Hydrodynamic limit of the Robinson–Schensted–Knuth algorithm

We investigate the evolution in time of the position of a fixed number in the insertion tableau when the Robinson–Schensted–Knuth algorithm is applied to a sequence of random numbers. When the length of the sequence tends to infinity, a typical trajectory after scaling converges uniformly in probability to some deterministic curve.     

Ballistic Impact Behaviour of Glass/Epoxy Composite Laminates Embedded with Shape Memory Alloy (SMA) Wires

This paper aims to estimate the enhancement in the energy absorption characteristics of the glass fiber reinforced composites (GFRP) by embedding prestrained pseudo-elastic shape memory alloy (SMA) that was used as a secondary reinforcement. The pseudo-elastic SMA (PE-SMA) embedded were in the form of wires and have an equiatomic composition (i.e., 50%–50%) of nickel (Ni) and titanium (Ti). These specimens are fabricated using a vacuum-assisted resin infusion process. The estimation is done for the GFRP and SMA/GFRP specimens at four different impact velocities (65, 75, 85, and 103 m/s) using a gas-gun impact set-up. At all different impact velocities, the failure modes change as we switch from GFRP to SMA/GFRP specimen. In the SMA/GFRP specimen, the failure mode changed from delamination in the primary region to SMA-pull out and SMA deformation. This leads to an increase in the ballistic limit. It is observed that energy absorbed by SMA/GFRP specimens is higher than the GFRP specimens subjected to the same levels of impact energy. To understand the damping capabilities of SMA embedment, vibration signals are captured, and the damping ratio is calculated. SMA dampens the vibrations imparted by the projectile to the specimen. The damping ratio of the SMA/GFRP specimens is higher than the GFRP specimens. The damping effect is more prominent below the ballistic limit when the projectile got rebounded (65 m/s).     

Aggregating Knockoffs for False Discovery Rate Control with an Application to Gut Microbiome Data

Recent discoveries suggest that our gut microbiome plays an important role in our health and wellbeing. However, the gut microbiome data are intricate; for example, the microbial diversity in the gut makes the data high-dimensional. While there are dedicated high-dimensional methods, such as the lasso estimator, they always come with the risk of false discoveries. Knockoffs are a recent approach to control the number of false discoveries. In this paper, we show that knockoffs can be aggregated to increase power while retaining sharp control over the false discoveries. We support our method both in theory and simulations, and we show that it can lead to new discoveries on microbiome data from the American Gut Project. In particular, our results indicate that several phyla that have been overlooked so far are associated with obesity.     

Magnetic Micromotors for Multiple Motile Sperm Cells Capture,Transport, and Enzymatic Release

An integrated system combining a magnetically‐driven micromotor and a synthetized protein‐based hyaluronic acid (HA) microflake is presented for the in situ selection and transport of multiple motile sperm cells (ca. 50). The system appeals for targeted sperm delivery in the reproductive system to assist fertilization or to deliver drugs. The binding mechanism between the HA microflake and sperm relies on the interactions between HA and the corresponding sperm HA receptors. Once sperm are captured within the HA microflake, the assembly is trapped and transported by a magnetically‐driven helical microcarrier. The trapping of the sperm‐microflake occurs by a local vortex induced by the microcarrier during rotation‐translation under a rotating magnetic field. After transport, the microflake is enzymatically hydrolyzed by local proteases, allowing sperm to escape and finally reach the target location. This cargo‐delivery system represents a new concept to transport not only multiple motile sperm but also other actively moving biological cargoes.     

Approximation of Attainable Sets of an Evolution Inclusion of Subdifferential Type

In a separable Hilbert space we consider an evolution inclusion with a multivalued perturbation and evolution operators that are subdifferentials of a proper convex lower semicontinuous function depending on time. Along with the original inclusion, we consider a sequence of approximating evolution inclusions with the same perturbation and the evolution operators that are subdifferentials of the Moreau–Yosida regularizations of the original function. We show that the attainable set of the original inclusion, regarded as a multivalued function of time, is the uniform (in time) limit in the Hausdorff metric of the sequence of attainable sets of the approximating inclusions. As an application we consider an example of a control system with discontinuous nonlinearity.     

Ni-Mn粉末触媒中固溶碳的作用效果和机理初探

 在国产DS6×800A型六面顶压机上，对比研究了含与不含固溶碳的Ni-Mn粉末触媒，采用直热式静压触媒法合成金刚石的差异。实验表明：Ni-Mn粉末触媒中固溶碳的存在，不仅可以提高金刚石的合成单产、细化金刚石晶粒，而且在同工艺条件下，能得到晶形完整度较高的金刚石单晶。     

Love Dynamics Between Secure Individuals: A Modeling Approach

A mathematical model composed of two differential equations, which qualitatively describe the dynamics of love between secure individuals, is presented in this paper with two goals. The general goal is to show how dynamic phenomena in the field of social psychology can be analyzed following the modelling approach traditionally used in all other fields of sciences. The specific goal is to derive, from very general assumptions on the behavior of secure individuals, a series of rather detailed properties of the dynamics of their feelings. The analysis shows, in particular, why couples can be partitioned into fragile and robust couples, how romantic relationships are influenced by behavioral parameters and in which sense individual appeal creates order in a community.     

r-regular shape reconstruction from unorganized points

In this paper, the problem of reconstructing a surface, given a set of scattered data points is addressed. First, a precise formulation of the reconstruction problem is proposed. The solution is mathematically defined as a particular mesh of the surface called the normalized mesh. This solution has the property to be included inside the Delaunay graph. A criterion to detect faces of the normalized mesh inside the Delaunay graph is proposed. This criterion is proved to provide the exact solution in 2D for points sampling a r-regular shapes with a sampling path < sin(π/8)r. In 3D, this result cannot be extended and the criterion cannot retrieve every face. A heuristic is proposed in order to complete the surface.     

Extreme value analysis within a parametric outlier detection framework

Threshold selection is a key aspect in extreme values analysis, especially when the sample size is small. The main idea underpinning this work is that extreme observations are assumed to be outliers of a specified parametric model. We propose a threshold selection method based on outlier detection using a suitable measure of surprise. Copyright © 2006 John Wiley & Sons, Ltd.