Sorin Solomon | The Hebrew University of Jerusalem (original) (raw)

Papers by Sorin Solomon

Physical Review Letters, 2003

The formation of vegetation patterns in the arid and the semi-arid climatic zones is studied. Thr... more The formation of vegetation patterns in the arid and the semi-arid climatic zones is studied. Threshold for the biomass of the perennial flora is shown to be a relevant factor, leading to a frozen disordered patterns in the arid zone. In this "glassy" state, vegetation appears as a singular plant spots separated by irregular distances, and an indirect repulsive interaction among shrubs is induced by the competition for water. At higher precipitation rates, the diminish of hydrological losses in the presence of flora becomes important and yields spatial attraction and clustering of biomass. Turing-like patterns with characteristic length scale may emerge from the disordered structure due to this positive feedback instability.

PLoS ONE, 2011

Language comprehension is a complex task that involves a wide network of brain regions. We used t... more Language comprehension is a complex task that involves a wide network of brain regions. We used topological measures to qualify and quantify the functional connectivity of the networks used under various comprehension conditions. To that aim we developed a technique to represent functional networks based on EEG recordings, taking advantage of their excellent time resolution in order to capture the fast processes that occur during language comprehension. Networks were created by searching for a specific causal relation between areas, the negative feedback loop, which is ubiquitous in many systems. This method is a simple way to construct directed graphs using event-related activity, which can then be analyzed topologically. Brain activity was recorded while subjects read expressions of various types and indicated whether they found them meaningful. Slightly different functional networks were obtained for event-related activity evoked by each expression type. The differences reflect the special contribution of specific regions in each condition and the balance of hemispheric activity involved in comprehending different types of expressions and are consistent with the literature in the field. Our results indicate that representing event-related brain activity as a network using a simple temporal relation, such as the negative feedback loop, to indicate directional connectivity is a viable option for investigation which also derives new information about aspects not reflected in the classical methods for investigating brain activity.

PLoS ONE, 2011

Language comprehension is a complex task that involves a wide network of brain regions. We used t... more Language comprehension is a complex task that involves a wide network of brain regions. We used topological measures to qualify and quantify the functional connectivity of the networks used under various comprehension conditions. To that aim we developed a technique to represent functional networks based on EEG recordings, taking advantage of their excellent time resolution in order to capture the fast processes that occur during language comprehension. Networks were created by searching for a specific causal relation between areas, the negative feedback loop, which is ubiquitous in many systems. This method is a simple way to construct directed graphs using event-related activity, which can then be analyzed topologically. Brain activity was recorded while subjects read expressions of various types and indicated whether they found them meaningful. Slightly different functional networks were obtained for event-related activity evoked by each expression type. The differences reflect the special contribution of specific regions in each condition and the balance of hemispheric activity involved in comprehending different types of expressions and are consistent with the literature in the field. Our results indicate that representing event-related brain activity as a network using a simple temporal relation, such as the negative feedback loop, to indicate directional connectivity is a viable option for investigation which also derives new information about aspects not reflected in the classical methods for investigating brain activity.

Physica A: Statistical Mechanics and its Applications, 2000

We here relate the occurrence of extreme market shares, close to either 0 or 100%, in the media i... more We here relate the occurrence of extreme market shares, close to either 0 or 100%, in the media industry to a percolation phenomenon across the social network of customers. We further discuss the possibility of observing self-organized criticality when customers and cinema producers adjust their preferences and the quality of the produced ÿlms according to previous experience. Comprehensive computer simulations on square lattices do indeed exhibit self-organized criticality towards the usual percolation threshold and related scaling behaviour.

Risk and Decision Analysis

The stochastic spatially extended generalized Lokta-Volterra approach introduced in Solomon [48],... more The stochastic spatially extended generalized Lokta-Volterra approach introduced in Solomon [48], Challet et al. [18], Yaari et al. [58], is extended to the study of interactions between economic sectors, countries and blocks. The theory predicts robustly in a very wide range of conditions systematic regularities in the growth rates evolution of various subsystems. The J-curve phenomenon which was studied in Challet et al. [18] is revisited and more empirical support is given to the theory. In particular to the connection between the economic minimum and the crossover of the new emergent leading sector with the old decaying one. We describe the 'Growth Alignment Effect' (GAE), it's theoretical basis and demonstrate it empirically for numerous cases in the international and intra-national economies. The GAE is the concept that in steady state the growth rates of the GDP per capita of the various system components align. We differentiate the GAE predictions from the usual convergence or divergence conceptual framework. Further investigations of GAE and subsidiaries are suggested and possible uses are proposed. Due to it's simple and robust nature, the method can be used as a tool for economic decisions and policy making.

Physical Review E

To quantify the mechanism of a complex network growth we focus on the network of citations of sci... more To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on copying/redirection/triadic closure mechanism. In a complementary and coherent way, the model accounts both for statistics of references of scientific papers and for their citation dynamics. Originating in empirical measurements, the model is cast in such a way that it can be verified quantitatively in every aspect. Such verification is performed by measuring citation dynamics of Physics papers. The measurements revealed nonlinear citation dynamics, the nonlinearity being intricately related to network topology. The nonlinearity has far-reaching consequences including non-stationary citation distributions, diverging citation trajectory of similar papers, runaways or "immortal papers" with infinite citation lifetime etc. Thus, our most important finding is nonlinearity in complex network growth. In a more specific context, our results can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.

International Journal of Modern Physics C

The convergence rates for inverting the Dirac matrix in the SU(2) gauge theory on a square two-di... more The convergence rates for inverting the Dirac matrix in the SU(2) gauge theory on a square two-dimensional lattice are compared for different lattice sizes in the physical region. The Parallel-Transported Multigrid algorithm (PTMG) turns out to be superior to the Conjugate-Gradient (CG) approach. As the lattice size L increases (together with the correlation length ξ) the PTMG becomes more and more efficient. On a 256×256 lattice with the bare quark mass mbare=0.0005 and ξ=20, the PTMG is at least ten times faster than the CG. It seems reasonable to expect similar results in four dimensions.

Ijmpa, 1990

The concept of interpolation relates lattice configurations to continuum configurations. This rel... more The concept of interpolation relates lattice configurations to continuum configurations. This relation induces from the continuum to the lattice the definitions of “continuous deformation”, topological classification and homotopy classes. The lattice homotopy classes obtained this way are separated by boundaries made out of “exceptional configurations” (EC). The EC boundaries allow the topological classification of the lattice configurations even in models in which it is impossible (or cumbersome) to give in a close form, a definition of the topological charge in terms of lattice variables. We give the description of the EC boundaries for the 2 dimensional XY spin model and the 4 dimensional SU(2) gauge model.

Physics Letters B, 1989

We obtain higher spin linearized field theories through the BRST second quantization of the class... more We obtain higher spin linearized field theories through the BRST second quantization of the classical D=4 massless point particle. By applying the same procedure to the classical supersymmetric particles, one obtains linearized N-extended off-shell unconstrained superfield actions. By extending the procedure to D= 10, one is led to a new spacetime geometry which reduces in some limit to the usual D= 10 Minkowski geometry.

In our innovation-driven world we tend to lay concepts that have lost their attractiveness to res... more In our innovation-driven world we tend to lay concepts that have lost their attractiveness to rest and rush to embrace the next giant leap. However, in most fields of creation, patterns of reawakening of old, extinct innovations can be found. It often looks as if new technological and social concepts have a life of their own, survival instincts and adaptive properties: They simply refuse to die. Should these phenomena be resolved on an ad hoc basis or are they grounded in the foundation of social behavior or evolutionary processes of technology? In conditions in which continuum equations would predict the extinction of a population, the presently offered microscopic representation proves that individuals self-organize in spatiotemporally localized adaptive patches that ensure their survival, resilience, and development as a collective. A similar treatment can explain why so many innovations are inevitably reborn. Accordingly, in assessing the value of social ideas, trends and even wants we ought to consider longer time frames following the decline of innovations, otherwise we might prematurely and erroneously discard successful promising concepts.

Technological Forecasting and Social Change, May 1, 1999

A systematic framework for the enhancement of inventiveness is introduced. According to the propo... more A systematic framework for the enhancement of inventiveness is introduced. According to the proposed approach, the starting point is an existing system rather than external pressures. By a sequence of formal operations (defined as templates) on the initial structure of a system, an innovative structure involving a new system is obtained. The sequence of operations is prescribed by well-defined procedures. The replacement template is illustrated in this work by two field cases and its potential value is tested empirically. Given the abundance of innovations in which the templates are manifested, the replacement template can be considered an exemplar for utilizing intrinsic information about a system in the development of innovations.

Eprint Arxiv 0802 3541, 2008

In this paper, we show how simple logistic growth that was studied intensively during the last 20... more In this paper, we show how simple logistic growth that was studied intensively during the last 200 years in many domains of science could be extended in a rather simple way and with these extensions is capable to produce a collection of behaviors widely observed in an enormous number of real-life systems in Economics, Sociology, Biology, Ecology and more.

We study the emergence of the collective spatio-temporal macroscopic properties of the immune sys... more We study the emergence of the collective spatio-temporal macroscopic properties of the immune system, by representing individually the elementary interactions between its microscopic components (antibodies, antigens, cytokines). The results of this detailed explicit analysis are compared with the traditional procedure of averaging over individuals and representing the collective dynamics in terms of densities that obey partial differential equations (PDE). The simulations show even for very simple elementary reactions the spontaneous emergence of localized complex structures. In turn the effective dynamics of these structures affects the average behavior of the system in a very decisive way: systems which would according to the differential equations approximation die, display in reality a very lively behavior. Our conclusions are supported both by explicit microscopic simulations and by analytic calculations. As the optimal method we propose a mixture of microscopic simulation (MS) systems describing each reaction separately, and average methods describing the average behavior of the agents.

ABSTRACT With this paper, we suggest a general simulation framework to analyze the impact on the ... more ABSTRACT With this paper, we suggest a general simulation framework to analyze the impact on the sales of a newly introduced product of (a) advertising; and (b) of (positive or negative) word-of-mouth in a market where numerous agents are interconnected through a socioeconomic network and provide their neighbors with subjective information about the quality of the product. The information transmitted by an agent is based on (i) advertising messages from the firm distributing the product, and/or (ii) on messages received from the ...

Eprint Arxiv 0801 0121, Dec 30, 2007

This article introduces into the whole section on Social Sciences, edited by A. Nowak for this En... more This article introduces into the whole section on Social Sciences, edited by A. Nowak for this Encyclopedia, concentrating on the applications of mathematics and physics. Here under "mathematics" we include also all computer simulations if they are not taken from physics, while physics applications include simulations of models which basically existed already in physics before they were applied to social simulations. Thus obviously there is no sharp border between applications from physics and from mathematics in the sense of our definition. Also social science is not defined precisely. We will include some economics as well as some linguistics, but not social insects or fish swarms, nor human epidemics or demography. Also, we mention not only this section by also the section on agent-based modelling edited by F. Castiglione as containing articles of social interest.

Microscopic Simulation (MS) uses a computer to represent and keep track of individual (&a... more Microscopic Simulation (MS) uses a computer to represent and keep track of individual (" microscopic") elements in order to investigate complex systems which are analytically intractable. A methodology that was developed to solve physics problems, MS has been used to study the relation between microscopic behavior and macroscopic phenomena in systems ranging from those of atomic particles, to cars, animals, and even humans. In finance, MS can help explain, among other things, the effects of various elements of ...

Physical Review Letters, 2003

The formation of vegetation patterns in the arid and the semi-arid climatic zones is studied. Thr... more The formation of vegetation patterns in the arid and the semi-arid climatic zones is studied. Threshold for the biomass of the perennial flora is shown to be a relevant factor, leading to a frozen disordered patterns in the arid zone. In this "glassy" state, vegetation appears as a singular plant spots separated by irregular distances, and an indirect repulsive interaction among shrubs is induced by the competition for water. At higher precipitation rates, the diminish of hydrological losses in the presence of flora becomes important and yields spatial attraction and clustering of biomass. Turing-like patterns with characteristic length scale may emerge from the disordered structure due to this positive feedback instability.

PLoS ONE, 2011

Language comprehension is a complex task that involves a wide network of brain regions. We used t... more Language comprehension is a complex task that involves a wide network of brain regions. We used topological measures to qualify and quantify the functional connectivity of the networks used under various comprehension conditions. To that aim we developed a technique to represent functional networks based on EEG recordings, taking advantage of their excellent time resolution in order to capture the fast processes that occur during language comprehension. Networks were created by searching for a specific causal relation between areas, the negative feedback loop, which is ubiquitous in many systems. This method is a simple way to construct directed graphs using event-related activity, which can then be analyzed topologically. Brain activity was recorded while subjects read expressions of various types and indicated whether they found them meaningful. Slightly different functional networks were obtained for event-related activity evoked by each expression type. The differences reflect the special contribution of specific regions in each condition and the balance of hemispheric activity involved in comprehending different types of expressions and are consistent with the literature in the field. Our results indicate that representing event-related brain activity as a network using a simple temporal relation, such as the negative feedback loop, to indicate directional connectivity is a viable option for investigation which also derives new information about aspects not reflected in the classical methods for investigating brain activity.

PLoS ONE, 2011

Language comprehension is a complex task that involves a wide network of brain regions. We used t... more Language comprehension is a complex task that involves a wide network of brain regions. We used topological measures to qualify and quantify the functional connectivity of the networks used under various comprehension conditions. To that aim we developed a technique to represent functional networks based on EEG recordings, taking advantage of their excellent time resolution in order to capture the fast processes that occur during language comprehension. Networks were created by searching for a specific causal relation between areas, the negative feedback loop, which is ubiquitous in many systems. This method is a simple way to construct directed graphs using event-related activity, which can then be analyzed topologically. Brain activity was recorded while subjects read expressions of various types and indicated whether they found them meaningful. Slightly different functional networks were obtained for event-related activity evoked by each expression type. The differences reflect the special contribution of specific regions in each condition and the balance of hemispheric activity involved in comprehending different types of expressions and are consistent with the literature in the field. Our results indicate that representing event-related brain activity as a network using a simple temporal relation, such as the negative feedback loop, to indicate directional connectivity is a viable option for investigation which also derives new information about aspects not reflected in the classical methods for investigating brain activity.

Physica A: Statistical Mechanics and its Applications, 2000

We here relate the occurrence of extreme market shares, close to either 0 or 100%, in the media i... more We here relate the occurrence of extreme market shares, close to either 0 or 100%, in the media industry to a percolation phenomenon across the social network of customers. We further discuss the possibility of observing self-organized criticality when customers and cinema producers adjust their preferences and the quality of the produced ÿlms according to previous experience. Comprehensive computer simulations on square lattices do indeed exhibit self-organized criticality towards the usual percolation threshold and related scaling behaviour.

Risk and Decision Analysis

The stochastic spatially extended generalized Lokta-Volterra approach introduced in Solomon [48],... more The stochastic spatially extended generalized Lokta-Volterra approach introduced in Solomon [48], Challet et al. [18], Yaari et al. [58], is extended to the study of interactions between economic sectors, countries and blocks. The theory predicts robustly in a very wide range of conditions systematic regularities in the growth rates evolution of various subsystems. The J-curve phenomenon which was studied in Challet et al. [18] is revisited and more empirical support is given to the theory. In particular to the connection between the economic minimum and the crossover of the new emergent leading sector with the old decaying one. We describe the 'Growth Alignment Effect' (GAE), it's theoretical basis and demonstrate it empirically for numerous cases in the international and intra-national economies. The GAE is the concept that in steady state the growth rates of the GDP per capita of the various system components align. We differentiate the GAE predictions from the usual convergence or divergence conceptual framework. Further investigations of GAE and subsidiaries are suggested and possible uses are proposed. Due to it's simple and robust nature, the method can be used as a tool for economic decisions and policy making.

Physical Review E

To quantify the mechanism of a complex network growth we focus on the network of citations of sci... more To quantify the mechanism of a complex network growth we focus on the network of citations of scientific papers and use a combination of the theoretical and experimental tools to uncover microscopic details of this network growth. Namely, we develop a stochastic model of citation dynamics based on copying/redirection/triadic closure mechanism. In a complementary and coherent way, the model accounts both for statistics of references of scientific papers and for their citation dynamics. Originating in empirical measurements, the model is cast in such a way that it can be verified quantitatively in every aspect. Such verification is performed by measuring citation dynamics of Physics papers. The measurements revealed nonlinear citation dynamics, the nonlinearity being intricately related to network topology. The nonlinearity has far-reaching consequences including non-stationary citation distributions, diverging citation trajectory of similar papers, runaways or "immortal papers" with infinite citation lifetime etc. Thus, our most important finding is nonlinearity in complex network growth. In a more specific context, our results can be a basis for quantitative probabilistic prediction of citation dynamics of individual papers and of the journal impact factor.

International Journal of Modern Physics C

The convergence rates for inverting the Dirac matrix in the SU(2) gauge theory on a square two-di... more The convergence rates for inverting the Dirac matrix in the SU(2) gauge theory on a square two-dimensional lattice are compared for different lattice sizes in the physical region. The Parallel-Transported Multigrid algorithm (PTMG) turns out to be superior to the Conjugate-Gradient (CG) approach. As the lattice size L increases (together with the correlation length ξ) the PTMG becomes more and more efficient. On a 256×256 lattice with the bare quark mass mbare=0.0005 and ξ=20, the PTMG is at least ten times faster than the CG. It seems reasonable to expect similar results in four dimensions.

Ijmpa, 1990

The concept of interpolation relates lattice configurations to continuum configurations. This rel... more The concept of interpolation relates lattice configurations to continuum configurations. This relation induces from the continuum to the lattice the definitions of “continuous deformation”, topological classification and homotopy classes. The lattice homotopy classes obtained this way are separated by boundaries made out of “exceptional configurations” (EC). The EC boundaries allow the topological classification of the lattice configurations even in models in which it is impossible (or cumbersome) to give in a close form, a definition of the topological charge in terms of lattice variables. We give the description of the EC boundaries for the 2 dimensional XY spin model and the 4 dimensional SU(2) gauge model.

Physics Letters B, 1989

We obtain higher spin linearized field theories through the BRST second quantization of the class... more We obtain higher spin linearized field theories through the BRST second quantization of the classical D=4 massless point particle. By applying the same procedure to the classical supersymmetric particles, one obtains linearized N-extended off-shell unconstrained superfield actions. By extending the procedure to D= 10, one is led to a new spacetime geometry which reduces in some limit to the usual D= 10 Minkowski geometry.

In our innovation-driven world we tend to lay concepts that have lost their attractiveness to res... more In our innovation-driven world we tend to lay concepts that have lost their attractiveness to rest and rush to embrace the next giant leap. However, in most fields of creation, patterns of reawakening of old, extinct innovations can be found. It often looks as if new technological and social concepts have a life of their own, survival instincts and adaptive properties: They simply refuse to die. Should these phenomena be resolved on an ad hoc basis or are they grounded in the foundation of social behavior or evolutionary processes of technology? In conditions in which continuum equations would predict the extinction of a population, the presently offered microscopic representation proves that individuals self-organize in spatiotemporally localized adaptive patches that ensure their survival, resilience, and development as a collective. A similar treatment can explain why so many innovations are inevitably reborn. Accordingly, in assessing the value of social ideas, trends and even wants we ought to consider longer time frames following the decline of innovations, otherwise we might prematurely and erroneously discard successful promising concepts.

Technological Forecasting and Social Change, May 1, 1999

A systematic framework for the enhancement of inventiveness is introduced. According to the propo... more A systematic framework for the enhancement of inventiveness is introduced. According to the proposed approach, the starting point is an existing system rather than external pressures. By a sequence of formal operations (defined as templates) on the initial structure of a system, an innovative structure involving a new system is obtained. The sequence of operations is prescribed by well-defined procedures. The replacement template is illustrated in this work by two field cases and its potential value is tested empirically. Given the abundance of innovations in which the templates are manifested, the replacement template can be considered an exemplar for utilizing intrinsic information about a system in the development of innovations.

Eprint Arxiv 0802 3541, 2008

In this paper, we show how simple logistic growth that was studied intensively during the last 20... more In this paper, we show how simple logistic growth that was studied intensively during the last 200 years in many domains of science could be extended in a rather simple way and with these extensions is capable to produce a collection of behaviors widely observed in an enormous number of real-life systems in Economics, Sociology, Biology, Ecology and more.

We study the emergence of the collective spatio-temporal macroscopic properties of the immune sys... more We study the emergence of the collective spatio-temporal macroscopic properties of the immune system, by representing individually the elementary interactions between its microscopic components (antibodies, antigens, cytokines). The results of this detailed explicit analysis are compared with the traditional procedure of averaging over individuals and representing the collective dynamics in terms of densities that obey partial differential equations (PDE). The simulations show even for very simple elementary reactions the spontaneous emergence of localized complex structures. In turn the effective dynamics of these structures affects the average behavior of the system in a very decisive way: systems which would according to the differential equations approximation die, display in reality a very lively behavior. Our conclusions are supported both by explicit microscopic simulations and by analytic calculations. As the optimal method we propose a mixture of microscopic simulation (MS) systems describing each reaction separately, and average methods describing the average behavior of the agents.

ABSTRACT With this paper, we suggest a general simulation framework to analyze the impact on the ... more ABSTRACT With this paper, we suggest a general simulation framework to analyze the impact on the sales of a newly introduced product of (a) advertising; and (b) of (positive or negative) word-of-mouth in a market where numerous agents are interconnected through a socioeconomic network and provide their neighbors with subjective information about the quality of the product. The information transmitted by an agent is based on (i) advertising messages from the firm distributing the product, and/or (ii) on messages received from the ...

Eprint Arxiv 0801 0121, Dec 30, 2007

This article introduces into the whole section on Social Sciences, edited by A. Nowak for this En... more This article introduces into the whole section on Social Sciences, edited by A. Nowak for this Encyclopedia, concentrating on the applications of mathematics and physics. Here under "mathematics" we include also all computer simulations if they are not taken from physics, while physics applications include simulations of models which basically existed already in physics before they were applied to social simulations. Thus obviously there is no sharp border between applications from physics and from mathematics in the sense of our definition. Also social science is not defined precisely. We will include some economics as well as some linguistics, but not social insects or fish swarms, nor human epidemics or demography. Also, we mention not only this section by also the section on agent-based modelling edited by F. Castiglione as containing articles of social interest.

Microscopic Simulation (MS) uses a computer to represent and keep track of individual (&a... more Microscopic Simulation (MS) uses a computer to represent and keep track of individual (" microscopic") elements in order to investigate complex systems which are analytically intractable. A methodology that was developed to solve physics problems, MS has been used to study the relation between microscopic behavior and macroscopic phenomena in systems ranging from those of atomic particles, to cars, animals, and even humans. In finance, MS can help explain, among other things, the effects of various elements of ...