A Comparison of Risk and Return Characteristics of Efficient Crop Portfolios for the Brown Soil Zones Saskatchewan and Mecklenburg, Germany

Two efficient farms are constructed for the brown soils of Saskatchewan, Canada and for Mecklenburg, Germany based on producer panels. Both farms feature highly integrated cropping systems which take advantage of cropping synergies. However, farm risk is inherently different between the two because differences in 1) climate that gives rise to very different yield risk and cost structure, and 2) EU programs which offer fixed cash payments and stable sugar beet prices. As expected, risk is much higher for the Saskatchewan case farm - it has a chance of a negative cash flow of approximately one year in five. In sharp contrast, the Mecklenburg has very little chance of generating a negative cash flow. Hence, it is easy to understand why crop insurance and other risk reducing types of programs have long been popular in Saskatchewan grain and oilseed price and yield risk make for a very real possibility of cash shortfalls on even the most efficient farm with moderate debt. On the other hand, there is little need for such risk reducing programs by efficient German farms because risk remains relatively low unless he/she is financially imprudent. Moving to higher farmland rents associated with an equilibrated land market or removing government payments increases risk considerably, but still at levels well below those of the Saskatchewan case farm.risk and return, EV model, Saskatchewan and German grain farms, Crop Production/Industries,

Wigner Functions versus WKB-Methods in Multivalued Geometrical Optics

We consider the Cauchy-problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of high-frequency asymptotics of such models is reviewed,in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods. Using Wigner measures we present an alternative approach to such asymptotic problems. We first discuss the connection of the naive WKB solutions to transport equations of Liouville type (with mono-kinetic solutions) in the prebreaking regime. Further we show that the Wigner measure approach can be used to analyze high-frequency limits in the post-breaking regime, in comparison with the traditional Fourier integral operator method. Finally we present some illustrating examples.Comment: 38 page

Optimal bilinear control of Gross-Pitaevskii equations

A mathematical framework for optimal bilinear control of nonlinear Schr\"odinger equations of Gross-Pitaevskii type arising in the description of Bose-Einstein condensates is presented. The obtained results generalize earlier efforts found in the literature in several aspects. In particular, the cost induced by the physical work load over the control process is taken into account rather then often used $L^2$- or $H^1$-norms for the cost of the control action. Well-posedness of the problem and existence of an optimal control is proven. In addition, the first order optimality system is rigorously derived. Also a numerical solution method is proposed, which is based on a Newton type iteration, and used to solve several coherent quantum control problems.Comment: 30 pages, 14 figure

Depth of interocular suppression associated with continuous flash suppression, flash suppression, and binocular rivalry

When conflicting images are presented to the corresponding regions of the two eyes, only one image may be consciously perceived. In binocular rivalry (BR), two images alternate in phenomenal visibility; even a salient image is eventually suppressed by an image of low saliency. Recently, N. Tsuchiya and C. Koch (2005) reported a technique called continuous flash suppression (CFS), extending the suppression duration more than 10-fold. Here, we investigated the depth of this prolonged form of interocular suppression as well as conventional BR and flash suppression (FS) using a probe detection task. Compared to monocular viewing condition, CFS elevated detection thresholds more than 20-fold, whereas BR did so by 3-fold. In subsequent experiments, we dissected CFS into several components. By manipulating the number and timing of flashes with respect to the probe, we found that the stronger suppression in CFS is not due to summation between BR and FS but is caused by the summation of the suppression due to multiple flashes. Our results support the view that CFS is not a stronger version of BR but is due to the accumulated suppressive effects of multiple flashes

Damage Spreading and Criticality in Finite Random Dynamical Networks

We systematically study and compare damage spreading at the sparse percolation (SP) limit for random boolean and threshold networks with perturbations that are independent of the network size $N$. This limit is relevant to information and damage propagation in many technological and natural networks. Using finite size scaling, we identify a new characteristic connectivity $K_s$, at which the average number of damaged nodes $\bar d$, after a large number of dynamical updates, is independent of $N$. Based on marginal damage spreading, we determine the critical connectivity $K_c^{sparse}(N)$ for finite $N$ at the SP limit and show that it systematically deviates from $K_c$, established by the annealed approximation, even for large system sizes. Our findings can potentially explain the results recently obtained for gene regulatory networks and have important implications for the evolution of dynamical networks that solve specific computational or functional tasks.Comment: 4 pages, 4 eps figure

Augmented Mitotic Cell Count using Field Of Interest Proposal

Histopathological prognostication of neoplasia including most tumor grading systems are based upon a number of criteria. Probably the most important is the number of mitotic figures which are most commonly determined as the mitotic count (MC), i.e. number of mitotic figures within 10 consecutive high power fields. Often the area with the highest mitotic activity is to be selected for the MC. However, since mitotic activity is not known in advance, an arbitrary choice of this region is considered one important cause for high variability in the prognostication and grading. In this work, we present an algorithmic approach that first calculates a mitotic cell map based upon a deep convolutional network. This map is in a second step used to construct a mitotic activity estimate. Lastly, we select the image segment representing the size of ten high power fields with the overall highest mitotic activity as a region proposal for an expert MC determination. We evaluate the approach using a dataset of 32 completely annotated whole slide images, where 22 were used for training of the network and 10 for test. We find a correlation of r=0.936 in mitotic count estimate.Comment: 6 pages, submitted to BVM 2019 (bvm-workshop.org

Emergence of slow-switching assemblies in structured neuronal networks

Unraveling the interplay between connectivity and spatio-temporal dynamics in neuronal networks is a key step to advance our understanding of neuronal information processing. Here we investigate how particular features of network connectivity underpin the propensity of neural networks to generate slow-switching assembly (SSA) dynamics, i.e., sustained epochs of increased firing within assemblies of neurons which transition slowly between different assemblies throughout the network. We show that the emergence of SSA activity is linked to spectral properties of the asymmetric synaptic weight matrix. In particular, the leading eigenvalues that dictate the slow dynamics exhibit a gap with respect to the bulk of the spectrum, and the associated Schur vectors exhibit a measure of block-localization on groups of neurons, thus resulting in coherent dynamical activity on those groups. Through simple rate models, we gain analytical understanding of the origin and importance of the spectral gap, and use these insights to develop new network topologies with alternative connectivity paradigms which also display SSA activity. Specifically, SSA dynamics involving excitatory and inhibitory neurons can be achieved by modifying the connectivity patterns between both types of neurons. We also show that SSA activity can occur at multiple timescales reflecting a hierarchy in the connectivity, and demonstrate the emergence of SSA in small-world like networks. Our work provides a step towards understanding how network structure (uncovered through advancements in neuroanatomy and connectomics) can impact on spatio-temporal neural activity and constrain the resulting dynamics.Comment: The first two authors contributed equally -- 18 pages, including supplementary material, 10 Figures + 2 SI Figure

Thresholds for Linear Optics Quantum Computing with Photon Loss at the Detectors

We calculate the error threshold for the linear optics quantum computing proposal by Knill, Laflamme and Milburn [Nature 409, pp. 46--52 (2001)] under an error model where photon detectors have efficiency <100% but all other components -- such as single photon sources, beam splitters and phase shifters -- are perfect and introduce no errors. We make use of the fact that the error model induced by the lossy hardware is that of an erasure channel, i.e., the error locations are always known. Using a method based on a Markov chain description of the error correction procedure, our calculations show that, with the 7 qubit CSS quantum code, the gate error threshold for fault tolerant quantum computation is bounded below by a value between 1.78% and 11.5% depending on the construction of the entangling gates.Comment: 7 pages, 6 figure