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Simple Summary Proximity to major vessels increases risk of local recurrence in soft tissue sarcomas of the thigh. When major vessels were observed to be surrounded by the tumor on preoperative MRI, vascular resection and by-pass reconstruction offered a better local control. Abstract The aim of this study was to establish the prognostic effects of the proximity of the tumor to the main vessels in patients affected by soft tissue sarcomas (STS) of the thigh. A total of 529 adult patients with deeply seated STS of the thigh and popliteal fossa were included. Vascular proximity was defined on MRI: type 1 > 5 mm; type 2 ≤ 5 mm and >0 mm; type 3 close to the tumor; type 4 enclosed by the tumor. Proximity to major vessels type 1–2 had a local recurrence (LR) rate lower than type 3–4 (p < 0.001). In type 4, vascular by-pass reduced LR risk. On multivariate analysis infiltrative histotypes, high FNLCC grade, radiotherapy administration, and type 3–4 of proximity to major vessels were found to be independent prognostic factors for LR. We observed an augmented risk of recurrence, but not of survival as the tumor was near to the major vessels. When major vessels were found to be surrounded by the tumor on preoperative MRI, vascular resection and bypass reconstruction offered a better local control.

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting, that is, accurate predictions despite overfitting training data. In this article, we survey recent progress in statistical learning theory that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behaviour of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favourable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.

Zhang Tongzhi (1875–1948) was a Chinese scholar, educator, and gourmet from Nanjing, today the capital of Jiangsu province. In 1947, he published the List of Jinling's Delicacies, in which he described and extolled the best raw ingredients, processed foods, and cooked dishes he had tasted in Nanjing throughout his life. In this article, I offer a translation of twenty-four of the sixty-one entries of the List and I read them as portraying not only the city's delicacies but also the practice of gastronomy, of Zhang as well as of the people of Nanjing. As a social and consumption practice, gastronomy can be defined, with Priscilla Parkhurst Ferguson, as “the systematic, socially valorized pursuit of culinary excellence.” Yet gastronomy, in the context of Western and especially French culinary history, has mainly been analyzed as a textualized discourse. While I do not challenge the idea that gastronomic words matter, in this article I suggest that gastronomic practice matters, too, and that, as far as the development of Chinese culinary culture is concerned, it may have mattered more than words. The List affords us glimpses into a little-known foodscape and it vividly captures this “applied” dimension of gastronomy. My hope is that this text will also stimulate more comparative thinking about culinary cultures and their sociohistorical development.

In the tensor completion problem, one seeks to estimate a low-rank tensor based on a random sample of revealed entries. In terms of the required sample size, earlier work revealed a large gap between estimation with unbounded computational resources (using, for instance, tensor nuclear norm minimization) and polynomial-time algorithms. Among the latter, the best statistical guarantees have been proved, for third-order tensors, using the sixth level of the sum-of-squares (SOS) semidefinite programming hierarchy (Barak and Moitra, 2014). However, the SOS approach does not scale well to large problem instances. By contrast, spectral methods --- based on unfolding or matricizing the tensor --- are attractive for their low complexity, but have been believed to require a much larger sample size. This paper presents two main contributions. First, we propose a new unfolding-based method, which outperforms naive ones for symmetric $k$-th order tensors of rank $r$. For this result we make a study of singular space estimation for partially revealed matrices of large aspect ratio, which may be of independent interest. For third-order tensors, our algorithm matches the SOS method in terms of sample size (requiring about $rd^{3/2}$ revealed entries), subject to a worse rank condition ($r\ll d^{3/4}$ rather than $r\ll d^{3/2}$). We complement this result with a different spectral algorithm for third-order tensors in the overcomplete ($r\ge d$) regime. Under a random model, this second approach succeeds in estimating tensors of rank $d\le r \ll d^{3/2}$ from about $rd^{3/2}$ revealed entries.