Spatio-Temporal Low Count Processes with Application to Violent Crime Events

There is significant interest in being able to predict where crimes will happen, for example to aid in the efficient tasking of police and other protective measures. We aim to model both the temporal and spatial dependencies often exhibited by violent crimes in order to make such predictions. The temporal variation of crimes typically follows patterns familiar in time series analysis, but the spatial patterns are irregular and do not vary smoothly across the area. Instead we find that spatially disjoint regions exhibit correlated crime patterns. It is this indeterminate inter-region correlation structure along with the low-count, discrete nature of counts of serious crimes that motivates our proposed forecasting tool. In particular, we propose to model the crime counts in each region using an integer-valued first order autoregressive process. We take a Bayesian nonparametric approach to flexibly discover a clustering of these region-specific time series. We then describe how to account for covariates within this framework. Both approaches adjust for seasonality. We demonstrate our approach through an analysis of weekly reported violent crimes in Washington, D.C. between 2001-2008. Our forecasts outperform standard methods while additionally providing useful tools such as prediction intervals

Defect-induced modification of low-lying excitons and valley selectivity in monolayer transition metal dichalcogenides

We study the effect of point-defect chalcogen vacancies on the optical properties of monolayer transition metal dichalcogenides using ab initio GW and Bethe-Salpeter equation calculations. We find that chalcogen vacancies introduce unoccupied in-gap states and occupied resonant defect states within the quasiparticle continuum of the valence band. These defect states give rise to a number of strongly-bound defect excitons and hybridize with excitons of the pristine system, reducing the valley-selective circular dichroism. Our results suggest a pathway to tune spin-valley polarization and other optical properties through defect engineering

Origins of singlet fission in solid pentacene from an ab initio Green's-function approach

We develop a new first-principles approach to predict and understand rates of singlet fission with an ab initio Green's-function formalism based on many-body perturbation theory. Starting with singlet and triplet excitons computed from a GW plus Bethe-Salpeter equation approach, we calculate the exciton--bi-exciton coupling to lowest order in the Coulomb interaction, assuming a final state consisting of two non-interacting spin-correlated triplets with finite center-of-mass momentum. For crystalline pentacene, symmetries dictate that the only purely Coulombic fission decay from a bright singlet state requires a final state consisting of two inequivalent nearly degenerate triplets of nonzero, equal and opposite, center-of-mass momenta. For such a process, we predict a singlet lifetime of 40 to 150 fs, in very good agreement with experimental data, indicating that this process can dominate singlet fission in crystalline pentacene. Our approach is general and provides a framework for predicting and understanding multiexciton interactions in solids

Decay of Quasi-Particle in a Quantum Dot: the role of Energy Resolution

The disintegration of quasiparticle in a quantum dot due to the electron interaction is considered. It was predicted recently that above the energy \eps^{*} = \Delta(g/\ln g)^{1/2} each one particle peak in the spectrum is split into many components ($\Delta$ and $g$ are the one particle level spacing and conductance). We show that the observed value of \eps^{*} should depend on the experimental resolution \delta \eps. In the broad region of variation of \delta \eps the $\ln g$ should be replaced by \ln(\Delta/ g\delta \eps). We also give the arguments against the delocalization transition in the Fock space. Most likely the number of satellite peaks grows continuously with energy, being $\sim 1$ at \eps \sim \eps^{*}, but remains finite at \eps > \eps^{*}. The predicted logarithmic distribution of inter-peak spacings may be used for experimental confirmation of the below-Golden-Rule decay.Comment: 5 pages, REVTEX, 2 eps figures, version accepted for publication in Phys. Rev. Let

Energy Level Alignment at Molecule-Metal Interfaces from an Optimally-Tuned Range-Separated Hybrid Functional

The alignment of the frontier orbital energies of an adsorbed molecule with the substrate Fermi level at metal-organic interfaces is a fundamental observable of significant practical importance in nanoscience and beyond. Typical density functional theory calculations, especially those using local and semi-local functionals, often underestimate level alignment leading to inaccurate electronic structure and charge transport properties. In this work, we develop a new fully self-consistent predictive scheme to accurately compute level alignment at certain classes of complex heterogeneous molecule-metal interfaces based on optimally-tuned range-separated hybrid functionals. Starting from a highly accurate description of the gas-phase electronic structure, our method by construction captures important nonlocal surface polarization effects via tuning of the long-range screened exchange in a range-separated hybrid in a non-empirical and system-specific manner. We implement this functional in a plane-wave code and apply it to several physisorbed and chemisorbed molecule-metal interface systems. Our results are in quantitative agreement with experiments, both the level alignment and work function changes. Our approach constitutes a new practical scheme for accurate and efficient calculations of the electronic structure of molecule-metal interfaces.Comment: 15 pages, 8 figure

Time-reversal in dynamically-tuned zero-gap periodic systems

We show that short pulses propagating in zero-gap periodic systems can be reversed with 100% efficiency by using weak non-adiabatic tuning of the wave velocity at time-scales that can be much slower than the period. Unlike previous schemes, we demonstrate reversal of {\em broadband} (few cycle) pulses with simple structures. Our scheme may thus open the way to time-reversal in a variety of systems for which it was not accessible before.Comment: Accepted for publication in Phys. Rev. Letter

Searching for additional heating - [OII] emission in the diffuse ionized gas of NGC891, NGC4631 and NGC3079

We present spectroscopic data of ionized gas in the disk--halo regions of three edge-on galaxies, NGC 891, NGC 4631 and NGC 3079, covering a wavelength range from [\ion{O}{2}] $\lambda$3727\AA to [\ion{S}{2}] $\lambda$6716.4\AA. The inclusion of the [\ion{O}{2}] emission provides new constraints on the properties of the diffuse ionized gas (DIG), in particular, the origin of the observed spatial variations in the line intensity ratios. We used three different methods to derive electron temperatures, abundances and ionization fractions along the slit. The increase in the [\ion{O}{2}]/H$\alpha$ line ratio towards the halo in all three galaxies requires an increase either in electron temperature or in oxygen abundance. Keeping the oxygen abundance constant yields the most reasonable results for temperature, abundances, and ionization fractions. Since a constant oxygen abundance seems to require an increase in temperature towards the halo, we conclude that gradients in the electron temperature play a significant role in the observed variations in the optical line ratios from extraplanar DIG in these three spiral galaxies.Comment: 43 pages, 29 figure

Properties of low-lying states in a diffusive quantum dot and Fock-space localization

Motivated by an experiment by Sivan et al. (Europhys. Lett. 25, 605 (1994)) and by subsequent theoretical work on localization in Fock space, we study numerically a hierarchical model for a finite many-body system of Fermions moving in a disordered potential and coupled by a two-body interaction. We focus attention on the low-lying states close to the Fermi energy. Both the spreading width and the participation number depend smoothly on excitation energy. This behavior is in keeping with naive expectations and does not display Anderson localization. We show that the model reproduces essential features of the experiment by Sivan et al.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev. Let

Energy level statistics of electrons in a 2D quasicrystal

A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics for the randomized tilings follow the predictions of random matrix theory, while for the perfect tilings a new type of level statistics is found. In this case, the first-, second- level spacing distributions are well described by lognormal laws with power law tails for large spacing. In addition, level spacing properties being related to properties of the density of states, the latter quantity is studied and the multifractal character of the spectral measure is exhibited.Comment: 9 pages including references and figure captions, 6 figures available upon request, LATEX, report-number els