Finiteness in derived categories of local rings

New homotopy invariant finiteness conditions on modules over commutative rings are introduced, and their properties are studied systematically. A number of finiteness results for classical homological invariants like flat dimension, injective dimension, and Gorenstein dimension, are established. It is proved that these specialize to give results concerning modules over complete intersection local rings. A noteworthy feature is the use of techniques based on thick subcategories of derived categories.Comment: 40 pages. Minor revisions. To appear in Commentarii Math. Helvetic

DG algebras with exterior homology

We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is the integers, or the prime field of characteristic p>0, and n is greater than or equal to -1. The examples are unexpectedly interesting.Comment: 15 page

Application of geographical information systems

Natural resources and environmental management of military lands is becoming increasingly complex and diverse. As military missions change and new equipment is fielded out training lands become increasingly more restricted due to environmental, logistical, and financial constraints. We must become better stewards of the land if we are going to continue to train troops to meet the next mission. GIS is a powerful tool for military trainers, environmentalists, and natural resource planners. This paper will discuss the applications of GIS in military training and environmental/ natural resources management. It will also discuss the use of map layers in the analysis of Endangered Species Habitats, Cultural Resource Surveys, Soils, cover types, wetlands, and others

Magnetic field effects on TcT_c and the pseudogap onset temperature in cuprate superconductors

We study the sensitivity of $T_c$ and the pseudogap onset temperature, $T^*$, to low fields, $H$, for cuprate superconductors, using a BCS-based approach extended to arbitrary coupling. We find that $T^*$ and $T_c$, which are of the same superconducting origin, have very different $H$ dependences. The small coherence length makes $T^*$ rather insensitive to the field. However, the presence of the pseudogap at $T_c$ makes $T_c$ more sensitive to $H$. Our results for the coherence length $\xi$ fit well with existing experiments. We predict that very near the insulator $\xi$ will rapidly increase.Comment: 4 pages, 1 figure, contribution to the PPHMF-IV conference, Oct. 200

Geometric principles of second messenger dynamics in dendritic spines.

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity

Excitations from Filled Landau Levels in Graphene

We consider graphene in a strong perpendicular magnetic field at zero temperature with an integral number of filled Landau levels and study the dispersion of single particle-hole excitations. We first analyze the two-body problem of a single Dirac electron and hole in a magnetic field interacting via Coulomb forces. We then turn to the many-body problem, where particle-hole symmetry and the existence of two valleys lead to a number of effects peculiar to graphene. We find that the coupling together of a large number of low-lying excitations leads to strong many-body corrections, which could be observed in inelastic light scattering or optical absorption. We also discuss in detail how the appearance of different branches in the exciton dispersion is sensitive to the number of filled spin and valley sublevels.Comment: 15 pages, 19 figure

Exact summation of vertex corrections to the penetration depth in d-wave superconductors

A variety of experiments suggest that in the cuprates, the low-energy superconducting quasiparticles undergo forward scattering from extended impurity potentials. We argue that when such potentials dominate the scattering, the penetration depth may be computed in a simple zero-angle scattering approximation (ZSA), in which the vertex corrections to the Meissner effect may be summed exactly. We find a remarkably simple relationship between the normal fluid density and the quasiparticle density of states of the disordered system which holds for every realization of the disorder. We expect this result to be relevant to the $ab$-plane penetration depth in high-purity single crystals of underdoped YBCO.Comment: 4 pages, submitted to PR

Consumer Dynamic Usage Allocation and Learning under Multi-Part Tariffs

Multipart tariffs are widely favored within service industries as an efficient means of mapping prices to differential levels of consumer demand. Whether they benefit consumers, however, is far less clear as they pose individuals with a potentially difficult task of dynamically allocating usage over the course of each billing cycle. In this paper we explore this welfare issue by examining the ability of individuals to optimally allocate consumption over time in a stylized cellular-phone usage task for which there exists a known optimal dynamic utilization policy. Actual call behavior over time is modeled using a dynamic choice model that allows decision makers to both discount the future (be myopic) and be subject to random errors when making call decisions. Our analysis provides a “half empty, half full” view of intuitive optimality. Participants rapidly learn to exhibit farsightedness, yet learning is incomplete with some level of allocation errors persisting even after repeated experience. We also find evidence for an asymmetric effect in which participants who are exogenously switched from a low (high) to high (low) allowance plan make more (fewer) errors in the new plan. The effect persists even when participants make their own plan choices. Finally, interventions that provide usage information to help participants eradicate errors have limited effectiveness

Screening for melanoma modifiers using a zebrafish autochthonous tumor model

Genomic studies of human cancers have yielded a wealth of information about genes that are altered in tumors. A challenge arising from these studies is that many genes are altered, and it can be difficult to distinguish genetic alterations that drove tumorigenesis from that those arose incidentally during transformation. To draw this distinction it is beneficial to have an assay that can quantitatively measure the effect of an altered gene on tumor initiation and other processes that enable tumors to persist and disseminate. Here we present a rapid means to screen large numbers of candidate melanoma modifiers in zebrafish using an autochthonous tumor model that encompasses steps required for melanoma initiation and maintenance. A key reagent in this assay is the miniCoopR vector, which couples a wild-type copy of the mitfa melanocyte specification factor to a Gateway recombination cassette into which candidate melanoma genes can be recombined. The miniCoopR vector has a mitfa rescuing minigene which contains the promoter, open reading frame and 3\u27-untranslated region of the wild-type mitfa gene. It allows us to make constructs using full-length open reading frames of candidate melanoma modifiers. These individual clones can then be injected into single cell Tg(mitfa:BRAF(V600E));p53(lf);mitfa(lf) zebrafish embryos. The miniCoopR vector gets integrated by Tol2-mediated transgenesis and rescues melanocytes. Because they are physically coupled to the mitfa rescuing minigene, candidate genes are expressed in rescued melanocytes, some of which will transform and develop into tumors. The effect of a candidate gene on melanoma initiation and melanoma cell properties can be measured using melanoma-free survival curves, invasion assays, antibody staining and transplantation assays

Evolutionary history and identification of conservation units in the giant otter, Pteronura brasiliensis.

The giant otter, Pteronura brasiliensis, occupies a range including the major drainage basins of South America, yet the degree of structure that exists within and among populations inhabiting these drainages is unknown. We sequenced portions of the mitochondrial DNA (mtDNA) cytochrome b (612 bp) and control region (383 bp) genes in order to determine patterns of genetic variation within the species. We found high levels of mtDNA haplotype diversity (h = 0.93 overall) and support for subdivision into four distinct groups of populations, representing important centers of genetic diversity and useful units for prioritizing conservation within the giant otter. We tested these results against the predictions of three hypotheses of Amazonian diversification (Pleistocene Refugia, Paleogeography, and Hydrogeology). While the phylogeographic pattern conformed to the predictions of the Refugia Hypothesis, molecular dating using a relaxed clock revealed the phylogroups diverged from one another between 1.69 and 0.84 Ma, ruling out the influence of Late Pleistocene glacial refugia. However, the role of Plio-Pleistocene climate change could not be rejected. While the molecular dating also makes the influence of geological arches according to the Paleogeography Hypothesis extremely unlikely, the recent Pliocene formation of the Fitzcarrald Arch and its effect of subsequently altering drainage pattern could not be rejected. The data presented here support the interactions of both climatic and hydrological changes resulting from geological activity in the Plio-Pleistocene, in shaping the phylogeographic structure of the giant otter