Ultra-Scalable Spectral Clustering and Ensemble Clustering

This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable ensemble clustering (U-SENC). In U-SPEC, a hybrid representative selection strategy and a fast approximation method for K-nearest representatives are proposed for the construction of a sparse affinity sub-matrix. By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. In U-SENC, multiple U-SPEC clusterers are further integrated into an ensemble clustering framework to enhance the robustness of U-SPEC while maintaining high efficiency. Based on the ensemble generation via multiple U-SEPC's, a new bipartite graph is constructed between objects and base clusters and then efficiently partitioned to achieve the consensus clustering result. It is noteworthy that both U-SPEC and U-SENC have nearly linear time and space complexity, and are capable of robustly and efficiently partitioning ten-million-level nonlinearly-separable datasets on a PC with 64GB memory. Experiments on various large-scale datasets have demonstrated the scalability and robustness of our algorithms. The MATLAB code and experimental data are available at https://www.researchgate.net/publication/330760669.Comment: To appear in IEEE Transactions on Knowledge and Data Engineering, 201

Early Transition Metal Oxides as Catalysts: Crossing Scales from Clusters to Single Crystals to Functioning Materials

The overall goal of this program is to investigate the electronic structure and chemical bonding of early transition metal oxide clusters and use them as well-defined molecular models to obtain insight into properties and mechanisms of oxide catalysts, as well as to provide accurate spectroscopic and molecular information to verify theoretical methods used to predict materials properties. A laser vaporization cluster source is used to produce metal oxide clusters with different sizes, structures, and compositions. Well-defined inorganic polyoxometalate clusters in solution are transported in the gas phase using electrospray. Two state-of-the-art photoelectron spectroscopy apparatuses are used to interrogate the oxide clusters and polyoxometalate anions in the gas phase to obtain spectroscopic and electronic structure information. The experimental effort is assisted by theoretical calculations to understanding the structures, chemical bonding, and catalytical properties of the transition metal oxide clusters. The research approach combines novel and flexible experimental techniques and advanced theoretical/computational methodologies and seeks molecular-level information to aiding the design of new catalysts, as well as mechanistic understanding. We have focused on the investigation of tungsten oxide clusters containing three W atoms: W{sub 3}O{sub x}{sup -} (x = 7-11). A number of interesting findings have been made. We observed that the oxygen-poor W{sub 3}O8 cluster contains a localized W{sup 4+} center, which can be used as a molecular model for O-deficient defect sites. A chemisorption energy was obtained through density functional calculations for W{sub 3}O8 + O{sub 2} {yields} W{sub 3}O{sub 10} as -78 kcal/mol. We further found that the neutral stoichiometric W{sub 2}O{sub 6} and W{sub 3}O{sub 9} clusters do not react with O{sub 2} and they only form physi-sorbed complexes, W{sub 2}O{sub 6}(O{sub 2}) and W{sub 3}O{sub 9}(O{sub 2}). However, the negatively charged W{sub 2}O{sub 6}{sup -} and W{sub 3}O{sub 9}{sup -} clusters are found to form chemisorbed complexes due to the presence of the extra electron. Thus, the W{sub 2}O{sub 6}{sup -} and W{sub 3}O{sub 9}{sup -} negative clusters can be viewed as models for O{sub 2} interaction with a reduced W site (W{sup 5+}) on the oxide surface. These studies also led to the surprising observation of the first d-orbital aromatic clusters in W{sub 3}O{sub 9}{sup 2-} and Mo{sub 3}O{sub 9}{sup 2-}, which each contains a completely delocalized three-center two-electron bond made entirely made of the metal d orbitals. This last result was highlighted in both Chem & Eng. News and Nature. We further studied a series of small metalate anions using electrospray, including the hydroxo and methoxo oxometalate MO{sub 3}(OH){sup -} and MO{sub 3}(OCH{sub 3}){sup -}, and the dimetalates: M{sub 2}O{sub 7}{sup 2-}, MM{prime}O{sub 7}{sup 2-}, and M{sub 2}O{sub 7}{sup -} (M, M{prime} = Cr, Mo, and W)

Retraction and Generalized Extension of Computing with Words

Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a formal model of computing with values. Motivated by Zadeh's paradigm of computing with words rather than numbers, Ying proposed a kind of fuzzy automata, whose input alphabet consists of all fuzzy subsets of a set of symbols, as a formal model of computing with all words. In this paper, we introduce a somewhat general formal model of computing with (some special) words. The new features of the model are that the input alphabet only comprises some (not necessarily all) fuzzy subsets of a set of symbols and the fuzzy transition function can be specified arbitrarily. By employing the methodology of fuzzy control, we establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling fuzzy inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with words. Some algebraic properties of retractions and generalized extensions are addressed as well.Comment: 13 double column pages; 3 figures; to be published in the IEEE Transactions on Fuzzy System

Gold as hydrogen: Structural and electronic properties and chemical bonding in Si3Au3+/0/- and comparisons to Si3H3+/0/-

A single Au atom has been shown to behave like H in its bonding to Si in several mono- and disilicon gold clusters. In the current work, we investigate the Au∕H analogy in trisilicon gold clusters, Si3Au+∕0∕−3. Photoelectron spectroscopy and density functional calculations are combined to examine the geometric and electronic structure of Si3Au−3. We find that there are three isomers competing for the ground state of Si3Au−3 as is the case for Si3H−3. Extensive structural searches show that the potential energy surfaces of the trisilicon gold clusters (Si3Au−3, Si3Au3, and Si3Au+3) are similar to those of the corresponding silicon hydrides. The lowest energy isomers for Si3Au−3 and Si3Au3 are structurally similar to a Si3Au four-membered ring serving as a common structural motif. For Si3Au+3, the 2π aromatic cyclotrisilenylium auride ion, analogous to the aromatic cyclotrisilenylium ion (Si3H+3), is the most stable species. Comparison of the structures and chemical bonding between Si3Au+∕0∕−3 and the corresponding silicon hydrides further extends the isolobal analogy between Au and H

Au\u3csub\u3e60\u3c/sub\u3e\u3csup\u3e–\u3c/sup\u3e: The Smallest Gold Cluster with the High-Symmetry Icosahedral Core Au\u3csub\u3e13\u3c/sub\u3e

Among coinage metal nanoclusters with 55 atoms, only Ag55– and Cu55– are the geometric magic-number clusters, as both exhibit icosahedral symmetry. Au55–, however, exhibits much lower symmetry due largely to the strong relativistic bonding effect. In this study, we collect a much larger population (\u3e10,000 isomers) of low-energy isomers of Au55– to Au60– by using the combined density-functional theory and basin-hopping global optimization method. We also include the spin−orbit effect in the density-functional theory computation to achieve simulated photoelectron spectra in quantitative fashion. Remarkably, we uncover that the Au13 core with the highest icosahedral (Ih) symmetry emerges at the size of Au60–. Stability analysis suggests that Au57– with 58 valence electrons, an electronic magic number, is the relatively more stable cluster in the size range considered. Overall, in this size range we reveal a compromise between the trend toward having a perfect icosahedral 13-atom core and the strong relativistic bonding effect

Electronic structure of chromium oxides, CrOn- and CrOn (n=1-5) from photoelectron spectroscopy and density functional theory calculations

The electronic structure of CrO−n and CrOn (n=1–5) was investigated using anion photoelectron spectroscopy and density functional theory. Photoelectron spectra of CrO−n were obtained at several photon energies and yielded electron affinities, vibrational and electronic structure information about the neutral CrOn species. Density functional theory calculations were carried out for both the neutrals and anions and were used to interpret the experimental spectra. Several low-lying electronic states of CrO were observed and assigned from photodetachment of the CrO− ground state(6∑+) and an excited state (4∏), which is only 0.1 eV higher. The main spectral features of CrO−2 were interpreted based on a C2v CrO−2 (4B1). A very weak Cr(O2)− isomer was also observed with lower electron binding energies. Relatively simple and vibrationally resolved spectra were observed for CrO−3, which was determined to be D3h. The CrO3 neutral was calculated to be C3v with the Cr atom slightly out of the plane of the three O atoms. The spectrum of CrO−4 revealed a very high electron binding energy. Several isomers of CrO−4 were predicted and the ground state has a distorted tetrahedral structure (C2) without any O–O bonding. Only one stable structure was predicted forCrO−5 with a superoxo O2 bonded to a C3v CrO3

Observation of earlier two-to-three dimensional structural transition in gold cluster anions by isoelectronic substitution: Mau\u3csub\u3e\u3ci\u3en\u3c/i\u3e\u3csup\u3e- \u3c/sup\u3e\u3c/sub\u3e (n=8–11; M=Ag,Cu)

The effects of isoelectronic substitution on the electronic and structural properties of gold clusters are investigated in the critical size range of the two-dimensional (2D)-three-dimensional (3D) structural transition (MAun −, n=8–11; M=Ag,Cu) using photoelectron spectroscopy and density functional calculations. Photoelectron spectra of MAun − are found to be similar to those of the bare gold clusters Aun+1 − , indicating that substitution of a Au atom by a Ag or Cu atom does not significantly alter the geometric and electronic structures of the clusters. The only exception occurs at n=10, where very different spectra are observed for MAu10 − from Au11 −, suggesting a major structural change in the doped clusters. Our calculations confirm that MAu8 − − possesses the same structure as Au9 − with Ag or Cu simply replacing one Au atom in its C2v planar global minimum structure. Two close-lying substitution isomers are observed, one involves the replacement of a center Au atom and another one involves an edge site. For Au10 − we identify three coexisting low-lying planar isomers along with the D3h global minimum. The coexistence of so many low-lying isomers for the small-sized gold cluster Au10 − is quite unprecedented. Similar planar structures and isomeric forms are observed for the doped MAu9 − clusters. Although the global minimum of Au11 − is planar, our calculations suggest that only simulated spectra of 3D structures agree with the observed spectra for MAu10 −. For MAu11 −, only a 3D isomer is observed, in contrast to Au12 − which is the critical size for the 2D-3D structural transition with both the 2D and 3D isomers coexisting. The current work shows that structural perturbations due to even isoelectronic substitution of a single Au atom shift the 2D to 3D structural transition of gold clusters to a smaller size

Observation of earlier two-to-three dimensional structural transition in gold cluster anions by isoelectronic substitution: Mau\u3csub\u3e\u3ci\u3en\u3c/i\u3e\u3csup\u3e- \u3c/sup\u3e\u3c/sub\u3e (n=8–11; M=Ag,Cu)

The effects of isoelectronic substitution on the electronic and structural properties of gold clusters are investigated in the critical size range of the two-dimensional (2D)-three-dimensional (3D) structural transition (MAun −, n=8–11; M=Ag,Cu) using photoelectron spectroscopy and density functional calculations. Photoelectron spectra of MAun − are found to be similar to those of the bare gold clusters Aun+1 − , indicating that substitution of a Au atom by a Ag or Cu atom does not significantly alter the geometric and electronic structures of the clusters. The only exception occurs at n=10, where very different spectra are observed for MAu10 − from Au11 −, suggesting a major structural change in the doped clusters. Our calculations confirm that MAu8 − − possesses the same structure as Au9 − with Ag or Cu simply replacing one Au atom in its C2v planar global minimum structure. Two close-lying substitution isomers are observed, one involves the replacement of a center Au atom and another one involves an edge site. For Au10 − we identify three coexisting low-lying planar isomers along with the D3h global minimum. The coexistence of so many low-lying isomers for the small-sized gold cluster Au10 − is quite unprecedented. Similar planar structures and isomeric forms are observed for the doped MAu9 − clusters. Although the global minimum of Au11 − is planar, our calculations suggest that only simulated spectra of 3D structures agree with the observed spectra for MAu10 −. For MAu11 −, only a 3D isomer is observed, in contrast to Au12 − which is the critical size for the 2D-3D structural transition with both the 2D and 3D isomers coexisting. The current work shows that structural perturbations due to even isoelectronic substitution of a single Au atom shift the 2D to 3D structural transition of gold clusters to a smaller size