Showing papers in "Physical Review E in 2020"
TL;DR: It is argued that the ergodicity breaking transition in interacting spin chains occurs when both time scales are of the same order, t_{Th}≈t_{H}, and g becomes a system-size independent constant, and carries certain analogies with the Anderson localization transition.
Abstract: Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic ergodicity breaking phenomenon, which extends the concept of Anderson localization to interacting systems. At the same time, random matrix theory has established a powerful framework for characterizing the onset of quantum chaos and ergodicity (or the absence thereof) in quantum many-body systems. Here we numerically study the spectral statistics of disordered interacting spin chains, which represent prototype models expected to exhibit MBL. We study the ergodicity indicator $g={log}_{10}({t}_{\mathrm{H}}/{t}_{\mathrm{Th}})$, which is defined through the ratio of two characteristic many-body time scales, the Thouless time ${t}_{\mathrm{Th}}$ and the Heisenberg time ${t}_{\mathrm{H}}$, and hence resembles the logarithm of the dimensionless conductance introduced in the context of Anderson localization. We argue that the ergodicity breaking transition in interacting spin chains occurs when both time scales are of the same order, ${t}_{\mathrm{Th}}\ensuremath{\approx}{t}_{\mathrm{H}}$, and $g$ becomes a system-size independent constant. Hence, the ergodicity breaking transition in many-body systems carries certain analogies with the Anderson localization transition. Intriguingly, using a Berezinskii-Kosterlitz-Thouless correlation length we observe a scaling solution of $g$ across the transition, which allows for detection of the crossing point in finite systems. We discuss the observation that scaled results in finite systems by increasing the system size exhibit a flow towards the quantum chaotic regime.
232 citations
TL;DR: In this article, a class of random walks defined on higher-order structures and grounded on a microscopic physical model where multibody proximity is associated with highly probable exchanges among agents belonging to the same hyperedge is proposed.
Abstract: In the past 20 years network science has proven its strength in modeling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Nevertheless, in many relevant cases, interactions are not pairwise but involve larger sets of nodes at a time. These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multibody interactions. Here we propose and study a class of random walks defined on such higher-order structures and grounded on a microscopic physical model where multibody proximity is associated with highly probable exchanges among agents belonging to the same hyperedge. We provide an analytical characterization of the process, deriving a general solution for the stationary distribution of the walkers. The dynamics is ultimately driven by a generalized random-walk Laplace operator that reduces to the standard random-walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings. We illustrate our results on synthetic models for which we have full control of the high-order structures and on real-world networks where higher-order interactions are at play. As the first application of the method, we compare the behavior of random walkers on hypergraphs to that of traditional random walkers on the corresponding projected networks, drawing interesting conclusions on node rankings in collaboration networks. As the second application, we show how information derived from the random walk on hypergraphs can be successfully used for classification tasks involving objects with several features, each one represented by a hyperedge. Taken together, our work contributes to unraveling the effect of higher-order interactions on diffusive processes in higher-order networks, shedding light on mechanisms at the heart of biased information spreading in complex networked systems.
124 citations
TL;DR: In this article, it was shown that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime, and the same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable.
Abstract: Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical correspondence between the OTOC exponential growth and chaos in the classical limit has indeed been corroborated theoretically for some systems and there are several projects to do the same experimentally. The Dicke model, in particular, which has a regular and a chaotic regime, is currently under intense investigation by experiments with trapped ions. We show, however, that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime. The same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable. The exponential behavior in these cases are due to unstable stationary points, not to chaos.
120 citations
TL;DR: This work generalizes the master stability approach to hypergraphs and provides a blueprint for how to generalize dynamical structures and results from graphs tohypergraphs.
Abstract: In the study of dynamical systems on networks or graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that, instead of microscopic details of the individual nodes or vertices, rather make the influence of the network coupling topology visible. The master stability function is an important such tool to achieve this goal. Here, we generalize the master stability approach to hypergraphs. A hypergraph coupling structure is important as it allows us to take into account arbitrary higher-order interactions between nodes. As, for instance, in the theory of coupled map lattices, we study Laplace-type interaction structures in detail. Since the spectral theory of Laplacians on hypergraphs is richer than on graphs, we see the possibility of different dynamical phenomena. More generally, our arguments provide a blueprint for how to generalize dynamical structures and results from graphs to hypergraphs.
100 citations
TL;DR: This work derives a TUR for the short-time region and proves that it can provide the exact value, not only a lower bound, of the entropy production rate for Langevin dynamics, if the observed current is optimally chosen.
Abstract: Thermodynamic uncertainty relations (TURs) are the inequalities which give lower bounds on the entropy production rate using only the mean and the variance of fluctuating currents. Since the TURs do not refer to the full details of the stochastic dynamics, it would be promising to apply the TURs for estimating the entropy production rate from a limited set of trajectory data corresponding to the dynamics. Here we investigate a theoretical framework for estimation of the entropy production rate using the TURs along with machine learning techniques without prior knowledge of the parameters of the stochastic dynamics. Specifically, we derive a TUR for the short-time region and prove that it can provide the exact value, not only a lower bound, of the entropy production rate for Langevin dynamics, if the observed current is optimally chosen. This formulation naturally includes a generalization of the TURs with the partial entropy production of subsystems under autonomous interaction, which reveals the hierarchical structure of the estimation. We then construct estimators on the basis of the short-time TUR and machine learning techniques such as the gradient ascent. By performing numerical experiments, we demonstrate that our learning protocol performs well even in nonlinear Langevin dynamics. We also discuss the case of Markov jump processes, where the exact estimation is shown to be impossible in general. Our result provides a platform that can be applied to a broad class of stochastic dynamics out of equilibrium, including biological systems.
99 citations
TL;DR: By proving the saturation of the thermodynamic uncertainty relation in the short-time limit, the exact estimate of the entropy production can be obtained for overdamped Langevin systems, irrespective of the underlying dynamics.
Abstract: Entropy production characterizes the thermodynamic irreversibility and reflects the amount of heat dissipated into the environment and free energy lost in nonequilibrium systems. According to the thermodynamic uncertainty relation, we propose a deterministic method to estimate the entropy production from a single trajectory of system states. We explicitly and approximately compute an optimal current that yields the tightest lower bound using predetermined basis currents. Notably, the obtained tightest lower bound is intimately related to the multidimensional thermodynamic uncertainty relation. By proving the saturation of the thermodynamic uncertainty relation in the short-time limit, the exact estimate of the entropy production can be obtained for overdamped Langevin systems, irrespective of the underlying dynamics. For Markov jump processes, because the attainability of the thermodynamic uncertainty relation is not theoretically ensured, the proposed method provides the tightest lower bound for the entropy production. When entropy production is the optimal current, a more accurate estimate can be further obtained using the integral fluctuation theorem. We illustrate the proposed method using three systems: a four-state Markov chain, a periodically driven particle, and a multiple bead-spring model. The estimated results in all examples empirically verify the effectiveness and efficiency of the proposed method.
84 citations
TL;DR: In this paper, the critical exponents ν, η and ω of O(N) models for various values of N were computed by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-toleading order [usually denoted O(∂^{4})].
Abstract: We compute the critical exponents ν, η and ω of O(N) models for various values of N by implementing the derivative expansion of the nonperturbative renormalization group up to next-to-next-to-leading order [usually denoted O(∂^{4})]. We analyze the behavior of this approximation scheme at successive orders and observe an apparent convergence with a small parameter, typically between 1/9 and 1/4, compatible with previous studies in the Ising case. This allows us to give well-grounded error bars. We obtain a determination of critical exponents with a precision which is similar or better than those obtained by most field-theoretical techniques. We also reach a better precision than Monte Carlo simulations in some physically relevant situations. In the O(2) case, where there is a long-standing controversy between Monte Carlo estimates and experiments for the specific heat exponent α, our results are compatible with those of Monte Carlo but clearly exclude experimental values.
81 citations
TL;DR: In this article, the authors consider a random two-phase process which they call a reset-return one, and provide general expressions for the stationary probability density function of the particle's position and for the mean hitting time in one dimension.
Abstract: We consider a random two-phase process which we call a reset-return one. The particle starts its motion at the origin. The first, displacement, phase corresponds to a stochastic motion of a particle and is finished at a resetting event. The second, return, phase corresponds to the particle's motion toward the origin from the position it attained at the end of the displacement phase. This motion toward the origin takes place according to a given equation of motion. The whole process is a renewal one. We provide general expressions for the stationary probability density function of the particle's position and for the mean hitting time in one dimension. We perform explicit analysis for the Brownian motion during the displacement phase and three different types of the return motion: return at a constant speed, return at a constant acceleration with zero initial speed, and return under the action of a harmonic force. We assume that the waiting times for resetting events follow an exponential distribution or that resetting takes place after a fixed waiting period. For the first two types of return motion and the exponential resetting, the stationary probability density function of the particle's position is invariant under return speed (acceleration), while no such invariance is found for deterministic resetting, and for exponential resetting with return under the action of the harmonic force. We discuss necessary conditions for such invariance of the stationary PDF of the positions with respect to the properties of the return process, and we demonstrate some additional examples when this invariance does or does not take place.
81 citations
TL;DR: A generalized mean-field model is presented to enable the calculation of bond percolation thresholds for polymers with multiple types of stickers and it is demonstrated how cooperativity in bond formation can give rise to reentrant phase behavior.
Abstract: Polymers with stickers-and-spacers architectures can drive phase-separation-aided bond percolation transitions. Here, we present a generalized mean-field model to enable the calculation of bond percolation thresholds for polymers with multiple types of stickers. Further, using graph-based Monte Carlo simulations we demonstrate how cooperativity in bond formation can give rise to reentrant phase behavior. When combined with recent advances for modeling phase separation, our approaches for calculating percolation lines could be useful for modeling hardening transitions for multivalent proteins.
76 citations
TL;DR: In this paper, the authors derive and analyze models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs, and reveal that multibody dynamical effects that go beyond rescaled pairwise interactions can appear only if the interaction function is nonlinear.
Abstract: Multibody interactions can reveal higher-order dynamical effects that are not captured by traditional two-body network models. In this work, we derive and analyze models for consensus dynamics on hypergraphs, where nodes interact in groups rather than in pairs. Our work reveals that multibody dynamical effects that go beyond rescaled pairwise interactions can appear only if the interaction function is nonlinear, regardless of the underlying multibody structure. As a practical application, we introduce a specific nonlinear function to model three-body consensus, which incorporates reinforcing group effects such as peer pressure. Unlike consensus processes on networks, we find that the resulting dynamics can cause shifts away from the average system state. The nature of these shifts depends on a complex interplay between the distribution of the initial states, the underlying structure, and the form of the interaction function. By considering modular hypergraphs, we discover state-dependent, asymmetric dynamics between polarized clusters where multibody interactions make one cluster dominate the other.
75 citations
TL;DR: An exact series solution is found for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions in the presence of translational diffusion.
Abstract: We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions in the presence of translational diffusion. This series solution allows us to efficiently explore the behavior of the system in different parameter regimes. Identifying ``active'' and ``passive'' regimes, we predict a surprising re-entrant active-to-passive transition with increasing trap stiffness. Our numerical simulations validate this finding. We discuss various interesting limiting cases wherein closed-form expressions for the distributions can be obtained.
TL;DR: In this article, the authors present an alternative and rather general approach that addresses this difficulty by using a weak formulation of the sparse regression problem, which allows accurate reconstruction of PDEs involving high-order derivatives, such as the Kuramoto-Sivashinsky equation, from data with a considerable amount of noise.
Abstract: Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations (PDEs); hence sparse regression typically requires the evaluation of various partial derivatives. However, accurate evaluation of derivatives, especially of high order, is infeasible when the data are noisy, which has a dramatic negative effect on the result of regression. We present an alternative and rather general approach that addresses this difficulty by using a weak formulation of the problem. For instance, it allows accurate reconstruction of PDEs involving high-order derivatives, such as the Kuramoto-Sivashinsky equation, from data with a considerable amount of noise. The flexibility of our approach also allows reconstruction of PDE models that involve latent variables which cannot be measured directly with acceptable accuracy. This is illustrated by reconstructing a model for a weakly turbulent flow in a thin fluid layer, where neither the forcing nor the pressure field is known.
TL;DR: This work uses neural networks that incorporate Hamiltonian dynamics to efficiently learn phase space orbits even as nonlinear systems transition from order to chaos.
Abstract: Artificial neural networks are universal function approximators. They can forecast dynamics, but they may need impractically many neurons to do so, especially if the dynamics is chaotic. We use neural networks that incorporate Hamiltonian dynamics to efficiently learn phase space orbits even as nonlinear systems transition from order to chaos. We demonstrate Hamiltonian neural networks on a widely used dynamics benchmark, the Henon-Heiles potential, and on nonperturbative dynamical billiards. We introspect to elucidate the Hamiltonian neural network forecasting.
TL;DR: A comparison of the four popular analysis methods that have been used to obtain the macroscopic Navier-Stokes and nonlinear convection-diffusion equations from the MRT-LB method shows that these four analysis methods can give the same equations at the second-order of expansion parameters.
Abstract: In this paper, we first present a unified framework of multiple-relaxation-time lattice Boltzmann (MRT-LB) method for the Navier-Stokes and nonlinear convection-diffusion equations where a block-lower-triangular-relaxation matrix and an auxiliary source distribution function are introduced. We then conduct a comparison of the four popular analysis methods (Chapman-Enskog analysis, Maxwell iteration, direct Taylor expansion, and recurrence equations approaches) that have been used to obtain the macroscopic Navier-Stokes and nonlinear convection-diffusion equations from the MRT-LB method and show that from mathematical point of view, these four analysis methods can give the same equations at the second-order of expansion parameters. Finally, we give some elements that are needed in the implementation of the MRT-LB method and also find that some available LB models can be obtained from this MRT-LB method.
TL;DR: It is shown that the signature of activity at long times can be found in the atypical fluctuations, which is characterized by computing the large deviation functions explicitly.
Abstract: We study a set of run-and-tumble particle (RTP) dynamics in two spatial dimensions. In the first case of the orientation θ of the particle can assume a set of n possible discrete values, while in the second case θ is a continuous variable. We calculate exactly the marginal position distributions for n=3,4 and the continuous case and show that in all cases the RTP shows a crossover from a ballistic to diffusive regime. The ballistic regime is a typical signature of the active nature of the systems and is characterized by nontrivial position distributions which depend on the specific model. We also show that the signature of activity at long times can be found in the atypical fluctuations, which we also characterize by computing the large deviation functions explicitly.
TL;DR: This work obtains a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes and demonstrates that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation.
Abstract: The total entropy production quantifies the extent of irreversibility in thermodynamic systems, which is nonnegative for any feasible dynamics. When additional information such as the initial and final states or moments of an observable is available, it is known that tighter lower bounds on the entropy production exist according to the classical speed limits and the thermodynamic uncertainty relations. Here we obtain a universal lower bound on the total entropy production in terms of probability distributions of an observable in the time forward and backward processes. For a particular case, we show that our universal relation reduces to a classical speed limit, imposing a constraint on the speed of the system's evolution in terms of the Hatano-Sasa entropy production. Notably, the obtained classical speed limit is tighter than the previously reported bound by a constant factor. Moreover, we demonstrate that a generalized thermodynamic uncertainty relation can be derived from another particular case of the universal relation. Our uncertainty relation holds for systems with time-reversal symmetry breaking and recovers several existing bounds. Our approach provides a unified perspective on two closely related classes of inequality: classical speed limits and thermodynamic uncertainty relations.
TL;DR: A mathematical framework to study the economic impact of infectious diseases by integrating epidemiological dynamics with a kinetic model of wealth exchange and simulations confirm the ability of the model to describe different phenomenon characteristics of economic trends in situations compromised by the rapid spread of an epidemic.
Abstract: We develop a mathematical framework to study the economic impact of infectious diseases by integrating epidemiological dynamics with a kinetic model of wealth exchange. The multiagent description leads to the study of the evolution over time of a system of kinetic equations for the wealth densities of susceptible, infectious, and recovered individuals, whose proportions are driven by a classical compartmental model in epidemiology. Explicit calculations show that the spread of the disease seriously affects the distribution of wealth, which, unlike the situation in the absence of epidemics, can converge toward a stationary state with a bimodal form. Furthermore, simulations confirm the ability of the model to describe different phenomenon characteristics of economic trends in situations compromised by the rapid spread of an epidemic, such as the unequal impact on the various wealth classes and the risk of a shrinking middle class.
TL;DR: In this paper, the authors propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep GNNs that provide an exact sampling probability.
Abstract: We propose a general framework for the estimation of observables with generative neural samplers focusing on modern deep generative neural networks that provide an exact sampling probability. In this framework, we present asymptotically unbiased estimators for generic observables, including those that explicitly depend on the partition function such as free energy or entropy, and derive corresponding variance estimators. We demonstrate their practical applicability by numerical experiments for the two-dimensional Ising model which highlight the superiority over existing methods. Our approach greatly enhances the applicability of generative neural samplers to real-world physical systems.
TL;DR: A data-driven framework is developed to represent chaotic dynamics on an inertial manifold and applied to solutions of the Kuramoto-Sivashinsky equation, reproducing very well key dynamic and statistical features of the attractor.
Abstract: A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM) and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension reduction transforms between coordinates in the full state space and on the IM. Additional neural networks predict time evolution on the IM. The formalism accounts for translation invariance and energy conservation, and substantially outperforms linear dimension reduction, reproducing very well key dynamic and statistical features of the attractor.
TL;DR: In this paper, a full-six-degrees-of-freedom model was developed and employed to provide insight into the axial and off-axis dynamic responses, revealing that the variation of key geometric parameters may lead to regions with qualitatively distinct mechanical responses.
Abstract: Origami-inspired structures have a rich design space, offering new opportunities for the development of deployable systems that undergo large and complex yet predictable shape transformations. There has been growing interest in such structural systems that can extend uniaxially into tubes and booms. The Kresling origami pattern, which arises from the twist buckling of a thin cylinder and can exhibit multistability, offers great potential for this purpose. However, much remains to be understood regarding the characteristics of Kresling origami deployment. Prior studies have been limited to Kresling structures' kinematics, quasistatic mechanics, or low-amplitude wave responses, while their dynamic behaviors with large shape change during deployment remain unexplored. These dynamics are critical to the system design and control processes, but are complex due to the strong nonlinearity, bistability, and potential for off-axis motions. To advance the state of the art, this research seeks to uncover the deployment dynamics of Kresling structures with various system geometries and operating strategies. A full, six-degrees-of-freedom model is developed and employed to provide insight into the axial and off-axis dynamic responses, revealing that the variation of key geometric parameters may lead to regions with qualitatively distinct mechanical responses. Results illustrate the sensitivity of dynamic deployment to changes in initial condition and small variations in geometric design. Further, analyses show how certain geometries and configurations affect the stiffness of various axial and off-axis deformation modes, offering guidance on the design of systems that deploy effectively while mitigating the effects of off-axis disturbances. Overall, the research outcomes suggest the strong potential of Kresling-based designs for deployable systems with robust and tunable performance.
TL;DR: The stationary probability distribution as well as the mean and global first passage times are obtained, which allow us to characterize the effect of resetting on the capacity of a random walker to reach a particular target or to explore a finite network.
Abstract: We study random walks with stochastic resetting to the initial position on arbitrary networks. We obtain the stationary probability distribution as well as the mean and global first passage times, which allow us to characterize the effect of resetting on the capacity of a random walker to reach a particular target or to explore a finite network. We apply the results to rings, Cayley trees, and random and complex networks. Our formalism holds for undirected networks and can be implemented from the spectral properties of the random walk without resetting, providing a tool to analyze the search efficiency in different structures with the small-world property or communities. In this way, we extend the study of resetting processes to the domain of networks.
TL;DR: It is demonstrated that at much smaller energy scales, the eigenvalue distribution approximately assumes the universal semicircle shape, indicating transition to the random-matrix behavior, and in particular that matrix elements become uncorrelated.
Abstract: Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented as random matrices and, in particular, to what extent matrix elements can be considered as uncorrelated. As a main result, we show that the eigenvalue distribution of band submatrices at a fixed energy density is a sensitive probe of the correlations between matrix elements. We find that, on the scales where the matrix elements are in a good agreement with all standard indicators of the eigenstate thermalization hypothesis, the eigenvalue distribution still exhibits clear signatures of the original operator, implying correlations between matrix elements. Moreover, we demonstrate that at much smaller energy scales, the eigenvalue distribution approximately assumes the universal semicircle shape, indicating transition to the random-matrix behavior, and in particular that matrix elements become uncorrelated.
TL;DR: This work defines a form of adaptive (or coevolutionary) voter model posed on a simplicial complex, i.e., on a certain class of hypernetworks or hypergraphs, and introduces a peer-pressure rule applied to three nodes connected via a 2-simplex.
Abstract: Collective decision making processes lie at the heart of many social, political, and economic challenges. The classical voter model is a well-established conceptual model to study such processes. In this work, we define a form of adaptive (or coevolutionary) voter model posed on a simplicial complex, i.e., on a certain class of hypernetworks or hypergraphs. We use the persuasion rule along edges of the classical voter model and the recently studied rewiring rule of edges towards like-minded nodes, and introduce a peer-pressure rule applied to three nodes connected via a 2-simplex. This simplicial adaptive voter model is studied via numerical simulation. We show that adding the effect of peer pressure to an adaptive voter model leaves its fragmentation transition, i.e., the transition upon varying the rewiring rate from a single majority state into a fragmented state of two different opinion subgraphs, intact. Yet, above and below the fragmentation transition, we observe that the peer pressure has substantial quantitative effects. It accelerates the transition to a single-opinion state below the transition and also speeds up the system dynamics towards fragmentation above the transition. Furthermore, we quantify that there is a multiscale hierarchy in the model leading to the depletion of 2-simplices, before the depletion of active edges. This leads to the conjecture that many other dynamic network models on simplicial complexes may show a similar behavior with respect to the sequential evolution of simplices of different dimensions.
TL;DR: A beam-driven fusion scheme is used to explain the total number of α particles generated in the nuclear reaction, and protons accelerated inside the plasma, moving forward into the bulk of the target, can interact with ^{11}B atoms, thus efficiently triggering fusion reactions.
Abstract: The nuclear reaction known as proton-boron fusion has been triggered by a subnanosecond laser system focused onto a thick boron nitride target at modest laser intensity (∼10^{16}W/cm^{2}), resulting in a record yield of generated α particles. The estimated value of α particles emitted per laser pulse is around 10^{11}, thus orders of magnitude higher than any other experimental result previously reported. The accelerated α-particle stream shows unique features in terms of kinetic energy (up to 10 MeV), pulse duration (∼10 ns), and peak current (∼2 A) at 1 m from the source, promising potential applications of such neutronless nuclear fusion reactions. We have used a beam-driven fusion scheme to explain the total number of α particles generated in the nuclear reaction. In this model, protons accelerated inside the plasma, moving forward into the bulk of the target, can interact with ^{11}B atoms, thus efficiently triggering fusion reactions. An overview of literature results obtained with different laser parameters, experimental setups, and target compositions is reported and discussed.
TL;DR: A general design for a quantum battery based on an energy current observable quantifying the energy transfer rate to a consumption hub and an asymptotically stable discharge mechanism is proposed, which is achieved through an adiabatic evolution eventually yielding vanishing EC.
Abstract: A fully operational loss-free quantum battery requires an inherent control over the energy transfer process, with the ability of keeping the energy retained with no leakage. Moreover, it also requires a stable discharge mechanism, which entails that no energy revivals occur as the device starts its energy distribution. Here we provide a scalable solution for both requirements. To this aim, we propose a general design for a quantum battery based on an energy current (EC) observable quantifying the energy transfer rate to a consumption hub. More specifically, we introduce an instantaneous EC operator describing the energy transfer process driven by an arbitrary interaction Hamiltonian. The EC observable is shown to be the root for two main applications: (1) a trapping energy mechanism based on a common eigenstate between the EC operator and the interaction Hamiltonian, in which the battery can indefinitely retain its energy even if it is coupled to the consumption hub, and (2) an asymptotically stable discharge mechanism, which is achieved through an adiabatic evolution eventually yielding vanishing EC. These two independent but complementary applications are illustrated in quantum spin chains, where the trapping energy control is realized through Bell pairwise entanglement and the stability arises as a general consequence of the adiabatic spin dynamics.
TL;DR: It is argued that traditional community detection does in fact give a significant amount of insight into network structure, and an information theoretic method for discovering the building blocks in specific networks is proposed.
Abstract: The most widely used techniques for community detection in networks, including methods based on modularity, statistical inference, and information theoretic arguments, all work by optimizing objective functions that measure the quality of network partitions. There is a good case to be made, however, that one should not look solely at the single optimal community structure under such an objective function but rather at a selection of high-scoring structures. If one does this, one typically finds that the resulting structures show considerable variation, which could be taken as evidence that these community detection methods are unreliable, since they do not appear to give consistent answers. Here we argue that, upon closer inspection, the structures found are in fact consistent in a certain way. Specifically, we show that they can all be assembled from a set of underlying "building blocks," groups of network nodes that are usually found together in the same community. Different community structures correspond to different arrangements of blocks, but the blocks themselves are largely invariant. We propose an information theoretic method for discovering the building blocks in specific networks and demonstrate it with several example applications. We conclude that traditional community detection does in fact give a significant amount of insight into network structure.
TL;DR: It is shown that protein distributions are well approximated by the solution of implicit models (a negative binomial) when the mean number of mRNAs produced per cycle is low and the cell cycle length variability is large and when these conditions are not met, the distributions are either almost bimodal or else display very flat regions near the mode and cannot be described by implicit models.
Abstract: The bulk of stochastic gene expression models in the literature do not have an explicit description of the age of a cell within a generation and hence they cannot capture events such as cell division and DNA replication. Instead, many models incorporate the cell cycle implicitly by assuming that dilution due to cell division can be described by an effective decay reaction with first-order kinetics. If it is further assumed that protein production occurs in bursts, then the stationary protein distribution is a negative binomial. Here we seek to understand how accurate these implicit models are when compared with more detailed models of stochastic gene expression. We derive the exact stationary solution of the chemical master equation describing bursty protein dynamics, binomial partitioning at mitosis, age-dependent transcription dynamics including replication, and random interdivision times sampled from Erlang or more general distributions; the solution is different for single lineage and population snapshot settings. We show that protein distributions are well approximated by the solution of implicit models (a negative binomial) when the mean number of mRNAs produced per cycle is low and the cell cycle length variability is large. When these conditions are not met, the distributions are either almost bimodal or else display very flat regions near the mode and cannot be described by implicit models. We also show that for genes with low transcription rates, the size of protein noise has a strong dependence on the replication time, it is almost independent of cell cycle variability for lineage measurements, and increases with cell cycle variability for population snapshot measurements. In contrast for large transcription rates, the size of protein noise is independent of replication time and increases with cell cycle variability for both lineage and population measurements.
TL;DR: A new set of features used to transform the raw trajectories data into input vectors required by the classifiers are presented and the resulting models are applied to real data for G protein-coupled receptors and G proteins.
Abstract: Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of molecules in living cells. Inferring the character of their dynamics is important, because it determines the organization and functions of the cells. For this reason, one of the first steps in the analysis of SPT data is the identification of the diffusion type of the observed particles. The most popular method to identify the class of a trajectory is based on the mean-square displacement (MSD). However, due to its known limitations, several other approaches have been already proposed. With the recent advances in algorithms and the developments of modern hardware, the classification attempts rooted in machine learning (ML) are of particular interest. In this work, we adopt two ML ensemble algorithms, i.e., random forest and gradient boosting, to the problem of trajectory classification. We present a new set of features used to transform the raw trajectories data into input vectors required by the classifiers. The resulting models are then applied to real data for G protein-coupled receptors and G proteins. The classification results are compared to recent statistical methods going beyond MSD.
TL;DR: This work proposes a cycle-consistent generative adversarial network (CycleGAN)-based SR approach for real-world rock MCT images, namely, SRCycleGAN, which can model the mapping between rock M CT images at different resolutions and shows good agreement with the targets in terms of both the visual quality and the statistical parameters.
Abstract: Digital rock imaging plays an important role in studying the microstructure and macroscopic properties of rocks, where microcomputed tomography (MCT) is widely used. Due to the inherent limitations of MCT, a balance should be made between the field of view (FOV) and resolution of rock MCT images-a large FOV at low resolution (LR) or a small FOV at high resolution (HR). However, large FOV and HR are both expected for reliable analysis results in practice. Super-resolution (SR) is an effective solution to break through the mutual restriction between the FOV and resolution of rock MCT images, for it can reconstruct an HR image from a LR observation. Most of the existing SR methods cannot produce satisfactory HR results on real-world rock MCT images. One of the main reasons for this is that paired images are usually needed to learn the relationship between LR and HR rock images. However, it is challenging to collect such a dataset in a real scenario. Meanwhile, the simulated datasets may be unable to accurately reflect the model in actual applications. To address these problems, we propose a cycle-consistent generative adversarial network (CycleGAN)-based SR approach for real-world rock MCT images, namely, SRCycleGAN. In the off-line training phase, a set of unpaired rock MCT images is used to train the proposed SRCycleGAN, which can model the mapping between rock MCT images at different resolutions. In the on-line testing phase, the resolution of the LR input is enhanced via the learned mapping by SRCycleGAN. Experimental results show that the proposed SRCycleGAN can greatly improve the quality of simulated and real-world rock MCT images. The HR images reconstructed by SRCycleGAN show good agreement with the targets in terms of both the visual quality and the statistical parameters, including the porosity, the local porosity distribution, the two-point correlation function, the lineal-path function, the two-point cluster function, the chord-length distribution function, and the pore size distribution. Large FOV and HR rock MCT images can be obtained with the help of SRCycleGAN. Hence, this work makes it possible to generate HR rock MCT images that exceed the limitations of imaging systems on FOV and resolution.
TL;DR: By using a general approach to a two- and three-cell battery, the results suggest that entanglement is not the main resource in quantum batteries, where there is a nontrivial correlation-coherence tradeoff as a resource for the high efficiency of such quantum devices.
Abstract: Quantum devices are systems that can explore quantum phenomena, such as entanglement or coherence, for example, to provide some enhancement performance concerning their classical counterparts In particular, quantum batteries are devices that use entanglement as the main element in their high performance in powerful charging In this paper, we explore quantum battery performance and its relationship with the amount of entanglement that arises during the charging process By using a general approach to a two- and three-cell battery, our results suggest that entanglement is not the main resource in quantum batteries, where there is a nontrivial correlation-coherence tradeoff as a resource for the high efficiency of such quantum devices