Signed degree sets in signed graphs

The set D of distinct signed degrees of the vertices in a signed graph G is called its signed degree set. In this paper, we prove that every non-empty set of positive (negative) integers is the signed degree set of some connected signed graph and determine the smallest possible order for such a signed graph. We also prove that every non-empty set of integers is the signed degree set of some connected signed graph

Oscillator strengths and excited-state couplings for double excitations in time-dependent density functional theory

Although useful to extract excitation energies of states of double-excitation character in time-dependent density functional theory that are missing in the adiabatic approximation, the frequency-dependent kernel derived earlier [J. Chem. Phys. {\bf 120}, 5932 (2004)] was not designed to yield oscillator strengths. These are required to fully determine linear absorption spectra and they also impact excited-to-excited-state couplings that appear in dynamics simulations and other quadratic response properties. Here we derive a modified non-adiabatic kernel that yields both accurate excitation energies and oscillator strengths for these states. We demonstrate its performance on a model two-electron system, the Be atom, and on excited-state transition dipoles in the LiH molecule at stretched bond-lengths, in all cases producing significant improvements over the traditional approximations

The Exact Exchange-Correlation Potential in Time-Dependent Density Functional Theory: Choreographing Electrons with Steps and Peaks

The time-dependent exchange-correlation potential has an unusual task in directing fictitious non-interacting electrons to move with exactly the same probability density as true interacting electrons. This has intriguing implications for its structure, especially in the non-perturbative regime, leading to step and peak features that cannot be captured by bootstrapping any ground-state functional approximations. We review what has been learned about these features in the exact exchange-correlation potential in time-dependent density functional theory in the past decade or so, and implications for the performance of simulations when electrons are driven far from any ground-state

Exact time-dependent density-functional theory for nonperturbative dynamics of the helium atom

By inverting the time-dependent Kohn-Sham equation for a numerically exact dynamics of the helium atom, we show that the dynamical step and peak features of the exact correlation potential found previously in one-dimensional models persist for real three-dimensional systems. We demonstrate that the Kohn-Sham and true current densities differ by a rotational component. The results have direct implications for approximate time-dependent density functional theory calculations of atoms and molecules in strong fields, emphasizing the need to go beyond the adiabatic approximation, and highlighting caution in the quantitative use of the Kohn-Sham currentFinancial support from the National Science Foundation Award No. CHE-1940333 (DD) and from the Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under Award No. DESC0020044 (NTM, LL) are gratefully acknowledged. J.F. acknowledges financial support from the European Research Council through Grant No. ERC-2016- StG-714870, and by the Spanish Ministry for Science, Innovation, and Universities: Agencia Estatal de Investigación through Grant No. RTI2018-099737-B-I0

Probing Pseudo-Dirac Neutrino through Detection of Neutrino Induced Muons from GRB Neutrinos

The possibility to verify the pseudo-Dirac nature of neutrinos is investigated here via the detection of ultra high energy neutrinos from distant cosmological objects like GRBs. The very long baseline and the energy range from $\sim$ TeV to $\sim$ EeV for such neutrinos invokes the likelihood to probe very small pseude-Dirac splittings. The expected secondary muons from such neutrinos that can be detected by a kilometer scale detector such as ICECUBE is calculated. The pseudo-Dirac nature, if exists, will show a considerable departure from flavour oscillation scenario in the total yield of the secondary muons induced by such neutrinos.Comment: 11 pages, 3figure

Neutrino Induced Upward Going Muons from a Gamma Ray Burst in a Neutrino Telescope of Km^2 Area

The number of neutrino induced upward going muons from a single Gamma Ray Burst (GRB) expected to be detected by the proposed kilometer scale IceCube detector at the South Pole location has been calculated. The effects of the Lorentz factor, total energy of the GRB emitted in neutrinos and its distance from the observer (red shift) on the number of neutrino events from the GRB have been examined. The present investigation reveals that there is possibility of exploring the early Universe with the proposed kilometer scale IceCube neutrino telescope.Comment: 18pages, 5 figures. Physical Review D in pres

Numerical characterisation of label free optical biosensors

There is a significant need for the development and use of numerical methods to simulate advance and complex optical biosensor structures. Finite Element Method (FEM) has been established as one of the most powerful and versatile numerical method and has been implemented in this thesis to characterize, analyse and optimise label-free optical biosensors for the detection of micron size biological objects like bacteria such as E.coli and nanometre size biomolecules such as antibody, nucleic acids and proteins. These sensors are all suitable for deep-probe sensing as large evanescent field can be excited in the sensing medium with substantial penetration depth achieved by techniques like Surface Plasmon Resonance (SPR) and sensor architectures based on nanowires and slot waveguides. This thesis presents three different architectures of label-free optical biosensors. First, a fiber optic surface plasmon resonance (SPR) biosensor for the detection of E.Coli is optically modeled by using the finite-element approach in conjunction with the perturbation technique which is computationally more efficient and can be used for waveguides with low or medium loss values. The same sensing architecture is used when surrounding index is varied from 1.30 -1.44 to cover most of the biological elements that are used in the biosensing applications. Second one is based on evanescent-wave guiding properties of nanowire waveguides a theoretical investigation of silica nanowires employing a wire assembled Mach-Zehnder structure to detect the presence of E.Coli is studied second. Finally, a slot-waveguide based micro-ring resonator is investigated for the detection of DNA Hybridization using H-field FEM based full-vector formulation. It is found that all of the numerical methods provide good agreement with the experimental sensitivities and detection limits

Category-selective top-down modulation in the fusiform face area of the human brain during visual search

Several regions in the ventral-temporal cortex of the human brain are thought to have representations of specific categories of objects. Furthermore, a distributed network of frontal and parietal brain regions is implicated in attentional control. It is assumed that during visual search, attention-control regions send top-down signals to the target category-selective areas to bias the processing in favour of the attended object category. However, little is known about such causal interactions during naturalistic visual search. Here we assess the influence of attention-control brain regions on a well-known face selective area fusiform face area (FFA) during natural visual search using Granger causality analysis. Our results indicate that attending to humans enhances the influence of attention-control regions on the fusiform face area. © 2017 IEEE