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We prove that the higher rho invariant is a homomorphism from the structure group of a compact manifold to the K-group of certain geometric C*-algebra. In particular, we apply this result to show that the structure group is infinitely generated for a class of manifolds. 

Abstract CUPID, the CUORE Upgrade with Particle Identification, is a next-generation experiment to search for neutrinoless double beta decay ($$0\mathrm {\nu \beta \beta }$$ $0\nu \beta \beta$) and other rare events using enriched Li$$_{2}$$ $_2^{}$$$^{100}$$ $_{}^{100}$MoO$$_{4}$$ $_4^{}$scintillating bolometers. It will be hosted by the CUORE cryostat located at the Laboratori Nazionali del Gran Sasso in Italy. The main physics goal of CUPID is to search for$$0\mathrm {\nu \beta \beta }$$ $0\nu \beta \beta$of$$^{100}$$ $_{}^{100}$Mo with a discovery sensitivity covering the full neutrino mass regime in the inverted ordering scenario, as well as the portion of the normal ordering regime with lightest neutrino mass larger than 10 meV. With a conservative background index of 10$$^{-4}$$ $_{}^{-4}$ cts$$/($$ $/($keV$$\cdot $$ $·$kg$$\cdot $$ $·$yr$$)$$ $)$, 240 kg isotope mass, 5 keV FWHM energy resolution at 3 MeV and 10 live-years of data taking, CUPID will have a 90% C.L. half-life exclusion sensitivity of$$1.8\cdot 10^{27}$$ $1.8·{10}^{27}$ yr, corresponding to an effective Majorana neutrino mass ($$m_{\beta \beta }$$ $m_{\beta \beta }$) sensitivity of 9–15 meV, and a$$3\sigma $$ $3\sigma$discovery sensitivity of$$1\cdot 10^{27}$$ $1·{10}^{27}$ yr, corresponding to an$$m_{\beta \beta }$$ $m_{\beta \beta }$range of 12–21 meV. 

The Cryogenic Underground Observatory for Rare Events (CUORE) is a detector array comprised by 988 $5\mathrm{cm}\times 5\mathrm{cm}\times 5\mathrm{cm}$ ${\mathrm{TeO}}_2$crystals held below 20 mK, primarily searching for neutrinoless double-beta decay in ${}^{130}\mathrm{Te}$. Unprecedented in size among cryogenic calorimetric experiments, CUORE provides a promising setting for the study of exotic throughgoing particles. Using the first tonne year of CUORE’s exposure, we perform a search for hypothesized (FCPs), which are well-motivated by various standard model extensions and would have suppressed interactions with matter. Across the searched range of charges $e/24-e/2$no excess of FCP candidate tracks is observed over background, setting leading limits on the underground FCP flux with charges $e/24-e/5$at 90% confidence level. Using the low background environment and segmented geometry of CUORE, we establish the sensitivity of tonne-scale subkelvin detectors to diverse signatures of new physics. Published by the American Physical Society2024 

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.