Related papers: Concentrated N-dimensional AMM with Polar Coordina…
In this paper, we explore the short- and long-term stability of backed stablecoins offering constant mint and redeem prices to all agents. We refer to such designs as price window-based, since the mint and redeem prices constrain the…
This paper studies liquid staking tokens (LSTs) on automated market makers (AMMs), both theoretically and empirically. LSTs are tokenized representations of staked assets on proof-of-stake blockchains. First, we model LST-liquidity on AMMs…
The price volatility of cryptocurrencies is often cited as a major hindrance to their wide-scale adoption. Consequently, during the last two years, multiple so called stablecoins have surfaced---cryptocurrencies focused on maintaining…
We develop a new type of automated market maker (AMM) that helps to maintain stability and long-term viability in a stablecoin. This primary market AMM (P-AMM) is an autonomous mechanism for pricing minting and redemption of stablecoins in…
In this paper, we introduce a novel framework to model the exchange rate dynamics between two intrinsically linked cryptoassets, such as stablecoins pegged to the same fiat currency or a liquid staking token and its associated native token.…
We systematically investigate the existence, stability, and propagation dynamics of multipole-mode (necklace-shaped) solitons in the two-dimensional model of an optical medium with the defocusing saturable nonlinearity and an annular…
Monte Carlo simulation, experiment and continuum theory are used to examine the anchoring exhibited by a nematic liquid crystal at a patterned substrate comprising a periodic array of rectangles that, respectively, promote vertical and…
Decentralized exchange platforms such as Uniswap and Balancer operate on several pools where each pool contains two or more cryptocurrencies and constitutes direct trading pairs. The drawbacks here are that liquidity providing requires…
We report an experimental approach to control the position of molecular aggregates on surfaces by vacuum deposition. The control is accomplished by regulating the molecular density on the surface in a confined area. The diffusing molecules…
An algorithmic stablecoin is a type of cryptocurrency managed by algorithms (i.e., smart contracts) to dynamically minimize the volatility of its price relative to a specific form of asset, e.g., US dollar. As algorithmic stablecoins have…
We address necklace solitons supported by circular waveguide arrays with out-of-phase modulation of nonlinearity and linear refractive index. Such two-dimensional necklace solitons appear as rings of multiple out-of-phase bright spots. We…
The ability to manipulate polar entities with multiple external fields opens exciting possibilities for emerging functionalities and novel applications in spin systems, photonics, metamaterials, and soft matter. Liquid crystals (LCs),…
The matter of the stability for multi-asset American option pricing problems is a present remaining challenge. In this paper a general transformation of variables allows to remove cross derivative terms reducing the stencil of the proposed…
We consider the constrained stabilization problem of second-order systems evolving on the n-sphere. We propose a control strategy with a constraint proximity-based dynamic damping mechanism that ensures safe and almost global asymptotic…
Layer-2 (L2) blockchains inherit Ethereums security guarantees while reducing gas fees. As a result, they are gaining traction among traders at Automated Market Makers (AMMs), sparking debate over whether they contribute to liquidity…
We demonstrate the formation and trapping of different stationary solutions, oscillatory solutions, and rotating solutions of a polariton condensate in a planar semiconductor microcavity with a built-in ring-shaped potential well.…
Stablecoins, which are primarily intended to function as a global reserve of value are insubstantial in their design and present many failure points. The primary mechanism to enable these coins to hold on to a fixed value is by backing them…
Convex optimisation has provided a mechanism to determine arbitrage trades on automated market markets (AMMs) since almost their inception. Here we outline generic closed-form solutions for $N$-token geometric mean market maker pool…
Dark solitons carrying quantized phase information arouse great interest in different nonlinear systems. A dark soliton in 1D can be stabilized in microcavity polariton condensates as a confinement is imposed on it to prevent its decay.…
This paper reviews theoretical advances on the formation and stabilization of multidimensional solitons in nonlinear Schr\"odinger systems with attractive interactions, focusing on atomic Bose-Einstein condensates and nonlinear optics.…