Optimal Auction Duration: A Price Formation Viewpoint

Optimal Auction Duration in Financial Markets In the considered auction market, market makers fill the order book during a given time period while some other investors send market orders. The clearing price is set to maximize the exchanged volume at the clearing time according to the supply and demand of each market participant. The error made between this clearing price and the efficient price is derived as a function of the auction duration. We study the impact of the behavior of market takers on this error to minimize their transaction costs. We compute the optimal duration of the auctions for 77 stocks traded on Euronext and compare the quality of the price formation process under this optimal value to the case of a continuous limit order book. Continuous limit order books are usually found to be suboptimal. Order of magnitude of optimal auction durations is from 2–10 minutes.

A focusing and defocusing semi-discrete complex short-pulse equation and its various soliton solutions

In this paper, we are concerned with a semi-discrete complex short-pulse (sdCSP) equation of both focusing and defocusing types, which can be viewed as an analogue to the Ablowitz–Ladik lattice in the ultra-short-pulse regime. By using a generalized Darboux transformation method, various soliton solutions to this newly integrable semi-discrete equation are studied with both zero and non-zero boundary conditions. To be specific, for the focusing sdCSP equation, the multi-bright solution (zero boundary conditions), multi-breather and high-order rogue wave solutions (non-zero boundary conditions) are derived, while for the defocusing sdCSP equation with non-zero boundary conditions, the multi-dark soliton solution is constructed. We further show that, in the continuous limit, all the solutions obtained converge to the ones for its original CSP equation (Ling et al . 2016 Physica D 327 , 13–29 ( doi:10.1016/j.physd.2016.03.012 ); Feng et al . 2016 Phys. Rev. E 93 , 052227 ( doi:10.1103/PhysRevE.93.052227 )).

A resource efficient approach for quantum and classical simulations of gauge theories in particle physics

Gauge theories establish the standard model of particle physics, and lattice gauge theory (LGT) calculations employing Markov Chain Monte Carlo (MCMC) methods have been pivotal in our understanding of fundamental interactions. The present limitations of MCMC techniques may be overcome by Hamiltonian-based simulations on classical or quantum devices, which further provide the potential to address questions that lay beyond the capabilities of the current approaches. However, for continuous gauge groups, Hamiltonian-based formulations involve infinite-dimensional gauge degrees of freedom that can solely be handled by truncation. Current truncation schemes require dramatically increasing computational resources at small values of the bare couplings, where magnetic field effects become important. Such limitation precludes one from `taking the continuous limit' while working with finite resources. To overcome this limitation, we provide a resource-efficient protocol to simulate LGTs with continuous gauge groups in the Hamiltonian formulation. Our new method allows for calculations at arbitrary values of the bare coupling and lattice spacing. The approach consists of the combination of a Hilbert space truncation with a regularization of the gauge group, which permits an efficient description of the magnetically-dominated regime. We focus here on Abelian gauge theories and use 2+1 dimensional quantum electrodynamics as a benchmark example to demonstrate this efficient framework to achieve the continuum limit in LGTs. This possibility is a key requirement to make quantitative predictions at the field theory level and offers the long-term perspective to utilise quantum simulations to compute physically meaningful quantities in regimes that are precluded to quantum Monte Carlo.

Sub-nanograin metal based high efficiency multilayer reflective optics for high energies

The present finding illuminates the physics of the formation of interfaces of metal based hetero-structures near layer continuous limit as an approach to develop high-efficiency W/B4C multilayer optics with varying periods at a fixed large layer pairs.

General methods and properties to evaluate continuum limits of the 1D discrete time quantum walk

Models of quantum walks which admit continuous time and continuous spacetime limits have recently led to quantum simulation schemes for simulating fermions in relativistic and nonrelativistic regimes (Molfetta GD, Arrighi P. A quantum walk with both a continuous-time and a continuous-spacetime limit, 2019). This work continues the study of relationships between discrete time quantum walks (DTQW) and their ostensive continuum counterparts by developing a more general framework than was done in Molfetta and Arrighi (A quantum walk with both a continuous-time and a continuous-spacetime limit, 2019) to evaluate the continuous time limit of these discrete quantum systems. Under this framework, we prove two constructive theorems concerning which internal discrete transitions (“coins”) admit nontrivial continuum limits. We additionally prove that the continuous space limit of the continuous time limit of the DTQW can only yield massless states which obey the Dirac equation. Finally, we demonstrate that for general coins the continuous time limit of the DTQW can be identified with the canonical continuous time quantum walk when the coin is allowed to transition through the continuous limit process.

Stationary currents in long-range interacting magnetic systems

We construct a solution for the 1d integro-differential stationary equation derived from a finite-volume version of the mesoscopic model proposed in Giacomin and Lebowitz (J. Stat. Phys. 87(1), 37–61, 1997). This is the continuous limit of an Ising spin chain interacting at long range through Kac potentials, staying in contact at the two edges with reservoirs of fixed magnetizations. The stationary equation of the model is introduced here starting from the Lebowitz-Penrose free energy functional defined on the interval [−ε− 1, ε− 1], ε > 0. Below the critical temperature, and for ε small enough, we obtain a solution that is no longer monotone when opposite in sign, metastable boundary conditions are imposed. Moreover, the mesoscopic current flows along the magnetization gradient. This can be considered as an analytic proof of the existence of diffusion along the concentration gradient in one-component systems undergoing a phase transition, a phenomenon generally known as uphill diffusion. In our proof uniqueness is lacking, and we have clues that the stationary solution obtained is not unique, as suggested by numerical simulations.

The Limit Situation And The Narrative Of War (On The Material Of The Novel “My Lieutenant” By Daniil Granin)

The purpose of this study is the analysis of limit situation in the narrative of war. The material of the study is the novel of Daniil Granin “My Lieutenant” and related texts. In the first part of the paper, the authors explore existing approaches to the term “limit situation” and similar concepts into scientific and philosophical traditions; limits of its applicability in literary studies and its relation to the categories of “narrative instances” and “event”. Proposed a literary-theoretical definition of the limit situation, which can be used in the analysis of fiction texts. Existing approaches to the examination of the situation of war are analyzed: philosophical-existential, psychoanalytic, sociological, literary. In the second part of the paper, the authors propose their method for analyzing limit situations in texts about war, which basis on existing approaches and preserves the text-centric principle of studying the structure of the story. Two interrelated areas of research have been identified: the study of war as a continuous limit situation in the intertextual aspect (the discourse of war); the study of limit situations (death, suffering, guilt, accident) in the narrative of war as part of a specific text. In the third part of the scientific work,the analysis of war as a continuous limit situation results in the study of the concept of “limit” (border) in a fiction text. The role of “limit” (border) concept in the texts about the war is studied, the possible types of limits in the discourse of war are examined. Limit situations in the narrative of war are analyzed on the basis of the novel “My Lieutenant” by Daniil Granin. A review of journalistic and scientific works about the novel revealed both the continuity and the differences between the novel and the “lieutenant” prose of the 20th century. An analysis of the limit situations in the novel revealed their key position in the narrative. These situations are independent of the fiction time, of the fluctuation of the point of view’; the function of the abstract author is to build the narrative as a “directive” immersion of the hero and narrator in these situations.