We propose a deep signature/log-signature FBSDE algorithm to solve forward-backward stochastic differential equations (FBSDEs) with state and path dependent features. By incorporating the deep signature/log-signature transformation into the recurrent
neural network (RNN) model, our algorithm shortens the training time, improves the accuracy, and extends the time horizon comparing to methods in the existing literature. Moreover, our algorithms can be applied to a wide range of applications such as state and path dependent option pricing involving high-frequency data, model ambiguity, and stochastic games, which are linked to parabolic partial differential equations (PDEs), and path-dependent PDEs (PPDEs). Lastly, we also derive the convergence analysis of the deep signature/log-signature FBSDE algorithm.
The highest-energy blazars exhibit non-thermal radiation extending beyond 1 TeV with high luminosities and strong variabilities, indicating extreme particle acceleration in their relativistic jets. The gamma-ray spectra of blazars contain information
about the distribution and cooling processes of high-energy particles in jets, the extragalactic background light between the source and the observer, and potentially, the environment of the gamma-ray emitting region and exotic physics that may modify the opacity of the universe to gamma rays. We use data from Fermi-LAT and VERITAS to study the variability and spectra of a sample of TeV blazars across a wide range of gamma-ray energies, taking advantage of more than ten years of data from both instruments. The variability in both the GeV and TeV gamma-ray bands is investigated using a Bayesian blocks method to identify periods with a steady flux, during which the average gamma-ray spectra, after correcting for the pair absorption effect from propagation, can be parameterized without the risk of mixing different flux states. We report on the search for intrinsic spectral curvature and spectral variability in these blazars, in an effort to understand the physical mechanisms behind the high-energy gamma-ray spectra of TeV blazars.
In this paper, we focus on the $(si,t)$-derivation theory of Lie conformal superalgebras. Firstly, we study the fundamental properties of conformal $(si,t)$-derivations. Secondly, we mainly research the interiors of conformal $G$-derivations. Finally
, we discuss the relationships between the conformal $(si,t)$-derivations and some generalized conformal derivations of Lie conformal superalgebras.
Electrochemical reduction of CO2 to CO is a promising strategy. However, achieving high Faradaic efficiency with high current density using ILs electrolyte remains a challenge. In this study, the IL N octyltrimethyl 1,2,4 triazole ammonium shows outs
tanding performance for electrochemical reduction of CO2 to CO on the commercial Ag electrode, and the current density can be up to 50.8 mA cm-2 with a Faradaic efficiency of 90.6%. The current density of CO is much higher than those reported in the ILs electrolyte. In addition, the density functional theory calculation further proved that IL interacts with CO2 to form IL CO2 complex which played a key role in reducing the activation energy of CO2. According to the molecular orbital theory, the electrons obtained from ILs was filled in the anti bonding orbit of the CO2, resulting in reducing the C=O bond energy. This work provides a new strategy to design novel ILs for high efficiency electrochemical reduction of CO2 to CO.
We study convergence behaviors of degenerate and non-reversible stochastic differential equations. Our method follows a Lyapunov method in probability density space, in which the Lyapunov functional is chosen as a weighted relative Fisher information
functional. We construct a weighted Fisher information induced Gamma calculus method with a structure condition. Under this condition, an explicit algebraic tensor is derived to guarantee the convergence rate for the probability density function converging to its invariant distribution. We provide an analytical example for underdamped Langevin dynamics with variable diffusion coefficients.
Natural Language (NL) descriptions can be one of the most convenient or the only way to interact with systems built to understand and detect city scale traffic patterns and vehicle-related events. In this paper, we extend the widely adopted CityFlow
Benchmark with NL descriptions for vehicle targets and introduce the CityFlow-NL Benchmark. The CityFlow-NL contains more than 5,000 unique and precise NL descriptions of vehicle targets, making it the first multi-target multi-camera tracking with NL descriptions dataset to our knowledge. Moreover, the dataset facilitates research at the intersection of multi-object tracking, retrieval by NL descriptions, and temporal localization of events. In this paper, we focus on two foundational tasks: the Vehicle Retrieval by NL task and the Vehicle Tracking by NL task, which take advantage of the proposed CityFlow-NL benchmark and provide a strong basis for future research on the multi-target multi-camera tracking by NL description task.
One of the exciting recent developments in decentralized finance (DeFi) has been the development of decentralized cryptocurrency exchanges that can autonomously handle conversion between different cryptocurrencies. Decentralized exchange protocols su
ch as Uniswap, Curve and other types of Automated Market Makers (AMMs) maintain a liquidity pool (LP) of two or more assets constrained to maintain at all times a mathematical relation to each other, defined by a given function or curve. Examples of such functions are the constant-sum and constant-product AMMs. Existing systems however suffer from several challenges. They require external arbitrageurs to restore the price of tokens in the pool to match the market price. Such activities can potentially drain resources from the liquidity pool. In particular, dramatic market price changes can result in low liquidity with respect to one or more of the assets and reduce the total value of the LP. We propose in this work a new approach to constructing the AMM by proposing the idea of dynamic curves. It utilizes input from a market price oracle to modify the mathematical relationship between the assets so that the pool price continuously and automatically adjusts to be identical to the market price. This approach eliminates arbitrage opportunities and, as we show through simulations, maintains liquidity in the LP for all assets and the total value of the LP over a wide range of market prices.
Replica exchange Monte Carlo (reMC), also known as parallel tempering, is an important technique for accelerating the convergence of the conventional Markov Chain Monte Carlo (MCMC) algorithms. However, such a method requires the evaluation of the en
ergy function based on the full dataset and is not scalable to big data. The naive implementation of reMC in mini-batch settings introduces large biases, which cannot be directly extended to the stochastic gradient MCMC (SGMCMC), the standard sampling method for simulating from deep neural networks (DNNs). In this paper, we propose an adaptive replica exchange SGMCMC (reSGMCMC) to automatically correct the bias and study the corresponding properties. The analysis implies an acceleration-accuracy trade-off in the numerical discretization of a Markov jump process in a stochastic environment. Empirically, we test the algorithm through extensive experiments on various setups and obtain the state-of-the-art results on CIFAR10, CIFAR100, and SVHN in both supervised learning and semi-supervised learning tasks.
2HWC J1928+177 is a Galactic TeV gamma-ray source detected by the High Altitude Water Cherenkov (HAWC) Observatory up to ~ 56 TeV. The HAWC source, later confirmed by H.E.S.S., still remains unidentified as a dark accelerator since there is no appare
nt supernova remnant or pulsar wind nebula detected in the lower energy bands. The radio pulsar PSR J1928+1746, coinciding with the HAWC source position, has no X-ray counterpart. Our SED modeling shows that inverse Compton scattering in the putative pulsar wind nebula can account for the TeV emission only if the unseen nebula is extended beyond r ~ 4 [arcmin]. Alternatively, TeV gamma rays may be produced by hadronic interactions between relativistic protons from an undetected supernova remnant associated with the radio pulsar and a nearby molecular cloud G52.9+0.1. NuSTAR and Chandra observations detected a variable X-ray point source within the HAWC error circle, potentially associated with a bright IR source. The X-ray spectra can be fitted with an absorbed power-law model with $N_{rm H} = (9pm3)times10^{22}$ cm$^{-2}$ and $Gamma_X = 1.6pm0.3$ and exhibit long-term X-ray flux variability over the last decade. If the X-ray source, possibly associated with the IR source (likely an O star), is the counterpart of the HAWC source, it may be a new TeV gamma-ray binary powered by collisions between the pulsar wind and stellar wind. Follow-up X-ray observations are warranted to search for diffuse X-ray emission and determine the nature of the HAWC source.
We derive sub-Riemannian Ricci curvature tensor for sub-Riemannian manifolds. We provide examples including the Heisenberg group, displacement group ($textbf{SE}(2)$), and Martinet sub-Riemannian structure with arbitrary weighted volumes, in which we
establish analytical bounds for sub-Riemannian curvature dimension bounds and log-Sobolev inequalities. {These bounds can be used to establish the entropy dissipation results for sub-Riemannian drift diffusion processes on a compact spatial domain, in term of $L_1$ distance.} Our derivation of Ricci curvature is based on generalized Gamma $z$ calculus and $z$--Bochners formula, where $z$ stands for extra directions introduced into the sub-Riemannian degenerate structure.
