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1. Learning in the Presence of Low-dimensional Structure: A Spiked Random Matrix Perspective

   Ba, Jimmy; Erdogdu, Murat A; Suzuki, Taiji; Wang, Zhichao; Wu, Denny (December 2023, Advances in Neural Information Processing Systems 36 (NeurIPS 2023))

   Oh, A; Naumann, T; Globerson, A; Saenko, K; Hardt, M; Levine, S (Ed.)

   We consider the problem of learning a single-index target function f∗ : Rd → R under the spiked covariance data: f∗(x) = σ∗   √ 1 1+θ ⟨x,μ⟩   , x ∼ N(0, Id + θμμ⊤), θ ≍ dβ for β ∈ [0, 1), where the link function σ∗ : R → R is a degree-p polynomial with information exponent k (defined as the lowest degree in the Hermite expansion of σ∗), and it depends on the projection of input x onto the spike (signal) direction μ ∈ Rd. In the proportional asymptotic limit where the number of training examples n and the dimensionality d jointly diverge: n, d → ∞, n/d → ψ ∈ (0,∞), we ask the following question: how large should the spike magnitude θ be, in order for (i) kernel methods, (ii) neural networks optimized by gradient descent, to learn f∗? We show that for kernel ridge regression, β ≥ 1 − 1 p is both sufficient and necessary. Whereas for two-layer neural networks trained with gradient descent, β > 1 − 1 k suffices. Our results demonstrate that both kernel methods and neural networks benefit from low-dimensional structures in the data. Further, since k ≤ p by definition, neural networks can adapt to such structures more effectively. 

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2. Silicone implant surface roughness, friction, and wear

   https://doi.org/10.1088/2051-672X/ac9f5a  

   Atkins, Dixon J; Chau, Allison L; Rosas, Jonah M; Chen, Yen-Tsung; Chan, Samantha T; Manuel Urueña, Juan; Pitenis, Angela A (March 2023, Surface Topography: Metrology and Properties)

   Abstract Some textured silicone breast implants with high average surface roughness (‘macrotextured’) have been associated with a rare cancer of the immune system, Breast Implant-Associated Anaplastic Large Cell Lymphoma (BIA-ALCL). Silicone elastomer wear debris may lead to chronic inflammation, a key step in the development of this cancer. Here, we model the generation and release of silicone wear debris in the case of a folded implant-implant (‘shell-shell’) sliding interface for three different types of implants, characterized by their surface roughness. The ‘smooth’ implant shell with the lowest average surface roughness tested (R a = 2.7 ± 0.6 μ m) resulted in average friction coefficients of μ avg = 0.46 ± 0.11 across 1,000 mm of sliding distance and generated 1,304 particles with an average particle diameter of D avg = 8.3 ± 13.1 μ m. The ‘microtextured’ implant shell (R a = 32 ± 7.0 μ m) exhibited μ avg = 1.20 ± 0.10 and generated 2,730 particles with D avg = 4.7 ± 9.1 μ m. The ‘macrotextured’ implant shell (R a = 80 ± 10 μ m) exhibited the highest friction coefficients, μ avg = 2.82 ± 0.15 and the greatest number of wear debris particles, 11,699, with an average particle size of D avg = 5.3 ± 3.3 μ m. Our data may provide guidance for the design of silicone breast implants with lower surface roughness, lower friction, and smaller quantities of wear debris. 

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3. Turbulence and Particle Acceleration in a Relativistic Plasma

   https://doi.org/10.3847/2041-8213/ac441e  

   Vega, Cristian; Boldyrev, Stanislav; Roytershteyn, Vadim; Medvedev, Mikhail (January 2022, The Astrophysical Journal Letters)

   Abstract In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameterσ≫ 1) quickly evolves into a state with ultrarelativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponentαin the power-law particle-energy distribution function,f(γ)dγ∝γ^−αdγ, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponentαis in good agreement with the numerical results. 

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4. Strangeness Photoproduction at the BGO-OD experiment

   https://doi.org/10.1051/epjconf/202024101008  

   Jude, Thomas; Alef, Stefan; Bauer, Patrick; Beck, Reinhard; Braghieri, Alessandro; Cole, Philip; Di Salvo, Rachele; Elsner, Daniel; Fantini, Alessia; Freyermuth, Oliver; et al (January 2020, EPJ Web of Conferences)

   Beck, R.; Thiel, A.; Thoma, U.; Wunderlich, Y. (Ed.)

   The BGO-OD experiment at the ELSA accelerator facility uses an energy tagged bremsstrahlung photon beam to investigate the excitation structure of the nucleon. The setup consists of a highly segmented BGO calorimeter surrounding the target, with a particle tracking magnetic spectrometer at forward angles. BGO-OD is ideal for investigating low momentum transfer processes due to the acceptance and high momentum resolution at forward angles. In particular, this enables the investigation of strangeness photoproduction where t-channel exchange mechanisms play an important role. This also allows access to low momentum exchange kinematics where extended, molecular structure may manifest in reaction mechanisms. First key results at low t indicate a cusp-like structure in K + Σ 0 photoproduction at W = 1900 MeV, line shapes and differential cross sections for K + Λ(1405)→ K + Σ 0 π 0 , and a peak structure in K 0 S Σ 0 photoproduction. The peak in the K 0 S Σ 0 channel appears consistent with meson-baryon generated states, where equivalent models have been used to describe the P C pentaquark candidates in the heavy charmed quark sector. 

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5. Experimental study of the $$ \gamma p \rightarrow K^{0}\Sigma^{+}$$, $$ \gamma n \rightarrow K^{0} \Lambda$$, and $$ \gamma n \rightarrow K^{0} \Sigma^{0}$$ reactions at the Mainz Microtron

   https://doi.org/10.1140/epja/i2019-12924-x  

   Akondi, C. S.; Bantawa, K.; Manley, D. M.; Abt, S.; Achenbach, P.; Afzal, F.; Aguar-Bartolomé, P.; Ahmed, Z.; Annand, J. R.; Arends, H. J.; et al (November 2019, The European Physical Journal A)

   null (Ed.)

   Abstract. This work measured $$ \mathrm{d}\sigma/\mathrm{d}\Omega$$ d σ / d Ω for neutral kaon photoproduction reactions from threshold up to a c.m. energy of 1855MeV, focussing specifically on the $$ \gamma p\rightarrow K^0\Sigma^+$$ γ p → K 0 Σ + , $$ \gamma n\rightarrow K^0\Lambda$$ γ n → K 0 Λ , and $$ \gamma n\rightarrow K^0 \Sigma^0$$ γ n → K 0 Σ 0 reactions. Our results for $$ \gamma n\rightarrow K^0 \Sigma^0$$ γ n → K 0 Σ 0 are the first-ever measurements for that reaction. These data will provide insight into the properties of $$ N^{\ast}$$ N * resonances and, in particular, will lead to an improved knowledge about those states that couple only weakly to the $$ \pi N$$ π N channel. Integrated cross sections were extracted by fitting the differential cross sections for each reaction as a series of Legendre polynomials and our results are compared with prior experimental results and theoretical predictions. 

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