On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Peripartum management of glycemia in women with type 1 diabetes

OBJECTIVE We aimed to 1) describe the peripartum management of type 1 diabetes at an Australian teaching hospital and 2) discuss factors influencing the apparent transient insulin independence postpartum. RESEARCH DESIGN AND METHODS We conducted a retrospective review of women with type 1 diabetes delivering singleton pregnancies from 2005 to 2010. Information was collected regarding demographics, medical history, peripartum management and outcome, and breast-feeding. To detect a difference in time to first postpartum blood glucose level (BGL) >8 mmol/L between women with an early (<4 h) and late (>12 h) requirement for insulin postpartum, with a power of 80% and a type 1 error of 0.05, at least 24 patients were required. RESULTS An intravenous insulin infusion was commenced in almost 95% of women. Univariate analysis showed that increased BMI at term, lower creatinine at term, longer duration from last dose of long- or intermediate-acting insulin, and discontinuation of an insulin infusion postpartum were associated with a shorter time to first requirement of insulin postpartum (P = 0.005, 0.026, 0.026, and <0.001, respectively). There was a correlation between higher doses of insulin commenced postpartum and number of out-of-range BGLs (r[36] = 0.358, P = 0.030) and hypoglycemia (r[36] = 0.434, P = 0.007). Almost 60% had at least one BGL <3.5 mmol/L between delivery and discharge. CONCLUSIONS Changes in the pharmacodynamic profile of insulin may contribute to the transient insulin independence sometimes observed postpartum in type 1 diabetes. A dose of 50–60% of the prepregnancy insulin requirement resulted in the lowest rate of hypoglycemia and glucose excursions. These results require validation in a larger, prospective study.

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes: Part 14. The infrared and Raman characteristics of phthalocyanine in “pinwheel-like” homoleptic bis[1,8,15,22-tetrakis(3-pentyloxy)phthalocyaninato] rare earth(III) double-decker complexes

The infrared (IR) spectroscopic data and Raman spectroscopic properties for a series of 13 “pinwheel-like” homoleptic bis(phthalocyaninato) rare earth complexes M[Pc(α-OC5H11)4]2 [M = Y and Pr–Lu except Pm; H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected and comparatively studied. Both the IR and Raman spectra for M[Pc(α-OC5H11)4]2 are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues, namely M(Pc)2 and M[Pc(OC8H17)8]2, but resemble (for IR) or are a bit more complicated (for Raman) than those of heteroleptic counterparts M(Pc)[Pc(α-OC5H11)4], revealing the decreased molecular symmetry of these double-decker compounds, namely S8. Except for the obvious splitting of the isoindole breathing band at 1110–1123 cm−1, the IR spectra of M[Pc(α-OC5H11)4]2 are quite similar to those of corresponding M(Pc)[Pc(α-OC5H11)4] and therefore are similarly assigned. With laser excitation at 633 nm, Raman bands derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. The IR spectra reveal that the frequencies of pyrrole stretching and pyrrole stretching coupled with the symmetrical CH bending of –CH3 groups are sensitive to the rare earth ionic size, while the Raman technique shows that the bands due to the isoindole stretchings and the coupled pyrrole and aza stretchings are similarly affected. Nevertheless, the phthalocyanine monoanion radical Pc′− IR marker band of bis(phthalocyaninato) complexes involving the same rare earth ion is found to shift to lower energy in the order M(Pc)2 > M(Pc)[Pc(α-OC5H11)4] > M[Pc(α-OC5H11)4]2, revealing the weakened π–π interaction between the two phthalocyanine rings in the same order.

Peripherally η1-Platinated Organometallic Porphyrins as Building Blocks for Multiporphyrin Arrays

The modification of peripherally metalated meso-η1-platiniometalloporphyrins, such as trans-[PtBr(NiDAPP)(PPh3)2] (H2DAPP = 5-phenyl-10,20-bis(3‘,5‘-di-tert-butylphenyl)porphyrin), leads to the analogous platinum(II) nitrato and triflato electrophiles in almost quantitative yields. Self-assembly reactions of these meso-platinioporphyrin tectons with pyridine, 4,4‘-bipyridine, or various meso-4-pyridylporphyrins in chloroform generate new multicomponent organometallic porphyrin arrays containing up to five porphyrin units. These new types of supramolecular arrays are formed exclusively in high yields and are stable in solution or in the solid state for extended periods. They were characterized by multinuclear NMR and UV−visible spectroscopy as well as high-resolution electrospray ionization mass spectrometry.