Two-dimensional Parameter Space Research Articles

Deep learning based bilateral filtering for edge-preserving denoising of respiratory-gated PET

BackgroundResidual image noise is substantial in positron emission tomography (PET) and one of the factors limiting lesion detection, quantification, and overall image quality. Thus, improving noise reduction remains of considerable interest. This is especially true for respiratory-gated PET investigations. The only broadly used approach for noise reduction in PET imaging has been the application of low-pass filters, usually Gaussians, which however leads to loss of spatial resolution and increased partial volume effects affecting detectability of small lesions and quantitative data evaluation. The bilateral filter (BF) — a locally adaptive image filter — allows to reduce image noise while preserving well defined object edges but manual optimization of the filter parameters for a given PET scan can be tedious and time-consuming, hampering its clinical use. In this work we have investigated to what extent a suitable deep learning based approach can resolve this issue by training a suitable network with the target of reproducing the results of manually adjusted case-specific bilateral filtering.MethodsAltogether, 69 respiratory-gated clinical PET/CT scans with three different tracers ([18F]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[^{18}\ ext {F}]$$\\end{document}FDG, [18F]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[^{18}\ ext {F}]$$\\end{document}L-DOPA, [68Ga]\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[^{68}\ ext {Ga}]$$\\end{document}DOTATATE) were used for the present investigation. Prior to data processing, the gated data sets were split, resulting in a total of 552 single-gate image volumes. For each of these image volumes, four 3D ROIs were delineated: one ROI for image noise assessment and three ROIs for focal uptake (e.g. tumor lesions) measurements at different target/background contrast levels. An automated procedure was used to perform a brute force search of the two-dimensional BF parameter space for each data set to identify the “optimal” filter parameters to generate user-approved ground truth input data consisting of pairs of original and optimally BF filtered images. For reproducing the optimal BF filtering, we employed a modified 3D U-Net CNN incorporating residual learning principle. The network training and evaluation was performed using a 5-fold cross-validation scheme. The influence of filtering on lesion SUV quantification and image noise level was assessed by calculating absolute and fractional differences between the CNN, manual BF, or original (STD) data sets in the previously defined ROIs.ResultsThe automated procedure used for filter parameter determination chose adequate filter parameters for the majority of the data sets with only 19 patient data sets requiring manual tuning. Evaluation of the focal uptake ROIs revealed that CNN as well as BF based filtering essentially maintain the focal SUVmax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {SUV}_\ ext {max}$$\\end{document} values of the unfiltered images with a low mean ± SD difference of δSUVmaxCNN,STD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \ ext {SUV}_\ ext {max}^{\ ext {CNN},\ ext {STD}}$$\\end{document} = (−3.9 ± 5.2)% and δSUVmaxBF,STD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \ ext {SUV}_\ ext {max}^{\ ext {BF},\ ext {STD}}$$\\end{document} = (−4.4 ± 5.3)%. Regarding relative performance of CNN versus BF, both methods lead to very similar SUVmax\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {SUV}_\ ext {max}$$\\end{document} values in the vast majority of cases with an overall average difference of δSUVmaxCNN,BF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \ ext {SUV}_\ ext {max}^{\ ext {CNN},\ ext {BF}}$$\\end{document} = (0.5 ± 4.8)%. Evaluation of the noise properties showed that CNN filtering mostly satisfactorily reproduces the noise level and characteristics of BF with δNoiseCNN,BF\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta \ ext {Noise}^{\ ext {CNN},\ ext {BF}}$$\\end{document} = (5.6 ± 10.5)%. No significant tracer dependent differences between CNN and BF were observed.ConclusionsOur results show that a neural network based denoising can reproduce the results of a case by case optimized BF in a fully automated way. Apart from rare cases it led to images of practically identical quality regarding noise level, edge preservation, and signal recovery. We believe such a network might proof especially useful in the context of improved motion correction of respiratory-gated PET studies but could also help to establish BF-equivalent edge-preserving CNN filtering in clinical PET since it obviates time consuming manual BF parameter tuning.

Measurement of t-channel production of single top quarks and antiquarks in pp collisions at 13 TeV using the full ATLAS Run 2 data sample

The production of single top quarks and top antiquarks via the t-channel exchange of a virtual W boson is measured in proton-proton collisions at a centre-of-mass energy of 13 TeV at the LHC using 140 fb−1 of ATLAS data. The total cross-sections are determined to be σtq=137−8+8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sigma (tq)={137}_{-8}^{+8} $$\\end{document} pb and σt¯q=84−5+6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sigma \\left(\\overline{t}q\\right)={84}_{-5}^{+6} $$\\end{document} pb for top-quark and top-antiquark production, respectively. The combined cross-section is found to be σtq+t¯q=221−13+13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sigma \\left( tq+\\overline{t}q\\right)={221}_{-13}^{+13} $$\\end{document} pb and the cross-section ratio is Rt=σtq/σt¯q=1.636−0.034+0.036\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {R}_t=\\sigma (tq)/\\sigma \\left(\\overline{t}q\\right)={1.636}_{-0.034}^{+0.036} $$\\end{document}. The predictions at next-to-next-to-leading-order in quantum chromodynamics are in good agreement with these measurements. The predicted value of Rt using different sets of parton distribution functions is compared with the measured value, demonstrating the potential to further constrain the functions when using this result in global fits. The measured cross-sections are interpreted in an effective field theory approach, setting limits at the 95% confidence level on the strength of a four-quark operator and an operator coupling the third quark generation to the Higgs boson doublet: −0.37<CQq3,1/Λ2<0.06\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ -0.37<{C}_{Qq}^{3,1}/{\\Lambda}^2<0.06 $$\\end{document} and −0.87<CϕQ3/Λ2<1.42\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ -0.87<{C}_{\\phi Q}^3/{\\Lambda}^2<1.42 $$\\end{document}. The constraint |Vtb| > 0.95 at the 95% confidence level is derived from the measured value of σtq+t¯q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sigma \\left( tq+\\overline{t}q\\right) $$\\end{document}, assuming that the Wtb interaction is a left-handed weak coupling and that |Vtb| ≫ |Vtd|, |Vts|. In a more general approach, pairs of CKM matrix elements involving top quarks are simultaneously constrained, leading to confidence contours in the corresponding two-dimensional parameter spaces.

Design and fabrication of a coupled high-Q photonic nanocavity system with large coupling coefficients.

In a previous work, we demonstrated a coupled cavity system where photons in one storage cavity can be transferred to another storage cavity at an arbitrary time by applying a voltage pulse to a third cavity placed in a p-i-n junction. In this work, we demonstrate methods to improve the transfer efficiency and photon lifetimes of such a coupled system. Firstly, we designed a photonic-crystal structure that achieves a large coupling coefficient without reducing the radiation quality factor compared to the previously proposed structure: The photonic-crystal design was changed to a more symmetric configuration to suppress radiation losses and then optimized using an automatic structure tuning method based on the Covariance Matrix Adaptive Evolutional Strategy (CMAES). Here we added two improvements to achieve an evolution toward the desired direction in the two-dimensional target parameter space (spanned by the coupling coefficient and the inverse radiation loss). Secondly, to improve the experimental cavity quality factors, we developed a fabrication process that reduces the surface contamination associated with the fabrication of the p-i-n junction: We covered the photonic structure with a SiO2 mask to avoid the contamination and the electrode material was changed from Al to Au/Cr to enable cleaning by a weak acid. Owing to these improvements of the cavity design and the fabrication process, the obtained system provides coupling strengths that are about three times stronger and photon lifetimes that are about two times longer, compared to the previously reported system.

Predicting optical properties of different photonic crystal fibers from 2D structural images using convolutional neural network and transfer learning

An efficient and accurate joint neural network has been established to predict the optical properties of different photonic crystal fibers using two-dimensional structural images. The input variables of this network are structural images derived from the two-dimensional material refractive index distribution of the fiber cross-section. The structural images have greater flexibility and facilitate generalization research and transfer learning testing on various types of optical fibers. The generalization properties of this neural network for other photonic crystal fibers with different lattice arrangements have been investigated, and the corresponding transfer learning method is also proposed. With this transfer learning method, only a small amount of data is required to train and update the parameter weights of the last fully connected hidden layers. As a result, efficient and accurate prediction performance can be achieved for other photonic crystal fibers with different lattice arrangements. The proposed joint neural network and the transfer learning method are flexible and efficient, which provide new approaches for more flexible optimization and reverse design of optical fiber structures in the two-dimensional parameter space.

Resolving the topology of encircling multiple exceptional points

Non-Hermiticity has emerged as a new paradigm for controlling coupled-mode systems in ways that cannot be achieved with conventional techniques. One aspect of this control that has received considerable attention recently is the encircling of exceptional points (EPs). To date, most work has focused on systems consisting of two modes that are tuned by two control parameters and have isolated EPs. While these systems exhibit exotic features related to EP encircling, it has been shown that richer behavior occurs in systems with more than two modes. Such systems can be tuned by more than two control parameters, and contain EPs that form a knot-like structure. Control loops that encircle this structure cause the system’s eigenvalues to trace out non-commutative braids. Here we consider a hybrid scenario: a three-mode system with just two control parameters. We describe the relationship between control loops and their topology in the full and two-dimensional parameter space. We demonstrate this relationship experimentally using a three-mode mechanical system in which the control parameters are provided by optomechanical interaction with a high-finesse optical cavity.

The Higgs-gluon form factor at three loops in QCD with three mass scales

We report on the complete three-loop corrections to the Higgs-gluon form factor in QCD. While previous calculations are based on QCD with a single heavy quark of arbitrary mass, we extend the study to QCD involving two different massive quark flavors. Thereby, the full set of possible Feynman diagrams at three-loop order is taken into account. Employing differential equations for the relevant master integrals, we determine the form factor in terms of analytic expansions. Outside the radii of convergence, we compute high-precision numerical samples over the two-dimensional physical parameter space. Our new findings will enter as virtual corrections the computation of the top-bottom interference in hadronic Higgs-boson production at next-to-next-to-leading order (NNLO) in QCD.

Optimization of laser pumping for the generation of multi-pulse structures in fiber lasers

We address the challenge of configuring a fiber laser cavity to enable efficient access to multi-pulse structures such as dissipative soliton molecules. We theoretically compare multi-pulsing routes in the parameter space of the laser. By using a two-dimensional parameter space, we experimentally demonstrate an important reduction in the laser pumping power required to form soliton molecules.

Topological Singularity Pair in Nonreciprocal Non-Hermitian Lossy-dielectric Gyromagnetic Metasurface

The transmission properties of a nonreciprocal non-Hermitian metasurface composed of lossy dielectric and gyromagnetic materials are studied with closed-form analytical solutions. It is found that a pair of opposite topological singularities of isolation ratio exist in a two-dimensional (2D) parameter space, and their evolution with parameter adjustment is preliminarily studied. These results provide clues for the design of optical devices. Further study of the mechanism of this singular behavior may reveal the complex systematic effect of non-Hermiticity and non-reciprocity on optical performance.

Search for periodic signals in the dielectron and diphoton invariant mass spectra using 139 fb−1 of pp collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV with the ATLAS detector

A search for physics beyond the Standard Model inducing periodic signals in the dielectron and diphoton invariant mass spectra is presented using 139 fb−1 of s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV pp collision data collected by the ATLAS experiment at the LHC. Novel search techniques based on continuous wavelet transforms are used to infer the frequency of periodic signals from the invariant mass spectra and neural network classifiers are used to enhance the sensitivity to periodic resonances. In the absence of a signal, exclusion limits are placed at the 95% confidence level in the two-dimensional parameter space of the clockwork gravity model. Model-independent searches for deviations from the background-only hypothesis are also performed.

Nonlinear dynamics of a single-gap terahertz split-ring resonator under electromagnetic radiation.

Research into metasurfaces is developing rapidly and is topical due to their importance and applications in various fields such as communications, cryptography, and sensing, to name a few. These materials are artificially engineered to manipulate/control electromagnetic (EM) waves, in order to present a particular functionality. In this regard, nonlinear metasurfaces may present particular functionalities that remain to be discovered. In this paper, we numerically investigate the dynamic behaviors caused by the motion of charge carriers under the intense EM field at the gap of a single nonlinear split-ring resonator (NSRR) in the terahertz (THz) frequency range. We derive the mathematical model that is used to examine the excitation properties of the NSRR and then demonstrate various tuning regions. Analysis of the two-dimensional parameter space reveals that the NSRR exhibits periodic, chaotic patterns as the amplitude of the excitation field and the loss parameter vary. However, this chaotic behavior disappears when the loss parameter is very large. The period doubling that confirms the transition between the periodic and chaotic modes is explored using the bifurcation diagram. The sensitivity of the initial conditions is examined on three dynamic region plots. Our results correctly demonstrate that the NSRR exhibits the attractive phenomenon of multistability. The coexistence of two stable states is studied and confirmed on the basin of attractions for a fixed set of amplitude or loss parameters. The energy balance of the proposed model is well analyzed on the dynamic states and parameters to characterize the different oscillation regimes. The study of the multistability in the work represents an important first step toward the development of photonic memory devices in the THz frequency range.

Image encryption application and security analysis based on current modulated edge-emitting semiconductor lasers with pulse packages embedded in the microcontroller

This paper investigates the dynamical characteristics of current-modulated edge-emitting semiconductor lasers (CMEESLs) and their image encryption application. The associated dynamical characteristic of the CMEESL is divulged in the two-dimensional coordinate space of the system parameters by altering the modulation’s frequency and amplitude. The CMEESL divulges cyclical pulse packages preceded by cyclic-doubling cascade follow by complex pulse packages when the modulation current density frequency is limited below 1 GHz. The microcontroller implementation of the CMEESL is realized and its results find agreement compared with the numerical dynamics of the CMEESL. The chaotic equations describing CMEESL are first modeled in the LabVIEW program and random number generation (RNG) is performed. The obtained random numbers are subjected to the NIST 800–22 statistical standard package, proving its worth to be employed for encryption applications. Employing the random numbers gotten, the LabVIEW environment is used in encrypting the image. The encrypted image is subjected to histogram, correlation, number of pixel change rates (NPCR) - unified average changing intensity (UACI), and entropy analyses. The reliability of the method is proven by the success achieved in the encryption process.

Euclidean dynamical triangulations revisited

We conduct numerical simulations of a model of four-dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume, the model contains a discrete Einstein-Hilbert term with coupling $\ensuremath{\kappa}$ and a local measure term with coupling $\ensuremath{\beta}$ that weights triangulations according to the number of simplices sharing each vertex. We map out the phase diagram in this two-dimensional parameter space and compute a variety of observables that yield information on the nature of any continuum limit. Our results are consistent with a line of first-order phase transitions with a latent heat that decreases as $\ensuremath{\kappa}\ensuremath{\rightarrow}\ensuremath{\infty}$. We find a Hausdorff dimension along the critical line that approaches ${D}_{H}=4$ for large $\ensuremath{\kappa}$ and a spectral dimension consistent with ${D}_{s}=\frac{3}{2}$ at short distances. These results are broadly in agreement with earlier works on Euclidean dynamical triangulation models which utilize degenerate triangulations and/or different measure terms and indicate that such models exhibit a degree of universality.

Classical analogous quantum coherent superposition through the Hertz-type nonlinearity of elastic granules

The theory of quantum superposition of states is one of the fundamental concepts related to quantum information science and technology (QIST). Two or more pure quantum states can be superposed to get a distinct quantum state, and one of the examples is the quantum bit, or qubit, state. But decoherence makes it easy for the current qubits, the most critical part of QIST platforms, to lose their superposition of states. Therefore, we theoretically propose and experimentally realize a classical analogous to the coherent superposition of energy states through the Hertz-type nonlinearity of elastic granules driven externally. The granules’ nonlinear vibrations depend mutually through phase and form a coherent superposition when projected into linear modes of vibration. We demonstrate how the state vector components can emerge from the amplitudes of coherent states, spanning to the two-dimensional time-dependent parametric Hilbert space. These amplitudes represent an actual amplitude rather than a probability amplitude, which opens the possibility of exploring two-state quantum-like computations through the superposition of states without decoherence and wave function collapse. These characteristics make it possible to understand the material-based quantum analogous information technology through experimentation of elastic bit.

The cost of an ALP solution to the neutral B-anomalies

The neutral anomalies in B decays are analysed in terms of the tree-level exchange of an axion-like-particle (ALP), within the effective field theory framework. The complete two-dimensional parameter space for ALP couplings to electrons and muons is explored. The solutions to RK and to the two energy bins of {R}_{K^{ast }} are confronted with the impact of ALP exchange on other observables (meson oscillations, leptonic and semileptonic decays of B mesons including searches for new resonances, astrophysical constraints), as well as with the theoretical domain of validity of the effective theory. Solutions based on ALPs heavier than B mesons, or lighter than twice the muon mass, are shown to be excluded. In contrast, the exchange of on-shell ALPs provides solutions to RK and/or {R}_{K^{ast }} within 2σ sensitivity which are technically compatible with those constraints. Furthermore, a “golden ALP mass” is identified at the frontier between the two energy bin windows of {R}_{K^{ast }} , which could simultaneously explain these two {R}_{K^{ast }} anomalies together with RK; this calls for the convenience of different energy binning which would easily clear up this (unlikely) possibility. The impact of smearing on data analysis is also discussed. When loop effects are taken into account, the solutions found can be in addition compatible with the data on the g − 2 of the electron but not simultaneously with those on the g − 2 of the muon. Furthermore, loop effects may require fine-tunings of some coupling values.

Fate of exceptional points under interactions: Reduction of topological classifications

Despite recent extensive studies of the non-Hermitian topology, understanding interaction effects is left as a crucial question. In this paper, we address interaction effects on exceptional points which are protected by the non-trivial point-gap topology unique to non-Hermitian systems. Our analysis in a two-dimensional parameter space elucidates the existence of exceptional points and symmetry-protected exceptional rings fragile against interactions; they are topologically protected only in non-interacting cases. This fragility of exceptional points and symmetry-protected exceptional rings arises from the reduction of non-Hermitian topological classifications, which is elucidated by introducing topological invariants of the second-quantized Hamiltonian for both non-interacting and interacting cases. These topological invariants are also available to analyze the reduction phenomena of gapped systems. The above results strongly suggest similar reduction phenomena of exceptional points in generic cases and open up a new direction of research in the non-Hermitian topology.

Stability and bifurcation analysis of a discrete-time host-parasitoid model with Holling III functional response

&lt;abstract&gt;&lt;p&gt;We study the dynamical properties of a discrete-time host-parasitoid model with Holling type III functional response. It is shown that flip bifurcation and Neimark-Sacker bifurcation occur in certain parameter regimes. A sufficient condition based on the model parameters for which both populations can coexist is derived. The boundedness, existence and local stability of the unique equilibrium are proved. In addition, the numerical simulations have been done, in addition to supporting the analytical findings, more behaviors are extracted from the model in a two-dimensional parameter space. Finally, we emphasize the importance of clearly presenting biological assumptions that are inherent to the structure of a discrete model.&lt;/p&gt;&lt;/abstract&gt;

Quantum and classical branching flow in space and time

Branching flow, a phenomenon known for steady wave propagation in two-dimensional weakly correlated random potential, is also present in the time-dependent Schr\"odinger equation for a single particle in one dimension, moving in a fluctuating random potential. We explore the two-dimensional parameter space of this model using numerical simulations and identify its classical regions, where just one classical parameter is sufficient for its specification, and its quantum region, where such a simplification is not possible. We also identify the region of the parameter space where known analytical results of a classical white noise model are relevant. Qualitative behavior of quantum and classical particle dynamics is discussed in terms of branching time scale and a new time scale related to a particle's kinetic energy.

Fermion-axion stars: Static solutions and dynamical stability

We construct spherically symmetric static solutions of the Einstein-Klein-Gordon-Euler system involving a complex scalar field governed by a periodic potential that emerges in models of axionlike particles and fermionic matter modeled by a perfect fluid with a polytropic equation of state. Such solutions describe gravitationally bound composites of fermions and axions, which we dub fermion-axion stars. Sequences of pure axion stars in the existence domain may show the presence of multiple stable branches depending on the value of the decay constant parameter in the potential; this reflects in the appearance of multiple islands of stability in the two-dimensional parameter space of fermion-axion configurations. We investigate the domain of existence for three different values of the decay constant, identifying one or more regions of linear stability, making use of a method we already employed in previous works. We confirm the results from the linear analysis performing fully nonlinear numerical relativity evolutions. In this context, we perform several numerical simulations to identify regions in the parameter space where unstable models face different fates: the collapse to a Schwarzschild black hole, the migration to a stable model, and finally the dispersion of the scalar field together with the dilution of the fermionic matter, which approaches a static fermion star model with very low mass. This latter scenario was never observed in previous models without the periodic potential.

Understanding noise in cell signalling in the prospect of drug-targets

The introduction of noise to signals can alter central regulatory switches of cellular processes leading to diseases. Noise is inherently present in the cellular signalling system and plays a decisive role in the input–output (I/O) relation. The current study aims to understand the noise tolerance of motif structures in the cell signalling processes. The vulnerability of a node to noise could be a significant factor in causing signalling error and need to be controlled. We developed stochastic differential equation (SDE) based mathematical models for different network motifs with two nodes and studied the association between motif structure and signal–noise relation. A two-dimensional parameter space analysis on motif sensitivity with noise and input signal variation was performed to classify and rank the motifs. Identifying sensitive motifs and their high druggability infers their significance in screening potential drug-target candidates. Finally, we proposed a theoretical framework to identify nodes from a network as potential drug targets. We applied this mathematical formalism to three cancer networks to identify drug-targets and validated them with existing databases.

On the Formation of Over-ionized Plasma in Evolved Supernova Remnants

One of the outstanding mysteries surrounding the rich diversity found in supernova remnants (SNRs) is the recent discovery of over-ionized or recombining plasma from a number of dynamically evolved objects. To help decipher its formation mechanism, we have developed a new simulation framework capable of modeling the time evolution of the ionization state of the plasma in an SNR. The platform is based on a one-dimensional hydrodynamics code coupled to a fully time-dependent nonequilibrium ionization calculation, accompanied by a spectral synthesis code to generate space-resolved broadband X-ray spectra for SNRs at arbitrary ages. We perform a comprehensive parametric survey to investigate the effects of different circumstellar environments on the ionization state evolution in SNRs up to a few 104 yr. A two-dimensional parameter space, spanned by arrays of interstellar medium (ISM) densities and mass-loss rates of the progenitor, is used to create a grid of models for the surrounding environment, in which a core-collapse explosion is triggered. Our results show that a recombining plasma can be successfully reproduced in the case of a young SNR (a few 100 to 1000 yr old) expanding fast in a spatially extended low-density wind, an old SNR (>a few 1000 yr) expanding in a dense ISM, or an old SNR broken out from a confined dense wind region into a tenuous ISM. Finally, our models are confronted with observations of evolved SNRs, and an overall good agreement is found except for a couple of outliers.