Combining decision procedures for the reals

We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted forms of distributivity. At the same time, we explore ways in which "local" decision or heuristic procedures for fragments of the theory of the reals can be amalgamated into global ones. Let Tadd[Q] be the first-order theory of the real numbers in the language of ordered groups, with negation, a constant 1, and function symbols for multiplication by rational constants. Let Tmult[Q] be the analogous theory for the multiplicative structure, and let T[Q] be the union of the two. We show that although T[Q] is undecidable, the universal fragment of T[Q] is decidable. We also show that terms of T[Q]can fruitfully be put in a normal form. We prove analogous results for theories in which Q is replaced, more generally, by suitable subfields F of the reals. Finally, we consider practical methods of establishing quantifier-free validities that approximate our (impractical) decidability results.Comment: Will appear in Logical Methods in Computer Scienc

A language for mathematical knowledge management

We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathematical knowledge. We then describe a syntactic sugaring of that language that provides a way of writing remarkably readable assertions without straying far from the set-theoretic semantics. We illustrate with some examples of formalized textbook definitions from elementary set theory and point-set topology. We also present statistics concerning the complexity of these definitions, under various complexity measures

CB2 Receptor Deficiency Increases Amyloid Pathology and Alters Tau Processing in a Transgenic Mouse Model of Alzheimer\u27s Disease

The endocannabinoid CB2 receptor system has been implicated in the neuropathology of Alzheimer\u27s disease (AD). In order to investigate the impact of the CB2 receptor system on AD pathology, a colony of mice with a deleted CB2 receptor gene, CNR2, was established on a transgenic human mutant APP background for pathological comparison with CB2 receptor-sufficient transgenic mice. J20 APP (PDGFB-APPSwInd) mice were bred over two generations with CNR2(-/-) (Cnr2(tm1Dgen)/J) mice to produce a colony of J20 CNR2(+/+) and J20 CNR2(-/-)mice. Seventeen J20 CNR2(+/+) mice (12 females, 5 males) and 16 J20 CNR2(-/-) mice (11 females, 5 males) were killed at 12 months, and their brains were interrogated for AD-related pathology with both biochemistry and immunocytochemistry (ICC). In addition to amyloid-dependent endpoints such as soluble A beta production and plaque deposition quantified with 6E10 staining, the effect of CB2 receptor deletion on total soluble mouse tau production was assayed by using a recently developed high-sensitivity assay. Results revealed that soluble A beta 42 and plaque deposition were significantly increased in J20 CNR2(-/-) mice relative to CNR2(1/1) mice. Microgliosis, quantified with ionized calcium-binding adapter molecule 1 (Iba-1) staining, did not differ between groups, whereas plaque associated microglia was more abundant in J20 CNR2(-/-) mice. Total tau was significantly suppressed in J20 CNR2(-/-) mice relative to J20 CNR2(+/+) mice. The results confirm the constitutive role of the CB2 receptor system both in reducing amyloid plaque pathology in AD and also support tehpotential of cannabinoid therapies targeting CB2 to reduce A beta; however, the results suggest that interventions may have a divergent effect on tau pathology

Gravitational Radiation from Strongly Magnetized White Dwarfs

The magnetic fields of white dwarfs distort their shape generating an anisotropic moment of inertia. A magnetized white dwarf which rotates obliquely relative to the symmetry axis has a mass quadrupole moment which varies in time, so it will emit gravitational radiation. LISA may be able to detect the gravitational waves from two nearby, quickly rotating white dwarfs.Comment: 9 pages, 2 figures, to appear in MNRAS, corrected a ubiquitous typo and added two reference

Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles

Phosphorene, the single layer counterpart of black phosphorus, is a novel two-dimensional semiconductor with high carrier mobility and a large fundamental direct band gap, which has attracted tremendous interest recently. Its potential applications in nano-electronics and thermoelectrics call for a fundamental study of the phonon transport. Here, we calculate the intrinsic lattice thermal conductivity of phosphorene by solving the phonon Boltzmann transport equation (BTE) based on first-principles calculations. The thermal conductivity of phosphorene at $300\,\mathrm{K}$ is $30.15\,\mathrm{Wm^{-1}K^{-1}}$ (zigzag) and $13.65\,\mathrm{Wm^{-1}K^{-1}}$ (armchair), showing an obvious anisotropy along different directions. The calculated thermal conductivity fits perfectly to the inverse relation with temperature when the temperature is higher than Debye temperature ($\Theta_D = 278.66\,\mathrm{K}$). In comparison to graphene, the minor contribution around $5\%$ of the ZA mode is responsible for the low thermal conductivity of phosphorene. In addition, the representative mean free path (MFP), a critical size for phonon transport, is also obtained.Comment: 5 pages and 6 figures, Supplemental Material available as http://www.rsc.org/suppdata/cp/c4/c4cp04858j/c4cp04858j1.pd

The Hispanic Paradox: Race/Ethnicity and Nativity, Immigrant Enclave Residence and Cognitive Impairment Among Older US Adults

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137472/1/jgs14806.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137472/2/jgs14806_am.pd

Cuts and flows of cell complexes

We study the vector spaces and integer lattices of cuts and flows associated with an arbitrary finite CW complex, and their relationships to group invariants including the critical group of a complex. Our results extend to higher dimension the theory of cuts and flows in graphs, most notably the work of Bacher, de la Harpe and Nagnibeda. We construct explicit bases for the cut and flow spaces, interpret their coefficients topologically, and give sufficient conditions for them to be integral bases of the cut and flow lattices. Second, we determine the precise relationships between the discriminant groups of the cut and flow lattices and the higher critical and cocritical groups with error terms corresponding to torsion (co)homology. As an application, we generalize a result of Kotani and Sunada to give bounds for the complexity, girth, and connectivity of a complex in terms of Hermite's constant.Comment: 30 pages. Final version, to appear in Journal of Algebraic Combinatoric

A Brownian particle in a microscopic periodic potential

We study a model for a massive test particle in a microscopic periodic potential and interacting with a reservoir of light particles. In the regime considered, the fluctuations in the test particle's momentum resulting from collisions typically outweigh the shifts in momentum generated by the periodic force, and so the force is effectively a perturbative contribution. The mathematical starting point is an idealized reduced dynamics for the test particle given by a linear Boltzmann equation. In the limit that the mass ratio of a single reservoir particle to the test particle tends to zero, we show that there is convergence to the Ornstein-Uhlenbeck process under the standard normalizations for the test particle variables. Our analysis is primarily directed towards bounding the perturbative effect of the periodic potential on the particle's momentum.Comment: 60 pages. We reorganized the article and made a few simplifications of the conten

Clustering Properties of restframe UV selected galaxies I: the correlation length derived from GALEX data in the local Universe

We present the first measurements of the angular correlation function of galaxies selected in the far (1530 A) and near (2310 A) Ultraviolet from the GALEX survey fields overlapping SDSS DR5 in low galactic extinction regions. The area used covers 120 sqdeg (GALEX - MIS) down to magnitude AB = 22, yielding a total of 100,000 galaxies. The mean correlation length is ~ 3.7 \pm 0.6 Mpc and no significant trend is seen for this value as a function of the limiting apparent magnitude or between the GALEX bands. This estimate is close to that found from samples of blue galaxies in the local universe selected in the visible, and similar to that derived at z ~ 3 for LBGs with similar rest frame selection criteria. This result supports models that predict anti-biasing of star forming galaxies at low redshift, and brings an additional clue to the downsizing of star formation at z<1.Comment: Accepted for publication in GALEX Special ApJs, December 200