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1. A Complete Study of P.K.I. (PKI’s Known Incidents)

   https://doi.org/10.2139/ssrn.3425554  

   Serrano, Nicolas; Hadan, Hilda; Camp, L. Jean (September 2019, SSRN Electronic Journal)

   null (Ed.)

   In this work, we report on a comprehensive analysis of PKI resulting from Certificate Authorities’ (CAs) behavior using over 1300 instances. We found several cases where CAs designed business models that favored the issuance of digital certificates over the guidelines of the CA Forum, root management programs, and other PKI requirements. Examining PKI from the perspective of business practices, we identify a taxonomy of failures and identify systemic vulnerabilities in the governance and practices in PKI. Notorious cases include the “backdating” of digital certificates, the issuance of these for MITM attempts, the lack of verification of a requester’s identity, and the unscrupulous issuance of rogue certificates. We performed a detailed study of 379 of these 1300 incidents. Using this sample, we developed a taxonomy of the different types of incidents and their causes. For each incident, we determined if the incident was disclosed by the problematic CA. We also noted the Root CA and the year of the incident. We identify the failures in terms of business practices, geography, and outcomes from CAs. We analyzed the role of Root Program Owners (RPOs) and differentiated their policies. We identified serial and chronic offenders in the PKI trusted root programs. Some of these were distrusted by RPOs, while others remain being trusted despite failures. We also identified cases where the concentration of power of RPOs was arguably a contributing factor in the incident. We identify these cases where there is a risk of concentration of power and the resulting conflict of interests. Our research is the first comprehensive academic study addressing all verified reported incidents. We approach this not from a machine learning or statistical perspective but, rather, we identify each reported public incident with a focus on identifying patterns of individual lapses. Here we also have a specific focus on the role of CAs and RPOs. Building on this study, we identify the issues in incentive structures that are contributors to the problems. 

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2. Finite element algorithms for nonlocal minimal graphs

   https://doi.org/10.3934/mine.2022016  

   Borthagaray, Juan Pablo; Li, Wenbo; Nochetto, Ricardo H. (January 2021, Mathematics in Engineering)

   null (Ed.)

   We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems. 

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3. Nonparametric Regression with Comparisons: Escaping the Curse of Dimensionality with Ordinal Information

   Xu, Yichong; Muthakana, Hariank; Balakrishnan, Sivaraman; Singh, Aarti; Dubrawski, Artur (July 2018, International Conference on Machine Learning)

   In supervised learning, we leverage a labeled dataset to design methods for function estimation. In many practical situations, we are able to obtain alternative feedback, possibly at a low cost. A broad goal is to understand the usefulness of, and to design algorithms to exploit, this alternative feedback. We focus on a semi-supervised setting where we obtain additional ordinal (or comparison) information for potentially unlabeled samples. We consider ordinal feedback of varying qualities where we have either a perfect ordering of the samples, a noisy ordering of the samples or noisy pairwise comparisons between the samples. We provide a precise quantification of the usefulness of these types of ordinal feedback in non-parametric regression, showing that in many cases it is possible to accurately estimate an underlying function with a very small labeled set, effectively escaping the curse of dimensionality. We develop an algorithm called Ranking-Regression (RR) and analyze its accuracy as a function of size of the labeled and unlabeled datasets and various noise parameters. We also present lower bounds, that establish fundamental limits for the task and show that RR is optimal in a variety of settings. Finally, we present experiments that show the efficacy of RR and investigate its robustness to various sources of noise and model-misspecification. 

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4. A hierarchy of Plateau problems and the approximation of Plateau's laws via the Allen--Cahn equation

   Maggi, Francesco; Novack, Michael; Restrepo, Daniel (December 2023, arxiv)

   We introduce a diffused interface formulation of the Plateau problem, where the Allen--Cahn energy is minimized under a volume constraint and a spanning condition on the level sets of the densities. We discuss two singular limits of these Allen--Cahn Plateau problems: when , we prove convergence to the Gauss' capillarity formulation of the Plateau problem with positive volume ; and when , and , we prove convergence to the classical Plateau problem (in the homotopic spanning formulation of Harrison and Pugh). As a corollary of our analysis we resolve the incompatibility between Plateau's laws and the Allen--Cahn equation implied by a regularity theorem of Tonegawa and Wickramasekera. In particular, we show that Plateau-type singularities can be approximated by energy minimizing solutions of the Allen--Cahn equation with a volume Lagrange multiplier and a transmission condition on a spanning free boundary. 

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5. Energetically-optimal Discrete And Continuous Stabilization Of The Rimless Wheel With Torso

   Sirichotiyakul, Wankun; Satici, Aykut C; Sanchez, Sebastian; Bhounsule, Pranav A (October 2019, ASME-International Design Engineering & Technical Conference)

   In this work, we discuss the modeling, control, and implementation of a rimless wheel with a torso. We derive and compare two control methodologies: a discrete-time controller (DT) that updates the controls once-per-step and a continuous-time controller (CT) that updates gains continuously. For the discrete controller, we use least-squares estimation method to approximate the Poincare ́ map on a certain section and use discrete- linear-quadratic-regulator (DQLR) to stabilize a (closed-form) linearization of this map. For the continuous controller, we introduce moving Poincare ́ sections and stabilize the transverse dynamics along these moving sections. For both controllers, we estimate the region of attraction of the closed-loop system using sum-of-squares methods. Analysis of the impact map yields a refinement of the controller that stabilizes a steady-state walking gait with minimal energy loss. We present both simulation and experimental results that support the validity of the proposed approaches. We find that the CT controller has a larger region of attraction and smoother stabilization as compared with the DT controller. 

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