A regularity result for minimal configurations of a free interface problem

AbstractWe prove a regularity result for minimal configurations of variational problems involving both bulk and surface energies in some bounded open region $$\varOmega \subseteq {\mathbb {R}}^n$$ Ω ⊆ R n . We will deal with the energy functional $${\mathscr {F}}(v,E):=\int _\varOmega [F(\nabla v)+1_E G(\nabla v)+f_E(x,v)]\,dx+P(E,\varOmega )$$ F ( v , E ) : = ∫ Ω [ F ( ∇ v ) + 1 E G ( ∇ v ) + f E ( x , v ) ] d x + P ( E , Ω ) . The bulk energy depends on a function v and its gradient $$\nabla v$$ ∇ v . It consists in two strongly quasi-convex functions F and G, which have polinomial p-growth and are linked with their p-recession functions by a proximity condition, and a function $$f_E$$ f E , whose absolute valuesatisfies a q-growth condition from above. The surface penalization term is proportional to the perimeter of a subset E in $$\varOmega$$ Ω . The term $$f_E$$ f E is allowed to be negative, but an additional condition on the growth from below is needed to prove the existence of a minimal configuration of the problem associated with $${\mathscr {F}}$$ F . The same condition turns out to be crucial in the proof of the regularity result as well. If (u, A) is a minimal configuration, we prove that u is locally Hölder continuous and A is equivalent to an open set $${\tilde{A}}$$ A ~ . We finally get $$P(A,\varOmega )={\mathscr {H}}^{n-1}(\partial {\tilde{A}}\cap \varOmega$$ P ( A , Ω ) = H n - 1 ( ∂ A ~ ∩ Ω )

Variational analysis in one and two dimensions of a frustrated spin system: chirality transitions and magnetic anisotropic transitions

We study the energy of a ferromagnetic/antiferromagnetic frustrated spin system with values on two disjoint circumferences of the 3-dimensional unit sphere in a one-dimensional and two-dimensional domain. It consists on the sum of a term that depends on the nearest and next-to-nearest interactions and a penalizing term that counts the spin's magnetic anisotropy transitions. We analyze the asymptotic behaviour of the energy, that is when the system is close to the helimagnet/ferromagnet transition point as the number of particles diverges. In the one-dimensional setting we compute the $\Gamma$-limit of renormalizations of the energy at first and second order. As a result, it is shown how much energy the system spends for any magnetic anistropy transition and chirality transition. In the two-dimensional setting, by computing the $\Gamma$-limit of the renormalization of the energy at second order, we we prove the emergence and study the geometric rigidity of chirality transitions

A Fitness-Fatigue Model of Performance in Peripheral Artery Disease: Predicted and Measured Effects of a Pain-Free Exercise Program

Banister impulse-response (IR) model estimates the performance in response to the training impulses (TRIMPs). In 100 patients with peripheral artery disease (PAD), we tested by an IR model the predictability of the effects of a 6-month structured home-based exercise program. The daily TRIMPs obtained from prescribed walking speed, relative intensity and time of exercise determined the fitness-fatigue components of performance. The estimated performance values, calculated from the baseline 6-min and pain-free walking distance (6MWD and PFWD, respectively) were compared with values measured at visits through regression models. Interval pain-free walking at controlled speed prescribed during circa-monthly hospital visits (5 ± 1) was safely performed at home with good adherence (92% of scheduled sessions, 144 ± 25 km walked in 50 ± 8 training hours). The mean TRIMP rose throughout the program from 276 to 601 a.u. The measured 6MWD and PFWD values increased (+33 m and +121 m, respectively) showing a good fit with those estimated by the IR model (6MWD: R2 0.81; PFWD: R2 0.68) and very good correspondence (correlation coefficients: 0.91 to 0.95), without sex differences. The decay of performance without training was estimated at 18 ± 3 weeks. In PAD, an IR model predicted the walking performance following a pain-free exercise program. IR models may contribute to design and verify personalized training programs

Prediction of bench press performance in powerlifting: The role of upper limb anthropometry

The bench press (BP) is a complex, multiarticular exercise known as one of the three powerlifting specialties. Although several variables contribute to the maximum load lifted, upper limb variables may also play an important role in BP performance. In this study, a cohort of 47 male Italian classic powerlifters underwent a direct anthropometric evaluation during two official competitions. The recorded parameters included body mass index, body composition, and variables of the upper limb (indirectly evaluated cross-sectional areas and lengths). IPF-GL points and maximal strength (1RM) adjusted for weight were used as proxies for performance. Statistical comparisons between weaker and stronger powerlifters, Pearson correlation and partial correlation analyses, and multiple linear regression models were performed. The upper arm cross muscular area (r = 0.56) and fat-free mass (r = 0.31) were positively correlated with Wilks points, whereas the arm fat index was negatively correlated with 1RM BP (r = -0.37). Moreover, we proposed two new indices (UALR and UAMR) that represent the ratio between upper arm areas and length. Both univariate and multivariate analyses confirmed the strong association between these two variables and BP performance. Further improvement of this study may confirm the important role of body proportion and body composition as predictors of performance in strength sports

Lightweight Neural Architecture Search for Temporal Convolutional Networks at the Edge

Neural Architecture Search (NAS) is quickly becoming the go-to approach to optimize the structure of Deep Learning (DL) models for complex tasks such as Image Classification or Object Detection. However, many other relevant applications of DL, especially at the edge, are based on time-series processing and require models with unique features, for which NAS is less explored. This work focuses in particular on Temporal Convolutional Networks (TCNs), a convolutional model for time-series processing that has recently emerged as a promising alternative to more complex recurrent architectures. We propose the first NAS tool that explicitly targets the optimization of the most peculiar architectural parameters of TCNs, namely dilation, receptive-field and number of features in each layer. The proposed approach searches for networks that offer good trade-offs between accuracy and number of parameters/operations, enabling an efficient deployment on embedded platforms. We test the proposed NAS on four real-world, edge-relevant tasks, involving audio and bio-signals. Results show that, starting from a single seed network, our method is capable of obtaining a rich collection of Pareto optimal architectures, among which we obtain models with the same accuracy as the seed, and 15.9-152x fewer parameters. Compared to three state-of-the-art NAS tools, ProxylessNAS, MorphNet and FBNetV2, our method explores a larger search space for TCNs (up to 10^12x) and obtains superior solutions, while requiring low GPU memory and search time. We deploy our NAS outputs on two distinct edge devices, the multicore GreenWaves Technology GAP8 IoT processor and the single-core STMicroelectronics STM32H7 microcontroller. With respect to the state-of-the-art hand-tuned models, we reduce latency and energy of up to 5.5x and 3.8x on the two targets respectively, without any accuracy loss.Comment: Accepted for publication at the IEEE Transactions on Computer