Equidistant Codes in the Grassmannian

Equidistant codes over vector spaces are considered. For $k$-dimensional subspaces over a large vector space the largest code is always a sunflower. We present several simple constructions for such codes which might produce the largest non-sunflower codes. A novel construction, based on the Pl\"{u}cker embedding, for 1-intersecting codes of $k$-dimensional subspaces over \F_q^n, $n \geq \binom{k+1}{2}$, where the code size is $\frac{q^{k+1}-1}{q-1}$ is presented. Finally, we present a related construction which generates equidistant constant rank codes with matrices of size $n \times \binom{n}{2}$ over \F_q, rank $n-1$, and rank distance $n-1$.Comment: 16 page

Distributed Storage Systems based on Equidistant Subspace Codes

Distributed storage systems based on equidistant constant dimension codes are presented. These equidistant codes are based on the Pl\"{u}cker embedding, which is essential in the repair and the reconstruction algorithms. These systems posses several useful properties such as high failure resilience, minimum bandwidth, low storage, simple algebraic repair and reconstruction algorithms, good locality, and compatibility with small fields

Microscopy Cell Segmentation via Adversarial Neural Networks

We present a novel method for cell segmentation in microscopy images which is inspired by the Generative Adversarial Neural Network (GAN) approach. Our framework is built on a pair of two competitive artificial neural networks, with a unique architecture, termed Rib Cage, which are trained simultaneously and together define a min-max game resulting in an accurate segmentation of a given image. Our approach has two main strengths, similar to the GAN, the method does not require a formulation of a loss function for the optimization process. This allows training on a limited amount of annotated data in a weakly supervised manner. Promising segmentation results on real fluorescent microscopy data are presented. The code is freely available at: https://github.com/arbellea/DeepCellSeg.gitComment: Accepted to IEEE International Symposium on Biomedical Imaging (ISBI) 201

Scale Invariant Metrics of Volumetric Datasets

Nature reveals itself in similar structures of different scales. A child and an adult share similar organs yet dramatically differ in size. Comparing the two is a challenging task to a computerized approach as scale and shape are coupled. Recently, it was shown that a local measure based on the Gaussian curvature can be used to normalize the local metric of a surface and then to extract global features and distances. In this paper we consider higher dimensions; specifically, we construct a scale invariant metric for volumetric domains which can be used in analysis of medical datasets such as computed tomography (CT) and magnetic resonance imaging (MRI)

The Valuation of Inflation-Indexed and FX Convertible Bonds

Issuing convertible bonds has become a popular way of raising capital by corporations in the last few years. An important subgroup is convertibles linked to a price index or exchange rate. In this paper we extend the convertible pricing models of Tsiveriotis and Fernandes (1998) and McConnell and Schwartz (1986) to the case of indexation of the promised payments of the convertible to a general price index or to the price of foreign exchange. The theoretical framework derived in this paper considers two sources of uncertainty: both the underlying stock price and the consumer-price-index (or equivalently foreign-currency) are stochastic, and incorporate credit risk in the analysis. The extensions of two models enable to establish upper and lower bounds for the price of the indexed convertible. We approximate the pricing equations by using Rubinstein (1994) three-dimensional binomial tree, and we describe the numerical solution. We investigate and compare the models with respect to the characteristics of the issuer, the economic environment and the security’s characteristics. Moreover, we demonstrate the usefulnes and the limitations of the pricing model by using convertible traded on the Tel- Aviv stock exchange.Convertible Bonds, Credit Spread, Pricing, Inflation, Foreign- Exchange

The changing needs with time for mineral nutrition of organic stone fruit orchard under Mediterranean conditions

Mediterranean climatic conditions for stone fruit production are good but soil fertility is low, mainly due to low (< 2.0%) soil organic matter (OM). Consequently, conventional growers apply high fertiliser rates (typically ~350 Kg N ha-1 yr-1). Our main objectives were to compare the effects of 2 modes of nitrogen nutrition, suitable for organically certified orchard vs a conventional control on tree development, yield, and some soil chemical, physical and biological properties. The orchard is located on a Grumosol soil, in the Jezreel Valley, Israel and is treated organically in terms of plant protection and weed control. The orchard was planted to peach, plums and nectarines in 1998, all grafted onto rootstock CV. 677. The tested treatments were: A. conventional control, receiving an average of 350 Kg N ha-1 yr-1; B. fertilization using cattle manure compost (40 m3ha-1 yr-1) + feather meal (1 tonne ha-1 yr-1); and C. a combination of the same amount of compost + 500 Kg feather meal ha-1 yr-1 + leguminous cover crop (Alfalfa, Medicago sativa cv. Gilboa). The cover crop was mowed 7–8 times per year. There were five replicates per treatment, of nine trees per replicate and the experiment was arranged in a randomised block design. The experiment lasted 6 years. OM content of the native soil (5–30 cm) was 1.8–2.0%. By 2003 the OM content of the conventional control treatment remained stable; that of treatment B increased by 36% while that of treatment C increased by 91%. This change was refl ected in a clear and statistically significant change in soil’s bulk density values which were 0.80, 0.73 and 0.71 gr cm3 for treatments A, B and C, respectively. At the beginning of the experiment levels of soil nitrate, phosphate and potassium ions were somewhat lower in treatments B and C than those in A but they became consistently higher after 2–3 years. The levels of these ions in the 30–60 cm soil layer followed the same trend at a 1–2 years lag. Nitrification capacity of the soils of treatments B and C were twice as high as those of treatment A. Consequently, beginning 2002 application rates of organic amendments were reduced. Yet, no decline in nutrients levels in the organic treatments could be detected over the period 2002–2004, presumably due to continued mineralisation of the OM pool. In 2004 various soil microbial characteristics (microbial counts, fl uorescein diacetate hydrolytic activity, functional richness and diversity) were determined. In all these parameters the organic treatments showed higher levels than treatment A. From the autumn of 2002 on, stem circumference are similar for all treatments and for all species. No statistical differences could be found among the treatments in any of the tested species for the 3 year cumulative yields. It can be concluded that once a significant buildup of organic matter in the soil is occurring, organic matter application can be reduced considerably, as a signifi cant soil’s potential productivity has been built