Persian Articles:
Statistical Physics of Small-World Networks, PhD Thesis (1383)
Small-World Networks, Gamma 4, 16 (1383)
Statistical Physics of Optimization, Physic-e Rooz 8, 18 (1394)
Book Chapters:
Public Goods in Networks: A Statistical Mechanics Approach, L. Dall'Asta, P. Pin, and A. Ramezanpour, Game Theory and Applications, Vol 16, editors: Leon Petrosjan and Vladimir Mazalov, NOVA Publishers (New York, 2013)
Statistical Physics and Network Optimization Problems, C. Baldassi, A. Braunstein, A. Ramezanpour, and R. Zecchina, Mathematical Foundations of Complex Networked Information Systems, F. Fagnani, S.M. Fosson, C. Ravazzi Eds., Lecture Notes in Mathematics Volume 2141, 2015, pp 27-49
Recent Publications:
Noise tolerance via reinforcement: Learning a reinforced quantum dynamics
arXiv:2506.12418 [quant-ph]
Abstract: The performance of quantum simulations heavily depends on the efficiency of noise mitigation techniques and error correction algorithms. Reinforcement has emerged as a powerful strategy to enhance the performance of learning and optimization algorithms. In this study, we demonstrate that reinforced quantum dynamics can exhibit significant robustness against interactions with a noisy environment. We study a quantum annealing process where, through reinforcement, the system is encouraged to maintain its current state or follow a noise-free evolution. A learning algorithm is employed to find a concise approximation of this reinforced dynamics, reducing the total evolution time and, consequently, the system's exposure to noisy interactions. This approach also avoids the complexities associated with implementing quantum feedback in such algorithms. The efficacy of our method is demonstrated through numerical simulations of reinforced quantum annealing with one- and two-qubit systems under Pauli noise
Messenger size optimality in cellular communications
Arash Tirandaz, Abolfazl Ramezanpour, Vivi Rottschäfer, Mehrad Babaei, Andrei Zinovyev, Alireza Mashaghi
Phys. Rev. E 111, 044406 (2025) , arXiv:2412.00771 [physics.bio-ph]
Abstract: Living cells presumably employ optimized information transfer methods, enabling efficient communication even in noisy environments. As expected, the efficiency of chemical communications between cells depends on the properties of the molecular messenger. Evidence suggests that proteins from narrow ranges of molecular masses have been naturally selected to mediate cellular communications, yet the underlying communication design principles are not understood. Using a simple physical model that considers the cost of chemical synthesis, diffusion, molecular binding, and degradation, we show that optimal mass values exist that ensure efficient communication of various types of signals. Our findings provide insights into the design principles of biological communications and can be used to engineer chemically communicating biomimetic systems.
Efficiency of energy-consuming random walkers: Variability in energy helps
Mohsen Ghasemi Nezhadhaghighi and Abolfazl Ramezanpour
Phys. Rev. E 111, 014301 (2025), arXiv:2411.07771 [cond-mat.dis-nn]
Abstract: Energy considerations can significantly affect the behavior of a population of energy-consuming agents with limited energy budgets, for instance, in the movement process of people in a city. We consider a population of interacting agents with an initial energy budget walking on a graph according to an exploration and return (to home) strategy that is based on the current energy of the person. Each move reduces the available energy depending on the flow of movements and the strength of interactions, and the movement ends when an agent returns home with a negative energy. We observe that a uniform distribution of initial energy budgets results in a larger number of visited sites per consumed energy (efficiency) compared to case that all agents have the same initial energy if return to home is relevant from the beginning of the process. The uniform energy distribution also reduces the amount of uncertainties in the total travel times (entropy production) which is more pronounced when the strength of interactions and exploration play the relevant role in the movement process. That is variability in the energies can help to increase the efficiency and reduce the entropy production specially in presence of strong interactions.
Loop corrections for hard spheres in Hamming space
A. Ramezanpour, and Saman Moghimi-Araghi
J. Stat. Mech. (2025) 033401, arXiv:2409.03670 [cond-mat.dis-nn]
Abstract: We begin with an exact expression for the entropy of a system of hard spheres within the Hamming space. This entropy relies on probability marginals, which are determined by an extended set of Belief Propagation (BP) equations. The BP probability marginals are functions of auxiliary variables which are introduced to model the effects of loopy interactions on a tree-structured interaction graph. We explore various reasonable and approximate probability distributions, ensuring they align with the exact solutions of the BP equations. Our approach is based on an ansatz of (in)homogeneous cavity marginals respecting the permutation symmetry of the problem. Through thorough analysis, we aim to minimize errors in the BP equations. Our findings support the conjecture that the maximum packing density asymptotically conforms to the lower bound proposed by Gilbert and Varshamov, further validated by the solution of the loopy BP equations.
Statistical physics of principal minors: Cavity approach
A. Ramezanpour, and M. A. Rajabpour
Phys. Rev. E 109. 064141 (2024), arXiv:2405.19904 [cond-mat.stat-mech]
Abstract: Determinants are useful to represent the state of an interacting system of (effectively) repulsive and independent elements, like fermions in a quantum system and training samples in a learning problem. A computationally challenging problem is to compute the sum of powers of principal minors of a matrix which is relevant to the study of critical behaviors in quantum fermionic systems and finding a subset of maximally informative training data for a learning algorithm. Specifically, principal minors of positive square matrices can be considered as statistical weights of a random point process on the set of the matrix indices. The probability of each subset of the indices is in general proportional to a positive power of the determinant of the associated sub-matrix. We use Gaussian representation of the determinants for symmetric and positive matrices to estimate the partition function (or free energy) and the entropy of principal minors within the Bethe approximation. The results are expected to be asymptotically exact for diagonally dominant matrices with locally tree-like structures. We consider the Laplacian matrix of random regular graphs of degree K=2,3,4 and exactly characterize the structure of the relevant minors in a mean-field model of such matrices. No (finite-temperature) phase transition is observed in this class of diagonally dominant matrices by increasing the positive power of the principal minors, which here plays the role of an inverse temperature.
A field theory representation of sum of powers of principal minors and physical applications
M. N. Najafi, A. Ramezanpour, and M. A. Rajabpour
SciPost Phys. Core 8, 051 (2025), arXiv:2403.09874 [quant-ph]
Abstract: We introduce a novel field theory representation for the Sum of Powers of Principal Minors (SPPM), a mathematical construct with profound implications in quantum mechanics and statistical physics. We begin by establishing a Berezin integral formulation of the SPPM problem, showcasing its versatility through various symmetries including SU(n), its subgroups, and particle-hole symmetry. This representation not only facilitates new analytical approaches but also offers deeper insights into the symmetries of complex quantum systems. For instance, it enables the representation of the Hubbard model's partition function in terms of the SPPM problem. We further develop three mean field techniques to approximate SPPM, each providing unique perspectives and utilities: the first method focuses on the evolution of symmetries post-mean field approximation, the second, based on the bosonic representation, enhances our understanding of the stability of mean field results, and the third employs a variational approach to establish a lower bound for SPPM. These methods converge to identical consistency relations and values for SPPM, illustrating their robustness. The practical applications of our theoretical advancements are demonstrated through two compelling case studies. First, we exactly solve the SPPM problem for the Laplacian matrix of a chain, a symmetric tridiagonal matrix, allowing for precise benchmarking of mean-field theory results. Second, we present the first analytical calculation of the Shannon-Rényi entropy for the transverse field Ising chain, revealing critical insights into phase transitions and symmetry breaking in the ferromagnetic phase. This work not only bridges theoretical gaps in understanding principal minors within quantum systems but also sets the stage for future explorations in more complex quantum and statistical physics models.
Learning capacity and function of stochastic reaction networks
Abolfazl Ramezanpour and Alireza Mashaghi
J. Phys. Complex. 4 035006 (2023)
Abstract: Biochemical reaction networks are expected to encode an efficient representation of the function of cells in a variable environment. It is thus important to see how these networks do learn and implement such representations. The first step in this direction is to characterize the function and learning capabilities of basic artificial reaction networks. In this study, we consider multilayer networks of reversible reactions that connect two layers of signal and response species through an intermediate layer of hidden species. We introduce a stochastic learning algorithm that updates the reaction rates based on the correlation values between reaction products and responses. Our findings indicate that the function of networks with random reaction rates, as well as their learning capacity for random signal-response activities, are critically determined by the number of reactants and reaction products. Moreover, the stored patterns exhibit different levels of robustness and qualities as the reaction rates deviate from their optimal values in a stochastic model of defect evolution. These findings can help suggest network modules that are better suited to specific functions, such as amplifiers or dampeners, or to the learning of biologically relevant signal-response activities.
Quantum walk in a reinforced free-energy landscape: Quantum annealing with reinforcement
Abolfazl Ramezanpour
Phys. Rev. A 106. 012418 (2022)
Abstract: Providing an optimal path to a quantum annealing algorithm is key to finding good approximate solutions to computationally hard optimization problems. Reinforcement is one of the strategies that can be used to circumvent the exponentially small energy gaps of the system in the annealing process. Here a time-dependent reinforcement term is added to the Hamiltonian in order to give lower energies to the most probable states of the evolving system. In this study, we take local entropy in the configuration space for the reinforcement and apply the algorithm to a number of easy and hard optimization problems. The reinforced algorithm performs better than the standard quantum annealing algorithm in the quantum search problem, where the optimal parameters behave very differently depending on the number of solutions. Moreover, the reinforcements can change the discontinuous phase transitions of the mean-field p-spin model (p>2) to a continuous transition. The algorithm's performance in the binary perceptron problem is also superior to that of the standard quantum annealing algorithm, which already works better than a classical simulated annealing algorithm.
Entropy production of selfish drivers: implications for efficiency and predictability of movements in a city
Indaco Biazzo, Mohsen Ghasemi Nezhadhaghighi and Abolfazl Ramezanpour
J. Phys. Complex. 2 035026 (2021)
Abstract: Characterizing the efficiency of movements is important for a better management of the cities. More specifically, the connection between the efficiency and uncertainty (entropy) production of a transport process is not established yet. In this study, we consider the movements of selfish drivers from their homes (origins) to work places (destinations) to see how interactions and randomness in the movements affect a measure of efficiency and entropy production (uncertainty in the destination time intervals) in this process. We employ realistic models of population distributions and mobility laws to simulate the movement process, where interactions are modeled by dependence of the local travel times on the local flows. We observe that some level of information (the travel times) sharing enhances a measure of predictability in the process without any coordination. Moreover, the larger cities display smaller efficiencies, for the same model parameters and population density, which limits the size of an efficient city. We find that entropy production is a good order parameter to distinguish the low- and high-congestion phases. In the former phase, the entropy production grows monotonically with the probability of random moves, whereas it displays a minimum in the congested phase; that is randomness in the movements can reduce the uncertainty in the destination time intervals. The findings highlight the role of entropy production in the study of efficiency and predictability of similar processes in a complex system like the city.
Statistical Physics for Medical Diagnostics: Learning, Inference, and Optimization Algorithms
Abolfazl Ramezanpour, Andrew L. Beam, Jonathan H. Chen, and Alireza Mashaghi,
Diagnostics 2020, 10, 972,
Abstract: It is widely believed that cooperation between clinicians and machines may address many of the decisional fragilities intrinsic to current medical practice. However, the realization of this potential will require more precise definitions of disease states as well as their dynamics and interactions. A careful probabilistic examination of symptoms and signs, including the molecular profiles of the relevant biochemical networks, will often be required for building an unbiased and efficient diagnostic approach. Analogous problems have been studied for years by physicists extracting macroscopic states of various physical systems by examining microscopic elements and their interactions. These valuable experiences are now being extended to the medical field. From this perspective, we discuss how recent developments in statistical physics, machine learning and inference algorithms are coming together to improve current medical diagnostic approaches.
Disease evolution in reaction networks: Implications for a diagnostic problem
Abolfazl Ramezanpour and Alireza Mashaghi,
PLoS Comput Biol 16(6): e1007889 (2020),
Abstract: We study the time evolution of symptoms (signs) with some defects in the dynamics of a reaction network as a (microscopic) model for the progress of disease phenotypes. To this end, we take a large population of reaction networks and follow the stochastic dynamics of the system to see how the development of defects affects the macroscopic states of the signs probability distribution. We start from some plausible definitions for the healthy and disease states along with a dynamical model for the emergence of diseases by a reverse simulated annealing algorithm. The healthy state is defined as a state of maximum objective function, which here is the sum of mutual information between a subset of signal variables and the subset of assigned response variables. A disease phenotype is defined with two parameters controlling the rate of mutations in reactions and the rate of accepting mutations that reduce the objective function. The model can provide the time dependence of the sign probabilities given a disease phenotype. This allows us to obtain the accuracy of diagnosis as a function of time by using a probabilistic model of signs and diseases. The trade-off between the diagnosis accuracy (increasing in time) and the objective function (decreasing in time) can be used to suggest an optimal time for medical intervention. Our model would be useful in particular for a dynamical (history-based) diagnostic problem, to estimate the likelihood of a disease hypothesis given the temporal evolution of the signs.
Efficiency and irreversibility of movements in a city
Indaco Biazzo and Abolfazl Ramezanpour,
Scientific Reports 10, 4334 (2020),
Abstract: We know that maximal efficiency in physical systems is attained by reversible processes. It is then interesting to see how irreversibility affects efficiency in other systems, e.g., in a city. In this study, we focus on a cyclic process of movements (home to workplace and back to home) in a city to investigate the above question. To this end, we present a minimal model of the movements, along with plausible definitions for the efficiency and irreversibility of the process; more precisely, we take the inverse of the total travel time per number of trips for efficiency and the relative entropy of the forward and backward flow distributions for the process irreversibility. We perform numerical simulations of the model for reasonable choices of the population distribution, the mobility law, and the movement strategy. The results show that the efficiency of movements is indeed negatively correlated with the above measure of irreversibility. The structure of the network and the impact of the flows on the travel times are the main factors here that affect the time intervals of arriving to destinations and returning to origins, which are usually larger than the time interval of the departures. This in turn gives rise to diverging of the backward flows from the forward ones and results to entropy (disorder or uncertainty) production in the system. The findings of this study might be helpful in characterizing more accurately the city efficiency and in better understanding of the main working principles of these complex systems.