Non-vanishing Gram determinants for cyclotomic Nazarov–Wenzl and Birman–Murakami–Wenzl algebras

AbstractIn this paper, we use the method in Rui and Si (2011) [35] to give a necessary and sufficient condition on non-vanishing Gram determinants for cyclotomic NW and cyclotomic BMW algebras over an arbitrary field. Equivalently, we give a necessary and sufficient condition for each cell module of such algebras being equal to its simple head over an arbitrary field

Singular parameters for the Birman-Murakami-Wenzl algebra

In this paper, we classify the singular parameters for the Birman-Murakami-Wenzl algebra over an arbitrary field. Equivalently, we give a criterion for the Birman-Murakami-Wenzl algebra being Morita equivalent to the direct sum of the Hecke algebras associated to certain symmetric groups.Comment: 1

Reinforcement Learning with Quantum Variational Circuits

The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate reinforcement learning problems. Quantum computing approaches offer important potential improvements in time and space complexity over traditional algorithms because of its ability to exploit the quantum phenomena of superposition and entanglement. Specifically, we investigate the use of quantum variational circuits, a form of quantum machine learning. We present our techniques for encoding classical data for a quantum variational circuit, we further explore pure and hybrid quantum algorithms for DQN and Double DQN. Our results indicate both hybrid and pure quantum variational circuit have the ability to solve reinforcement learning tasks with a smaller parameter space. These comparison are conducted with two OpenAI Gym environments: CartPole and Blackjack, The success of this work is indicative of a strong future relationship between quantum machine learning and deep reinforcement learning.Comment: Accepted to AIIDE 2020 Updated to better reflect AAAI formattin

Prompt to GPT-3: Step-by-Step Thinking Instructions for Humor Generation

Artificial intelligence has made significant progress in natural language processing, with models like GPT-3 demonstrating impressive capabilities. However, these models still have limitations when it comes to complex tasks that require an understanding of the user, such as mastering human comedy writing strategies. This paper explores humor generation using GPT-3 by modeling human comedy writing theory and leveraging step-by-step thinking instructions. In addition, we explore the role of cognitive distance in creating humor.Comment: 5 pages, 1 figure; ICCC '23 preprin

The Jucys-Murphy basis and semisimplicty criteria for the qq-Brauer algebra

We construct the Jucys-Murphy elements and the Jucys-Murphy basis for the $q$-Brauer algebra in the sense of Mathas[11]. We also give a necessary and sufficient condition for the $q$-Brauer algebra being (split) semisimple over an arbitrary field.Comment: 21 page

Crossing at a Red Light: Behavior of Cyclists at Urban Intersections

To investigate the relationship between cyclist violation and waiting duration, the red-light running behavior of nonmotorized vehicles is examined at signalized intersections. Violation waiting duration is collected by video cameras and it is assigned as censored and uncensored data to distinguish between normal crossing and red-light running. A proportional hazard-based duration model is introduced, and variables revealing personal characteristics and traffic conditions are used to describe the effects of internal and external factors. Empirical results show that the red-light running behavior of cyclist is time dependent. Cyclist’s violating behavior represents positive duration dependence, that the longer the waiting time elapsed, the more likely cyclists would end the wait soon. About 32% of cyclists are at high risk of violation and low waiting time to cross the intersections. About 15% of all the cyclists are generally nonrisk takers who can obey the traffic rules after waiting for 95 seconds. The human factors and external environment play an important role in cyclists’ violation behavior. Minimizing the effects of unfavorable condition in traffic planning and designing may be an effective measure to enhance traffic safety