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Physical review / A 105(5), 053524 (2022). doi:10.1103/PhysRevA.105.053524, The advent of free-electron lasers (FELs) in the soft- and hard-x-ray spectral regions has introduced the possibility to probe electronic, magnetic, and structural dynamics, in both diluted and condensed matter samples, with femtosecond time resolution. In particular, FELs have strongly enhanced the capabilities of several analytical techniques, which have taken advantage of the high degree of transverse coherence provided. Free-electron lasers based on the harmonic up-conversion of an external coherent source (seed) are characterized also by a high degree of longitudinal coherence, since electrons inherit the coherence properties of the seed. For the state of the art, the shortest wavelength delivered to user experiments by an externally seeded FEL light source is about 4 nm. In this paper we demonstrate that pulses with a high longitudinal degree of coherence (first and second order) covering the water window and with photon energy extending up to 790 eV can be generated by exploiting the so-called nonlinear harmonic regime, which allows generation of radiation at harmonics of the resonant FEL wavelength. In order to show the suitability of the nonlinear harmonics generated by a seeded FEL for research in the water window and beyond, we report the results of two proof-of-principle experiments: one measuring the oxygen $K$-edge absorption in water (∼$530$ eV) and the other analyzing the spin dynamics of Fe and Co through magnetic small-angle x-ray scattering at their $L$ edges (707 and 780 eV, respectively)., Published by Inst., Woodbury, NY

Monophonic, geodesic and 2-geodesic convexities ([Formula: see text]-convexity, [Formula: see text]-convexity and [Formula: see text]-convexity, for short) on graphs are based on the families of induced paths, shortest paths and shortest paths of length [Formula: see text], respectively. We introduce a class of graphs, the class of cross-cyclicgraphs, in which every connected [Formula: see text]-convex set is also [Formula: see text]-convex and [Formula: see text]-convex. We show that this class is properly contained in the class, say [Formula: see text], of graphs in which geodesic and monophonic convexities are equivalent and properly contains the class of distance-hereditary graphs. Moreover, we show that (1) an [Formula: see text]-hull set (i.e., a subset of vertices, with minimum cardinality, whose [Formula: see text]-convex hull equals the whole vertex set) and, hence, the m-hull number and the g-hull number of a graph in [Formula: see text] can be computed in polynomial time and that (2) both the geodesic-convex hull and the monophonic-convex hull can be computed in linear time in a cross-cyclic graph without cycles of length [Formula: see text] and, hence, in a bipartite distance-hereditary graph.

An abstract convexity space on a connected hypergraph H with vertex set V (H) is a family C of subsets of V (H) (to be called the convex sets of H) such that: (i) C contains the empty set and V (H), (ii) C is closed under intersection, and (iii) every set in C is connected in H. A convex set X of H is a minimal vertex convex separator of H if there exist two vertices of H that are separated by X and are not separated by any convex set that is a proper subset of X. A nonempty subset X of V (H) is a cluster of H if in H every two vertices in X are not separated by any convex set. The cluster hypergraph of H is the hypergraph with vertex set V (H) whose edges are the maximal clusters of H. A convexity space on H is called decomposable if it satisfies the following three properties

In order to answer a “joint” query from multiple data cubes, Pourabass and Shoshani [2007] distinguish the data cube on the measure of interest (called the “primary” data cube) from the other data cubes (called “proxy” data cubes) that are used to involve the dimensions (in the query) not in the primary data cube. They demonstrate in study cases that, if the measures of the primary and proxy data cubes are correlated, then the answer to a joint query is an accurate estimate of its true value. Needless to say, for two or more proxy data cubes, the result depends upon the way the primary and proxy data cubes are combined together; however, for certain combination schemes Pourabass and Shoshani provide a sufficient condition , that they call proxy noncommonality , for the invariance of the result. In this article, we introduce: (1) a merge operator combining the contents of a primary data cube with the contents of a proxy data cube, (2) merge expressions for general combination schemes, and (3) an equivalence relation between merge expressions having the same pattern. Then, we prove that proxy noncommonality characterizes patterns for which every two merge expressions are equivalent. Moreover, we provide an efficient procedure for answering joint queries in the special case of perfect merge expressions. Finally, we show that our results apply to data cubes in which measures are obtained from unaggregated data using the aggregate functions SUM, COUNT, MAX, and MIN, and a lot more.

We generalize Jirousek's (right) composition operator in such a way that it can be applied to distribution functions with values in a "semifield", and introduce (parenthesized) compositional expressions, which in some sense generalize Jirousek's "generating sequences" of compositional models. We say that two compositional expressions are equivalent if their evaluations always produce the same results whenever they are defined. Our first result is that a set system H is star-like with centre X if and only if every two compositional expressions with "base scheme" H and "key" X are equivalent. This result is stronger than Jirousek's result which states that, if H is star-like with centre X, then every two generating sequences with base scheme H and key X are equivalent. Then, we focus on canonical expressions, by which we mean compositional expressions such that the sequence of the sets featured in and arranged in order of appearance enjoys the "running intersection property". Since every compositional expression, whose base scheme is a star-like set system with centre X and whose key is X, is a canonical expression, we investigate the equivalence between two canonical expressions with the same base scheme and the same key. We state a graphical characterization of those set systems H such that every two canonical expressions with base scheme H and key X are equivalent, and also provide a graphical algorithm for their recognition. Finally, we discuss the problem of detecting conditional independences that hold in a compositional model.

Known properties of ''canonical connections'' from database theory and of ''closed sets'' from statistics implicitly define a hypergraph convexity, here called canonical convexity (c-convexity), and provide an efficient algorithm to compute c-convex hulls. We characterize the class of hypergraphs in which c-convexity enjoys the Minkowski-Krein-Milman property. Moreover, we compare c-convexity with the natural extension to hypergraphs of monophonic convexity (or m-convexity), and prove that: (1) m-convexity is coarser than c-convexity, (2) m-convexity and c-convexity are equivalent in conformal hypergraphs, and (3) m-convex hulls can be computed in the same efficient way as c-convex hulls.

Data take the form of a triple that consists of a summary attribute, a category and a numeric value. The inference problem of summary data consists in deciding whether or not a summary data of interest is evaluable (i.e., can be computed) from a given set of summary data. We address the special case of the inference problem with homogeneous summary data (i.e., summary data with the same summary attribute), where the summary attribute is of additive nature. Owing to additivity, one can model the information content of the given summary data by a linear equation system whose variables are constrained to take their values from the domain of the summary attribute. We state two evaluability criteria, one for a real or integral summary attribute, and the other for a nonnegative-real or nonnegative-integral summary attribute. Using the two evaluability criteria, we show that our inference problem can be solved in strongly polynomial time for a real or integral or nonnegative real summary attribute, and is coNP-complete for a nonnegative-integral summary attribute. Moreover, we prove that, given a summary data of interest that is not evaluable, even in the (simplest) case that the summary attribute is of a real type, finding an evaluable summary data whose category is maximally contained in (or minimally contains) the category of the summary data of interest is an NP-hard problem. (c) 2007 Elsevier B.V. All rights reserved.

Ag-Ge alloy samples in equilibrium with excess Ge have been studied in situ using a combination of high resolution energy scanning X-ray diffraction (ESXD). X-ray absorption spectroscopic (XAS), and temperature scanning techniques at the European Synchrotron Radiation Facility. The lattice expansion of the f.c.c. Ag 1-G e terminal solid solution with respect to Ag was determined with high accuracy as a function of temperature in the 695-912 K range. The data provide evidence for a Ge solubility, greater than the one commonly accepted, which increases above the 15% level close to the eutectic temperature.

Factorization constraints are introduced as a generalization of the multiplicative formulation of conditional independence, and some computational and logic properties are stated. More precisely, we prove that factorization constraints characterize those cases in which a probability distribution can be represented “without loss of information” by a suitable set of its marginals. Moreover, we provide a sound formal system for factorization constraints, which covers the set of the so-called semi-graphoid axioms of conditional independence. Finally, we solve the implication problem for factorization constraints in two special cases, and for the general case we state two conditions, one necessary and the other sufficient for an implication to hold.

We introduce a new notion of convexity in digraphs, which we call incoming-path convexity, and prove that the incoming-path convexity space of a digraph is a convex geometry (that is, it satisfies the Minkowski–Krein–Milman property) if and only if the digraph is acyclic. Moreover, we prove that incoming-path convexity is adequate to characterize collapsibility of models generated by Bayesian networks. Based on these results, we also provide simple linear algorithms to solve two topical problems on Markov properties of a Bayesian network (that is, on conditional independences valid in a Bayesian network).

The space-saving implementation of the iterative proportional fitting procedure proposed by Jirousek and Preucil (Comput. Statist. Data Anal. 19 (1995) 177) on this journal can be improved by applying the tree-computation techniques designed for Markov networks. The optimisation problem raised by the use of Markovian propagation trees is solved. Next, an even better implementation is obtained using certain trees, here introduced and called fast propagation trees , which are obtained by “simplifying” optimal Markovian propagation trees.

Extended log-linear models (ELMs) are the natural generalization of log-linear models when the positivity assumption is relaxed. The hypergraph language, which is currently used to specify the syntax of ELMs, both provides an insight into key notions of the theory of ELMs such as collapsibility and decomposability, and allows to work out efficient algorithms to solve some problems of inference. This is the case for the three search problems addressed in this paper and referred to as the approximation problem, the selective-reduction problem and the synthesis problem. The approximation problem consists in finding the smallest decomposable ELM that contains a given ELM and is such that the given ELM is collapsible onto each of its generators. The selective-reduction problem consists in deleting the maximum number of generators of a given ELM in such a way that the resulting ELM is a submodel and none of certain variables of interest is missing. The synthesis problem consists in finding a minimal ELM containing the intersection of ELMs specified by given independence relations. We show that each of the three search problems above can be reduced to an equivalent search problem on hypergraphs, which can be solved in polynomial time.

A sound and complete formal system for full acyclic join dependencies is obtained by adding three derivation rules to the axioms of multivalued dependencies.

The method of the canonical connection introduced by Maier and Ullman provides an optimal procedure for query processing in universal-relation databases. We present an algorithm for computing canonical connections in a database scheme which is more efficient than the classical algorithm based on tableau reduction. Moreover, with a slight modification of the algorithm we obtain a join plan which succeeds in controlling the nonmonotonicity of cyclic canonical connections.

The technique of data suppression for protecting sensitive information in a two-dimensional table from exact disclosure raises the computational problems of testing a given table of censored data for security, and searching for a secure suppression pattern of minimum size for a given table. We provide a polynomial security test to solve the former problem, and prove that the latter problem is intractable in the general case, but can be solved in linear time in the special case in which only sensitive cells are to be protected.

We investigate the electronic structure of the Sr${}_{n+1}$Ru${}_{n}$O${}_{3n+1}$ family $(n=1,2,3)$ in the vicinity the Fermi level by means of polarization-dependent resonant O 1$s$ x-ray emission spectroscopy. Using both energy window and polarization analysis we disentangle the contribution of apical and planar oxygen, and compare it with first-principles calculations. Our results provide a new insight on the nature of the oxygen bonds and the role of Sr $3d$ states.

Given a connected hypergraph with vertex set V, a convexity space on is a subset of the powerset of V that contains ∅, V, and the singletons; furthermore, is closed under intersection and every set in is connected in . The members of are called convex sets. The convex hull of a subset X of V is the smallest convex set containing X. By a cluster of we mean any nonempty subset of V in which every two vertices are separated by no convex set. We say that a convexity space on is decomposable if it satisfies the following three axioms: (i) the maximal clusters of form an acyclic hypergraph, (ii) every maximal cluster of is a convex set, and (iii) for every nonempty vertex set X, a vertex does not belong to the convex hull of X if and only if it is separated from X by a convex cluster. We prove that a decomposable convexity space on is fully specified by the maximal clusters of in that (1) there is a closed formula which expresses the convex hull of a set in terms of certain convex clusters of and (2) is a convex geometry if and only if the subspaces of induced by maximal clusters of are all convex geometries. Finally, we prove the decomposability of some known convexities in graphs and hypergraphs taken from the literature (such as “monophonic” and “canonical” convexities in hypergraphs and “all-paths” convexity in graphs).

The problem of the logical implication between two hierarchical log-linear models is proved to be equivalent to the problem of deciding whether their generating classes satisfy the graphtheoretic condition of hinging. Moreover, a polynomial-time procedure is worked out to test implication.

In an on-line statistical database, the query system should leave unanswered queries asking for sums that could lead to the disclosure of confidential data. To check that, every sum query and previously answered sum queries should be audited. We show that, under a suitable query-overlap restriction, an auditing procedure can be efficiently worked out using flow-network computation.

In a connected hypergraph a vertex set X is simple-path convex (sp-convex, for short) if either |X|≤1 or X contains every vertex on every simple path between two vertices in X (Faber and Jamison, 1986 [7]), and the sp-convex hull of a vertex set X is the minimal superset of X that is sp-convex. In this paper, we give a polynomial algorithm to compute sp-convex hulls in an arbitrary hypergraph. © 2010 Elsevier B.V.

Let G be a connected graph on V. A subset X of V is all-paths convex (or ap -convex) if X contains each vertex on every path joining two vertices in X and is monophonically convex (or m-convex) if X contains each vertex on every chordless path joining two vertices in X. First of all, we prove that ap -convexity and m-convexity coincide in G if and only if G is a tree. Next, in order to generalize this result to a connected hypergraph H, in addition to the hypergraph versions of ap -convexity and m-convexity, we consider canonical convexity (or c-convexity) and simple-path convexity (or sp -convexity) for which it is well known that m-convexity is finer than both c-convexity and sp -convexity and sp -convexity is finer than ap -convexity. After proving sp -convexity is coarser than c-convexity, we characterize the hypergraphs in which each pair of the four convexities above is equivalent. As a result, we obtain a convexity-theoretic characterization of Berge-acyclic hypergraphs and of γ-acyclic hypergraphs.

In many situations a statistical database contains multiple summary tables, which report summary statistics on the same summary variable for the same population of individuals or objects using different classification criteria («homogeneous» summary tables). Existing query languages consider only those queries which may aggregate data stored in a single summary table. When a statistical database contains homogeneous summary tables, such query languages do not allow an integrated view of data, whereas statisticians are inclined to view and query a collection of homogeneous summary tables as if they were actually a single higher-dimensional summary table. This legitimizes the search for a universal-scheme solution to the problem of data integration is such statistical databases

A heuristic procedure is presented for approximating an n-dimensional discrete probability distribution with a decomposable model of a given complexity. It is shown that, without loss of generality, the search space can be restricted to a suitable subclass of decomposable models, whose members are called elementary models. The selected elementary model is constructed in an incremental manner according to a local-optimality criterion that consists of minimizing a suitable cost function. It is shown by an example that the solution computed by the procedure is sometimes optimal. >

The electronic structure in the normal state of CeFeAsO0.89F0.11 oxypnictide superconductors has been investigated with x-ray absorption and photoemission spectroscopy. All of the data exhibit signatures of Fe d-electron itinerancy. Exchange multiplets appearing in the Fe 3s core level indicate the presence of itinerant spin fluctuations. These findings suggest that the underlying physics and the origin of superconductivity in these materials are likely to be quite different from those of the cuprate high-temperature superconductors. These materials provide opportunities for elucidating the role of magnetic fluctuations in high-temperature superconductivity.

The evaluability of queries on a statistical database containing joinable tables connected by an intersection hypergraph is considered. A characterization of evaluable queries is given, which allows one to define polynomial-time procedures both for testing evaluability and for evaluating queries. These results are useful in designing an 'informed query system' for statistical databases which promotes an integrated use of stored information. Such a query system allows the user to formulate a query involving attributes from several joinable tables as if they were all contained in a single universal table. >

A weighting of vertices of a graph is admissible if there exists an edge weighting such that the weight of each vertex equals the sum of weights of its incident edges. Given an admissible vertex weighting of a graph, an invariant set is an edge set such that the sum of the weights of its edges is the same for every edge weighting, and a nonempty invariant set is minimal if none of its nonempty proper subsets is an invariant set. It is easily seen that every nonempty invariant set is a disjoint union of minimal invariant sets. A graphical characterisation of minimal invariant sets in a bipartite graph is known both in the case the vertex weights are reals and in the case the vertex weights are nonnegative reals. We shall state a graphical characterisation of minimal invariant sets in an arbitrary vertex-weighted graph. Moreover, we give a linear algorithm to test an invariant set for minimality. Finally, we state a complete axiomatisation of invariant sets and give a polynomial algorithm to find a set of minimal invariant sets that completely characterise the set of all invariant sets. (C) 2006 Elsevier B.V. All rights reserved.