Isomorphous Analogue Research Articles

Analogical mapping by constraint satisfaction

A theory of analogical mapping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of isomorphism encourages mappings that maximize the consistency of relational corresondences between the elements of the two analogs. The constraint of semantic similarity supports mapping hypotheses to the degree that mapped predicates have similar meanings. The constraint of pragmatic centrality favors mappings involving elements the analogist believes to be important in order to achieve the purpose for which the analogy is being used. The theory is implemented in a computer program called ACME (Analogical Constraint Mapping Engine), which represents constraints by means of a network of supporting and competing hypotheses regarding what elements to map. A cooperative algorithm for parallel constraint satisfaction identities mapping hypotheses that collectively represent the overall mapping that best fits the interacting constraints. ACME has been applied to a wide range of examples that include problem analogies, analogical arguments, explanatory analogies, story analogies, formal analogies, and metaphors. ACME is sensitive to semantic and pragmatic information if it is available, and yet able to compute mappings between formally isomorphic analogs without any similar or identical elements. The theory is able to account for empirical findings regarding the impact of consistency and similarity on human processing of analogies.

Analogical Mapping by Constraint Satisfaction

A theory of analogical mapping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of isomorphism encourages mappings that maximize the consistency of relational corresondences between the elements of the two analogs. The constraint of semantic similarity supports mapping hypotheses to the degree that mapped predicates have similar meanings. The constraint of pragmatic centrality favors mappings involving elements the analogist believes to be important in order to achieve the purpose for which the analogy is being used. The theory is implemented in a computer program called ACME (Analogical Constraint Mapping Engine), which represents constraints by means of a network of supporting and competing hypotheses regarding what elements to map. A cooperative algorithm for parallel constraint satisfaction identities mapping hypotheses that collectively represent the overall mapping that best fits the interacting constraints. ACME has been applied to a wide range of examples that include problem analogies, analogical arguments, explanatory analogies, story analogies, formal analogies, and metaphors. ACME is sensitive to semantic and pragmatic information if it is available, and yet able to compute mappings between formally isomorphic analogs without any similar or identical elements. The theory is able to account for empirical findings regarding the impact of consistency and similarity on human processing of analogies.

Measures on spaces of operators and isometries

One considers a question that arises at the investigation of isometric operators in vector-valued Lp -spaces. Let E, F be Banach spaces, let p>0, let μ be a probability Borel measure on the space on continuous linear operators from E into F such that for any e e E one has $$\left\| e \right\|^p = \int {\left\| {Te} \right\|^p } d\mu \left( T \right)$$ . In the cases when: 1) E=C(K), K is a metric compactum, F is an arbitrary space, p>1 and 2) 2)E=F=Lq,p>1, q>1 q ∉[p,2] it is Proved that the support of the measure μ is contained in the set of the operators that are scalar multiples of isometries. For E=C(K) one obtains an isomorphic analogue of this result: if the Banach-Mazur distance between C(K) and the P -sum of Banach spaces is small, then the distance between C(K) and one of the spaces is small.

SUGAR INTERACTION WITH ALKALI METAL IONS. SYNTHESIS AND VIBRATIONAL SPECTRA OF CRYSTALLINE SUCROSE AND ITS SODIUM HALIDE ADDUCTS

Abstract Sucrose interacts with NaCl. NaBr and NaI to give adducts of the type Na(sucrose)Cl·2H2O Na(sucrose)Br·2H 2O and Na 3(sucrose) 2I3·3H2O. A comparison between the infrared spectra of free sucrose and its metal adducts has been made and a correlation between spectral changes and the binding sites used by the sugar molecule has been established. X-ray structural information shows that the Na− ion is six-coordinated in the structurally identified compound Na(sucrose)Br·2H2O and its isomorphous analogue Na(sucrose)Cl·2H2O, but differs from this in the Na3(sucrose)2I3·3H2O compound. The sodium ion binds through 0(4), 0(6), 0(6′) of the sugar and to two water molecules as well as to a halide anion, resulting a six-coordinated metal ion based on a distorted octahedron geometry. The strong sugar hydrogen bonding network is rearranged upon sugar metallation and the assignments of the absorption bands in the OH stretching region of the spectra have been made based on the X-ray structural analysis and neutro...

Direct synthesis and characterization of the Fe3+ analogue of Naβ″-alumina

A new isomorphic analogue ofβ″-alumina, a potassium-free Na-ferrite (Na2O · ∼5 (Al0.10Fe1.90)O3, referred to as Naβ″-ferrite), has been synthesized and is characterized using X-ray powder and single crystal diffraction, wet chemical analysis, and transmission electron microscopy (TEM). In addition, Naβ″-aluminate-gallate-ferrate phases were also successfully synthesized, but were not characterized in detail. Naβ″-ferrite grew in a slowly cooling melt or partial melt from 1250° C in air using Na2CO3 and Fe3O4 (magnetite) as starting materials. The compound was also synthesized usingα-Fe2O3 instead of Fe3O4 under the same conditions, but its abundance was much less andα-Fe2O3 and NaFeO2 were the dominant phases. The new material (cell dimensionsa = 0.5955,c = 3.5623 nm) is reversibly hygroscopic, andc increases 2% after hydration. TEM images dearly show the 1.19 nm lattice spacing corresponding to the ionic conduction planes, and these planes are observed to be both straight and curled. The origin of the curled lattice planes, the existence of which is also evident in the single crystal precession photographs, is not clear, although we believe it may involve a structural misfit between the ferric oxide spineI block and soda layer.

Luminescence energy transfer studies of C-reactive protein. Binding of terbium (III) ions in C-reactive protein.

The acute phase of inflammation is characterized by numerous changes in blood composition, perhaps the most dramatic of these being the elevation of C-reactive protein levels. C-reactive protein (CRP) is known to bind to molecules containing phosphocholine-substituents following reaction with Ca2+ ions. Luminescence energy transfer (LET) has been used effectively to study the Ca2+ and Mg2+ binding properties of many proteins by employing appropriate lanthanides (III). We have used Tb3+ as an isomorphous analogue to study Ca2+ binding to CRP. Energy transfer occurs effectively and demonstrates the importance of aromatic residues (viz., tyrosine and tryptophan) in the binding of Tb3+. The binding of Tb3+ is remarkably dependent on the pH and indicates the requirement of a deprotonated residue in the pH range 6.4 +/- 0.2 for effective Tb3+ binding. A 50-fold molar excess of Ca2+ is sufficient to displace the Tb3+ suggesting that Tb3+ is bound with greater affinity to CRP than the natural analogue Ca2+. We propose that Tb3+ (by inference Ca2+) binding takes place near the CRP subunit disulfide bond, where two histidine residues are present. The pH dependency of Tb3+ binding is best explained by the deprotonation of a histidine residue(s) in CRP.

Crystal and molecular structure of dimorpholinotetrasulphane

The tetrasulphane S4(NC4H8O)2 crystallizes in the tetragonal space group l41/a(no. 88) with a=b= 12.812(1), c= 16.733(2)A, and Z= 8. The structure has been determined by X-ray diffraction from Mo-Kα diffractometer data and refined by full-matrix least squares to R 0.045 for 948 observed reflections. The molecules lie across crystallographic two-fold axes. The N–S–S–S–S–N chains occur in the trans-trans form, with N–S 1.668(3), S–S (terminal) 2.061(2), S–S (central) 2.078(3)A, N–S–S 109.1(2), S–S–S 105.8(1)°, NSS–SSS 90.3 and SSS–SSS 79.9°. The morpholine groups occur in the chair form, with N–S equatorial. The S–S bonds alternate only slightly in length along the chain, like the Se–Se bonds in the isomorphous tetraselane analogue.

Infinite dimensional 𝐿-spaces do not have preduals of all orders

It is shown that if E is an infinite dimensional Banach space with first dual E’, second dual E", and nth dual E [ n ] {E^{[n]}} and if E [ n ] {E^{[n]}} is either an L- or M-space all duals are either L- or M-spaces except possibly E which could be a Lindenstrauss space. If E is an L- or M-space there is an integer n ( E ) n(E) so that if m > n ( E ) m > n(E) there is no Banach space F with E = F [ m ] E = {F^{[m]}} . The linear isomorphic analogues to these isometric results are also established. In particular if E is an L 1 {\mathcal {L}_1} or L ∞ {\mathcal {L}_\infty } space there is an integer n ¯ ( E ) \bar n(E) so that E is not linearly isomorphic to F [ m ] {F^{[m]}} for any Banach space F when m > n ¯ ( E ) m > \bar n(E) .

Side-chain mobility and the calculation of tyrosyl circular dichroism of proteins. Implications of a test with insulin and des-B1-phenylalanine insulin

Previous calculations using crystal structure coordinates (Strickland and Mercola [1976], Biochemistry. 15: 3857) have predicted that about 40 percent of the calculated tyrosyl circular dichroism of hexameric insulin is due to one of the four tyrosine residues: viz. the A14-tyrosine interacting with the nearby B1-phenylalanine ring group. We have tested this prediction by measuring the tyrosyl circular dichroism of an isomorphous analogue of insulin, des-B1-phenylalanine-insulin. Contrary to expectation, the resulting circular dichroism was the same as that of insulin. It is concluded that the B1-phenylalanine residue does not in fact make a large contribution to the circular dichroism of A14-tyrosine. This result is probably due to the thermal motion of the B1 and A14 ring groups not taken into account by the calculations. An example of the effects of thermal motion on the calculated circular dichroism is given and improvements that do take into account thermal motion are discussed.

A carbon-13 spin lattice relaxation study of alumichrome at 25.1 MHz and 90.5 MHz

The effect of metal binding on the structure of ferrichrome in [ 2H 6]Me 2SO solutions at 45 °C, was studied by comparing the 13C spin-lattice relaxation of deferriferrichrome and alumichrome at 25.1 MHz. As has been found for other flexible cyclic oligopeptides, the metal-free siderophore exhibits consistent NT 1 values for α-carbons with a marked trend towards smaller relaxation rates for sidechain carbons. The rotational correlation time, τ r, calculated on the basis of the average NT 1 for the cyclohexapeptide backbone, < NT 1> = 93 ms, and under the assumption of isotropic motion is ≈ 0.56 ns. After binding Al 3+ the overall carbon skeleton exhibits rather uniform N ∗T 1 values, with a mean value <N ∗T 1> = 125 ms which yields an effective τ r ≈ 0.40 ns. Compared with the results for deferriferrichrome, these data indicate a more rigid compact structure with a faster rotational motion for the coordination compound. The 13C T 1 values were also measured at 90.5 MHz. It was found that agreement between the low and high field data can be obtained by assuming the C-H bond to be somewhat longer than 1.09 Å. A consistent value for the alumichrome isotropic rotational correlation time, τ r = 0.58 ns, was thus derived under the assumption that the effective <r CH > = 1.15 A ̊ . Nuclear Overhauser enhancements as well as the T 1 data indicate that at 25.1 MHz the 1H- 13C dipolar interaction is the dominant relaxation mechanism for the various peptide carbonyls. The observations agree well with expectations from σ i r −6 CHI calculations based on the crystallographic coordinates for the isomorphic analogue ferrichrome A.