Theory of Coster-Kronig preceded Auger processes in solids

We propose the foundations of an extended Auger line-shape analysis of solids aiming to include three-hole features such as the ones due to core-valence-valence Auger decays following Coster-Kronig transitions. In transition metals, such features show up as intense high binding energy satellites of the diagrammatic core-valence-valence lines. Our theory is grounded on the full one-step approach, but to keep the complications to a minimum, in the present exploratory paper, the valence band is assumed fully below the Fermi level. In this way, explicit model calculations can be confidently based on a three-step approach. The line-shape analysis then amounts to compute a three-body Green's function, which, however, is much less known than one- and two-body ones. Our treatment covers the whole range between weak and strong correlations. Furthermore, we show that the relevant physics can be captured by a transparent, computationally simple closed formula. We find that, in general, the satellites cover separated spectral regions with three-hole multiplets, shifted and broadened two-hole features, and distorted bandlike continua

Prediction of Search Targets From Fixations in Open-World Settings

Previous work on predicting the target of visual search from human fixations only considered closed-world settings in which training labels are available and predictions are performed for a known set of potential targets. In this work we go beyond the state of the art by studying search target prediction in an open-world setting in which we no longer assume that we have fixation data to train for the search targets. We present a dataset containing fixation data of 18 users searching for natural images from three image categories within synthesised image collages of about 80 images. In a closed-world baseline experiment we show that we can predict the correct target image out of a candidate set of five images. We then present a new problem formulation for search target prediction in the open-world setting that is based on learning compatibilities between fixations and potential targets

Wild ramification kinks

Given a branched cover $f:Y\to X$ between smooth projective curves over a non-archimedian mixed-characteristic local field and an open rigid disk $D\subset X$, we study the question under which conditions the inverse image $f^{-1}(D)$ is again an open disk. More generally, if the cover $f$ varies in an analytic family, is this true at least for some member of the family? Our main result gives a criterion for this to happen.Comment: Final version, to appear in Research in the Mathematical Sciences. 29 page

Redundancy, Deduction Schemes, and Minimum-Size Bases for Association Rules

Association rules are among the most widely employed data analysis methods in the field of Data Mining. An association rule is a form of partial implication between two sets of binary variables. In the most common approach, association rules are parameterized by a lower bound on their confidence, which is the empirical conditional probability of their consequent given the antecedent, and/or by some other parameter bounds such as "support" or deviation from independence. We study here notions of redundancy among association rules from a fundamental perspective. We see each transaction in a dataset as an interpretation (or model) in the propositional logic sense, and consider existing notions of redundancy, that is, of logical entailment, among association rules, of the form "any dataset in which this first rule holds must obey also that second rule, therefore the second is redundant". We discuss several existing alternative definitions of redundancy between association rules and provide new characterizations and relationships among them. We show that the main alternatives we discuss correspond actually to just two variants, which differ in the treatment of full-confidence implications. For each of these two notions of redundancy, we provide a sound and complete deduction calculus, and we show how to construct complete bases (that is, axiomatizations) of absolutely minimum size in terms of the number of rules. We explore finally an approach to redundancy with respect to several association rules, and fully characterize its simplest case of two partial premises.Comment: LMCS accepted pape

Counting matroids in minor-closed classes

A flat cover is a collection of flats identifying the non-bases of a matroid. We introduce the notion of cover complexity, the minimal size of such a flat cover, as a measure for the complexity of a matroid, and present bounds on the number of matroids on $n$ elements whose cover complexity is bounded. We apply cover complexity to show that the class of matroids without an $N$-minor is asymptotically small in case $N$ is one of the sparse paving matroids $U_{2,k}$, $U_{3,6}$, $P_6$, $Q_6$, or $R_6$, thus confirming a few special cases of a conjecture due to Mayhew, Newman, Welsh, and Whittle. On the other hand, we show a lower bound on the number of matroids without $M(K_4)$-minor which asymptoticaly matches the best known lower bound on the number of all matroids, due to Knuth.Comment: 13 pages, 3 figure