Testing isomorphism of lattices over CM-orders

A CM-order is a reduced order equipped with an involution that mimics complex conjugation. The Witt-Picard group of such an order is a certain group of ideal classes that is closely related to the "minus part" of the class group. We present a deterministic polynomial-time algorithm for the following problem, which may be viewed as a special case of the principal ideal testing problem: given a CM-order, decide whether two given elements of its Witt-Picard group are equal. In order to prevent coefficient blow-up, the algorithm operates with lattices rather than with ideals. An important ingredient is a technique introduced by Gentry and Szydlo in a cryptographic context. Our application of it to lattices over CM-orders hinges upon a novel existence theorem for auxiliary ideals, which we deduce from a result of Konyagin and Pomerance in elementary number theory.Comment: To appear in SIAM Journal on Computin

Accounting for housing in a CPI

In this paper, we take stock of how statistical agencies in different nations are currently accounting for housing in their consumer price indexes (CPIs). The rental equivalence and user cost approaches have been favourites of economists. Both can be derived from the fundamental equation of capital theory. Concerns about these approaches are taken up. We go on to argue that an opportunity cost approach is the correct theoretical framework for accounting for owner-occupied housing (OOH) in a CPI. This approach, first mentioned in a 2006 OECD paper by Diewert, is developed more fully here. We explore the relationship of this new approach to the usual rental equivalency and user cost approaches. The new approach leads to an owner-occupied housing opportunity cost (OOHOC) index that is a weighted average of the rental and the financial opportunity costs. ; We call attention to the need for more direct measures of inflation for owner-occupied housing services. In a 2007 paper, Mishkin argues that central banks with supervisory authority can reduce the likelihood of bubbles forming through prudential supervision of the financial system. However, the official mandates of central banks typically focus on managing measured inflation. Barack Obama has pledged to give the Federal Reserve greater oversight of a broader array of financial institutions. We believe that an important addition to this pledge should be to give the BLS, BEA, and Census Bureau the funds and the mandate to aggressively develop improved measures of inflation for owner-occupied housing services. Central banks and national governments have many policy instruments at their disposal that they could use, in the future, to control inflation in housing markets. What they lack are appropriate measures of inflation in the market for owner-occupied housing services. The proposed new opportunity cost measure for accounting for OOH in a CPI will not be simple or cheap to implement. However, the current financial crisis makes it clear that the costs of not having an adequate measure for inflation in the cost of owner-occupied housing services can be far greater.Durable goods, Consumer ; Consumer price indexes ; Cost of living adjustments ; Housing

Substructure within the SSA22 protocluster at z≈3.09z\approx3.09

We present the results of a densely sampled spectroscopic survey of the SSA22 protocluster at $z\approx 3.09$. Our sample with Keck/LRIS spectroscopy includes 106 Ly$\alpha$ Emitters (LAEs) and 40 Lyman Break Galaxies (LBGs) at $z=3.05-3.12$. These galaxies are contained within the $9'\times9'$ region in which the protocluster was discovered, which also hosts the maximum galaxy overdensity in the SSA22 region. The redshift histogram of our spectroscopic sample reveals two distinct peaks, at $z=3.069$ (blue, 43 galaxies) and $z=3.095$ (red, 103 galaxies). Furthermore, objects in the blue and red peaks are segregated on the sky, with galaxies in the blue peak concentrating towards the western half of the field. These results suggest that the blue and red redshift peaks represent two distinct structures in physical space. Although the double-peaked redshift histogram is traced in the same manner by LBGs and LAEs, and brighter and fainter galaxies, we find that nine out of 10 X-ray AGNs in SSA22, and all seven spectroscopically-confirmed giant Ly$\alpha$ "blobs," reside in the red peak. We combine our dataset with sparsely sampled spectroscopy from the literature over a significantly wider area, finding preliminary evidence that the double-peaked structure in redshift space extends beyond the region of our dense spectroscopic sampling. In order to fully characterize the three-dimensional structure, dynamics, and evolution of large-scale structure in the SSA22 overdensity, we require the measurement of large samples of LAE and LBG redshifts over a significantly wider area, as well as detailed comparisons with cosmological simulations of massive cluster formation.Comment: 6 pages, 4 figures, Accepted to ApJ Letter

The association of agricultural information services and technical efficiency among maize producers in Kakamega, western Kenya

Maize is the staple food for most Kenyan households, and grown in almost all the farming systems. Due to diminishing farm sizes in Kakamega District, crop productivity and the efficiency of farming systems are of great concern. This paper aims to provide empirical evidence on the links between efficiency in maize production and access to soil-related agricultural information services. Using cluster sampling, a total of 154 farmers in Kakamega District were interviewed. A 2–step estimation technique (Data Envelopment Analysis (DEA) and Tobit model) were used to evaluate the technical efficiencies among the farmers and the factors explaining the estimated efficiency scores. Data was disaggregated into farmers with and those without access to soil-related agricultural information services. The results shows that farmers with access to soil-related agricultural information services were more technically efficient (average technical efficiency of 90%) in maize production compared to those without access to information (technical efficiency at 70%). Given the significant role that access to soil-related agricultural information services play on technical efficiency in maize production in the study area, the paper recommends improvements in farmers access to this important resources through: (i) the strengthening of the formal and informal agricultural extension services, (ii) a stronger linkage among agricultural research, agricultural extension, and farm level activities; and (iii) policy support for increased distribution of soil management inputs.Maize, Soil information, Technical efficiency, Tobit analysis, DEA, Teaching/Communication/Extension/Profession,

Interpreting Flux from Broadband Photometry

We discuss the transformation of observed photometry into flux for the creation of spectral energy distributions and the computation of bolometric luminosities. We do this in the context of supernova studies, particularly as observed with the Swift spacecraft, but the concepts and techniques should be applicable to many other types of sources and wavelength regimes. Traditional methods of converting observed magnitudes to flux densities are not very accurate when applied to UV photometry. Common methods for extinction and the integration of pseudo-bolometric fluxes can also lead to inaccurate results. The sources of inaccuracy, though, also apply to other wavelengths. Because of the complicated nature of translating broad-band photometry into monochromatic flux densities, comparison between observed photometry and a spectroscopic model is best done by comparing in the natural units of the observations. We recommend that integrated flux measurements be made using a spectrum or spectral energy distribution which is consistent with the multi-band photometry rather than converting individual photometric measurements to flux densities, linearly interpolating between the points, and integrating. We also highlight some specific areas where the UV flux can be mischaracterized.Comment: Accepted for publication in the Astronomical Journal. 16 pages, 9 figures. A PDF file with wide-screen friendly figures is linked from this blog post http://ultravioletsupernova.blogspot.com/2016/08/interpreting-flux-from-broadband.htm