Related papers: Optimal measures for p-frame energies on spheres
We construct optimal measurements, achieving the ultimate precision predicted by quantum theory, for the simultaneous estimation of centroid, separation, and relative intensities of two incoherent point sources using a linear optical…
This is the first of a pair of papers which address the problem of measuring the unredshifted power spectrum in optimal fashion from a survey of galaxies, with arbitrary geometry, for Gaussian or non-Gaussian fluctuations, in real or…
We describe a measure quantization procedure i.e., an algorithm which finds the best approximation of a target probability law (and more generally signed finite variation measure) by a sum of $Q$ Dirac masses ($Q$ being the quantization…
In the quest to unlock the maximum potential of quantum sensors, it is of paramount importance to have practical measurement strategies that can estimate incompatible parameters with best precisions possible. However, it is still not known…
Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to…
Constraint Programming is a powerful paradigm to model and solve combinatorial problems. While there are many kinds of constraints, the table constraint is perhaps the most significant-being the most well-studied and has the ability to…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
We present an instance of the optimal sensor scheduling problem with the additional relaxation that our observer makes active choices whether or not to observe and how to observe. We mask the nodes in a directed acyclic graph of the model…
In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on…
High precision measurements are essential to solve major scientific and technological challenges, from gravitational wave detection to healthcare diagnostics. Quantum sensing delivers greater precision, but an in-depth optimisation of…
Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner…
We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
We obtain new restrictions on the linear programming bound for sphere packing, by optimizing over spaces of modular forms to produce feasible points in the dual linear program. In contrast to the situation in dimensions 8 and 24, where the…
We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…
We introduce a new technique to optimize a linear cost function subject to a one-dimensional affine homogeneous quadratic integral inequality, i.e., the requirement that a homogeneous quadratic integral functional, affine in the…