Papers by Ricardo Monge-Gapper
ScienceOpen Preprints, 2024
A Post-Quantum Encryption Approach (PQEA) is presented. Its main advantages are 1) its high level... more A Post-Quantum Encryption Approach (PQEA) is presented. Its main advantages are 1) its high level of efficiency and effectiveness, and 2) the simplicity of its development and use. In messages encrypted with the PQEA there are no visible patterns or regularities which could give any idea of the corresponding original messages.
Preprints, 2024
A presentation is provided of a structural approach for the concurrent teaching of introductory p... more A presentation is provided of a structural approach for the concurrent teaching of introductory propositional calculus and set theory. The existence of isomorphism is shown between each law (or tautology) of propositional calculus and the form of a corresponding set which is equal to the universal set U considered.
A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences... more A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences of bases of human DNA. The results obtained are displayed using the Square Wave Transform (SWT), an SWM tool. It is hypothesized that the results of this analysis can be of interest, in certain cases, to understand the functional role of some of those sequences. Preliminary data which make this hypothesis plausible are presented.
bioRxiv, 2023
A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences... more A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences of bases of human DNA. The results obtained are displayed using the Square Wave Transform (SWT), an SWM tool. It is hypothesized that the results of this analysis can be of interest, in certain cases, to understand the functional role of some of those sequences. Preliminary data which make this hypothesis plausible are presented.
A review is presented of the correspondence existing in both classical bivalent logic (BL) and ca... more A review is presented of the correspondence existing in both classical bivalent logic (BL) and canonical fuzzy logic (CFL) between each law or tautology in propositional calculus and a law in set theory. The latter law consists of the equality of a) a set whose structure is isomorphic to the law considered in propositional calculus and b) the universal set. In addition to the operations of CFL considered previously by the authors, initial attention is given to the operations with infinite sets by considering two of them: the union of sets and the intersection of sets. Attention is also given to how propositional calculus in BL can be considered a particular case of propositional calculus in CFL, and how the theory of classical sets can be considered a particular case of the theory of fuzzy sets according to CFL.
arXiv (Cornell University), Nov 21, 2012
A novel Mathematical Random Number Generator (MRNG) is presented here. In this case, "mathematica... more A novel Mathematical Random Number Generator (MRNG) is presented here. In this case, "mathematical" refers to the fact that to construct that generator it is not necessary to resort to a physical phenomenon, such as the thermal noise of an electronic device, but rather to a mathematical procedure. The MRNG generates binary strings-in principle, as long as desired-which may be considered genuinely random in the sense that they pass the statistical tests currently accepted to evaluate the randomness of those strings. From those strings, the MRNG also generates random numbers expressed in base 10. An MRNG has been installed as a facility on the following web page: www.appliedmathgroup.org. This generator may be used for applications in tasks in: a) computational simulation of probabilistic-type systems, and b) the random selection of samples of different populations. Users interested in applications in cryptography can build another MRNG, but they would have to withhold information-specified in section 5-from people who are not authorized to decode messages encrypted using that resource.
arXiv (Cornell University), May 25, 2021
A presentation is provided of the basic notions and operations of a) the propositional calculus o... more A presentation is provided of the basic notions and operations of a) the propositional calculus of a variant of fuzzy logic-canonical fuzzy logic, CFL-and in a more succinct and introductory way, of b) the theory of fuzzy sets according to that same logic. The propositional calculus of bivalent classical logic and classical set theory can be considered as particular cases of the corresponding theories of CFL if the numerical value of a specific parameter w is restricted to only two possibilities, 0 and 1.
Revista de Matemática: Teoría y Aplicaciones, 2007
This new method for characterizing clusters is based on the simulation of a diffusionlike process... more This new method for characterizing clusters is based on the simulation of a diffusionlike process. A resolution-parameter—R—is introduced such that when assigned successive values from an increasing sequence, it is possible to detect the following:(a) a unique cluster which can be visualized as an object with no internal structure; (b) a set of n first-order subclusters—given they exist—which are constituents of the cluster mentioned in (a); (c) n sets of second-order subclusters—each of which are constituents of one of the first-order subclusters mentioned in (b)—and so on, successively. Convexity is not required either for the cluster mentioned in (a) or for the subclusters of different orders. Although in this paper the method presented is applied to bidimensional objects, it may be generalized for the n-dimensional case.
Revista de Matemática: Teoría y Aplicaciones, 2008
The “Square-Wave Method” (SWM) presented here is a new method for the systematic analysis of sign... more The “Square-Wave Method” (SWM) presented here is a new method for the systematic analysis of signals – either locally or globally – depending on only one variable (time). The SWM is based on a technique (previously described elsewhere) for the representation of this type of signals using a sum of trains of square waves. The SWM is applied here to several analytically characterized signals and to an audio signal.
A description is provided of a method – the Set Equality Method (SEM) – to determine the validity... more A description is provided of a method – the Set Equality Method (SEM) – to determine the validity, or lack of validity, of each categorical syllogism. A justification is given for the presentation of a new method to solve a problem which has already been solved using different approaches. First, the SEM assigns an equality of certain sets (or two of those equalities in specific cases as will be indicated) to each of the categorical propositions composing each syllogism considered – that is, to each of the two premises and to the conclusion. Each syllogism considered is valid if and only if a) it is possible to select one of those equalities corresponding to one of the premises such that one of its members is a certain set and the other of those equalities corresponding to the other premise such that one of its members is a subset of the set mentioned, and b) it is possible to deduce an equality corresponding to the conclusion of the two equalities corresponding to the premises. In s...
ArXiv, 2018
A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although i... more A new cryptographic approach -- Iterated Random Encryption (IRE) -- is presented here. Although it is very simple, and easy to implement, it provides a very high level of security. According to this approach, a sequence of operations applied to a message ($M$) yields the encrypted message ($M_E$). In that series of operations, the one with the most important role is operation 6, which involves a random binary sequence (RBS) generated by using the Hybrid Random Number Generator (HRNG) or the Mathematical Random Number Generator (MRNG). A sequence of anti-operations applied to $M_E$ makes it possible to recover $M$.
ArXiv, 2020
A characterization is provided for each natural number except one (1) by means of an ordered pair... more A characterization is provided for each natural number except one (1) by means of an ordered pair of elements. The first element is a natural number called the type of the natural number characterized, and the second is a natural number called the order of the number characterized within those of its type. A one-to-one correspondence is specified between the set of binary trees such that a) a given node has no child nodes (that is, it is a terminal node), or b) it has exactly two child nodes. Thus, binary trees such that one of their parent nodes has only one child node are excluded from the set considered here.
A presentation is provided of a method — the Membership Table Method (MTM) — to determine the val... more A presentation is provided of a method — the Membership Table Method (MTM) — to determine the validity of categorical syllogisms. This method makes it possible for each syllogism to be assigned a specific set. If this set is equal to the universal set U, then the categorical syllogism considered is valid, and if that set is not equal to U, then that categorical syllogism is not valid. In other words, any categorical syllogism is valid if and only if its respective set, according to the MTM, is equal to the universal set U. The conclusion of a valid categorical syllogism whose premises are true is true.
Revista de Matemática: Teoría y Aplicaciones, 2017
The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously... more The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT is used to analyze a sequence of samples (that is, of measured values) taken from an electroencephalographic recording. A computational tool, available at www.appliedmathgroup.org/, has been developed and may be used to obtain automatically the SWTs of sequences of samples taken from registers of interest for biomedical purposes, such as those of an EEG or an ECG.
Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the valid... more Inclusion diagrams are introduced as an alternative to using Venn diagrams to determine the validity of categorical syllogisms, and are used here for the analysis of diverse categorical syllogisms. As a preliminary example of a possible generalization of the use of inclusion diagrams, consideration is given also to an argument that includes more than two premises and more than three terms, the classic major, middle and minor terms in categorical syllogisms.
A brief review is provided of the use of the Square Wave Method (SWM) in the field of signal and ... more A brief review is provided of the use of the Square Wave Method (SWM) in the field of signal and image analysis and it is specified how results thus obtained are expressed using the Square Wave Transform (SWT), in the frequency domain. To illustrate the new approach introduced in this field, the results of two cases are analyzed: a) a sequence of samples (that is, measured values) of an electromyographic recording; and b) the classic image of Lenna.
Revista de Matemática: Teoría y Aplicaciones, 2009
The notions “regularity index” and “randomness index” previously introduced for binary strings (2... more The notions “regularity index” and “randomness index” previously introduced for binary strings (2-ary) have been modified slightly and generalized for m-ary strings (m = 2, 3, 4, . . .). These notions are complementary and the regular/random dichotomy has been replaced by a gradation of values of regularity and of randomness. With this approach, the more regular an m-ary string, the less random it is, and vice versa. The distributions of frequencies of different length strings —2-ary and 3-ary strings— according to their indices of randomness, are shown by histograms.
ScienceOpen Preprints, 2023
A review is presented of the correspondence existing in both classical bivalent logic (BL) and ca... more A review is presented of the correspondence existing in both classical bivalent logic (BL) and canonical fuzzy logic (CFL) between each law or tautology in propositional calculus and a law in set theory. The latter law consists of the equality of a) a set whose structure is isomorphic to the law considered in propositional calculus and b) the universal set. In addition to the operations of CFL considered previously by the authors, initial attention is given to the operations with infinite sets by considering two of them: the union of sets and the intersection of sets. Attention is also given to how propositional calculus in BL can be considered a particular case of propositional calculus in CFL, and how the theory of classical sets can be considered a particular case of the theory of fuzzy sets according to CFL.
Zenodo, 2022
A description is provided of a method -- the Set Equality Method (SEM) -- to determine the validi... more A description is provided of a method -- the Set Equality Method (SEM) -- to determine the validity, or lack of validity, of each categorical syllogism. A justification is given for the presentation of a new method to solve a problem which has already been solved using different approaches. First, the SEM assigns an equality of certain sets (or two of those equalities in specific cases as will be indicated) to each of the categorical propositions composing each syllogism considered -- that is, to each of the two premises and to the conclusion. Each syllogism considered is valid if and only if a) it is possible to select one of those equalities corresponding to one of the premises such that one of its members is a certain set and the other of those equalities corresponding to the other premise such that one of its members is a subset of the set mentioned, and b) it is possible to deduce an equality corresponding to the conclusion of the two equalities corresponding to the premises. In some cases, as will be specified, it is possible to provide a second test for the validity of a syllogism whose validity was already proven, thus providing information about the logical form of categorical syllogisms.
Select entropy-based indicators (such as Kolmogorov Complexity, Shannon Information Entropy and t... more Select entropy-based indicators (such as Kolmogorov Complexity, Shannon Information Entropy and the Index of Regularity) have been used in this preliminary study to classify genes with acceptable results. This need for classification is driven by the interest of the scientific community in determining whether a given gene possesses or lacks cancer-related characteristics. A subset of genes was chosen, based on previous studies and on random selection. These genes have been represented by their DNA sub-sequence and have been divided into two groups: those that have a relation to cancer (that is, they either cause cancer, as in oncogenes, or are tumor suppressors) and those that are not related to cancer issues (i.e., normal genes). Initially, eleven classifiers were used and compared, some of which reflected an accuracy rate of over 70%. This accuracy rate represents the percentage of correct predictions (cancer-related or not) within a test set of genes. These results shed some ligh...
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Papers by Ricardo Monge-Gapper