Related papers: Extremal Configurations of Hinge Structures
The recent discovery of superconductivity under high pressure in the ladder compound BaFe$_2$S$_3$ has opened a new field of research in iron-based superconductors with focus on quasi one-dimensional geometries. In this publication, using…
Lessons from Anderson localization highlight the importance of dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focussed on the phenomenon in one dimension using techniques…
We prove that any finite collection of polygons of equal area has a common hinged dissection. That is, for any such collection of polygons there exists a chain of polygons hinged at vertices that can be folded in the plane continuously…
Estimating a 3D human pose has proven to be a challenging task, primarily because of the complexity of the human body joints, occlusions, and variability in lighting conditions. In this paper, we introduce a higher-order graph convolutional…
The cutoff phenomenon describes a sharp transition in the convergence of a Markov chain to equilibrium. In recent work, the authors established cutoff and its location for the stochastic Ising model on the $d$-dimensional torus $(Z/nZ)^d$…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
This paper introduces a general regularized thresholded least-square procedure estimating a structured signal $\theta_*\in\mathbb{R}^d$ from the following observations: $y_i = f(\langle\mathbf{x}_i, \theta_*\rangle,…
Many vertebrate motor and sensory systems decussate, or cross the midline to the opposite side of the body. The successful crossing of millions of axons during development requires a complex of tightly controlled regulatory processes.…
We first introduce a configuration of arbitrary isogonal conjugates related to a known property concerning the spiral center of two pairs of isogonal conjugates. We then consider a special case where two conics are tangent at exactly two…
High-order meshes are crucial for achieving optimal convergence rates in curvilinear domains, preserving symmetry, and aligning with key flow features in moving mesh simulations, but their quality is challenging to control. In prior work,…
A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge selective surface (electric membrane, electrode, or system of micro-/nanochannels) is carried out and analyzed. A special finite-difference…
Contact can be conceptualized as a set of constraints imposed on two bodies that are interacting with one another in some way. The nature of a contact, whether a point, line, or surface, dictates how these bodies are able to move with…
Rigidity of the interaction graph is a fundamental condition for achieving the desired formation which can be defined in terms of distance or bearing constraints between agents. In this paper, for reaching a unique formation with the same…
Commutative rings of one-dimensional difference operators of rank l>1 and their deformations are effectively constructed. Our analytical constructions are based on the so-called ''Tyurin parameters'' for the stable framed holomorphic vector…
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…
A hybrid continuum robot design is introduced that combines a proximal tendon-actuated section with a distal telescoping section comprised of permanent-magnet spheres actuated using an external magnet. While, individually, each section can…
We study a gauge theory in a 5D warped space via the dimensional deconstruction that a higher dimensional gauge theory is constructed from a moose of 4D gauge groups. By the AdS/CFT correspondence, a 5D warped gauge theory is dual to a 4D…
We study the problem of determining optimal coordinated motions for two disc robots in an otherwise obstacle-free plane. Using the total path length traced by the two disc centres as a measure of distance, we give an exact characterization…
We study chiral models in one spatial dimension, both static and periodically driven. We demonstrate that their topological properties may be read out through the long time limit of a bulk observable, the mean chiral displacement. The…
We investigate the build-up of quasi-long-range order in the XX chain with transverse magnetic field at finite size. As the field is varied, the ground state of the system displays multiple level crossings producing a sequence of…