Interests

Optimal Routing

I have been researching how game-theoretic concepts such as Nash equilibria and Stackelberg games can be used in conjunction with first-order PDE highway models to gain insights into how optimal rerouting policies can be generated when only a subset of drivers on the network are controllable. I have been collaborating with Walid Krichene and Saurabh Amin on this research.

• Managing demand on shared resources that can be processed in parallel.
  • Stackelberg routing
  • References: 2 5 6 7
• Using game-theoretic concepts to analyze and implement partial-control routing problems.
  • References: 4 2 5 6 7
  • See Eulerian/Lagrangian and Nash/Stackelberg work below.
• Applications to traffic systems and cloud-based architectures

Adjoint-based Freeway Control

Using the adjoint of a PDE system (discretized or continuous), one can sometimes greatly reduce the complexity of computing the gradient of an objective with respect to some control parameters. In our work, the state-space is usually of a greater complexity than the control space, which enables the effective use of the adjoint system. We seek to apply the method to a number of control problems in order to have optimal policies generated from realistic underlying physical models. This work is done as a collaboration with Walid Krichene, Samitha Samaranayake, and Maria Laura Delle Monache, and as a part of the ORESTE collaboration with INRIA in France.

• Coordinating ramp metering lights to reduce congestion on freeways.
• Multi-source, multi-sink optimal rerouting policies using network-based PDE models.
• Developing PDE models for accurate modeling of general onramp/offramp junctions and incorporating ODE buffer models for strong boundary conditions.

ECC 2013 Presentation Slides

1. Introduction
2. Adjoint method for ramp metering
3. Dynamic rerouting model

Distributed Optimization

• Iterative, in-memory map-reduce algorithms for large-scale machine learning
  • CacheReduce
• Using collaborative filtering techniques to coordinate sub-networks towards global optimality

Mobile/Participatory Sensing

• Using accelerometers and GPS in smartphones to collect geolocalized seismic information and developing filtering techniques for sensing in uncontrolled environments
  • iShake Project
  • References: 1 3 8 10
• Live generation of emissions heat maps based on real-time weather and traffic estimation on highways.
  • ClearSky

Nash/Stackelberg Games

Optimization-based Framework for Rerouting a Subset of Users with Mixed Lagrangian-Eulerian Demand

With the growing popularity of location-aware smartphones, it is becoming more realistic to have individual-level control of drivers on a freeway network, where a central service could provide alternative routes to drivers to improve overall traffic conditions.

It is clear that such an approach would only have partial penetration of the total flow on the freeway network, and any control policy must consider the unequipped drivers to find an optimal policy. We look into solving this problem using the cell-transmission model as the underlying discrete dynamics.

Additionally, there is limited information on the behavior of the uncontrolled drivers. Only total flow across links is known (from stationary sensors), which provides "Eulerian" type information. Since controlled drivers are assumed to have provided start-end goals via smartphone, then path-based "Lagrangian" information is available for these users.

We developed a game-theoretic approach to solving this problem, and pose it as a convex optimization problem. The work enables central agencies to understand equilibrium behavior of such policies, while providing asymmetric input due to the varying levels of information from the drivers. Source code.. See 4 for more information.

iShake

Emergency responders must "see" the effects of a major earthquake clearly and rapidly so that they can effectively respond to the damage it has produced. The goal of the iShake project is to create a system that moves beyond DYFI ("Did You Feel It?") by taking advantage of the accelerometers most people have already in their cell phones, which would collect ground motion intensity parameters during the earthquake, so that an accurate portrayal of the damage effects of an earthquake can be provided to government officials and emergency responders immediately after an event.

Through iShake people will be able to make use of their own smart phones and participate in an effective and valuable process to inform emergency responders in the event of an earthquake.

I developed the iShake iPhone application and the backend server to collect the accelerometer and GPS information. I also worked on developing filtering techniques for coping with the variable environments in which the samples could be taken.

See 1, 3, 8, 10 for publications, and check out the official site.

ClearSky

The ClearSky project aimed to create real-time pollution maps based on live traffic estimations, current weather conditions and dispersion models. Additionally, there were efforts made to have standalone sensors attached to municipal vehicles to get "ground-truth" measurements to supplement the map creation.

I contributed to the project by desigining and implement the system architecture that allowed the submodules to communicate and database design. Additionally, I set up the feed that allowed the standalone sensors to feed back to the server via UDP.

CacheReduce

Some promising results have come out of the research into the alternating-directions method-of-multipliers (ADMM) approach to optimization. Particularly promising is its applications to distributed optimization, as the problem formulation allows one to easily parallelize the computations and distribute large datasets across many clusters.

Map-reduce style algorithms work well within this context, as it is a natural architecture for collaborative filtering problems, but since most implementations are stateless after a single map-reduce operation, the network costs of transmitting large datasets on every iteration is often prohibitive for iterative map-reduce applications, such as this.

To overcome this, we used the Spark Scala framework to allow for intermediate caching calls to reduce the network costs for large datasets.

Visit here for more information, including source code and report.

TrustScore

I worked on a team named TrustScore (demo site) as a part of the Creative Currency project in San Francisco that challenged technical people to come up with beneficial systems to serve the public good. We created a graph-based trust propagation system that encouraged agents to endorse one another in order to provide non-standard metrics when considering loan applications.

A demonstration is given below of how our algorithm works and how trust propagation can lead to a more efficient loaning network.

Source code.

Year 1 Year 2 Year 3 Year 4 Year 1 The social network is very sparse, and not much information has been understood about who is in the network. All networks must start somehwere! All loanee scores are equal Both successful and unsuccessful loanees remain in the system and can endorse others. Year 2 While it will take some time to create an fully efficient referral system, the algorithms set up encourage taking loans from trustworthy endorsers. This further introduces trustworthiness into the network while reward those with successful endorsements. Some nodes have larger loanee scores based on back-propogation algorithm that rewards successful endoresments. Year 3 The network has very few unsuccessful endoresments, yet those with poor credit scores are still being given loans from good endoresments. The network is beginning to grow much more rapidly, as there are more referral nodes. Central nodes are growing very fast Successful nodes are clustering around other successful nodes Unsuccessful nodes have limited endoresement power and exist on the "fringes" of the network Year 4 Dominant endorsers are becoming obvious and should be upgraded to a "trusted" partner. The number of loans increases as well as the success rate. There is now a complete referral system that curated a successful user base!

Team Buildit

My friend Devon Laduzinsky and I created and taught a 10 day project which exposed a group of six promising minority freshmen in high school to the discipline of engineering and automation. More accurately, we somehow got permission to smash concrete beams and make model bridges with kids, and call it volunteering. Check out the website here to see more pictures and details of the lessons taught! Source code.

JDR Music System

Being a guitar player and mathematically-inclined guy, I have always viewed music in terms of numbers, intervals, building modules out of submodules, as opposed to the "traditional" letters-based representation that musical notation usually takes. To make the music composition process more in-line with the way I conceptualize, I created the JDR musical notation system, which enables one to specify scores in relative intervallic terms, and to define musical "riffs" of certain parts which can be composed and combined and modulated in different ways to create full instrumental parts.

I successfully implemented this language to create the classical musical notation from a JDR input file. Below check out a demo of the program and a sample JDR file.

Source code.

              Ob-la-di Ob-la-da
              header:h1:[100,treble_up,Bb,4/4,mf,piano]

              phrase:verse_p1: 3.8 3.8 3.8 3.8 3.8 3.8 2.8 1.8 {octave_down} 7.8 {octave_up} 2.4 2.4 ~.4 4.4 4.8 4.8 4.8 4.8 4.8 3.8 2.8 1.2 ~.2
              phrase:verse_p2: 5.8 5.8 5.8 5.8 5.8 5.8 4.8 3.8 4.8 5.4 6.4 6.8 5.8 4.8 3.8 3.8 4.8 3.8 2.8 4.8 3.8 2.8 1.2 ~.8
              phrase:mel_chorus: {length_8} 1 3 5 ~ 1 3 5 ~ 1 3 {length_off} 5.2 {octave_up} 1.2 {octave_down} 5.4 {length_8} 4 3 4 3 2 ~ 1 ~ ~ ~ {octave_up} 1 {octave_down} ~

              phrase:melody:verse_p1 verse_p2 mel_chorus mel_chorus

              phrase:ch1:{octave_up} ~.8 {staccato_on} {pitch_*1_}  4 8
              phrase:ch4:{octave_up} ~.8 {staccato_on} {pitch_*4_}  4 8
              phrase:ch5:{octave_up} ~.8 {staccato_on} {pitch_*5_7}  4 8
              phrase:ch6:{octave_up} ~.8 {staccato_on} {pitch_*6_m}  4 8
              phrase:ch3:{octave_up} ~.8 {staccato_on} {pitch_*3_m}  4 8

              phrase:rhythm-verse:ch1 ch1 ch5 ch5 ch5 ch5 ch1 ch1 ch1 ch1 ch4  ch4  ch1 ch5 ch1 ch1
              phrase:rhythm-chorus:ch1 ch1 ch3 ch6 ch1 ch5 ch1 ch1

              phrase:rhythm:rhythm-verse rhythm-chorus rhythm-chorus

              phrase:rest_4:{pitch_~} 1 1 1 1
              phrase:chorus_lahs:{length_8} {octave_up} [1_5] [1_5] [1_5] [1_5] [1_5] [1_5] [1_5] [1_5] [7_5] [7_5] [7_5] [7_5] [1_6] [1_6] [1_6] [1_6]  [1_5] [1_5] [1_5] [1_5] [7_5] [7_5] [7_5] [7_5] [1_5] [1_5] [1_5] [1_5] [1_5] [1_5] [1_5] [1_5]

              phrase:lahs:rest_4 rest_4 rest_4 chorus_lahs

              staff:h1:melody
              staff:h1:rhythm
              staff:h1:lahs
            

ScenicGPS

Dan Lynch and I developed an iPhone application which suggested scenic routes for users to take by pulling in interesting and scenic factors along alternate routes. Additionally, users could submit their own scenic pieces to be included for others to see. Check out more details and videos here! iPhone application source. Server source.

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Music

Pull in SoundCloud Music! Pull in Youtube Music!