Correlation bound for distant parts of factor of IID processes

We study factor of i.i.d. processes on the $d$-regular tree for $d \geq 3$. We show that if such a process is restricted to two distant connected subgraphs of the tree, then the two parts are basically uncorrelated. More precisely, any functions of the two parts have correlation at most $k(d-1) / (\sqrt{d-1})^k$, where $k$ denotes the distance of the subgraphs. This result can be considered as a quantitative version of the fact that factor of i.i.d. processes have trivial 1-ended tails.Comment: 18 pages, 5 figure

Skin lesion classification with ensembles of deep convolutional neural networks

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Correlation bounds for distant parts of factor of IID processes

We study factor of i.i.d. processes on the d-regular tree for d ≥ 3. We show that if such a process is restricted to two distant connected subgraphs of the tree, then the two parts are basically uncorrelated. More precisely, any functions of the two parts have correlation at most , where k denotes the distance between the subgraphs. This result can be considered as a quantitative version of the fact that factor of i.i.d. processes have trivial 1-ended tails

Mutual information decay for factors of iid

This paper is concerned with factor of i.i.d. processes on the d-regular tree for d≥3. We study the mutual information of the values on two given vertices. If the vertices are neighbors (i.e., their distance is 1), then a known inequality between the entropy of a vertex and the entropy of an edge provides an upper bound for the (normalized) mutual information. In this paper we obtain upper bounds for vertices at an arbitrary distance k, of order (d−1)−k/2. Although these bounds are sharp, we also show that an interesting phenomenon occurs here: for any fixed process the rate of decay of the mutual information is much faster, essentially of order (d−1)−k

Invariant Gaussian processes and independent sets on regular graphs of large Girth

We prove that every 3-regular, n-vertex simple graph with sufficiently large girth contains an independent set of size at least 0.4361n. (The best known bound is 0.4352n.) In fact, computer simulation suggests that the bound our method provides is about 0.438n. Our method uses invariant Gaussian processes on the d-regular tree that satisfy the eigenvector equation at each vertex for a certain eigenvalue λ. We show that such processes can be approximated by i.i.d. factors provided that |λ|≤2d-1. We then use these approximations for λ=-2d-1 to produce factor of i.i.d. independent sets on regular trees. © 2014 Wiley Periodicals, Inc

Entropy inequalities for factors of iid

This paper is concerned with certain invariant random processes (called factors of IID) on infinite trees. Given such a process, one can assign entropies to different finite subgraphs of the tree. There are linear inequalities between these entropies that hold for any factor of IID process (e.g. "edge versus vertex" or "star versus edge"). These inequalities turned out to be very useful: they have several applications already, the most recent one is the Backhausz-Szegedy result on the eigenvectors of random regular graphs. We present new entropy inequalities in this paper. In fact, our approach provides a general "recipe" for how to find and prove such inequalities. Our key tool is a generalization of the edge-vertex inequality for a broader class of factor processes with fewer symmetries

Acute Sets of Exponentially Optimal Size

We present a simple construction of an acute set of size (Formula presented.) in (Formula presented.) for any dimension d. That is, we explicitly give (Formula presented.) points in the d-dimensional Euclidean space with the property that any three points form an acute triangle. It is known that the maximal number of such points is less than (Formula presented.). Our result significantly improves upon a recent construction, due to Dmitriy Zakharov, with size of order (Formula presented.) where (Formula presented.) is the golden ratio. © 2018 Springer Science+Business Media, LLC, part of Springer Natur

Origin and geodynamic relationships of the Late Miocene to Quaternary alkaline basalt volcanism in the Pannonian Basin, eastern-central Europe

Alkaline basaltic volcanism has been taking place in the Carpathian-Pannonian Region since 11 Ma and the last eruptions occurred only at 100-500 ka. It resulted in scattered low-magma volume volcanic fields located mostly at the margins of the Pannonian basin. Many of the basalts have compositions close to those of the primitve magmas and therefore can be used to constrain the conditions of the magma generation. Low degree (2-3%) melting could occur in the convective asthenosphere within the garnet-spinel transition zone. Melting started at about 100 km depth and continued usually up to the base of the lithosphere. Thus, the final melting pressure could indicate the ambient lithosphere-asthenosphere boundary. The asthenospheric mantle source regions of the basalts were heterogeneous, presumably in small scale, and included either some water or pyroxenite/eclogite lithology in addition to the fertile to slightly depleted peridotite. Based on the prevailing estimated mantle potential temperature (1300-1400oC) along with number of further observations we exclude the existence of mantle plume or plume fingers beneath this region. Instead, we propose that plate tectonic processes controlled the magma generation. The Pannonian basin acted as a thin-spot after the 20-12 Ma syn-rift phase and provided suction in the sublithospheric mantle, generating asthenospheric flow from below the adjoining thick lithospheric domains. A near vertical upwelling along the steep lithosphere-asthenosphere boundary beneath the western and northern margin of the Pannonian basin could result in decompressional melting producing low-volume melts. The youngest basalt volcanic field (Perşani) in the region is inferred to have been formed due to the dragging effect of the descending lithospheric slab beneath the Vrancea zone that could result in narrow rupture at the base of the lithosphere. Continuation of the basaltic volcanism cannot be excluded as inferred from the still fusible condition of the asthenospheric mantle. This is reinforced by the detected low-velocity seismic anomalies in the upper mantle beneath the volcanic fields

Enhancing CNNs through the use of hand-crafted features in automated fundus image classification

Eye diseases such as diabetic retinopathy and diabetic macular edema pose a major threat in today’s world as they affect a significant portion of the global population. Therefore, it is of utmost importance to develop robust solutions that can accurately detect these diseases, especially in their early stages. However, current methods, based on hand-crafted features devised by experts, are not sufficiently accurate. Several solutions have been proposed that use deep learning techniques to improve the performance of such systems. However, they ignore the highly valuable hand-crafted features, that could contribute to more accurate prediction, which underlines the significance of our research. In this paper, we revisit the problem of combining these hand-crafted features with the features extracted by neural networks with the objective of delivering more accurate predictions. We systematically study several state-of-the-art neural networks and methods and propose a number of ways to integrate them into our framework. We show that we arrived at the conclusion that it is possible to achieve significantly better results and outperform networks that do not consider hand-crafted features using the proposed methods