Topological properties and fractal analysis of a recurrence network constructed from fractional Brownian motions

Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the average degree exponent 〈λ〉 increases first and then decreases with the increase of Hurst index H of the associated FBMs; the relationship between H and 〈λ〉 can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e., the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension 〈dB〉 of recurrence networks decreases with the Hurst index H of the associated FBMs, and their dependence approximately satisfies the linear formula 〈dB〉≈2-H, which means that the fractal dimension of the associated recurrence network is close to that of the graph of the FBM. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5 possesses the strongest multifractality. In addition, the dependence relationships of the average information dimension 〈D(1)〉 and the average correlation dimension 〈D(2)〉 on the Hurst index H can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.

Multifocal electroretinogram responses in Nepalese diabetic patients without retinopathy

Purpose To determine neuroretinal function with multifocal electroretinogram (mfERG) in diabetic subjects without retinopathy. Methods Multifocal electroretinogram (mfERG) was performed in 18 eyes of 18 diabetic subjects without retinopathy and 17 eyes of 17 age and gender-matched healthy control participants. Among 18 diabetic subjects, two had type 1 and 16 had type 2 diabetes. MfERG responses were averaged by the retinal areas of six concentric rings and four quadrants, and 103 retinal locations; N1–P1 amplitude and P1-implicit time were analysed. Results Average mfERG N1–P1 amplitude (in nv/deg2) of 103 retinal locations was 56.3 ± 17.2 (mean ± SD) in type 1 diabetic subjects, 47.2 ± 9.3 in type 2 diabetic subjects and 71.5 ± 12.7 in controls. Average P1-implicit time (in ms) was 43.0 ± 1.3 in type 1 diabetic subjects, 43.9 ± 2.3 in type 2 diabetic subjects and 41.9 ± 2.1 in controls. There was significant reduction in average N1–P1 amplitude and delay in P1-implicit time in type 2 diabetic subjects in comparison to controls. mfERG amplitude did not show any significant correlation with diabetes duration and blood sugar level. However, implicit time showed a positive correlation with diabetes duration in type 2 diabetic subjects with diabetes duration ≥5 years. Conclusions This is the first study in a Nepalese population with diabetes using multifocal electroretinography. We present novel findings that mfERG N1–P1 amplitude is markedly reduced along with delay in P1-implicit time in type 2 diabetic subjects without retinopathy. These findings indicate that there might be significant dysfunction of inner retina before the development of diabetic retinopathy in the study population, which have higher prevalence of diabetes than the global estimate and uncontrolled blood sugar level.

X-Ray Studies On The Bilayer Structure Of Trypsin-Treated Rat-Brain Myelin

Trypsin-treated rat brain myelin was subjected to biochemical and X-ray studies. Untreated myelin gave rise to a pattern of three rings with a fundamental repeat period of 155 Angstrom consisting of two bilayers per repeat period, whereas myelin treated with trypsin showed a fundamental repeat period of 75 Angstrom with one bilayer per repeat period. The integrated raw intensity of the h=4 reflection with respect to the h=2 reflection is 0.38 for untreated myelin. The corresponding value reduced to 0.23, 0.18, 0.17 for myelin treated with 5, 10, 40 units of trypsin per mg of myelin, respectively, for 30 min at 30 degrees C. The decrease in relative raw intensity of the higher-order reflection relative to the lower-order reflection is suggestive of a disordering of the phosphate groups upon trypsin treatment or an increased mosaicity of the membrane or a combination of both these effects, However, trypsin treatment does not lead to a complete breakdown of the membrane, The integrated intensity of the h=1 reflection, though weak, is above the measurable threshold for untreated myelin, whereas the corresponding intensity is below the measurable threshold for trypsin-treated myelin, indicating a possible asymmetric to symmetric transition of the myelin bilayer structure about its centre after trypsin treatment.

2-[2-(Hydroxymethyl)phenyl]-1-phenylethanol

The title compound, C15H16O2, has a dihedral angle of 19.10 (5)degrees between the mean planes of the two benzene rings. There is an intramolecular O-H center dot center dot center dot O hydrogen bond and the C-C-C-C torsion angle across the bridge between the two rings is 173.13 (14)degrees. The molecules form intermolecular O-H center dot center dot center dot O hydrogen-bonded chains extending along the a axis. C-H center dot center dot center dot pi contacts are also observed between molecules within the chains.

1,3-Dimethyl-2,6-diphenylpiperidin-4-one

In the title moleclue, C19H21NO, the 4-piperidone ring adopts a chair conformation in which the two benzene rings and the methyl group attached to C atoms all have equatorial orientations. In the crystal structure, centrosymmetric dimers are formed through weak intermolecular C-H center dot center dot center dot O hydrogen bonds [the dihedral angle between the aromatic rings is 58.51 (5)degrees].

Synthesis, reactivity and structural characterisation of bicyclic tetraphosphapentazanes

The diphenoxy bicyclic tetraphosphapentazane derivatives (EtN)(5)P-4(OPh)(2) 2 and its monoxide (EtN)(5)P-4(O)(OPh)(2) 3 have been prepared. Both 2 and 3 exist as a mixture of two isomers. One isomer of (EtN)(5)P-4(O)(OPh)(2) 3a has been isolated and its reaction with tetrachloro-1,2-benzoquinone yielded (EtN)(5)P-4(O)(OPh)(2)(O2C6Cl4) 5 in which the junction phosphorus atom becomes five-co-ordinated. Treatment of 2 or 3a with [Mo(CO)(4)(nbd)] (nbd = norbornadiene, bicyclo[2.2.1]hepta-2,5-diene), on the other hand, yielded the chelate complex [Mo(CO)(4){(EtN)(5)P-4(O)(n)(OPh)(2)}] (n = 0 or 1; 6 or 7) in which the peripheral phosphorus atoms are bonded to the metal. The structures of 3a and 5-7 have been confirmed by single-crystal X-ray diffraction studies. The two P3N3 rings in 3a and 5 adopt twist/twist and irregular/twist conformations respectively; the phenoxy substituents occupy the 'pseudo axial' positions. However, an ideal chair conformation is observed for the P3N3 rings in 6 and 7 with the phenoxy substituents taking up the 'pseudo equatorial' positions. The NMR spectroscopic data for the compounds are discussed.

Synthesis, structure and spectroscopic studies on hydroxo-bridged heterotrinuclear complexes of cobalt(m) with ethane-l,2-diamine and ammonia as terminal ligands

Hydroxo-bridged homo- and hetero-trinuclear cobalt(III) complexes of the type [MII(H2O)2{(OH)2CoIII(N4)}2]X2·nH2O [MII= a divalent metal ion such as CoII, NiII or ZnII; N4=(en)2(en = ethane-1,2-diamine) or (NH3)4; X = SO4 or (ClO4)2; n= 3 or 5] have been prepared and spectroscopically characterized. The structure of [Cu{(OH)2Co(en)2}2][SO4]2·2H2O 1 has been determined. The geometry around copper atom is a pseudo-square-based pyramid, with the basal sites occupied by four bridging hydroxide oxygens and the apical site is occupied by a weakly co-ordinated sulfate anion [Cu–O 2.516(4)Å]. The hydroxo groups bridge pairs of cobalt(III) ions which are in near-octahedral environments. The ethylenediamine chelate rings have the twist conformation. In the crystal structure of [Cu{(OH)2Co(en)2}2][ClO4]4·2H2O 2 the perchlorate ion is not co-ordinated and the en ligands have envelope conformations. The sulfate ion in [Cu{(OH)2Co(NH3)4}2][SO4]2·4H2O 3 is not co-ordinated to the central copper ion. Electronic, infrared and variable-temperature EPR spectral data are discussed.

3,3,6,6-Tetramethyl-9-phenyl-3,4,5,6-tetrahydro-9H-xanthene-1,8(2H,7H)-dione

In the title compound, C23H26O3, the three six-membered rings of the xanthene system are non-planar, having total puckering amplitudes, QT, of 0.443 (2), 0.202 (2) and 0.449 (2) Å. The central ring adopts a boat conformation and the outer rings adopt sofa conformations. The crystal structure is stabilized by van der Waals interactions.

N-Phenylnicotinamide

In the title compound, C12H10N2O, the dihedral angle between the phenyl and pyridine rings is 64.81 (1)degrees. Intermolecular N-H center dot center dot center dot O hydrogen bonds connect the molecules into chains running along the b axis.

Graphene, the new nanocarbon

Graphene is a fascinating new nanocarbon possessing, single-, bi- or few- (<= ten) layers of carbon atoms forming six-membered rings. Different types of graphene have been investigated by X-ray diffraction, atomic force microscopy, transmission electron microscopy, scanning tunneling microscopy and Raman spectroscopy. The extraordinary electronic properties of single-and bi-layer graphenes are indeed most unique and unexpected. Other properties of graphene such as gas adsorption characteristics, magnetic and electrochemical properties and the effects of doping by electrons and holes are equally noteworthy. Interestingly, molecular charge-transfer also markedly affects the electronic structure and properties of graphene. Many aspects of graphene are yet to be explored, including synthetic strategies which can yield sufficient quantities of graphene with the desired number of layers.

Study on tracheal collapsibility, compliance, and stress by considering nonlinear mechanical property of cartilage

Tracheal cartilage has been widely regarded as a linear elastic material either in experimental studies or in analytic and numerical models. However, it has been recently demonstrated that, like other fiber-oriented biological tissues, tracheal cartilage is a nonlinear material, which displays higher strength in compression than in extension. Considering the nonlinearity requires a more complex theoretical frame work and costs more to simulate. This study aims to quantify the deviation due to the simplified treatment of the tracheal cartilage as a linear material. It also evaluates the improved accuracy gained by considering the nonlinearity. Pig tracheal rings were used to exam the mechanical properties of cartilage and muscular membrane. By taking into account the asymmetric shape of tracheal cartilage, the collapse behavior of complete rings was simulated, and the compliance of airway and stress in the muscular membrane were discussed. The results obtained were compared with those assuming linear mechanical properties. The following results were found: (1) Models based on both types of material properties give a small difference in representing collapse behavior; (2) regarding compliance, the relative difference is big, ranging from 10 to 40% under negative pressure conditions; and (3) the difference in determining stress in the muscular membrane is small too: <5%. In conclusion, treating tracheal cartilage as a linear material will not cause big deviations in representing the collapse behavior, and mechanical stress in the muscular part, but it will induce a big deviation in predicting the compliance, particularly when the transmural pressure is lower than -0.5 kPa. The results obtained in this study may be useful in both understanding the collapse behavior of trachea and in evaluating the error induced by the simplification of treating the tracheal cartilage as a linear elastic material.

A thermal molecular migration in the solid-state - structures of isomeric 5-amino-4-(2,6-dichlorophenyl)-1-(2-nitrophenyl)-1h-1,2,3-triazole (yellow form i) and 4-(2,6-dichlorophenyl)-5-(2-nitroanilino)-2h-1,2,3-triazole (red form-ii), c14h9cl2n5o2

Yellow form (I): Mr= 350.09, monoclinic, P2Jn, Z--4, a=9.525(1), b=14.762(1), c= 11.268(1),/t, fl= 107.82 (1) o , V= 1508.3 A 3 , Din(flotation in aqueous KI)= 1.539 (2), D x= 1.541 (2) g cm -3, #(Cu Ka, 2 = 1.5418 A) = 40.58 cm -~, F(000) = 712, T= 293 K, R = 8.8% for 2054 significant refections. Red form (II): Mr= 350.09, triclinic, Pi, Z=2, a=9.796(2), b= 10.750 (2), c= 7.421 (1)A, a= 95.29 (2), fl= 0108-2701/84/111901-05501.50 70.18 (1), y = 92-.76 (2) °, V= 731.9 A 3, Din(flotation in KI) = 1.585 (3), D x = 1.588 (3) g cm -3, ~t(Cu Ka, 2 = 1.5418/~) = 40.58 cm -1, F(000) = 356, T=293 K, R = 5.8% for 1866 significant reflections. There are no unusual bond distances or angles. The triazole and two phenyl rings are planar. On the basis of packing considerations the possibility of intermolecular interactions playing a role in the reactivity of the starting material is ruled out.

Thermal conductivity of a new carbon nanotube analog: The diamond nanothread

Based on the non-equilibrium molecular dynamics simulations, we have studied the thermal conductivities of a novel ultra-thin one-dimensional carbon nanomaterial - diamond nanothread (DNT). Unlike single-wall carbon nanotube (CNT), the existence of the Stone-Wales transformations in DNT endows it with richer thermal transport characteristics. There is a transition from wave-dominated to particle-dominated transport region, which depends on the length of poly-benzene rings. However, independent of the transport region, strong length dependence in thermal conductivity is observed in DNTs with different lengths of poly-benzene ring. The distinctive SW characteristic in DNT provides more degrees of freedom to tune the thermal conductivity not found in the homogeneous structure of CNT. Therefore, DNT is an ideal platform to investigate various thermal transport mechanisms at the nanoscale. Its high tunability raises the potential to design DNTs for different applications, such as thermal connection and temperature management.

Structure Of 5'-Deoxy-5',6-Epithio-5,6-Dihydro-2',3'-O-Isopropylideneuridine, C12h16n2o5s

Mr=300.33 , triclinic, P1, a=5.635 (2), b=11.077(2), c=11.582(2)A, a= 70.48 (1), fl= 88.16 (3), y=80.56(3) ° , V= 670.325 A3, Z=2, D x = 1.49 Mg m -3, Cu Ka, n= 1.54184 ,A, g = 2.308mm -1, F(000)=316, T=301K, R=0.054, R w = 0.093 for 1944 observed counter reflections. The sulphur position with respect to the dihydrouracil ring, which is of possible relevance to the action of thymidylate synthetase, is axial in molecule A and equatorial in B. Both molecules show the anti conformation about the glycosidic bond [torsion angle C(6)-N(1)-C(1')-O(4'), 2'CN = 21.6 (9) and 29.4 (10) °] and have the C(4')-endo, O(4')-exo (40T) sugar conformation. The dioxolane-ring conformation is O(2')-endo in A and C(7)-endo in B. The dihydrouracil rings show self base pairing with hydrogen bondsN(3A)...O(ZB) and N(3B)...O(ZA).

Structural studies of analgesics and their interactions .10. A hydrated 1-1 complex between niflumic acid and ethanolamine, c13h8f3n2o-2.c2h8no+.h2o.

Mr= 361.3, triclinic, P1, a = 6-239 (2), b=11.280(2), c=12-451(2)A, a=101.2 (1), B= 92.3 (1), 7=99.9(1)°, V=844.123 A3, Z=2, Dx= 1.42, D m = 1.42 (1) Mg m -3, n(Cu Ka) = 1.5418 ,A., g = 1-102 mm -1, F(000) = 376, T= 293 K. Final R = 0.064 for 2150 observed reflections. The niflumic acid anions consist essentially of three planar groupings, namely, two six-membered rings and a carboxylate group attached to one of them. The invariant common structural features observed in the crystal structures of fenamates, namely, the coplanarity of the carboxyl group and the six-membered ring bearing it, and the internal hydrogen bond between the carboxyl group and the imino N atom that bridges the two sixmembered rings, are retained in the complex. The amino N atom is gauche with respect to the terminal hydroxyl group in the ethanolamine cation. The complexation between the two molecules is achieved through ionic and hydrogen-bonded interactions involving the carboxylate group in niflumic acid.