Chain Reduction for Binary and Zero-Suppressed Decision Diagrams

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation. The chain-reduced BDD (CBDD) of a function will be no larger than its BDD representation, and at most three times the size of its CZDD representation. Extensions to the standard algorithms for operating on BDDs and ZDDs enable them to operate on the chain-reduced versions. Experimental evaluations on representative benchmarks for encoding word lists, solving combinatorial problems, and operating on digital circuits indicate that chain reduction can provide significant benefits in terms of both memory and execution time

Spin(7)-manifolds and symmetric Yang--Mills instantons

In this Letter we establish a relationship between symmetric SU(2) Yang--Mills instantons and metrics with Spin(7)-holonomy. Our method is based on a slight extension of that of Bryant and Salamon developed to construct explicit manifolds with special holonomies in 1989. More precisely, we prove that making use of symmetric SU(2) Yang--Mills instantons on Riemannian spin-manifolds, we can construct metrics on the chiral spinor bundle whose holonomies are within Spin(7). Moreover if the resulting space is connected, simply connected and complete, the holonomy coincides with Spin(7). The basic example is the metric constructed on the chiral spinor bundle of the round four-sphere by using a generic SU(2)-instanton of unit action; hence it is a five-parameter deformation of the Bryant--Salamon example, also found by Gibbons, Page and Pope.Comment: 10 pages, no figures, LaTeX. More references have been added; but this version differs from the published on

Octonionic Gravitational Instantons

We construct eight-dimensional gravitational instantons by solving appropriate self-duality equations for the spin-connection. The particular gravitational instanton we present has $Spin(7)$ holonomy and, in a sense, it is the eight-dimensional analog of the Eguchi-Hanson 4D space. It has a removable bolt singularity which is topologically S^4 and its boundary at infinity is the squashed S^7. We also lift our solutions to ten and eleven dimensions and construct fundamental string and membrane configurations that preserve 1/16 of the original supersymmetries.Comment: 17 pages, latex, no figures. References to earlier works adde

Manifolds with parallel differential forms and Kaehler identities for G_2-manifolds

Let M be a compact Riemannian manifold equipped with a parallel differential form \omega. We prove a version of Kaehler identities in this setting. This is used to show that the de Rham algebra of M is weakly equivalent to its subquotient $(H^*_c(M), d)$, called {\bf the pseudocohomology} of M. When M is compact and Kaehler and \omega is its Kaehler form, $(H^*_c(M), d)$ is isomorphic to the cohomology algebra of M. This gives another proof of homotopy formality for Kaehler manifolds, originally shown by Deligne, Griffiths, Morgan and Sullivan. We compute $H^i_c(M)$ for a compact G_2-manifold, showing that it is isomorphic to cohomology unless i=3,4. For i=3,4, we compute $H^*_c(M)$ explicitly in terms of the first order differential operator *d: \Lambda^3(M)\arrow \Lambda^3(M).Comment: 34 pages, minor corrections, bibliography expande

A search for distant radio galaxies from SUMSS and NVSS: II. Optical Spectroscopy

This is the second in a series of papers presenting observations and results for a sample of 76 ultra-steep-spectrum (USS) radio sources in the southern hemisphere designed to find galaxies at high redshift. Here we focus on the optical spectroscopy program for 53 galaxies in the sample. We report 35 spectroscopic redshifts, based on observations with the Very Large Telescope (VLT), the New Technology Telescope (NTT) and the Australian National University's 2.3m telescope; they include five radio galaxies with z>3. Spectroscopic redshifts for the remaining 18 galaxies could not be confirmed: three are occulted by Galactic stars, eight show continuum emission but no discernible spectral lines, whilst the remaining seven galaxies are undetected in medium-deep VLT integrations. The latter are either at very high redshift (z >~7) or heavily obscured by dust. A discussion of the efficiency of the USS technique is presented. Based on the similar space density of z>3 radio galaxies in our sample compared with other USS-selected samples, we argue that USS selection at 843-1400 MHz is an efficient and reliable technique for finding distant radio galaxies.Comment: 15 Pages including 49 PostScript figures. Accepted for publication in MNRAS. Corrected one author name; text unchange

Analysis of data on the certificate of advanced graduate specialization program as collected by means of questionnaire

Thesis (Ed.M.)--Boston Universit

A search for distant radio galaxies from SUMSS and NVSS: III. radio spectral energy distributions and the z-alpha correlation

This is the third in a series of papers that present observations and results for a sample of 76 ultra-steep-spectrum radio sources designed to find galaxies at high redshift. Here we present multi-frequency radio observations, from the Australia Telescope Compact Array, for a subset of 37 galaxies from the sample. Matched resolution observations at 2.3, 4.8 and 6.2GHz are presented for all galaxies, with the z<2 galaxies additionally observed at 8.6 and 18GHz. New angular size constraints are reported for 19 sources based on high resolution 4.8 and 6.2GHz observations. Functional forms for the rest-frame spectral energy distributions are derived: 89% of the sample is well characterised by a single power law, whilst the remaining 11% show some flattening toward higher frequencies: not one source shows any evidence for high frequency steepening. We discuss the implications of this result in light of the empirical correlation between redshift and spectral index seen in flux limited samples of radio galaxies. Finally, a new physical mechanism to explain the redshift -- spectral index correlation is posited: extremely steep spectrum radio galaxies in the local universe usually reside at the centres of rich galaxy clusters. We argue that if a higher fraction of radio galaxies, as a function of redshift, are located in environments with densities similar to nearby rich clusters, then this could be a natural interpretation for the correlation. We briefly outline our plans to pursue this line of investigation.Comment: MNRAS in pres

The effect of feeding fodder beet or kale during winter on growth and behaviour of rising-one-year-old dairy heifers

While fodder beet (FB) has been used by the dairy industry for winter grazing over the last 10 years, there is no published information on its effect on heifer performance. Farmers have recently expressed concern regarding the suitability of fodder beet for wintering growing dairy heifers due to the low crude protein (CP) content of the FB bulb. To compare liveweight gain and grazing behaviour, 191, 9- to 12-month-old heifers at the Southern Dairy Hub were offered either FB (n=93; HFR-FB) or kale (n=98; HFR-Kale), both with pasture baleage as a feed supplement, in winter 2019. Allocations were formulated to achieve similar energy intake, but HFR-Kale were offered a higher proportion of their diet as baleage. There were no differences in apparent DM intake, but HFR-FB consumed a diet with overall lower CP (11.4%) than did HFR-Kale (13.4%). Heifers in both treatments had a similar average daily liveweight gain (0.45 ± 0.083 kg/day) but neither group achieved the 0.6 kg/day average daily gain target for heifer growth. Differences were observed in eating and ruminating behaviour between the two groups, but more research is required to validate the measurement devices used in this study for animals grazing crop. The results indicate the challenges of achieving industry-recommended growth rates over winter in heifers grazing forage crops and highlight the importance of feed testing for nutritive value to ensure nutrient requirements are being met

Binary Decision Diagrams: from Tree Compaction to Sampling

Any Boolean function corresponds with a complete full binary decision tree. This tree can in turn be represented in a maximally compact form as a direct acyclic graph where common subtrees are factored and shared, keeping only one copy of each unique subtree. This yields the celebrated and widely used structure called reduced ordered binary decision diagram (ROBDD). We propose to revisit the classical compaction process to give a new way of enumerating ROBDDs of a given size without considering fully expanded trees and the compaction step. Our method also provides an unranking procedure for the set of ROBDDs. As a by-product we get a random uniform and exhaustive sampler for ROBDDs for a given number of variables and size