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This paper studies the expressive and computational power of discrete Ordinary Differential Equations (ODEs), a.k.a. (Ordinary) Difference Equations. It presents a new framework using these equations as a central tool for computation and…
Self-assembly of particles with short-range attraction and long-range repulsion (SALR) interactions on a flat and on a spherical surface is compared. Molecular dynamics (MD) simulations are performed for the two systems having the same area…
Topological disclinations, crystallographic defects that break rotation lattice symmetry, have attracted great interest and exhibited wide applications in cavities, waveguides, and lasers. However, topological disclinations have thus far…
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems. In this work, we explain the mathematical assumptions and detailed…
Quantum gas microscopy has developed into a powerful tool to explore strongly correlated quantum systems. However, discerning phases with topological or off-diagonal long range order requires the ability to extract these correlations from…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
This paper describes the notion of \sigma -symmetry, which extends the one of \lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider…
Orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has recently emerged as a promising paradigm for ensuring reliable communications in doubly-selective channels. This work investigates the spectra and orthogonality…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
Orientation estimation is a fundamental task in 3D shape analysis which consists of estimating a shape's orientation axes: its side-, up-, and front-axes. Using this data, one can rotate a shape into canonical orientation, where its…
In the Mott insulating phase of the transition metal oxides, the effective orbital-orbital interaction is directional both in the orbital space and in the real space. We discuss a classical realization of directional coupling in two…
Light beams can be characterized by their complex spatial profiles in both intensity and phase. Analogous to time signals, which can be decomposed into multiple orthogonal frequency functions, a light beam can also be decomposed into a set…
We elaborate on the recently proposed orthogonal time frequency space (OTFS) modulation technique, which provides significant advantages over orthogonal frequency division multiplexing (OFDM) in Doppler channels. We first derive the…
We study the problem of identification of linear dynamical system from a single trajectory, via excitations of isotropic Gaussian. In stark contrast with previously reported results, Ordinary Least Squares (OLS) estimator for even…
We present a method that generalizes the periodic orbit dividing surface construction for Hamiltonian systems with three or more degrees of freedom. We construct a torus using as a basis a periodic orbit and we extend this to a $2n-2$…
We show that phase separation in ordered polar active fluids belongs to a new universality class. This describes large collections of self-propelled entities (``flocks"), all spontaneously moving in the same direction, in which attractive…
We develop a cosmological model where primordial inflation is driven by a 'solid', defined as a system of three derivatively coupled scalar fields obeying certain symmetries and spontaneously breaking a certain subgroup of these. The…
Occupancy prediction infers fine-grained 3D geometry and semantics from camera images of the surrounding environment, making it a critical perception task for autonomous driving. Existing methods either adopt dense grids as scene…
Deep learning has led to remarkable strides in scene understanding with panoptic segmentation emerging as a key holistic scene interpretation task. However, the performance of panoptic segmentation is severely impacted in the presence of…