A hierarchically blocked Jacobi SVD algorithm for single and multiple graphics processing units

We present a hierarchically blocked one-sided Jacobi algorithm for the singular value decomposition (SVD), targeting both single and multiple graphics processing units (GPUs). The blocking structure reflects the levels of GPU's memory hierarchy. The algorithm may outperform MAGMA's dgesvd, while retaining high relative accuracy. To this end, we developed a family of parallel pivot strategies on GPU's shared address space, but applicable also to inter-GPU communication. Unlike common hybrid approaches, our algorithm in a single GPU setting needs a CPU for the controlling purposes only, while utilizing GPU's resources to the fullest extent permitted by the hardware. When required by the problem size, the algorithm, in principle, scales to an arbitrary number of GPU nodes. The scalability is demonstrated by more than twofold speedup for sufficiently large matrices on a Tesla S2050 system with four GPUs vs. a single Fermi card.Comment: Accepted for publication in SIAM Journal on Scientific Computin

Prospectives in Deep Space Infrastructures, Development, and Colonization

The realization of the long studied cost reduction benefits of reusable rockets is expected to revolutionize and enable both commercial deep space beyond Geostationary Earth Orbit (GEO) and solar system human colonization. The projections for a myriad of space commercialization activities beyond the current largely positional Earth utilities and Humans Mars both safe and affordable may now be realizable. This report considers these putative commercial and colonizationrelated activities, the emerging technologies, the space functionalities to support and further enable them, and envisions the nature of space developments beyond GEO going forward

Dynamic order submission strategies with competition between a dealer market and a crossing network

We present a dynamic microstructure model where a dealer market (DM) and a crossing network (CN) interact. Sequentially arriving traders with different valuations for an asset maximise their profits either by trading on a DM or by submitting an order for (possibly) uncertain execution via a CN. We develop the analysis for three different informational settings: transparency, "complete" opaqueness of all order flow, and "partial" opaqueness (with observable DM trades). A key result is that the interaction of trading systems generates systematic patterns in order flow for the transparency and partial opaqueness settings. The precise nature of these patterns depends on the degree of transparency at the CN. While unambiguous with a transparent CN, they may reverse direction if the CN is opaque. Moreover, in all three informational settings, we find that a CN and a DM cater for different types of traders. Investors with a high willingness to trade are more likely to prefer a DM. The introduction of a CN next to a DM also affects welfare as it increases total order flow by attracting traders who would otherwise not submit orders ("order creation"); in addition, it diverts trade from the DM ("trade diversion"). We find that the coexistence of a CN and DM produces more trader welfare than a DM in isolation. Also, more transparent markets lead to greater trader welfare but may reduce overall welfare.alternative trading systems, crossing network, dealer market, order flow, transparency, welfare

Using a Bayesian change-point statistical model with autoregressive terms to study the monthly number of dispensed asthma medications by public health services

In this paper, it is proposed a Bayesian analysis of a time series in the presence of a random change-point and autoregressive terms. The development of this model was motivated by a data set related to the monthly number of asthma medications dispensed by the public health services of Ribeirão Preto, Southeast Brazil, from 1999 to 2011. A pronounced increase trend has been observed from 1999 to a specific change-point, with a posterior decrease until the end of the series. In order to obtain estimates for the parameters of interest, a Bayesian Markov Chain Monte Carlo (MCMC) simulation procedure using the Gibbs sampler algorithm was developed. The Bayesian model with autoregressive terms of order 1 fits well to the data, allowing to estimate the change-point at July 2007, and probably reflecting the results of the new health policies and previously adopted programs directed toward patients with asthma. The results imply that the present model is useful to analyse the monthly number of dispensed asthma medications and it can be used to describe a broad range of epidemiological time series data where a change-point is present.Peer Reviewe

Complexity Hierarchies and Higher-order Cons-free Term Rewriting

Constructor rewriting systems are said to be cons-free if, roughly, constructor terms in the right-hand sides of rules are subterms of the left-hand sides; the computational intuition is that rules cannot build new data structures. In programming language research, cons-free languages have been used to characterize hierarchies of computational complexity classes; in term rewriting, cons-free first-order TRSs have been used to characterize the class PTIME. We investigate cons-free higher-order term rewriting systems, the complexity classes they characterize, and how these depend on the type order of the systems. We prove that, for every K $\geq$ 1, left-linear cons-free systems with type order K characterize E$^K$TIME if unrestricted evaluation is used (i.e., the system does not have a fixed reduction strategy). The main difference with prior work in implicit complexity is that (i) our results hold for non-orthogonal term rewriting systems with no assumptions on reduction strategy, (ii) we consequently obtain much larger classes for each type order (E$^K$TIME versus EXP$^{K-1}$TIME), and (iii) results for cons-free term rewriting systems have previously only been obtained for K = 1, and with additional syntactic restrictions besides cons-freeness and left-linearity. Our results are among the first implicit characterizations of the hierarchy E = E$^1$TIME $\subsetneq$ E$^2$TIME $\subsetneq$ ... Our work confirms prior results that having full non-determinism (via overlapping rules) does not directly allow for characterization of non-deterministic complexity classes like NE. We also show that non-determinism makes the classes characterized highly sensitive to minor syntactic changes like admitting product types or non-left-linear rules.Comment: extended version of a paper submitted to FSCD 2016. arXiv admin note: substantial text overlap with arXiv:1604.0893

Depth, Highness and DNR degrees

We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions of O(1)-deepK, O(1)-deepC , order-deep K and order-deep C sequences. Our main results are that Martin-Loef random sets are not order-deepC , that every many-one degree contains a set which is not O(1)-deepC , that O(1)-deepC sets and order-deepK sets have high or DNR Turing degree and that no K-trival set is O(1)-deepK.Comment: journal version, dmtc