On the B-twisted topological sigma model and Calabi-Yau geometry

We provide a rigorous perturbative quantization of the B-twisted topological sigma model via a first order quantum field theory on derived mapping space in the formal neighborhood of constant maps. We prove that the first Chern class of the target manifold is the obstruction to the quantization via Batalin-Vilkovisky formalism. When the first Chern class vanishes, i.e. on Calabi-Yau manifolds, the factorization algebra of observables gives rise to the expected topological correlation functions in the B-model. We explain a twisting procedure to generalize to the Landau-Ginzburg case, and show that the resulting topological correlations coincide with Vafa's residue formula.Comment: 73 pages. Comments welcom

Implicit Asymptotic Preserving Method for Linear Transport Equations

The computation of the radiative transfer equation is expensive mainly due to two stiff terms: the transport term and the collision operator. The stiffness in the former comes from the fact that particles (such as photons) travels at the speed of light, while that in the latter is due to the strong scattering in the diffusive regime. We study the fully implicit scheme for this equation to account for the stiffness. The main challenge in the implicit treatment is the coupling between the spacial and velocity coordinates that requires the large size of the to-be-inverted matrix, which is also ill-conditioned and not necessarily symmetric. Our main idea is to utilize the spectral structure of the ill-conditioned matrix to construct a pre-conditioner, which, along with an exquisite split of the spatial and angular dependence, significantly improve the condition number and allows matrix-free treatment. We also design a fast solver to compute this pre-conditioner explicitly in advance. Meanwhile, we reformulate the system via an even-odd parity, which results in a symmetric and positive definite matrix that can be inverted using conjugate gradient method. This idea can also be implemented to the original non-symmetric system whose inversion is solved by GMRES. A qualitative comparison with the conventional methods, including Krylov iterative method pre-conditioned with diffusive synthetic acceleration and asymptotic preserving scheme via even-odd decomposition, is also discussed

On the Number of Zeros and Poles of Dirichlet Series

This paper investigates lower bounds on the number of zeros and poles of a general Dirichlet series in a disk of radius $r$ and gives, as a consequence, an affirmative answer to an open problem of Bombieri and Perelli on the bound. Applications will also be given to Picard type theorems, global estimates on the symmetric difference of zeros, and uniqueness problems for Dirichlet series.Comment: 24 page

Second Stop and Sbottom Searches with a Stealth Stop

The top squarks (stops) may be the most wanted particles after the Higgs boson discovery. The searches for the lightest stop have put strong constraints on its mass. However, there is still a search gap in the low mass region if the spectrum of the stop and the lightest neutralino is compressed. In that case, it may be easier to look for the second stop since naturalness requires both stops to be close to the weak scale. The current experimental searches for the second stop are based on the simplified model approach with the decay modes $\tilde{t}_2 \to \tilde{t}_1 Z$ and $\tilde{t}_2 \to \tilde{t}_1 h$. However, in a realistic supersymmetric spectrum there is always a sbottom lighter than the second stop, hence the decay patterns are usually more complicated than the simplified model assumptions. In particular, there are often large branching ratios of the decays $\tilde{t}_2 \to \tilde{b}_1 W$ and $\tilde{b}_1 \to \tilde{t}_1 W$ as long as they are open. The decay chains can be even more complex if there are intermediate states of additional charginos and neutralinos in the decays. By studying several MSSM benchmark models at the 14 TeV LHC, we point out the importance of the multi-$W$ final states in the second stop and the sbottom searches, such as the same-sign dilepton and multilepton signals, aside from the traditional search modes. The observed same-sign dilepton excesses at LHC Run 1 and Run 2 may be explained by some of our benchmark models. We also suggest that the vector boson tagging and a new kinematic variable may help to suppress the backgrounds and increase the signal significance for some search channels. Due to the complex decay patterns and lack of the dominant decay channels, the best reaches likely require a combination of various search channels at the LHC for the second stop and the lightest sbottom.Comment: 46 pages, 9 figures, updated experimental constraints and benchmark points after the ICHEP2016 data, published in JHE

A characterization of rational functions

We give an elementary characterization of rational functions among meromorphic functions in the complex plane

Response to "Reply to comment on 'Divergent and Ultrahigh Thermal Conductivity in Millimeter-Long Nanotubes'"

More than one year ago, Prof. Chih-Wei Chang and the co-authors published "Divergent and Ultrahigh Thermal Conductivity in Millimeter-Long Nanotubes" in PRL and we submitted a comment. After some while we received Prof. Chang et al.'s reply, which is almost the same as their arXiv preprint, and responded to the reply promptly. On the request of some readers, I personally post here the detailed response to "Reply to comment on 'Divergent and Ultrahigh Thermal Conductivity in Millimeter-Long Nanotubes'"

Constraining the Compressed Top Squark and Chargino along the W Corridor

Studying superpartner production together with a hard initial state radiation (ISR) jet has been a useful strategy for searches of supersymmetry with a compressed spectrum at the Large Hadron Collider (LHC). In the case of the top squark (stop), the ratio of the missing transverse momentum from the lightest neutralinos and the ISR momentum, defined as $\bar{R}_M$, turns out to be an effective variable to distinguish the signal from the backgrounds. It has helped to exclude the stop mass below 590 GeV along the top corridor where $m_{\tilde{t}} - m_{\tilde{\chi}_1^0} \approx m_t$. On the other hand, the current experimental limit is still rather weak in the $W$ corridor where $m_{\tilde{t}} - m_{\tilde{\chi}_1^0} \approx m_W +m_b$. In this work we extend this strategy to the parameter region around the $W$ corridor by considering the one lepton final state. In this case the kinematic constraints are insufficient to completely determine the neutrino momentum which is required to calculate $\bar{R}_M$. However, the minimum value of $\bar{R}_M$ consistent with the kinematic constraints still provides a useful discriminating variable, allowing the exclusion reach of the stop mass to be extended to $\sim 550$ GeV based on the current 36 fb$^{-1}$ LHC data. The same method can also be applied to the chargino search with $m_{\tilde{\chi}_1^\pm} -m_{\tilde{\chi}_1^0} \approx m_W$ because the analysis does not rely on $b$ jets. If no excess is present in the current data, a chargino mass of 300 GeV along the $W$ corridor can be excluded, beyond the limit obtained from the multilepton search.Comment: 29 pages,8 figure

A new numerical approach to inverse transport equation with error analysis

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover the optical properties, denoted as absorption and scattering coefficient of the media, through the source-measurement pairs. A typical computational approach is to form the inverse problem as a PDE-constraint optimization, with the minimizer being the to-be-recovered coefficients. The method is tested to be efficient in practice, but lacks analytical justification: there is no guarantee of the existence or uniqueness of the minimizer, and the error is hard to quantify. In this paper, we provide a different algorithm by levering the ideas from singular decomposition analysis. Our approach is to decompose the measurements into three components, two out of which encode the information of the two coefficients respectively. We then split the optimization problem into two subproblems and use those two components to recover the absorption and scattering coefficients separately. In this regard, we prove the well-posedness of the new optimization, and the error could be quantified with better precision. In the end, we incorporate the diffusive scaling and show that the error is harder to control in the diffusive limit

Stability of Stationary Inverse Transport Equation in Diffusion Scaling

We consider the inverse problem of reconstructing the optical parameters for stationary radiative transfer equation (RTE) from velocity-averaged measurement. The RTE often contains multiple scales characterized by the magnitude of a dimensionless parameter---the Knudsen number ($K_n$). In the diffusive scaling ($K_n \ll 1$), the stationary RTE is well approximated by an elliptic equation in the forward setting. However, the inverse problem for the elliptic equation is acknowledged to be severely ill-posed as compared to the well-posedness of inverse transport equation, which raises the question of how uniqueness being lost as $K_n \rightarrow 0$. We tackle this problem by examining the stability of inverse problem with varying $K_n$. We show that, the discrepancy in two measurements is amplified in the reconstructed parameters at the order of $K_n^p~ (p = 1\text{ or} ~2)$, and as a result lead to ill-posedness in the zero limit of $K_n$. Our results apply to both continuous and discrete settings. Some numerical tests are performed in the end to validate these theoretical findings

Transport Protocols in Cognitive Radio Networks: A Survey

Cognitive radio networks (CRNs) have emerged as a promising solution to enhance spectrum utilization by using unused or less used spectrum in radio environments. The basic idea of CRNs is to allow secondary users (SUs) access to licensed spectrum, under the condition that the interference perceived by the primary users (PUs) is minimal. In CRNs, the channel availability is uncertainty due to the existence of PUs, resulting in intermittent communication. Transmission control protocol (TCP) performance may significantly degrade in such conditions. To address the challenges, some transport protocols have been proposed for reliable transmission in CRNs. In this paper we survey the state-of-the-art transport protocols for CRNs. We firstly highlight the unique aspects of CRNs, and describe the challenges of transport protocols in terms of PU behavior, spectrum sensing, spectrum changing and TCP mechanism itself over CRNs. Then, we provide a summary and comparison of existing transport protocols for CRNs. Finally, we discuss several open issues and research challenges. To the best of our knowledge, our work is the first survey on transport protocols for CRNs.Comment: to appear in KSII Transactions on Internet and Information System