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Amos Maritan

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Kinshuk Banerjee

University of Calcutta

University of California, San Diego

Sreekanth Manikandan

Paul Romatschke

Katja Lindenberg

University of California, San Diego

Weizmann Institute of Science

Robert Marsland

Pontifical University of the Holy Cross - Rome

Nickolay Korabel

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Papers by Amos Maritan

Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems

Physical Review Research

A general framework to describe a vast majority of biology-inspired systems is to model them as s... more A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes, and particles exchanging heat with different baths, constitute some interesting examples of such a modelization. Moreover, they usually operate out of equilibrium, being characterized by a net production of entropy, which entails a constrained efficiency. Hitherto, in order to investigate multiple processes simultaneously driving a system, all theoretical approaches deal with them independently, at a coarse-grained level, or employing a separation of time scales. Here, we explicitly take in consideration the interplay among time scales of different processes and whether or not their own evolution eventually relaxes toward an equilibrium state in a given subspace. We propose a general framework for multiple coupling, from which the well-known formulas for the entropy production can be derived, depending on the available information about each single process. Furthermore, when one of the processes does not equilibrate in its subspace, even if much faster than all the others, it introduces a finite correction to the entropy production. We employ our framework in various simple and pedagogical examples, for which such a corrective term can be related to a typical scaling of physical quantities in play.

Upscaling species richness and abundances in tropical forests

Science advances, 2017

The quantification of tropical tree biodiversity worldwide remains an open and challenging proble... more The quantification of tropical tree biodiversity worldwide remains an open and challenging problem. More than two-fifths of the number of worldwide trees can be found either in tropical or in subtropical forests, but only ≈0.000067% of species identities are known. We introduce an analytical framework that provides robust and accurate estimates of species richness and abundances in biodiversity-rich ecosystems, as confirmed by tests performed on both in silico-generated and real forests. Our analysis shows that the approach outperforms other methods. In particular, we find that upscaling methods based on the log-series species distribution systematically overestimate the number of species and abundances of the rare species. We finally apply our new framework on 15 empirical tropical forest plots and quantify the minimum percentage cover that should be sampled to achieve a given average confidence interval in the upscaled estimate of biodiversity. Our theoretical framework confirms t...

Reaction-field calculation for the quantum Potts model

Journal of Physics C: Solid State Physics

ABSTRACT The reaction-field approximation is applied to the d-dimensional q-state quantum Potts m... more ABSTRACT The reaction-field approximation is applied to the d-dimensional q-state quantum Potts model in an external transverse field. With the exception of d&lt;or approximately=3, the tricritical value qc(d), below which the system has a second-order phase transition, decreases with increasing external field strength. From the ground state of the quantum d-dimensional model, an improved value of qc is obtained for the classical model in d+1 dimensions. A direct explanation is also obtained for the expected tricritical point in finite-thickness slabs of cubic ferromagnets (like DyAl2) with a field in the (111) direction.

Wilson-Kadanoff and conventional renormalization for a massless ϕ4 theory

Lettere Al Nuovo Cimento Series 2

Species survival and scaling laws in hostile and disordered environments

Physical review. E, 2016

In this work we study the likelihood of survival of single-species in the context of hostile and ... more In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate, except in some random spatially distributed patches that may support life. In particular, we are interested in the phase diagram of the survival probability and in the critical size problem, i.e., the minimum patch size required for surviving in the long-time dynamics. We propose a measure for the critical patch size as being proportional to the participation ratio of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We obtain the (extinction-survival) phase diagram and the probability distribution function (PDF) of the critical patch sizes for two topologies, namely, the one-dimensional system and the fractal Peano basin. We show that both topologies share the same qualitative features, but the fra...

What one can learn from experiments about the elusive transition state?

Protein Sci, 2004

... Iksoo Chang1,2, Marek Cieplak1,3 Jayanth R. Banavar1, and Amos Maritan4,5 1 Department of Phy... more

Phenomenological Modeling of the Motility of Self-Propelled Microorganisms

The motility of microorganisms in liquid media is an important issue in active matter and it is n... more The motility of microorganisms in liquid media is an important issue in active matter and it is not yet fully understood. Previous theoretical approaches dealing with the microscopic description of microbial movement have modeled the propelling force exerted by the organism as a Gaussian white noise term in the equation of motion. We present experimental results for ciliates of the genus Colpidium, which do not agree with the Gaussian white noise hypothesis. We propose a new stochastic model that goes beyond such assumption and displays good agreement with the experimental statistics of motion, such as velocity distribution and velocity autocorrelation.

Simplified Exactly Solvable Model for �-Amyloid Aggregation

Phys Rev Lett, 2010

We propose an exactly solvable simplified statistical mechanical model for the thermodynamics of ... more We propose an exactly solvable simplified statistical mechanical model for the thermodynamics of beta-amyloid aggregation, generalizing a well-studied model for protein folding. The monomer concentration is explicitly taken into account as well as a non trivial dependence on the microscopic degrees of freedom of the single peptide chain, both in the alpha-helix folded isolated state and in the fibrillar one. The phase diagram of the model is studied and compared to the outcome of fibril formation experiments which is qualitatively reproduced.

Protein Structures and Optimal Folding from a Geometrical Variational Principle

Physical Review Letters, 1999

A novel approach, validated by an analysis of barnase and chymotrypsin inhibitor, is introduced t... more A novel approach, validated by an analysis of barnase and chymotrypsin inhibitor, is introduced to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the native state. It is found that native states of proteins, compared with compact artificial backbones, have an exceedingly large number of conformations with a given amount of

Determination of optimal effective interactions between amino acids in globular proteins

Eprint Arxiv Cond Mat 9902364, Feb 26, 1999

An optimization technique is used to determine the pairwise interactions between amino acids in g... more An optimization technique is used to determine the pairwise interactions between amino acids in globular proteins. A numerical strategy is applied to a set of proteins for maximizing the native fold stability with respect to alternative structures obtained by gapless threading. The extracted parameters are shown to be very reliable for identifying the native states of proteins (unrelated to those in the training set) among thousands of conformations. The only poor performers are proteins with heme groups and/or poor compactness whose complexity cannot be captured by standard pairwise energy functionals.

Publisher’s Note: Fluctuation Mediated Interaction and Phase Separation of Nanoparticles in a Liquid Crystal Solvent [Phys. Rev. Lett.PRLTAO0031-9007 91, 085704 (2003)]

Phys Rev Lett, 2003

Effects of Mixing Interaction Types on Ecological Community Stability

In the last years, a remarkable theoretical effort has been made in order to understand stability... more In the last years, a remarkable theoretical effort has been made in order to understand stability and complexity in ecological communities. The non-random structures of real ecological interaction networks has been recognized as one key ingredient contributing to the coexistence between high complexity and stability in real ecosystems. However most of the theoretical studies have considered communities with only one interaction type (either antagonistic, competitive, or mutualistic). Recently it has been proposed a theoretical analysis on multiple interaction types in ecological systems, concluding that: a) Mixture of antagonistic and mutualistic interactions stabilize the system with respect to the less realistic case of only one interaction type; b) Complexity, measured in terms of the number of interactions and the number of species, increases stability in systems with different types of interactions. By introducing new theoretical investigations and analyzing 21 empirical data sets representing mutualistic plant-pollinator networks, we show that that conclusions are incorrect. We will prove that the positive complexity-stability effect observed in systems with different kind of interactions is a mere consequence of a rescaling of the interaction strengths, and thus unrelated to the mixing of interaction types.

$Figure 3. The relative strengt hs of mutualistic and antagonistic interactions strongly affects the stability. The figures show the eigenvalues in the complex plane for randomly generated matrices with S = 200 and C' = 0.8 and two values of py (while z;, n7, Ajj, gi; and e;; are drawn from an uniform distribution between 0 and 1). As shown in [7], there is always an eigenvalue w this case the eigenvalue is equa hich depends only on the average interaction strength, in to (fu — fa — 1)/4 (black arrows). If fy > fa +1 the system is, for a sufficiently large S, always unstable independently of the fraction of mutualistic interactions py and the number of species S. In this case fy = 3 and fa =1. If fi < fa +1 the destabilizing effect of pj, is also observed (see Figure 4). Figure 3. The relative strengths of mutualistic and antagonistic interactions strongly Figure 3 shows that the stability does depend on the choice of the relative strength of mutualistic and antagonistic interactions, even in the case of structured interactions, showing that the prediction of equation (7) is valid in that case too. Indeed the system is always unstable when fj), > f4 +1. These results confirm the important role that mutualistic interactions play in ecological networks [10,17] and poses the crucial problem on the estimation of these parameters from real data, a challenging but difficult task (18, 19].$

$Figure 4. Relationship between complexity, stability and fraction of mutualistic links (par) for cascade networks [7] with Holling type I linear respo nse. The interaction strengths are rescaled by summing over both mutualistic partners and preys (see Eq. 5, assumption (7)). Panel A shows the community stability (measured as the probability that the linearized matrix is stable) vs. the fraction of mutua indicate different values of connectance. S is fixed to 50. Pan listic links pjy. Colors el B shows the complexity-stability relationship with varying py. Both the panels shows that mixing of interaction type in the community dynamics model given by | Eq. (5) and based on assumption (7) does not increase stability. The parameters z;, n*, Aj;, gi; and e;; are drawn from an uniform distribution between 0 and 1, while fy, = f4 = 1.$

From polymers to proteins -- novel phases of short compact tubes

Rev Mod Phys, Jan 14, 2003

A framework is presented for understanding the common character of proteins. Proteins are linear ... more A framework is presented for understanding the common character of proteins. Proteins are linear chain molecules. However, the simple model of a polymer viewed as spheres tethered together does not account for many of the observed characteristics of protein structures. The authors show here that proteins may be regarded as tubes of nonzero thickness. This approach allows one to bridge the conventional compact polymer phase with a novel phase employed by Nature to house biomolecular structures. The continuum description of a tube (or a sheet) of arbitrary thickness entails using appropriately chosen many-body interactions rather than two-body interactions. The authors suggest that the structures of folded proteins are selected based on geometrical considerations and are poised at the edge of compaction, thus accounting for their versatility and flexibility. This approach also offers an explanation for why helices and sheets are the building blocks of protein structures.

Stretching of a Polymer below the ? Point

Phys Rev Lett, 2003

COMMENT: About diffusion processes in disordered systems

J Phys a Math Gen, 1988

Effect of Localization on the Stability of Mutualistic Ecological Networks

The relationships between the core-periphery architecture of the species interaction network and ... more The relationships between the core-periphery architecture of the species interaction network and the mechanisms ensuring the stability in mutualistic ecological communities are still unclear. In particular, most studies have focused their attention on asymptotic resilience or persistence, neglecting how perturbations propagate through the system. Here we develop a theoretical framework to evaluate the relationship between architecture of the interaction networks and the impact of perturbations by studying localization, a measure describing the ability of the perturbation to propagate through the network. We show that mutualistic ecological communities are localized, and localization reduces perturbation propagation and attenuates its impact on species abundance. Localization depends on the topology of the interaction networks, and it positively correlates with the variance of the weighted degree distribution, a signature of the network topological hetereogenity. Our results provide ...

Predicting the stability of large structured food webs

Nature Communications, 2015

The stability of ecological systems has been a long-standing focus of ecology. Recently, tools fr... more The stability of ecological systems has been a long-standing focus of ecology. Recently, tools from random matrix theory have identified the main drivers of stability in ecological communities whose network structure is random. However, empirical food webs differ greatly from random graphs. For example, their degree distribution is broader, they contain few trophic cycles, and they are almost interval. Here we derive an approximation for the stability of food webs whose structure is generated by the cascade model, in which 'larger' species consume 'smaller' ones. We predict the stability of these food webs with great accuracy, and our approximation also works well for food webs whose structure is determined empirically or by the niche model. We find that intervality and broad degree distributions tend to stabilize food webs, and that average interaction strength has little influence on stability, compared with the effect of variance and correlation.

Adhesion of solids

Physical Review E, 1997

... 1995); [SPIN];[INSPEC];[MEDLINE]. PHYSICAL REVIEW E VOLUME 56, NUMBER 3 SEPTEMBER 1997 Adhesi... more

Bethe approximation for a semiflexible polymer chain

Physical Review E, 1998

We present a Bethe approximation to study lattice models of linear polymers. The approach is vari... more We present a Bethe approximation to study lattice models of linear polymers. The approach is variational in nature and based on the cluster variation method (CVM). We focus on a model with (i) a nearest neighbor attractive energy ǫ v between pair of non-bonded monomers, (ii) a bending energy ǫ h for each pair of successive chain segments which are not collinear. We determine the phase diagram of the system as a function of the reduced temperature t = T ǫv and of the parameter x = ǫ h ǫv. We find two different qualitative behaviors, on varying t. For small values of x the system undergoes a θ collapse from an extended coil to a compact globule; subsequently, on decreasing further t, there is a first order transition to an anisotropic phase, characterized by global orientational order. For sufficiently large values of x, instead, there is directly a first order transition from the coil to the orientational ordered phase. Our results are in good agreement with previous Monte Carlo simulations and contradict in some aspects mean-field theory. In the limit of Hamiltonian walks, our approximation recovers results of the Flory-Huggins theory for polymer melting.

Statistical Mechanics of Self-Avoiding Random Surfaces

Fractals in Physics, 1986

Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems

Physical Review Research

A general framework to describe a vast majority of biology-inspired systems is to model them as s... more A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes, and particles exchanging heat with different baths, constitute some interesting examples of such a modelization. Moreover, they usually operate out of equilibrium, being characterized by a net production of entropy, which entails a constrained efficiency. Hitherto, in order to investigate multiple processes simultaneously driving a system, all theoretical approaches deal with them independently, at a coarse-grained level, or employing a separation of time scales. Here, we explicitly take in consideration the interplay among time scales of different processes and whether or not their own evolution eventually relaxes toward an equilibrium state in a given subspace. We propose a general framework for multiple coupling, from which the well-known formulas for the entropy production can be derived, depending on the available information about each single process. Furthermore, when one of the processes does not equilibrate in its subspace, even if much faster than all the others, it introduces a finite correction to the entropy production. We employ our framework in various simple and pedagogical examples, for which such a corrective term can be related to a typical scaling of physical quantities in play.

Upscaling species richness and abundances in tropical forests

Science advances, 2017

The quantification of tropical tree biodiversity worldwide remains an open and challenging proble... more The quantification of tropical tree biodiversity worldwide remains an open and challenging problem. More than two-fifths of the number of worldwide trees can be found either in tropical or in subtropical forests, but only ≈0.000067% of species identities are known. We introduce an analytical framework that provides robust and accurate estimates of species richness and abundances in biodiversity-rich ecosystems, as confirmed by tests performed on both in silico-generated and real forests. Our analysis shows that the approach outperforms other methods. In particular, we find that upscaling methods based on the log-series species distribution systematically overestimate the number of species and abundances of the rare species. We finally apply our new framework on 15 empirical tropical forest plots and quantify the minimum percentage cover that should be sampled to achieve a given average confidence interval in the upscaled estimate of biodiversity. Our theoretical framework confirms t...

Reaction-field calculation for the quantum Potts model

Journal of Physics C: Solid State Physics

ABSTRACT The reaction-field approximation is applied to the d-dimensional q-state quantum Potts m... more ABSTRACT The reaction-field approximation is applied to the d-dimensional q-state quantum Potts model in an external transverse field. With the exception of d&lt;or approximately=3, the tricritical value qc(d), below which the system has a second-order phase transition, decreases with increasing external field strength. From the ground state of the quantum d-dimensional model, an improved value of qc is obtained for the classical model in d+1 dimensions. A direct explanation is also obtained for the expected tricritical point in finite-thickness slabs of cubic ferromagnets (like DyAl2) with a field in the (111) direction.

Wilson-Kadanoff and conventional renormalization for a massless ϕ4 theory

Lettere Al Nuovo Cimento Series 2

Species survival and scaling laws in hostile and disordered environments

Physical review. E, 2016

In this work we study the likelihood of survival of single-species in the context of hostile and ... more In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate, except in some random spatially distributed patches that may support life. In particular, we are interested in the phase diagram of the survival probability and in the critical size problem, i.e., the minimum patch size required for surviving in the long-time dynamics. We propose a measure for the critical patch size as being proportional to the participation ratio of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We obtain the (extinction-survival) phase diagram and the probability distribution function (PDF) of the critical patch sizes for two topologies, namely, the one-dimensional system and the fractal Peano basin. We show that both topologies share the same qualitative features, but the fra...

What one can learn from experiments about the elusive transition state?

Protein Sci, 2004

... Iksoo Chang1,2, Marek Cieplak1,3 Jayanth R. Banavar1, and Amos Maritan4,5 1 Department of Phy... more

Phenomenological Modeling of the Motility of Self-Propelled Microorganisms

The motility of microorganisms in liquid media is an important issue in active matter and it is n... more The motility of microorganisms in liquid media is an important issue in active matter and it is not yet fully understood. Previous theoretical approaches dealing with the microscopic description of microbial movement have modeled the propelling force exerted by the organism as a Gaussian white noise term in the equation of motion. We present experimental results for ciliates of the genus Colpidium, which do not agree with the Gaussian white noise hypothesis. We propose a new stochastic model that goes beyond such assumption and displays good agreement with the experimental statistics of motion, such as velocity distribution and velocity autocorrelation.

Simplified Exactly Solvable Model for �-Amyloid Aggregation

Phys Rev Lett, 2010

We propose an exactly solvable simplified statistical mechanical model for the thermodynamics of ... more We propose an exactly solvable simplified statistical mechanical model for the thermodynamics of beta-amyloid aggregation, generalizing a well-studied model for protein folding. The monomer concentration is explicitly taken into account as well as a non trivial dependence on the microscopic degrees of freedom of the single peptide chain, both in the alpha-helix folded isolated state and in the fibrillar one. The phase diagram of the model is studied and compared to the outcome of fibril formation experiments which is qualitatively reproduced.

Protein Structures and Optimal Folding from a Geometrical Variational Principle

Physical Review Letters, 1999

A novel approach, validated by an analysis of barnase and chymotrypsin inhibitor, is introduced t... more A novel approach, validated by an analysis of barnase and chymotrypsin inhibitor, is introduced to elucidate the paramount role played by the geometry of the protein backbone in steering the folding to the native state. It is found that native states of proteins, compared with compact artificial backbones, have an exceedingly large number of conformations with a given amount of

Determination of optimal effective interactions between amino acids in globular proteins

Eprint Arxiv Cond Mat 9902364, Feb 26, 1999

An optimization technique is used to determine the pairwise interactions between amino acids in g... more An optimization technique is used to determine the pairwise interactions between amino acids in globular proteins. A numerical strategy is applied to a set of proteins for maximizing the native fold stability with respect to alternative structures obtained by gapless threading. The extracted parameters are shown to be very reliable for identifying the native states of proteins (unrelated to those in the training set) among thousands of conformations. The only poor performers are proteins with heme groups and/or poor compactness whose complexity cannot be captured by standard pairwise energy functionals.

Publisher’s Note: Fluctuation Mediated Interaction and Phase Separation of Nanoparticles in a Liquid Crystal Solvent [Phys. Rev. Lett.PRLTAO0031-9007 91, 085704 (2003)]

Phys Rev Lett, 2003

Effects of Mixing Interaction Types on Ecological Community Stability

In the last years, a remarkable theoretical effort has been made in order to understand stability... more In the last years, a remarkable theoretical effort has been made in order to understand stability and complexity in ecological communities. The non-random structures of real ecological interaction networks has been recognized as one key ingredient contributing to the coexistence between high complexity and stability in real ecosystems. However most of the theoretical studies have considered communities with only one interaction type (either antagonistic, competitive, or mutualistic). Recently it has been proposed a theoretical analysis on multiple interaction types in ecological systems, concluding that: a) Mixture of antagonistic and mutualistic interactions stabilize the system with respect to the less realistic case of only one interaction type; b) Complexity, measured in terms of the number of interactions and the number of species, increases stability in systems with different types of interactions. By introducing new theoretical investigations and analyzing 21 empirical data sets representing mutualistic plant-pollinator networks, we show that that conclusions are incorrect. We will prove that the positive complexity-stability effect observed in systems with different kind of interactions is a mere consequence of a rescaling of the interaction strengths, and thus unrelated to the mixing of interaction types.

$Figure 3. The relative strengt hs of mutualistic and antagonistic interactions strongly affects the stability. The figures show the eigenvalues in the complex plane for randomly generated matrices with S = 200 and C' = 0.8 and two values of py (while z;, n7, Ajj, gi; and e;; are drawn from an uniform distribution between 0 and 1). As shown in [7], there is always an eigenvalue w this case the eigenvalue is equa hich depends only on the average interaction strength, in to (fu — fa — 1)/4 (black arrows). If fy > fa +1 the system is, for a sufficiently large S, always unstable independently of the fraction of mutualistic interactions py and the number of species S. In this case fy = 3 and fa =1. If fi < fa +1 the destabilizing effect of pj, is also observed (see Figure 4). Figure 3. The relative strengths of mutualistic and antagonistic interactions strongly Figure 3 shows that the stability does depend on the choice of the relative strength of mutualistic and antagonistic interactions, even in the case of structured interactions, showing that the prediction of equation (7) is valid in that case too. Indeed the system is always unstable when fj), > f4 +1. These results confirm the important role that mutualistic interactions play in ecological networks [10,17] and poses the crucial problem on the estimation of these parameters from real data, a challenging but difficult task (18, 19].$

$Figure 4. Relationship between complexity, stability and fraction of mutualistic links (par) for cascade networks [7] with Holling type I linear respo nse. The interaction strengths are rescaled by summing over both mutualistic partners and preys (see Eq. 5, assumption (7)). Panel A shows the community stability (measured as the probability that the linearized matrix is stable) vs. the fraction of mutua indicate different values of connectance. S is fixed to 50. Pan listic links pjy. Colors el B shows the complexity-stability relationship with varying py. Both the panels shows that mixing of interaction type in the community dynamics model given by | Eq. (5) and based on assumption (7) does not increase stability. The parameters z;, n*, Aj;, gi; and e;; are drawn from an uniform distribution between 0 and 1, while fy, = f4 = 1.$

From polymers to proteins -- novel phases of short compact tubes

Rev Mod Phys, Jan 14, 2003

A framework is presented for understanding the common character of proteins. Proteins are linear ... more A framework is presented for understanding the common character of proteins. Proteins are linear chain molecules. However, the simple model of a polymer viewed as spheres tethered together does not account for many of the observed characteristics of protein structures. The authors show here that proteins may be regarded as tubes of nonzero thickness. This approach allows one to bridge the conventional compact polymer phase with a novel phase employed by Nature to house biomolecular structures. The continuum description of a tube (or a sheet) of arbitrary thickness entails using appropriately chosen many-body interactions rather than two-body interactions. The authors suggest that the structures of folded proteins are selected based on geometrical considerations and are poised at the edge of compaction, thus accounting for their versatility and flexibility. This approach also offers an explanation for why helices and sheets are the building blocks of protein structures.

Stretching of a Polymer below the ? Point

Phys Rev Lett, 2003

COMMENT: About diffusion processes in disordered systems

J Phys a Math Gen, 1988

Effect of Localization on the Stability of Mutualistic Ecological Networks

The relationships between the core-periphery architecture of the species interaction network and ... more The relationships between the core-periphery architecture of the species interaction network and the mechanisms ensuring the stability in mutualistic ecological communities are still unclear. In particular, most studies have focused their attention on asymptotic resilience or persistence, neglecting how perturbations propagate through the system. Here we develop a theoretical framework to evaluate the relationship between architecture of the interaction networks and the impact of perturbations by studying localization, a measure describing the ability of the perturbation to propagate through the network. We show that mutualistic ecological communities are localized, and localization reduces perturbation propagation and attenuates its impact on species abundance. Localization depends on the topology of the interaction networks, and it positively correlates with the variance of the weighted degree distribution, a signature of the network topological hetereogenity. Our results provide ...

Predicting the stability of large structured food webs

Nature Communications, 2015

The stability of ecological systems has been a long-standing focus of ecology. Recently, tools fr... more The stability of ecological systems has been a long-standing focus of ecology. Recently, tools from random matrix theory have identified the main drivers of stability in ecological communities whose network structure is random. However, empirical food webs differ greatly from random graphs. For example, their degree distribution is broader, they contain few trophic cycles, and they are almost interval. Here we derive an approximation for the stability of food webs whose structure is generated by the cascade model, in which 'larger' species consume 'smaller' ones. We predict the stability of these food webs with great accuracy, and our approximation also works well for food webs whose structure is determined empirically or by the niche model. We find that intervality and broad degree distributions tend to stabilize food webs, and that average interaction strength has little influence on stability, compared with the effect of variance and correlation.

Adhesion of solids

Physical Review E, 1997

... 1995); [SPIN];[INSPEC];[MEDLINE]. PHYSICAL REVIEW E VOLUME 56, NUMBER 3 SEPTEMBER 1997 Adhesi... more

Bethe approximation for a semiflexible polymer chain

Physical Review E, 1998

We present a Bethe approximation to study lattice models of linear polymers. The approach is vari... more We present a Bethe approximation to study lattice models of linear polymers. The approach is variational in nature and based on the cluster variation method (CVM). We focus on a model with (i) a nearest neighbor attractive energy ǫ v between pair of non-bonded monomers, (ii) a bending energy ǫ h for each pair of successive chain segments which are not collinear. We determine the phase diagram of the system as a function of the reduced temperature t = T ǫv and of the parameter x = ǫ h ǫv. We find two different qualitative behaviors, on varying t. For small values of x the system undergoes a θ collapse from an extended coil to a compact globule; subsequently, on decreasing further t, there is a first order transition to an anisotropic phase, characterized by global orientational order. For sufficiently large values of x, instead, there is directly a first order transition from the coil to the orientational ordered phase. Our results are in good agreement with previous Monte Carlo simulations and contradict in some aspects mean-field theory. In the limit of Hamiltonian walks, our approximation recovers results of the Flory-Huggins theory for polymer melting.

Statistical Mechanics of Self-Avoiding Random Surfaces

Fractals in Physics, 1986