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Explaining the results of Machine learning algorithms is crucial given the rapid growth and potential applicability of these methods in critical domains including healthcare, defense, autonomous driving, etc. In this paper, we address this problem in the context of Markov Logic Networks (MLNs) which are highly expressive statistical relational models that combine first-order logic with probabilistic graphical models. MLNs in general are known to be interpretable models, i.e., MLNs can be understood more easily by humans as compared to models learned by approaches such as deep learning. However, at the same time, it is not straightforward to obtain human-understandable explanations specific to an observed inference result (e.g. marginal probability estimate). This is because, the MLN provides a lifted interpretation, one that generalizes to all possible worlds/instantiations, which are not query/evidence specific. In this paper, we extract grounded-explanations, i.e., explanations defined w.r.t specific inference queries and observed evidence. We extract these explanations from importance weights defined over the MLN formulas that encode the contribution of formulas towards the final inference results. We validate our approach in real world problems related to analyzing reviews from Yelp, and show through user-studies that our explanations are richer than state-of-the-art non-relational explainers such as LIME . 

We present a measurement of the branching fraction and fraction of longitudinal polarization of $B^0\to {\rho }^{+}{\rho }^{-}$decays, which have two ${\pi }^0$’s in the final state. We also measure time-dependent $CP$violation parameters for decays into longitudinally polarized ${\rho }^{+}{\rho }^{-}$pairs. This analysis is based on a data sample containing $(387\pm 6)\times {10}^6$ $\mathrm{\Upsilon }\left(4S\right)$mesons collected with the Belle II detector at the SuperKEKB asymmetric-energy $e^{+}{e}^{-}$collider in 2019–2022. We obtain $\mathcal{B}(B^0\to {\rho }^{+}{\rho }^{-})=\left(2.89_{-0.22}^{+0.23}{}_{-0.27}^{+0.29}\right)\times {10}^{-5}$, $f_L=0.921_{-0.025}^{+0.024}{}_{-0.015}^{+0.017}$, $S=-0.26\pm 0.19\pm 0.08$, and $C=-0.02\pm 0.12_{-0.05}^{+0.06}$, where the first uncertainties are statistical and the second are systematic. We use these results to perform an isospin analysis to constrain the Cabibbo-Kobayashi-Maskawa angle ${\varphi }_2$and obtain two solutions; the result consistent with other Standard Model constraints is ${\varphi }_2=\left({92.6}_{-4.7}^{+4.5}\right)°$. Published by the American Physical Society2025 

Abstract The XLZD collaboration is developing a two-phase xenon time projection chamber with an active mass of 60–80 t capable of probing the remaining weakly interacting massive particle-nucleon interaction parameter space down to the so-called neutrino fog. In this work we show that, based on the performance of currently operating detectors using the same technology and a realistic reduction of radioactivity in detector materials, such an experiment will also be able to competitively search for neutrinoless double beta decay in¹³⁶Xe using a natural-abundance xenon target. XLZD can reach a 3σdiscovery potential half-life of 5.7 × 10²⁷years (and a 90% CL exclusion of 1.3 × 10²⁸years) with 10 years of data taking, corresponding to a Majorana mass range of 7.3–31.3 meV (4.8–20.5 meV). XLZD will thus exclude the inverted neutrino mass ordering parameter space and will start to probe the normal ordering region for most of the nuclear matrix elements commonly considered by the community. 

A<sc>bstract</sc> Using data samples of 983.0 fb⁻¹and 427.9 fb⁻¹accumulated with the Belle and Belle II detectors operating at the KEKB and SuperKEKB asymmetric-energye⁺e⁻colliders, singly Cabibbo-suppressed decays$$ {\Xi}_c^{+}\to p{K}_S^0 $$ ${\Xi }_c^{+}\to p{K}_S^0$,$$ {\Xi}_c^{+}\to \Lambda {\pi}^{+} $$ ${\Xi }_c^{+}\to \Lambda {\pi }^{+}$, and$$ {\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+} $$ ${\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}$are observed for the first time. The ratios of branching fractions of$$ {\Xi}_c^{+}\to p{K}_S^0 $$ ${\Xi }_c^{+}\to p{K}_S^0$,$$ {\Xi}_c^{+}\to \Lambda {\pi}^{+} $$ ${\Xi }_c^{+}\to \Lambda {\pi }^{+}$, and$$ {\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+} $$ ${\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}$relative to that of$$ {\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+} $$ ${\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}$are measured to be$$ {\displaystyle \begin{array}{c}\frac{\mathcal{B}\left({\Xi}_c^{+}\to p{K}_S^0\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(2.47\pm 0.16\pm 0.07\right)\%,\\ {}\frac{\mathcal{B}\left({\Xi}_c^{+}\to \Lambda {\pi}^{+}\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(1.56\pm 0.14\pm 0.09\right)\%,\\ {}\frac{\mathcal{B}\left({\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+}\right)}{\mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)}=\left(4.13\pm 0.26\pm 0.22\right)\%.\end{array}} $$ $\begin{array}{c}\frac{B\left({\Xi }_c^{+}\to p{K}_S^0\right)}{B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=\left(2.47\pm 0.16\pm 0.07\right)\%,\\ \frac{B\left({\Xi }_c^{+}\to \Lambda {\pi }^{+}\right)}{B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=\left(1.56\pm 0.14\pm 0.09\right)\%,\\ \frac{B\left({\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}\right)}{B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=\left(4.13\pm 0.26\pm 0.22\right)\%.\end{array}$ Multiplying these values by the branching fraction of the normalization channel,$$ \mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right)=\left(2.9\pm 1.3\right)\% $$ $B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)=\left(2.9\pm 1.3\right)\%$, the absolute branching fractions are determined to be$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^{+}\to p{K}_S^0\right)=\left(7.16\pm 0.46\pm 0.20\pm 3.21\right)\times {10}^{-4},\\ {}\mathcal{B}\left({\Xi}_c^{+}\to \Lambda {\pi}^{+}\right)=\left(4.52\pm 0.41\pm 0.26\pm 2.03\right)\times {10}^{-4},\\ {}\mathcal{B}\left({\Xi}_c^{+}\to {\Sigma}^0{\pi}^{+}\right)=\left(1.20\pm 0.08\pm 0.07\pm 0.54\right)\times {10}^{-3}.\end{array}} $$ $\begin{array}{c}B\left({\Xi }_c^{+}\to p{K}_S^0\right)=\left(7.16\pm 0.46\pm 0.20\pm 3.21\right)\times {10}^{-4},\\ B\left({\Xi }_c^{+}\to \Lambda {\pi }^{+}\right)=\left(4.52\pm 0.41\pm 0.26\pm 2.03\right)\times {10}^{-4},\\ B\left({\Xi }_c^{+}\to {\Sigma }^0{\pi }^{+}\right)=\left(1.20\pm 0.08\pm 0.07\pm 0.54\right)\times {10}^{-3}.\end{array}$ The first and second uncertainties above are statistical and systematic, respectively, while the third ones arise from the uncertainty in$$ \mathcal{B}\left({\Xi}_c^{+}\to {\Xi}^{-}{\pi}^{+}{\pi}^{+}\right) $$ $B\left({\Xi }_c^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)$. 

We report a search for a heavy neutral lepton (HNL) that mixes predominantly with ${\nu }_{\tau }$. The search utilizes data collected with the Belle detector at the KEKB asymmetric energy $e^{+}{e}^{-}$collider. The data sample was collected at and just below the center-of-mass energies of the $\mathrm{\Upsilon }\left(4S\right)$and $\mathrm{\Upsilon }\left(5S\right)$resonances and has an integrated luminosity of $915{\mathrm{fb}}^{-1}$, corresponding to $(836\pm 12)\times {10}^6$ $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$events. We search for production of the HNL (denoted $N$) in the decay ${\tau }^{-}\to {\pi }^{-}N$followed by its decay via $N\to {\mu }^{+}{\mu }^{-}{\nu }_{\tau }$. The search focuses on the parameter-space region in which the HNL is long-lived, so that the ${\mu }^{+}{\mu }^{-}$originate from a common vertex that is significantly displaced from the collision point of the KEKB beams. Consistent with the expected background yield, one event is observed in the data sample after application of all the event-selection criteria. We report limits on the mixing parameter of the HNL with the $\tau$neutrino as a function of the HNL mass. Published by the American Physical Society2024 

We measure the branching fraction and $CP$-violating flavor-dependent rate asymmetry of $B^0\to {\pi }^0{\pi }^0$decays reconstructed using the Belle II detector in an electron-positron collision sample containing $387\times {10}^6\mathrm{\Upsilon }\left(4S\right)$mesons. Using an optimized event selection, we find $125\pm 20$signal decays in a fit to background-discriminating and flavor-sensitive distributions. The resulting branching fraction is $(1.25\pm 0.23)\times {10}^{-6}$and the $CP$-violating asymmetry is $0.03\pm 0.30$. Published by the American Physical Society2025