A hierarchy of languages, logics, and mathematical theories

We present mathematics from a foundational perspective as a hierarchy in which each tier consists of a language, a logic, and a mathematical theory. Each tier in the hierarchy subsumes all preceding tiers in the sense that its language, logic, and mathematical theory generalize all preceding languages, logics, and mathematical theories. Starting from the root tier, the mathematical theories in this hierarchy are: combinatory logic restricted to the identity I, combinatory logic, ZFC set theory, constructive type theory, and category theory. The languages of the first four tiers correspond to the languages of the Chomsky hierarchy: in combinatory logic Ix = x gives rise to a regular language; the language generated by S, K in combinatory logic is context-free; first-order logic is context-sensitive; and the typed lambda calculus of type theory is recursively enumerable. The logic of each tier can be characterized in terms of the cardinality of the set of its truth values: combinatory logic restricted to I has 0 truth values, while combinatory logic has 1, first-order logic 2, constructive type theory 3, and categeory theory omega_0. We conjecture that the cardinality of objects whose existence can be established in each tier is bounded; for example, combinatory logic is bounded in this sense by omega_0 and ZFC set theory by the least inaccessible cardinal. We also show that classical recursion theory presents a framework for generating the above hierarchy in terms of the initial functions zero, projection, and successor followed by composition and m-recursion, starting with the zero function I in combinatory logic This paper begins with a theory of glossogenesis, i.e. a theory of the origin of language, since this theory shows that natural language has deep connections to category theory and since it was through these connections that the last tier and ultimately the whole hierarchy were discovered. The discussion covers implications of the hierarchy for mathematics, physics, cosmology, theology, linguistics, extraterrestrial communication, and artificial intelligence

Decoherence of electron spin qubits in Si-based quantum computers

Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate $1/T_1$ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.Comment: 8 figures. To appear in PRB-July 2002. Revisions include: some references added/corrected, several typos fixed, a few things clarified. Nothing dramati

Effect of Non-Magnetic Impurities (Zn,Li) in a Hole Doped Spin-Fermion Model for Cuprates

The effect of adding non-magnetic impurities (NMI), such as Zn or Li, to high-Tc cuprates is studied applying Monte Carlo techniques to a spin-fermion model. It is observed that adding Li is qualitatively similar to doping with equal percentages of Sr and Zn. The mobile holes (MH) are trapped by the NMI and the system remains insulating and commensurate with antiferromagnetic (AF) correlations. This behavior persists in the region %NMI > %MH. On the other hand, when %NMI < %MH magnetic and charge incommensurabilities are observed. The vertical or horizontal hole-rich stripes, present when % NMI=0 upon hole doping, are pinned by the NMI and tend to become diagonal, surrounding finite AF domains. The %MH-%NMI plane is investigated. Good agreement with experimental results is found in the small portion of this diagram where experimental data are available. Predictions about the expected behavior in the remaining regions are made.Comment: Four pages with four figures embedded in tex

Fractional quantum Hall effect in a quantum point contact at filling fraction 5/2

Recent theories suggest that the excitations of certain quantum Hall states may have exotic braiding statistics which could be used to build topological quantum gates. This has prompted an experimental push to study such states using confined geometries where the statistics can be tested. We study the transport properties of quantum point contacts (QPCs) fabricated on a GaAs/AlGaAs two dimensional electron gas that exhibits well-developed fractional quantum Hall effect, including at bulk filling fraction 5/2. We find that a plateau at effective QPC filling factor 5/2 is identifiable in point contacts with lithographic widths of 1.2 microns and 0.8 microns, but not 0.5 microns. We study the temperature and dc-current-bias dependence of the 5/2 plateau in the QPC, as well as neighboring fractional and integer plateaus in the QPC while keeping the bulk at filling factor 3. Transport near QPC filling factor 5/2 is consistent with a picture of chiral Luttinger liquid edge-states with inter-edge tunneling, suggesting that an incompressible state at 5/2 forms in this confined geometry

Persistent Exposure to Mycoplasma Induces Malignant Transformation of Human Prostate Cells

Recent epidemiologic, genetic, and molecular studies suggest infection and inflammation initiate certain cancers, including those of the prostate. The American Cancer Society, estimates that approximately 20% of all worldwide cancers are caused by infection. Mycoplasma, a genus of bacteria that lack a cell wall, are among the few prokaryotes that can grow in close relationship with mammalian cells, often without any apparent pathology, for extended periods of time. In this study, the capacity of Mycoplasma genitalium, a prevalent sexually transmitted infection, and Mycoplasma hyorhinis, a mycoplasma found at unusually high frequency among patients with AIDS, to induce a malignant phenotype in benign human prostate cells (BPH-1) was evaluated using a series of in vitro and in vivo assays. After 19 weeks of culture, infected BPH-1 cells achieved anchorage-independent growth and increased migration and invasion. Malignant transformation of infected BPH-1 cells was confirmed by the formation of xenograft tumors in athymic mice. Associated with these changes was an increase in karyotypic entropy, evident by the accumulation of chromosomal aberrations and polysomy. This is the first report describing the capacity of M. genitalium or M. hyorhinis infection to lead to the malignant transformation of benign human epithelial cells and may serve as a model to further study the relationship between prostatitis and prostatic carcinogenesis

Surveying the Agents of Galaxy Evolution in the Tidally-Stripped, Low Metallicity Small Magellanic Cloud (SAGE-SMC) II. Cool Evolved Stars

We investigate the infrared (IR) properties of cool, evolved stars in the Small Magellanic Cloud (SMC), including the red giant branch (RGB) stars and the dust-producing red supergiant (RSG) and asymptotic giant branch (AGB) stars using observations from the Spitzer Space Telescope Legacy program entitled: "Surveying the Agents of Galaxy Evolution in the Tidally-stripped, Low Metallicity SMC", or SAGE-SMC. The survey includes, for the first time, full spatial coverage of the SMC bar, wing, and tail regions at infrared (IR) wavelengths (3.6 - 160 microns). We identify evolved stars using a combination of near-IR and mid-IR photometry and point out a new feature in the mid-IR color-magnitude diagram that may be due to particularly dusty O-rich AGB stars. We find that the RSG and AGB stars each contribute ~20% of the global SMC flux (extended + point-source) at 3.6 microns, which emphasizes the importance of both stellar types to the integrated flux of distant metal-poor galaxies. The equivalent SAGE survey of the higher-metallicity Large Magellanic Cloud (SAGE-LMC) allows us to explore the influence of metallicity on dust production. We find that the SMC RSG stars are less likely to produce a large amount of dust (as indicated by the [3.6]-[8] color). There is a higher fraction of carbon-rich stars in the SMC, and these stars appear to able to reach colors as red as their LMC counterparts, indicating that C-rich dust forms efficiently in both galaxies. A preliminary estimate of the dust production in AGB and RSG stars reveals that the extreme C-rich AGB stars dominate the dust input in both galaxies, and that the O-rich stars may play a larger role in the LMC than in the SMC.Comment: Accepted for publication in AJ. 25 pages, 36 figures, Table 4 will be available electronically from A

A Large-Scale Rheumatoid Arthritis Genetic Study Identifies Association at Chromosome 9q33.2

Rheumatoid arthritis (RA) is a chronic, systemic autoimmune disease affecting both joints and extra-articular tissues. Although some genetic risk factors for RA are well-established, most notably HLA-DRB1 and PTPN22, these markers do not fully account for the observed heritability. To identify additional susceptibility loci, we carried out a multi-tiered, case-control association study, genotyping 25,966 putative functional SNPs in 475 white North American RA patients and 475 matched controls. Significant markers were genotyped in two additional, independent, white case-control sample sets (661 cases/1322 controls from North America and 596 cases/705 controls from The Netherlands) identifying a SNP, rs1953126, on chromosome 9q33.2 that was significantly associated with RA (ORcommon = 1.28, trend Pcomb = 1.45E-06). Through a comprehensive fine-scale-mapping SNP-selection procedure, 137 additional SNPs in a 668 kb region from MEGF9 to STOM on 9q33.2 were chosen for follow-up genotyping in a staged-approach. Significant single marker results (Pcomb<0.01) spanned a large 525 kb region from FBXW2 to GSN. However, a variety of analyses identified SNPs in a 70 kb region extending from the third intron of PHF19 across TRAF1 into the TRAF1-C5 intergenic region, but excluding the C5 coding region, as the most interesting (trend Pcomb: 1.45E-06 → 5.41E-09). The observed association patterns for these SNPs had heightened statistical significance and a higher degree of consistency across sample sets. In addition, the allele frequencies for these SNPs displayed reduced variability between control groups when compared to other SNPs. Lastly, in combination with the other two known genetic risk factors, HLA-DRB1 and PTPN22, the variants reported here generate more than a 45-fold RA-risk differential

CMS physics technical design report : Addendum on high density QCD with heavy ions

Peer reviewe

Virtual Morality: Transitioning from Moral Judgment to Moral Action?

The nature of moral action versus moral judgment has been extensively debated in numerous disciplines. We introduce Virtual Reality (VR) moral paradigms examining the action individuals take in a high emotionally arousing, direct action-focused, moral scenario. In two studies involving qualitatively different populations, we found a greater endorsement of utilitarian responses–killing one in order to save many others–when action was required in moral virtual dilemmas compared to their judgment counterparts. Heart rate in virtual moral dilemmas was significantly increased when compared to both judgment counterparts and control virtual tasks. Our research suggests that moral action may be viewed as an independent construct to moral judgment, with VR methods delivering new prospects for investigating and assessing moral behaviour

Current and prospective pharmacological targets in relation to antimigraine action

Migraine is a recurrent incapacitating neurovascular disorder characterized by unilateral and throbbing headaches associated with photophobia, phonophobia, nausea, and vomiting. Current specific drugs used in the acute treatment of migraine interact with vascular receptors, a fact that has raised concerns about their cardiovascular safety. In the past, α-adrenoceptor agonists (ergotamine, dihydroergotamine, isometheptene) were used. The last two decades have witnessed the advent of 5-HT1B/1D receptor agonists (sumatriptan and second-generation triptans), which have a well-established efficacy in the acute treatment of migraine. Moreover, current prophylactic treatments of migraine include 5-HT2 receptor antagonists, Ca2+ channel blockers, and β-adrenoceptor antagonists. Despite the progress in migraine research and in view of its complex etiology, this disease still remains underdiagnosed, and available therapies are underused. In this review, we have discussed pharmacological targets in migraine, with special emphasis on compounds acting on 5-HT (5-HT1-7), adrenergic (α1, α2, and β), calcitonin gene-related peptide (CGRP 1 and CGRP2), adenosine (A1, A2, and A3), glutamate (NMDA, AMPA, kainate, and metabotropic), dopamine, endothelin, and female hormone (estrogen and progesterone) receptors. In addition, we have considered some other targets, including gamma-aminobutyric acid, angiotensin, bradykinin, histamine, and ionotropic receptors, in relation to antimigraine therapy. Finally, the cardiovascular safety of current and prospective antimigraine therapies is touched upon