Convex subquivers and the finitistic dimension

Let \cQ be a quiver and $K$ a field. We study the interrelationship of homological properties of algebras associated to convex subquivers of \cQ and quotients of the path algebra K\cQ. We introduce the homological heart of \cQ which is a particularly nice convex subquiver of \cQ. For any algebra of the form K\cQ/I, the algebra associated to K\cQ/I and the homological heart have similar homological properties. We give an application showing that the finitistic dimension conjecture need only be proved for algebras with path connected quivers

Stratifying systems over hereditary algebras

This paper deals with stratifying systems over hereditary algebras. In the case of tame hereditary algebras we obtain a bound for the size of the stratifying systems composed only by regular modules and we conclude that stratifying systems can not be complete. For wild hereditary algebras with more than 2 vertices we show that there exists a complete stratifying system whose elements are regular modules. In the other case, we conclude that there are no stratifing system over them with regular modules. In one example we built all the stratifying systems, with a specific form, having maximal number of regular summads

dd-Koszul algebras, 2-dd determined algebras and 2-dd-Koszul algebras

The relationship between an algebra and its associated monomial algebra is investigated when at least one of the algebras is $d$-Koszul. It is shown that an algebra which has a reduced \grb basis that is composed of homogeneous elements of degree $d$ is $d$-Koszul if and only if its associated monomial algebra is $d$-Koszul. The class of 2-$d$-determined algebras and the class 2-$d$-Koszul algebras are introduced. In particular, it shown that 2-$d$-determined monomial algebras are 2-$d$-Koszul algebras and the structure of the ideal of relations of such an algebra is completely determined

Efficient tensor completion for color image and video recovery: Low-rank tensor train

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor train (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via tensor train (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher-orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.Comment: Submitted to the IEEE Transactions on Image Processing. arXiv admin note: substantial text overlap with arXiv:1601.0108

Concatenated image completion via tensor augmentation and completion

This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor, applying a dimensionality augmentation technique to the tensor, utilizing a tensor completion algorithm for recovering its missing entries, and finally extracting the recovered image from the tensor. The solution relies on two key components that have been recently proposed to take advantage of the tensor train (TT) rank: A tensor augmentation tool called ket augmentation (KA) that represents a low-order tensor by a higher-order tensor, and the algorithm tensor completion by parallel matrix factorization via tensor train (TMac-TT), which has been demonstrated to outperform state-of-the-art tensor completion algorithms. Simulation results for color image recovery show the clear advantage of our framework against current state-of-the-art tensor completion algorithms.Comment: 7 pages, 6 figures, submitted to ICSPCS 201

Spherically-symmetric solutions in general relativity

We present a tetrad-based method for solving the Einstein field equations for spherically-symmetric systems and compare it with the widely-used Lema\^itre-Tolman-Bondi (LTB) model. In particular, we focus on the issues of gauge ambiguity and the use of comoving versus 'physical' coordinate systems. We also clarify the correspondences between the two approaches, and illustrate their differences by applying them to the classic examples of the Schwarzschild and Friedmann-Robertson-Walker spacetimes. We demonstrate that the tetrad-based method does not suffer from the gauge freedoms inherent to the LTB model, naturally accommodates non-zero pressure and has a more transparent physical interpretation. We further apply our tetrad-based method to a generalised form of 'Swiss cheese' model, which consists of an interior spherical region surrounded by a spherical shell of vacuum that is embedded in an exterior background universe. In general, we allow the fluid in the interior and exterior regions to support pressure, and do not demand that the interior region be compensated. We pay particular attention to the form of the solution in the intervening vacuum region and verify the validity of Birkhoff's theorem at both the metric and tetrad level. We then reconsider critically the original theoretical arguments underlying the so-called $R_h = ct$ cosmological model, which has recently received considerable attention. These considerations in turn illustrate the interesting behaviour of a number of 'horizons' in general cosmological models.Comment: 21 pages, 3 figures, submitted to Physical Review

Tracking objects using 3D object proposals

3D object proposals, quickly detected regions in a 3D scene that likely contain an object of interest, are an effective approach to improve the computational efficiency and accuracy of the object detection framework. In this work, we propose a novel online method that uses our previously developed 3D object proposals, in a RGB-D video sequence, to match and track static objects in the scene using shape matching. Our main observation is that depth images provide important information about the geometry of the scene that is often ignored in object matching techniques. Our method takes less than a second in MATLAB on the UW-RGBD scene dataset on a single thread CPU and thus, has potential to be used in low-power chips in Unmanned Aerial Vehicles (UAVs), quadcopters, and drones.Comment: 4 pages, 4 figures, published in APSIPA 201

Correlating Cellular Features with Gene Expression using CCA

To understand the biology of cancer, joint analysis of multiple data modalities, including imaging and genomics, is crucial. The involved nature of gene-microenvironment interactions necessitates the use of algorithms which treat both data types equally. We propose the use of canonical correlation analysis (CCA) and a sparse variant as a preliminary discovery tool for identifying connections across modalities, specifically between gene expression and features describing cell and nucleus shape, texture, and stain intensity in histopathological images. Applied to 615 breast cancer samples from The Cancer Genome Atlas, CCA revealed significant correlation of several image features with expression of PAM50 genes, known to be linked to outcome, while Sparse CCA revealed associations with enrichment of pathways implicated in cancer without leveraging prior biological understanding. These findings affirm the utility of CCA for joint phenotype-genotype analysis of cancer.Comment: To appear at IEEE International Symposium on Biomedical Imaging (ISBI) 201

An alternative approach to modelling a cosmic void and its effect on the cosmic microwave background

We apply our tetrad-based approach for constructing spherically-symmetric solutions in general relativity to modelling a void, and compare it with the standard Lema\^itre-Tolman-Bondi (LTB) formalism. In particular, we construct models for the void observed in the direction of Draco in the WISE-2MASS galaxy survey, and a corresponding cosmic microwave background (CMB) temperature decrement in the Planck data in the same direction. We find that the present-day density and velocity profiles of the void are not well constrained by the existing data, so that void models produced from the two approaches can differ substantially while remaining broadly consistent with the observations. We highlight the importance of considering the velocity as well as the density profile in constraining voids.Comment: 12 pages, 14 figures, submitted to MNRA

Light curves of a shock-breakout material and a relativistic off-axis jet from a Binary Neutron Star system

Binary neutron star mergers are believed to eject significant masses with a diverse range of velocities. Once these ejected materials begin to be decelerated by a homogeneous medium, relativistic electrons are mainly cooled down by synchrotron radiation, generating a multiwavelength long-lived afterglow. Analytic and numerical methods illustrate that the outermost matter, the merger shock-breakout material, can be parametrized by power-law velocity distributions $\propto \left(\beta_{\rm c}\Gamma \right)^{-\alpha_s}$. Considering that the shock-breakout material is moving on-axis towards the observer and the relativistic jet off-axis, we compute the light curves during the relativistic and the lateral expansion phase. As a particular case, we successfully describe the X-ray, optical and radio light curves alongside the spectral energy distribution from the recently discovered gravitational-wave transient GW170817, when the merger shock-breakout material moves with mildly relativistic velocities near-Newtonian phase and the jet with relativistic velocities. Future electromagnetic counterpart observations of this binary system could be able to evaluate different properties of these light curves.Comment: 19 pages, 8 figures and one table. The model of an off-axis jet was introduced to fit the multiwavelength data. Accepted for publication in Ap