General formulation of Luria-Delbr{\"u}ck distribution of the number of mutants

The Luria-Delbr{\"u}ck experiment is a cornerstone of evolutionary theory, demonstrating the randomness of mutations before selection. The distribution of the number of mutants in this experiment has been the subject of intense investigation during the last 70 years. Despite this considerable effort, most of the results have been obtained under the assumption of constant growth rate, which is far from the experimental condition. We derive here the properties of this distribution for arbitrary growth function, for both the deterministic and stochastic growth of the mutants. The derivation we propose uses the number of wild type bacteria as the independent variable instead of time. The derivation is surprisingly simple and versatile, allowing many generalizations to be taken easily into account

GeV Photons from Ultra High Energy Cosmic Rays accelerated in Gamma Ray Bursts

Gamma-ray bursts are produced by the dissipation of the kinetic energy of a highly relativistic fireball, via the formation of a collisionless shock. When this happens, Ultra High Energy Cosmic Rays up to 10^20 eV are produced. I show in this paper that these particles produce, via synchrotron emission as they cross the acceleration region, photons up to 300 GeV which carry away a small, ~0.01, but non-negligible fraction of the total burst energy. I show that, when the shock occurs with the interstellar medium, the optical depth to photon-photon scattering, which might cause energy degradation of the photons, is small. The burst thusly produced would be detected at Earth simultaneoulsy with the parent gamma-ray burst, although its duration may differ significantly from that of the lower energy photons. The expected fluences, ~10^{-5}-10^{-6} erg/cm^2 are well within the range of planned detectors. A new explanation for the exceptional burst GRB 940217 is discussed.Comment: Accepted for publication in The Physical Review Letters. 4 pages, RevTeX needed, no figure

Prompt GeV-TeV Emission of Gamma-Ray Bursts Due to High-Energy Protons, Muons and Electron-Positron Pairs

In the framework of the internal shock scenario, we model the broadband prompt emission of gamma-ray bursts (GRBs) with emphasis on the GeV-TeV bands, utilizing Monte Carlo simulations that include various processes associated with electrons and protons accelerated to high energies. While inverse Compton emission from primary electrons is often dominant, different proton-induced mechanisms can also give rise to distinct high-energy components, such as synchrotron emission from protons, muons or secondary electrons/positrons injected via photomeson interactions. In some cases, they give rise to double spectral breaks that can serve as unique signatures of ultra-high-energy protons. We discuss the conditions favorable for such emission, and how they are related to the production of ultra-high-energy cosmic rays and neutrinos in internal shocks. Ongoing and upcoming observations by {\it GLAST}, atmospheric Cerenkov telescopes and other facilities will test these expectations and provide important information on the physical conditions in GRB outflows.Comment: 11 pages, 8 figures and 14 appendix figures, accepted for publication in ApJ vol. 671 with minor revision

Should Courts Always Enforce What Contracting Parties Write?

We find an economic rationale for the common sense answer to the question in our title — courts should not always enforce what the contracting parties write. We describe and analyze a contractual environment that allows a role for an active court. An active court can improve on the outcome that the parties would achieve without it. The institutional role of the court is to maximize the parties’ welfare under a veil of ignorance. We study a buyer-seller model with asymmetric information and ex-ante investments, in which some contingencies cannot be contracted on. The court must decide when to uphold a contract and when to void it. The parties know their private information at the time of contracting, and this drives a wedge between ex-ante and interim-efficient contracts. In particular, some types pool in equilibrium. By voiding some contracts that the pooling types would like the court to enforce, the court is able to induce them to separate, and hence to improve ex-ante welfare.Optimal Courts, Informational Externalities, Ex-ante Welfare

TET-GAN: Text Effects Transfer via Stylization and Destylization

Text effects transfer technology automatically makes the text dramatically more impressive. However, previous style transfer methods either study the model for general style, which cannot handle the highly-structured text effects along the glyph, or require manual design of subtle matching criteria for text effects. In this paper, we focus on the use of the powerful representation abilities of deep neural features for text effects transfer. For this purpose, we propose a novel Texture Effects Transfer GAN (TET-GAN), which consists of a stylization subnetwork and a destylization subnetwork. The key idea is to train our network to accomplish both the objective of style transfer and style removal, so that it can learn to disentangle and recombine the content and style features of text effects images. To support the training of our network, we propose a new text effects dataset with as much as 64 professionally designed styles on 837 characters. We show that the disentangled feature representations enable us to transfer or remove all these styles on arbitrary glyphs using one network. Furthermore, the flexible network design empowers TET-GAN to efficiently extend to a new text style via one-shot learning where only one example is required. We demonstrate the superiority of the proposed method in generating high-quality stylized text over the state-of-the-art methods.Comment: Accepted by AAAI 2019. Code and dataset will be available at http://www.icst.pku.edu.cn/struct/Projects/TETGAN.htm

Derivation of the Gross-Pitaevskii Hierarchy

We report on some recent results regarding the dynamical behavior of a trapped Bose-Einstein condensate, in the limit of a large number of particles. These results were obtained in \cite{ESY}, a joint work with L. Erd\H os and H.-T. Yau.Comment: 15 pages; for the proceedings of the QMath9 International Conference, Giens, France, Sept. 200