Controlling complex tasks in robotic systems, such as circular motion for cleaning or following curvy lines, can be dealt with using nonlinear vector fields. This article introduces a novel approach called the rotational obstacle avoidance method (ROAM) fo ...
These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...
We investigate the properties of a frustrated spin-5/2 chain with next-nearest-neighbor two- and three-site interactions, with two questions in mind: the nature of the transition into the dimerized phase induced by the three-site interaction, and the possi ...
Determination of the local void fraction in BWRs from in-core neutron noise measurements requires the knowledge of the axial velocity of the void. The purpose of this paper is to revisit the problem of determining the axial void velocity profile from the t ...
Consider F is an element of C(RxX,Y) such that F(lambda, 0) = 0 for all lambda is an element of R, where X and Y are Banach spaces. Bifurcation from the line Rx{0} of trivial solutions is investigated in cases where F(lambda, center dot ) need not be Frech ...
We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with L layers of minimal widths r1∗,…,rL−1∗ reaches a zero-loss minimum at $ r_1^*! \c ...
Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...
We consider the singular set in the thin obstacle problem with weight vertical bar x(n +1)vertical bar(a) for a epsilon (-1, 1), which arises as the local extension of the obstacle problem for the fractional Laplacian (a nonlocal problem). We develop a ref ...
We consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Lojasiewicz inequality. The difficulty lies in the fact that, ...
We consider bifurcation from the line of trivial solutions for a nonlinear eigenvalue problem on a bounded open subset, Omega, of R-N with N >= 3, containing 0. The leading term is a degenerate elliptic operator of the form L(u) = del . A del u where A is ...
It is well known that an N-parameter d-dimensional Brownian sheet has no k-multiple points when (k - 1)d > 2kN, and does have such points when (k - 1)d < 2kN. We complete the study of the existence of k-multiple points by showing that in the critical cases ...
For Banach spaces X and Y, we consider bifurcation from the line of trivial solutions for the equation F(lambda, u) = 0, where F : R x X -> Y with F(lambda, 0) = 0 for all lambda is an element of R. The focus is on the situation where F(lambda, center dot) ...
Royal Society of Edinburgh Scotland Foundation, Cambridge2014
We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An N-parameter Brownian sheet in R-d has double points if and only if d < 4N. In particular, in the critical case where d = 4N, the Brownian sheet does not hav ...
The depolarization temperature T-d of piezoelectric materials is an important figure of merit for their application at elevated temperatures. Until now, there are several methods proposed in the literature to determine the depolarization temperature of pie ...
In this thesis we contribute to the inverse kinematics solution of serial positional manipulators with three rotational joints (3R). This type of linkage is frequently used for 6R manipulators, where three – mostly the last – joint axes intersect at one po ...
