Quantized mirror curves and resummed WKB

Based on previous insights, we present an ansatz to obtain quantization conditions and eigenfunctions for a family of difference equations which arise from quantized mirror curves in the context of local mirror symmetry of toric Calabi-Yau threefolds. It is a first principles construction, which yields closed expressions for the quantization conditions and the eigenfunctions when $\hbar/2\pi \in \mathbb Q$. The key ingredient is the modular duality structure of the underlying quantum integrable system. We use our ansatz to write down explicit results in some examples, which are successfully checked against purely numerical results for both the spectrum and the eigenfunctions. Concerning the quantization conditions, we also provide evidence that, in the rational case, this method yields a resummation of conjectured quantization conditions involving enumerative invariants of the underlying toric Calabi-Yau threefold.Comment: 37 pages, 8 figures, 1 table; v2: minor corrections, more details added in section

Matrix models from operators and topological strings, 2

The quantization of mirror curves to toric Calabi--Yau threefolds leads to trace class operators, and it has been conjectured that the spectral properties of these operators provide a non-perturbative realization of topological string theory on these backgrounds. In this paper, we find an explicit form for the integral kernel of the trace class operator in the case of local P1xP1, in terms of Faddeev's quantum dilogarithm. The matrix model associated to this integral kernel is an O(2) model, which generalizes the ABJ(M) matrix model. We find its exact planar limit, and we provide detailed evidence that its 1/N expansion captures the all genus topological string free energy on local P1xP1.Comment: 37 pages, 4 figures; v2: misprints corrected, comments and Appendix adde

The Contribution of the International Court of Justice to the Development of International Environmental Law: A Contemporary Assessment

The article provides a detailed and up-to-date assessment of the contribution of the International Court of Justice (ICJ) to the development of International Environmental Law (IEL), including the potential in this respect of the cases currently pending before the Court. The author argues that the ICJ\u27s contribution to IEL can be organized in two main waves of cases. The legacy of the first wave, which covered essentially the Corfu Channel and the Nuclear Tests cases, as well as an important obiter dictum made in the Barcelona Traction case, was the confirmation of previous case-law on transboundary damages as well as the introduction of the concept of obligations erga omnes, potentially applicable to some environmental norms. The second wave, constituted mainly by the Nauru and the Gabcikovo-Nagymaros cases, the Advisory Opinion on the Legality of Nuclear Weapons, and a number of separate/dissenting opinions, was important in consolidating the previous achievements and pointing to a number of interconnections between IEL and other sub-fields of international law such as boundary delimitation and international humanitarian law. In this context, the Pulp Mills and Aerial Herbicides cases, currently pending before the ICJ, could potentially pave the way for a third wave, providing much needed clarifications of issues such as the specific contents of IEL as well as the hierarchy and enforceability of its principles

TBA-like integral equations from quantized mirror curves

Quantizing the mirror curve of certain toric Calabi-Yau (CY) three-folds leads to a family of trace class operators. The resolvent function of these operators is known to encode topological data of the CY. In this paper, we show that in certain cases, this resolvent function satisfies a system of non-linear integral equations whose structure is very similar to the Thermodynamic Bethe Ansatz (TBA) systems. This can be used to compute spectral traces, both exactly and as a semiclassical expansion. As a main example, we consider the system related to the quantized mirror curve of local $\mathbb P^2$. According to a recent proposal, the traces of this operator are determined by the refined BPS indices of the underlying CY. We use our non-linear integral equations to test that proposal.Comment: 30 pages, 1 figure, 1 table; v2: minor correction

Resumming the string perturbation series

We use the AdS/CFT correspondence to study the resummation of a perturbative genus expansion appearing in the type II superstring dual of ABJM theory. Although the series is Borel summable, its Borel resummation does not agree with the exact non-perturbative answer due to the presence of complex instantons. The same type of behavior appears in the WKB quantization of the quartic oscillator in Quantum Mechanics, which we analyze in detail as a toy model for the string perturbation series. We conclude that, in these examples, Borel summability is not enough for extracting non-perturbative information, due to non-perturbative effects associated to complex instantons. We also analyze the resummation of the genus expansion for topological string theory on local $\mathbb P^1 \times \mathbb P^1$, which is closely related to ABJM theory. In this case, the non-perturbative answer involves membrane instantons computed by the refined topological string, which are crucial to produce a well-defined result. We give evidence that the Borel resummation of the perturbative series requires such a non-perturbative sector.Comment: 31 pages, 9 figures; v3 : clarifications added and misprints correcte

Control of growth and gut maturation by HoxD genes and the associated lncRNA Haglr.

During embryonic development, Hox genes participate in the building of a functional digestive system in metazoans, and genetic conditions involving these genes lead to important, sometimes lethal, growth retardation. Recently, this phenotype was obtained after deletion of Haglr, the Hoxd antisense growth-associated long noncoding RNA (lncRNA) located between Hoxd1 and Hoxd3 In this study, we have analyzed the function of Hoxd genes in delayed growth trajectories by looking at several nested targeted deficiencies of the mouse HoxD cluster. Mutant pups were severely stunted during the suckling period, but many recovered after weaning. After comparing seven distinct HoxD alleles, including CRISPR/Cas9 deletions involving Haglr, we identified Hoxd3 as the critical component for the gut to maintain milk-digestive competence. This essential function could be abrogated by the dominant-negative effect of HOXD10 as shown by a genetic rescue approach, thus further illustrating the importance of posterior prevalence in Hox gene function. A role for the lncRNA Haglr in the control of postnatal growth could not be corroborated

Adipose, Bone Marrow and Synovial Joint-Derived Mesenchymal Stem Cells for Cartilage Repair

Current cell-based repair strategies have proven unsuccessful for treating cartilage defects and osteoarthritic lesions, consequently advances in innovative therapeutics are required and mesenchymal stem cell-based (MSC) therapies are an expanding area of investigation. MSCs are capable of differentiating into multiple cell lineages and exerting paracrine effects. Due to their easy isolation, expansion, and low immunogenicity, MSCs are an attractive option for regenerative medicine for joint repair. Recent studies have identified several MSC tissue reservoirs including in adipose tissue, bone marrow, cartilage, periosteum, and muscle. MSCs isolated from these discrete tissue niches exhibit distinct biological activities, and have enhanced regenerative potentials for different tissue types. Each MSC type has advantages and disadvantages for cartilage repair and their use in a clinical setting is a balance between expediency and effectiveness. In this review we explore the challenges associated with cartilage repair and regeneration using MSC-based cell therapies and provide an overview of phenotype, biological activities, and functional properties for each MSC population. This paper also specifically explores the therapeutic potential of each type of MSC, particularly focusing on which cells are capable of producing stratified hyaline-like articular cartilage regeneration. Finally we highlight areas for future investigation. Given that patients present with a variety of problems it is unlikely that cartilage regeneration will be a simple “one size fits all,” but more likely an array of solutions that need to be applied systematically to achieve regeneration of a biomechanically competent repair tissue

The Creation of a Niche Market Magazine: Panache, the Magazine for the Affluent Palm Beach Couple

This thesis is missing from our Archive. If you have a copy (digital or hard copy) of this thesis, please contact the Lynn University Archives