Syzygies of Segre embeddings and Delta-modules

We study syzygies of the Segre embedding of P(V_1) x ... x P(V_n), and prove two finiteness results. First, for fixed p but varying n and V_i, there is a finite list of "master p-syzygies" from which all other p-syzygies can be derived by simple substitutions. Second, we define a power series f_p with coefficients in something like the Schur algebra, which contains essentially all the information of p-syzygies of Segre embeddings (for all n and V_i), and show that it is a rational function. The list of master p-syzygies and the numerator and denominator of f_p can be computed algorithmically (in theory). The central observation of this paper is that by considering all Segre embeddings at once (i.e., letting n and the V_i vary) certain structure on the space of p-syzygies emerges. We formalize this structure in the concept of a Delta-module. Many of our results on syzygies are specializations of general results on Delta-modules that we establish. Our theory also applies to certain other families of varieties, such as tangent and secant varieties of Segre embeddings.Comment: 34 page

Alcohol Availability and Violence: A Closer Look at Space and Time

Alcohol availability plays an important role in violence. Less is known about how spatiotemporal patterns of alcohol–violence association vary across time of day and across various crime types. This study examined whether and how the associations between on- and off-premise alcohol outlets and assaults, and between on- and off-premise alcohol outlets and robberies, vary across different times of day (morning, daytime, evening, and late night). This cross-sectional study used socioeconomic, alcohol license, and crime data from Milwaukee, Wisconsin, aggregated to US Census block groups and estimated spatially lagged maximum likelihood regression models that controlled for spatial dependence. On-premise outlets were negatively associated with evening assaults and positively associated with daytime and late-night robberies. Off-premise outlets were positively associated with evening assaults, late-night assaults, daytime robberies, and evening robberies. Spatiotemporal alcohol–violence associations vary across crime types and across time of day. On- and off-premise alcohol outlets play a unique role across four different temporal categories and across two violent crime types. These findings have the potential to inform theoretical explanations of the alcohol–violence relationship and may be beneficial when considering and designing custom-tailored local alcohol policy to reduce alcohol-related harm

The Relationship Between Alcohol Beverage Types and Violence

There is substantial evidence of an ecological association between off-premise alcohol outlets and violence. We know less, however, about how specific beverage types that are sold in the outlets might explain the difference in violence rates across different alcohol outlets. Data on alcohol beverage types were collected for all off-premise alcohol outlets in Milwaukee, Wisconsin, using a systematic social observation instrument. Spatially lagged regression models were estimated to determine whether the variation in alcohol beverage types is related to robbery density net of important neighborhood predictors of crime rates. Availability of all alcohol beverage types (beer, wine, spirits, premixed, single beer, single spirits, single premixed) was positively associated with the density of robberies, net of neighborhood characteristics. Reducing alcohol beverages, regardless of the beverage type, sold at off-premise alcohol outlets may reduce violence in communities

U.S. securities markets and the banking system, 1790-1840 - commentary

Banks and banking - History ; Stock market ; Securities ; Bank stocks

Hilbert series for twisted commutative algebras

Suppose that for each n >= 0 we have a representation $M_n$ of the symmetric group S_n. Such sequences arise in a wide variety of contexts, and often exhibit uniformity in some way. We prove a number of general results along these lines in this paper: our prototypical theorem states that if $M_n$ can be given a suitable module structure over a twisted commutative algebra then the sequence $M_n$ follows a predictable pattern. We phrase these results precisely in the language of Hilbert series (or Poincar\'e series, or formal characters) of modules over tca's.Comment: 28 page

GL-equivariant modules over polynomial rings in infinitely many variables

Consider the polynomial ring in countably infinitely many variables over a field of characteristic zero, together with its natural action of the infinite general linear group G. We study the algebraic and homological properties of finitely generated modules over this ring that are equipped with a compatible G-action. We define and prove finiteness properties for analogues of Hilbert series, systems of parameters, depth, local cohomology, Koszul duality, and regularity. We also show that this category is built out of a simpler, more combinatorial, quiver category which we describe explicitly. Our work is motivated by recent papers in the literature which study finiteness properties of infinite polynomial rings equipped with group actions. (For example, the paper by Church, Ellenberg and Farb on the category of FI-modules, which is equivalent to our category.) Along the way, we see several connections with the character polynomials from the representation theory of the symmetric groups. Several examples are given to illustrate that the invariants we introduce are explicit and computable.Comment: 59 pages, uses ytableau.sty; v2: expanded details in many proofs especially in Sections 2 and 4, Section 6 substantially expanded, added references; v3: corrected typos and Remark 4.3.3 from published versio

An XMM-Newton Survey of the Soft X-ray Background. II. An All-Sky Catalog of Diffuse O VII and O VIII Emission Intensities

We present an all-sky catalog of diffuse O VII and O VIII line intensities, extracted from archival XMM observations. The O VII and O VIII intensities are typically ~2-11 and <~3 ph/cm^2/s/sr (LU), respectively, although much brighter intensities were also recorded. Our data set includes 217 directions observed multiple times by XMM. The time variation of the intensities from such directions may be used to constrain SWCX models. The O VII and O VIII intensities typically vary by <~5 and <~2 LU between repeat observations, although several intensity enhancements of >10 LU were observed. We compared our measurements with SWCX models. The heliospheric SWCX intensity is expected to vary with ecliptic latitude and solar cycle. We found that the observed oxygen intensities generally decrease from solar maximum to solar minimum, both at high ecliptic latitudes (as expected) and at low ecliptic latitudes (not as expected). The geocoronal SWCX intensity is expected to depend on the solar wind proton flux and on the sightline's path through the magnetosheath. The intensity variations seen in directions that have been observed multiple times are in poor agreement with the predictions of a geocoronal SWCX model. The oxygen lines account for ~40-50% of the 3/4 keV X-ray background that is not due to unresolved AGN, in good agreement with a previous measurement. However, this fraction is not easily explained by a combination of SWCX emission and emission from hot plasma in the halo. The line intensities tend to increase with longitude toward the inner Galaxy, possibly due to an increase in the supernova rate in that direction or the presence of a halo of accreted material centered on the Galactic Center. The variation of intensity with Galactic latitude differs in different octants of the sky, and cannot be explained by a single simple plane-parallel or constant-intensity halo model. (Abridged)Comment: Accepted for publication in the Astrophysical Journal Supplement Series. 29 pages (main body of paper) plus 85 pages (full versions of Tables 1, 2, and 4 - these tables will be published as machine-readable tables in the journal, and appear in abbreviated form in the main body of the paper). 12 figures. v2: Minor corrections, conclusions unaltere