Related papers: Entropy bounds for Glass networks
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…
Bounds on the entropy of patterns of sequences generated by independently identically distributed (i.i.d.) sources are derived. A pattern is a sequence of indices that contains all consecutive integer indices in increasing order of first…
A mesoscopic model is proposed to explain the anomalous dynamics in a supercooled liquid as its glass transition temperature is approached from above. The model is based on the assumption of $\beta$ organized $\alpha$ process, with the…
Boolean control networks (BCNs) are discrete-time dynamical systems with Boolean state-variables and inputs that are interconnected via Boolean functions. BCNs are recently attracting considerable interest as computational models for…
Near-critical quantum circuits are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from the environment. The design of…
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
The multiplicative depth of a logic network over the gate basis $\{\land, \oplus, \neg\}$ is the largest number of $\land$ gates on any path from a primary input to a primary output in the network. We describe a dynamic programming based…
We present a simple setup to implement truly random number generator based on the measurement of the laser phase noise. From the entropy point of view, we estimate the number of truly random bits that can be extracted from the sampled Byte.…
We study the effect of intrinsic noise on the thermodynamic balance of complex chemical networks subtending cellular metabolism and gene regulation. A topological network property called deficiency, known to determine the possibility of…
We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world…
The configurational entropy is one of the most important thermodynamic quantities characterizing supercooled liquids approaching the glass transition. Despite decades of experimental, theoretical, and computational investigation, a widely…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
A computation of the dynamical structure factor of topologically disordered systems, where the disorder can be described in terms of euclidean random matrices, is presented. Among others, structural glasses and supercooled liquids belong to…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
Generative Adversarial Networks (GANs) can produce high-quality samples, but do not provide an estimate of the probability density around the samples. However, it has been noted that maximizing the log-likelihood within an energy-based…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
We propose a new numerical method to estimate the fault tolerance of failure modes in digital circuit structures with a generative network sampling technique. From a random input of generated bitwise configurations of ideally digitalised…
Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
A glass is a non-equilibrium thermodynamic state whose physical properties depend on time. Glass formation from the melt, as well as the inverse process of liquid structural recovery from the glass are non-equilibrium processes. A positive…