Towards Certain Fixes with Editing Rules and Master Data

A variety of integrity constraints have been studied for data cleaning. While these constraints can detect the presence of errors, they fall short of guiding us to correct the errors. Indeed, data repairing based on these constraints may not find certain fixes that are absolutely correct, and worse, may introduce new errors when repairing the data. We propose a method for finding certain fixes, based on master data, a notion of certain regions , and a class of editing rules . A certain region is a set of attributes that are assured correct by the users. Given a certain region and master data, editing rules tell us what attributes to fix and how to update them. We show how the method can be used in data monitoring and enrichment. We develop techniques for reasoning about editing rules, to decide whether they lead to a unique fix and whether they are able to fix all the attributes in a tuple, relative to master data and a certain region. We also provide an algorithm to identify minimal certain regions, such that a certain fix is warranted by editing rules and master data as long as one of the regions is correct. We experimentally verify the effectiveness and scalability of the algorithm. </jats:p

Angular distribution of the FCNC process Bc→Ds∗(→Dsπ)ℓ+ℓ−B_{c}\to{D}_{s}^{*}(\to{D}_{s}\pi)\ell^{+}\ell^{-}

In this work, we study the flavor-changing neutral-current process $B_{c}\to{D}_{s}^{*}(\to{D}_{s}\pi)\ell^{+}\ell^{-}$ ($\ell$= $e$, $\mu$, $\tau$). The relevant weak transition form factors are obtained by using the covariant light-front quark model, in which, the main inputs, i.e., the meson wave functions of $B_{c}$ and $D_{s}^{*}$, are adopted as the numerical wave functions from the solution of the Schr\"{o}dinger equation with the modified Godfrey-Isgur model. With the obtained form factors, we further investigate the relevant branching fractions and their ratios, and some angular observables, i.e., the forward-backward asymmetry $A_{FB}$, the polarization fractions $F_{L(T)}$, and the $CP$-averaged angular coefficients $S_{i}$ and the $CP$ asymmetry coefficients $A_{i}$. We also present our results of the clean angular observables $P_{1,2,3}$ and $P^{\prime}_{4,5,6,8}$, which can reduce the uncertainties from the form factors. Our results show that the corresponding branching fractions of the electron or muon channels can reach up to $10^{-8}$. With more data being accumulated in the LHCb experiment, our results are helpful for exploring this process, and deepen our understanding of the physics around the $b\to{s}\ell^{+}\ell^{-}$ process.Comment: 25 pages, 8 tables and 9 figure

A Descriptive Model of Robot Team and the Dynamic Evolution of Robot Team Cooperation

At present, the research on robot team cooperation is still in qualitative analysis phase and lacks the description model that can quantitatively describe the dynamical evolution of team cooperative relationships with constantly changeable task demand in Multi-robot field. First this paper whole and static describes organization model HWROM of robot team, then uses Markov course and Bayesian theorem for reference, dynamical describes the team cooperative relationships building. Finally from cooperative entity layer, ability layer and relative layer we research team formation and cooperative mechanism, and discuss how to optimize relative action sets during the evolution. The dynamic evolution model of robot team and cooperative relationships between robot teams proposed and described in this paper can not only generalize the robot team as a whole, but also depict the dynamic evolving process quantitatively. Users can also make the prediction of the cooperative relationship and the action of the robot team encountering new demands based on this model. Journal web page & a lot of robotic related papers www.ars-journal.co

The Closeness of In-Context Learning and Weight Shifting for Softmax Regression

Large language models (LLMs) are known for their exceptional performance in natural language processing, making them highly effective in many human life-related or even job-related tasks. The attention mechanism in the Transformer architecture is a critical component of LLMs, as it allows the model to selectively focus on specific input parts. The softmax unit, which is a key part of the attention mechanism, normalizes the attention scores. Hence, the performance of LLMs in various NLP tasks depends significantly on the crucial role played by the attention mechanism with the softmax unit. In-context learning, as one of the celebrated abilities of recent LLMs, is an important concept in querying LLMs such as ChatGPT. Without further parameter updates, Transformers can learn to predict based on few in-context examples. However, the reason why Transformers becomes in-context learners is not well understood. Recently, several works [ASA+22,GTLV22,ONR+22] have studied the in-context learning from a mathematical perspective based on a linear regression formulation $\min_x\| Ax - b \|_2$, which show Transformers' capability of learning linear functions in context. In this work, we study the in-context learning based on a softmax regression formulation $\min_{x} \| \langle \exp(Ax), {\bf 1}_n \rangle^{-1} \exp(Ax) - b \|_2$ of Transformer's attention mechanism. We show the upper bounds of the data transformations induced by a single self-attention layer and by gradient-descent on a $\ell_2$ regression loss for softmax prediction function, which imply that when training self-attention-only Transformers for fundamental regression tasks, the models learned by gradient-descent and Transformers show great similarity

Imaginary-time Quantum Relaxation Critical Dynamics with Semi-ordered Initial States

We explore the imaginary-time relaxation dynamics near quantum critical points with semi-ordered initial states. Different from the case with homogeneous ordered initial state, in which the order parameter $M$ decays homogeneously as $M\propto \tau^{-\beta/\nu z}$, here $M$ depends on the location $x$, showing rich scaling behaviors. Similar to the classical Model A critical dynamics with an initial domain wall, here as the imaginary time evolves, the domain wall expands into an interfacial region with growing size. In the interfacial region, the local order parameter decays as $M\propto \tau^{-\beta_1/\nu z}$, with $\beta_1$ being an additional dynamic critical exponent. Far away from the interfacial region the local order parameter decays as $M\propto \tau^{-\beta/\nu z}$ in the short-time stage, then crosses over to the scaling behavior of $M\propto \tau^{-\beta_1/\nu z}$ when the location $x$ is absorbed in the interfacial region. A full scaling form characterizing these scaling properties is developed. The quantum Ising model in both one and two dimensions are taken as examples to verify the scaling theory. In addition, we find that for the quantum Ising model the scaling function is an analytical function and $\beta_1$ is not an independent exponent.Comment: 8 pages, 5 figure

Whole BcB_c meson spectroscopy under the unquenched picture

In this work, we investigate the spectroscopy of higher $B_c$ mesons, with a special focus on the consideration of the unquenched effects. To account for such effects, we employ the modified Godfrey-Isgur model and introduce a screening potential. The resulting mass spectrum of the concerned higher $B_c$ states is then presented, showing significant deviations after considering the unquenched effects. This emphasizes the importance of considering the unquenched effects when studying of the higher $B_c$ mesons. Furthermore, we determine the corresponding spatial wave functions of these $B_c$ mesons, which have practical applications in subsequent studies of their decays. These decays include two-body Okuba-Zweig-Iizuka allowed strong decays, dipion transitions between $B_c$ mesons, radiative decays, and some typical weak decays. With the ongoing high-luminosity upgrade of the Large Hadron Collider, we expect the discovery of additional $B_c$ states in the near future. The knowledge gained from the mass spectrum and the different decay modes will undoubtedly provide valuable insights for future experimental explorations of these higher $B_c$ mesons.Comment: 30 pages, 7 figures and 17 table