We show that the two notions are inherently connected via aligning them with the linear program of the weakly dominating set and its dual -- the fractional vertex packing set respectively.

We first develop a private variant of the regularized cubic Newton method of Nesterov and Polyak [NP06], and show that for the class of strongly convex loss functions, our algorithm has quadratic convergence and achieves the optimal excess loss.

Effective resistances have a broad range of algorithmic implications.

Our estimators assume that there is no interference between the units, i.e., that the treatment of one The first assumption is quite realistic as in most peer review systems the reviewers cannot see other reviews until they submit their own. The second assumption is important to understand, as there could be "batch effects": a Monte Carlo methods to tightly estimate these covariances. AAAI datasets, we sampled 1 million assignments and computed the empirical covariance. In our setting, small amounts of attrition (relative to the number of policy-induced positivity violations) mean that the fraction of data that is missing is not exactly known before assignment, but almost. To get more robust estimates of the performance, we repeat this process 10 times.

In our case, it boils down to: ' The smoothing effect induced by the average helps to reduce the visual noise, and hence improves the explanations. For the experiment, m and are the same as SmoothGrad. We start by deriving the closed form of Saliency (SA) and naturally Gradient-Input (GI): ' The case of V arGrad is specific, as the gradient of a linear system being constant, its variance is null. W We recall that for Gradient Input, Integrated Gradients, Occlusion, ' It was quickly realized that they unified properties of various domains such as graph theory, linear algebra or geometry. Later, in the '60s, a connection was made At each step, the insertion metric selects the concepts of maximum score given a cardinality constraint.

CoLA and discuss modifications to improve lower precision performance. In Appendix D we expand on the details of the experiments in the main text. We now present the linear algebra identities that we use to exploit structure in CoLA. I null Finally, for sum we have the Woodbury identity and its variants. Besides the compositional operators, we have some rules for some special operators.

Classical joint modeling approaches often rely on competing risks or recurrent event formulations to account for complex real-world processes involving evolving longitudinal markers and discrete event occurrences. However, these frameworks typically capture only limited aspects of the underlying event dynamics. Multi-state joint models offer a more flexible alternative by representing full event histories through a network of possible transitions, including recurrent cycles and terminal absorptions, all potentially influenced by longitudinal covariates. In this paper, we propose a general framework that unifies longitudinal biomarker modeling with multi-state event processes defined on arbitrary directed graphs. Our approach accommodates both Markovian and semi-Markovian transition structures, and extends classical joint models by coupling nonlinear mixed-effects longitudinal submodels with multi-state survival processes via shared latent structures. We derive the full likelihood and develop scalable inference procedures based on stochastic gradient descent. Furthermore, we introduce a dynamic prediction framework, enabling individualized risk assessments along complex state-transition trajectories. To facilitate reproducibility and dissemination, we provide an open-source Python library \texttt{jmstate} implementing the proposed methodology, available on \href{https://pypi.org/project/jmstate/}{PyPI}. Simulation experiments and a biomedical case study demonstrate the flexibility and performance of the framework in representing complex longitudinal and multi-state event dynamics. The full Python notebooks used to reproduce the experiments as well as the source code of this paper are available on \href{https://gitlab.com/felixlaplante0/jmstate-paper/}{GitLab}.