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Free, publicly-accessible full text available June 1, 2024
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In this paper, we prove bounds for the unique, positive zero of O G (z) := 1 −O G (z) , where O G ( z ) is the so-called orbit polynomial [1]. The orbit polynomial is based on the multiplic- ity and cardinalities of the vertex orbits of a graph. In [1] , we have shown that the unique, positive zero δ≤1 of O G (z) can serve as a meaningful measure of graph symmetry. In this paper, we study special graph classes with a specified number of orbits and obtain bounds on the value of δ.more » « less
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Free, publicly-accessible full text available June 1, 2024
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Abstract The Cryogenic Underground Observatory for Rare Events (CUORE) is the first cryogenic experiment searching for
decay that has been able to reach the one-tonne mass scale. The detector, located at the Laboratori Nazionali del Gran Sasso (LNGS) in Italy, consists of an array of 988$$0\nu \beta \beta $$ crystals arranged in a compact cylindrical structure of 19 towers. CUORE began its first physics data run in 2017 at a base temperature of about 10 mK and in April 2021 released its$${\mathrm{TeO}}_{2}$$ result of the search for$$3{\mathrm{rd}}$$ , corresponding to a tonne-year of$$0\nu \beta \beta $$ exposure. This is the largest amount of data ever acquired with a solid state detector and the most sensitive measurement of$$\mathrm{TeO}_{2}$$ decay in$$0\nu \beta \beta $$ ever conducted . We present the current status of CUORE search for$${}^{130}\mathrm{Te}$$ with the updated statistics of one tonne-yr. We finally give an update of the CUORE background model and the measurement of the$$0\nu \beta \beta $$ $${}^{130}\mathrm{Te}$$ decay half-life and decay to excited states of$$2\nu \beta \beta $$ , studies performed using an exposure of 300.7 kg yr.$${}^{130}\mathrm{Xe}$$