Maximum size binary matroids with no AG(3,2)-minor are graphic

We prove that the maximum size of a simple binary matroid of rank $r \geq 5$ with no AG(3,2)-minor is $\binom{r+1}{2}$ and characterise those matroids achieving this bound. When $r \geq 6$, the graphic matroid $M(K_{r+1})$ is the unique matroid meeting the bound, but there are a handful of smaller examples. In addition, we determine the size function for non-regular simple binary matroids with no AG(3,2)-minor and characterise the matroids of maximum size for each rank

Monte Carlo Simulation of Ising Models with Dipole Interaction

Recently, a new memory effect was found in the metamagnetic domain structure of the diluted Ising antiferromagnet $Fe_x Mg_{1-x} Cl_2$ by domain imaging with Faraday contrast. Essential for this effect is the dipole interaction. We simulate the low temperature behavior of diluted Ising-antiferromagnets by a Monte Carlo simulation considering long range interaction. The metamagnetic domain structure occurring due to the dipole interaction is investigated by graphical representation. In the model considered the antiferromagnetic state is stable for an external magnetic field smaller than a lower boundary $B_{c1}$ while for fields larger than an upper boundary $B_{c2}$ the system is in the saturated paramagnetic phase, where the spins are ferromagnetically polarized. For magnetic fields in between these two boundaries a mixed phase occurs consisting of ferromagnetic domains in an antiferromagnetic background. The position of these ferromagnetic domains is stored in the system: after a cycle in which the field is first removed and afterwards applied again the domains reappear at their original positions. The reason for this effect can be found in the frozen antiferromagnetic domain state which occurs after removing the field.Comment: Latex, 10 pages; 3 postsript-figures, compressed tar-file, uuencoded, report 10109

Role of climate change in recovery of acidified surface waters

International audienceSurface waters in Europe and North America have begun to recover in response to decreases in emissions of acidifying pollutants to the atmosphere. Variations in climate influence chemical and biological recovery. Part of the EU project Eurolimpacs (Integrated project to evaluate the impacts of global change on European freshwater ecosystems) focuses on the interactive effects of acid deposition and climate on freshwater ecosystems. This special issue of Hydrology and Earth System Sciences is devoted to this topic, and consists of studies conducted in 8 countries on aspects regarding episodes, nitrate, dissolved organic carbon, recovery and biological effects

Shape-dependent Depinning of a Domain Wall by a Magnetic Field and a Spin-Polarized Current

The effect of sample shape on the depinning of the domain wall (DW) driven by an applied magnetic field or a spin-polarized current is studied theoretically. The shape effect resulting from the modulation of the sample width (geometric pinning) can essentially affect the DW depinning. We found a good agreement between the ratios of the critical values of the magnetic field and the spin-polarized current predicted by the theory and measured in the experiment.Comment: 9 pages, 5 figure

Origin of adiabatic and non-adiabatic spin transfer torques in current-driven magnetic domain wall motion

A consistent theory to describe the correlated dynamics of quantum mechanical itinerant spins and semiclassical local magnetization is given. We consider the itinerant spins as quantum mechanical operators, whereas local moments are considered within classical Lagrangian formalism. By appropriately treating fluctuation space spanned by basis functions, including a zero-mode wave function, we construct coupled equations of motion for the collective coordinate of the center-of-mass motion and the localized zero-mode coordinate perpendicular to the domain wall plane. By solving them, we demonstrate that the correlated dynamics is understood through a hierarchy of two time scales: Boltzmann relaxation time when a non-adiabatic part of the spin-transfer torque appears, and Gilbert damping time when adiabatic part comes up.Comment: 4 pages, 2 figure

Machine Learning in XENON1T Analysis

In process of analyzing large amounts of quantitative data, it can be quite time consuming and challenging to uncover populations of interest contained amongst the background data. Therefore, the ability to partially automate the process while gaining additional insight into the interdependencies of key parameters via machine learning seems quite appealing. As of now, the primary means of reviewing the data is by manually plotting data in different parameter spaces to recognize key features, which is slow and error prone. In this experiment, many well-known machine learning algorithms were applied to a dataset to attempt to semi-automatically identify known populations, and potentially identify other features of interest such as detector artefacts. Additionally, using the results of the machine learning process it became possible to cross-check the results of the XENON1T selection cuts. Clustering algorithms were used to segment the dataset into populations, which then recursively split those into additional subpopulations. Upon capturing a subpopulation, a classifier was trained and used to predict if other data could potentially belong to the same population. From this process, it was observed that there were two clustering algorithms that were capable of identifying the electronic recoil band accurately. It was also seen that a few XENON1T selection cuts may need relaxed. These algorithms may be able to be used to tweak the cuts, or continue in search of artefacts. The process of automating the analysis stage by means of machine learning could be further extended by automating the recognition of waveforms using neural networks

The nature of the crust under Cayman Trough from gravity

This paper is not subject to U.S. copyright. The definitive version was published in Marine and Petroleum Geology 19 (2002): 971-987, doi:10.1016/S0264-8172(02)00132-0.Considerable crustal thickness variations are inferred along Cayman Trough, a slow-spreading ocean basin in the Caribbean Sea, from modeling of the gravity field. The crust to a distance of 50 km from the spreading center is only 2–3 km thick in agreement with dredge and dive results. Crustal thickness increases to ∼5.5 km at distances between 100 and 430 km west of the spreading center and to 3.5–6 km at distances between 60 and 370 km east of the spreading center. The increase in thickness is interpreted to represent serpentinization of the uppermost mantle lithosphere, rather than a true increase in the volume of accreted ocean crust. Serpentinized peridotite rocks have indeed been dredged from the base of escarpments of oceanic crust rocks in Cayman Trough. Laboratory-measured density and P-wave speed of peridotite with 40–50% serpentine are similar to the observed speed in published refraction results and to the inferred density from the model. Crustal thickness gradually increases to 7–8 km at the far ends of the trough partially in areas where sea floor magnetic anomalies were identified. Basement depth becomes gradually shallower starting 250 km west of the rise and 340 km east of the rise, in contrast to the predicted trend of increasing depth to basement from cooling models of the oceanic lithosphere. The gradual increase in apparent crustal thickness and the shallowing trend of basement depth are interpreted to indicate that the deep distal parts of Cayman Trough are underlain by highly attenuated crust, not by a continuously accreted oceanic crust.DFC was partly supported by NSF grant EAR-92-19796

Effect of Strain of Holstein-Friesian Cow and Feed System on Reproductive Performance in Seasonal-Calving Milk Production Systems Over Four Years

In Ireland most dairy farms operate seasonal calving grass-based milk production systems. Feed demand and supply are matched by having calving highly concentrated in spring. This requires high pregnancy rates within a short time following the start of mating in late April or early May, but has become increasingly difficult to achieve due to declining fertility in Irish dairy herds (Mee, 2004). In New Zealand, cows of North American Holstein-Friesian origin have poorer fertility than New Zealand Holstein-Friesians on pasture-based seasonal calving systems (Harris & Kolver, 2001). The present study sought to determine the effect of strain of Holstein-Friesian (HF) cow and feed system on reproductive performance within Irish milk production systems

Domain-wall profile in the presence of anisotropic exchange interactions: Effective on-site anisotropy

Starting from a D-dimensional XXZ ferromagnetic Heisenberg model in an hypercubic lattice, it is demonstrated that the anisotropy in the exchange coupling constant leads to a D-dependent effective on-site anisotropy interaction often ignored for D>1. As a result the effective width of the wall depends on the dimensionality of the system. It is shown that the effective one-dimensional Hamiltonian is not the one-dimensional XXZ version as assumed in previous theoretical work. We derive a new expression for the wall profile that generalizes the standard Landau-Lifshitz form. Our results are found to be in very good agreement with earlier numerical work using the Monte Carlo method. Preceding theories concerning the domain wall contribution to magnetoresistance have considered the role of D only through the modification of the density of states in the electronic band structure. This Brief Report reveals that the wall profile itself contains an additional D dependence for the case of anisotropic exchange interactions.Comment: 4 pages; new title and abstract; 1 figure comparing our results with earlier numerical work; a more general model containing the usual on-site anisotropy; new remarks and references on the following two topics: (a) experimental evidence for the existence of spin exchange anisotropy, and (b) preceding theories concerning the domain wall contribution to magnetoresistance; to appear in Phys. Rev.