The Amplitude of Non-Equilibrium Quantum Interference in Metallic Mesoscopic Systems

We study the influence of a DC bias voltage V on quantum interference corrections to the measured differential conductance in metallic mesoscopic wires and rings. The amplitude of both universal conductance fluctuations (UCF) and Aharonov-Bohm effect (ABE) is enhanced several times for voltages larger than the Thouless energy. The enhancement persists even in the presence of inelastic electron-electron scattering up to V ~ 1 mV. For larger voltages electron-phonon collisions lead to the amplitude decaying as a power law for the UCF and exponentially for the ABE. We obtain good agreement of the experimental data with a model which takes into account the decrease of the electron phase-coherence length due to electron-electron and electron-phonon scattering.Comment: New title, refined analysis. 7 pages, 3 figures, to be published in Europhysics Letter

Fermionization, Convergent Perturbation Theory, and Correlations in the Yang-Mills Quantum Field Theory in Four Dimensions

We show that the Yang-Mills quantum field theory with momentum and spacetime cutoffs in four Euclidean dimensions is equivalent, term by term in an appropriately resummed perturbation theory, to a Fermionic theory with nonlocal interaction terms. When a further momentum cutoff is imposed, this Fermionic theory has a convergent perturbation expansion. To zeroth order in this perturbation expansion, the correlation function $E(x,y)$ of generic components of pairs of connections is given by an explicit, finite-dimensional integral formula, which we conjecture will behave as $$E(x,y) \sim |x - y|^{-2 - 2 d_G},$$ \noindent for $|x-y|>>0,$ where $d_G$ is a positive integer depending on the gauge group $G.$ In the case where $G=SU(n),$ we conjecture that $$d_G = {\rm dim}SU(n) - {\rm dim}S(U(n-1) \times U(1)),$$ \noindent so that the rate of decay of correlations increases as $n \to \infty.$Comment: Minor corrections of notation, style and arithmetic errors; correction of minor gap in the proof of Proposition 1.4 (the statement of the Proposition was correct); further remark and references adde

Toric Structures on the Moduli Space of Flat Connections on a Riemann Surface: Volumes and the Moment Map

AbstractIn earlier papers we constructed a Hamiltonian torus action on an open dense set in the moduli space of flat SU(2) connections on a compact Riemann surface, where the dimension of the torus is half the dimension of the moduli space. This torus action shows that this set can be viewed symplectically as a (noncompact) toric variety. The number of integral points of the moment map for the torus action turns out to be identical to the Verlinde dimension D(g, k). As an application, we furnish a new proof of the relation between the large-k limit of D(g, k) and the volume of the moduli space. From our point of view, this relation follows from the equality between the symplectic volume of a toric variety and the Euclidean volume of the image of the moment map. Similar considerations are shown to give rise to the volumes of moduli spaces of parabolic bundles on a Riemann surface. Knowledge of these volumes has been shown to allow a proof of the Verlinde formula for the dimension of the space of holomorphic sections of line bundles on this space

On the Mechanical Response of Chopped Glass/Urethane Resin Composite: Data and Model

This report presents data on the creep response of a polymeric composite that is a candidate material for automotive applications. The above data were used to establish the basis for the mechanical characterization of the material's response over a wide range of stresses and temperatures, as well as under cyclic loading and due to exposure to distilled water. A constitutive model based upon fundamental principles of irreversible thermodynamics and continuum mechanics was employed to encompass the above mentioned database and to predict the response under more complex inputs. These latter tests verified the validity of the model

On Non-Abelian Symplectic Cutting

We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact groups. By using a degeneration based on the Vinberg monoid we give, in good cases, a global quotient description of a surgery construction introduced by Woodward and Meinrenken, and show it can be interpreted in algebro-geometric terms. A key ingredient is the `universal cut' of the cotangent bundle of the group itself, which is identified with a moduli space of framed bundles on chains of projective lines recently introduced by the authors.Comment: Various edits made, to appear in Transformation Groups. 28 pages, 8 figure

Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

HER2 mediates PSMA/mGluR1-driven resistance to the DS-7423 dual PI3K/mTOR inhibitor in PTEN wild-type prostate cancer models

Prostate cancer remains a major cause of male mortality. Genetic alteration of the PI3K/AKT/mTOR pathway is one of the key events in tumor development and progression in prostate cancer, with inactivation of the PTEN tumor suppressor being very common in this cancer type. Extensive evaluation has been performed on the therapeutic potential of PI3K/AKT/mTOR inhibitors and the resistance mechanisms arising in patients with PTEN-mutant background. However, in patients with a PTEN wild-type phenotype, PI3K/AKT/mTOR inhibitors have not demonstrated efficacy, and this remains an area of clinical unmet need. In this study, we have investigated the response of PTEN wild-type prostate cancer cell lines to the dual PI3K/mTOR inhibitor DS-7423 alone or in combination with HER2 inhibitors or mGluR1 inhibitors. Upon treatment with the dual PI3K/mTOR inhibitor DS-7423, PTEN wild-type prostate cancer CWR22/22RV1 cells upregulate expression of the proteins PSMA, mGluR1, and the tyrosine kinase receptor HER2, while PTEN-mutant LNCaP cells upregulate androgen receptor and HER3. PSMA, mGluR1, and HER2 exert control over one another in a positive feedback loop that allows cells to overcome treatment with DS-7423. Concomitant targeting of PI3K/mTOR with either HER2 or mGluR1 inhibitors results in decreased cell survival and tumor growth in xenograft studies. Our results suggest a novel therapeutic possibility for patients with PTEN wild-type PI3K/AKT-mutant prostate cancer based in the combination of PI3K/mTOR blockade with HER2 or mGluR1 inhibitors

HER2-HER3 heterodimer quantification by FRET-FLIM and patient subclass analysis of the COIN colorectal trial

BACKGROUND: The phase 3 MRC COIN trial showed no statistically significant benefit from adding the EGFR-target cetuximab to oxaliplatin-based chemotherapy in first-line treatment of advanced colorectal cancer. This study exploits additional information on HER2-HER3 dimerization to achieve patient stratification and reveal previously hidden subgroups of patients who had differing disease progression and treatment response. METHODS: HER2-HER3 dimerization was quantified by "FLIM Histology" in primary tumor samples from 550 COIN trial patients receiving oxaliplatin and fluoropyrimidine chemotherapy +/-cetuximab. Bayesian latent class analysis (LCA) and covariate reduction was performed to analyze the effects of HER2-HER3 dimer, RAS mutation and cetuximab on progression-free survival (PFS) and overall survival (OS). All statistical tests were two-sided. RESULTS: LCA on a cohort of 398 patients revealed two patient subclasses with differing prognoses (median OS: 1624 days [95%CI=1466-1816] vs 461 [95%CI=431-504]): Class 1 (15.6%) showed a benefit from cetuximab in OS (HR = 0.43 [95%CI=0.25-0.76]; p = 0.004). Class 2 showed an association of increased HER2-HER3 with better OS (HR = 0.64 [95%CI=0.44-0.94]; p = 0.02). A class prediction signature was formed and tested on an independent validation cohort (N = 152) validating the prognostic utility of the dimer assay. Similar subclasses were also discovered in full trial dataset (N = 1,630) based on 10 baseline clinicopathological and genetic covariates. CONCLUSIONS: Our work suggests that the combined use of HER dimer imaging and conventional mutation analyses will be able to identify a small subclass of patients (>10%) who will have better prognosis following chemotherapy. A larger prospective cohort will be required to confirm its utility in predicting the outcome of anti-EGFR treatment

Measures on Banach Manifolds and Supersymmetric Quantum Field Theory

We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum field theory. We give three concrete examples of our construction. The first example is a family $\mu_P^{s,t}$ of measures on a space of functions on the two-torus, parametrized by a polynomial $P$ (the Wess-Zumino-Landau-Ginzburg model). The second is a family \mu_\cG^{s,t} of measures on a space \cG of maps from $\P^1$ to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family $\mu_{M,G}^{s,t}$ of measures on the product of a space of connection s on the trivial principal bundle with structure group $G$ on a three-dimensional manifold $M$ with a space of \fg-valued three-forms on $M.$ We show that these measures are positive, and that the measures \mu_\cG^{s,t} are Borel probability measures. As an application we show that formulas arising from expectations in the measures \mu_\cG^{s,1} reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar computation for the measures $\mu_{M,SU(2)}^{s,t},$ where $M$ is a homology three-sphere, will yield the Casson invariant of $M.$Comment: Minor correction

Mappings of least Dirichlet energy and their Hopf differentials

The paper is concerned with mappings between planar domains having least Dirichlet energy. The existence and uniqueness (up to a conformal change of variables in the domain) of the energy-minimal mappings is established within the class $\bar{\mathscr H}_2(X, Y)$ of strong limits of homeomorphisms in the Sobolev space $W^{1,2}(X, Y)$, a result of considerable interest in the mathematical models of Nonlinear Elasticity. The inner variation leads to the Hopf differential $h_z \bar{h_{\bar{z}}} dz \otimes dz$ and its trajectories. For a pair of doubly connected domains, in which $X$ has finite conformal modulus, we establish the following principle: A mapping $h \in \bar{\mathscr H}_2(X, Y)$ is energy-minimal if and only if its Hopf-differential is analytic in $X$ and real along the boundary of $X$. In general, the energy-minimal mappings may not be injective, in which case one observes the occurrence of cracks in $X$. Nevertheless, cracks are triggered only by the points in the boundary of $Y$ where $Y$ fails to be convex. The general law of formation of cracks reads as follows: Cracks propagate along vertical trajectories of the Hopf differential from the boundary of $X$ toward the interior of $X$ where they eventually terminate before making a crosscut.Comment: 51 pages, 4 figure