Conchoidal transform of two plane curves

The conchoid of a plane curve $C$ is constructed using a fixed circle $B$ in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves $B$ and $C$ in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in \PP^2 \times \PP^2. We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve $C$ we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.Comment: 18 pages Revised version: slight title change, improved exposition, fixed proof of Theorem 5.3 Accepted for publication in Appl. Algebra Eng., Commun. Comput

Superconductors with Magnetic Impurities: Instantons and Sub-gap States

When subject to a weak magnetic impurity potential, the order parameter and quasi-particle energy gap of a bulk singlet superconductor are suppressed. According to the conventional mean-field theory of Abrikosov and Gor'kov, the integrity of the energy gap is maintained up to a critical concentration of magnetic impurities. In this paper, a field theoretic approach is developed to critically analyze the validity of the mean field theory. Using the supersymmetry technique we find a spatially homogeneous saddle-point that reproduces the Abrikosov-Gor'kov theory, and identify instanton contributions to the density of states that render the quasi-particle energy gap soft at any non-zero magnetic impurity concentration. The sub-gap states are associated with supersymmetry broken field configurations of the action. An analysis of fluctuations around these configurations shows how the underlying supersymmetry of the action is restored by zero modes. An estimate of the density of states is given for all dimensionalities. To illustrate the universality of the present scheme we apply the same method to study `gap fluctuations' in a normal quantum dot coupled to a superconducting terminal. Using the same instanton approach, we recover the universal result recently proposed by Vavilov et al. Finally, we emphasize the universality of the present scheme for the description of gap fluctuations in d-dimensional superconducting/normal structures.Comment: 18 pages, 9 eps figure

Liver fat in adults with GH deficiency: comparison to matched controls and the effect of GH replacement

CONTEXT: Existing data regarding the association between growth hormone deficiency (GHD) and liver fat content are conflicting. OBJECTIVE: We aimed i) to assess intrahepatocellular lipid (IHCL) content in hypopituitary adults with GHD compared to matched controls and ii) to evaluate the effect of growth hormone (GH) replacement on IHCL content. DESIGN: Cross-sectional comparison and controlled intervention study. PATIENTS, PARTICIPANTS: Cross-sectional comparison: 22 hypopituitary adults with GHD and 44 healthy controls matched for age, BMI, gender and ethnicity. Intervention study: 9 GHD patients starting GH replacement (GH Rx group), 9 GHD patients not starting replacement therapy (non-GH Rx group). INTERVENTION: Intervention study:GH replacement for 6 months in the GH Rx group, dosage was titrated to achieve normal IGF-1 levels. MAIN OUTCOME MEASURES: IHCL content determined by proton magnetic resonance spectroscopy (1 H MRS). RESULTS: Cross-sectional comparison: There was no difference in IHCL content between GHD patients and healthy controls (1.89% (0.30, 4.03) vs. 1.14% (0.22, 2.32); p=0.2), the prevalence of patients with hepatic steatosis (IHCL of ≥ 5.56%) was similar in the two groups (22.7% vs. 15.9%; chi square probability = 0.4). Intervention study: The change in IHCL content over 6 months did not differ between the GH Rx group and the non-GH Rx group (-0.63 ± 4.53% vs. +0.11 ± 1.46%; p=0.6). CONCLUSIONS: In our study liver fat content and the prevalence of hepatic steatosis did not differ between hypopituitary adults with GHD and matched controls. In GHD patients GH replacement had no effect on liver fat content

Peculiarities of sub-barrier fusion with quantum diffusion approach

With the quantum diffusion approach the unexpected behavior of fusion cross section, angular momentum, and astrophysical S-factor at sub-barrier energies has been revealed. Out of the region of short-range nuclear interaction and action of friction at turning point the decrease rate of the cross section under the barrier becomes smaller. The calculated results for the reactions with spherical nuclei are in a good agreement with the existing experimental data.Comment: 11 pages, 5 figure

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page

Topological doping and the stability of stripe phases

We analyze the properties of a general Ginzburg-Landau free energy with competing order parameters, long-range interactions, and global constraints (e.g., a fixed value of a total ``charge'') to address the physics of stripe phases in underdoped high-Tc and related materials. For a local free energy limited to quadratic terms of the gradient expansion, only uniform or phase-separated configurations are thermodynamically stable. ``Stripe'' or other non-uniform phases can be stabilized by long-range forces, but can only have non-topological (in-phase) domain walls where the components of the antiferromagnetic order parameter never change sign, and the periods of charge and spin density waves coincide. The antiphase domain walls observed experimentally require physics on an intermediate lengthscale, and they are absent from a model that involves only long-distance physics. Dense stripe phases can be stable even in the absence of long-range forces, but domain walls always attract at large distances, i.e., there is a ubiquitous tendency to phase separation at small doping. The implications for the phase diagram of underdoped cuprates are discussed.Comment: 18 two-column pages, 2 figures, revtex+eps

Measurement of the ttbar Production Cross Section in ppbar Collisions at sqrt(s)=1.96 TeV using Lepton + Jets Events with Lifetime b-tagging

We present a measurement of the top quark pair ($t\bar{t}$) production cross section ($\sigma_{t\bar{t}}$) in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV using 230 pb$^{-1}$ of data collected by the D0 experiment at the Fermilab Tevatron Collider. We select events with one charged lepton (electron or muon), missing transverse energy, and jets in the final state. We employ lifetime-based b-jet identification techniques to further enhance the $t\bar{t}$ purity of the selected sample. For a top quark mass of 175 GeV, we measure $\sigma_{t\bar{t}}=8.6^{+1.6}_{-1.5}(stat.+syst.)\pm 0.6(lumi.)$ pb, in agreement with the standard model expectation.Comment: 7 pages, 2 figures, 3 tables Submitted to Phys.Rev.Let

Development of a blood-based molecular biomarker test for identification of schizophrenia before disease onset

Recent research efforts have progressively shifted towards preventative psychiatry and prognostic identification of individuals before disease onset. We describe the development of a serum biomarker test for the identification of individuals at risk of developing schizophrenia based on multiplex immunoassay profiling analysis of 957 serum samples. First, we conducted a meta-analysis of five independent cohorts of 127 first-onset drug-naive schizophrenia patients and 204 controls. Using least absolute shrinkage and selection operator regression, we identified an optimal panel of 26 biomarkers that best discriminated patients and controls. Next, we successfully validated this biomarker panel using two independent validation cohorts of 93 patients and 88 controls, which yielded an area under the curve (AUC) of 0.97 (0.95-1.00) for schizophrenia detection. Finally, we tested its predictive performance for identifying patients before onset of psychosis using two cohorts of 445 pre-onset or at-risk individuals. The predictive performance achieved by the panel was excellent for identifying USA military personnel (AUC: 0.90 (0.86-0.95)) and help-seeking prodromal individuals (AUC: 0.82 (0.71-0.93)) who developed schizophrenia up to 2 years after baseline sampling. The performance increased further using the latter cohort following the incorporation of CAARMS (Comprehensive Assessment of At-Risk Mental State) positive subscale symptom scores into the model (AUC: 0.90 (0.82-0.98)). The current findings may represent the first successful step towards a test that could address the clinical need for early intervention in psychiatry. Further developments of a combined molecular/symptom-based test will aid clinicians in the identification of vulnerable patients early in the disease process, allowing more effective therapeutic intervention before overt disease onset

Forward pi^0 Production and Associated Transverse Energy Flow in Deep-Inelastic Scattering at HERA

Deep-inelastic positron-proton interactions at low values of Bjorken-x down to x \approx 4.10^-5 which give rise to high transverse momentum pi^0 mesons are studied with the H1 experiment at HERA. The inclusive cross section for pi^0 mesons produced at small angles with respect to the proton remnant (the forward region) is presented as a function of the transverse momentum and energy of the pi^0 and of the four-momentum transfer Q^2 and Bjorken-x. Measurements are also presented of the transverse energy flow in events containing a forward pi^0 meson. Hadronic final state calculations based on QCD models implementing different parton evolution schemes are confronted with the data.Comment: 27 pages, 8 figures and 3 table