On weighted structured total least squares

In this contribution we extend the result of (Markovsky et. al, SIAM J. of Matrix Anal. and Appl., 2005) to the case of weighted cost function. It is shown that the computational complexity of the proposed algorithm is preserved linear in the sample size when the weight matrix is banded with bandwidth that is independent of the sample size

Algorithms and literate programs for weighted low-rank approximation with missing data

Linear models identification from data with missing values is posed as a weighted low-rank approximation problem with weights related to the missing values equal to zero. Alternating projections and variable projections methods for solving the resulting problem are outlined and implemented in a literate programming style, using Matlab/Octave's scripting language. The methods are evaluated on synthetic data and real data from the MovieLens data sets

Data-based system representations from irregularly measured data

Non-parametric representations of dynamical systems based on the image of a Hankel matrix of data are extensively used for data-driven control. However, if samples of data are missing, obtaining such representations becomes a difficult task. By exploiting the kernel structure of Hankel matrices of irregularly measured data generated by a linear time-invariant system, we provide computational methods for which any complete finite-length behavior of the system can be obtained. For the special case of periodically missing outputs, we provide conditions on the input such that the former result is guaranteed. We illustrate with an example how the resulting representation provides a more computationally efficient method for low-rank matrix completion when compared to an alternative method.Comment: submitted to IEEE Transactions on Automatic Contro

Identification from data with periodically missing output samples

The identification problem in case of data with missing values is challenging and currently not fully understood. For example, there are no general nonconservative identifiability results, nor provably correct data efficient methods. In this paper, we consider a special case of periodically missing output samples, where all but one output sample per period may be missing. The novel idea is to use a lifting operation that converts the original problem with missing data into an equivalent standard identification problem. The key step is the inverse transformation from the lifted to the original system, which requires computation of a matrix root. The well-posedness of the inverse transformation depends on the eigenvalues of the system. Under an assumption on the eigenvalues, which is not verifiable from the data, and a persistency of excitation-type assumption on the data, the method based on lifting recovers the data-generating system. (Preprint submitted to Automatica)European Research Council (ERC)/European Union’s Horizon 2020 research and innovation programme/948679/E

Berry Phase of a Resonant State

We derive closed analytical expressions for the complex Berry phase of an open quantum system in a state which is a superposition of resonant states and evolves irreversibly due to the spontaneous decay of the metastable states. The codimension of an accidental degeneracy of resonances and the geometry of the energy hypersurfaces close to a crossing of resonances differ significantly from those of bound states. We discuss some of the consequences of these differences for the geometric phase factors, such as: Instead of a diabolical point singularity there is a continuous closed line of singularities formally equivalent to a continuous distribution of `magnetic' charge on a diabolical circle; different classes of topologically inequivalent non-trivial closed paths in parameter space, the topological invariant associated to the sum of the geometric phases, dilations of the wave function due to the imaginary part of the Berry phase and others.Comment: 28 pages Latex, three uuencoded postcript figure

Diffusion bonding of TiC or TiB reinforced Ti–6Al–4V matrix composites to conventional Ti–6Al–4V alloy

The diffusion bonding of conventional alloy Ti–6Al–4V (Ti-64) and composites of this alloy with 10% of TiC or TiB fabricated using blended elemental powder metallurgy was successfully carried out at 850–1000°C, with a holding time of 60 min under 0.7–1.5 MPa pressure. The metallographic and electron backscattered diffraction studies as well as the bending and microhardness tests across the bonds are presented as the evidence of joint integrity. The selected experimental parameters do not cause undesirable structural changes (degradation) in the base metals adjacent to the bond interface. Particle reinforcement at ∼10% did not appear to modify bonding parameters when compared to the unreinforced Ti-64 alloy

Dynamic behavior analysis via structured rank minimization

Human behavior and affect is inherently a dynamic phenomenon involving temporal evolution of patterns manifested through a multiplicity of non-verbal behavioral cues including facial expressions, body postures and gestures, and vocal outbursts. A natural assumption for human behavior modeling is that a continuous-time characterization of behavior is the output of a linear time-invariant system when behavioral cues act as the input (e.g., continuous rather than discrete annotations of dimensional affect). Here we study the learning of such dynamical system under real-world conditions, namely in the presence of noisy behavioral cues descriptors and possibly unreliable annotations by employing structured rank minimization. To this end, a novel structured rank minimization method and its scalable variant are proposed. The generalizability of the proposed framework is demonstrated by conducting experiments on 3 distinct dynamic behavior analysis tasks, namely (i) conflict intensity prediction, (ii) prediction of valence and arousal, and (iii) tracklet matching. The attained results outperform those achieved by other state-of-the-art methods for these tasks and, hence, evidence the robustness and effectiveness of the proposed approach