Public and private provision of infrastructure and economic development.

This paper examines the role of infrastructure in long run economic growth. The paper consists of two sections, the first concentrates on the theoretical role of government spending in models of growth and the second details examples of private participation in infrastructure development. Using a simple endogenous growth model we find that while the hypothesized benefits of infrastructure expenditures may be large they require care in matching appropriate financing. As the development and maintenance of infrastructure will continue to be pivotal to the long term success of growing economies, we emphasize the lessons on financing and the caveats of private participation to those who are exploring innovative mechanisms for infrastructure design.

Parameter estimation for macroscopic pedestrian dynamics models from microscopic data

In this paper we develop a framework for parameter estimation in macroscopic pedestrian models using individual trajectories -- microscopic data. We consider a unidirectional flow of pedestrians in a corridor and assume that the velocity decreases with the average density according to the fundamental diagram. Our model is formed from a coupling between a density dependent stochastic differential equation and a nonlinear partial differential equation for the density, and is hence of McKean--Vlasov type. We discuss identifiability of the parameters appearing in the fundamental diagram from trajectories of individuals, and we introduce optimization and Bayesian methods to perform the identification. We analyze the performance of the developed methodologies in various situations, such as for different in- and outflow conditions, for varying numbers of individual trajectories and for differing channel geometries

Spiro donor–acceptor TADF emitters: naked TADF free from inhomogeneity caused by donor acceptor bridge bond disorder. Fast rISC and invariant photophysics in solid state hosts

We have studied the thermally activated delayed fluorescence (TADF) properties of the spiro-bridged donor–acceptor molecule, 10-phenyl-10H,10′H-spiro[acridine-9,9-anthracen]-10′-one, (ACRSA) in guest–host films and used it as a probe to explore the details of host effects on the TADF mechanism in typical OLED host materials. Linked by the rigid spiro C–C bond rather than a flexible C–N bond, we observe no inhomogeneous effects arising from distributions of donor–acceptor bridge dihedral angles. ACRSA displays no time dependent ‘apparent’ red shift of the prompt or delayed charge transfer (CT) emission. Moreover, using a range of different hosts, we show that the ground state dipole moment (dielectric value) of the host has very little effect on the ACRSA CT energy, i.e. there is no so-called ‘solid state solvatochromism’. This leads to weak stabilisation of the CT state in all hosts, but has a very small singlet triplet gap and very fast and efficient monoexponential rISC rates in films (reaching nearly 107 s−1 in zeonex host). We observe no power law decaying DF tail because there is no dispersion of the dihedral angle between donor and acceptor units. The previously much lower reported rISC rates in ACRSA are instead reattributed to intermolecular excimer states. The intermolecular species give rise to additional slow TADF contributions and broaden the overall CT emission band at 10% ACRSA loading and in neat films. Harnessing the rapid and homogenous rISC displayed by isolated ACRSA molecules may unlock higher efficiencies and – crucially – extended operational lifetimes in future TADF OLEDs

The Critical Role of nπ* States in the Photophysics and Thermally Activated Delayed Fluorescence of Spiro Acridine-Anthracenone

The molecular photophysics and thermally activated delayed fluorescence (TADF) in spiro compounds are distinct because of the rigid orthogonal C–C bridging bond between donor and acceptor. The photophysics is found to be highly complex, with unprecedented multiple anti-Kasha emissions from three different singlet states, two of which are one-photon forbidden. The TADF mechanism is critically controlled by local acceptor nπ* states; the singlet nπ* state undergoes rapid intersystem crossing populating an energetically close acceptor ππ* triplet state. The acceptor triplet nπ* state couples nonadiabatically to a CT triplet state mediating reverse intersystem crossing. When the nπ* and CT states are energetically close, TADF is greatly enhanced with rISC rate reaching 107 s–1. We observe neither DF from the singlet nπ* state nor electron transfer (ET) to form the 1CT because there is no ET driving force; however, ET from the higher-energy donor singlet ππ* state readily occurs along with donor emission

Superfloccinaucinihilipilification: Semisimple unifications of any gauge theory

We present a Mathematica package that takes any reductive gauge algebra and fully-reducible fermion representation, and outputs all semisimple gauge extensions under the condition that they have no additional fermions, and are free of local anomalies. These include all simple completions, also known as grand unified theories (GUT). We additionally provide a list of all semisimple completions for 5835 fermionic extensions of the one-generation Standard Model.Comment: 12 page

Propagation of singularities and Fredholm analysis for the time-dependent Schr\"odinger equation

We study the time-dependent Schr\"odinger operator $P = D_t + \Delta_g + V$ acting on functions defined on $\mathbb{R}^{n+1}$, where, using coordinates $z \in \mathbb{R}^n$ and $t \in \mathbb{R}$, $D_t$ denotes $-i \partial_t$, $\Delta_g$ is the positive Laplacian with respect to a time dependent family of non-trapping metrics $g_{ij}(z, t) dz^i dz^j$ on $\mathbb{R}^n$ which is equal to the Euclidean metric outside of a compact set in spacetime, and $V = V(z, t)$ is a potential function which is also compactly supported in spacetime. In this paper we introduce a new approach to studying $P$, by finding pairs of Hilbert spaces between which the operator acts invertibly. Using this invertibility it is straightforward to solve the `final state problem' for the time-dependent Schr\"odinger equation, that is, find a global solution $u(z, t)$ of $Pu = 0$ having prescribed asymptotics as $t \to \infty$. These asymptotics are of the form $$u(z, t) \sim t^{-n/2} e^{i|z|^2/4t} f_+\big( \frac{z}{2t} \big), \quad t \to +\infty$$ where $f_+$, the `final state' or outgoing data, is an arbitrary element of a suitable function space $\mathcal{W}^k(\mathbb{R}^n)$; here $k$ is a regularity parameter simultaneously measuring smoothness and decay at infinity. We can of course equally well prescribe asymptotics as $t \to -\infty$; this leads to incoming data $f_-$. We consider the `Poisson operators' $\mathcal{P}_\pm : f_\pm \to u$ and precisely characterize the range of these operators on $\mathcal{W}^k(\mathbb{R}^n)$ spaces. Finally we show that the scattering matrix, mapping $f_-$ to $f_+$, preserves these spaces.Comment: 63 pages, 3 figure

Polynomial Time Construction for Spatially Balanced Latin Squares

In this paper we propose a construction that generates spatially balanced Latin squares (SBLSs) in polynomial time. These structures are central to the design of agronomic experiments, as they avoid biases that are otherwise unintentionally introduced due to spatial auto-correlation. Previous approaches were able to generate SBLSs of order up to 35 and required about two weeks of computation. Our algorithm runs in O(n2) and generates SBLSs of arbitrary order n where 2n + 1 is prime. For example, this algorithm generates a SBLS of order 999 in a fraction of a second.National Science Foundation (NSF Expeditions in Computing award for Computational Sustainability, grant 0832782; NSF IIS award, grant 0514429), Intelligent Information Systems Institute, Cornell University (Air Force O ce of Scienti c Research, AFOSR, grant FA9550-04-1-0151), Natural Sciences and Engineering Research Council of Canada (NSERC