Gluon quasidistribution function at one loop

We study the unpolarized gluon quasidistribution function in the nucleon at one loop level in the large momentum effective theory. For the quark quasidistribution, power law ultraviolet divergences arise in the cut-off scheme and an important observation is that they all are subjected to Wilson lines. However for the gluon quasidistribution function, we first point out that the linear ultraviolet divergences also exist in the real diagram which is not connected to any Wilson line. We then study the one loop corrections to parton distribution functions in both cut-off scheme and dimensional regularization to deal with the ultraviolet divergences. In addition to the ordinary quark and gluon distributions, we also include the quark to gluon and gluon to quark splitting diagrams. The complete one-loop matching factors between the quasi and light cone parton distribution functions are presented in the cut-off scheme. We derive the $P^z$ evolution equation for quasi parton distribution functions, and find that the $P^z$ evolution kernels are identical to the DGLAP evolution kernels.Comment: 26 pages,8 figures;accepted by Eur.Phys.J

Quasi parton distribution functions at NNLO: flavor non-diagonal quark contributions

We present a next-to-next-to-leading order (NNLO) calculation of the quasi parton distribution functions (Quasi-PDFs) in the large momentum effective theory (LaMET). We focus on the flavor non-diagonal quark-quark channel and demonstrate the LaMET factorization at the NNLO accuracy in the modified minimal subtraction scheme. The matching coefficient between the quasi-PDF and the light-cone PDF is derived. This provides a first step towards a complete NNLO analysis of quasi-PDFs and to better understand the nucleon structures from the first principle of QCD.Comment: 10 pages, 3 figures; v2: accepted for publication in Physical Review D as a rapid communicatio

Equilibrium Lending Mechanism and Aggregate Activity

What determines the firm's choice of its mechanism of investment financing? How is the choice of the firm's financing mechanism at the micro level related to the economy's business cycle movements at the aggregate level? This paper develops a model of the credit market where the equilibrium lending mechanism, as well as the economy's aggregate investment and output, are endogenously determined. Among other things, our model predicts that a negative productivity shock can cause an economic downturn that is accompanied not only by a contraction in total outstanding loans, but also by a decline in the ratio of bank loans to non-bank lending, as observed in the 1990-91 U.S. recession.

Equilibrium lending mechanism and aggregate activity

This paper develops a model of the credit market where the equilibrium lending mechanism, as well as the economy's aggregate investment and output, are endogenously determined. It focuses on two crucial elements. One is the micro theory of optimal lending mechanism. Instead of imposing a particular lending contract form exogenously, we solve for the optimal contract between a borrower and a lender designed to circumvent adverse-selection and moral-hazard problems in the model environment. The other important element is the effect of credit market condition on the lending mechanism. We embed the micro model of the two-agent contracting problem into a competitive credit market. Hence, we are able to study the interaction among credit market tightness, equilibrium financing mechanism and aggregate economic activity.> On the optimal contract, the paper provides a formal theory that explains why some firms choose to borrow from banks, while others decide to issue bond to finance their investment. It postulates that the optimal contract is one of two kinds: either with intensive monitoring by the lender to overcome borrower's incentive problems, such as most of intermediated financing (bank or venture-capital financing), or with heavy reliance on the borrower, such as market financing. The model predicts that intermediated financing is optimal when investment returns are high, cost of lender monitoring is low, investment's liquidation value is low, and credit market is tight for the borrowers.> On the general equilibrium effect, we show that the observation that bank lending falls relative to corporate bond issuance during recessions can be explained by movements in the economy's real factors, such as the decline in the average investment returns (which is considered as a contributing factor to the ``credit crunch'' occurred during 1990-91 recession), and paradoxically, the increase of investment demand which worsens credit market condition and hence intensifies the incentive problems. It can also be explained by the drop of credit supply, possibly brought about by a contractionary monetary policy in the short run.Bank loans ; Loans

The Application of Driver Models in the Safety Assessment of Autonomous Vehicles: A Survey

Driver models play a vital role in developing and verifying autonomous vehicles (AVs). Previously, they are mainly applied in traffic flow simulation to model realistic driver behavior. With the development of AVs, driver models attract much attention again due to their potential contributions to AV certification. The simulation-based testing method is considered an effective measure to accelerate AV testing due to its safe and efficient characteristics. Nonetheless, realistic driver models are prerequisites for valid simulation results. Additionally, an AV is assumed to be at least as safe as a careful and competent driver. Therefore, driver models are inevitable for AV safety assessment. However, no comparison or discussion of driver models is available regarding their utility to AVs in the last five years despite their necessities in the release of AVs. This motivates us to present a comprehensive survey of driver models in the paper and compare their applicability. Requirements for driver models in terms of their application to AV safety assessment are discussed. A summary of driver models for simulation-based testing and AV certification is provided. Evaluation metrics are defined to compare their strength and weakness. Finally, an architecture for a careful and competent driver model is proposed. Challenges and future work are elaborated. This study gives related researchers especially regulators an overview and helps them to define appropriate driver models for AVs

Concentration of Data Encoding in Parameterized Quantum Circuits

Variational quantum algorithms have been acknowledged as a leading strategy to realize near-term quantum advantages in meaningful tasks, including machine learning and combinatorial optimization. When applied to tasks involving classical data, such algorithms generally begin with quantum circuits for data encoding and then train quantum neural networks (QNNs) to minimize target functions. Although QNNs have been widely studied to improve these algorithms' performance on practical tasks, there is a gap in systematically understanding the influence of data encoding on the eventual performance. In this paper, we make progress in filling this gap by considering the common data encoding strategies based on parameterized quantum circuits. We prove that, under reasonable assumptions, the distance between the average encoded state and the maximally mixed state could be explicitly upper-bounded with respect to the width and depth of the encoding circuit. This result in particular implies that the average encoded state will concentrate on the maximally mixed state at an exponential speed on depth. Such concentration seriously limits the capabilities of quantum classifiers, and strictly restricts the distinguishability of encoded states from a quantum information perspective. We further support our findings by numerically verifying these results on both synthetic and public data sets. Our results highlight the significance of quantum data encoding in machine learning tasks and may shed light on future encoding strategies.Comment: 26 pages including appendi