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Outliers contaminating data sets are a challenge to statistical estimators. Even a small fraction of outlying observations can heavily influence most classical statistical methods. In this paper we propose generalized spherical principal…
Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces,…
We present a method for computing locally varying nonlinear mechanical properties in particle simulations of amorphous solids. Plastic rearrangements outside a probed region are suppressed by introducing an external field that directly…
This paper explores features of an idealized mathematical machine (algorithm) that would be capable of reconstructing the gravitational nature (the multipolar structure or spacetime metric) of a compact object, by observing gravitational…
Useful relations describing arbitrary parameters of given quantum systems can be derived from simple physical constraints imposed on the vectors in the corresponding Hilbert space. This is well known and it usually proceeds by partitioning…
In these lectures I cover a number of topics in cosmological data analysis. I concentrate on general techniques which are common in cosmology, or techniques which have been developed in a cosmological context. In fact they have very general…
The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity…
A classical approach for surface classification is to find a compact algebraic representation for each surface that would be similar for objects within the same class and preserve dissimilarities between classes. We introduce Self…
Because of its nonequilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain…
This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…
This paper describes the Conic Operator Splitting Method (COSMO) solver, an operator splitting algorithm for convex optimisation problems with quadratic objective function and conic constraints. At each step the algorithm alternates between…
Strictly incoherent operations (SIO) proposed in [Phys. Rev. Lett. 116, 120404 (2016)] are promising to be a good candidate of free operations in the resource theory of quantum coherence, setting against the central role of local operations…
Time-translation symmetry strongly constrains physical dynamics, yet systematic characterization for continuous-variable systems lags behind its discrete-variable counterpart. We close this gap by providing a rigorous classification of…
The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
Geospace phenomena such as the aurora, plasma motion, ionospheric currents and associated magnetic field disturbances are highly organized by Earth's main magnetic field. This is due to the fact that the charged particles that comprise…
When modeling physical properties of molecules with machine learning, it is desirable to incorporate $SO(3)$-covariance. While such models based on low body order features are not complete, we formulate and prove general completeness…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…