Perturbation Theory for Arbitrary Coupling Strength ?

We present a \emph{new} formulation of perturbation theory for quantum systems, designated here as: `mean field perturbation theory'(MFPT), which is free from power-series-expansion in any physical parameter, including the coupling strength. Its application is thereby extended to deal with interactions of \textit{arbitrary} strength and to compute system-properties having non-analytic dependence on the coupling, thus overcoming the primary limitations of the `standard formulation of perturbation theory' ( SFPT). MFPT is defined by developing perturbation about a chosen input Hamiltonian, which is exactly solvable but which acquires the non-linearity and the analytic structure~(in the coupling-strength)~of the original interaction through a self-consistent, feedback mechanism. We demonstrate Borel-summability of MFPT for the case of the quartic- and sextic-anharmonic oscillators and the quartic double-well oscillator (QDWO) by obtaining uniformly accurate results for the ground state of the above systems for arbitrary physical values of the coupling strength. The results obtained for the QDWO may be of particular significance since `renormalon'-free, unambiguous results are achieved for its spectrum in contrast to the well-known failure of SFPT in this case. \pacs{11.15.Bt,11.10.Jj,11.25.Db,12.38.Cy,03.65.Ge}Comment: 9 Pages, 1-Table, Accepted for for publication (Mod. Phys. Lett. A

Efficient Active Learning for Image Classification and Segmentation using a Sample Selection and Conditional Generative Adversarial Network

Training robust deep learning (DL) systems for medical image classification or segmentation is challenging due to limited images covering different disease types and severity. We propose an active learning (AL) framework to select most informative samples and add to the training data. We use conditional generative adversarial networks (cGANs) to generate realistic chest xray images with different disease characteristics by conditioning its generation on a real image sample. Informative samples to add to the training set are identified using a Bayesian neural network. Experiments show our proposed AL framework is able to achieve state of the art performance by using about 35% of the full dataset, thus saving significant time and effort over conventional methods

Deformations of special geometry: in search of the topological string

The topological string captures certain superstring amplitudes which are also encoded in the underlying string effective action. However, unlike the topological string free energy, the effective action that comprises higher-order derivative couplings is not defined in terms of duality covariant variables. This puzzle is resolved in the context of real special geometry by introducing the so-called Hesse potential, which is defined in terms of duality covariant variables and is related by a Legendre transformation to the function that encodes the effective action. It is demonstrated that the Hesse potential contains a unique subsector that possesses all the characteristic properties of a topological string free energy. Genus $g\leq3$ contributions are constructed explicitly for a general class of effective actions associated with a special-K\"ahler target space and are shown to satisfy the holomorphic anomaly equation of perturbative type-II topological string theory. This identification of a topological string free energy from an effective action is primarily based on conceptual arguments and does not involve any of its more specific properties. It is fully consistent with known results. A general theorem is presented that captures some characteristic features of the equivalence, which demonstrates at the same time that non-holomorphic deformations of special geometry can be dealt with consistently.Comment: 44 pages, LaTex; v2, v3: minor text improvement

Expectation of forward-backward rapidity correlations in p+pp+p collisions at the LHC energies

Forward-backward correlation strength ($b$) as a function of pesudorapidity intervals for experimental data from $p+\bar{p}$ non-singly diffractive collisions are compared to PYTHIA and PHOJET model calculations. The correlations are discussed as a function of rapidity window ($\Delta \eta$) symmetric about the central rapidity as well as rapidity window separated by a gap ($\eta_{gap}$) between forward and backward regions. While the correlations are observed to be independent of $\Delta \eta$, it is found to decrease with increase in $\eta_{gap}$. This reflects the role of short range correlations and justifies the use of $\eta_{gap}$ to obtain the accurate information about the physics of interest, the long range correlations. The experimental $b$ value shows a linear dependence on $\ln \sqrt{s}$ with the maximum value of unity being reached at $\sqrt{s}$ = 16 TeV, beyond the top LHC energy. However calculations from the PYTHIA and PHOJET models indicate a deviation from linear dependence on $\ln \sqrt{s}$ and saturation in the $b$ values being reached beyond $\sqrt{s}$ = 1.8 TeV. Such a saturation in correlation values could have interesting physical interpretations related to clan structures in particle production. Strong forward-backward correlations are associated with cluster production in the collisions. The average number of charged particles to which the clusters fragments, called the cluster size, are found to also increase linearly with $\ln \sqrt{s}$ for both data and the models studied. The rate of increase in cluster size vs. $\ln \sqrt{s}$ from models studied are larger compared to those from the data and higher for PHOJET compared to PYTHIA. Our study indicates that the forward-backward measurements will provide a clear distinguishing observable for the models studied at LHC energies.Comment: 15 pages, 14 Figures, accepted for publication in International Journal of Modern Physics