Versatile regularisation toolkit for iterative image reconstruction with proximal splitting algorithms

Ill-posed image recovery requires regularisation to ensure stability. The presented open-source regularisation toolkit consists of state-of-the-art variational algorithms which can be embedded in a plug-and-play fashion into the general framework of proximal splitting methods. The packaged regularisers aim to satisfy various prior expectations of the investigated objects, e.g., their structural characteristics, smooth or non-smooth surface morphology. The flexibility of the toolkit helps with the design of more advanced model-based iterative reconstruction methods for different imaging modalities while operating with simpler building blocks. The toolkit is written for CPU and GPU architectures and wrapped for Python/MATLAB. We demonstrate the functionality of the toolkit in application to Positron Emission Tomography (PET) and X-ray synchrotron computed tomography (CT)

The diplomat's dilemma: Maximal power for minimal effort in social networks

Closeness is a global measure of centrality in networks, and a proxy for how influential actors are in social networks. In most network models, and many empirical networks, closeness is strongly correlated with degree. However, in social networks there is a cost of maintaining social ties. This leads to a situation (that can occur in the professional social networks of executives, lobbyists, diplomats and so on) where agents have the conflicting objectives of aiming for centrality while simultaneously keeping the degree low. We investigate this situation in an adaptive network-evolution model where agents optimize their positions in the network following individual strategies, and using only local information. The strategies are also optimized, based on the success of the agent and its neighbors. We measure and describe the time evolution of the network and the agents' strategies.Comment: Submitted to Adaptive Networks: Theory, Models and Applications, to be published from Springe

Spin-spin Correlation in Some Excited States of Transverse Ising Model

We consider the transverse Ising model in one dimension with nearest-neighbour interaction and calculate exactly the longitudinal spin-spin correlation for a class of excited states. These states are known to play an important role in the perturbative treatment of one-dimensional transverse Ising model with frustrated second-neighbour interaction. To calculate the correlation, we follow the earlier procedure of Wu, use Szego's theorem and also use Fisher-Hartwig conjecture. The result is that the correlation decays algebraically with distance ($n$) as $1/\surd n$ and is oscillatory or non-oscillatory depending on the magnitude of the transverse field.Comment: 5 pages, 1 figur

High precision measurement of the associated strangeness production in proton proton interactions

A new high precision measurement of the reaction pp -> pK+Lambda at a beam momentum of 2.95 GeV/c with more than 200,000 analyzed events allows a detailed analysis of differential observables and their inter-dependencies. Correlations of the angular distributions with momenta are examined. The invariant mass distributions are compared for different regions in the Dalitz plots. The cusp structure at the N Sigma threshold is described with the Flatt\'e formalism and its variation in the Dalitz plot is analyzed.Comment: accepted for publication in Eur. Phys. J.

Painlev\'e V and time dependent Jacobi polynomials

In this paper we study the simplest deformation on a sequence of orthogonal polynomials, namely, replacing the original (or reference) weight $w_0(x)$ defined on an interval by $w_0(x)e^{-tx}.$ It is a well-known fact that under such a deformation the recurrence coefficients denoted as $\alpha_n$ and $\beta_n$ evolve in $t$ according to the Toda equations, giving rise to the time dependent orthogonal polynomials, using Sogo's terminology. The resulting "time-dependent" Jacobi polynomials satisfy a linear second order ode. We will show that the coefficients of this ode are intimately related to a particular Painlev\'e V. In addition, we show that the coefficient of $z^{n-1}$ of the monic orthogonal polynomials associated with the "time-dependent" Jacobi weight, satisfies, up to a translation in $t,$ the Jimbo-Miwa $\sigma$-form of the same $P_{V};$ while a recurrence coefficient $\alpha_n(t),$ is up to a translation in $t$ and a linear fractional transformation $P_{V}(\alpha^2/2,-\beta^2/2, 2n+1+\alpha+\beta,-1/2).$ These results are found from combining a pair of non-linear difference equations and a pair of Toda equations. This will in turn allow us to show that a certain Fredholm determinant related to a class of Toeplitz plus Hankel operators has a connection to a Painlev\'e equation

First Model-Independent Measurement of the Spin Triplet pΛp\Lambda Scattering Length from Final State Interaction in the p⃗p→pK+Λ\vec{p}p \rightarrow pK^{+}\Lambda Reaction

The $\vec{p}p \rightarrow pK^{+}\Lambda$ reaction has been measured with the COSY-TOF detector at a beam momentum of $2.7\,\mathrm{GeV}/c$. The polarized proton beam enables the measurement of the beam analyzing power by the asymmetry of the produced kaon ($A_N^{K}$). This observable allows the $p\Lambda$ spin triplet scattering length to be extracted for the first time model independently from the final-state interaction in the reaction. The obtained value is $a_{t} = (-2.55 ^{+0.72}_{-1.39} {}_{\textrm{stat.}} \pm 0.6_{\textrm{syst.}} \pm 0.3_{\textrm{theo.}})\mathrm{fm}$. This value is compatible with theoretical predictions and results from model-dependent analyses.Comment: Revised version as accepted for publication in PR

Complete Break Up of Ortho Positronium (Ps)- Hydrogenic ion System

The dynamics of the complete breakup process in an Ortho Ps - He+ system including electron loss to the continuum (ELC) is studied where both the projectile and the target get ionized. The process is essentially a four body problem and the present model takes account of the two centre effect on the electron ejected from the Ps atom which is crucial for a proper description of the ELC phenomena. The calculations are performed in the framework of Coulomb Distorted Eikonal Approximation. The exchange effect between the target and the projectile electron is taken into account in a consistent manner. The proper asymptotic 3-body boundary condition for this ionization process is also satisfied in the present model. A distinct broad ELC peak is noted in the fully differential cross sections (5DCS) for the Ps electron corroborating qualitatively the experiment for the Ps - He system. Both the dynamics of the ELC from the Ps and the ejected electron from the target He+ in the FDCS are studied using coplanar geometry. Interesting features are noted in the FDCS for both the electrons belonging to the target and the projectile.Comment: 14 pages,7 figure