This paper establishes a new and comprehensive theoretical analysis for the application of reinforcement learning (RL) in high-frequency market making. We bridge the modern RL theory and the continuous-time statistical models in high-frequency financial economics. Different with most existing literature on methodological research about developing various RL methods for market making problem, our work is a pilot to provide the theoretical analysis. We target the effects of sampling frequency, and find an interesting tradeoff between error and complexity of RL algorithm when tweaking the values of the time increment $Δ$ $-$ as $Δ$ becomes smaller, the error will be smaller but the complexity will be larger. We also study the two-player case under the general-sum game framework and establish the convergence of Nash equilibrium to the continuous-time game equilibrium as $Δ\rightarrow0$. The Nash Q-learning algorithm, which is an online multi-agent RL method, is applied to solve the equilibrium. Our theories are not only useful for practitioners to choose the sampling frequency, but also very general and applicable to other high-frequency financial decision making problems, e.g., optimal executions, as long as the time-discretization of a continuous-time markov decision process is adopted. Monte Carlo simulation evidence support all of our theories.

Predicting the future evolutionary trajectory of SARS-CoV-2 remains a critical challenge, particularly due to the pivotal role of spike protein mutations. It is therefore essential to develop evolutionary models capable of continuously integrating new experimental data. In this study, we employ a cladogram algorithm that incorporates established assumptions for mutant representation -- using both four-letter and two-letter formats -- along with an n-mer distance algorithm to construct a cladogenetic tree of SARS-CoV-2 mutations. This tree accurately captures the observed changes across macro-lineages. We introduce a stochastic method for generating new strains on this tree based on spike protein mutations. For a given set A of existing mutation sites, we define a set X comprising x randomly generated mutation sites on the spike protein. The intersection of A and X, denoted as set Y, contains y sites. Our analysis indicates that the position of a generated strain on the tree is primarily determined by x. Through large-scale stochastic sampling, we predict the emergence of new macro-lineages. As x increases, the dominance among macro-lineages shifts: lineage O surpasses N, P surpasses O, and eventually Q surpasses P. We identify threshold values of x that delineate transitions between these macro-lineages. Furthermore, we propose an algorithm for predicting the timeline of macro-lineage emergence. In conclusion, our findings demonstrate that SARS-CoV-2 evolution adheres to statistical principles: the emergence of new strains can be driven by randomly generated spike protein sites, and large-scale stochastic sampling reveals evolutionary patterns underlying the rise of distinct macro-lineages.

This document presents some insights and observations regarding the paper that was published in IEEE Transactions on Signal Processing (TSP), titled "Self-Localization of Ad-Hoc Arrays Using Time Difference of Arrivals". In the spirit of constructive feedback, I wish to highlight two key areas of consideration. The first pertains to aspects related to methodology, experimental results, and statements made in the paper. The second part addresses specific equation/typographical errors. This work aims to initiate a constructive dialogue concerning certain aspects of the paper published in IEEE TSP. Our intention is to provide feedback that contributes to the ongoing improvement of the paper's robustness and clarity.

Strong-field manipulation of autoionizing states is a crucial aspect of electronic quantum control. Recent measurements of the attosecond transient absorption spectrum of helium dressed by a few-cycle visible pulse [Ott et al., arXiv:1205.0519[physics.atom-ph] ] provide evidence of novel ultrafast resonant phenomena, namely, two-photon Rabi oscillations between doubly-excited states and the inversion of Fano profiles. Here we present the results of accurate \emph{ab-initio} calculations that agree with these observations and in addition predict that (i) inversion of Fano profiles is actually periodic in the coupling laser intensity and (ii) the supposedly dark $2p^2$ {$^1$S} state also appears in the spectrum. Closer inspection of the experimental data confirms the latter prediction.

We propose a platform for observing and controlling the interactions between atomic ions and a quantum gas of polar molecules in the ultracold regime. This approach is based on the combination of several recently developed methods in two so-far complementary research domains: ion-atom collisions and studies of ultracold polar molecules. In contrast to collisions between ions and ground-state atoms, which are dominated by losses due to three-body recombination (TBR) already at densities far below those typical for quantum degenerate ensembles, our proposal makes use of polar molecules, their rich level structure, and sensitivity to electric fields to design effective interaction potentials where ion-neutral TBR losses and molecule-molecule losses due to sticky collisions could be strongly suppressed. This may open a broad range of applications including precise control of collisional properties in molecular ensembles using ions, quantum simulations, and cold quantum chemistry between polyatomic molecules.

The paper is an extension of quant-ph/9912102. The new framework is tested on the 2-photon spontaneous emission and blackbody radiation. The new effects are rather subtle. The probability of the 2-photon emission is shown to consist of a product of several terms: One which is identical to this from standard quantum optics and the remaining ones formally resembling detector inefficiencies (here arising from nontrivial vacuum structure). The blackbody distribution is indistinguishable from the Planck law for T<T_{critical} but for T>T_{critical} the maximum of the distribution gets lowered and shifts towards higher frequencies. T_{critical} is a parameter that, in principle, should be observable. No normal ordering of operators is needed and vacuum energy is nonzero but finite. Vacuum is represented by a subspace spanned by ground states of the oscillators and is not equivalent to the cyclic vector of the GNS construction. The non-CCR algebra is discussed in more detail.

Molecular chirality is conventionally understood as space-inversion-symmetry breaking in the equilibrium structure of molecules. Less well known is that achiral molecules can be made chiral through extreme rotational excitation. Here, we theoretically demonstrate a clear strategy for generating rotationally-induced chirality (RIC): An optical centrifuge rotationally excites the phosphine molecule (PH$_3$) into chiral cluster states that correspond to clockwise ($R$-enantiomer) or anticlockwise ($L$-enantiomer) rotation about axes almost coinciding with single P-H bonds. Application of a strong dc electric field during the centrifuge pulse favors the production of one rotating enantiomeric form over the other, creating dynamically chiral molecules with $permanently$ oriented rotational angular momentum. This essential step toward characterizing RIC promises a fresh perspective on chirality as a fundamental aspect of nature.

Conventional noise analysis in atomic-ensemble sensing assumes a continuous-medium approximation, thereby treating the atomic system as a deterministic dielectric. Here, we demonstrate that this assumption breaks down due to the discrete, particulate nature of the ensemble, giving rise to an intrinsic "atomic granularity noise" (AGN) that fundamentally competes with the optical measurement noise (OMN, typically photon shot noise). By introducing a discrete-atom statistical framework, we derive a unified noise-scaling law governed by a single dimensionless resource ratio, $\mathcal{R} = \bar{N}_{\mathrm{ph}}/\bar{N}_{\mathrm{at}}$ at (the photon-to-atom flux ratio). This law predicts a continuous crossover from an OMN-limited regime to an AGN-limited regime. Crucially, our results reveal a counter-intuitive constraint for sensor optimization: increasing optical probe power -- standard practice to mitigate OMN -- can paradoxically degrade sensitivity by driving the system into the AGN-dominated regime. Furthermore, we identify a critical resource threshold, $\mathcal{R}_{\mathrm{crit}}$, beyond which quantum-enhanced metrology using non-classical light fails to improve sensitivity, as it becomes limited by the AGN.

We study the equation of state, polarization and radiation properties for nonideal, strongly magnetized plasmas which compose outer envelopes of magnetic neutron stars. Detailed calculations are performed for partially ionized hydrogen atmospheres and for condensed hydrogen or iron surfaces of these stars. This is a companion paper to astro-ph/0511803

In this paper, we propose to combine two promising research topics in accelerator physics, i.e., optical stochastic cooling (OSC) and steady-state microbunching (SSMB). The motivation is to provide a powerful radiation source which could benefit fundamental science research and industry applications. Our study shows that such a compact OSC-SSMB storage ring using present technology can deliver EUV light with an average power of kilowatt, and spectral flux $>10^{20}$ phs/s/0.1\%b.w., which is four orders of magnitude higher than existing synchrotron sources. It is expected that the presented work is of value for the development of both OSC and SSMB.