The I/O Complexity of Computing Prime Tables

International audienceWe revisit classical sieves for computing primes and analyze their performance in the external-memory model. Most prior sieves are analyzed in the RAM model, where the focus is on minimizing both the total number of operations and the size of the working set. The hope is that if the working set fits in RAM, then the sieve will have good I/O performance, though such an outcome is by no means guaranteed by a small working-set size. We analyze our algorithms directly in terms of I/Os and operations. In the external-memory model, permutation can be the most expensive aspect of sieving, in contrast to the RAM model, where permutations are trivial. We show how to implement classical sieves so that they have both good I/O performance and good RAM performance, even when the problem size N becomes huge—even superpolynomially larger than RAM. Towards this goal, we give two I/O-efficient priority queues that are optimized for the operations incurred by these sieves

The Range 1 Query (R1Q) Problem

Abstract: Given a bit array of size n and two indices i and j, find efficiently if there is a 1 in the subarray [i, j]. We call this problem the "Range 1 Query" (R1Q) problem. The problem can be easily generalized to higher dimensions. We give exact and approximation algorithms to solve the problem in 1D and higher dimensions. We can also answer queries for right triangles, isosceles triangles and in general, polygons with certain constraints. The applications include the Pochoir stencil compiler [1], where we have to answer octagonal queries to select optimized code clones. Exact Algorithm: The 1D algorithm is as follows. We divide the input array into blocks of size 2 p for different values of p greater than some threshold. We preprocess these blocks so that any query of length exactly 2 p that crosses a block boundary or lies completely inside a block can be answered in constant time. To answer intra-block queries, we use Four Russians trick. To answer the query R1Q(i, j), we find at most two possibly overlapping blocks of size 2 k <= j − i + 1 (for some positive integer k) that completely cover the range, and then compute the answer from the two queries. For input size of n bits, preprocessing takes o(n) bits of space and O(n) time and query execution takes O(1) time. The algorithm can be extended to higher dimensions. Approximation Algorithm: As in the exact algorithm, we preprocess the blocks of size 2 p for different values of p, and this time we use CormodeMuthukrishnan's Count Min (CM) sketch data structure [2] to store the preprocessed data. We create separate CM sketches for different block sizes so that queries of different sizes can be answered approximately in sublinear space and constant time. By setting the value of the error rate, the space usage of the approximation algorithm can be made arbitrarily small compared to the exact algorithm. The query execution is similar to the exact algorithm. Other Shapes: We answer right triangular queries as follows. We preprocess all the right triangles with horizontal base in eight orientations, with either bas

The Range 1 Query (R1Q) Problem

Abstract. We define the range 1 query (R1Q) problem as follows. Given a d-dimensional (d ≥ 1) input bit matrix A, preprocess A so that for any given region R of A, one can efficiently answer queries asking if R contains a 1 or not. We consider both orthogonal and non-orthogonal shapes for R including rectangles, axis-parallel right-triangles, certain types of polygons, and spheres. We provide space-efficient deterministic and randomized algorithms with constant query times (in constant dimensions) for solving the problem in the word RAM model. The space usage in bits is sublinear, linear, or near linear in the size of A, depending on the algorithm

Hole Injection and Rectifying Heterojunction Photodiodes through Vacancy Engineering in MoS2

The lack of techniques for counter doping in two dimensional (2D) semiconductors has hindered the development of p/n junctions, which are the basic building blocks of electronic devices. In this work, low-energy argon ions are used to create sulfur vacancies and are subsequently ``filled'' with oxygen to create p-doped MoS2-xOx. The incorporation of oxygen into the MoS2 lattice and hence band-structure modification reveal the nature of the p-type doping. These changes are validated by X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy, Raman spectroscopy, and photoluminescence measurements combined with density functional theory calculations. Electrical measurements reveal a complete flip in carrier polarity from n-type to p-type, which is further examined using temperature-dependent transport measurements. The enhancement of p-field-effect transistor characteristics is facilitated by employing top-gated transistors and area-selective vacancy engineering only in the contact regions. Finally, on the same flake, an in-plane MoS2 (n)/MoS2-xOx (p) type-I (straddling) heterojunction with rectifying behavior and excellent broadband photoresponse is demonstrated and explained using band diagrams. The spatial/metallurgical abruptness (<100 nm) of the heterojunctions is ascertained using Raman mapping. This process of vacancy engineering, which enables air-stable, area-selective, controlled, CMOS-compatible doping of 2D semiconductors is envisioned to open new vistas in the development of high-performance electronic and optoelectronic devices

Efficacy and safety of canagliflozin in patients with type 2 diabetes mellitus from India

Background: This post hoc analysis evaluated the efficacy and safety of canagliflozin, a sodium glucose co-transporter 2 inhibitor, in patients with type 2 diabetes mellitus (T2DM) from India. Methods: Changes from baseline in HbA1c, fasting plasma glucose (FPG), body weight, and blood pressure (BP) with canagliflozin 100 and 300 mg were evaluated in a subgroup of patients from India (n = 124) from 4 randomized, double-blind, placebo- and active-controlled, Phase 3 studies (N = 2313; Population 1). Safety was assessed based on adverse event (AE) reports in these patients and in a broader subgroup of patients from India (n = 1038) from 8 randomized, double-blind, placebo- and active-controlled, Phase 3 studies (N = 9439; Population 2). Results: Reductions in HbA1cwith canagliflozin 100 and 300 mg were −0.74% and −0.88%, respectively, in patients from India, and −0.81% and −1.00%, respectively, in the 4 pooled Phase 3 studies. In the Indian subgroup, both canagliflozin doses provided reductions in FPG, body weight, and BP that were consistent with findings in the overall population. The incidence of overall AEs in patients from India was generally similar with canagliflozin 100 and 300 mg and noncanagliflozin. The AE profile in patients from India was generally similar to the overall population, with higher rates of genital mycotic infections and osmotic diuresis–related and volume depletion–related AEs with canagliflozin versus noncanagliflozin. Conclusion: Canagliflozin provided glycemic control, body weight reduction, and was generally well tolerated in patients with T2DM from India

Autogen: Automatic Discovery of Efficient Recursive Divide-8-Conquer Algorithms for Solving Dynamic Programming Problems

© 2017 ACM. We present Autogen-an algorithm that for a wide class of dynamic programming (DP) problems automatically discovers highly efficient cache-oblivious parallel recursive divide-And-conquer algorithms from inefficient iterative descriptions of DP recurrences. Autogen analyzes the set of DP table locations accessed by the iterative algorithm when run on a DP table of small size and automatically identifies a recursive access pattern and a corresponding provably correct recursive algorithm for solving the DP recurrence.We use Autogen to autodiscover efficient algorithms for several well-known problems. Our experimental results show that several autodiscovered algorithms significantly outperform parallel looping and tiled loop-based algorithms. Also, these algorithms are less sensitive to fluctuations of memory and bandwidth compared with their looping counterparts, and their running times and energy profiles remain relatively more stable. To the best of our knowledge, Autogen is the first algorithm that can automatically discover new nontrivial divide-And-conquer algorithms

Complete mitogenome reveals genetic divergence and phylogenetic relationships among Indian cattle (<i>Bos indicus</i>) breeds

<p>Indigenous cattle of India belong to the species, <i>Bos indicus</i> and they possess various adaptability and production traits. However, little is known about the genetic diversity and origin of these breeds. To investigate the status, we sequenced and analyzed the whole mitochondrial DNA (mtDNA) of seven Indian cattle breeds. In total, 49 single-nucleotide variants (SNVs) were identified among the seven breeds analyzed. We observed a common synonymous SNV in the COII gene (m.7583G > A) of all the breeds studied. The phylogenetic analysis and genetic distance estimation showed the close genetic relationship among the Indian cattle breeds, whereas distinct genetic differences were observed between <i>Bos indicus</i> and <i>Bos taurus</i> cattle. Our results indicate a common ancestor for European Zwergzebu breed and South Indian cattle. The estimated divergence time demonstrated that the <i>Bos indicus</i> and <i>Bos taurus</i> cattle lineages diverged 0.92 million years ago. Our study also demonstrates that ancestors of present zebu breeds originated in South and North India separately ∼30,000 to 20,000 years ago. In conclusion, the identified genetic variants and results of the phylogenetic analysis may provide baseline information to develop appropriate strategies for management and conservation of Indian cattle breeds.</p