Calabi-Yau manifolds from pairs of non-compact Calabi-Yau manifolds

Most of Calabi-Yau manifolds that have been considered by physicists are complete intersection Calabi-Yau manifolds of toric varieties or some quotients of product types. Purpose of this paper is to introduce a different and rather new kind of construction method of Calabi-Yau manifolds by pasting two non-compact Calabi-Yau manifolds. We will also in some details explain a curious and mysterious similarity with construction of some $G_2$-manifolds (also called Joyce manifolds), which are base spaces for M-theory.Comment: 10 pages. Accepted for publication in JHE

Hawking Radiation as Tunneling

We present a short and direct derivation of Hawking radiation as a tunneling process, based on particles in a dynamical geometry. The imaginary part of the action for the classically forbidden process is related to the Boltzmann factor for emission at the Hawking temperature. Because the derivation respects conservation laws, the exact spectrum is not precisely thermal. We compare and contrast the problem of spontaneous emission of charged particles from a charged conductor.Comment: LaTeX, 10 pages; v2. journal version, added section on relation of black hole radiation to electric charge emission from a charged conducting sphere; v3. restored cut referenc

Ultrasound is not useful as a screening tool for dengue fever

Background: Dengue fever is a tropical disease that is transmitted by female Aedes Aegypti mosquitos. Early diagnosis is necessary to reduce the mortality and morbidity associated with the disease. A combination of clinical, laboratory, and sonography findings can be potentially helpful in making an early diagnosis of dengue fever. There is paucity of literature on the use of ultrasound for dengue fever screening; hence, the primary objective of the study was to evaluate the utility of ultrasound as a screening tool in dengue fever. Material/Methods: A total of 160 patients of suspected dengue fever were included in the study. They underwent ultrasound examinations in order to search for thickening of the gallbladder wall, pleural effusion, and ascites. On the basis of ultrasound findings, 65 cases were positive and 95 cases were negative for dengue fever. Serological tests were also used for diagnosing dengue fever, 93 cases were seropositive and 67 cases were seronegative. The ultrasonically diagnosed cases were compared with serologically diagnosed cases, and appropriate descriptive statistical analyses were applied. Results: The ultrasound findings included gall bladder wall thickening in 66 patients (41.2%). The sensitivity, specificity, and positive predictive value of ultrasound in diagnosing dengue fever were 58%, 84%, and 83%, respectively. The negative predictive value and accuracy were 59% and 68.8%, respectively. Conclusions: The present study suggests that increased gall bladder wall thickness, pleural effusion, ascites, hepatomegaly, and splenomegaly are highly suggestive of dengue fever in clinically suspected cases. However, ultrasound should not be used as a screening tool, as negative ultrasound findings cannot rule out dengue fever due to the low sensitivity of this examination

Enumerative geometry of Calabi-Yau 4-folds

Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation. Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including the sextic Calabi-Yau in CP5, are also studied. A complete solution of the Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic anomaly equation.Comment: 44 page

Comparative study of the binding characteristics to and inhibitory potencies towards PARP and in vivo antidiabetogenic potencies of taurine, 3-aminobenzamide and nicotinamide

<p>Abstract</p> <p>Background</p> <p>Poly(ADP-ribose) is a NAD⁺-requiring, DNA-repairing, enzyme playing a central role in pancreatic β-cell death and in the development of endothelial dysfunction in humans and experimental animals. PARP activation is also relevant to the development of complications of diabetes. Hence, agents capable of inhibiting PARP may be useful in preventing the development of diabetes and in slowing down complications of diabetes.</p> <p>Methods</p> <p>PARP inhibition was assessed with a colorimetric assay kit. Molecular docking studies on the active site of PARP were conducted using the crystalline structure of the enzyme available as Protein Data Bank Identification No. 1UK1. Type 2 diabetes was induced in male Sprague-Dawley rats with streptozotocin (STZ, 60 mg/kg, i.p.). The test compounds (3-aminobenzamide = 3-AB, nicotinamide = NIC, taurine = TAU) were given by the i.p. route 45 min before STZ at 2.4 mM/kg (all three compounds) or 1.2 and 3.6 mM/kg (only NIC and TAU). Blood samples were collected at 24 hr after STZ and processed for their plasma. The plasma samples were used to measure glucose, insulin, cholesterol, triglycerides, malondialdehyde, nitric oxide, and glutathione levels using reported methods.</p> <p>Results</p> <p>3-AB, NIC and TAU were able to inhibit PARP, with the inhibitory potency order being 3-AB>NIC>>TAU. Molecular docking studies at the active site of PARP showed 3-AB and NIC to interact with the binding site for the nicotinamide moiety of NAD⁺ and TAU to interact with the binding site for the adenine moiety of NAD⁺. While STZ-induced diabetes elevated all the experimental parameters examined and lowered the insulin output, a pretreatment with 3-AB, NIC or TAU reversed these trends to a significant extent. At a dose of 2.4 mm/kg, the protective effect decreased in the approximate order 3-AB>NIC≥TAU. The attenuating actions of both NIC and TAU were dose-related except for the plasma lipids since NIC was without a significant effect at all doses tested.</p> <p>Conclusions</p> <p>At equal molar doses, 3-AB was generally more potent than either TAU or NIC as an antidiabetogenic agent, but the differences were not as dramatic as would have been predicted from their differences in PARP inhibitory potencies. NIC and TAU demonstrated dose-related effects, which in the case of TAU were only evident at doses ≥2.4 mM/kg. The present results also suggest that in the case of NIC and TAU an increase in dose will enhance the magnitude of their attenuating actions on diabetes-related biochemical alterations to that achieved with a stronger PARP inhibitor such as 3-AB. Hence, dosing will play a critical role in clinical studies assessing the merits of NIC and TAU as diabetes-preventing agents.</p

Neonatal diethylstilbestrol exposure alters the metabolic profile of uterine epithelial cells

Developmental exposure to diethylstilbestrol (DES) causes reproductive tract malformations, affects fertility and increases the risk of clear cell carcinoma of the vagina and cervix in humans. Previous studies on a well-established mouse DES model demonstrated that it recapitulates many features of the human syndrome, yet the underlying molecular mechanism is far from clear. Using the neonatal DES mouse model, the present study uses global transcript profiling to systematically explore early gene expression changes in individual epithelial and mesenchymal compartments of the neonatal uterus. Over 900 genes show differential expression upon DES treatment in either one or both tissue layers. Interestingly, multiple components of peroxisome proliferator-activated receptor-γ (PPARγ)-mediated adipogenesis and lipid metabolism, including PPARγ itself, are targets of DES in the neonatal uterus. Transmission electron microscopy and Oil-Red O staining further demonstrate a dramatic increase in lipid deposition in uterine epithelial cells upon DES exposure. Neonatal DES exposure also perturbs glucose homeostasis in the uterine epithelium. Some of these neonatal DES-induced metabolic changes appear to last into adulthood, suggesting a permanent effect of DES on energy metabolism in uterine epithelial cells. This study extends the list of biological processes that can be regulated by estrogen or DES, and provides a novel perspective for endocrine disruptor-induced reproductive abnormalities

Learning the temporal evolution of multivariate densities via normalizing flows

In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced by integrating local or nonlocal Fokker-Planck equations). We analyze this evolution through machine learning assisted construction of a time-dependent mapping that takes a reference distribution (say, a Gaussian) to each and every instance of our evolving distribution. If the reference distribution is the initial condition of a Fokker-Planck equation, what we learn is the time-T map of the corresponding solution. Specifically, the learned map is a multivariate normalizing flow that deforms the support of the reference density to the support of each and every density snapshot in time. We demonstrate that this approach can approximate probability density function evolutions in time from observed sampled data for systems driven by both Brownian and L\'evy noise. We present examples with two- and three-dimensional, uni- and multimodal distributions to validate the method

Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms

Given any smooth toric surface S, we prove a SYM-HILB correspondence which relates the 3-point, degree zero, extended Gromov-Witten invariants of the n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal Gromov-Witten invariants of the Hilbert scheme Hilb^n(S) of n points on S. As we do not specialize the values of the quantum parameters involved, this result proves a strengthening of Ruan's Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphism from Hilb^n(S) to Sym^n(S) and yields a method of reconstructing the cup product for Hilb^n(S) from the orbifold invariants of [Sym^n(S)].Comment: Revised versio

Holomorphic anomaly equations and the Igusa cusp form conjecture

Let $S$ be a K3 surface and let $E$ be an elliptic curve. We solve the reduced Gromov-Witten theory of the Calabi-Yau threefold $S \times E$ for all curve classes which are primitive in the K3 factor. In particular, we deduce the Igusa cusp form conjecture. The proof relies on new results in the Gromov-Witten theory of elliptic curves and K3 surfaces. We show the generating series of Gromov-Witten classes of an elliptic curve are cycle-valued quasimodular forms and satisfy a holomorphic anomaly equation. The quasimodularity generalizes a result by Okounkov and Pandharipande, and the holomorphic anomaly equation proves a conjecture of Milanov, Ruan and Shen. We further conjecture quasimodularity and holomorphic anomaly equations for the cycle-valued Gromov-Witten theory of every elliptic fibration with section. The conjecture generalizes the holomorphic anomaly equations for ellliptic Calabi-Yau threefolds predicted by Bershadsky, Cecotti, Ooguri, and Vafa. We show a modified conjecture holds numerically for the reduced Gromov-Witten theory of K3 surfaces in primitive classes.Comment: 68 page