On Chiral Symmetry Restoration at Finite Density in Large N_c QCD

At large N_c, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is on aspects of chiral symmetry breaking and its possible restoration that are by construction independent of the nature of translational symmetry breaking---namely spatial averages of chiral order parameters. A system will be considered to be chirally restored provided all spatially-averaged chiral order parameters are zero. A critical question is whether chiral restoration in this sense is possible for phases in which chiral order parameters are locally non-zero but whose spatial averages all vanish. We show that this is not possible unless all chirally-invariant observables are spatially uniform. This result is first derived for Skyrme-type models, which are based on a nonlinear sigma model and by construction break chiral symmetry on a point-by-point basis. A no-go theorem for chiral restoration (in the average sense) for all models of this type is obtained by showing that in these models there exist chirally symmetric order parameters which cannot be spatially uniform. Next we show that the no-go theorem applies to large N_c QCD in any phase which has a non-zero but spatially varying chiral condensate. The theorem is demonstrated by showing that in a putative chirally-restored phase, the field configuration can be reduced to that of a nonlinear sigma model.Comment: 12 pages, 1 tabl

Fault detection in operating helicopter drive train components based on support vector data description

The objective of the paper is to develop a vibration-based automated procedure dealing with early detection of mechanical degradation of helicopter drive train components using Health and Usage Monitoring Systems (HUMS) data. An anomaly-detection method devoted to the quantification of the degree of deviation of the mechanical state of a component from its nominal condition is developed. This method is based on an Anomaly Score (AS) formed by a combination of a set of statistical features correlated with specific damages, also known as Condition Indicators (CI), thus the operational variability is implicitly included in the model through the CI correlation. The problem of fault detection is then recast as a one-class classification problem in the space spanned by a set of CI, with the aim of a global differentiation between normal and anomalous observations, respectively related to healthy and supposedly faulty components. In this paper, a procedure based on an efficient one-class classification method that does not require any assumption on the data distribution, is used. The core of such an approach is the Support Vector Data Description (SVDD), that allows an efficient data description without the need of a significant amount of statistical data. Several analyses have been carried out in order to validate the proposed procedure, using flight vibration data collected from a H135, formerly known as EC135, servicing helicopter, for which micro-pitting damage on a gear was detected by HUMS and assessed through visual inspection. The capability of the proposed approach of providing better trade-off between false alarm rates and missed detection rates with respect to individual CI and to the AS obtained assuming jointly-Gaussian-distributed CI has been also analysed

Optimal experiment design revisited: fair, precise and minimal tomography

Given an experimental set-up and a fixed number of measurements, how should one take data in order to optimally reconstruct the state of a quantum system? The problem of optimal experiment design (OED) for quantum state tomography was first broached by Kosut et al. [arXiv:quant-ph/0411093v1]. Here we provide efficient numerical algorithms for finding the optimal design, and analytic results for the case of 'minimal tomography'. We also introduce the average OED, which is independent of the state to be reconstructed, and the optimal design for tomography (ODT), which minimizes tomographic bias. We find that these two designs are generally similar. Monte-Carlo simulations confirm the utility of our results for qubits. Finally, we adapt our approach to deal with constrained techniques such as maximum likelihood estimation. We find that these are less amenable to optimization than cruder reconstruction methods, such as linear inversion.Comment: 16 pages, 7 figure

Approximate quantum data storage and teleportation

In this paper we present an optimal protocol by which an unknown state on a Hilbert space of dimension $N$ can be approximately stored in an $M$-dimensional quantum system or be approximately teleported via an $M$-dimensional quantum channel. The fidelity of our procedure is determined for pure states as well as for mixed states and states which are entangled with auxiliary quantum systems of varying Hilbert space dimension, and it is compared with theoretical results for the maximally achievable fidelity.Comment: More detailed discussion of teleportation of entangled and mixed states. Added reference to work by Banaszek. 8 pages, 1 figur

A General Framework for Fair Regression

Fairness, through its many forms and definitions, has become an important issue facing the machine learning community. In this work, we consider how to incorporate group fairness constraints in kernel regression methods, applicable to Gaussian processes, support vector machines, neural network regression and decision tree regression. Further, we focus on examining the effect of incorporating these constraints in decision tree regression, with direct applications to random forests and boosted trees amongst other widespread popular inference techniques. We show that the order of complexity of memory and computation is preserved for such models and tightly bound the expected perturbations to the model in terms of the number of leaves of the trees. Importantly, the approach works on trained models and hence can be easily applied to models in current use and group labels are only required on training data.Comment: 8 pages, 4 figures, 2 pages reference