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Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces (2018)
Journal Article
Olegovich Manturov, V., & Rushworth, W. (2018). Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces. Journal of Knot Theory and Its Ramifications, 27(9), https://doi.org/10.1142/S0218216518420014

We define additional gradings on two generalisations of Khovanov homology (one due to the first author, the other due to the second), and use them to define invariants of various kinds of embeddings. These include invariants of links in thickened sur... Read More about Additional gradings on generalisations of Khovanov homology and invariants of embedded surfaces.

Primordial Gravitational Waves and Reheating in a New Class of Plateau-Like Inflationary Potentials (2018)
Journal Article
Chongchitnan, S. (2018). Primordial Gravitational Waves and Reheating in a New Class of Plateau-Like Inflationary Potentials. Universe, 4(7), Article 77. https://doi.org/10.3390/universe4070077

We study a new class of inflation model parametrized by the Hubble radius, such that aH∝exp(−αφ)n. These potentials are plateau-like, and reduce to the power-law potentials in the simplest case n=2. We investigate the range of model parameters that i... Read More about Primordial Gravitational Waves and Reheating in a New Class of Plateau-Like Inflationary Potentials.

The boundary integral formulation of Stokes flows includes slender-body theory (2018)
Journal Article
Koens, L., & Lauga, E. (2018). The boundary integral formulation of Stokes flows includes slender-body theory. Journal of Fluid Mechanics, 850, Article R1. https://doi.org/10.1017/jfm.2018.483

The incompressible Stokes equations can classically be recast in a boundary integral (BI) representation, which provides a general method to solve low-Reynolds-number problems analytically and computationally. Alternatively, one can solve the Stokes... Read More about The boundary integral formulation of Stokes flows includes slender-body theory.

Algorithms for experimenting with Zariski dense subgroups (2018)
Journal Article
Detinko, A. S., Flannery, D. L., & Hulpke, A. (2020). Algorithms for experimenting with Zariski dense subgroups. Experimental Mathematics, 29(3), 296-305. https://doi.org/10.1080/10586458.2018.1466217

We give a method to describe all congruence images of a finitely generated Zariski dense group . The method is applied to obtain efficient algorithms for solving this problem in odd prime degree n; if n = 2 then we compute all congruence images only... Read More about Algorithms for experimenting with Zariski dense subgroups.

Half-plane partial slip contact problems with a constant normal load subject to a shear force and differential bulk tension (2018)
Journal Article
Moore, M., Ramesh, R., Hills, D., & Barber, J. (2018). Half-plane partial slip contact problems with a constant normal load subject to a shear force and differential bulk tension. Journal of the Mechanics and Physics of Solids, 118, 245-253. https://doi.org/10.1016/j.jmps.2018.05.017

This article provides a new form of solution to half-plane contact problems in partial slip where a normal load has been applied, held constant and is subsequently loaded with both a shear force and differential bulk tension. It uses a formulation wh... Read More about Half-plane partial slip contact problems with a constant normal load subject to a shear force and differential bulk tension.

On the deflection of a liquid jet by an air-cushioning layer (2018)
Journal Article
Moore, M. R., Whiteley, J. P., & Oliver, J. M. (2018). On the deflection of a liquid jet by an air-cushioning layer. Journal of Fluid Mechanics, 846, 711-751. https://doi.org/10.1017/jfm.2018.310

A hierarchy of models is formulated for the deflection of a thin two-dimensional liquid jet as it passes over a thin air-cushioning layer above a rigid flat impermeable substrate. We perform a systematic derivation of the leading-order equations of m... Read More about On the deflection of a liquid jet by an air-cushioning layer.

Solution of half-plane contact problems by distributing climb dislocations (2018)
Journal Article
Moore, M., & Hills, D. (2018). Solution of half-plane contact problems by distributing climb dislocations. International Journal of Solids and Structures, 147, 61-66. https://doi.org/10.1016/j.ijsolstr.2018.04.017

We derive a novel method for addressing half-plane contact problems by using distributions of climb dislocations over the contact patch to balance the relative overlapping profile of the contacting bodies. Using this technique, we are able to forgo i... Read More about Solution of half-plane contact problems by distributing climb dislocations.

Large deviations for the annealed Ising model on inhomogeneous random graphs: spins and degrees (2018)
Journal Article
Dommers, S., Giardinà, C., Giberti, C., & Hofstad, R. V. D. (2018). Large deviations for the annealed Ising model on inhomogeneous random graphs: spins and degrees. Journal of statistical physics, 173(3-4), 1045-1081. https://doi.org/10.1007/s10955-018-2027-8

We prove a large deviations principle for the total spin and the number of edges under the annealed Ising measure on generalized random graphs. We also give detailed results on how the annealing over the Ising model changes the degrees of the vertice... Read More about Large deviations for the annealed Ising model on inhomogeneous random graphs: spins and degrees.

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. https://doi.org/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 about Congruences on direct products of transformation and matrix monoids.

Speculative bubbles or explosive fundamentals in stock prices? New evidence from SADF and GSADF tests (2018)
Journal Article
El Montasser, G., Naoui, K., & Fry, J. (2018). Speculative bubbles or explosive fundamentals in stock prices? New evidence from SADF and GSADF tests. Journal of Statistics and Management Systems, 21(1), 93-106. https://doi.org/10.1080/09720510.2017.1401799

This paper uses recently developed sequential ADF tests to distinguish between rational speculative bubbles and explosive fundamentals in the US Stock market. The sequential ADF tests are shown to be more sensitive than the conventional ADF test. Res... Read More about Speculative bubbles or explosive fundamentals in stock prices? New evidence from SADF and GSADF tests.

Microscale flow dynamics of ribbons and sheets (2017)
Journal Article
Montenegro-Johnson, T. D., Koens, L., & Lauga, E. (2017). Microscale flow dynamics of ribbons and sheets. Soft matter, 13(3), 546-553. https://doi.org/10.1039/c6sm02105k

Numerical study of the hydrodynamics of thin sheets and ribbons presents difficulties associated with resolving multiple length scales. To circumvent these difficulties, asymptotic methods have been developed to describe the dynamics of slender fibre... Read More about Microscale flow dynamics of ribbons and sheets.

High-dimensional limit theorems for random vectors in ℓpn-balls (2017)
Journal Article
Kabluchko, Z., Prochno, J., & Thäle, C. (2019). High-dimensional limit theorems for random vectors in ℓpn-balls. Communications in contemporary mathematics, 21(1), 1750092. https://doi.org/10.1142/S0219199717500924

In this paper, we prove a multivariate central limit theorem for ℓq-norms of high-dimensional random vectors that are chosen uniformly at random in an ℓnp-ball. As a consequence, we provide several applications on the intersections of ℓnp-balls in th... Read More about High-dimensional limit theorems for random vectors in ℓpn-balls.

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. https://doi.org/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 about On the testability of coarsening assumptions: a hypothesis test for subgroup independence.

Metastability in the reversible inclusion process (2017)
Journal Article
Bianchi, A., Dommers, S., & Giardinà, C. (2017). Metastability in the reversible inclusion process. Electronic journal of probability, 22, Article 70. https://doi.org/10.1214/17-EJP98

We study the condensation regime of the finite reversible inclusion process, i.e., the inclusion process on a finite graph S with an underlying random walk that admits a reversible measure. We assume that the random walk kernel is irreducible and its... Read More about Metastability in the reversible inclusion process.

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. https://doi.org/10.1016/j.ijar.2017.08.006

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 about The likelihood interpretation as the foundation of fuzzy set theory.

Zariski density and computing in arithmetic groups (2017)
Journal Article
Detinko, A., Flannery, D. L., & Hulpke, A. (2018). Zariski density and computing in arithmetic groups. Mathematics of Computation, 87(310), 967-986. https://doi.org/10.1090/mcom/3236

For n > 2, let Gamma _n denote either SL(n, {Z}) or Sp(n, {Z}). We give a practical algorithm to compute the level of the maximal principal congruence subgroup in an arithmetic group H\leq \Gamma _n. This forms the main component of our methods for c... Read More about Zariski density and computing in arithmetic groups.

Analytical solutions to slender-ribbon theory (2017)
Journal Article
Koens, L., & Lauga, E. (2017). Analytical solutions to slender-ribbon theory. Physical Review Fluids, 2(8), Article 084101. https://doi.org/10.1103/PhysRevFluids.2.084101

The low-Reynolds-number hydrodynamics of slender ribbons is accurately captured by slender-ribbon theory, an asymptotic solution to the Stokes equation which assumes that the three length scales characterizing the ribbons are well separated. We show... Read More about Analytical solutions to slender-ribbon theory.

Empirical interpretation of imprecise probabilities (2017)
Journal Article
Cattaneo, M. (2017). Empirical interpretation of imprecise probabilities. Proceedings of Machine Learning Research, 62, 61-72

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 about Empirical interpretation of imprecise probabilities.