Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic-Vafa [arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in the total space of the canonical line bundle of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]), and (iii) an outer brane at zero framing in the total space of the canonical line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure

Temperature dependence of the nitrogen-vacancy magnetic resonance in diamond

The temperature dependence of the magnetic resonance spectra of nitrogen-vacancy (NV-) ensembles in the range of 280-330 K was studied. Four samples prepared under different conditions were studied with NV- concentrations ranging from 10 ppb to 15 ppm. For all of these samples, the axial zero-field splitting (ZFS) parameter, D, was found to vary significantly with temperature, T, as dD/dT = -74.2(7) kHz/K. The transverse ZFS parameter, E, was non-zero (between 4 and 11 MHz) in all samples, and exhibited a temperature dependence of dE/(EdT) = -1.4(3) x 10^(-4) K^(-1). The results might be accounted for by considering local thermal expansion. The observation of the temperature dependence of the ZFS parameters presents a significant challenge for room-temperature diamond magnetometers and may ultimately limit their bandwidth and sensitivity.Comment: 5 pages, 2 figures, 1 tabl

Bidding process in online auctions and winning strategy:rate equation approach

Online auctions have expanded rapidly over the last decade and have become a fascinating new type of business or commercial transaction in this digital era. Here we introduce a master equation for the bidding process that takes place in online auctions. We find that the number of distinct bidders who bid $k$ times, called the $k$-frequent bidder, up to the $t$-th bidding progresses as $n_k(t)\sim tk^{-2.4}$. The successfully transmitted bidding rate by the $k$-frequent bidder is obtained as $q_k(t) \sim k^{-1.4}$, independent of $t$ for large $t$. This theoretical prediction is in agreement with empirical data. These results imply that bidding at the last moment is a rational and effective strategy to win in an eBay auction.Comment: 4 pages, 6 figure

Universality of Cluster Dynamics

We have studied the kinetics of cluster formation for dynamical systems of dimensions up to $n=8$ interacting through elastic collisions or coalescence. These systems could serve as possible models for gas kinetics, polymerization and self-assembly. In the case of elastic collisions, we found that the cluster size probability distribution undergoes a phase transition at a critical time which can be predicted from the average time between collisions. This enables forecasting of rare events based on limited statistical sampling of the collision dynamics over short time windows. The analysis was extended to L$^p$-normed spaces ($p=1,...,\infty$) to allow for some amount of interpenetration or volume exclusion. The results for the elastic collisions are consistent with previously published low-dimensional results in that a power law is observed for the empirical cluster size distribution at the critical time. We found that the same power law also exists for all dimensions $n=2,...,8$, 2D L$^p$ norms, and even for coalescing collisions in 2D. This broad universality in behavior may be indicative of a more fundamental process governing the growth of clusters

Open orbifold Gromov-Witten invariants of [C^3/Z_n]: localization and mirror symmetry

We develop a mathematical framework for the computation of open orbifold Gromov-Witten invariants of [C^3/Z_n], and provide extensive checks with predictions from open string mirror symmetry. To this aim we set up a computation of open string invariants in the spirit of Katz-Liu, defining them by localization. The orbifold is viewed as an open chart of a global quotient of the resolved conifold, and the Lagrangian as the fixed locus of an appropriate anti-holomorphic involution. We consider two main applications of the formalism. After warming up with the simpler example of [C^3/Z_3], where we verify physical predictions of Bouchard, Klemm, Marino and Pasquetti, the main object of our study is the richer case of [C^3/Z_4], where two different choices are allowed for the Lagrangian. For one choice, we make numerical checks to confirm the B-model predictions; for the other, we prove a mirror theorem for orbifold disc invariants, match a large number of annulus invariants, and give mirror symmetry predictions for open string invariants of genus \leq 2.Comment: 44 pages + appendices; v2: exposition improved, misprints corrected, version to appear on Selecta Mathematica; v3: last minute mistake found and fixed for the symmetric brane setup of [C^3/Z_4]; in pres

Swing Options Valuation: a BSDE with Constrained Jumps Approach

We introduce a new probabilistic method for solving a class of impulse control problems based on their representations as Backward Stochastic Differential Equations (BSDEs for short) with constrained jumps. As an example, our method is used for pricing Swing options. We deal with the jump constraint by a penalization procedure and apply a discrete-time backward scheme to the resulting penalized BSDE with jumps. We study the convergence of this numerical method, with respect to the main approximation parameters: the jump intensity $\lambda$, the penalization parameter $p > 0$ and the time step. In particular, we obtain a convergence rate of the error due to penalization of order $(\lambda p)^{\alpha - \frac{1}{2}}, \forall \alpha \in \left(0, \frac{1}{2}\right)$. Combining this approach with Monte Carlo techniques, we then work out the valuation problem of (normalized) Swing options in the Black and Scholes framework. We present numerical tests and compare our results with a classical iteration method.Comment: 6 figure

Assignment of the Human TYRP (brown) Locus to Chromosome Region 9p23 by Nonradioactive in Situ Hybridization

The TYRP (brown) locus determines pigmentation and coat color in the mouse. The human homolog of the TYRP locus has been recently identified and shown to encode a 75-KDA transmembrane melanosomal glycoprotein called gp75. The gp 75 glycoprotein is homologous to tyrosinase, an enzyme in evolved in the synthesis of melanin, forming a family of tyrosinase-related proteins. A genomic clone of human gp75 was used to map the human TYRP locus to chromosome 9, region 9p23, by nonradioactive fluorescent in situ hybridization. Specificity of hybridization was tested with a genomic fragment of hu- man tyrosinase that mapped to a distinct site on 1lq2 1. The 9p region has been reported to be nonrandomly altered in human melanoma, suggesting a role for the region near the TYRP locus in melanocyte transformation