General and Interval Type-2 Fuzzy Face-Space Approach to Emotion Recognition

Facial expressions of a person representing similar emotion are not always unique. Naturally, the facial features of a subject taken from different instances of the same emotion have wide variations. In the presence of two or more facial features, the variation of the attributes together makes the emotion recognition problem more complicated. This variation is the main source of uncertainty in the emotion recognition problem, which has been addressed here in two steps using type-2 fuzzy sets. First a type-2 fuzzy face space is constructed with the background knowledge of facial features of different subjects for different emotions. Second, the emotion of an unknown facial expression is determined based on the consensus of the measured facial features with the fuzzy face space. Both interval and general type-2 fuzzy sets (GT2FS) have been used separately to model the fuzzy face space. The interval type-2 fuzzy set (IT2FS) involves primary membership functions for m facial features obtained from n-subjects, each having l-instances of facial expressions for a given emotion. The GT2FS in addition to employing the primary membership functions mentioned above also involves the secondary memberships for individual primary membership curve, which has been obtained here by formulating and solving an optimization problem. The optimization problem here attempts to minimize the difference between two decoded signals: the first one being the type-1 defuzzification of the average primary membership functions obtained from the n-subjects, while the second one refers to the type-2 defuzzified signal for a given primary membership function with secondary memberships as unknown. The uncertainty management policy adopted using GT2FS has resulted in a classification accuracy of 98.333% in comparison to 91.667% obtained by its interval type-2 counterpart. A small improvement (approximately 2.5%) in classification accuracy by IT2FS has been attained by pre-processing measurements using - he well-known interval approach

Synthesis, structural analysis, and magnetic behaviour of three fumarate bridged coordination polymers: five-fold interpenetrated diamond-like net of Ni-II, sheets of Ni-II and Co-II

The hydrothermal reactions of Ni(NO3)(2).6H(2)O, disodium fumarate (fum) and 1,2-bis(4-pyridyl)ethane (bpe)/1,3-bis(4-pyridyl) propane (bpp) in aqueous-methanol medium yield one 3-D and one 2-D metal-organic hybrid material, [Ni(fum)(bpe)] (1) and [Ni(fum)(bpp)(H2O)] (2), respectively. Complex 1 possesses a novel unprecedented structure, the first example of an "unusual mode" of a five-fold distorted interpenetrated network with metal-ligand linkages where the four six-membered windows in each adamantane-type cage are different. The structural characterization of complex 2 evidences a buckled sheet where nickel ions are in a distorted octahedral geometry, with two carboxylic groups, one acting as a bis-chelate, the other as a bis-monodentate ligand. The metal ion completes the coordination sphere through one water molecule and two bpp nitrogens in cis position. Variable-temperature magnetic measurements of complexes 1 and 2 reveal the existence of very weak antiferromagnetic intramolecular interactions and/or the presence of single-ion zero field splitting (D) of isolated Ni-II ions in both the compounds. Experimentally, both the J parameters are close, comparable and very small. Considering zero-field splitting of Ni-II, the calculated D values are in agreement with values reported in the literature for Ni-II ions. Complex 3, [{Co(phen)}(2)(fum)(2)] (phen=1,10-phenanthroline) is obtained by diffusing methanolic solution of 1,10-phenanthroline on an aqueous layer of disodium fumarate and Co(NO3)(2).6H(2)O. It consists of dimeric Co-II(phen) units, doubly bridged by carboxylate groups in a distorted syn-syn fashion. These fumarate anions act as bis-chelates to form corrugated sheets. The 2D layer has a (4,4) topology, with the nodes represented by the centres of the dimers. The magnetic data were fitted ignoring the very weak coupling through the fumarate pathway and using a dimer model

Syntheses of two new 1D and 3D networks of Cu(II) and Co(II) using malonate and urotropine as bridging ligands: Crystal structures and magnetic studies

Two new metal-organic based polymeric complexes, [Cu-4(O2CCH2CO2)(4)(L)].7H(2)O (1) and [CO2(O2CCH2CO2)(2)(L)].2H(2)O (2) [L = hexamethylenetetramine (urotropine)], have been synthesized and characterized by X-ray crystal structure determination and magnetic studies. Complex 1 is a 1D coordination polymer comprising a carboxylato, bridged Cu-4 moiety linked by a tetradentate bridging urotropine. Complex 2 is a 3D coordination polymer made of pseudo-two-dimensional layers of Co(II) ions linked by malonate anions in syn-anticonformation which are bridged by bidentate urotropine in trans fashion, Complex 1 crystallizes in the orthothombic system, space group Pmmn, with a = 14,80(2) Angstrom, b = 14.54(2) Angstrom, c = 7.325(10) Angstrom, beta = 90degrees, and Z = 4. Complex 2 crystallizes in the orthorhombic system, space group Imm2, a = 7.584(11) Angstrom, b = 15.80(2) Angstrom, c = 6.939(13) Angstrom, beta = 90.10degrees(1), and Z = 4. Variable temperature (300-2 K) magnetic behavior reveals the existence of ferro- and antiferromagnetic interactions in 1 and only antiferromagnetic interactions in 2. The best fitted parameters for complex 1 are J = 13.5 cm(-1), J = -18.1 cm(-1), and g = 2.14 considering only intra-Cu-4 interactions through carboxylate and urotropine pathways. In case of complex 2, the fit of the magnetic data considering intralayer interaction through carboxylate pathway as well as interlayer interaction via urotropine pathway gave no satisfactory result at this moment using any model known due to considerable orbital contribution of Co(II) ions to the magnetic moment and its complicated structure. Assuming isolated Co(II) ions (without any coupling, J = 0) the shape of the chi(M)T curve fits well with experimental data except at very low temperatures

Two new Ni-II complexes with mu(1.5)-dicyanamide as bridging ligand

One 3D and one 2D mu(1,5)-dicyanamide bridged Ni-II complexes having molecular formula [Ni(L1)(dca)(2)] (1) and [Ni-2(L-2)(2)(dca)(4)] (.) 0.5H(2)O (2) (L1 = 4-(2-aminoethyl)-morpholine, L2 = 1-(2-aminoethyl)-piperidine and dca = dicyanamide dianion) have been synthesized. X-ray single crystal analyses and low temperature magnetic measurements were used to characterize the complexes. Complex 1 represents a 3D structure where each metal ion is chelated by morpholine ligand (L1) and connected by four mu(1,5)-dca. Whereas complex 2 shows an undulated 2D structure with grid of (4,4) topology having two crystallographically independent Ni-II centers in similar octahedral environment where each metal center is chelated by one piperidine ligand (L2) and coordinated by four mu(1,5)-dca. Magnetic measurements of both the complexes indicate weak antiferromagnetic interactions through the mu-(1,5)-dca bridging ligands. (c) 2004 Elsevier B.V. All rights reserved

Syntheses, structural analyses, and magneto-structural correlations of three polymeric Fe(II) complexes with azide ligand

Three new metal-organic polymeric complexes, [Fe(N-3)(2)(bPP)(2)] (1), [Fe(N-3)(2)(bpe)] (2), and [Fe(N-3)(2)(phen)] (3) [bpp = (1,3-bis(4-pyridyl)-propane), bpe = (1,2-bis(4-pyridyl)-ethane), phen = 1,10-phenanthroline], have been synthesized and characterized by single-crystal X-ray diffraction studies and low-temperature magnetic measurements in the range 300-2 K. Complexes 1 and 2 crystallize in the monoclinic system, space group C2/c, with the following cell parameters: a = 19.355(4) Angstrom, b = 7.076(2) Angstrom, c = 22.549(4) Angstrom, beta = 119.50(3)degrees, Z = 4, and a = 10.007(14) Angstrom, b = 13.789(18) Angstrom, c = 10.377(14) Angstrom, beta = 103.50(1)degrees, Z = 4, respectively. Complex 3 crystallizes in the triclinic system, space group P (1) over bar, with a = 7.155(12) Angstrom, b = 10.066(14) Angstrom, c = 10.508(14) Angstrom, alpha = 109.57(1)degrees, beta = 104.57(1)degrees, gamma = 105.10(1)degrees, and Z = 2. All coordination polymers exhibit octahedral Fe(II) nodes. The structural determination of 1 reveals a parallel interpenetrated structure of 2D layers of (4,4) topology, formed by Fe(II) nodes linked through bpp ligands, while mono-coordinated azide anions are pendant from the corrugated sheet. Complex 2 has a 2D arrangement constructed through 1D double end-to-end azide bridged iron(11) chains interconnected through bpe ligands. Complex 3 shows a polymeric arrangement where the metal ions are interlinked through pairs of end-on and end-to-end azide ligands exhibiting a zigzag arrangement of metals (Fe-Fe-Fe angle of 111.18degrees) and an intermetallic separation of 3.347 Angstrom (through the EO azide) and of 5.229 Angstrom (EE azide). Variable-temperature magnetic susceptibility data suggest that there is no magnetic interaction between the metal centers in 1, whereas in 2 there is an antiferromagnetic interaction through the end-to-end azide bridge. Complex 3 shows ferro- as well as anti-ferromagnetic interactions between the metal centers generated through the alternating end-on and end-to-end azide bridges. Complex I has been modeled using the D parameter (considering distorted octahedral Fe(II) geometry and with any possible J value equal to zero) and complex 2 has been modeled as a one-dimensional system with classical and/or quantum spin where we have used two possible full diagonalization processes: without and with the D parameter, considering the important distortions of the Fe(II) ions. For complex 3, the alternating coupling model impedes a mathematical solution for the modeling as classical spins. With quantum spin, the modeling has been made as in 2

A new porous 2D coordination polymer built by copper(II) and trimesic acid

A 2D porous material, Cu-3(tmen)(3)(tma)(2)(H2O)(2)(.)6.5H(2)O [tmen = N,N,N',N'-tetramethylethane-1,2-diamine; tmaH(3) = 1,3,5-benzenetricarboxylic acid/trimesic acid], has been synthesized and characterized by X-ray single crystal analysis, variable temperature magnetic measurements, IR spectra and XRPD pattern. The complex consists of 2D layers built by three crystallographically independent Cu(tmen) moieties bridged by tma anions. Of the three copper ions, Cu(1) and Cu(2) present distorted square pyramidal coordination geometry, while the third exhibits a severely distorted octahedral environment. The Cu(1)(tmen) and Cu(2)(tmen) building blocks bridged by tma anions give rise to chains with a zig-zag motif, which are cross-connected by Cu(3)(tmen)-tma polymers sharing metal ions Cu(2) through pendant tma carboxylates. The resulting 2D architecture extends in the crystallographic ab-plane. The adjacent sheets are embedded through the Cu(3)(tmen) tma chains, leaving H2O-filled channels. There are 6.5 lattice water molecules per formula unit, some of which are disordered. Upon heating, the lattice water molecules get eliminated without destroying the crystal morphology and the compound rehydrated reversibly on exposure to humid atmosphere. Magnetic data of the complex have been fitted considering isolated irregular Cu-3 triangles (three different J parameters) by applying the CLUMAG program. The best fit indicates three close comparable J parameters and very weak antiferromagnetic interactions are operative between the metal centers. (C) 2004 Elsevier B.V. All rights reserved