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

Editorial: Nck has a knack for T cell differentiation

Peer Reviewe

Phase 1 repolarization rate defines Ca2+ dynamics and contractility on intact mouse hearts.

In the heart, Ca2+ influx through L-type Ca2+ channels triggers Ca2+ release from the sarcoplasmic reticulum. In most mammals, this influx occurs during the ventricular action potential (AP) plateau phase 2. However, in murine models, the influx through L-type Ca2+ channels happens in early repolarizing phase 1. The aim of this work is to assess if changes in the open probability of 4-aminopyridine (4-AP)-sensitive Kv channels defining the outward K+ current during phase 1 can modulate Ca2+ currents, Ca2+ transients, and systolic pressure during the cardiac cycle in intact perfused beating hearts. Pulsed local-field fluorescence microscopy and loose-patch photolysis were used to test the hypothesis that a decrease in a transient K+ current (Ito) will enhance Ca2+ influx and promote a larger Ca2+ transient. Simultaneous recordings of Ca2+ transients and APs by pulsed local-field fluorescence microscopy and loose-patch photolysis showed that a reduction in the phase 1 repolarization rate increases the amplitude of Ca2+ transients due to an increase in Ca2+ influx through L-type Ca2+ channels. Moreover, 4-AP induced an increase in the time required for AP to reach 30% repolarization, and the amplitude of Ca2+ transients was larger in epicardium than endocardium. On the other hand, the activation of Ito with NS5806 resulted in a reduction of Ca2+ current amplitude that led to a reduction of the amplitude of Ca2+ transients. Finally, the 4-AP effect on AP phase 1 was significantly smaller when the L-type Ca2+ current was partially blocked with nifedipine, indicating that the phase 1 rate of repolarization is defined by the competition between an outward K+ current and an inward Ca2+ current

On the \phi(1020)f_0(980) S-wave scattering and the Y(2175) resonance

We have studied the \phi(1020)f_0(980) S-wave scattering at energies around threshold employing chiral Lagrangians coupled to vector mesons through minimal coupling. The interaction kernel is obtained by considering the f_0(980) as a K\bar{K} bound state. The Y(2175) resonance is generated in this approach by the self-interactions between the \phi(1020) and the f_0(980) resonances. We are able to describe the e^+e^-\to \phi(1020)f_0(980) recent scattering data to test experimentally our scattering amplitudes, concluding that the Y(2175) resonance has a large \phi(1020)f_0(980) meson-meson component.Comment: 20 pages, 8 figure

Multiscale modelling of vascular tumour growth in 3D: the roles of domain size & boundary condition

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour

Executing the Will of the Voters?: A Roadmap to Mend or End the California Legislature’s Multi-Billion-Dollar Death Penalty Debacle

Since reinstating the death penalty in 1978, California taxpayers have spent roughly $4 billion to fund a dysfunctional death penalty system that has carried out no more than 13 executions. The current backlog of death penalty cases is so severe that most of the 714 prisoners now on death row will wait well over 20 years before their cases are resolved. Many of these condemned inmates will thus languish on death row for decades, only to die of natural causes while still waiting for their cases to be resolved. Despite numerous warnings of the deterioration of California’s capital punishment system and its now imminent collapse, the Legislature has repeatedly failed to enact measures that would improve this death row deadlock. At the same time, voters have continued to expand the death penalty through the direct voter initiative process to increase the number of death-eligible crimes. This Article uncovers the true costs of administering the death penalty in California by tracing how much taxpayers are spending for death penalty trials versus non–death penalty trials and for costs incurred due to the delay from the initial sentence of death to the execution. In addition, the Article examines how the voter initiative process has misled voters into agreeing to the wasteful expenditure of billions of dollars on a system that has been ineffective in carrying out punishment against those who commit the worst of crimes. Our research reveals that in every proposition expanding the list of deatheligible crimes between 1978 and 2000, the information provided by the Legislative Analyst’s Office in the Voter Information Guides told voters that the fiscal impact of these initiatives would be “none,” “unknown,” “indeterminable,” or “minor.” Relying, at least in part, on this information, Californians have used the voter initiative process to enact “tough on crime” laws that, without adequate funding from the Legislature to create an effective capital punishment system, have wasted immense taxpayer resources and created increasingly serious due process problems. Finally, this Article analyzes corrective measures that the Legislature could take to reduce the death row backlog, and proposes several voter initiatives that California voters may wish to consider if the Legislature continues to ignore the problem. It is the authors’ view that unless California voters want to tolerate the continued waste of billions of tax dollars on the state’s now-defunct death penalty system, they must either demand meaningful reforms to ensure that the system is administered in a fair and effective manner or, if they do not want to be taxed to fund the needed reforms, they must recognize that the only alternative is to abolish the death penalty and replace it with a sentence of life imprisonment without the possibility of parole

Dynamic factors for underpasses in high speed train lines

Los pasos inferiores son muy numerosos en las líneas de ferrocarril. Su comportamiento dinámico ha recibido mucha menos atención que el de otras estructuras como los puentes, pero su elevado número hace que su estudio sea económicamente relevante con vista a optimizar su forma, manteniendo la seguridad. El proyecto de puentes según el Eurocódigo incluye comprobaciones de estados límite de tensiones bajo carga dinámica. En el caso de pasos inferiores, las comprobaciones pueden resultar tan costosas como aquellas de puentes, pese a que su coste es mucho menor. Por tanto, se impone la búsqueda de unas reglas de cálculo simplificado que pongan en consonancia el coste de la estructura con el esfuerzo necesario para su proyecto. Este artículo propone un conjunto de reglas basadas en un estudio paramétrico.Underpasses are common in modern railway lines. Wildlife corridors and drainage conduits often fall into this category of partially buried structures. Their dynamic behavior has received far less attention than that of other structures such as bridges, but their large number makes their study an interesting challenge from the viewpoint of safety and cost savings. The bridge design rules in accordance with the Eurocode involve checks on stresses according to dynamic loading. In the case of underpasses, those checks may be as much as those for bridges. Therefore, simplified design rules may align the design effort with their cost. Such a set of rules may provide estimations of response parameters based on the key parameters influencing the result. This paper contains a proposal based on a parametric study.Peer Reviewe

Structure and Composition of Rhodolith Beds from the Sergipe-Alagoas Basin (NE Brazil, Southwestern Atlantic)

This study was funded by the CoordenacAo de Aperfeicoamento de Pessoal de Nivel Superior (CAPES-Finance Code 001) and FundacAo de Amparo a Pesquisa do Estado do Rio de Janeiro- Jovem Cientista do Nosso Estado (FAPERJ/JCNE-Fellow to Leonardo T. Salgado).Rhodolith beds are biogenic benthic habitats mainly formed by unattached, non-geniculate coralline algae, which can be inhabited by many associated species. The Brazilian continental shelf encompasses the largest continuous rhodolith bed in the world. This study was based on samples obtained from seven sites and videos taken by a Remotely Operated Vehicle (ROV) at four transects off the Sergipe-Alagoas Coast on the northeast Brazilian shelf. ROV operations and bottom trawl sampling revealed the occurrence of rhodolith beds between 25 and 54 m depths. At the shallower depths, fruticose (branching) rhodoliths (maërl) appear in troughs of ripples, and other non-branching rhodoliths occur associated with corals and sponge patches surrounded by bioclastic sand. Rhodoliths also occur in patches from 30 to 39 m depth; some are fused, forming larger, complex tridimensional structures. At deeper depths, from 40 to 54 m, the abundance of rhodoliths increases and occur associated with fleshy macroalgae on a smooth seafloor; some rhodoliths are fused into complex structures, locally some are fruticose (maërl), and others are partially buried by fine-grained sediment. The collected rhodoliths vary from fruticose in two sites to encrusting to lumpy, concentric and boxwork nodules in the rest; their size ranges from small (<1.5 cm) to large (~6 cm) and are mostly sub-spheroidal to spheroidal. A total of 16 red algal morpho-taxa were identified in the study sites. Two phases of growth can be distinguished in some rhodoliths by changes in color. The brownish inner cores yielded ages of 1600–1850 cal years before the present, whereas outer layers were much younger (180–50 years BP old). Growth layers appeared to have been separated by a long period of burial in the seafloor sediment. Other rhodoliths have ages of hundreds of years.Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES) 001Fundacao de Amparo a Pesquisa do Estado do Rio de Janeiro-Jovem Cientista do Nosso Estado (FAPERJ/JCNE

Deterministic Conditions for Subspace Identifiability from Incomplete Sampling

Consider a generic $r$-dimensional subspace of $\mathbb{R}^d$, $r<d$, and suppose that we are only given projections of this subspace onto small subsets of the canonical coordinates. The paper establishes necessary and sufficient deterministic conditions on the subsets for subspace identifiability.Comment: To appear in Proc. of IEEE ISIT, 201