Related Experiment Video
Updated: May 17, 2026
11:52
Temporal Ordering of Dynamic Expression Data from Detailed Spatial Expression Maps
Published on: February 9, 2017
Maximum entropy temporal networks
1University College London, Department of Computer Science, London, United Kingdom.
Physical Review. E
|May 16, 2026
Summary
This study introduces a maximum-entropy framework for continuous-time temporal networks. This approach models network dynamics using global time processes and static edge probabilities, improving log-likelihood over standard methods.
Area of Science:
- Network Science
- Statistical Physics
- Data Science
Background:
- Temporal networks capture time-stamped interactions, but continuous-time modeling remains challenging.
- Existing models often struggle with the continuous nature of temporal network data.
Purpose of the Study:
- To develop a novel maximum-entropy approach for modeling continuous-time temporal networks.
- To provide a modular and interpretable framework for analyzing temporal network dynamics.
Main Methods:
- Introduced a maximum-entropy framework with constraints leading to a time-edge factorization.
- Derived nonhomogeneous Poisson process (NHPP) intensities from path entropy optimization.
- Developed effective generative models based on the maximum-entropy ensemble.
Main Results:
- The proposed framework yields closed-form log-likelihoods and expectations for network properties.
- NHPP intensities derived from maximum entropy improve log-likelihood compared to generic Poisson processes.
- Maximum-entropy edge labels successfully recover strength constraints and unique-degree curves.
Conclusions:
- The maximum-entropy approach offers a robust method for continuous-time temporal network analysis.
- This framework connects NHPP modeling with maximum-entropy principles and provides interpretable generative models.
- Future work can integrate this approach with advanced methods like Hawkes processes and graph neural networks.
Related Concept Videos
01:10Entropy Change in Reversible Processes
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
02:39Entropy
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
01:18Entropy
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
01:23Absolute Entropies and the Third Law of Thermodynamics
Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...
01:21Entropy Changes Accompanying Specific Processes
Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
01:14The Entropy as a State Function
Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...