Exact Matching Conditions Research Articles

Pure State v-Representability of Density Matrix Embedding Theory.

Density matrix embedding theory (DMET) formally requires the matching of density matrix blocks obtained from high-level and low-level theories, but this is sometimes not achievable in practical calculations. In such a case, the global band gap of the low-level theory vanishes, and this can require additional numerical considerations. We find that both the violation of the exact matching condition and the vanishing low-level gap are related to the assumption that the high-level density matrix blocks are noninteracting pure-state v-representable (NI-PS-V), which assumes that the low-level density matrix is constructed following the Aufbau principle. To relax the NI-PS-V condition, we develop an augmented Lagrangian method to match the density matrix blocks without referring to the Aufbau principle. Numerical results for the 2D Hubbard and hydrogen model systems indicate that, in some challenging scenarios, the relaxation of the Aufbau principle directly leads to exact matching of the density matrix blocks, which also yields improved accuracy.

A novel simultaneous isotope dilution strategy as a powerful tool in the two-track certification process of trace metal mass fractions: a case study of mercury, cadmium and lead in soil and sediment materials.

An analytical methodology based on isotope dilution (ID) principles was developed to establish the reference procedure for the simultaneous assignation of aqua regia extractable and total mass fractions of Hg, Cd, and Pb in soil and sediment matrix samples. The 'twin sample-spike blends' were prepared under close to the exact matching conditions, resulting in almost identical mass ratios of the spike to the sample in the blends, which followed either the aqua regia extraction method or total digestion procedure. The isotope ratios in 'twin-blends' were measured by inductively coupled plasma mass spectrometry (ICP-MS). The two-track IDMS strategy proposed in this work was successfully applied to three certified reference materials (CRMs): ERM-CC141 loam soil, EnvCRM 03 soil, and MODAS-2 bottom sediment. This ensured an adequate method validation. For two CRMs (EnvCRM 03 and MODAS-2) it was found that the isotope ratio values in 'twin-blends' for Hg, Cd, and Pb were almost identical with a variability of less than 2.4%. This confirmed that there is no measurable difference between the aqua regia extractable and the total mass fractions within the uncertainty ranges. Therefore, aqua regia mass fractions assigned in this study were found to be equal to certified element contents. For ERM-CC141 loam soil, the Hg isotope ratio values measured in the 'twin-blends' were found to be identical within their measurement uncertainties, and thus, it was concluded that the aqua regia extractable Hg content is identical to the total Hg content. However, in the case of Cd and Pb isotope ratio values in 'twin-blends' varied around 24% or 16%, respectively and because this significant difference was noticed, for both elements it is necessary to calculate the aqua regia content and the total content separately. Because this significant difference was noticed for both elements, it is necessary to calculate the aqua regia content and the total content separately. A detailed comparison of the isotope ratio values between the 'twin-blends' provided unambiguous information about aqua regia extractability of metals and it is a strong indicator for making decisions related to the assignment of either a single mass fraction valid for both procedures or two separate element mass fraction values. To our knowledge and based on the relevant literature survey, this is a novel strategy based on IDMS, and such studies have not been undertaken and presented so far.

Hydrogen-like spectrum of spontaneously created brane universes with de-Sitter ground state

Unification of Randall–Sundrum and Regge–Teitelboim brane cosmologies gives birth to a serendipitous Higgs–deSitter interplay. A localized Dvali–Gabadadze–Porrati scalar field, governed by a particular (analytically derived) double-well quartic potential, becomes a mandatory ingredient for supporting a deSitter brane universe. When upgraded to a general Higgs potential, the brane surface tension gets quantized, resembling a Hydrogen atom spectrum, with deSitter universe serving as the ground state. This reflects the local/global structure of the Euclidean manifold: From finite energy density no-boundary initial conditions, via a novel acceleration divide filter, to exact matching conditions at the exclusive nucleation point. Imaginary time periodicity comes as a bonus, with the associated Hawking temperature vanishing at the continuum limit. Upon spontaneous creation, while a finite number of levels describe universes dominated by a residual dark energy combined with damped matter oscillations, an infinite tower of excited levels undergo a Big Crunch.

Exact matching at a joint of multiply-connected box beams under out-of-plane bending and torsion

Accurate analysis of thin-walled box beams meeting at a joint requires not only consideration of higher-order deformation degrees (such as warping and distortion) but also exact matching conditions at the joint. Especially when more than two box beams are connected at a joint, the deformation of the beam-joint system is so complicated that no one-dimensional beam analysis has yet predicted its structural behavior correctly. Since a beam theory incorporating higher-order deformations is available, the main difficulty is determining the exact matching conditions at the joint. In this paper, we derive the exact matching conditions for five field variables—bending deflection, bending/torsional rotations, warping, and distortion—of multiply connected box beams under out-of-plane bending and torsional loads. The derived relations are valid irrespective of the number of beams and angles. We introduced a new concept called “edge resultants” besides conventional (sectional) resultants, and demonstrated its effectiveness for exact derivation and physical interpretations of the derived equations. The accuracy and validity of the proposed theory are checked by comparing the predicted results with those of shell finite element analysis.

Analysis of two box beams-joint systems under in-plane bending and axial loads by one-dimensional higher-order beam theory

• Two box beams-joint systems are analyzed by one-dimensional beam theory. • The beam systems are subjected to in-plane loads. • Higher-order deformation (bending warping and distortion) degrees are considered. • Exact matching conditions at a joint of two box beams are newly derived. • The proposed approach effectively handles arbitrarily-angled box beam systems. If two thin-walled box beams meet at a joint, significant flexibilities that cannot be dealt with by the classical Euler or Timoshenko beam theory are observed. Especially under in-plane bending and axial loads, the deformation of the two box beams-joint system near the joint region is so complicated that no theoretical one-dimensional approach that interprets its mechanical behavior correctly has yet been proposed. To establish an effective higher-order beam theory, we introduce a new additional bending distortion degree representing anticlastic curvature effects and also redefine the section-shape functions of the bending warping and bending distortion degrees. In box beams-joint systems, it is crucial to find the matching conditions among field variables at the joint, but no exact conditions applicable for the systems under in-plane bending and axial loads are available. In this paper, we newly derive the explicit form of the transformation matrix relating six field variables of two box beams at a joint–axial displacement, transverse displacement, in-plane bending/shear rotation, bending warping, and two bending distortions. The accuracy and validity of the developed higher-order beam theory and the exact matching conditions are checked by comparing the present beam based results and ABAQUS shell analysis results for various box beams with different joint angles.

Formula omitted]-affinity privacy: Releasing infrequent query refinements safely

Search log k-anonymization is based on the elimination of infrequent queries under exact matching conditions, usually at the cost of high data loss. We present a semantic approach to k-anonymity, termed kΘ-affinity, in which a query can be protected by affine rather than identical queries. Based on the observation that many infrequent queries can be seen as refinements of a more general frequent query, we develop a three-step privacy model. We first represent query concepts as probabilistically weighted n-grams and extract them from the search log data. We then expand the original log queries with such concepts, defining the affinity between two queries as the similarity of their expanded representations. Finally, after building the graph of Θ-affine queries (for a given threshold Θ), we find the generalized k-cores of this graph, which coincide with the sets of queries satisfying kΘ-affinity privacy. Experimenting with the AOL dataset, we compare k-anonymity under affinity to k-anonymity under equality and under WordNet generalization. We show that kΘ-affinity achieves similar levels of privacy while at the same time reducing the data losses to a great extent. We also discuss its sensitivity to attacks.

Exact Matching Condition at a Joint of Thin-Walled Box Beams Under Out-of-Plane Bending and Torsion

To take into account the flexibility resulting from sectional deformations of a thin-walled box beam, higher-order beam theories considering warping and distortional degrees of freedom (DOF) in addition to the Timoshenko kinematic degrees have been developed. The objective of this study is to derive the exact matching condition consistent with a 5-DOF higher-order beam theory at a joint of thin-walled box beams under out-of-plane bending and torsion. Here we use bending deflection, bending/shear rotation, torsional rotation, warping, and distortion as the kinematic variables. Because the theory involves warping and distortion that do not produce any force/moment resultant, the joint matching condition cannot be obtained just by using the typical three equilibrium conditions. This difficulty poses considerable challenges because all elements of the 5×5 transformation matrix relating the field variables of one beam to those in another beam should be determined. The main contributions of the investigation are to propose additional necessary conditions to determine the matrix and to derive it exactly. The validity of the derived joint matching transformation matrix is demonstrated by showing good agreement between the shell finite element results and those obtained by the present box beam analysis in various angle box beams.

Transposition invariant string matching

Given strings A = a 1 a 2 … a m and B = b 1 b 2 … b n over an alphabet Σ ⊆ U , where U is some numerical universe closed under addition and subtraction, and a distance function d ( A , B ) that gives the score of the best (partial) matching of A and B, the transposition invariant distance is min t ∈ U { d ( A + t , B ) } , where A + t = ( a 1 + t ) ( a 2 + t ) … ( a m + t ) . We study the problem of computing the transposition invariant distance for various distance (and similarity) functions d, including Hamming distance, longest common subsequence ( LCS), Levenshtein distance, and their versions where the exact matching condition is replaced by an approximate one. For all these problems we give algorithms whose time complexities are close to the known upper bounds without transposition invariance, and for some we achieve these upper bounds. In particular, we show how sparse dynamic programming can be used to solve transposition invariant problems, and its connection with multidimensional range-minimum search. As a byproduct, we give improved sparse dynamic programming algorithms to compute LCS and Levenshtein distance.