Efficient estimation of AUC in a sliding window

In many applications, monitoring area under the ROC curve (AUC) in a sliding window over a data stream is a natural way of detecting changes in the system. The drawback is that computing AUC in a sliding window is expensive, especially if the window size is large and the data flow is significant. In this paper we propose a scheme for maintaining an approximate AUC in a sliding window of length $k$. More specifically, we propose an algorithm that, given $\epsilon$, estimates AUC within $\epsilon / 2$, and can maintain this estimate in $O((\log k) / \epsilon)$ time, per update, as the window slides. This provides a speed-up over the exact computation of AUC, which requires $O(k)$ time, per update. The speed-up becomes more significant as the size of the window increases. Our estimate is based on grouping the data points together, and using these groups to calculate AUC. The grouping is designed carefully such that ($i$) the groups are small enough, so that the error stays small, ($ii$) the number of groups is small, so that enumerating them is not expensive, and ($iii$) the definition is flexible enough so that we can maintain the groups efficiently. Our experimental evaluation demonstrates that the average approximation error in practice is much smaller than the approximation guarantee $\epsilon / 2$, and that we can achieve significant speed-ups with only a modest sacrifice in accuracy

Complex band structure and plasmon lattice Green's function of a periodic metal-nanoparticle chain

When the surface plasmon resonance in a metal-nanoparticle chain is excited at one point, the response signal will generally decay down the chain due to absorption and radiation losses. The decay length is a key parameter in such plasmonic systems. By studying the plasmon lattice Green's function, we found that the decay length is generally governed by two exponential decay constants with phase factors corresponding to guided Bloch modes and one power-law decay with a phase factor corresponding to that of free space photons. The results show a high level of similarity between the absorptive and radiative decay channels. By analyzing the poles (and the corresponding residues) of the Green's function in a transformed complex reciprocal space, the dominant decay channel of the real-space Green's function is understood.Comment: 19 pages, 3 figure

Information sharing and credit : firm-level evidence from transition countries

We investigate whether information sharing among banks has affected credit market performance in the transition countries of Eastern Europe and the former Soviet Union, using a large sample of firm-level data. Our estimates show that information sharing is associated with improved availability and lower cost of credit to firms. This correlation is stronger for opaque firms than transparent ones and stronger in countries with weak legal environments than in those with strong legal environments. In cross-sectional estimates, we control for variation in country-level aggregate variables that may affect credit, by examining the differential impact of information sharing across firm types. In panel estimates, we also control for the presence of unobserved heterogeneity at the firm level, as well as for changes in macroeconomic variables and the legal environment

Trust in the public sector: Is there any evidence for a long-term decline?

Concerns with declining public trust in government have become a permanent element of the contemporary political discourse. This concern also extends to levels of citizens’ trust in the public administration and public services. Trust is said to be declining, and this decline is generally seen as detrimental to public service delivery. In this article, we examine the main elements in this discussion, review the existing international survey data and summarise the main findings for OECD countries. Citizens’ trust in the public sector is found to fluctuate, and the data generally do not show consistently declining levels of trust. Furthermore, in some countries there simply is insufficient data to come to any conclusions at all about time trends in citizen trust in the public sector. Points for practitioners This article summarises some of the survey material on citizens’ trust in the public administration. It allows practitioners to compare trends in public trust in their country across time and space. The findings lead us to reject the hypothesis of a universal decline of trust in the public sector. The article warns against using opinion poll results without considering context. The long-term and comparative perspective on citizens’ trust in the public sector is all too often absent from the policy discourse that is frequently based on assumptions and ad-hoc approaches

Consequences of local gauge symmetry in empirical tight-binding theory

A method for incorporating electromagnetic fields into empirical tight-binding theory is derived from the principle of local gauge symmetry. Gauge invariance is shown to be incompatible with empirical tight-binding theory unless a representation exists in which the coordinate operator is diagonal. The present approach takes this basis as fundamental and uses group theory to construct symmetrized linear combinations of discrete coordinate eigenkets. This produces orthogonal atomic-like "orbitals" that may be used as a tight-binding basis. The coordinate matrix in the latter basis includes intra-atomic matrix elements between different orbitals on the same atom. Lattice gauge theory is then used to define discrete electromagnetic fields and their interaction with electrons. Local gauge symmetry is shown to impose strong restrictions limiting the range of the Hamiltonian in the coordinate basis. The theory is applied to the semiconductors Ge and Si, for which it is shown that a basis of 15 orbitals per atom provides a satisfactory description of the valence bands and the lowest conduction bands. Calculations of the dielectric function demonstrate that this model yields an accurate joint density of states, but underestimates the oscillator strength by about 20% in comparison to a nonlocal empirical pseudopotential calculation.Comment: 23 pages, 7 figures, RevTeX4; submitted to Phys. Rev.