Itinerant ferromagnetism and intrinsic anomalous Hall effect in amorphous iron-germanium

The amorphous iron-germanium system (a-FexGe1-x) lacks long-range structural order and hence lacks a meaningful Brillouin zone. The magnetization of a-FexGe1-x is well explained by the Stoner model for Fe concentrations x above the onset of magnetic order around x=0.4, indicating that the local order of the amorphous structure preserves the spin-split density of states of the Fe-3d states sufficiently to polarize the electronic structure despite k being a bad quantum number. Measurements reveal an enhanced anomalous Hall resistivity ρxyAH relative to crystalline FeGe; this ρxyAH is compared to density-functional theory calculations of the anomalous Hall conductivity to resolve its underlying mechanisms. The intrinsic mechanism, typically understood as the Berry curvature integrated over occupied k states but shown here to be equivalent to the density of curvature integrated over occupied energies in aperiodic materials, dominates the anomalous Hall conductivity of a-FexGe1-x (0.38≤x≤0.61). The density of curvature is the sum of spin-orbit correlations of local orbital states and can hence be calculated with no reference to k space. This result and the accompanying Stoner-like model for the intrinsic anomalous Hall conductivity establish a unified understanding of the underlying physics of the anomalous Hall effect in both crystalline and disordered systems

Tbr1 instructs laminar patterning of retinal ganglion cell dendrites.

Visual information is delivered to the brain by >40 types of retinal ganglion cells (RGCs). Diversity in this representation arises within the inner plexiform layer (IPL), where dendrites of each RGC type are restricted to specific sublaminae, limiting the interneuronal types that can innervate them. How such dendritic restriction arises is unclear. We show that the transcription factor Tbr1 is expressed by four mouse RGC types with dendrites in the outer IPL and is required for their laminar specification. Loss of Tbr1 results in elaboration of dendrites within the inner IPL, while misexpression in other cells retargets their neurites to the outer IPL. Two transmembrane molecules, Sorcs3 and Cdh8, act as effectors of the Tbr1-controlled lamination program. However, they are expressed in just one Tbr1+ RGC type, supporting a model in which a single transcription factor implements similar laminar choices in distinct cell types by recruiting partially non-overlapping effectors

3DQ: Compact Quantized Neural Networks for Volumetric Whole Brain Segmentation

Model architectures have been dramatically increasing in size, improving performance at the cost of resource requirements. In this paper we propose 3DQ, a ternary quantization method, applied for the first time to 3D Fully Convolutional Neural Networks (F-CNNs), enabling 16x model compression while maintaining performance on par with full precision models. We extensively evaluate 3DQ on two datasets for the challenging task of whole brain segmentation. Additionally, we showcase our method's ability to generalize on two common 3D architectures, namely 3D U-Net and V-Net. Outperforming a variety of baselines, the proposed method is capable of compressing large 3D models to a few MBytes, alleviating the storage needs in space critical applications.Comment: Accepted to MICCAI 201

Deep Learning networks with p-norm loss layers for spatial resolution enhancement of 3D medical images

Thurnhofer-Hemsi K., López-Rubio E., Roé-Vellvé N., Molina-Cabello M.A. (2019) Deep Learning Networks with p-norm Loss Layers for Spatial Resolution Enhancement of 3D Medical Images. In: Ferrández Vicente J., Álvarez-Sánchez J., de la Paz López F., Toledo Moreo J., Adeli H. (eds) From Bioinspired Systems and Biomedical Applications to Machine Learning. IWINAC 2019. Lecture Notes in Computer Science, vol 11487. Springer, ChamNowadays, obtaining high-quality magnetic resonance (MR) images is a complex problem due to several acquisition factors, but is crucial in order to perform good diagnostics. The enhancement of the resolution is a typical procedure applied after the image generation. State-of-the-art works gather a large variety of methods for super-resolution (SR), among which deep learning has become very popular during the last years. Most of the SR deep-learning methods are based on the min- imization of the residuals by the use of Euclidean loss layers. In this paper, we propose an SR model based on the use of a p-norm loss layer to improve the learning process and obtain a better high-resolution (HR) image. This method was implemented using a three-dimensional convolutional neural network (CNN), and tested for several norms in order to determine the most robust t. The proposed methodology was trained and tested with sets of MR structural T1-weighted images and showed better outcomes quantitatively, in terms of Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), and the restored and the calculated residual images showed better CNN outputs.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

An EPTAS for Scheduling on Unrelated Machines of Few Different Types

In the classical problem of scheduling on unrelated parallel machines, a set of jobs has to be assigned to a set of machines. The jobs have a processing time depending on the machine and the goal is to minimize the makespan, that is the maximum machine load. It is well known that this problem is NP-hard and does not allow polynomial time approximation algorithms with approximation guarantees smaller than $1.5$ unless P$=$NP. We consider the case that there are only a constant number $K$ of machine types. Two machines have the same type if all jobs have the same processing time for them. This variant of the problem is strongly NP-hard already for $K=1$. We present an efficient polynomial time approximation scheme (EPTAS) for the problem, that is, for any $\varepsilon > 0$ an assignment with makespan of length at most $(1+\varepsilon)$ times the optimum can be found in polynomial time in the input length and the exponent is independent of $1/\varepsilon$. In particular we achieve a running time of $2^{\mathcal{O}(K\log(K) \frac{1}{\varepsilon}\log^4 \frac{1}{\varepsilon})}+\mathrm{poly}(|I|)$, where $|I|$ denotes the input length. Furthermore, we study three other problem variants and present an EPTAS for each of them: The Santa Claus problem, where the minimum machine load has to be maximized; the case of scheduling on unrelated parallel machines with a constant number of uniform types, where machines of the same type behave like uniformly related machines; and the multidimensional vector scheduling variant of the problem where both the dimension and the number of machine types are constant. For the Santa Claus problem we achieve the same running time. The results are achieved, using mixed integer linear programming and rounding techniques

The inverse along a product and its applications

In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and expressions of the inverse along a matrix.The authors are highly grateful to the referee for valuable comments which led to improvements of the paper. In particular, Remarks 3.2 and 3.4 were suggested to the authors by the referee. The first author is grateful to China Scholarship Council for supporting him to purse his further study in University of Minho, Portugal. Pedro Patr´ıcio and Yulin Zhang were financed by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the “Funda¸c˜ao para a Ciˆencia e a Tecnologia”, through the Project PEst-OE/MAT/UI0013/2014. Jianlong Chen and Huihui Zhu were supported by the National Natural Science Foundation of China (No. 11201063 and No. 11371089), the Specialized Research Fund for the Doctoral Program of Higher Education (No. 20120092110020), the Natural Science Foundation of Jiangsu Province (No. BK20141327), the Foundation of Graduate Innovation Program of Jiangsu Province(No. CXLX13-072), the Scientific Research Foundation of Graduate School of Southeast University and the Fundamental Research Funds for the Central Universities (No. 22420135011)

A Technique for Obtaining True Approximations for kk-Center with Covering Constraints

There has been a recent surge of interest in incorporating fairness aspects into classical clustering problems. Two recently introduced variants of the $k$-Center problem in this spirit are Colorful $k$-Center, introduced by Bandyapadhyay, Inamdar, Pai, and Varadarajan, and lottery models, such as the Fair Robust $k$-Center problem introduced by Harris, Pensyl, Srinivasan, and Trinh. To address fairness aspects, these models, compared to traditional $k$-Center, include additional covering constraints. Prior approximation results for these models require to relax some of the normally hard constraints, like the number of centers to be opened or the involved covering constraints, and therefore, only obtain constant-factor pseudo-approximations. In this paper, we introduce a new approach to deal with such covering constraints that leads to (true) approximations, including a $4$-approximation for Colorful $k$-Center with constantly many colors---settling an open question raised by Bandyapadhyay, Inamdar, Pai, and Varadarajan---and a $4$-approximation for Fair Robust $k$-Center, for which the existence of a (true) constant-factor approximation was also open. We complement our results by showing that if one allows an unbounded number of colors, then Colorful $k$-Center admits no approximation algorithm with finite approximation guarantee, assuming that $\mathrm{P} \neq \mathrm{NP}$. Moreover, under the Exponential Time Hypothesis, the problem is inapproximable if the number of colors grows faster than logarithmic in the size of the ground set

Capacitated Center Problems with Two-Sided Bounds and Outliers

In recent years, the capacitated center problems have attracted a lot of research interest. Given a set of vertices $V$, we want to find a subset of vertices $S$, called centers, such that the maximum cluster radius is minimized. Moreover, each center in $S$ should satisfy some capacity constraint, which could be an upper or lower bound on the number of vertices it can serve. Capacitated $k$-center problems with one-sided bounds (upper or lower) have been well studied in previous work, and a constant factor approximation was obtained. We are the first to study the capacitated center problem with both capacity lower and upper bounds (with or without outliers). We assume each vertex has a uniform lower bound and a non-uniform upper bound. For the case of opening exactly $k$ centers, we note that a generalization of a recent LP approach can achieve constant factor approximation algorithms for our problems. Our main contribution is a simple combinatorial algorithm for the case where there is no cardinality constraint on the number of open centers. Our combinatorial algorithm is simpler and achieves better constant approximation factor compared to the LP approach