Smooth Value Functions for a Class of Nonsmooth Utility Maximization Problems

In this paper we prove that there exists a smooth classical solution to the HJB equation for a large class of constrained problems with utility functions that are not necessarily differentiable or strictly concave. The value function is smooth if admissible controls satisfy an integrability condition or if it is continuous on the closure of its domain. The key idea is to work on the dual control problem and the dual HJB equation. We construct a smooth, strictly convex solution to the dual HJB equation and show that its conjugate function is a smooth, strictly concave solution to the primal HJB equation satisfying the terminal and boundary conditions.Comment: 18 page

The Asymptotic Behaviours of a Class of Neutral Delay Fractional-Order Pantograph Differential Equations

By using fractional calculus and the summation by parts formula in this paper, the asymptotic behaviours of solutions of nonlinear neutral fractional delay pantograph equations with continuous arguments are investigated. The asymptotic estimates of solutions for the equation are obtained, which may imply asymptotic stability of solutions. In the end, a particular case is provided to illustrate the main result and the speed of the convergence of the obtained solutions

Simulating MCP secondary electron avalanche process by Geant4

Nowadays, Microchannel Plate (MCP), as a kind of electron multiplier based on the secondary electron emission, is widely used in many high-sensitive experiments, such as neutrino detection, which require as low noise as possible, while the conventional straight channel MCP will definitely have ion feedback, resulting in the sequential after-pulses being the major source of noise. Normally, the problem can be effectively avoided by coupling two straight MCPs in cascade and combining the channels into a "V" shape known as chevron MCPs, but this method is limited by the manufacturing techniques due to the inevitable gap that will worsen the resolution and peak-to-valley ratio. However, the ion feedback can be inhibited significantly for MCPs with curved-channels. Based on the Geant4 Monte Carlo simulation framework, we investigate how the geometrical parameters of curved-channel MCP influence the gain and get the optimum pore diameter for the maximum gain with a fixed thickness and applied voltage. Additionally, the track-by-track simulation reveals that the average acceleration distance of a secondary electron inside the curved-channel is approximately 20~$\mu$m with a voltage of 950~V, a length-to-diameter ratio of 100:1, and a pore diameter of 20~$\mu$m.Comment: 20 pages, 12 figure

SiGeC Near Infrared Photodetectors

A near infrared waveguide photodetector in Si-based ternary Si₁âxâyGexCy alloy was demonstrated for 0.85~1.06 µm wavelength fiber-optic interconnection system applications. Two sets of detectors with active absorption layer compositions of Si₀.₇₉Ge₀.₂C₀.₀₁ and Si₀.₇₀Ge₀.₂₈C₀.₀₂ were designed. The active absorption layer has a thickness of 120~450 nm. The external quantum efficiency can reach ~3% with a cut-off wavelength of around 1.2 µm.Singapore-MIT Alliance (SMA

Engineering the Ultrasensitive Transcription Factors by Fusing a Modular Oligomerization Domain

The dimerization and high-order oligomerization of transcription factors has endowed them with cooperative regulatory capabilities that play important roles in many cellular functions. However, such advanced regulatory capabilities have not been fully exploited in synthetic biology and genetic engineering. Here, we engineered a C-terminally fused oligomerization domain to improve the cooperativity of transcription factors. First, we found that two of three designed oligomerization domains significantly increased the cooperativity and ultrasensitivity of a transcription factor for the regulated promoter. Then, seven additional transcription factors were used to assess the modularity of the oligomerization domains, and their ultrasensitivity was generally improved, as assessed by their Hill coefficients. Moreover, we also demonstrated that the allosteric capability of the ligand-responsive domain remained intact when fusing with the designed oligomerization domain. As an example application, we showed that the engineered ultrasensitive transcription factor could be used to significantly improve the performance of a “stripe-forming” gene circuit. We envision that the oligomerization modules engineered in this study could act as a powerful tool to rapidly tune the underlying response profiles of synthetic gene circuits and metabolic pathway controllers

Neutrino Physics with JUNO

The Jiangmen Underground Neutrino Observatory (JUNO), a 20 kton multi-purposeunderground liquid scintillator detector, was proposed with the determinationof the neutrino mass hierarchy as a primary physics goal. It is also capable ofobserving neutrinos from terrestrial and extra-terrestrial sources, includingsupernova burst neutrinos, diffuse supernova neutrino background, geoneutrinos,atmospheric neutrinos, solar neutrinos, as well as exotic searches such asnucleon decays, dark matter, sterile neutrinos, etc. We present the physicsmotivations and the anticipated performance of the JUNO detector for variousproposed measurements. By detecting reactor antineutrinos from two power plantsat 53-km distance, JUNO will determine the neutrino mass hierarchy at a 3-4sigma significance with six years of running. The measurement of antineutrinospectrum will also lead to the precise determination of three out of the sixoscillation parameters to an accuracy of better than 1\%. Neutrino burst from atypical core-collapse supernova at 10 kpc would lead to ~5000inverse-beta-decay events and ~2000 all-flavor neutrino-proton elasticscattering events in JUNO. Detection of DSNB would provide valuable informationon the cosmic star-formation rate and the average core-collapsed neutrinoenergy spectrum. Geo-neutrinos can be detected in JUNO with a rate of ~400events per year, significantly improving the statistics of existing geoneutrinosamples. The JUNO detector is sensitive to several exotic searches, e.g. protondecay via the $p\to K^++\bar\nu$ decay channel. The JUNO detector will providea unique facility to address many outstanding crucial questions in particle andastrophysics. It holds the great potential for further advancing our quest tounderstanding the fundamental properties of neutrinos, one of the buildingblocks of our Universe

Potential of Core-Collapse Supernova Neutrino Detection at JUNO

JUNO is an underground neutrino observatory under construction in Jiangmen, China. It uses 20kton liquid scintillator as target, which enables it to detect supernova burst neutrinos of a large statistics for the next galactic core-collapse supernova (CCSN) and also pre-supernova neutrinos from the nearby CCSN progenitors. All flavors of supernova burst neutrinos can be detected by JUNO via several interaction channels, including inverse beta decay, elastic scattering on electron and proton, interactions on C12 nuclei, etc. This retains the possibility for JUNO to reconstruct the energy spectra of supernova burst neutrinos of all flavors. The real time monitoring systems based on FPGA and DAQ are under development in JUNO, which allow prompt alert and trigger-less data acquisition of CCSN events. The alert performances of both monitoring systems have been thoroughly studied using simulations. Moreover, once a CCSN is tagged, the system can give fast characterizations, such as directionality and light curve

Detection of the Diffuse Supernova Neutrino Background with JUNO

As an underground multi-purpose neutrino detector with 20 kton liquid scintillator, Jiangmen Underground Neutrino Observatory (JUNO) is competitive with and complementary to the water-Cherenkov detectors on the search for the diffuse supernova neutrino background (DSNB). Typical supernova models predict 2-4 events per year within the optimal observation window in the JUNO detector. The dominant background is from the neutral-current (NC) interaction of atmospheric neutrinos with 12C nuclei, which surpasses the DSNB by more than one order of magnitude. We evaluated the systematic uncertainty of NC background from the spread of a variety of data-driven models and further developed a method to determine NC background within 15\% with {\it{in}} {\it{situ}} measurements after ten years of running. Besides, the NC-like backgrounds can be effectively suppressed by the intrinsic pulse-shape discrimination (PSD) capabilities of liquid scintillators. In this talk, I will present in detail the improvements on NC background uncertainty evaluation, PSD discriminator development, and finally, the potential of DSNB sensitivity in JUNO

Real-time Monitoring for the Next Core-Collapse Supernova in JUNO

Core-collapse supernova (CCSN) is one of the most energetic astrophysical events in the Universe. The early and prompt detection of neutrinos before (pre-SN) and during the SN burst is a unique opportunity to realize the multi-messenger observation of the CCSN events. In this work, we describe the monitoring concept and present the sensitivity of the system to the pre-SN and SN neutrinos at the Jiangmen Underground Neutrino Observatory (JUNO), which is a 20 kton liquid scintillator detector under construction in South China. The real-time monitoring system is designed with both the prompt monitors on the electronic board and online monitors at the data acquisition stage, in order to ensure both the alert speed and alert coverage of progenitor stars. By assuming a false alert rate of 1 per year, this monitoring system can be sensitive to the pre-SN neutrinos up to the distance of about 1.6 (0.9) kpc and SN neutrinos up to about 370 (360) kpc for a progenitor mass of 30$M_{\odot}$ for the case of normal (inverted) mass ordering. The pointing ability of the CCSN is evaluated by using the accumulated event anisotropy of the inverse beta decay interactions from pre-SN or SN neutrinos, which, along with the early alert, can play important roles for the followup multi-messenger observations of the next Galactic or nearby extragalactic CCSN.Comment: 24 pages, 9 figure

Persistence and Turing instability in a cross-diffusive predator–prey system with generalist predator

Abstract In this paper, we propose and investigate persistence and Turing instability of a cross-diffusion predator–prey system with generalist predator. First, by virtue of the comparison principle, we obtain sufficient conditions of persistence for a corresponding reaction–diffusion system without self- and cross-diffusion. Second, by using the linear stability analysis, we prove that under some conditions the unique positive equilibrium solution is locally asymptotically stable for the corresponding ODE system and the corresponding reaction–diffusion system without cross-diffusion and self-diffusion. Hence it does not belong to the classical Turing instability. Third, under some appropriate sufficient conditions, we obtain that the uniform positive equilibrium solution is linearly unstable for the cross-reaction–diffusion and partial self-diffusion system. The results indicate that cross-diffusion and partial self-diffusion play an important role in the study of Turing instability about reaction–diffusion systems with generalist predator. Fourth, we elaborate on the relations between the theoretical results and the cross-diffusion predator–prey system by relying on some examples. In the end, we conclude our findings and give a brief discussion