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The rapid advancement of Generative Adversarial Networks (GANs) necessitates the need to robustly evaluate these models. Among the established evaluation criteria, the Fréchet Inception Distance (FID) has been widely adopted due to its conceptual simplicity, fast computation time, and strong correlation with human perception. However, FID has inherent limitations, mainly stemming from its assumption that feature embeddings follow a Gaussian distribution, and therefore can be defined by their first two moments. As this does not hold in practice, in this paper we explore the importance of third-moments in image feature data and use this information to define a new measure, which we call the Skew Inception Distance (SID). We prove that SID is a pseudometric on probability distributions, show how it extends FID, and present a practical method for its computation. Our numerical experiments support that SID either tracks with FID or, in some cases, aligns more closely with human perception when evaluating image features of ImageNet data. Our work also shows that principal component analysis can be used to speed up the computation time of both FID and SID. Although we focus on using SID on image features for GAN evaluation, SID is applicable much more generally, including for the evaluation of other generative models. 

Multiple experimental studies were performed on galling intiation for variety of tooling materials, coatings and surface treatments, sheet materials with various surface textures and lubrication. Majority of studies were performed for small number of samples in laboratory conditions. In this paper, the methodology of screening experiment using different combinations of tooling configurations and sheet material in the lab followed by the high volume small scale U-bend performed in the progressive die on the mechanical press is discussed. The experimental study was performed to understand the effect of the interface between the sheet metal and the die surface on sheet metal flow during stamping operations. Aluminum sheet AA5754 2.5mm thick was used in this experimentation. The sheet was tested in laboratory conditions by pulling between two flat insert with controllable clamping force and through the drawbead system with variable radii of the female bead. Comparing pulling forces during sheet metal flow through the testing setup provides information on flow resistance along the interface between the sheet and the tool surfaces. Onset of galling can be detected by the growth of the pulling force. In addition, it is defined by measurement of the surface of the tool and the scratches on the surface of the samples. Typical galling is seen as lines of sheet material deposit on the surface of the die parallel to the sheet material sliding. Most of galling is observed in the areas where lubricant can be forced out of the contact zone, such as edges of the strip, die entry radii or female bead radius. 

Abstract In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularization. Higher order regularity can be obtained via replacing the Laplacian regulariser with a poly-Laplacian regulariser. The methodology is readily adapted to graphs and here we consider graph poly-Laplacian regularization in a fully supervised, non-parametric, noise corrupted, regression problem. In particular, given a dataset$$\{x_i\}_{i=1}^n$$ ${\left\{x_i\right\}}_{i=1}^n$and a set of noisy labels$$\{y_i\}_{i=1}^n\subset \mathbb {R}$$ ${\left\{y_i\right\}}_{i=1}^n\subset R$we let$$u_n{:}\{x_i\}_{i=1}^n\rightarrow \mathbb {R}$$ $u_n:{\left\{x_i\right\}}_{i=1}^n\to R$be the minimizer of an energy which consists of a data fidelity term and an appropriately scaled graph poly-Laplacian term. When$$y_i = g(x_i)+\xi _i$$ $y_i=g\left(x_i\right)+{\xi }_i$, for iid noise$$\xi _i$$ ${\xi }_i$, and using the geometric random graph, we identify (with high probability) the rate of convergence of$$u_n$$ $u_n$togin the large data limit$$n\rightarrow \infty $$ $n\to \infty$. Furthermore, our rate is close to the known rate of convergence in the usual smoothing spline model. 

Abstract Overfishing remains a threat to coral reef fishes worldwide, with large carnivores often disproportionately vulnerable. Marine protected areas (MPAs) can restore fish populations and biodiversity, but their effect has been understudied in mesophotic coral ecosystems (MCEs), particularly in the Coral Triangle.Videos were analysed from baited remote underwater video systems deployed in 2016 to investigate the assemblage structure of large carnivorous fishes at shallow (4–12 m) and mesophotic (45–96 m) depths in two of the largest and most isolated MPAs in the Philippines: an uninhabited, fully no‐take MPA enacted in 1988 (Tubbataha Reefs Natural Park) and an archipelagic municipality surrounded by an extensive but not fully no‐take MPA declared in 2016 (Cagayancillo). Taxa focused on were groupers (Serranidae), snappers (Lutjanidae), emperors (Lethrinidae), jacks (Carangidae) and the endangeredCheilinus undulatus(Labridae).Mean abundance and species richness were not greater in TRNP than in Cagayancillo regardless of depth despite long‐term protection in the former. Limited impacts of fishing in Cagayancillo may explain this result. Differentiation of fish assemblages was evident between TRNP and Cagayancillo but more obvious between depths at each location, probably due more to habitat than MPA effects. In Cagayancillo, overall carnivorous reef fish, grouper and jack mean abundance were 2, 2 and 10 times higher, respectively, at mesophotic depths, suggesting that MCEs can serve as deep refugia from fishing.These findings of differentiation between depths and higher abundance of certain taxa in mesophotic depths emphasize that MCEs are distinct from shallow reefs, serve as important habitat for species susceptible to overfishing and, thus, must be explicitly included in the design of MPAs. This study also highlights the value of maintaining strict protection of MPAs like TRNP for the Coral Triangle and an opportunity to safeguard intact fish assemblages in Cagayancillo by expanding its no‐take zones. 

Abstract We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and a family of regularized risk minimization problems where the regularizer is a nonlocal perimeter functional. The resulting regularized risk minimization problems admit exact convex relaxations of the type $$L^1+\text{(nonlocal)}\operatorname{TV}$$, a form frequently studied in image analysis and graph-based learning. A rich geometric structure is revealed by this reformulation which in turn allows us to establish a series of properties of optimal solutions of the original problem, including the existence of minimal and maximal solutions (interpreted in a suitable sense) and the existence of regular solutions (also interpreted in a suitable sense). In addition, we highlight how the connection between adversarial training and perimeter minimization problems provides a novel, directly interpretable, statistical motivation for a family of regularized risk minimization problems involving perimeter/total variation. The majority of our theoretical results are independent of the distance used to define adversarial attacks. 

Abstract In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts. We consider proximity graphs built from data sampled from an underlying distribution supported on a generic smooth compact manifold$${\mathcal {M}}$$ $M$. In this setting, we obtain high probability convergence rates for both the Cheeger constant and the associated Cheeger cuts towards their continuum counterparts. The key technical tools are careful estimates of interpolation operators which lift empirical Cheeger cuts to the continuum, as well as continuum stability estimates for isoperimetric problems. To the best of our knowledge the quantitative estimates obtained here are the first of their kind.