Mason Porter | University of Oxford (original) (raw)

Papers by Mason Porter

Research paper thumbnail of Influence of network topology on sound propagation in granular materials

During the past 15 years, techniques from areas of physics such as statistical mechanics and nonl... more During the past 15 years, techniques from areas of physics such as statistical mechanics and nonlinear dynamics have been used to make important advances in studying networks across myriad disciplines [1].

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Two-Particle Circular Billiards Versus Randomly Perturbed One-Particle Circular Billiards

Abstract: We study a two-particle circular billiard containing two finite-size circular particles... more Abstract: We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an" intermittent" system. This billiard system behaves chaotically, but the time scale on which chaos manifests can become arbitrarily long as the sizes of the confined particles become smaller.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Dynamic Network Centrality Summarizes Learning in the Human Brain

Abstract: We study functional activity in the human brain using functional Magnetic Resonance Ima... more Abstract: We study functional activity in the human brain using functional Magnetic Resonance Imaging and recently developed tools from network science. The data arise from the performance of a simple behavioural motor learning task. Unsupervised clustering of subjects with respect to similarity of network activity measured over three days of practice produces significant evidence oflearning', in the sense that subjects typically move between clusters (of subjects whose dynamics are similar) as time progresses.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Small-World Network

A small-world network refers to an ensemble of networks in which the mean geodesic (ie, shortest-... more A small-world network refers to an ensemble of networks in which the mean geodesic (ie, shortest-path) distance between nodes increases sufficiently slowly as a function of the number of nodes in the network. The term is often applied to a single network in such a family, and the term" small-world network" is also used frequently to refer specifically to a Watts-Strogatz toy network.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The Unreasonable Effectiveness of Tree-Based Theory for Bond Percolation on Networks with Clustering

Abstract. We demonstrate that a tree-based theory for bond percolation yields extremely accurate ... more Abstract. We demonstrate that a tree-based theory for bond percolation yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance ℓ is sufficiently small—ie, as long as it is close to the value of ℓ in a random network with negligible clustering and the same degree-degree correlations. We confirm this hypothesis numerically using real-world networks from various domains and on several classes of synthetic clustered networks.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Supporting Information: What Evidence is There for the Homology of Protein-Protein Interactions?

We are considering the transfer of interactions between interacting proteins A and B in a source ... more We are considering the transfer of interactions between interacting proteins A and B in a source species to proteins A′ and B′ in a target species, where A and A′ are homologs and B and B′ are homologs. For any given inferred interaction in the target species, there can be multiple possible interactions in the source species from which it could have been inferred.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Structure to Characteristicsin OnlineCollegiateSocialNetworks

Abstract. We study the structure of social networks of students by examining the graphs of Facebo... more Abstract. We study the structure of social networks of students by examining the graphs of Facebook “friendships” at five US universities at a single point in time. We investigate the community structure of each single-institution network and employ visual and quantitative tools, including standardized pair-counting methods, to measure the correlations between the network communities and a set of self-identified user characteristics (residence, class year, major, and high school).

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Can Baseball Be Used to Teach Statistics?

" Statistics are the lifeblood of baseball. In no other sport are so many available and studied s... more " Statistics are the lifeblood of baseball. In no other sport are so many available and studied so assiduously by participants and fans. Much of the game's appeal, as a conversation piece, lies in the opportunity the fan gets to back up opinions and arguments with convincing figures, and it is entirely possible that more American boys have mastered long division by dealing with batting averages than in any other way."

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Limit order books

Abstract: As the pricing mechanism in more than half the world's financial markets, limit order b... more Abstract: As the pricing mechanism in more than half the world's financial markets, limit order books have featured extensively in the published literature from a wide range of disciplines over the past decade. This survey highlights the similarities and differences between key empirical and theoretical publications that have advanced understanding of limit order books to date.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Generalized master equations for non-Poisson dynamics on networks

Abstract: The traditional way of studying temporal networks is to aggregate the dynamics of the e... more Abstract: The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Consequently, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Synchronized lying in cattle in relation to time of day

Postural synchrony, in which cattle lie down or stand up at the same time as other members of the... more Postural synchrony, in which cattle lie down or stand up at the same time as other members of their herd, occurs both in animals housed indoors when enough resources are available and in those out at pasture, but the mechanisms by which such synchrony is achieved are poorly understood. We report a study of 6 groups of young cattle (Bos taurus) at pasture in which our aim was to study postural synchrony at different times of day and in relation to the postures of neighbouring cattle.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The radially vibrating spherical quantum billiard

Abstract: We consider the radially vibrating spherical quantum billiard as a representative examp... more Abstract: 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 states. These conditions are symmetry relations corresponding to the relative quantum numbers of eigenstates considered pairwise. In this discussion, we give special attention to eigenstates with null angular momentum (for which the aforementioned condition is automatically satisfied).

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fermi, Pasta, Ulam y el nacimiento de la matemática experimental

Hace cuatro años, en 2005, científicos de todo el mundo conmemoraron el centenario del annus mira... more Hace cuatro años, en 2005, científicos de todo el mundo conmemoraron el centenario del annus mirabilis de Einstein (1905), el año en que publicó trabajos asombrosos sobre el efecto fotoeléctrico, el movimiento browniano y la relatividad especial, golpes de genio que remodelaron la faz de la física. Curiosamente, el año 2005 correspondía también a otro importante aniversario en la física que ha pasado inadvertido para el público.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Core-Periphery Organisation of Human Brain Dynamics

Abstract: As a person learns a new skill, distinct synapses, brain regions, and networks are enga... more Abstract: As a person learns a new skill, distinct synapses, brain regions, and networks are engaged and change over time. To better understand the dynamic processes that integrate information across a set of regions to enable the emergence of novel behaviour, we measure brain activity during motor sequencing and characterise network properties based on coherent activity between brain regions.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Dynamics on Modular Networks with Heterogeneous Correlations

Abstract: We develop a new ensemble of modular random graphs in which degree-degree correlations ... more Abstract: We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The Hopf Fibration and its Applications

Among the most important topological constructions are Hopf brations. That they both play an impo... more Among the most important topological constructions are Hopf brations. That they both play an important role in topology itself and have numerous physical applications lends credence to this statement. In this paper, I will discuss some of these applications as motivation for mathematicians to learn about the physical signi cance of the Hopf bration in greater detail than that presented here. I will focus my attention primarily on rigid body rotation and the Hopf bration h: S3! S2.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of What Evidence Is There for the Homology of Protein-Protein Interactions?

The notion that sequence homology implies functional similarity underlies much of computational b... more The notion that sequence homology implies functional similarity underlies much of computational biology. In the case of protein-protein interactions, an interaction can be inferred between two proteins on the basis that sequence-similar proteins have been observed to interact. The use of transferred interactions is common, but the legitimacy of such inferred interactions is not clear. Here we investigate transferred interactions and whether data incompleteness explains the lack of evidence found for them.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of An Introduction to Quantum Chaos

Abstract: Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific t... more Abstract: 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, whereas the latter has revolutionized physics. Both chaos theory and quantum mechanics have achieved a fairly large level of glamour in the eyes of the general public. The study of quantum chaos encompasses the application of dynamical systems theory in the quantum regime.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A Hitchhiker’s Guide to LaTex (or how I learned to stop worrying and love writing my dissertation)

LaTex (which is pronounced LAY-TECK) is commonly used by scientists to write their research artic... more LaTex (which is pronounced LAY-TECK) is commonly used by scientists to write their research articles, as it is the easiest for them to include mathematical symbols, figures, tables, etc. in their work in a platform-independent manner. Increasingly many scientific journals require that submitted articles be typeset in LaTex. The purpose of this article is to provide a minimalist introduction to LaTex.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fractional-period excitations in continuum periodic systems

In the past few years, there has been considerable interest in both genuinely discrete and contin... more In the past few years, there has been considerable interest in both genuinely discrete and continuum but periodic systems 1. These arise in diverse physical contexts 2, including coupled waveguide arrays and photorefractive crystals in nonlinear optics 3, Bose-Einstein condensates BECs in optical lattices OLs in atomic physics 4, and DNA double-strand dynamics in biophysics 5. One of the most interesting themes that emerges in this context is the concept of “effective discreteness” induced by continuum periodic dynamics.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Influence of network topology on sound propagation in granular materials

During the past 15 years, techniques from areas of physics such as statistical mechanics and nonl... more During the past 15 years, techniques from areas of physics such as statistical mechanics and nonlinear dynamics have been used to make important advances in studying networks across myriad disciplines [1].

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Two-Particle Circular Billiards Versus Randomly Perturbed One-Particle Circular Billiards

Abstract: We study a two-particle circular billiard containing two finite-size circular particles... more Abstract: We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an" intermittent" system. This billiard system behaves chaotically, but the time scale on which chaos manifests can become arbitrarily long as the sizes of the confined particles become smaller.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Dynamic Network Centrality Summarizes Learning in the Human Brain

Abstract: We study functional activity in the human brain using functional Magnetic Resonance Ima... more Abstract: We study functional activity in the human brain using functional Magnetic Resonance Imaging and recently developed tools from network science. The data arise from the performance of a simple behavioural motor learning task. Unsupervised clustering of subjects with respect to similarity of network activity measured over three days of practice produces significant evidence oflearning', in the sense that subjects typically move between clusters (of subjects whose dynamics are similar) as time progresses.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Small-World Network

A small-world network refers to an ensemble of networks in which the mean geodesic (ie, shortest-... more A small-world network refers to an ensemble of networks in which the mean geodesic (ie, shortest-path) distance between nodes increases sufficiently slowly as a function of the number of nodes in the network. The term is often applied to a single network in such a family, and the term" small-world network" is also used frequently to refer specifically to a Watts-Strogatz toy network.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The Unreasonable Effectiveness of Tree-Based Theory for Bond Percolation on Networks with Clustering

Abstract. We demonstrate that a tree-based theory for bond percolation yields extremely accurate ... more Abstract. We demonstrate that a tree-based theory for bond percolation yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance ℓ is sufficiently small—ie, as long as it is close to the value of ℓ in a random network with negligible clustering and the same degree-degree correlations. We confirm this hypothesis numerically using real-world networks from various domains and on several classes of synthetic clustered networks.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Supporting Information: What Evidence is There for the Homology of Protein-Protein Interactions?

We are considering the transfer of interactions between interacting proteins A and B in a source ... more We are considering the transfer of interactions between interacting proteins A and B in a source species to proteins A′ and B′ in a target species, where A and A′ are homologs and B and B′ are homologs. For any given inferred interaction in the target species, there can be multiple possible interactions in the source species from which it could have been inferred.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Structure to Characteristicsin OnlineCollegiateSocialNetworks

Abstract. We study the structure of social networks of students by examining the graphs of Facebo... more Abstract. We study the structure of social networks of students by examining the graphs of Facebook “friendships” at five US universities at a single point in time. We investigate the community structure of each single-institution network and employ visual and quantitative tools, including standardized pair-counting methods, to measure the correlations between the network communities and a set of self-identified user characteristics (residence, class year, major, and high school).

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Can Baseball Be Used to Teach Statistics?

" Statistics are the lifeblood of baseball. In no other sport are so many available and studied s... more " Statistics are the lifeblood of baseball. In no other sport are so many available and studied so assiduously by participants and fans. Much of the game's appeal, as a conversation piece, lies in the opportunity the fan gets to back up opinions and arguments with convincing figures, and it is entirely possible that more American boys have mastered long division by dealing with batting averages than in any other way."

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Limit order books

Abstract: As the pricing mechanism in more than half the world's financial markets, limit order b... more Abstract: As the pricing mechanism in more than half the world's financial markets, limit order books have featured extensively in the published literature from a wide range of disciplines over the past decade. This survey highlights the similarities and differences between key empirical and theoretical publications that have advanced understanding of limit order books to date.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Generalized master equations for non-Poisson dynamics on networks

Abstract: The traditional way of studying temporal networks is to aggregate the dynamics of the e... more Abstract: The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Consequently, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Synchronized lying in cattle in relation to time of day

Postural synchrony, in which cattle lie down or stand up at the same time as other members of the... more Postural synchrony, in which cattle lie down or stand up at the same time as other members of their herd, occurs both in animals housed indoors when enough resources are available and in those out at pasture, but the mechanisms by which such synchrony is achieved are poorly understood. We report a study of 6 groups of young cattle (Bos taurus) at pasture in which our aim was to study postural synchrony at different times of day and in relation to the postures of neighbouring cattle.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The radially vibrating spherical quantum billiard

Abstract: We consider the radially vibrating spherical quantum billiard as a representative examp... more Abstract: 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 states. These conditions are symmetry relations corresponding to the relative quantum numbers of eigenstates considered pairwise. In this discussion, we give special attention to eigenstates with null angular momentum (for which the aforementioned condition is automatically satisfied).

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fermi, Pasta, Ulam y el nacimiento de la matemática experimental

Hace cuatro años, en 2005, científicos de todo el mundo conmemoraron el centenario del annus mira... more Hace cuatro años, en 2005, científicos de todo el mundo conmemoraron el centenario del annus mirabilis de Einstein (1905), el año en que publicó trabajos asombrosos sobre el efecto fotoeléctrico, el movimiento browniano y la relatividad especial, golpes de genio que remodelaron la faz de la física. Curiosamente, el año 2005 correspondía también a otro importante aniversario en la física que ha pasado inadvertido para el público.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Core-Periphery Organisation of Human Brain Dynamics

Abstract: As a person learns a new skill, distinct synapses, brain regions, and networks are enga... more Abstract: As a person learns a new skill, distinct synapses, brain regions, and networks are engaged and change over time. To better understand the dynamic processes that integrate information across a set of regions to enable the emergence of novel behaviour, we measure brain activity during motor sequencing and characterise network properties based on coherent activity between brain regions.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Dynamics on Modular Networks with Heterogeneous Correlations

Abstract: We develop a new ensemble of modular random graphs in which degree-degree correlations ... more Abstract: We develop a new ensemble of modular random graphs in which degree-degree correlations can be different in each module. We present an analytical approach that allows one to analyze several types of binary dynamics operating on such networks, and we illustrate our approach using bond percolation, site percolation, and the Watts threshold model.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The Hopf Fibration and its Applications

Among the most important topological constructions are Hopf brations. That they both play an impo... more Among the most important topological constructions are Hopf brations. That they both play an important role in topology itself and have numerous physical applications lends credence to this statement. In this paper, I will discuss some of these applications as motivation for mathematicians to learn about the physical signi cance of the Hopf bration in greater detail than that presented here. I will focus my attention primarily on rigid body rotation and the Hopf bration h: S3! S2.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of What Evidence Is There for the Homology of Protein-Protein Interactions?

The notion that sequence homology implies functional similarity underlies much of computational b... more The notion that sequence homology implies functional similarity underlies much of computational biology. In the case of protein-protein interactions, an interaction can be inferred between two proteins on the basis that sequence-similar proteins have been observed to interact. The use of transferred interactions is common, but the legitimacy of such inferred interactions is not clear. Here we investigate transferred interactions and whether data incompleteness explains the lack of evidence found for them.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of An Introduction to Quantum Chaos

Abstract: Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific t... more Abstract: 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, whereas the latter has revolutionized physics. Both chaos theory and quantum mechanics have achieved a fairly large level of glamour in the eyes of the general public. The study of quantum chaos encompasses the application of dynamical systems theory in the quantum regime.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of A Hitchhiker’s Guide to LaTex (or how I learned to stop worrying and love writing my dissertation)

LaTex (which is pronounced LAY-TECK) is commonly used by scientists to write their research artic... more LaTex (which is pronounced LAY-TECK) is commonly used by scientists to write their research articles, as it is the easiest for them to include mathematical symbols, figures, tables, etc. in their work in a platform-independent manner. Increasingly many scientific journals require that submitted articles be typeset in LaTex. The purpose of this article is to provide a minimalist introduction to LaTex.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fractional-period excitations in continuum periodic systems

In the past few years, there has been considerable interest in both genuinely discrete and contin... more In the past few years, there has been considerable interest in both genuinely discrete and continuum but periodic systems 1. These arise in diverse physical contexts 2, including coupled waveguide arrays and photorefractive crystals in nonlinear optics 3, Bose-Einstein condensates BECs in optical lattices OLs in atomic physics 4, and DNA double-strand dynamics in biophysics 5. One of the most interesting themes that emerges in this context is the concept of “effective discreteness” induced by continuum periodic dynamics.

Bookmarks Related papers MentionsView impact