We develop an efficient software package to test for the primality of p2^n+1, p prime and p>2^n. This aids in the determination of large, non-Sierpinski numbers p, for prime p, and in cryptography. It furthermore uniquely allows for the computation of the smallest...

["Cryptography","Data Science","Theory and Formal Methods"]

Evolutionary algorithms often incorporate ecological concepts to help maintain diverse populations and drive continued innovation. However, while there is strong evidence for the value of ecological dynamics, a lack of overarching theoretical framework renders...

["Computational Biology","Adaptive and Self-Organizing Systems","Data Mining and Machine Learning","Theory and Formal Methods"]

In this article we consider a certain sub class of Integer Equal Flow problem, which are known NP hard. Currently there exist no direct solutions for the same. It is a common problem in various inventory management systems. Here we discuss a local minima solution...

["Data Science","Optimization Theory and Computation","Theory and Formal Methods"]

We present a linear time-varying Luenberger observer (LTVLO) using compartmental models to estimate the unmeasurable states in patients with type 1 diabetes. The LTVLO proposed is based on the linearization in an operation point of the virtual patient (VP), where...

["Algorithms and Analysis of Algorithms","Scientific Computing and Simulation","Theory and Formal Methods"]

The growth function is the generating function for sizes of spheres around the identity in Cayley graphs of groups. We present a novel method to calculate growth functions for automatic groups with normal form recognizing automata that recognize a single normal...

An immune system inspired Artificial Immune System (AIS) algorithm is presented, and is used for the purposes of automated program verification. Relevant immunological concepts are discussed and the field of AIS is briefly reviewed. It is proposed to use this AIS...

["Computational Biology","Adaptive and Self-Organizing Systems","Theory and Formal Methods"]

I show that any elementary cellular automata -- a class of 1-dimensional, 2-state cellular automata originally formulated by Stephen Wolfram -- can be deconstructed into a set of two Boolean operators; I also present a conjecture concerning the relationship between...

Previous definitions of a Discrete Hankel Transform (DHT) have focused on methods to approximate the continuous Hankel integral transform without regard for the properties of the DHT itself. Recently, the theory of a Discrete Hankel Transform was proposed that...

["Algorithms and Analysis of Algorithms","Scientific Computing and Simulation","Theory and Formal Methods"]

Metric spaces provide a framework for analysis and have several very useful properties. Many of these properties follow in part from the triangle inequality. However, there are several applications in which the triangle inequality does not hold but in which we...

["Scientific Computing and Simulation","Theory and Formal Methods"]

We present a geometric model of image formation in Scheimpflug cameras that is most general. Scheimpflug imaging is commonly used is scientific and medical imaging either to increase the depth of field of the imager or to focus on tilted object surfaces. Existing...

Formal argument suggests that command, communication and control systems can remain stable in the sense of the Data Rate Theorem that mandates the minimum rate of control information required to stabilize inherently unstable 'plants', but may nonetheless, under...

["Autonomous Systems","Real-Time and Embedded Systems","Robotics","Theory and Formal Methods"]

Identifying patterns and associations in data is fundamental to discovery in science. This work investigates a very simple instance of the problem, where each data point consists of a vector of binary attributes, and attributes are treated equally. For example,...

["Data Mining and Machine Learning","Theory and Formal Methods"]

Background. P and NP are two classes (sets) of languages in Computer Science. An open problem is whether P = NP. This paper tests a new idea to compare the two language sets and attempts to prove that these two language sets consist of same languages by elementary...

["Algorithms and Analysis of Algorithms","Theory and Formal Methods"]

Agent-based modeling (ABM) is a bottom-up modeling approach, where each entity of the system being modeled is uniquely represented as an independent decision-making agent. ABMs are very sensitive to implementation details. Thus, it is very easy to inadvertently...

["Agents and Multi-Agent Systems","Scientific Computing and Simulation","Theory and Formal Methods"]

Agent-based modeling (ABM) is a bottom-up modeling approach, where each entity of the system being modeled is uniquely represented as an independent decision-making agent. ABMs are very sensitive to implementation details. Thus, it is very easy to inadvertently...

["Agents and Multi-Agent Systems","Scientific Computing and Simulation","Theory and Formal Methods"]

A PeerJ Preprint is a draft of an article, abstract, or poster that has not yet been peer-reviewed for formal publication. Submit a draft, incomplete, or final version of your work for free.

Submissions today can be approved by Editorial Staff and online in 24 hours.

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I told my colleagues that PeerJ is a journal where they need to publish if they want their paper to be published quickly and with the strict peer review expected from a good journal.