data organization to imaging of molecules
 Computational biology: fast search algorithms, statistics of DNA, sequencing, organization of biological data.
CryoEM
Cryoelectron microscopy (cryoEM) is a method for imaging molecules without crystallization. I work on various problems of alignment, classification and signal processing that are motivated by application in CryoEM.
Recently, I developed a representation theory approach to simultaneous alignment and classification of images for the heterogeneity problem in CryoEM.
Numerical Analysis and Signal Processing
The Laplace transform is frequently encountered in mathematics, physics, engineering and other areas. However, the spectral properties of the Laplace transform tend to complicate its numerical treatment; therefore, the closely related “Truncated” Laplace Transforms are often used in applications:
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The numerical and analytical properties of the Truncated Laplace Transform are discussed here.
Geometry of Data
Alternating Diffusion, a method for recovering the common variable in multisensor experiments, is discussed in this technical report and this project webpage.
A different approach to the common variable recovery problem, which also constructs representations that are invariable to unknown transformations, is discussed in this technical report.
What’s going on? Why is everything spinning? See project webpage,
this technical report and in this technical report.
Computational Biology
More information about my work in computational biology is available at http://roy.lederman.name/compbio/ .
Random Permutations Based Alignment
I have developed randomized algorithms for sequencing of DNA and RNA.
Paper: “A RandomPermutationsBased Approach to Fast Read Alignment” (RECOMBSEQ 2013).
Also see [Charikar, 2002] (random permutations in search without the special properties for the sequencing problem), and this report on the properties of sequencing.

Additional Application: Assembly.
The algorithm is also used to construct approximate overlap graphs. These graph are used for fast assembly. Unlike other algorithms, this algorithm allows errors in the reads, so no errorcorrection is necessary prior to the construction of the graph. See: technical report.
Additional Algorithms
LongRange “Independence”
The repetitive nature of DNA strings is one of the challenges in read alignment. When one examines longer substrings of DNA, they appear less repetitive, or more unique; permutationsbased algorithms benefit from this property. We describe a way of measuring the property in this report and ways of using this property in reads with many “indels,” in this report.
Homopolymer Length Filters
Homopolymer length filters eliminate the mapping problem caused by homopolymer length errors (ionTorrent/454). A technical report is available here.
Papers and Technical Reports
(In preparation) On the Analytical and Numerical Properties of the Truncated Laplace Transform III. 
Lederman, R. R., and Steinerberger, S., (2016) Stability Estimates for Truncated Fourier and Laplace Transforms. arXiv preprint arXiv:1605.03866 . 
Lederman, R. R., and Singer, A. (2016) A Representation Theory Perspective on Simultaneous Alignment and Classification. arXiv preprint arXiv:1607.03464. 
Lederman, R. R. and Rokhlin, V. (2016) On the Analytical and Numerical Properties of the Truncated Laplace Transform. Part II. SIAM Journal on Numerical Analysis 54.2: 665687. 
Shaham, U. and Lederman, R. R. (2015) Common Variable Discovery and Invariant Representation Learning using Artificial Neural Networks. Technical Report. 
Lederman, R. R. and Rokhlin, V. (2015). On the Analytical and Numerical Properties of the Truncated Laplace Transform I. SIAM Journal on Numerical Analysis, 53(3), 12141235. 
Lederman, R. R., Talmon, R., Wu, H., Lo, Y. and Coifman, R.R. (2015) Alternating Diffusion for Common Manifold Learning with Application to Sleep Stage Assessment. ICCASP. 
Lederman, R. R., and Talmon R. (2015) Learning the geometry of common latent variables using alternatingdiffusion. Applied and Computational Harmonic Analysis. 
Lederman, R. R. and Talmon, R. (2015), (technical report) Learning the geometry of common latent variables using alternatingdiffusion. 
Lederman, R. R. (2014) On the Analytical and Numerical Properties of the Truncated Laplace Transform. (Dissertation) 
Lederman, R. R. (2013) A RandomPermutationsBased Approach to Fast Read Alignment. BMC Bioinformatics 2013, 14(Suppl 5):S8 
Lederman, R. R. (2013) Using the Long Range “Independence” in DNA: CoupledSeeds and PreAlignment Filters. Technical Report. 
Lederman, R. R. (2013) A PermutationsBased Algorithm for Fast Alignment of Long PairedEnd Reads. Technical Report. 
Lederman, R. R. (2012) A Note About the ResolutionLength Characteristics of DNA. Technical Report. 
Lederman, R. R. (2012) Building Approximate Overlap Graphs for DNA Assembly Using RandomPermutationsBased Search. Technical Report. 
Lederman, R. R. (2012) Homopolymer Length Filters. Technical Report. 
Select Talks and Posters
Talk  SIAM CSE 2015  Salt Lake City, UT 2015  Common Manifold Learning Using Alternating Diffusion for Multimodal Signal Processing. 
Talk  Applied Mathematics Colloquia, Harvard  Cambridge, MA 2015  CommonVariable Learning and Equivalence Learning using AlternatingDiffusion. 
Talk  IDeAS seminar, Princeton  Princeton, NJ 2014  Common Manifold Learning Using AlternatingDiffusion. 
Talk  ICERM  Providence, RI 2014  Algorithms for DNA Sequencing. 
Talk  Seminar, Weizmann Institute  Rehovot, Israel 2014  On the Analytical and Numerical Properties of the Truncated Laplace Transform. 
Talk  Applied Mathematics Seminar, Tel Aviv University  Tel Aviv, Israel 2014  On the Analytical and Numerical Properties of the Truncated Laplace Transform. 
Posters  Genome Informatics conference  CSHL, NY 2013  Using the LongRange “independence” Property of DNA for Read Mapping. General Purpose and Customized RandomPermutationsBased Mappers. 
Talk  Broad Inst. of MIT and Harvard  Cambridge, MA 2013  New Randomized Approaches to Fast and Accurate Read Processing, Mapping and Assembly. 
Talk, Poster  Recomb and RecombSeq Conference  Beijing, China 2013  A RandomPermutationsBased Approach to Fast Read Alignment. 
Poster  HitSeq and ISMB conference  Long Beach, CA 2012  “ShufflingBased” Fast Read Alignment. 
Select Teaching
MATH555 / AMTH555 : Elements of Mathematical Machine Learning  Yale, Spring 2015 
MATH 112 : Calculus of Functions of One Variable I  Yale, Spring 2015 
AMTH 160 : The Structure of Networks – TA (Instructor: R.R. Coifman)  Yale, Spring 2014 
AMTH 160 : The Structure of Networks – TA (Instructor: R.R. Coifman)  Yale, Spring 2013 
AMTH 561 / CPSC 662 : Spectral Graph Theory – TA (Instructor: D.A. Spielman)  Yale, Fall 2012 
CPSC 365 : Design and Analysis of Algorithms – TA (Instructor: D.A. Spielman)  Yale, Spring 2012 
CPCS 445/545 : Introduction to Data Mining – TA (Instructor: V. Rokhlin)  Yale, Fall 2011 