22 papers · ranked by Valyu relevance
Hussain Rashed
| 1. | Introduction | 1 | | --- | --- | --- | | 2. | Boolean algebras and their homomorphisms | 2 | | 3. | Stone's space of a Boolean algebra | 5 | | 3.1. | Characterization of locally compact totally disconnected spaces | 5 | | 3.2. | Stone's space of a Boolean algebra as the family of its ultrafilters | 7 | | 3.3. |…
Branislav Boričić, Mirjana Ilić, Jelena Stanojević
In this paper we consider systems which consist of binary components with known reliabilities. We discuss their algebraic properties and define the corresponding algebraic structure, which we call the reliability algebra. We prove that the reliability algebra is a Boolean algebra. The reliability algebra seems an…
M. Ali Al-Radhawi, Anh Phong Tran, Elizabeth A. Ernst, Tianchi Chen + 2 more
Starting in the early 2000s, a sophisticated technology has been developed for the rational construction of synthetic genetic networks that implement specified logical functionalities. Despite impressive progress, however, the scaling necessary in order to achieve greater computational power has been hampered by many…
Tommaso Flaminio, Lluı́s Godo, Hykel Hosni
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) Boolean algebra of conditionals from any (finite) Boolean algebra of events. By doing so we distinguish…
Ali Muhammad Ali Rushdi
A task frequently encountered in digital circuit design is the solution of a two-valued Boolean equation of the form ℎ(, , ) = 1, where ℎ: 2 ++ → 2 and , , and are binary vectors of lengths , , and , representing inputs, intermediary values, and outputs, respectively. The resultant of the suppression of the variables…
Gael Tenkeu Kembang, Léonard Kwuida, Etienne R. A. Temgoua, Y. L. J. Tenkeu
'Y. L. J. Tenkeu'] Abstract. Double Boolean algebras are algebras D = (D; ⊓, ⊔, ¬, y, ⊥, ⊤) of type (2, 2, 1, 1, 0, 0) introduced by Rudolf Wille to capture the equational theory of the algebra of protoconcepts. Every double Boolean algebra D contains two Boolean algebras denoted by D⊓ and D⊔. A double Boolean algebra…
Dietmar Dorninger, Helmut Länger
With many physical processes in which quantum mechanical phenomena can occur, it is essential to take into account a decision mechanism based on measurement data. This can be achieved by means of so-called numerical events, which are specified as follows: Let S be a set of states of a physical system and p(s) the…
Chuyu Xiong
In this article, we continue our study on universal learning machine by introducing new tools. We first discuss boolean function and boolean circuit, and we establish one set of tools, namely, fitting extremum and proper sampling set. We proved the fundamental relationship between proper sampling set and complexity of…
Yukio-Pegio Gunji, Kyoko Nakamura, Kazuto Sasai, Iori Tani + 5 more
Artificial intelligence is typically formulated as an information-processing system composed of artificial neurons, where computation is understood as recursive operations connecting inputs and outputs. However, real neural systems are materially embodied and continuously reconfigured by metabolic and physical…
Zeno Toffano, François Dubois
Considering links between logic and physics is important because of the fast development of quantum information technologies in our everyday life. This paper discusses a new method in logic inspired from quantum theory using operators, named Eigenlogic. It expresses logical propositions using linear algebra. Logical…
Federico Holik, Giuseppe Sergioli, Hector Freytes, Angel Plastino
In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.
Juan Pablo Jorge, Federico Holik
In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations…
Aravind Karanam, David He, Po-Kai Hsu, Sebastian Schulze + 4 more
Signaling networks are at the heart of almost all biological processes. Most of these networks contain a large number of components and often the connections between these components are either not known, or the rate equations that govern the dynamics of soluble signaling components are not quantified. This uncertainty…
David Murrugarra, Alan Veliz-Cuba, Boris Aguilar, Reinhard Laubenbacher
'Reinhard Laubenbacher'] Background Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such…
Thomas Prévost, Bruno Martin
We propose a method for constructing 9-variable cryptographic Boolean functions from the iterates of 5-variable cellular automata rules. We then analyze, for important cryptographic properties of 5-variable cellular automata rules, how they are preserved after extension to 9-variable Boolean functions. For each…
Ivan Chajda, Helmut Länger
The concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to every such relational system, there can be assigned a Sheffer groupoid and also, conversely, every Sheffer groupoid induces a directed…
Ajay Subbaroyan, Olivier C. Martin, Areejit Samal
The properties of random Boolean networks as models of gene regulation have been investigated extensively by the statistical physics community. In the past two decades, there has been a dramatic increase in the reconstruction and analysis of Boolean models of biological networks. In such models, neither network…
Sara D. Cardell, A. Fuúter-Sabater, Verónica Requena, M. Beltrá
Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a connection between them which allows us to study some properties of Boolean functions…
Gina Partipilo, Sarah M. Coleman, Yang Gao, Ismar E. Miniel Mahfoud + 3 more
A significant advancement in synthetic biology is the development of synthetic gene circuits with predictive Boolean logic. However, there is no universally accepted or applied statistical test to analyze the performance of these circuits. Many basic statistical tests fail to capture the predicted logic (OR, AND, etc.)…
Arturo Tozzi
A wide range of biological and evolutionary processes is determined not merely by the occurrence of specific events, but by the exact order in which those events unfold. Gene regulation, developmental pathways, metabolic cascades and genetic evolution often display non-commutative behaviour, in which reversing the…
Thomas C. Draper, Claire Fullarton, Neil Phillips, Ben P. J. De Lacy Costello + 1 more
Liquid marbles are microlitre droplets of liquid, encapsulated by self-organised hydrophobic particles at the liquid/air interface. They offer an efficient approach for manipulating liquid droplets and compartmentalising reactions in droplets. Digital fluidic devices employing liquid marbles might benefit from having…
Richard Apodaca
Despite its widespread use, Simplified Molecular Input Line Entry System (SMILES) remains underspecified. The lack of a detailed specification encourages improvisation by software developers, complicates data standardization efforts, and undermines extension development. Balsa, a reformulation of SMILES, addresses…