Asymmetric exclusion model with several kinds of impurities

We formulate a new integrable asymmetric exclusion process with $N-1=0,1,2,...$ kinds of impurities and with hierarchically ordered dynamics. The model we proposed displays the full spectrum of the simple asymmetric exclusion model plus new levels. The first excited state belongs to these new levels and displays unusual scaling exponents. We conjecture that, while the simple asymmetric exclusion process without impurities belongs to the KPZ universality class with dynamical exponent 3/2, our model has a scaling exponent $3/2+N-1$. In order to check the conjecture, we solve numerically the Bethe equation with N=3 and N=4 for the totally asymmetric diffusion and found the dynamical exponents 7/2 and 9/2 in these cases.Comment: to appear in JSTA

Dynamic Posted-Price Mechanisms for the Blockchain Transaction Fee Market

In recent years, prominent blockchain systems such as Bitcoin and Ethereum have experienced explosive growth in transaction volume, leading to frequent surges in demand for limited block space and causing transaction fees to fluctuate by orders of magnitude. Existing systems sell space using first-price auctions; however, users find it difficult to estimate how much they need to bid in order to get their transactions accepted onto the chain. If they bid too low, their transactions can have long confirmation times. If they bid too high, they pay larger fees than necessary. In light of these issues, new transaction fee mechanisms have been proposed, most notably EIP-1559, aiming to provide better usability. EIP-1559 is a history-dependent mechanism that relies on block utilization to adjust a base fee. We propose an alternative design -- a {\em dynamic posted-price mechanism} -- which uses not only block utilization but also observable bids from past blocks to compute a posted price for subsequent blocks. We show its potential to reduce price volatility by providing examples for which the prices of EIP-1559 are unstable while the prices of the proposed mechanism are stable. More generally, whenever the demand for the blockchain stabilizes, we ask if our mechanism is able to converge to a stable state. Our main result provides sufficient conditions in a probabilistic setting for which the proposed mechanism is approximately welfare optimal and the prices are stable. Our main technical contribution towards establishing stability is an iterative algorithm that, given oracle access to a Lipschitz continuous and strictly concave function $f$, converges to a fixed point of $f$

Resistance exercise minimal dose strategies for increasing muscle strength in the general population: An overview

Many individuals do not participate in resistance exercise, with perceived lack of time being a key barrier. Minimal dose strategies, which generally reduce weekly exercise volumes to less than recommended guidelines, might improve muscle strength with minimal time investment. However, minimal dose strategies and their effects on muscle strength are still unclear. Here our aims are to define and characterize minimal dose resistance exercise strategies and summarize their effects on muscle strength in individuals who are not currently engaged in resistance exercise. The minimal dose strategies overviewed were: “Weekend Warrior,” single-set resistance exercise, resistance exercise “snacking,” practicing the strength test, and eccentric minimal doses. “Weekend Warrior,” which minimizes training frequency, is resistance exercise performed in one weekly session. Single-set resistance exercise, which minimizes set number and session duration, is one set of multiple exercises performed multiple times per week. “Snacks,” which minimize exercise number and session duration, are brief bouts (few minutes) of resistance exercise performed once or more daily. Practicing the strength test, which minimizes repetition number and session duration, is one maximal repetition performed in one or more sets, multiple days per week. Eccentric minimal doses, which eliminate or minimize concentric phase muscle actions, are low weekly volumes of submaximal or maximal eccentric-only repetitions. All approaches increase muscle strength, and some approaches improve other outcomes of health and fitness. “Weekend Warrior” and single-set resistance exercise are the approaches most strongly supported by current research, while snacking and eccentric minimal doses are emerging concepts with promising results. Public health programs can promote small volumes of resistance exercise as being better for muscle strength than no resistance exercise at all

Exactly solvable interacting vertex models

We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core interactions among pair of vertices at larger distances.The associated row-to-row transfer matrices are diagonalized by using the recently introduced matrix product {\it ansatz}. Similarly as the relation of the six-vertex model with the XXZ quantum chain, the row-to-row transfer matrices of these new models are also the generating functions of an infinite set of commuting conserved charges. Among these charges we identify the integrable generalization of the XXZ chain that contains hard-core exclusion interactions among the spins. These quantum chains already appeared in the literature. The present paper explains their integrability.Comment: 20 pages, 3 figure

FORPS: a FORTH-based production system and its application to a real-time robot control problem

A simple yet very powerful system has been developed that merges the artificial intelligence qualities of a production system with the real-time control capabilities of FORTH. FORPS (FORTH-based Production System) offers the advantages of intelligent, rule-based control in a small package offering high speed, extensibility, and simplicity. A practical example of the system is presented in the development of an obstacle avoidance program to aid in controlling an overhead manipulator transport system. Several other potential applications to the area of control are discussed

A study of pentaquarks on the lattice with overlap fermions

We present a quenched lattice QCD calculation of spin-1/2 five-quark states with $uudd\bar{s}$ quark content for both positive and negative parities. We do not observe any bound pentaquark state in these channels for either I = 0 or I =1. The states we found are consistent with KN scattering states which are checked to exhibit the expected volume dependence of the spectral weight. The results are based on overlap-fermion propagators on two lattices, 12^3 x 28 and 16^3 x 28, with the same lattice spacing of 0.2 fm, and pion mass as low as ~ 180 MeV.Comment: accepted for publication in Phys. Rev.