705 research outputs found
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 is
(zigzag) and
(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 (). In comparison to graphene, the minor contribution around
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
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