Tailoring electronic and optical properties of TiO2: nanostructuring, doping and molecular-oxide interactions

Titanium dioxide is one of the most widely investigated oxides. This is due to its broad range of applications, from catalysis to photocatalysis to photovoltaics. Despite this large interest, many of its bulk properties have been sparsely investigated using either experimental techniques or ab initio theory. Further, some of TiO2's most important properties, such as its electronic band gap, the localized character of excitons, and the localized nature of states induced by oxygen vacancies, are still under debate. We present a unified description of the properties of rutile and anatase phases, obtained from ab initio state of the art methods, ranging from density functional theory (DFT) to many body perturbation theory (MBPT) derived techniques. In so doing, we show how advanced computational techniques can be used to quantitatively describe the structural, electronic, and optical properties of TiO2 nanostructures, an area of fundamental importance in applied research. Indeed, we address one of the main challenges to TiO2-photocatalysis, namely band gap narrowing, by showing how to combine nanostructural changes with doping. With this aim we compare TiO2's electronic properties for 0D clusters, 1D nanorods, 2D layers, and 3D bulks using different approximations within DFT and MBPT calculations. While quantum confinement effects lead to a widening of the energy gap, it has been shown that substitutional doping with boron or nitrogen gives rise to (meta-)stable structures and the introduction of dopant and mid-gap states which effectively reduce the band gap. Finally, we report how ab initio methods can be applied to understand the important role of TiO2 as electron-acceptor in dye-sensitized solar cells. This task is made more difficult by the hybrid organic-oxide structure of the involved systems.Comment: 32 pages, 8 figure

Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

The occurrence of hyponatremia and its importance as a prognostic factor in a cross-section of cancer patients

BACKGROUND: Hyponatremia is prognostic of higher mortality in some cancers but has not been well studied in others. We used a longitudinal design to determine the incidence and prognostic importance of euvolemic and hypervolemic hyponatremia in patients following diagnosis with lymphoma, breast (BC), colorectal (CRC), small cell lung (SCLC), or non-small cell lung cancer (NSCLC). METHODS: Medical record and tumor registry data from two large integrated delivery networks were combined for patients diagnosed with lymphoma, BC, CRC, or lung cancers (2002-2010) who had ≥1 administration of radiation/chemotherapy within 6 months of diagnosis and no evidence of hypovolemic hyponatremia. Hyponatremia incidence was measured per 1000 person-years (PY). Cox proportional hazard models assessed the prognostic value of hyponatremia as a time-varying covariate on overall survival (OS) and progression-free survival (PFS). RESULTS: Hyponatremia incidence (%, rate) was 76 % each, 1193 and 2311 per 1000 PY, among NSCLC and SCLC patients, respectively; 37 %, 169 in BC; 64 %, 637 in CRC, and 60 %, 395 in lymphoma. Hyponatremia was negatively associated with OS in BC (HR 3.7; P = \u3c.01), CRC (HR 2.4; P \u3c .01), lung cancer (HR 2.4; P \u3c .01), and lymphoma (HR 4.5; P \u3c .01). Hyponatremia was marginally associated with shorter PFS (HR 1.3, P = .07) across cancer types. CONCLUSIONS: The incidence of hyponatremia is higher than previously reported in lung cancer, is high in lymphoma, BC, and CRC and is a negative prognostic indicator for survival. Hyponatremia incidence in malignancy may be underestimated. The effects of hyponatremia correction on survival in cancer patients require further study

Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence

We show that the Gromov-Witten theory of Calabi-Yau hypersurfaces matches, in genus zero and after an analytic continuation, the quantum singularity theory (FJRW theory) recently introduced by Fan, Jarvis and Ruan following ideas of Witten. Moreover, on both sides, we highlight two remarkable integral local systems arising from the common formalism of Gamma-integral structures applied to the derived category of the hypersurface {W=0} and to the category of graded matrix factorizations of W. In this setup, we prove that the analytic continuation matches Orlov equivalence between the two above categories.Comment: 72pages, v2: Appendix B and references added. Typos corrected, v3: several mistakes corrected, final versio

Tau-Structure for the Double Ramification Hierarchies

In this paper we continue the study of the double ramification hierarchy of Buryak (Commun Math Phys 336(3):1085–1107, 2015). After showing that the DR hierarchy satisfies tau-symmetry we define its partition function as the (logarithm of the) tau-function of the string solution and show that it satisfies various properties (string, dilaton, and divisor equations plus some important degree constraints). We then formulate a stronger version of the conjecture from Buryak (2015): for any semisimple cohomological field theory, the Dubrovin–Zhang and double ramification hierarchies are related by a normal [i.e. preserving the tau-structure (Dubrovin et al. in Adv Math 293:382–435, 2016)] Miura transformation which we completely identify in terms of the partition function of the CohFT. In fact, using only the partition functions, the conjecture can be formulated even in the non-semisimple case (where the Dubrovin–Zhang hierarchy is not defined). We then prove this conjecture for various CohFTs (trivial CohFT, Hodge class, Gromov–Witten theory of CP¹, 3-, 4- and 5-spin classes) and in genus 1 for any semisimple CohFT. Finally we prove that the higher genus part of the DR hierarchy is basically trivial for the Gromov–Witten theory of smooth varieties with non-positive first Chern class and their analogue in Fan–Jarvis–Ruan–Witten quantum singularity theory (Fan et al. in Ann Math 178(1):1–106, 2013)

A clock network for geodesy and fundamental science

Leveraging the unrivaled performance of optical clocks in applications in fundamental physics beyond the standard model, in geo-sciences, and in astronomy requires comparing the frequency of distant optical clocks truthfully. Meeting this requirement, we report on the first comparison and agreement of fully independent optical clocks separated by 700 km being only limited by the uncertainties of the clocks themselves. This is achieved by a phase-coherent optical frequency transfer via a 1415 km long telecom fiber link that enables substantially better precision than classical means of frequency transfer. The fractional precision in comparing the optical clocks of three parts in $10^{17}$ was reached after only 1000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than with any other existing frequency transfer method. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.Comment: 14 pages, 3 figures, 1 tabl

Global hybrids from the semiclassical atom theory satisfying the local density linear response

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetical and structural testings, including thermochemistry and geometry, transition metal complexes, non-covalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical dispersion corrections are also provided.Comment: 12 pages, 4 figure

Synthetic zwitterionic streptococcus pneumoniae Type 1 oligosaccharides carrying labile O-acetyl esters

We herein report the first total synthesis of the Streptococcus pneumoniae serotype 1 (Sp1) oligosaccharide, a unique zwitterionic capsular polysaccharide carrying labile O-acetyl esters. The target oligosaccharides, featuring rare α-2,4-diamino-2,4,6-trideoxy galactose (AAT) and α-galacturonic acids, were assembled up to the 9-mer level, in a highly stereoselective manner using trisaccharide building blocks. The lability of the O-acetyl esters imposed a careful deprotection scheme to prevent migration and hydrolysis. The migration was investigated in detail at various pD values using NMR spectroscopy, to show that migration and hydrolysis of the C-3-O-acetyl esters readily takes place under neutral conditions. Structural investigation showed the oligomers to adopt a right-handed helical structure with the acetyl esters exposed on the periphery of the helix in close proximity of the neighboring AAT residues, thereby imposing conformational restrictions on the AATα1-4GalA(3OAc) glycosidic linkages, supporting the helical shape of the polysaccharide, that has been proposed to be critical for its unique biological activity.Bio-organic Synthesi