Proof of the Dubrovin conjecture and analysis of the tritronqu\'ee solutions of PIP_I

We show that the tritronqu\'ee solution of the Painlev\'e equation $\P1$, $y"=6y^2+z$ which is analytic for large $z$ with $\arg z \in (-\frac{3\pi}{5}, \pi)$ is pole-free in a region containing the full sector ${z \ne 0, \arg z \in [-\frac{3\pi}{5}, \pi]}$ and the disk ${z: |z| < 37/20}$. This proves in particular the Dubrovin conjecture, an open problem in the theory of Painlev\'e transcendents. The method, building on a technique developed in Costin, Huang, Schlag (2012), is general and constructive. As a byproduct, we obtain the value of the tritronqu\'ee and its derivative at zero within less than 1/100 rigorous error bounds

The Potential Role of Aerobic Exercise-Induced Pentraxin 3 on Obesity-Related Inflammation and Metabolic Dysregulation

Obesity is defined as the excess accumulation of intra-abdominal body fat, resulting in a state of chronic, low-grade proinflammation that can directly contribute to the development of insulin resistance. Pentraxin 3 (PTX3) is an acute-phase protein that is expressed by a variety of tissue and cell sources and provides an anti-inflammatory property to downregulate the production of proinflammatory cytokines, in particular interleukin-1 beta and tumor necrosis factor alpha. Although PTX3 may therapeutically aid in altering the proinflammatory milieu in obese individuals, and despite elevated expression of PTX3 mRNA observed in adipose tissue, the circulating level of PTX3 is reduced with obesity. Interestingly, aerobic activity has been demonstrated to elevate PTX3 levels. Therefore, the purpose of this review is to discuss the therapeutic potential of PTX3 to positively regulate obesity-related inflammation and discuss the proposition for utilizing aerobic exercise as a nonpharmacological anti-inflammatory treatment strategy to enhance circulating PTX3 concentrations in obese individuals

Life Tables of Bactrocera cucurbitae (Coquillett) (Diptera: Tephritidae): with a Mathematical Invalidation for Applying the Jackknife Technique to the Net Reproductive Rate

Life table data for the melon fly, Bactrocera cucurbitae (Coquillett), reared on cucumber (Cucumis sativus L.) were collected under laboratory and simulated field conditions. Means and standard errors of life table parameters were estimated for two replicates using the jackknife technique. At 25&#xba;C, the intrinsic rates of increase (_r_) found for the two replicates were 0.1354 and 0.1002 day-1, and the net reproductive rates (_R_~0~) were 206.3 and 66.0 offspring, respectively. When the cucumbers kept under simulated field conditions were covered with leaves, the _r_ and _R_~0~ for the two replicates were 0.0935 and 0.0909 day-1, 17.5 and 11.4 offspring, respectively. However, when similar cucumbers were left uncovered, the _r_ and _R_~0~ for the two replicates were 0.1043 and 0.0904 day-1, and 27.7 and 10.1 offspring, respectively. Our results revealed that considerable variability between replicates in both laboratory and field conditions is possible; this variability should be taken into consideration in data collection and application of life tables. Mathematical analysis has demonstrated that applying the jackknife technique results in unrealistic pseudo-_R_~0~ and overestimation of its variance. We suggest that the jackknife technique should not be used for the estimation of variability of _R_~0~

Unimpeded tunneling in graphene nanoribbons

We studied the Klein paradox in zigzag (ZNR) and anti-zigzag (AZNR) graphene nanoribbons. Due to the fact that ZNR (the number of lattice sites across the nanoribbon (N is even) and AZNR (N is odd) configurations are indistinguishable when treated by the Dirac equation, we supplemented the model with a pseudo-parity operator whose eigenvalues correctly depend on the sublattice wavefunctions for the number of carbon atoms across the ribbon, in agreement with the tight-binding model. We have shown that the Klein tunneling in zigzag nanoribbons is related to conservation of the pseudo-parity rather than pseudo-spin in infinite graphene. The perfect transmission in the case of head-on incidence is replaced by perfect transmission at the center of the ribbon and the chirality is interpreted as the projection of the pseudo-parity on momentum at different corners of the Brillouin zone

Antibunched Emission of Photon-Pairs via Quantum Zeno Blockade

We propose a new methodology, namely "quantum Zeno blockade," for managing light scattering at a few-photon level in general nonlinear-optical media, such as crystals, fibers, silicon microrings, and atomic vapors. Using this tool, antibunched emission of photon pairs can be achieved, leading to potent quantum-optics applications such as deterministic entanglement generation without the need for heralding. In a practical implementation using an on-chip toroidal microcavity immersed in rubidium vapor, we estimate that high-fidelity entangled photons can be produced on-demand at MHz rates or higher, corresponding to an improvement of $\gtrsim10^7$ times from the state-of-the-art.Comment: to appear in Phys. Rev. Let

Ultra-bright omni-directional collective emission of correlated photon pairs from atomic vapors

Spontaneous four-wave mixing can generate highly correlated photon pairs from atomic vapors. We show that multi-photon pumping of dipole-forbidden transitions in a recoil-free geometry can result in ultra-bright pair-emission in the full 4\pi solid angle, while strongly suppresses background Rayleigh scattering and associated atomic heating, Such a system can produce photon pairs at rates of ~ 10 ^12 per second, given only moderate optical depths of 10 ~ 100, or alternatively, the system can generate paired photons with sub-natural bandwidths at lower production rates. We derive a rate-equation based theory of the collective atomic population and coherence dynamics, and present numerical simulations for a toy model, as well as realistic model systems based on 133 Cs and 171 Yb level structures. Lastly, we demonstrate that dark-state adiabatic following (EIT) and/or timescale hierarchy protects the paired photons from reabsorption as they propagate through an optically thick sample

Theory and Calibration of Swap Market Models

This paper introduces a general framework for market models, named Market Model Approach, through the concept of admissible sets of for-ward swap rates spanning a given tenor structure. We relate this concept to results in graph theory by showing that a set is admissible if and only if the associated graph is a tree. This connection enables us to enumerate all admissible models for a given tenor structure. Three main classes are identified within this framework, and correspond to the co-terminal, co-initial, and co-sliding model. We prove that the LIBOR market model is the only admissible model of a co-sliding type. By focusing on the co-terminal model in a lognormal setting, we develop and compare several approximating analytical formulae for caplets, while swaptions can be priced by a simple Black-type formula. A novel calibration technique is introduced to allow simultaneous calibration to caplet and swaption prices. Empirical calibration of the co-terminal model is shown to be faster, more robust and more efficient than the same procedure applied to the LIBOR market model. We then argue that the co-terminal approach is the simplest and most convenient market model for pricing and hedging a large variety of exotic interest-rate derivatives.Swap Market Model, Cap, Swaption, Calibration, Graph Theory