| 1. |
- Källström, Rolf, et al.
(författare)
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Hilbert series of modules over Lie algebroids
- 2015
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Ingår i: Journal of Algebra. - : Elsevier. - 0021-8693 .- 1090-266X. ; 432, s. 129-184
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Tidskriftsartikel (refereegranskat)abstract
- We consider modules M over Lie algebroids gA which are of finite type over a local noetherian ring A. Using ideals J ⊂ A such that gA ·J ⊂ J and the length ℓgA (M/JM) < ∞ we can define in a natural way the Hilbert series of M with respect to the defining ideal J. This notion is in particular studied for modules over the Lie algebroid of k-linear derivations gA = TA(I) that preserve an ideal I ⊂ A, for example when A = On, the ring of convergent power series. Hilbert series over Stanley-Reisner rings are also considered.
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| 2. |
- Izquierdo, Milagros, 1963-, et al.
(författare)
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Isometric Point-Circle Configurations on Surfaces from Uniform Maps
- 2016
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer-Verlag New York. - 2194-1009. ; 159, s. 201-212, s. 201-212
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Tidskriftsartikel (refereegranskat)abstract
- We embed neighborhood geometries of graphs on surfaces as point-circle configurations. We give examples coming from regular maps on surfaces with a maximum number of automorphisms for their genus, and survey geometric realization of pentagonal geometries coming from Moore graphs. An infinite family of point-circle v4'>v4v4 configurations on p-gonal surfaces with two p-gonal morphisms is given. The image of these configurations on the sphere under the two p-gonal morphisms is also described.
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| 3. |
- Tsougkas, Konstantinos
(författare)
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A connection between discrete and regularized Laplacian determinants on fractals
- 2024
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Ingår i: Journal of Physics A. - : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 57:28
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Tidskriftsartikel (refereegranskat)abstract
- The spectral zeta function of the Laplacian on self-similar fractal sets has been previously studied and shown to meromorphically extend to the complex plane. In this work we establish that under certain conditions a relationship exists between the logarithm of the determinant of the discrete graph Laplacian on the sequence of graphs approximating the fractal and the regularized Laplacian determinant on the fractal itself which is defined via help of the spectral zeta function. We then at the end present some concrete examples of this phenomenon.
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| 4. |
- Khamnei, Hossein Jabbari, et al.
(författare)
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Modeling income distribution : An econophysics approach
- 2023
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Ingår i: Mathematical Biosciences and Engineering. - : AIMS Press. - 1547-1063 .- 1551-0018. ; 20:7, s. 13171-13181
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Tidskriftsartikel (refereegranskat)abstract
- This study aims to develop appropriate models for income distribution in Iran using the econophysics approach for the 2006–2018 period. For this purpose, the three improved distributions of the Pareto, Lognormal, and Gibbs-Boltzmann distributions are analyzed with the data extracted from the target household income expansion plan of the statistical centers in Iran. The research results indicate that the income distribution in Iran does not follow the Pareto and Lognormal distributions in most of the study years but follows the generalized Gibbs-Boltzmann distribution function in all study years. According to the results, the generalized Gibbs-Boltzmann distribution also properly fits the actual data distribution and could clearly explain the income distribution in Iran. The generalized Gibbs-Boltzmann distribution also fits the actual income data better than both Pareto and Lognormal distributions
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| 5. |
- Khamnei, Hossein Jabbari, et al.
(författare)
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Parameter Estimation of the Exponentiated Pareto Distribution Using Ranked Set Sampling and Simple Random Sampling
- 2022
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Ingår i: Axioms. - : MDPI. - 2075-1680. ; 11:6, s. 1-9
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size.
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| 6. |
- Tadesse, Yohannes, 1978-
(författare)
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Derivations Preserving a Monomial Ideal
- 2009
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Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society. - 0002-9939 .- 1088-6826. ; 137:9, s. 2935-2942
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Tidskriftsartikel (refereegranskat)abstract
- Let I be a monomial ideal in a polynomial ring A = k[x1, . . . ,xn] over a field k of characteristic 0, TA/k(I) be the module of I-preserving k-derivations on A and G be the n-dimensional algebraic torus on k. We computethe weight spaces of TA/k(I) considered as a representation of G. Using this, we show that TA/k(I) preserves the integral closure of I and the multiplierideals of I.
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| 7. |
- Athanasopoulos, George, et al.
(författare)
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Forecast reconciliation : A review
- 2024
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Ingår i: International Journal of Forecasting. - : Elsevier. - 0169-2070 .- 1872-8200. ; 40:2, s. 430-456
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Forskningsöversikt (refereegranskat)abstract
- Collections of time series formed via aggregation are prevalent in many fields. These are commonly referred to as hierarchical time series and may be constructed cross-sectionally across different variables, temporally by aggregating a single series at different frequencies, or even generalised beyond aggregation as time series that respect linear constraints. When forecasting such time series, a desirable condition is for forecasts to be coherent: to respect the constraints. The past decades have seen substantial growth in this field with the development of reconciliation methods that ensure coherent forecasts and improve forecast accuracy. This paper serves as a comprehensive review of forecast reconciliation and an entry point for researchers and practitioners dealing with hierarchical time series. The scope of the article includes perspectives on forecast reconciliation from machine learning, Bayesian statistics and probabilistic forecasting, as well as applications in economics, energy, tourism, retail demand and demography.
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| 8. |
- Tadesse, Yohannes, 1978-
(författare)
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Tangential Derivations, Hilbert Series and Modules over Lie Algebroids
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Let A/k be a local commutative algebra over a field k of characteristic 0, and T_{A/k} be the module of k-linear derivations on A. We study, in two papers, the set of k-linear derivations on A which are tangential to an ideal I of A (preserves I), defining an A-submodule T_{A/k}(I) of T_{A/k}, which moreover is a k-Lie subalgebra. More generally we consider Lie algebroids g_A over A and modules over g_A. Paper I: Using the action of an algebraic torus on a monomial ideal in a polynomial ring A=k[x_1,..., x_n] we: give a new proof of a description of the set of tangential derivations T_{A/k}(I) along a monomial ideal I, first proven by Brumatti and Simis. give a new and direct proof to the fact that the integral closure of a monomial ideal is monomial. We also prove that a derivation which is tangential to a monomial ideal will remain tangential to its integral closure. prove that a derivation which is tangential to a monomial ideal is also tangential to any of its associated multiplier ideals. Paper II: We consider modules M over a Lie algebroid g_A which are of finite type over A. In particular, we study the Hilbert series of the associated graded module of such a module with respect to an ideal of definition. Our main results are: Hilbert's finiteness theorem in invariant theory is shown to hold also for a noetherian graded g_A-algebra S and a noetherian (S, g_A)-graded module which are semisimple over g_A. We define a class of local system g_A-modules and prove that the Hilbert series of such a graded module is rational. We also define an ideal of definition for a g_A-module M and prove rationality of the Hilbert series of M with respect to such an ideal. We introduce the notion of toral Lie algebroids over a regular noetherian local algebra R and give some properties of modules over such Lie algebroids. In particular, we compute the Hilbert series of submodules of R over a Lie algebroid containig a toral Lie algebroid.
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| 9. |
- Bennet, Christian, 1954, et al.
(författare)
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The Viability of Social Constructivism as a Philosophy of Mathematics
- 2013
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Ingår i: Croatian Journal of Philosophy. - 1333-1108 .- 1847-6139. ; XIII:39, s. 341-355
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Tidskriftsartikel (refereegranskat)abstract
- Attempts have been made to analyse features in mathematics within a social constructivist context. In this paper we critically examine some of those attempts recently made with focus on problems of the objectivity, ontology, necessity, and atemporality of mathematics. Our conclusion is that these attempts fare no better than traditional alternatives, and that they, furthermore, create new problems of their own.
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| 10. |
- Boström, Henrik
(författare)
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Maximizing the Area under the ROC Curve with Decision Lists and Rule Sets
- 2007
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Ingår i: Proceedings of the 7th SIAM International Conference on Data Mining. - : Society for Industrial and Applied Mathematics. - 9780898716306 ; , s. 27-34
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Konferensbidrag (refereegranskat)abstract
- Decision lists (or ordered rule sets) have two attractive properties compared to unordered rule sets: they require a simpler classi¯cation procedure and they allow for a more compact representation. However, it is an open question what effect these properties have on the area under the ROC curve (AUC). Two ways of forming decision lists are considered in this study: by generating a sequence of rules, with a default rule for one of the classes, and by imposing an order upon rules that have been generated for all classes. An empirical investigation shows that the latter method gives a significantly higher AUC than the former, demonstrating that the compactness obtained by using one of the classes as a default is indeed associated with a cost. Furthermore, by using all applicable rules rather than the first in an ordered set, an even further significant improvement in AUC is obtained, demonstrating that the simple classification procedure is also associated with a cost. The observed gains in AUC for unordered rule sets compared to decision lists can be explained by that learning rules for all classes as well as combining multiple rules allow for examples to be ranked according to a more fine-grained scale compared to when applying rules in a fixed order and providing a default rule for one of the classes.
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