A Characterization of Deterministic Sampling Patterns for Low-Rank Matrix Completion

Low-rank matrix completion (LRMC) problems arise in a wide variety of applications. Previous theory mainly provides conditions for completion under missing-at-random samplings. This paper studies deterministic conditions for completion. An incomplete $d \times N$ matrix is finitely rank-$r$ completable if there are at most finitely many rank-$r$ matrices that agree with all its observed entries. Finite completability is the tipping point in LRMC, as a few additional samples of a finitely completable matrix guarantee its unique completability. The main contribution of this paper is a deterministic sampling condition for finite completability. We use this to also derive deterministic sampling conditions for unique completability that can be efficiently verified. We also show that under uniform random sampling schemes, these conditions are satisfied with high probability if $O(\max\{r,\log d\})$ entries per column are observed. These findings have several implications on LRMC regarding lower bounds, sample and computational complexity, the role of coherence, adaptive settings and the validation of any completion algorithm. We complement our theoretical results with experiments that support our findings and motivate future analysis of uncharted sampling regimes.Comment: This update corrects an error in version 2 of this paper, where we erroneously assumed that columns with more than r+1 observed entries would yield multiple independent constraint

Detection of Very-High Energy Gamma-Rays from the BL Lac Object PG 1553+113 with the MAGIC Telescope

The MAGIC telescope has observed very-high energy gamma-ray emission from the BL Lac object PG 1553+113 in 2005 and 2006 at an overall significance is 8.8 sigma. The light curve shows no significant flux variations on a daily timescale. The flux level during 2005 was, however, significantly higher as compared to 2006. The differential energy spectrum between approx. 90 GeV and 500 GeV is well described by a power law with a spectral index of -4.2+-0.3. The photon energy spectrum and spectral modeling allow to pose upper limits of z=0.74 and z=0.56, respectively, on the yet undetermined redshift of PG 1553+113. Recent VLT observations of this blazar show featureless spectra in the near-IR, thus no direct redshift could be determined from these measurements.Comment: 4 pages, 4 figures, to appear in the proceedings of the 30th International Cosmic Ray Conference, Merida, July 200

The first record of Macrobiotus vladimiri Bertolani, Biserov, Rebecchi & Cesari, 2011 (Tardigrada : Eutardigrada : Macrobiotidae : hufelandi group) from Poland

Tardigrade studies in Poland have been carried out for more than a century and to date, 102 species have been reported from this central European country. This constitutes nearly 9% of all known species within the phylum. Although previous studies have been thorough, a number of taxa now known to belong to species complexes have been treated in only a very general way. One such complex is the Macrobiotus hufelandi group, which has a worldwide distribution. To date, only three hufelandi group species have been recorded from Poland: M. hufelandi hufelandi C.A.S. Schultze, 1834; M. macrocalix Bertolani & Rebecchi, 1993; and M. polonicus Pilato, Kaczmarek, Michalczyk & Lisi, 2003. Here we first report M. vladimiri Bertolani, Biserov, Rebecchi & Cesari, 2011 from Poland. Moreover, we provide new morphometric data for the type series of the species

Synchronization of dynamical hypernetworks: dimensionality reduction through simultaneous block-diagonalization of matrices

We present a general framework to study stability of the synchronous solution for a hypernetwork of coupled dynamical systems. We are able to reduce the dimensionality of the problem by using simultaneous block-diagonalization of matrices. We obtain necessary and sufficient conditions for stability of the synchronous solution in terms of a set of lower-dimensional problems and test the predictions of our low-dimensional analysis through numerical simulations. Under certain conditions, this technique may yield a substantial reduction of the dimensionality of the problem. For example, for a class of dynamical hypernetworks analyzed in the paper, we discover that arbitrarily large networks can be reduced to a collection of subsystems of dimensionality no more than 2. We apply our reduction techique to a number of different examples, including a class of undirected unweighted hypermotifs of three nodes.Comment: 9 pages, 6 figures, accepted for publication in Phys. Rev.

Predicting the outcomes of treatment to eradicate the latent reservoir for HIV-1

Massive research efforts are now underway to develop a cure for HIV infection, allowing patients to discontinue lifelong combination antiretroviral therapy (ART). New latency-reversing agents (LRAs) may be able to purge the persistent reservoir of latent virus in resting memory CD4+ T cells, but the degree of reservoir reduction needed for cure remains unknown. Here we use a stochastic model of infection dynamics to estimate the efficacy of LRA needed to prevent viral rebound after ART interruption. We incorporate clinical data to estimate population-level parameter distributions and outcomes. Our findings suggest that approximately 2,000-fold reductions are required to permit a majority of patients to interrupt ART for one year without rebound and that rebound may occur suddenly after multiple years. Greater than 10,000-fold reductions may be required to prevent rebound altogether. Our results predict large variation in rebound times following LRA therapy, which will complicate clinical management. This model provides benchmarks for moving LRAs from the lab to the clinic and can aid in the design and interpretation of clinical trials. These results also apply to other interventions to reduce the latent reservoir and can explain the observed return of viremia after months of apparent cure in recent bone marrow transplant recipients and an immediately-treated neonate.Comment: 8 pages main text (4 figures). In PNAS Early Edition http://www.pnas.org/content/early/2014/08/05/1406663111. Ancillary files: SI, 24 pages SI (7 figures). File .htm opens a browser-based application to calculate rebound times (see SI). Or, the .cdf file can be run with Mathematica. The most up-to-date version of the code is available at http://www.danielrosenbloom.com/reboundtimes

Breaking the Architecture Barrier: A Method for Efficient Knowledge Transfer Across Networks

Transfer learning is a popular technique for improving the performance of neural networks. However, existing methods are limited to transferring parameters between networks with same architectures. We present a method for transferring parameters between neural networks with different architectures. Our method, called DPIAT, uses dynamic programming to match blocks and layers between architectures and transfer parameters efficiently. Compared to existing parameter prediction and random initialization methods, it significantly improves training efficiency and validation accuracy. In experiments on ImageNet, our method improved validation accuracy by an average of 1.6 times after 50 epochs of training. DPIAT allows both researchers and neural architecture search systems to modify trained networks and reuse knowledge, avoiding the need for retraining from scratch. We also introduce a network architecture similarity measure, enabling users to choose the best source network without any training.Comment: 23 pages, 16 figure

Integracyjna rola muzyki w Kościele na podstawie nauczania papieży Benedykta XVI i Franciszka

In the liturgy of the Church, music, among other things, is a factor that supports a living relationship with God and unites believers. Pope-emeritus Benedict XVI and Pope Francis for the modern Church are guides and supreme guardians who point out the sense of maintaining the proper level of music in the Church. In his search for the right ways of church music, Benedict XVI does not deal thoroughly with musicological issues, but from the point of view of a theologian, he looks for points of contact between faith and art. For the pope, the musical expression of praise to God remains in harmony with the Christian dogma of the incarnation, which is realized in the Church and the sacraments. Music is one of the elements that create a space for the continuation of the events of the incarnation. Submitting to integration, it purifies the human being, liberates and inclines thoughts towards God. The current Pope Francis constantly recognizes music in the Church as a unifying element of the community and as a means of proclaiming the faith. He considers it necessary to constantly renew liturgical music and chant, especially in terms of quality, so that Church music is fully inculturated in the artistic and musical language of today. Getting to know the richness of music and traditions of different parts of the world helps to preserve the tradition of the Church in the modern world and to enrich it with what the modern times bring. Such an updating builds a living community which by listening or performing music unites diversity in one song of praise to God. The theological perspective on the meaning of sacred music and its qualities allows for the proper use of music as an integrating factor for both the individual believer and the whole community. The theological perspective on the importance of sacred music and its qualities helps to make the right use of music as an integrating factor for the individual believer and the community