相关论文: Can our number system be improved?
Recommender systems are ubiquitous in on-line services to drive businesses. And many sequential recommender models were deployed in these systems to enhance personalization. The approach of using the transformer decoder as the sequential…
We obtain new upper and lower bounds on the number of unit perimeter triangles spanned by points in the plane. We also establish improved bounds in the special case where the point set is a section of the integer grid.
In order to introduce an integrated research information system, this will provide scientific institutions with the necessary information on research activities and research results in assured quality. Since data collection, duplication,…
By bringing together code, text, and examples, Jupyter notebooks have become one of the most popular means to produce scientific results in a productive and reproducible way. As many of the notebook authors are experts in their scientific…
An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.
Prime number multiplet classifications and patterns are extended to negative integers. The extension from prime numbers to single prime powers is also studied. Prime number septets at equal distance are given. It is also shown that each…
The increasing role of recommender systems in many aspects of society makes it essential to consider how such systems may impact social good. Various modifications to recommendation algorithms have been proposed to improve their performance…
It is widely accepted that the selection of measurement bases can affect the efficiency of quantum state estimation methods, precision of estimating an unknown state can be improved significantly by simply introduce a set of symmetrical…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
Numbers are a basic part of how humans represent and describe the world around them. As a consequence, learning effective representations of numbers is critical for the success of large language models as they become more integrated into…
One challenge (or opportunity!) that many instructors face is how varied the backgrounds, abilities, and interests of students are. In order to simultaneously instill confidence in those with weaker preparations and still challenge those…
By some new recursive algorithms, in this paper, we will give some improvements on Waring's problem.
Optomechanical systems are often used for the measurement of weak forces. Feedback loops can be used in these systems for achieving noise reduction. Here we show that even though feedback is not able to improve the signal to noise ratio of…
The $\Lambda$CDM cosmology passes demanding tests that establish it as a good approximation to reality, but it could be improved. I present a list of possibly interesting and less well explored things that might yield hints to a better…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
The problem of feedback equivalence for control systems is considered. An algebra of differential invariants and criteria for the feedback equivalence for regular control systems are found.
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
I have been asked to discuss the status of QCD. It seems to me that there are three main points to be made about the present status of QCD: $\bullet$ QCD is right, and we can do many beautiful things with it. $\bullet$ There are several…
This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into…
Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…