Automated Market Makers (AMMs) have cemented themselves as an integral part of the decentralized finance (DeFi) space. AMMs are a type of exchange that allows users to trade assets without the need for a centralized exchange. They form the foundation for numerous decentralized exchanges (DEXs), which help facilitate the quick and efficient exchange of on-chain tokens. All present-day popular DEXs are static protocols, with fixed parameters controlling the fee and the curvature - they suffer from invariance and cannot adapt to quickly changing market conditions. This characteristic may cause traders to stay away during high slippage conditions brought about by intractable market movements. We propose an RL framework to optimize the fees collected on an AMM protocol. In particular, we develop a Q-Learning Agent for Market Making Protocols (QLAMMP) that learns the optimal fee rates and leverage coefficients for a given AMM protocol and maximizes the expected fee collected under a range of different market conditions. We show that QLAMMP is consistently able to outperform its static counterparts under all the simulated test conditions.

We study the statistical properties of the recurrence intervals $τ$ between successive trading volumes exceeding a certain threshold $q$. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period from January 2000 to May 2009, and two Chinese indices from January 2003 to April 2009. Similar to the recurrence interval distribution of the price returns, the tail of the recurrence interval distribution of the trading volumes follows a power-law scaling, and the results are verified by the goodness-of-fit tests using the Kolmogorov-Smirnov (KS) statistic, the weighted KS statistic and the Cram{é}r-von Mises criterion. The measurements of the conditional probability distribution and the detrended fluctuation function show that both short-term and long-term memory effects exist in the recurrence intervals between trading volumes. We further study the relationship between trading volumes and price returns based on the recurrence interval analysis method. It is found that large trading volumes are more likely to occur following large price returns, and the comovement between trading volumes and price returns is more pronounced for large trading volumes.

I compare two quantum-theoretical approaches to the phenomenon of adaptive mutations, termed here Q-cell and Q-genome. I use 'fluctuation trapping' model as a general framework. I introduce notions of R-error and D-error and argue that the 'fluctuation trapping' model has to employ a correlation between the R- and D- errors. Further, I compare how the two approaches can justify the R-D-error correlation, focusing on the advantages of the Q-cell approach. The positive role of environmentally induced decoherence (EID) on both steps of the adaptation process is emphasized. A starving bacterial cell is proposed to be in an einselected state. The intracellular dynamics in this state has a unitary character and I propose to interpret it as 'exponential growth in imaginary time', analogously to the commonly considered 'diffusion' interpretation of the Schroedinger equation. Addition of a substrate leads to Wick rotation and a switch from 'imaginary time' reproduction to a 'real time' reproduction regime. Due to the variations at the genomic level (such as base tautomery), the starving cell has to be represented as a superposition of different components, all 'reproducing in imaginary time'. Adidtion of a selective substrate, allowing only one of these components to amplify, will cause Wick rotation and amplification of this component, thus justifying the occurence of the R-D-error correlation. Further ramifications of the proposed ideas for evolutionary theory are discussed.

Global Style Tokens (GSTs) are a recently-proposed method to learn latent disentangled representations of high-dimensional data. GSTs can be used within Tacotron, a state-of-the-art end-to-end text-to-speech synthesis system, to uncover expressive factors of variation in speaking style. In this work, we introduce the Text-Predicted Global Style Token (TP-GST) architecture, which treats GST combination weights or style embeddings as "virtual" speaking style labels within Tacotron. TP-GST learns to predict stylistic renderings from text alone, requiring neither explicit labels during training nor auxiliary inputs for inference. We show that, when trained on a dataset of expressive speech, our system generates audio with more pitch and energy variation than two state-of-the-art baseline models. We further demonstrate that TP-GSTs can synthesize speech with background noise removed, and corroborate these analyses with positive results on human-rated listener preference audiobook tasks. Finally, we demonstrate that multi-speaker TP-GST models successfully factorize speaker identity and speaking style. We provide a website with audio samples for each of our findings.

A recently implemented relativistic four-component configuration interaction approach to study ${\cal{P}}$- and ${\cal{T}}$-odd interaction constants in atoms and molecules is employed to determine the electron electric dipole moment effective electric field in the $Ω=1$ first excited state of the ThO molecule. We obtain a value of $E_{\text{eff}} = 75.6 \left[\frac{\rm GV}{\rm cm}\right]$ with an estimated error bar of $3\%$ and $10\%$ smaller than a previously reported result [arXiv:1308.0414 [physics.atom-ph]]. Using the same wavefunction model we obtain an excitation energy of $T_v^{Ω=1} = 5329$ [\cm], in accord with the experimental value within $2\%$. In addition, we report the implementation of the magnetic hyperfine interaction constant $A_{||}$ as an expectation value, resulting in $A_{||} = -1335$ [MHz] for the $Ω=1$ state in ThO. The smaller effective electric field increases the previously measured upper bound to the electron electric dipole moment interaction constant [arXiv:1310.7534v2 [physics.atom-ph]] and thus mildly mitigates constraints to possible extensions of the Standard Model of particle physics.

We propose an improved scheme of perturbation theory based on our exact solution [An Min Wang, quant-ph/0611216] in general quantum systems independent of time. Our elementary start-point is to introduce the perturbing parameter as late as possible. Our main skills are Hamiltonian redivision so as to overcome a flaw of the usual perturbation theory, and the perturbing Hamiltonian matrix product decomposition in order to separate the contraction and anti-contraction terms. Our calculational technology is the limit process for eliminating apparent divergences. Our central idea is ``dynamical rearrangement and summation" for the sake of the partial contributions from the high order even all order approximations absorbed in our perturbed solution. Consequently, we obtain the improved forms of the zeroth, first, second and third order perturbed solutions absorbing the partial contributions from the high order even all order approximations of perturbation. Then we deduce the improved transition probability. In special, we propose the revised Fermi's golden rule. Moreover, we apply our scheme to obtain the improved forms of perturbed energy and perturbed state. In addition, we study an easy understanding example of two-state system to illustrate our scheme and show its advantages. All of this implies the physical reasons and evidences why our improved scheme of perturbation theory are actually calculable, operationally efficient, conclusively more accurate. Our improved scheme is the further development and interesting application of our exact solution, and it has been successfully used to study on open system dynamics [An Min Wang, quant-ph/0601051].

Michel Barat passed away in November 2018 at the age of 80 after a rich career in atomic and molecular collisions. He had participated actively in formalizing to the electron promotion model, contributed to low energy reactive collisions at the frontier of chemistry. He investigated electron capture mechanisms by highly charged ions, switched to collision induced cluster dissociation and finally to UV laser excitation induced fragmentation mechanisms of biological molecules. During this highly active time he created a lab, organized ICPEAC and participated actively in the administration of research. This paper covers the ten years where he mentored my scientific activity in the blossoming field of electron capture by highly charge ions (HCI). In spite of an impressive number of open channels, Michel found a way to capture the important parameters and to simplify the description of several electron capture processes; orientation propensity, electron promotion, true double electron capture, Transfer ionisation, Transfer excitation, formation of Rydberg states, and electron capture by metastable states. Each time Michel established fruitful collaborations with other groups.

The fundamental vibrational interval of H$_{2}^+$ has been determined to be $ΔG _{1/2} = 2191.126\,614(17)$ cm$^{-1}$ by continuous-wave laser spectroscopy of Stark manifolds of Rydberg states of H$_2$ with the H$_{2}^+$ ion core in the ground and first vibrationally excited states. Extrapolation of the Stark shifts to zero field yields the zero-quantum-defect positions $-R_{\textrm{H}_2}$/$n^2$, from which ionization energies can be determined. Our new result represents a four-order-of-magnitude improvement compared to earlier measurements. It agrees, within the experimental uncertainty, with the value of 2191.126\,626\,344(17)(100) cm$^{-1}$ determined in non-relativistic quantum electrodynamic calculations V. Korobov, L. Hilico and J.-Ph. Karr, Phys. Rev. Lett. 118, 233001 (2017) http://doi.org/10.1103/PhysRevLett.118.233001.

Endogenous chemical exchange saturation transfer (CEST) effects are always diluted by competing effects such as direct water proton saturation (spillover) and macromolecular magnetization transfer (MT). This leads to T2-and MT-shine-through effects in the actual biochemical contrast of CEST. Therefore, a simple evaluation algorithm which corrects the CEST signal was searched for. By employing a recent eigenspace theory valid for spinlock and continuous wave (cw) CEST we predict that the inverse Z-spectrum is beneficial to Z-spectrum itself. Based on this we propose a new spillover- and MT-corrected magnetization transfer ratio (MTRRex) yielding Rex, the exchange dependent relaxation rate in the rotating frame. For verification, the amine proton exchange of creatine in solutions with different agar concentration was studied experimentally at clinical field strength of 3T. In contrast to the compared standard evaluation for pulsed CEST experiments, MTRasym, our approach shows no T2 or MT shine through effect. We demonstrate that spillover can be corrected properly and also quantitative evaluation of pH and creatine concentration is possible which proves MTRRex as quantitative CEST-MRI method. A spillover correction is of special interest for clinical static field strengths and protons resonating near the water peak. This is the case for -OH-CEST effects like gagCEST or glucoCEST, but also amine exchange of creatine or glutamate which require high B1. Although, only showed for amine exchange, we propose our normalization to work generally for DIACEST, PARACEST in slow- and fast exchange regime not just as a correction, but also for quantitative CEST-MRI. Applied to acute stroke induced in rat brain, the corrected CEST signal shows significantly higher contrast between stroke area and normal tissue as well as less B1 dependency compared to conventional approaches.

This paper proposes to build a bridge between microscopic descriptions of matter with internal energy, composed of many fast interacting particles inside an environment, and their port-Hamiltonian (PH) descriptions at macroscopic scale. The environment, assumed to be slow, is modeled through experimental constraints on macroscopic quantities (e.g. energy, particle number, etc), with a partitioning into two classes: non fluctuating and fluctuating values. The method to derive the PH macroscopic laws is detailed in several steps and illustrated on two standard cases (ideal gas, Ising ferromagnets). It revisits equilibrium statistical physics with a focus on this partitioning. First, the Boltzmann's principle is used to provide the statistic law of the matter. It defines a macroscopic equilibrium characterized by a scalar value, the entropy, together with thermodynamic quantities emerging from each constraint. Then, the port-Hamiltonian system is derived. The Hamiltonian (macroscopic energy) is derived as a function of the macroscopic state (entropy and the macroscopic quantities associated with the fluctuating class). The ports (flows/efforts) are related to the time-derivative of the state and the Hamiltonian gradient in a conservative way. This open system defines the reversible laws that govern standard thermodynamic quantities. Lastly, this paper presents a strategy to extend this PH system to an irreversible conservative one, given a macroscopic dissipative law.