Related papers: Controlling energy landscapes with correlations be…
By dividing potential energy landscapes into basins of attractions surrounding minima and linking those basins that are connected by transition state valleys, a network description of energy landscapes naturally arises. These networks are…
We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others. This notion…
It has previously been shown that the network of connected minima on a potential energy landscape is scale-free, and that this reflects a power-law distribution for the areas of the basins of attraction surrounding the minima. Here, we set…
The ability to explain decisions made by machine learning models remains one of the most significant hurdles towards widespread adoption of AI in highly sensitive areas such as medicine, cybersecurity or autonomous driving. Great interest…
Many cognitive processes, including working memory, recruit multiple distributed interacting brain regions to encode information. How to understand the underlying cognition function mechanism of working memory is a challenging problem,…
Regime shifts in biology, ecology, and other complex systems are often interpreted through stability landscapes and early warning signals that implicitly assume dynamics without memory effects. Yet many real systems exhibit these effects,…
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the…
Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other…
Potential energy landscapes can be represented as a network of minima linked by transition states. The community structure of such networks has been obtained for a series of small Lennard-Jones clusters. This community structure is compared…
In systems characterized by a rough potential energy landscape, local energetic minima and saddles define a network of metastable states whose topology strongly influences the dynamics. Changes in temperature, causing the merging and…
We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamics and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A…
Free energy landscapes encode the kinetics, intermediates, and transition states that govern molecular processes and are thus a key target of single biomolecule research. Typical approaches to deriving optimal, error-minimizing,…
We apply energy landscape methods to digital alchemy, defining a system in which the parameters of the potential are treated as degrees of freedom. Using geometrical optimisation, we locate minima and transition states on the landscape for…
The complexity and unpredictability of postbuckling responses in even simple thin shells have raised great challenges to emerging technologies exploiting buckling transitions. Here we comprehensively survey the buckling landscapes to show…
In order to efficiently explore the chemical space of all possible small molecules, a common approach is to compress the dimension of the system to facilitate downstream machine learning tasks. Towards this end, we present a data driven…
Training neural networks involves finding minima of a high-dimensional non-convex loss function. Knowledge of the structure of this energy landscape is sparse. Relaxing from linear interpolations, we construct continuous paths between…
Energy landscapes provide a valuable means for studying the folding dynamics of short RNA molecules in detail by modeling all possible structures and their transitions. Higher abstraction levels based on a macro-state decomposition of the…
Many problems in physics, material sciences, chemistry and biology can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. Well-known examples include phase transitions of…
The existence and stability of the universality class associated to local minimal energy landscapes is investigated. Using extensive numerical simulations, we first study the dependence on a parameter $\gamma$ of a partial differential…
We provide an up-to-date view of the structure of the energy landscape of the low autocorrelation binary sequences problem, a typical representative of the $NP$-hard class. To study the landscape features of interest we use the local optima…