Algebra, matrices, and computers (2019)
Journal Article
Detinko, A., Flannery, D., & Hulpke, A. (2019). Algebra, matrices, and computers. Snapshots of modern mathematics from Oberwolfach, 5, 1-12. https://doi.org/10.14760/SNAP-2019-005-EN

What part does algebra play in representing the real world abstractly? How can algebra be used to solve hard mathematical problems with the aid of modern computing technology? We provide answers to these questions that rely on the theory of matrix gr... Read More

The strong approximation theorem and computing with linear groups (2019)
Journal Article
Detinko, A., Flannery, D., & Hulpke, A. (2019). The strong approximation theorem and computing with linear groups. Journal of Algebra, 529, 536-549. https://doi.org/10.1016/j.jalgebra.2019.04.011

We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group for . More generally, we are able to com... Read More

Passive memristor synaptic circuits with multiple timing dependent plasticity mechanisms (2018)
Journal Article
Šuch, O., Klimo, M., Kemp, N. T., & Škvarek, O. (2018). Passive memristor synaptic circuits with multiple timing dependent plasticity mechanisms. AEÜ - International Journal of Electronics and Communications / Archiv für Elektronik und Übertragungstechnik, 96, 252-259. doi:10.1016/j.aeue.2018.09.025

Adaptation of synaptic strength is central to memory and learning in biological systems, enabling important high-level processes such as the ability of animals to respond to a changing environment. Memristor devices are a promising new, nanoscale tec... Read More

Linear groups and computation (2018)
Journal Article
Detinko, A. S., & Flannery, D. L. (in press). Linear groups and computation. Expositiones Mathematicae, https://doi.org/10.1016/j.exmath.2018.07.002

We present an exposition of our ongoing project in a new area of applicable mathematics: practical computation with finitely generated linear groups over infinite fields. Methodology and algorithms available for this class of groups are surveyed. We... Read More

Congruences on direct products of transformation and matrix monoids (2018)
Journal Article
Araújo, J., Bentz, W., & Gomes, G. M. S. (2018). Congruences on direct products of transformation and matrix monoids. Semigroup Forum, 97(3), 384–416. doi:10.1007/s00233-018-9931-8

Malcev described the congruences of the monoid Tn of all full transformations on a finite set Xn={1,…,n}. Since then, congruences have been characterized in various other monoids of (partial) transformations on Xn, such as the symmetric inverse monoi... Read More

Reversible optical switching memristors with tunable STDP synaptic plasticity: a route to hierarchical control in artificial intelligent systems (2017)
Journal Article
Jaafar, A. H., Gray, R. J., Verrelli, E., O'Neill, M., Kelly, S. M., & Kemp, N. T. (2017). Reversible optical switching memristors with tunable STDP synaptic plasticity: a route to hierarchical control in artificial intelligent systems. Nanoscale, 9(43), 17091-17098. doi:10.1039/c7nr06138b

© 2017 The Royal Society of Chemistry. Optical control of memristors opens the route to new applications in optoelectronic switching and neuromorphic computing. Motivated by the need for reversible and latched optical switching we report on the devel... Read More

On the testability of coarsening assumptions: a hypothesis test for subgroup independence (2017)
Journal Article
Plass, J., Cattaneo, M., Schollmeyer, G., & Augustin, T. (2017). On the testability of coarsening assumptions: a hypothesis test for subgroup independence. International Journal of Approximate Reasoning, 90, 292-306. doi:10.1016/j.ijar.2017.07.014

Since coarse(ned) data naturally induce set-valued estimators, analysts often assume coarsening at random (CAR) to force them to be single-valued. Focusing on a coarse categorical response variable and a precisely observed categorical covariate, we r... Read More

The likelihood interpretation as the foundation of fuzzy set theory (2017)
Journal Article
Cattaneo, M. E. G. V. (2017). The likelihood interpretation as the foundation of fuzzy set theory. International Journal of Approximate Reasoning, 90, (333-340). doi:10.1016/j.ijar.2017.08.006. ISSN 0888-613X

In order to use fuzzy sets in real-world applications, an interpretation for the values of membership functions is needed. The history of fuzzy set theory shows that the interpretation in terms of statistical likelihood is very natural, although the... Read More

Empirical interpretation of imprecise probabilities (2017)
Journal Article
Cattaneo, M. (2017). Empirical interpretation of imprecise probabilities

This paper investigates the possibility of a frequentist interpretation of imprecise probabilities, by generalizing the approach of Bernoulli’s Ars Conjectandi. That is, by studying, in the case of games of chance, under which assumptions imprecise p... Read More

Finite affine algebras are fully dualizable (2017)
Journal Article
Bentz, W., Gillibert, P., & Sequeira, L. (2018). Finite affine algebras are fully dualizable. Communications in Algebra, 46(4), (1539-1553). doi:10.1080/00927872.2017.1350693. ISSN 0092-7872

We show that every finite affine algebra A admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structure (Formula presented.) of finite type. We give an explicit bound... Read More

Orbits of primitive k-homogenous groups on (n-k)-partitions with applications to semigroups (2017)
Journal Article
Araújo, J., Bentz, W., & Cameron, P. J. (2018). Orbits of primitive k-homogenous groups on (n-k)-partitions with applications to semigroups. Transactions of the American Mathematical Society, 371, 105-136. doi:10.1090/tran/7274

The purpose of this paper is to advance our knowledge of two of the most classic and popular topics in transformation semigroups: automorphisms and the size of minimal generating sets. In order to do this, we examine the k-homogeneous permutation gro... Read More

On the abundance of extreme voids II : a survey of void mass functions (2017)
Journal Article
Chongchitnan, S., & Hunt, M. (2017). On the abundance of extreme voids II : a survey of void mass functions. Journal of cosmology and astroparticle physics, 2017(03), doi:10.1088/1475-7516/2017/03/049. ISSN 1475-7516

The abundance of cosmic voids can be described by an analogue of halo mass functions for galaxy clusters. In this work, we explore a number of void mass functions: from those based on excursion-set theory to new mass functions obtained by modifying h... Read More

Automorphism groups of circulant digraphs with applications to semigroup theory (2017)
Journal Article
Araújo, J., Bentz, W., Dobson, E., Konieczny, J., & Morris, J. (2018). Automorphism groups of circulant digraphs with applications to semigroup theory. Combinatorica, 38(1), (1-28). doi:10.1007/s00493-016-3403-0. ISSN 0209-9683

We characterize the automorphism groups of circulant digraphs whose connection sets are relatively small, and of unit circulant digraphs. For each class, we either explicitly determine the automorphism group or we show that the graph is a "normal" ci... Read More

Inflation model building with an accurate measure of e-folding (2016)
Journal Article
Chongchitnan, S. (2016). Inflation model building with an accurate measure of e-folding. Physical Review D, 94(4), doi:10.1103/PhysRevD.94.043526

It has become standard practice to take the logarithmic growth of the scale factor as a measure of the amount of inflation, despite the well-known fact that this is only an approximation for the true amount of inflation required to solve the horizon... Read More

Testing of coarsening mechanisms: Coarsening at random versus subgroup independence (2016)
Journal Article
Cattaneo, M. E. G. V., Augustin, T., Plass, J., & Schollmeyer, G. (2017). Testing of coarsening mechanisms: Coarsening at random versus subgroup independence. Advances in Intelligent Systems and Computing, 456, 415-422. doi:10.1007/978-3-319-42972-4_51

Abstract Since coarse(ned) data naturally induce set-valued estimators, analysts often assume coarsening at random (CAR) to force them to be single-valued. Using the PASS data as an example, we re-illustrate the impossibility to test CAR and contrast... Read More

Excitonic optical Tamm states: a step towards a full molecular-dielectric photonic integration (2016)
Journal Article
Adawi, A. M., Abdel-Hady, A. G., Barnes, W. L., Lopez-Garcia, M., Murshidy, M. M., Núnez-Sánchez, S., …Serry, M. (2016). Excitonic optical Tamm states: a step towards a full molecular-dielectric photonic integration. ACS Photonics, 3(5), (743-748). doi:10.1021/acsphotonics.6b00060. ISSN 2330-4022

We report the first experimental observation of an excitonic optical Tamm state supported at the interface between a periodic multilayer dielectric structure and an organic dye-doped polymer layer. The existence of such states is enabled by the metal... Read More

On maxitive integration (2016)
Journal Article
Cattaneo, M. E. G. V. (2016). On maxitive integration. Fuzzy Sets and Systems, 304, (65-81). doi:10.1016/j.fss.2016.02.008. ISSN 0165-0114

A functional is said to be maxitive if it commutes with the (pointwise) supremum operation. Such functionals find application in particular in decision theory and related fields. In the present paper, maxitive functionals are characterized as integra... Read More

Improved decision for a resource-efficient fusion scheme in cooperative spectrum sensing (2015)
Conference Proceeding
Guimarães, D. A., Aquino, G. P., & Cattaneo, M. E. G. V. (2015). Improved decision for a resource-efficient fusion scheme in cooperative spectrum sensing. doi:10.1109/IWT.2015.7224556

Paper presented at at 2015 International Workshop on Telecommunications (IWT), 14th to 17th of June, Santa Rita do Sapucai, Brazil. Abstract Recently, a novel decision fusion scheme for cooperative spectrum sensing was proposed, aiming at saving reso... Read More

On the abundance of extreme voids (2015)
Journal Article
Chongchitnan, S. (2015). On the abundance of extreme voids. Journal of cosmology and astroparticle physics, May(05), (062-062). doi:10.1088/1475-7516/2015/05/062. ISSN 1475-7516

Cosmic voids have been shown to be an effective probe of cosmology, complementary to galaxy clusters. In this work, we present a simple theoretical framework for predicting of the size of the largest voids expected within a given redshift and volume.... Read More

Algorithms for arithmetic groups with the congruence subgroup property (2014)
Journal Article
Detinko, A., Flannery, D., & Hulpke, A. (2015). Algorithms for arithmetic groups with the congruence subgroup property. Journal of Algebra, 421, 234-259. https://doi.org/10.1016/j.jalgebra.2014.08.027