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《Journal of Pure and Applied Algebra》2022,226(8):107024
We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation. 相似文献
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《Indagationes Mathematicae》2022,33(1):218-237
We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set data for Weyl groups. Then we use this to determine explicitly the modular Springer correspondence for classical types (defined over a base field of odd characteristic , and with coefficients in a field of odd characteristic ): the modular case is obtained as a restriction of the ordinary case to a basic set. In order to do so, we compare the order on bipartitions introduced by Dipper and James with the order induced by the Springer correspondence. We provide a quick proof, by sorting characters according to the dimension of the corresponding Springer fibre, an invariant which is directly computable from symbols. 相似文献
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Machine learning is currently the most active interdisciplinary field having numerous applications;additionally,machine-learning techniques are used to research quantum many-body problems.In this study,we first propose neural network quantum states(NNQSs)with general input observables and explore a few related properties,such as the tensor product and local unitary operation.Second,we determine the necessary and sufficient conditions for the representability of a general graph state using normalized NNQS.Finally,to quantify the approximation degree of a given pure state,we define the best approximation degree using normalized NNQSs.Furthermore,we observe that some 7V-qubit states can be represented by a normalized NNQS,such as separable pure states,Bell states and GHZ states. 相似文献
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In this paper we survey some results on existence, and when possible also uniqueness, of solutions to certain evolution equations obtained by injecting randomness either on the set of initial data or as a perturbative term. 相似文献
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Clara Argerich Martín Ruben Ibáñez Pinillo Anais Barasinski Francisco Chinesta 《Comptes Rendus Mecanique》2019,347(11):754-761
The aim of this paper is to present a new classification and regression algorithm based on Artificial Intelligence. The main feature of this algorithm, which will be called Code2Vect, is the nature of the data to treat: qualitative or quantitative and continuous or discrete. Contrary to other artificial intelligence techniques based on the “Big-Data,” this new approach will enable working with a reduced amount of data, within the so-called “Smart Data” paradigm. Moreover, the main purpose of this algorithm is to enable the representation of high-dimensional data and more specifically grouping and visualizing this data according to a given target. For that purpose, the data will be projected into a vectorial space equipped with an appropriate metric, able to group data according to their affinity (with respect to a given output of interest). Furthermore, another application of this algorithm lies on its prediction capability. As it occurs with most common data-mining techniques such as regression trees, by giving an input the output will be inferred, in this case considering the nature of the data formerly described. In order to illustrate its potentialities, two different applications will be addressed, one concerning the representation of high-dimensional and categorical data and another featuring the prediction capabilities of the algorithm. 相似文献
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