Related papers: Network of localized magnetic textures revealed us…

We propose a practical computational framework for detecting structural changes in parameter-dependent topological data. In many applications, such as time-series data analysis, anomaly detection, and monitoring of systems under changing…

We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function.…

Spatially-embedded complex networks, such as nervous systems, the Internet and transportation networks, generally have non-trivial topological patterns of connections combined with nearly minimal wiring costs. However the growth rules…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

The concept of metastability has caused a lot of interest in recent years. The spectral decomposition of the generator matrix of a stochastic network exposes all of the transition processes in the system. The assumption of the existence of…

We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system…

Magnetic textures are central to emerging spintronic and unconventional computing technologies due to their rich dynamics, topological properties and nanoscale dimensions. A major challenge remains achieving tunable, reversible, and…

Motivation: Many biochemical pathways are known, but the numerous parameters required to correctly explore the dynamics of the pathways are not known. For this reason, algorithms that can make inferences by looking at the topology of a…

The permutation symmetry of neurons in each layer of a deep neural network gives rise not only to multiple equivalent global minima of the loss function, but also to first-order saddle points located on the path between the global minima.…

One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…

The idea of minimum curvilinearity (MC) is that the hidden geometry of complex networks, in particular when they are sufficiently sparse, clustered, small-world and heterogeneous, can be efficiently navigated using the minimum spanning tree…

We analyze the eigenstates of a two-dimensional lattice with additional harmonic confinement in the presence of an artificial magnetic field. While the softness of the confinement makes a distinction between bulk and edge states difficult,…

State-specific approximations can provide an accurate representation of challenging electronic excitations by enabling relaxation of the electron density. While state-specific wave functions are known to be local minima or saddle points of…

This paper focuses on characterizing the energy profile along pathways connecting different regions of configuration space in the context of a prototypical glass model, the pure spherical $p$-spin model with $p=3$. The study investigates…

We study the connected ensemble, a statistical-mechanics framework that characterizes the formation of low-loss paths in rugged landscapes. First introduced in a previous paper, this ensemble allows one to identify when a network can be…

We investigate saddle point configurations in spherical ferromagnets with perpendicular anisotropy. These are modeled by a micromagnetic energy functional on the unit sphere that leads to the emergence of the so-called curvature induced…

The properties of higher-index saddle points have been invoked in recent theories of the dynamics of supercooled liquids. Here we examine in detail a mapping of configurations to saddle points using minimization of $|\nabla E|^2$, which has…

In this paper, we present a general framework for constructively proving the existence and stability of stationary localized 1D solutions and saddle-node bifurcations in activator--inhibitor systems using computer-assisted proofs.…

In this article, we present a novel approach to reconstruct the topology of networked linear dynamical systems with latent nodes. The network is allowed to have directed loops and bi-directed edges. The main approach relies on the unique…

Within the racetrack memory paradigm, systems exploiting magnetic guiding potentials instead of geometrical ones, allow for enhancing the versatility of the final devices adding magnetic reconfigurable capabilities. Hard/soft magnetic…