Community Structure in Time-Dependent, Multiscale, and Multiplex Networks (2009)
Mucha, Peter J., Richardson, Thomas, Macon, Kevin, Porter, Mason A., Onnela, Jukka-Pekka
During the last decade, the science of networks has grown into an enormous interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences....
Agarwal, Sumeet, Deane, Charlotte M., Porter, Mason A., Jones, Nick S.
The idea of 'date' and 'party' hubs has been influential in the study of protein-protein interaction networks. Date hubs display low co-expression with their partners, whilst party hubs have high...
Mutually-Antagonistic Interactions in Baseball Networks (2009)
Saavedra, Serguei, Powers, Scott, McCotter, Trent, Porter, Mason A., Mucha, Peter J.
We formulate the head-to-head matchups between Major League Baseball pitchers and batters from 1954 to 2008 as a bipartite network of mutually-antagonistic interactions. We consider both the full...
Experimental Results Related to Discrete Nonlinear Schr\"odinger Equations (2009)
In this chapter, we discuss experiments that realize the discrete nonlinear Schr\"odinger (DNLS) equations. The relevance of such descriptions arises from the competition of three common features:...
Party Polarization in Congress: A Social Networks Approach (2009)
Waugh, Andrew Scott, Pei, Liuyi, Fowler, James H., Mucha, Peter J., Porter, Mason A.
We use the network science concept of modularity to measure polarization in the U.S. Congress. Modularity provides a conceptually-clear measure of polarization that directly reveals both the number...
Competition for Popularity in Catalog Networks (2009)
Beguerisse-Diaz, Mariano, Porter, Mason A., Onnela, Jukka-Pekka
We develop a dynamical model for rewiring and attachment in bipartite networks in which edges are added between nodes that belong to fixed-size catalogs. We motivate this model with an empirical...
Localized Breathing Modes in Granular Crystals with Defects (2009)
Theocharis, G., Kavousanakis, M., Kevrekidis, P. G., Daraio, Chiara, Porter, Mason A., Kevrekidis, I. G.
We investigate nonlinear localized modes at light-mass impurities in a one-dimensional, strongly-compressed chain of beads under Hertzian contacts. Focusing on the case of one or two such...
Dynamical Clustering of Exchange Rates (2009)
Fenn, Daniel J., Porter, Mason A., Mucha, Peter J., McDonald, Mark, Williams, Stacy, Johnson, Neil F., ...
We use techniques from network science to study correlations in the foreign exchange (FX) market over the period 1991--2008. We consider an FX market network in which each node represents an exchange...
Ponson, Laurent, Boechler, Nicholas, Lai, Yi Ming, Porter, Mason A., Kevrekidis, P. G., Daraio, Chiara
We investigate wave dynamics in elastic spin chains composed of one-dimensional granular crystals. Each "spin" consists of a dimer (two-mass) cell of spherical particles, and a spin chain is composed...
Highly nonlinear solitary waves in heterogeneous periodic granular media (2009)
Porter, Mason A., Daraio, Chiara, Szelengowicz, Ivan, Herbold, Eric B., Kevrekidis, P. G.
We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer...
Communities in Networks (2009)
Porter, Mason A., Onnela, Jukka-Pekka, Mucha, Peter J.
We survey some of the concepts, methods, and applications of community detection, which has become an increasingly important area of network science. To help ease newcomers into the field, we provide...
Dissipative Solitary Waves in Granular Crystals (2009)
Carretero-González, R., Khatri, D., Porter, Mason A., Kevrekidis, P. G., Daraio, C.
We provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. We use the propagation of highly nonlinear solitary waves as a diagnostic tool and develop...
Beyond Bisection: Eigenvector-Based Partitioning of Networks into Multiple Communities (2008)
Richardson, Thomas, Mucha, Peter J., Porter, Mason A.
We formulate a spectral graph-partitioning algorithm that uses the two leading eigenvectors of the modularity matrix to split a network into three communities at once. In so doing, we extend the...
Dissipative Solitary Waves in Granular Crystals (2008)
Carretero-Gonzalez, R., Khatri, D., Porter, Mason A., Kevrekidis, P. G., Daraio, C.
We provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. We use the propagation of highly nonlinear solitary waves as a diagnostic tool and develop...
Fenn, Daniel J., Porter, Mason A., McDonald, Mark, Williams, Stacy, Johnson, Neil F., Jones, Nick S.
We study the cluster dynamics of multichannel (multivariate) time series by representing their correlations as time-dependent networks and investigating the evolution of network communities. We...
Community Structure in Online Collegiate Social Networks (2008)
Traud, Amanda L., Kelsic, Eric D., Mucha, Peter J., Porter, Mason A.
We apply the tools of network analysis to study the roles of university organizations and affiliations in structuring the social networks of students by examining the graphs of Facebook "friendships"...
The Bowl Championship Series: A mathematical review (2008)
Thomas Callaghan, Peter J. Mucha, Mason A. Porter
Championship Series (BCS) announced a proposal to add a fifth game to the “BCS bowls ” to improve access for midmajor teams ordinarily denied invitations
Vortex lattice locking in rotating two-component Bose–Einstein condensates (2008)
Barnett, Ryan, Refael, Gil, Porter, Mason A., Büchler, Hans Peter
The vortex density of a rotating superfluid, divided by its particle mass, dictates the superfluid's angular velocity through the Feynman relation. To find how the Feynman relation applies to...
Averaging of Nonlinearity Management with Dissipation (2008)
Beheshti, S., Law, K. J. H., Kevrekidis, P. G., Porter, Mason A.
Motivated by recent experiments in optics and atomic physics, we derive an averaged nonlinear partial differential equation describing the dynamics of the complex field in a nonlinear Schroedinger...
Community structure in Congressional cosponsorship networks (2008)
Zhang, Y., Friend, A. J., Traud, Amanda L., Porter, Mason A., Fowler, James H., Mucha, Peter J.
We study the United States Congress by constructing networks between Members of Congress based on the legislation that they cosponsor. Using the concept of modularity, we identify the community...
Optimal design of composite granular protectors (2008)
Fraternali, Fernando, Porter, Mason A., Daraio, Chiara
We employ an evolutionary algorithm to investigate the optimal design of composite protectors using one-dimensional granular chains composed of beads of various sizes, masses, and stiffnesses. We...
Highly nonlinear solitary waves in periodic dimer granular chains (2008)
Porter, Mason A., Daraio, Chiara, Herbold, Eric B., Szelengowicz, Ivan, Kevrekidis, P. G.
We investigate the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic...
Overcoming data sparsity (2008)
Apple, Rosemary, Cawthorn, Chris, Yee Chan, Kwan, Lachish, Oded, Nonnenmacker, Achim, Porter, Mason A., ...
Unilever is currently designing and testing recommendation algorithms that would make recommendations about products to online customers given the customer ID and the current content of their basket....
Highly Nonlinear Solitary Waves in Heterogeneous Periodic Granular Media (2007)
Porter, Mason A., Daraio, Chiara, Szelengowicz, Ivan, Herbold, Eric B., Kevrekidis, P. G.
We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer...
Matter-wave solitons with a periodic, piecewise-constant nonlinearity (2007)
Rodrigues, A. S., Kevrekidis, P. G., Porter, Mason A., Frantzeskakis, D. J., Schmelcher, P., Bishop, A. R.
Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties...
Quantization of a free particle interacting linearly with a harmonic oscillator (2007)
Mainiero, Thomas, Porter, Mason A.
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an...
Avoided level crossings in the quantization of a mixed regular-chaotic system (2007)
Mainiero, Thomas, Porter, Mason A.
The study of avoided level crossings in the spectra of quantum Hamiltonians whose classical counterparts exhibit mixed regular-chaotic dynamics reveals important information about the quantum...
The Hopf Fibration and its Applications (2007)
this paper, I will discuss some of these applications as motivation for mathematicians to learn about the physical significance of the Hopf fibration in greater detail than that presented here. I...
Community Structure in Congressional Cosponsorship Networks (2007)
Zhang, Yan, Friend, A. J., Traud, Amanda L., Porter, Mason A., Fowler, James H., Mucha, Peter J.
We study the United States Congress by constructing networks between Members of Congress based on the legislation that they cosponsor. Using the concept of modularity, we identify the community...
Modulational instability in nonlinearity-managed optical media (2007)
Centurion, Martin, Porter, Mason A., Pu, Ye, Kevrekidis, P. G., Frantzeskakis, D. J., Psaltis, Demetri
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air....
Highly Nonlinear Solitary Waves in Periodic Dimer Granular Chains (2007)
Porter, Mason A., Daraio, Chiara, Herbold, Eric B., Szelengowicz, Ivan, Kevrekidis, P. G.
We report the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic...
Vortex Lattice Locking in Rotating Two-Component Bose-Einstein Condensates (2007)
Barnett, Ryan, Refael, Gil, Porter, Mason A., Buchler, Hans Peter
The vortex density of a rotating superfluid, divided by its particle mass, dictates the superfluid's angular velocity through the Feynman relation. To find how the Feynman relation applies to...
Modulated amplitude waves in collisionally inhomogeneous Bose–Einstein condensates (2007)
Porter, Mason A., Kevrekidis, P. G., Malomed, Boris A., Frantzeskakis, D. J.
We investigate the dynamics of an effectively one-dimensional Bose–Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This...
Quantization of a Free Particle Interacting Linearly with a Harmonic Oscillator (2007)
Mainiero, Thomas, Porter, Mason A.
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an...
Modulational Instability in a Layered Kerr Medium: Theory and Experiment (2006)
Centurion, Martin, Porter, Mason A., Pu, Ye, Kevrekidis, P. G., Frantzeskakis, D. J., Psaltis, Demetri
We present the first experimental investigation of modulational instability in a layered Kerr medium. The particularly interesting and appealing feature of our configuration, consisting of...
Community structure in the U.S. House of Representatives (2006)
Porter, Mason A., Friend, A. J., Mucha, Peter J., Newman, M. E. J.
Studies like these indicate that network theory can be of substantial use in uncovering collaborative structure in political bodies such as the U.S. Congress, without requiring input in the form of...
Fractional-period excitations in continuum periodic systems (2006)
Nistazakis, H. E., Porter, Mason A., Kevrekidis, P. G., Frantzeskakis, D. J., Nicolin, A., Chin, J. K.
We investigate the generation of fractional-period states in continuum periodic systems. As an example, we consider a Bose-Einstein condensate confined in an optical-lattice potential. We show that...
Modulational Instability in Nonlinearity-Managed Optical Media (2006)
Centurion, Martin, Porter, Mason A., Pu, Ye, Kevrekidis, P. G., Frantzeskakis, D. J., Psaltis, Demetri
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically-nonlinear (Kerr) optical medium that consists of alternating layers of glass and air....
Life on Both Sides of the Fence: Mentoring Versus Being Mentored (2006)
I have the rare experience of being on both sides of the mentor--undergraduate student relationship in the same program (Caltech's Summer Undergraduate Research Fellowship, or SURF, program). In this...
Feshbach resonance management of Bose-Einstein condensates in optical lattices (2006)
Porter, Mason A., Chugunova, Marina, Pelinovsky, Dmitry E.
We analyze gap solitons in trapped Bose-Einstein condensates (BECs) in optical lattice potentials under Feshbach resonance management. Starting with an averaged Gross-Pitaevsky equation with a...
Modulational instability in a layered Kerr medium: Theory and Experiment (2006)
Centurion, Martin, Porter, Mason A., Pu, Ye, Kevrekidis, P. G., Frantzeskakis, D. J., Psaltis, Demetri
We present the first experimental investigation of modulational instability in a layered Kerr medium. The particularly interesting and appealing feature of our configuration, consisting of...
Nonlinearity Management in Optics: Experiment, Theory, and Simulation (2006)
Centurion, Martin, Porter, Mason A., Kevrekidis, P. G., Psaltis, Demetri
We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over...
Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates (2006)
Porter, Mason A., Kevrekidis, P. G., Malomed, Boris A., Frantzeskakis, D. J.
We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length $a$ subjected to a spatially periodic modulation, $a=a(x)=a(x+L)$. This...
Nonlinearity Management in Optics: Experiment, Theory, and Simulation (2006)
Centurion, Martin, Porter, Mason A., Kevrekidis, P. G., Psaltis, Demetri
We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over...
One-particle and few-particle billiards (2006)
Lansel, Steven, Porter, Mason A., Bunimovich, Leonid A.
We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and...
Community Structure in the United States House of Representatives (2006)
Porter, Mason A., Mucha, Peter J., Newman, M. E. J., Friend, A. J.
We investigate the networks of committee and subcommittee assignments in the United States House of Representatives from the 101st--108th Congresses, with the committees connected by ``interlocks''...
Fractional-Period Excitations in Continuum Periodic Systems (2005)
Nistazakis, H. E., Porter, Mason A., Kevrekidis, P. G., Frantzeskakis, D. J., Nicolin, A., Chin, J. K.
We investigate the generation of fractional-period states in continuum periodic systems. As an example, we consider a Bose-Einstein condensate confined in an optical-lattice potential. We show that...
Bose-Einstein Condensates in Superlattices (2005)
Porter, Mason A., Kevrekidis, P. G.
We consider the Gross--Pitaevskii (GP) equation in the presence of periodic and quasi-periodic superlattices to study cigar-shaped Bose--Einstein condensates (BECs) in such potentials. We examine...
One-Particle and Few-Particle Billiards (2005)
Lansel, Steven, Porter, Mason A., Bunimovich, Leonid A.
We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and...
Dynamics and Manipulation of Matter-Wave Solitons in Optical Superlattices (2005)
Porter, Mason A., Kevrekidis, P. G., Carretero-González, R., Frantzeskakis, D. J.
We analyze the existence and stability of bright, dark, and gap matter-wave solitons in optical superlattices. Then, using these properties, we show that (time-dependent) ``dynamical superlattices''...
Feshbach Resonance Management of Bose-Einstein Condensates in Optical Lattices (2005)
Porter, Mason A., Chugunova, Marina, Pelinovsky, Dmitry E.
We analyze gap solitons in trapped Bose-Einstein condensates (BECs) in optical lattice potentials under Feshbach resonance management. Starting with an averaged Gross-Pitaevsky (GP) equation with a...
A network analysis of committees in the United States House of Representatives (2005)
Porter, Mason A., Mucha, Peter J., Newman, M. E. J., Warmbrand, Casey M.
Network theory provides a powerful tool for the representation and analysis of complex systems of interacting agents. Here we investigate the United States House of Representatives network of...
Ground Control to Niels Bohr: Exploring Outer Space with Atomic Physics (2005)
Porter, Mason A., Cvitanovic, Predrag
We provided an introduction to transition state theory and the connections it provides between atomic and celestial physics. We include brief discussions of historical background, recent applications...
Quasiperiodic and Chaotic Dynamics in Bose-Einstein Condensates in Periodic Lattices and (2005)
Martijn Van Noort, Mason A. Porter, Yingfei Yi, Shui-nee Chow
We employ KAM theory to rigorously investigate the transition between quasiperiodic and chaotic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward...
Nonlinear Lattice Dynamics of Bose-Einstein Condensates (2004)
Porter, Mason A., Carretero-González, R., Kevrekidis, P. G., Malomed, Boris A.
The Fermi-Pasta-Ulam (FPU) model, which was proposed 50 years ago to examine thermalization in non-metallic solids and develop ``experimental'' techniques for studying nonlinear problems, continues...
Bose-Einstein Condensates in Superlattices (2004)
Porter, Mason A., Kevrekidis, P. G.
We consider the Gross-Pitaevskii (GP) equation in the presence of periodic and quasiperiodic superlattices to study cigar-shaped Bose-Einstein condensates (BECs) in such potentials. We examine...
Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices (2004)
Van Noort, Martijn, Porter, Mason A., Yi, Yingfei, Chow, Shui-Nee
We employ KAM theory to rigorously investigate quasiperiodic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply a coherent...
A Graphical User Interface to Simulate Classical Billiard Systems (2004)
Lansel, Steven, Porter, Mason A.
Classical billiards constitute an important class of dynamical systems. They have not only been in used in mathematical disciplines such as ergodic theory, but their properties demonstrate...
The Bowl Championship Series: A Mathematical Review (2004)
Callaghan, Thomas, Mucha, Peter J., Porter, Mason A.
We discuss individual components of the college football Bowl Championship Series, compare with a simple algorithm defined by random walks on a biased graph, attempt to predict whether the proposed...
Porter, Mason A., Kevrekidis, P. G., Malomed, B. A.
We consider a system of two Gross-Pitaevskii (GP) equations, in the presence of an optical-lattice (OL) potential, coupled by both nonlinear and linear terms. This system describes a Bose-Einstein...
Mathematical Models of Bipolar Disorder (2003)
Daugherty, Darryl, Roque-Urrea, Tairi, Urrea-Roque, John, Snyder, Jessica, Wirkus, Stephen, Porter, Mason A.
We use limit cycle oscillators to model Bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about one percent of the United States adult...
Random Walker Ranking for NCAA Division I-A Football (2003)
Callaghan, Thomas, Mucha, Peter J., Porter, Mason A.
Each December, college football fans and pundits across America debate which two teams should meet in the NCAA Division I-A National Championship game. The Bowl Championship Series (BCS) standings...
A Perturbative Analysis of Modulated Amplitude Waves in Bose-Einstein Condensates (2003)
Porter, Mason A., Cvitanovic', Predrag
We apply Lindstedt's method and multiple scale perturbation theory to analyze spatio-temporal structures in nonlinear Schr\"odinger equations and thereby study the dynamics of quasi-one-dimensional...
Modulated Amplitude Waves in Bose-Einstein Condensates (2003)
Porter, Mason A., Cvitanovic, Predrag
We analyze spatio-temporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions. A coherent...
Modulated amplitude waves in Bose-Einstein condensates (2003)
Mason A. Porter, Predrag Cvitanović
We analyze spatiotemporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-onedimensional Bose-Einstein condensates �BECs � with mean-field interactions. A coherent...
A Study on the Relevance of Information in Discriminative and Non-Discriminative Media (2002)
Gershenson, Carlos, Porter, Mason A., Probst, Andrej, Marko, Matus, Das, Atin
In this paper we compare the relevance of information obtained from "discriminative" media and from "non-discriminative" media. Discriminative media are the ones which accumulate and deliver...
A Hitchhiker’s Guide to LaTex (2002)
(or how I learned to stop worrying and love writing my dissertation)
The Radially Vibrating Spherical Quantum Billiard (2001)
Porter, Mason A., Liboff, Richard L.
We consider the radially vibrating spherical quantum billiard as a representative example of vibrating quantum billiards. We derive necessary conditions for quantum chaos in $d$-term superposition...
Bifurcations in one degree-of-vibration quantum billiards (2001)
Porter, Mason A., Liboff, Richard L.
We classify the local bifurcations of one dov quantum billiards, showing that only saddle-center bifurcations can occur. We analyze the resulting planar system when there is no coupling in the...
Vibrating quantum billiards on Riemannian manifolds (2001)
Porter, Mason A., Liboff, Richard L.
Quantum billiards provide an excellent forum for the analysis of quantum chaos. Toward this end, we consider quantum billiards with time-varying surfaces, which provide an important example of...
Nonadiabatic dynamics in semiquantal physics (2001)
Every physical regime is some sort of approximation of reality. One lesser-known realm that is the semiquantal regime, which may be used to describe systems with both classical and quantum...
An Introduction to Quantum Chaos (2001)
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science,...
Ground Control to Niels Bohr: Exploring Outer Space with Atomic Physics (2001)
Mason A. Porter, Predrag Cvitanović, To The Sun, Predrag Cvitanović, Glen Robinson, Chair Nonlinear, ...
studying nonlinear dynamics. With a trajectory designed using techniques from the theory of dynamical systems, NASA launched the spacecraft Genesis towards the Sun to collect pieces of it (called...
A network analysis of committees in the U.S. House of Representatives
Porter, Mason A., Mucha, Peter J., Newman, M. E. J., Warmbrand, Casey M.
Network theory provides a powerful tool for the representation and analysis of complex systems of interacting agents. Here, we investigate the U.S. House of Representatives network of committees and...
A network analysis of committees in the U.S. House of Representatives
Porter, Mason A., Mucha, Peter J., Newman, M. E. J., Warmbrand, Casey M.
Network theory provides a powerful tool for the representation and analysis of complex systems of interacting agents. Here, we investigate the U.S. House of Representatives network of committees and...
Dynamical Clustering of Exchange Rates
Daniel J. Fenn, Mason A. Porter, Peter J. Mucha, Mark McDonald, Stacy Williams, Neil F. Johnson, ...
We use techniques from network science to study correlations in the foreign exchange (FX) market over the period 1991--2008. We consider an FX market network in which each node represents an exchange...
Daniel J. Fenn, Mason A. Porter, Mark McDonald, Stacy Williams, Neil F. Johnson, Nick S. Jones
We study the cluster dynamics of multichannel (multivariate) time series by representing their correlations as time-dependent networks and investigating the evolution of network communities. We...