Related papers: Parameter identification using the Hilbert transfo…
Calculating dipole moments with high-order basis sets is generally only possible for the light molecules, such as water. A simple, yet highly effective strategy of obtaining high-order dipoles with small, computationally less expensive…
Recent work has shown that probabilistic models based on pairwise interactions-in the simplest case, the Ising model-provide surprisingly accurate descriptions of experiments on real biological networks ranging from neurons to genes.…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of a matrix from its entries is presented. The main idea behind the method is based on the nested representation and the maximum-volume principle to select…
The theoretical information threshold for the planted clique problem is $2\log_2(N)$, however no polynomial algorithm is known to recover a planted clique of size $O(N^{1/2-\epsilon})$, $\epsilon>0$. In this paper we will apply a standard…
The paper addresses the model reduction problem for linear and nonlinear systems using the notion of least squares moment matching. For linear systems, the main idea is to approximate a transfer function by ensuring that the interpolation…
Quantization is the process of mapping an input signal from an infinite continuous set to a countable set with a finite number of elements. It is a non-linear irreversible process, which makes the traditional methods of system…
We propose a perturbative improvement of the hierarchical approximation for gaussian models. The procedure is based on a relabeling of the momenta which allows one to express the symmetries of the hierarchical model using a simple…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
Modern pattern recognition tasks use complex algorithms that take advantage of large datasets to make more accurate predictions than traditional algorithms such as decision trees or k-nearest-neighbor better suited to describe simple…
Replacing the quadratic proximal penalty familiar from Hilbert spaces by an unbalanced optimal transport distance, we develop forward-backward type optimisation methods in spaces of Radon measures. We avoid the actual computation of the…
In this paper, we address the model reduction problem for linear hybrid systems via the interconnection-based technique called moment matching. We consider two classical interconnections, namely the direct and swapped interconnections, in…
A simple least-squares optimisation enables the determination of the spectrum for irregularly sampled data that is readily reconstructed using an adjoint transformation of the Non-Uniform Fast Fourier Transform (NFFT). This is an…
Solving semiparametric models can be computationally challenging because the dimension of parameter space may grow large with increasing sample size. Classical Newton's method becomes quite slow and unstable with intensive calculation of…
In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
We propose the use of the probability integral transform (PIT) for model validation in point process models. The simple PIT diagnostics assess the calibration of the model and can detect inconsistencies in both the intensity and the…
We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology develops high dimensional data understanding in the point process setting. The method is based on modelling the…
Biclustering is a class of techniques that simultaneously clusters the rows and columns of a matrix to sort heterogeneous data into homogeneous blocks. Although many algorithms have been proposed to find biclusters, existing methods suffer…
Optimal model reduction for large-scale linear dynamical systems is studied. In contrast to most existing works, the systems under consideration are not required to be stable, neither in discrete nor in continuous time. As a consequence,…
System identification is a key enabling component for the implementation of quantum technologies, including quantum control. In this paper, we consider the class of passive linear input-output systems, and investigate several basic…