As a proof of concept, we focus on kernel machines and on two simple realizations of data structure introduced in recent physics literature k-dimensional simplexes with prescribed geometric relations and spherical manifolds (equivalent to margin classification). Entropy, contrary to what happens for unstructured data, is nonmonotonic in the sample size, in contrast with the rigorous bounds. Moreover, data structure induces a transition beyond the storage capacity, which we advocate as a proxy of the nonmonotonicity, and ultimately a cue of low generalization error. The identification of a synaptic volume vanishing at the transition allows a quantification of the impact of data structure within replica theory, applicable in cases where combinatorial methods are not available, as we demonstrate for margin learning.The resources needed for particle-in-cell simulations of laser wakefield acceleration can be greatly reduced in many cases of interest using an envelope model. However, the inclusion of tunneling ionization in this time-averaged treatment of laser-plasma acceleration is not straightforward, since the statistical features of the electron beams obtained through ionization should ideally be reproduced without resolving the high-frequency laser oscillations. In this context, an extension of an already known envelope ionization procedure is proposed, valid also for laser pulses with higher intensities, which consists in adding the initial longitudinal drift to the newly created electrons within the laser pulse ionizing the medium. The accuracy of the proposed procedure is shown with both linear and circular polarization in a simple benchmark where a nitrogen slab is ionized by a laser pulse and in a more complex benchmark of laser plasma acceleration with ionization injection in the nonlinear regime. With this addition to the envelope ionization algorithm, the main phase space properties of the bunches injected in a plasma wakefield with ionization by a laser (charge, average energy, energy spread, rms sizes, and normalized emittance) can be estimated with accuracy comparable to a nonenvelope simulation with significantly reduced resources, even in cylindrical geometry. Through this extended algorithm, preliminary studies of ionization injection in laser wakefield acceleration can be easily carried out even on a laptop.Zero-determinant (ZD) strategies are a novel class of strategies in the repeated prisoner's dilemma (RPD) game discovered by Press and Dyson. This strategy set enforces a linear payoff relationship between a focal player and the opponent regardless of the opponent's strategy. In the RPD game, games with discounting and observation errors represent an important generalization, because they are better able to capture real life interactions which are often noisy. However, they have not been considered in the original discovery of ZD strategies. In some preceding studies, each of them has been considered independently. Here, we analytically study the strategies that enforce linear payoff relationships in the RPD game considering both a discount factor and observation errors. As a result, we first reveal that the payoffs of two players can be represented by the form of determinants as shown by Press and Dyson even with the two factors. Then, we search for all possible strategies that enforce linear payoff relationships and find that both ZD strategies and unconditional strategies are the only strategy sets to satisfy the condition. We also show that neither Extortion nor Generous strategies, which are subsets of ZD strategies, exist when there are errors. Finally, we numerically derive the threshold values above which the subsets of ZD strategies exist. These results contribute to a deep understanding of ZD strategies in society.The interaction between thin elastic films and soft-adhesive foundations has recently gained interest due to technological applications that require control over such objects. Motivated by these applications we investigate the equilibrium configuration of an open cylindrical shell with natural curvature κ and bending modulus B that is adhered to soft and adhesive foundation with stiffness K. We derive an analytical model that predicts the delamination criterion, i.e., the critical natural curvature, κ_cr, at which delamination first occurs, and the ultimate shape of the shell. While in the case of a rigid foundation, K→∞, our model recovers the known two-states solution at which the shell either remains completely attached to the substrate or completely detaches from it, on a soft foundation our model predicts the emergence of a new branch of solutions. This branch corresponds to partially adhered shells, where the contact zone between the shell and the substrate is finite and scales as ℓ_w∼(B/K)^1/4.  https://www.selleckchem.com/products/Ilginatinib-hydrochloride.html  In addition, we find that the criterion for delamination depends on the total length of the shell along the curved direction, L. While relatively short shells, L∼ℓ_w, transform continuously between adhered and delaminated solutions, long shells, L≫ℓ_w, transform discontinuously. Notably, our work provides insights into the detachment phenomena of thin elastic sheets from soft and adhesive foundations.Design of slender artificial materials and morphogenesis of thin biological tissues typically involve stimulation of isolated regions (inclusions) in the growing body. These inclusions apply internal stresses on their surrounding areas that are ultimately relaxed by out-of-plane deformation (buckling). We utilize the Föppl-von Kármán model to analyze the interaction between two circular inclusions in an infinite plate that their centers are separated a distance of 2ℓ. In particular, we investigate a region in phase space where buckling occurs at a narrow transition layer of length ℓ_D around the radius of the inclusion, R (ℓ_D≪R). We show that the latter length scale defines two regions within the system, the close separation region, ℓ-R∼ℓ_D, where the transition layers of the two inclusions approximately coalesce, and the far separation region, ℓ-R≫ℓ_D. While the interaction energy decays exponentially in the latter region, E_int∝e^-(ℓ-R)/ℓ_D, it presents nonmonotonic behavior in the former region.