Jan Tobochnik | Kalamazoo College (original) (raw)

Papers by Jan Tobochnik

Research paper thumbnail of Efficient random walk algorithm for computing conductivity in continuum percolation systems

Computers in Physics, 1990

Random walks can be used to obtain the diffusion constant and thus the conductivity for continuum... more Random walks can be used to obtain the diffusion constant and thus the conductivity for continuum percolation problems. This paper presents an efficient algorithm that allows walkers to move very large distances in one step. The algorithm uses a first-passage time distribution for d-dimensional spherical surfaces. Results. are given for overlapping nonconducting disks in two dimensions. Depending on the density of disks, it is found that the present algorithm is about 5 to 50 times faster than an equivalent algorithm using fixed step lengths.

Research paper thumbnail of Statistical and Thermal Physics with Computer Applications

American Journal of Physics, 2011

This textbook carefully develops the main ideas and techniques of statistical and thermal physics... more This textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physics. Statistical and Thermal Physics begins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts on thermal physics, this book presents thermodynamic reasoning as an independent way of thinking about macroscopic systems. Probability concepts and techniques are introduced, including topics that are useful for understanding how probability and statistics are used. Magnetism and the Ising model are considered in greater depth than in most undergraduate texts, and ideal quantum gases are treated within a uniform framework. Advanced chapters on fluids and critical phenomena are appropriate for motivated undergraduates and beginning graduate students.Integrates Monte Carlo and molecular dynamics simulations as well as other numerical techniques throughout the text Provides self-contained introductions to thermodynamics and statistical mechanics Discusses probability concepts and methods in detail Contains ideas and methods from contemporary research Includes advanced chapters that provide a natural bridge to graduate study Features more than 400 problems Programs are open source and available in an executable cross-platform format Solutions manual (available only to teachers)

Research paper thumbnail of Law and the Science of Networks: An Overview and an Application to the 'Patent Explosion

SSRN Electronic Journal, 2000

Research paper thumbnail of Estimating the dynamics of kernel-based evolving networks

Unifying Themes in Complex Systems, 2008

In this paper we present the application of a novel methodology to scientific citation and collab... more In this paper we present the application of a novel methodology to scientific citation and collaboration networks. This methodology is designed for understanding the governing dynamics of evolving networks and relies on an attachment kernel, a scalar function of node properties, which stochastically drives the addition and deletion of vertices and edges. We illustrate how the kernel function of a given network can be extracted from the history of the network and discuss other possible applications.

Research paper thumbnail of Model framework for describing the dynamics of evolving networks

We present a model framework for describing the dynamics of evolving networks. In this framework ... more We present a model framework for describing the dynamics of evolving networks. In this framework the addition of edges is stochastically governed by some important intrinsic and structural properties of network vertices through an attractiveness function. We discuss the solution of the inverse problem: determining the attractiveness function from the network evolution data. We also present a number of example applications: the description of the US patent citation network using vertex degree, patent age and patent category variables, and we show how the time-dependent version of the method can be used to find and describe important changes in the internal dynamics. We also compare our results to scientific citation networks.

Research paper thumbnail of Network theory model of the United States Patent citation network

We report results of a network theory approach to the study of the United States patent system. W... more We report results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From data on more than two million patents and their citations, we extract an attractiveness function, A(k,l), which determines the likelihood that a patent will be cited. A(k,l) is approximately separable into a product of a function Ak(k) and a function Al(l), where k is the number of citations already received (in-degree) and l is the age measured in patent number units. Al(l) displays a peak at low l and a long power law tail, suggesting that some patented technologies have very long-term effects. Ak(k) exhibits super-linear preferential attachment. The preferential attachment exponent has been increasing since 1991, suggesting that patent citations are increasingly concentrated on a relatively small number of patents. The overall average probability that a new patent will be cited by a ...

Research paper thumbnail of The Inverse Problem of Evolving Networks — with Application to Social Nets

Bolyai Society Mathematical Studies, 2008

Many complex systems can be modeled by graphs [8]. The vertices of the graph represent objects of... more Many complex systems can be modeled by graphs [8]. The vertices of the graph represent objects of the system, and the edges of the graph the relationships between these objects. These relationships may be structural or functional, according to the modeler's needs [1, ...

Research paper thumbnail of Network Science and Law: A Sales Pitch and an Application to the "Patent Explosion

Research paper thumbnail of Patent Citation Networks

Patent applications contain citations which are similar to but different from those found in publ... more Patent applications contain citations which are similar to but different from those found in published scientific papers. In particular, patent citations are governed by legal rules. Moreover, a large fraction of citations are made not by the patent inventor, but by a patent examiner during the application procedure. Using a patent database, which contains the patent citations, assignees and inventors, we have applied network analysis and built network models. Our work includes determining the structure of the patent citation network and comparing it to existing results for scientific citation networks; identifying differences between various technological fields and comparing the observed differences to expectations based on anecdotal evidence about patenting practice; and developing models to explain the results.

Research paper thumbnail of Prediction of emerging technologies based on analysis of the US patent citation network

Scientometrics, 2012

The network of patents connected by citations is an evolving graph, which provides a representati... more The network of patents connected by citations is an evolving graph, which provides a representation of the innovation process. A patent citing another implies that the cited patent reflects a piece of previously existing knowledge that the citing patent builds upon. A methodology presented here (i) identifies actual clusters of patents: i.e. technological branches, and (ii) gives predictions about the temporal changes of the structure of the clusters. A predictor, called the citation vector, is defined for characterizing technological development to show how a patent cited by other patents belongs to various industrial fields. The clustering technique adopted is able to detect the new emerging recombinations, and predicts emerging new technology clusters. The predictive ability of our new method is illustrated on the example of USPTO subcategory 11, Agriculture, Food, Textiles.

Research paper thumbnail of Modeling innovation by a kinetic description of the patent citation system

Physica A: Statistical Mechanics and its Applications, 2007

This paper reports results of a network theory approach to the study of the United States patent ... more This paper reports results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From data on more than 2 million patents and their citations, we extract an attractiveness function, A(k, l), which determines the likelihood that a patent will be cited. A(k, l) is approximately separable into a product of a function A k (k) and a function A l (l), where k is the number of citations already received (in-degree) and l is the age measured in patent number units. A l (l) displays a peak at low l and a long power law tail, suggesting that some patented technologies have very long-term effects. A k (k) exhibits super-linear preferential attachment. The preferential attachment exponent has been increasing since 1991, suggesting that patent citations are increasingly concentrated on a relatively small number of patents. The overall average probability that a new patent will be cited by a given patent has increased slightly during the same period. We discuss some possible implications of our results for patent policy.

Research paper thumbnail of Patent Citation Networks Revisited: Signs of a Twenty-First Century Change?

This Article reports an empirical study of the network composed of patent “nodes” and citation “l... more This Article reports an empirical study of the network composed of patent “nodes” and citation “links” between them. It builds on an earlier study in which we argued that trends in the growth of the patent citation network provide evidence that the explosive growth in patenting in the late twentieth century was due at least in part to the issuance of increasingly trivial patents. We defined a measure of patent stratification based on comparative probability of citation; an increase in this measure suggests that the USPTO is issuing patents of comparatively less technological significance. Provocatively, we found that stratification increased in the 1990s during the “patent explosion.” Here we report a further study indicating that the trend toward increasing stratification leveled off beginning around 2000. This observation suggests that there was a de facto tightening of patentability standards well before the doctrinal shifts reflected in the Supreme Court’s flurry of patent activ...

Research paper thumbnail of Efficient random walk algorithm for computing conductivity in continuum percolation systems

Computers in Physics, 1990

Random walks can be used to obtain the diffusion constant and thus the conductivity for continuum... more Random walks can be used to obtain the diffusion constant and thus the conductivity for continuum percolation problems. This paper presents an efficient algorithm that allows walkers to move very large distances in one step. The algorithm uses a first-passage time distribution for d-dimensional spherical surfaces. Results. are given for overlapping nonconducting disks in two dimensions. Depending on the density of disks, it is found that the present algorithm is about 5 to 50 times faster than an equivalent algorithm using fixed step lengths.

Research paper thumbnail of Statistical and Thermal Physics with Computer Applications

American Journal of Physics, 2011

This textbook carefully develops the main ideas and techniques of statistical and thermal physics... more This textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physics. Statistical and Thermal Physics begins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts on thermal physics, this book presents thermodynamic reasoning as an independent way of thinking about macroscopic systems. Probability concepts and techniques are introduced, including topics that are useful for understanding how probability and statistics are used. Magnetism and the Ising model are considered in greater depth than in most undergraduate texts, and ideal quantum gases are treated within a uniform framework. Advanced chapters on fluids and critical phenomena are appropriate for motivated undergraduates and beginning graduate students.Integrates Monte Carlo and molecular dynamics simulations as well as other numerical techniques throughout the text Provides self-contained introductions to thermodynamics and statistical mechanics Discusses probability concepts and methods in detail Contains ideas and methods from contemporary research Includes advanced chapters that provide a natural bridge to graduate study Features more than 400 problems Programs are open source and available in an executable cross-platform format Solutions manual (available only to teachers)

Research paper thumbnail of Law and the Science of Networks: An Overview and an Application to the 'Patent Explosion

SSRN Electronic Journal, 2000

Research paper thumbnail of Estimating the dynamics of kernel-based evolving networks

Unifying Themes in Complex Systems, 2008

In this paper we present the application of a novel methodology to scientific citation and collab... more In this paper we present the application of a novel methodology to scientific citation and collaboration networks. This methodology is designed for understanding the governing dynamics of evolving networks and relies on an attachment kernel, a scalar function of node properties, which stochastically drives the addition and deletion of vertices and edges. We illustrate how the kernel function of a given network can be extracted from the history of the network and discuss other possible applications.

Research paper thumbnail of Model framework for describing the dynamics of evolving networks

We present a model framework for describing the dynamics of evolving networks. In this framework ... more We present a model framework for describing the dynamics of evolving networks. In this framework the addition of edges is stochastically governed by some important intrinsic and structural properties of network vertices through an attractiveness function. We discuss the solution of the inverse problem: determining the attractiveness function from the network evolution data. We also present a number of example applications: the description of the US patent citation network using vertex degree, patent age and patent category variables, and we show how the time-dependent version of the method can be used to find and describe important changes in the internal dynamics. We also compare our results to scientific citation networks.

Research paper thumbnail of Network theory model of the United States Patent citation network

We report results of a network theory approach to the study of the United States patent system. W... more We report results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From data on more than two million patents and their citations, we extract an attractiveness function, A(k,l), which determines the likelihood that a patent will be cited. A(k,l) is approximately separable into a product of a function Ak(k) and a function Al(l), where k is the number of citations already received (in-degree) and l is the age measured in patent number units. Al(l) displays a peak at low l and a long power law tail, suggesting that some patented technologies have very long-term effects. Ak(k) exhibits super-linear preferential attachment. The preferential attachment exponent has been increasing since 1991, suggesting that patent citations are increasingly concentrated on a relatively small number of patents. The overall average probability that a new patent will be cited by a ...

Research paper thumbnail of The Inverse Problem of Evolving Networks — with Application to Social Nets

Bolyai Society Mathematical Studies, 2008

Many complex systems can be modeled by graphs [8]. The vertices of the graph represent objects of... more Many complex systems can be modeled by graphs [8]. The vertices of the graph represent objects of the system, and the edges of the graph the relationships between these objects. These relationships may be structural or functional, according to the modeler's needs [1, ...

Research paper thumbnail of Network Science and Law: A Sales Pitch and an Application to the "Patent Explosion

Research paper thumbnail of Patent Citation Networks

Patent applications contain citations which are similar to but different from those found in publ... more Patent applications contain citations which are similar to but different from those found in published scientific papers. In particular, patent citations are governed by legal rules. Moreover, a large fraction of citations are made not by the patent inventor, but by a patent examiner during the application procedure. Using a patent database, which contains the patent citations, assignees and inventors, we have applied network analysis and built network models. Our work includes determining the structure of the patent citation network and comparing it to existing results for scientific citation networks; identifying differences between various technological fields and comparing the observed differences to expectations based on anecdotal evidence about patenting practice; and developing models to explain the results.

Research paper thumbnail of Prediction of emerging technologies based on analysis of the US patent citation network

Scientometrics, 2012

The network of patents connected by citations is an evolving graph, which provides a representati... more The network of patents connected by citations is an evolving graph, which provides a representation of the innovation process. A patent citing another implies that the cited patent reflects a piece of previously existing knowledge that the citing patent builds upon. A methodology presented here (i) identifies actual clusters of patents: i.e. technological branches, and (ii) gives predictions about the temporal changes of the structure of the clusters. A predictor, called the citation vector, is defined for characterizing technological development to show how a patent cited by other patents belongs to various industrial fields. The clustering technique adopted is able to detect the new emerging recombinations, and predicts emerging new technology clusters. The predictive ability of our new method is illustrated on the example of USPTO subcategory 11, Agriculture, Food, Textiles.

Research paper thumbnail of Modeling innovation by a kinetic description of the patent citation system

Physica A: Statistical Mechanics and its Applications, 2007

This paper reports results of a network theory approach to the study of the United States patent ... more This paper reports results of a network theory approach to the study of the United States patent system. We model the patent citation network as a discrete time, discrete space stochastic dynamic system. From data on more than 2 million patents and their citations, we extract an attractiveness function, A(k, l), which determines the likelihood that a patent will be cited. A(k, l) is approximately separable into a product of a function A k (k) and a function A l (l), where k is the number of citations already received (in-degree) and l is the age measured in patent number units. A l (l) displays a peak at low l and a long power law tail, suggesting that some patented technologies have very long-term effects. A k (k) exhibits super-linear preferential attachment. The preferential attachment exponent has been increasing since 1991, suggesting that patent citations are increasingly concentrated on a relatively small number of patents. The overall average probability that a new patent will be cited by a given patent has increased slightly during the same period. We discuss some possible implications of our results for patent policy.

Research paper thumbnail of Patent Citation Networks Revisited: Signs of a Twenty-First Century Change?

This Article reports an empirical study of the network composed of patent “nodes” and citation “l... more This Article reports an empirical study of the network composed of patent “nodes” and citation “links” between them. It builds on an earlier study in which we argued that trends in the growth of the patent citation network provide evidence that the explosive growth in patenting in the late twentieth century was due at least in part to the issuance of increasingly trivial patents. We defined a measure of patent stratification based on comparative probability of citation; an increase in this measure suggests that the USPTO is issuing patents of comparatively less technological significance. Provocatively, we found that stratification increased in the 1990s during the “patent explosion.” Here we report a further study indicating that the trend toward increasing stratification leveled off beginning around 2000. This observation suggests that there was a de facto tightening of patentability standards well before the doctrinal shifts reflected in the Supreme Court’s flurry of patent activ...