Related papers: From Local Atomic Environments to Molecular Inform…
Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…
This study investigates entropy's potential for analyzing scientific research patterns across disciplines. Originating from thermodynamics, entropy now measures uncertainty and diversity in information systems. We examine Shannon Entropy,…
This thesis is a multidisciplinary contribution to the information theory of single-particle Coulomb systems in their relativistic and not relativistic description, to the theory of special functions of mathematical physics with the…
Molecular data systems have the potential to store information at dramatically higher density than existing electronic media. Some of the first experimental demonstrations of this idea have used DNA, but nature also uses a wide diversity of…
We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that…
In this work, we present a new computational approach to characterize and classify molecular packing in the solid states. The key idea is to project each neighboring molecule (or short contact) from the centered molecule into a unit sphere…
Estimating mutual information from observed samples is a basic primitive, useful in several machine learning tasks including correlation mining, information bottleneck clustering, learning a Chow-Liu tree, and conditional independence…
In this work, we introduce Entropy Area Score (EAS), a simple yet effective metric to quantify uncertainty in the answer generation process of reasoning large language models (LLMs). EAS requires neither external models nor repeated…
Information entropy is applied to the analysis of time series generated by dynamical systems. Complexity of a temporal or spatio-temporal signal is defined as the difference between the sum of entropies of the local linear regions of the…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
A definition of entropy via the Kolmogorov algorithmic complexity is discussed. As examples, we show how the meanfield theory for the Ising model, and the entropy of a perfect gas can be recovered. The connection with computations are…
Computer simulations have been employed in recent years to evaluate the configurational entropy changes in model glass-forming liquids. We consider two methods, both of which involve the calculation of the `intra-basin' entropy as a means…
We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
It is proposed that nuclear (or electron) spins in a trapped molecule would be well isolated from the environment and the state of each spin can be measured by means of mechanical detection of magnetic resonance. Therefore molecular traps…
The predictive accuracy of Machine Learning (ML) models of molecular properties depends on the choice of the molecular representation. Based on the postulates of quantum mechanics, we introduce a hierarchy of representations which meet…
Enhanced sampling algorithms have emerged as powerful methods to extend the utility of molecular dynamics simulations and allow the sampling of larger portions of the configuration space of complex systems in a given amount of simulation…
Electronic transitions involving core-level orbitals offer a localized, atomic-site and element specific peek window into statistical systems such as molecular liquids. Although formally understood, the complex relation between structure…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (iid). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of…