Welcome to my website.

A summary of my academic and extracurricular activities. If you don't find what you are looking for feel free to contact me. Also, you may call me Amin for short.

Research Statement [PDF]

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Curriculum Vitae [PDF]

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Dissertation [PDF]

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Erdös number: ≤ 5 (source: MathSciNet)

Contact Information


Email: amin.rahman [at] ttu [dot] edu
Office: Math Building 117E
Office Phone: 806-834-2545
Vehicle: Bicycle

My research involves formulating mechanistic models that agree with experiments of real world systems and analyzing them via rigorous mathematics.  Brief summaries of recent projects can be found in the menus below, and a more detailed description can be found in my research statement above.

  • Transport and Population Dynamics in Oncology

    Drug DiffusionAccording to the National Cancer Institute, almost 40% of men and women in the United States end up developing cancer in their lifetime, and total national expenditure on cancer is $125 Billion.  While cancer deaths have fallen, the treatment of cancer is still predominant a trial and error process.  This may result in delays to administer the correct treatment, the use of more invasive procedures, or an increase in toxicity due to superfluous treatments.  Although these procedures may end up saving the patient, the treatment may also have an adverse effect on their quality of life.  To remedy this cruel paradox my collaborators and I have been developing a framework of complete scientific investigations for optimal treatment through the use of robust mathematical models and biological experiments rooted in the rigors of physics.

    Once again, borrowing statistics from the National Cancer Institute, over 60% of Dose SurfaceDose Curvecancer cases and over 70% of cancer related deaths occur in Africa, Asia, and South America, having the worst effect on the poorest populations.  Some of the easiest cancers to treat in the Western world, solid -- accessible tumors, are often fatal in poor nations.  In industrialized nations the answers to solid tumors is simple -- operate.  However, operation is generally quite complex, and costs a significant amount of money.  This can be remedied by the use of drug injections into solid tumors, which is cheap and does not require much skill.  We have developed mechanistic models for the fluidic interactions of the drug with the geometry and topography of the tumor coupled with statistical models of drug response for a population in order to achieve high predictive capabilities and show causality.  In oncological studies the data is represented by dose-response curves, which we also have from our model, however having a model also gives us the ability to plot dose-time-response surfaces, which gives us a more fine-grained picture for the effects of the drug.


    Animation of partial ablation

    Animation of partial ablation of a tumor.

    Animation of full ablation

    Animation of full ablation of a tumor.

    For more information please refer to my research statement.

    Relevant Publications:

    • Modeling of drug diffusion in a solid tumor leading to tumor cell death
      Aminur Rahman, Souparno Ghosh, and Ranadip Pal
      Physical Review E (2018). [Preliminary manuscript on Arxiv]
    • Recursive model for dose-time responses in pharmacological studies
      Saugato R. Dhruba, Aminur Rahman, Raziur Rahman, Souparno Ghosh, and Ranadip Pal
      BMC Bioinformatics (2019). Invited special issue on Computational Network Biology: Modeling, Analysis, and Control. doi: 10.1186/s12859-019-2831-4
    • Recursive model for dose-time responses in pharmacological studies
      Aminur Rahman, S.R. Dhruba, Souparno Ghosh, and Ranadip Pal
      Proceedings of the Fifth International Workshop on Computational Network Biology: Modeling, Analysis, and Control (2018).

  • Walking Droplets

    Walking droplets diagramIt has been known for decades that, given proper conditions, a fluid drop can be made to bounce on a vibrating fluid bath for long times scales.  In recent years, bouncing droplets have been observed to bifurcation from the bouncing state (no horizontal motion) to the walking state (horizontal motion).  Experiments with walking droplets (called walkers) exhibit analogs of wave-particle duality and more specifically quantum-like phenomena.  Studying walkers can enhance our understanding of quantum mechanics andWalker plots suggest viable alternatives to the Copenhagen interpretation.

    My research has focused on attacking walking dynamics on two fronts: developing simple models for various geometries and analyzing well established models via dynamical systems theory.  Recently, this has manifested in modeling multiple non -chaotic walkers and single chaotic walkers in an annulus, proving the existence of various bifurcations and chaotic dynamics for my models. and analyzing novel bifurcations arising in models from previous investigations.

    Animation of chaotic walking

    Animation of a single walker chaotically changing speed in an annulus.

    Animation of a chaotic walker

    Animation of a walker chaotically changing velocity.

    For more detailed information and references please refer to my research statement.

    Relevant Publications:

    • Standard map-like models for single and multiple walkers in an annular cavity
      Aminur Rahman
      Chaos (2018), Invited special issue on hydrodynamic quantum analogs.doi: 10.1063/1.5033949[Preliminary manuscript on Arxiv]
    • Sigma Map Dynamics and Bifurcations.
      Aminur Rahman, Yogesh Joshi, and Denis Blackmore
      Regular and Chaotic Dynamics (2017), Invited special issue dedicated to the memory of Vladimir Arnold (1937 - 2010). doi:10.1134/S1560354717060107
    • Interesting Bifurcations Inspired by Walking Droplet Dynamics [Preliminary manuscript on Arxiv]
      Aminur Rahman and Denis Blackmore
    • Neimark--Sacker bifurcation and evidence of chaos in a discrete dynamical model of walkers.
      Aminur Rahman and Denis Blackmore
      Chaos, Solitons & Fractal, (2016), doi: 10.1016/j.chaos.2016.06.016. [Arxiv]

  • Chaotic Logical Circuits

    RSFF experimentLogical circuits are an integral part of modern life that are traditionally designed with minimal uncertainty.  While this is straightforward to achieve with electronic logic, other logic families such as fluidic, chemical, and biological circuits naturally exhibit uncertainties due to the slower timescales of Boolean operations.  In addition, chaotic logical circuits have the potential to be employed in random number generation, encryption, and fault tolerance.  However, in order to exploit the properties of various nonlinear circuits they need to be studied further.  Since experiments with large systems become difficult, tractable mathematical models that are amenable to analysis via dynamical systems theory are of particular value.

    We developed a modeling framework for the chaotic Set/Reset flip-flop circuit and two types of chaotic NOR gates.  Through this framework we derive discrete dynamical models for Set/Reset - type circuits with any number of NOR gates.  Since the models are recurrence relations, the computational expense is quite low.  Further, we conducted experiments to test these models, which shows both qualitatively and quantitatively close behavior between the theory and experiments.
    RSFF plots

    For more detailed information and references please refer to my research statement.

    Relevant Publications:




  • Theoretical Developments in Dynamical Systems and Bifurcations

    Theoretical developments in Dynamical Systems:

    Sigma map bifurcations:

    Upon discovering a new global bifurcation in discrete dynamical models of walking droplets, we developed a generic dynamical system in order to generalize the theory of such bifurcations.  From a graphical point of view, the invariant circle from an initial Neimark--Sacker bifurcation "blinks" on and off.  This is due to the transition from tangential to transverse intersections of the unstable and stable manifolds of the saddle fixed point.
    Sigma map bifurcations

    Animation of colliding invariant circles

    Animation of colliding invariant circles during a global homoclinic-like bifurcation.

    For more detailed information and references please refer to my research statement.

    Relevant Publications:

    • Sigma Map Dynamics and Bifurcations.
      Aminur Rahman, Yogesh Joshi, and Denis Blackmore
      Regular and Chaotic Dynamics (2017), Invited special issue dedicated to the memory of Vladimir Arnold (1937 - 2010). doi:10.1134/S1560354717060107
    • Interesting Bifurcations Inspired by Walking Droplet Dynamics [Preliminary manuscript on Arxiv]
      Aminur Rahman and Denis Blackmore




    Generalized Attracting Horseshoe:

    We had previously shown that attracting horseshoes may be generalized to be contained within a quadrilateral trapping Trapping regionregion.  Through the NJIT Provost high school internship and the Provost Phase 1 undergraduate research grant, I mentored Karthik murthy (Bridgewater - Raritan High School) and Parth Sojitra (NJIT-ECE), under the supervision of Denis Blackmore, in finding numerical evidence of generalized attracting horseshoes (GAH) in Poincare maps of the Rossler attractor.  I developed the algorithms to go from a first return map to a Poincare map and finally to find the quadrilateral trapping region for the supposed GAH.  I then guided our students in writing the MATLAB codes to carry out the algorithms.  While finding the trapping region numerically is not a proof, it does give us confidence that there exists a GAH in the Poincare map of the Rossler attractor.

    For more detailed information and references please refer to my research statement.

    Relevant Publications:

    • Generalized attracting horseshoes and chaotic strange attractors.
      Yogesh Joshi, Denis Blackmore, and Aminur Rahman




  • Miscellaneous

    Chaotic scattering:

    Chaotic scattering has been studied from the early 70s and 80s in solitary wave collisions from the Phi-Four equation (called Kink-Antikink collisions).  These were mainly numerical studies that gave insight into the phenomena.  However, since the equation is so difficult to work with there has been very little analysis done.  In more recent years reduction techniques have been used to approximate the Phi-Four PDE with a system of ODEs and also as an iterated map.

    We have gone further and developed a mechanical analog (a ball rolling on a special surface) of chaotic scattering in Kink-Antikink collisions.  This was done in order to conduct experiments.  In addition to experiments we have analyzed the system thoroughly, including the dissipation that comes from friction.  The experimental setup is shown bellow.

               


    For more detailed information and references please refer to my research statement.

    Relevant Publications:

    • A mechanical analog of the two-bounce resonance of solitary waves: modeling and experiment.
      Roy H. Goodman, Aminur Rahman, Michael J. Bellanich, and Catherine N. Morrison.
      Chaos (2015), doi: 10.1063/1.4917047. [Arxiv]




    Pedagogical proof of Peixoto's theorem in 1-D:

    Peixoto's theorem is one of the most important theorems in Dynamical Systems.  It was proved by Dr. Mauricio Matos Peixoto in 1962.  This proof is extremely involved - far too involved for most undergraduate students to follow.  We develop an alternate - pedagogical proof of the simpler 1-D case, with the goal of allowing senior undergraduate students to follow and understand the proof and consequently some of the ideas involved in the much bigger proof of the 2-D case.

    For more detailed information and references please refer to my research statement.

    Relevant Publications:

    • Peixoto's structural stability theorem: the one dimensional version.
      Aminur Rahman.
      SIAM-dswebtutorials, (2013), eprint. Arxiv





    Particle Accelerator Physics:

    We numerically simulate the beam dynamics of the Energy Recovery Linear Particle Accelerator (ERL) design for Argonne National Lab's (ANL) Advanced Photon Source (APS).  The code BI, created by Ivan Bazarov, is benchmarked against our own code for simpler Accelerators.  Then the full ERL is simulated and the results analyzed.  We conclude that the ERL, if built, would theoretically be stable.  Therefore, it would be feasible to build it.

    For more detailed information and references please refer to my research statement.

    Relevant Publications:

    • Benchmarking the multipass beam-breakup simulation code BI
      Aminur Rahman, Nicholas Sereno, and Hairong Shang
      OAG-TN-2008-029, (2008), [PDF]




Publications

Journal Publications:

Sorted by date submitted.

  1. Recursive model for dose-time responses in pharmacological studies
    Saugato R. Dhruba, Aminur Rahman, Raziur Rahman, Souparno Ghosh, and Ranadip Pal
    BMC Bioinformatics (2019). Invited special issue on Computational Network Biology: Modeling, Analysis, and Control. doi: 10.1186/s12859-019-2831-4
  2. Generalized Attracting Horseshoe in the Rossler Attractor [Preliminary manuscript on Arxiv] (Submitted)
    Karthik Murthy, Parth Sojitra, Aminur Rahman, Ian Jordan, and Denis Blackmore
  3. Modeling of drug diffusion in a solid tumor leading to tumor cell death
    Aminur Rahman, Souparno Ghosh, and Ranadip Pal
    Physical Review E (2018). doi: 10.1103/PhysRevE.98.062408 [Preliminary version on Arxiv]
  4. Interesting Bifurcations Inspired by Walking Droplet Dynamics [Preliminary manuscript on Arxiv] (Submitted)
    Aminur Rahman and Denis Blackmore
  5. Standard map-like models for single and multiple walkers in an annular cavity
    Aminur Rahman
    Chaos (2018), Invited special issue on hydrodynamic quantum analogs.doi: 10.1063/1.5033949 [Preliminary manuscript on Arxiv]
  6. Generalized attracting horseshoes and chaotic strange attractors. (Submitted)
    Yogesh Joshi, Denis Blackmore, and Aminur Rahman
  7. Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops
    Aminur Rahman, Ian Jordan, and Denis Blackmore
    Proceedings of the Royal Society A (2018), doi: 10.1098/rspa.2017.0111[Preliminary version on Arxiv]
  8. Sigma Map Dynamics and Bifurcations.
    Aminur Rahman, Yogesh Joshi, and Denis Blackmore
    Regular and Chaotic Dynamics (2017), Invited special issue dedicated to the memory of Vladimir Arnold (1937 - 2010). doi:10.1134/S1560354717060107
  9. Threshold voltage dynamics of chaotic RS flip-flops.
    Aminur Rahman and Denis Blackmore
    Chaos, Solitons & Fractal, (2017),doi: 10.1016/j.chaos.2017.07.014 [Preliminary manuscript on Arxiv]
  10. Neimark--Sacker bifurcation and evidence of chaos in a discrete dynamical model of walkers.
    Aminur Rahman and Denis Blackmore
    Chaos, Solitons & Fractal, (2016), doi: 10.1016/j.chaos.2016.06.016. [Arxiv]
  11. A mechanical analog of the two-bounce resonance of solitary waves: modeling and experiment.
    Roy H. Goodman, Aminur Rahman, Michael J. Bellanich, and Catherine N. Morrison.
    Chaos (2015), doi: 10.1063/1.4917047. [Arxiv]
  12. Discrete dynamical modeling and analysis of the R-S flip-flop circuit.
    Denis Blackmore, Aminur Rahman, and Jigar Shah.
    Chaos, Solitons & Fractal, (2009), doi: 10.1016/j.chaos.2009.02.032. [Arxiv]

Conference Proceedings:

  1. Recursive model for dose-time responses in pharmacological studies
    Aminur Rahman, S.R. Dhruba, Souparno Ghosh, and Ranadip Pal
    Proceedings of the Fifth International Workshop on Computational Network Biology: Modeling, Analysis, and Control (2018).

Other Publications:

  1. Peixoto's structural stability theorem: the one dimensional version.
    Aminur Rahman.
    SIAM-dswebtutorials, (2013), eprint. Arxiv
  2. Benchmarking the multipass beam-breakup simulation code BI
    Aminur Rahman, Nicholas Sereno, and Hairong Shang
    OAG-TN-2008-029, (2008), [PDF]
Presentations

Invited Talks:

  1. Coupled transport-population models for drug distribution and tumor cell death.
    Mechanical Engineering Seminar, Purdue University, West Lafayette, IN, January 9, 2019
  2. Simple transport-population models for drug distribution and tumor cell death.
    Applied mathematics Seminar, Texas Tech University, Lubbock, TX, November 28, 2018
  3. Simple transport-population models for drug distribution and tumor cell death.
    Biomathematics Seminar, Texas Tech University, Lubbock, TX, November 6, 2018
  4. Discrete dynamical models of walking droplets.
    Applied mathematics Seminar, Texas Tech University, Lubbock, TX, October 31, 2018
  5. Tumor ablation through drug diffusion.
    Mathematical Biology Seminar, New Jersey Institute of Technology, Newark, NJ, April 3, 2018
  6. Simple Models in a Complex World.
    SIAM TTU Graduate Student Chapter Junior Scholar Symposium, Texas Tech University, Lubbock, TX, February 27, 2018
  7. Tumor ablation through drug diffusion.
    Biomathematics Seminar, Texas Tech University, Lubbock, TX, February 6, 2018
  8. Bifurcations in Walking Droplet Dynamics.
    Society for Industrial and Applied Mathematics Dynamical Systems Conference 2017, Snowbird Resort, Snowbird, UT, May 21, 2017
  9. Dynamical modeling and analysis of walking droplets and chaotic logical circuits.
    Numerical Methods for PDEs Seminar, Massachusetts Institute of Technology, Cambridge, MA, February 22, 2017
  10. Dynamical modeling and analysis of chaotic logical circuits and walking droplets.
    Dynamical Systems Seminar, University of Rhode Island, South Kingstown, RI, February 8, 2017
  11. Neimark-Sacker Bifurcation and Evidence of Chaos in a Discrete Dynamical Model of Walkers.
    American Mathematical Society Fall Northeast Sectional Conference 2015, Rutgers University, New Brunswick, NJ, November 14, 2015
  12. The Chaotic Ballet of Walking Droplets.
    Mechanical and Industrial Engineering Colloquium, New Jersey Institute of Technology, Newark, NJ, October 7, 2015
  13. A Scheme for Modeling and Analyzing the Dynamics of Logical Circuits
    Center for Nonlinear Studies Seminar, Los Alamos National Laboratory, Los Alamos, NM, May 21, 2015
  14. A Scheme for Modeling and Analyzing the Dynamics of Logical Circuits
    Society for Industrial and Applied Mathematics Dynamical Systems Conference 2015, Snowbird Resort, Snowbird, UT, May 18, 2015
  15. A Mechanical Analog and Discrete Modeling of the n-bounce Resonance of Solitary Waves.
    American Mathematical Society Spring Northeast Sectional Conference 2015, Georgetown University, Washington DC, March 7, 2015
  16. Further Analysis of Discrete Dynamical Models of the RS Flip-Flop Circuit
    American Mathematical Society Fall Southeast Sectional Conference 2014, University of North Carolina at Greensboro, Greensboro, NC, November 8, 2014
  17. [Video] A Scheme for Modeling and Analyzing the Dynamics of Logical Circuits
    American Mathematical Society Spring Sectional Northeast Conference 2014, University of Maryland Baltimore County, Baltimore, MD, March 29, 2014

Contributed Talks:

  1. The Chaotic Ballet of Walking Droplets.
    Dynamic Days 2018, Hilton Denver City Center, Denver, CO, January 4, 2018
  2. Dynamics of Discrete Dynamical Models of a Walker in an Annulus.
    Workshop on Wave-Particle Duality and Hydrodynamic Quantum Analogs, University of Liège, Liège, BE., July 3, 2017
  3. The Chaotic Ballet of Walking Droplets.
    Joint Math Meetings, Hyatt Regency Atlanta and Marriott Atlanta Marquis, Atlanta, GA, January 4, 2017
  4. Neimark-Sacker Bifurcation and Evidence of Chaos in a Discrete Dynamical Model of Walkers.
    American Mathematical Society Fall Northeast Sectional Conference 2016, Bowdoin College, Brunswick, ME, September 24, 2016
  5. A Tempest in The Mathematics of Time: A brief history of chaos and its appearance in walking droplets and electronic circuits.
    NJIT Graduate Student Seminar, New Jersey Institute of Technology, Newark, NJ, June 21, 2016
  6. Neimark-Sacker Bifurcation and Evidence of Chaos in a Discrete Dynamical Model of Walkers.
    American Physical Society 68th Annual Division of Fluid Dynamics Meeting, Hynes Convention Center, Boston, MA, November 24, 2015
  7. Neimark-Sacker Bifurcation and Evidence of Chaos in a Discrete Dynamical Model of Walkers.
    NJIT Graduate Student Seminar, New Jersey Institute of Technology, Newark, NJ, June 11, 2015
  8. A Mechanical Analog of the Chaotic Scattering in Solitary Waves.
    NJIT Graduate Student Seminar, New Jersey Institute of Technology, Newark, NJ, July 24, 2014
  9. Peixoto's structural stability theorem:  the one-dimensional version.
    Joint Mathematics Meetings 2014, Baltimore, MD, January 17, 2014
  10. A Scheme for Modeling and Analyzing the Dynamics of Logical Circuits
    Joint Mathematics Meetings 2014, Baltimore, MD, January 15, 2014
  11. Phase Field Formulation for Microstructure Evolution in Oxide Ceramics.
    Modeling Problems in Industry 2013, Worcester Polytechnic Institute, Worcester, MA, June 21, 2013
  12. Peixoto's Structural Stability Theorem:  The One-dimensional Version.
    NJIT Graduate Student Seminar, New Jersey Institute of Technology, Newark, NJ, June 11, 2013
  13. Logical circuits: A Scheme for Discrete Modeling and Analysis.
    NJIT Graduate Student Seminar, New Jersey Institute of Technology, Newark, NJ, July 10, 2012
  14. Mechanical Chaotic Scattering: The Adventures in the Valley of Chaos.
    Hallenbeck Graduate Student Seminar, University of Delaware, Newark, DE, April 20, 2011
  15. A Scheme for Modeling and Analyzing the Dynamics of Logical Circuits.
    Hallenbeck Graduate Student Seminar, University of Delaware, Newark, DE, October 20, 2010

Posters:

  1. Standard map-like models for single and multiple walkers in an annular cavity
    Dynamic Days 2019, Hilton Orrington Hotel, Evanston, IL, January 4 - 6, 2019
  2. A prospective analysis tool to assess potential success for extra-femoral mechanical thrombectomy
    Congress of Neurological Surgeons 2018, Mariott Marquis, Houston, TX, October 6 - 11, 2018
  3. A Scheme for Analyzing the Dynamics of Logical Circuits
    Frontiers in Applied and Computational Mathematics 2015, New Jersey Institute of Technology, Newark, NJ, June 5 - 6, 2015
  4. A Scheme for Analyzing the Dynamics of Logical Circuits
    Frontiers in Applied and Computational Mathematics 2014, New Jersey Institute of Technology, Newark, NJ, May 22 - 23, 2014
  5. A Scheme for Analyzing the Dynamics of Logical Circuits
    Joint Mathematics Meetings 2014, Baltimore, MD, January 16, 2014
  6. A Scheme for Analyzing the Dynamics of Logical Circuits
    Graduate Student Association Research Day 2013, New Jersey Institute of Technology, Newark, NJ, October 31, 2013
  7. A Scheme for Analyzing the Dynamics of Logical Circuits
    Frontiers in Applied and Computational Mathematics 2013, New Jersey Institute of Technology, Newark, NJ, May 31 - June 2, 2013
  8. A Scheme for Analyzing the Dynamics of Logical Circuits
    Frontiers in Applied and Computational Mathematics 2010, New Jersey Institute of Technology, Newark, NJ, May 21 - 23, 2010
  9. Discrete Dynamical Modeling and Analysis of the R-S flip-flop circuit
    NJIT Experience Day, New Jersey Institute of Technology, Newark, NJ, April 19, 2009
  10. Discrete Dynamical Modeling and Analysis of the R-S flip-flop circuit
    Dana Knox Student Research Showcase, New Jersey Institute of Technology, Newark, NJ, April 8, 2009
  11. Discrete Dynamical Modeling and Analysis of the R-S flip-flop circuit
    Garden State Undergraduate Mathematics Conference, Monmouth University, Monmouth, NJ, March 29, 2009
  12. Chaos of the R-S flip-flop circuit
    Frontiers in Applied and Computational Mathematics 2008, New Jersey Institute of Technology, Newark, NJ, May 19 - 21, 2008
  13. Chaos of the R-S flip-flop circuit
    NJIT Experience Day, New Jersey Institute of Technology, Newark, NJ, April 5, 2008

I am honored to be the recipient of the 2016 NJIT Excellence in Teaching award.


I have included lecture notes in the menus below.


Graduate courses: Undergraduate courses:

Recitations:

  1. Calculus II (NJIT)
  2. Calculus I (NJIT)
  3. Calculus I (UD)
  4. Pre-Calculus (NJIT)

As guest lecturer:

  1. Complex Variables (NJIT)
  2. Real Analysis (NJIT)
  3. Dynamical Systems (NJIT)
  4. Linear Algebra (NJIT)
  5. Ordinary Differential Equations (NJIT)
  6. Numerical Methods Lab (NJIT)
  7. Calculus II (NJIT)
  8. Calculus I (NJIT)
  9. Trigonometry and Calculus (NJIT)
Bicycling, Hiking, Football (Soccer), Chess, and Running with my wife, Moira, and our dog Aurora (Australian Shepherd)
Me and MoGroupWedding

My main bike is a Surly Crosscheck that I take to various places.

Places I like to hike:
Breakneck Ridge (Bear Mountain)
Boroughs Range (Catskills: Slide Mountain, Cornell, Whitenberg)
Veerkerderkill Falls and Ice Caves (Sam's point)
Mount Tamany (Delaware Watergap)
Palisades (Shore trail + Great Steps)
Acadia National Park
Great Smokey Mountain National Park
Green Mountain National Forest
White Mountain National Forest

Some interesting places I have biked through:
Cycling around North Jersey

Here is a video of my bike commute:
Kearny to Newark

I used to play football in high school, and still try to play from time to time.  Now I'm more of a spectator, though.  I mostly follow the USMNT, Juventus, Liverpool, and Sheffield Wednesday.

Here's an album of the USMNT training session:

USMNT training 2011
I have uploaded relevant codes and videos below. It should be noted that some papers use codes from my co-authors, and therefore are not included here.

SIAM video pitch entry [top four]

SIAM video pitch entry.