Resource Allocation with Population Dynamics

Many analyses of resource-allocation problems employ simplistic models of the population. Using the example of a resource-allocation problem of Marecek et al. [arXiv:1406.7639], we introduce rather a general behavioural model, where the evolution of a heterogeneous population of agents is governed by a Markov chain. Still, we are able to show that the distribution of agents across resources converges in distribution, for suitable means of information provision, under certain assumptions. The model and proof techniques may have wider applicability

Transport in disordered interacting systems: Numerical results for one-dimensional spinless electrons

The combined influence of disorder and interactions on the transport properties of electrons in one dimension is investigated. The numerical simulations are carried out by means of the Hartree-Fock-based diagonalization (HFD), a very efficient method to determine the low-energy properties of a disordered many-particle system. We find that the conductance of a strongly localized system can become considerably enhanced by the interactions. The enhancement for long-range interactions is significantly larger than for short-range interactions. In contrast, the conductance of weakly localized systems becomes suppressed by the interactions.Comment: Invited talk presented at Percolation 98, submitted to Physica A, 8 pages, elsart style, 4 eps figures include

Hartree-Fock based diagonalization: an efficient method for simulating disordered interacting electrons

We present an efficient numerical method for simulating the low-energy properties of disordered many-particle systems. The method which is based on the quantum-chemical configuration interaction approach consists in diagonalizing the Hamiltonian in an energetically truncated basis build of the low-energy states of the corresponding Hartree-Fock Hamiltonian. As an example we investigate the quantum Coulomb glass, a model of spinless electrons in a random potential interacting via long-range Coulomb interaction. We find that the Coulomb interaction increases the conductance of strongly disordered systems but reduces the conductance of weakly disordered systems.Comment: 7 pages, 3 eps figures included, invited talk at Conference on Computational Physics (Granada, Sep 1998

Projects, participation and planning across boundaries in Göttingen

This paper explores efforts to coordinate strategies promoting sustainable development – with specific focus on mobility and transport in climate change mitigation – across administrative boundaries in the city and county of Göttingen, Germany. The paper questions the possibility to develop and align strategic objectives and implementation across administrative boundaries when relying on short-term project funds. The experiences of key stakeholders in Göttingen are presented, with reference to empirical data from a document and interview study. Results indicate that reliance on short-term, project-based funding from external sources offers both opportunities and challenges for locally and regionally integrated strategy formulation and implementation. Five factors shaping the strategy space of actors are used to frame the analysis, with findings suggesting the need for further research on how local authorities overcome capacity and resource limitations, particularly with respect to complex challenges such as climate change

Fock space localization, return probability, and conductance of disordered interacting electrons

We numerically simulate the low-energy properties of interacting electrons in a random potential using the Hartree-Fock based exact diagonalization method. In particular, we investigate how the transport properties are influenced by the combined effects of disorder and correlations in the presence of the electron spin. To this end we calculate the participation number of many-particle states in Fock space, the return probability of single-particle excitations, and the Kubo-Greenwood conductance. It turns out that in the strongly localized regime interactions increase the conductance whereas for weak disorder interactions decrease the conductance. In contrast, single-particle excitations in general experience a localizing influence of the interactions.Comment: 4 pages, 4 eps figures, Proc. of the Symposium on Wave Propagation and Electronic Structure in Disordered Systems, FORTH, Heraklion, Crete, Greece (June 2000

Meso-scale obstructions to stability of 1D center manifolds for networks of coupled differential equations with symmetric Jacobian

A linear system $\dot x = Ax$, $A \in \mathbb{R}^{n \times n}$, $x \in \mathbb{R}^n$, with $\mathrm{rk} A = n-1$, has a one-dimensional center manifold $E^c = \{v \in \mathbb{R}^n : Av=0\}$. If a differential equation $\dot x = f(x)$ has a one-dimensional center manifold $W^c$ at an equilibrium $x^*$ then $E^c$ is tangential to $W^c$ with $A = Df(x^*)$ and for stability of $W^c$ it is necessary that $A$ has no spectrum in $\mathbb{C}^+$, i.e.\ if $A$ is symmetric, it has to be negative semi-definite. We establish a graph theoretical approach to characterize semi-definiteness. Using spanning trees for the graph corresponding to $A$, we formulate meso-scale conditions with certain principal minors of $A$ which are necessary for semi-definiteness. We illustrate these results by the example of the Kuramoto model of coupled oscillators

Analysis of cranial neural crest migratory pathways in axolotl using cell markers and transplantation

We have examined the ability of normal and heterotopically transplanted neural crest cells to migrate along cranial neural crest pathways in the axolotl using focal DiI injections and in situ hybridization with the neural crest marker, AP-2. DiI labeling demonstrates that cranial neural crest cells migrate as distinct streams along prescribed pathways to populate the maxillary and mandibular processes of the first branchial arch, the hyoid arch and gill arches 1-4, following migratory pathways similar to those observed in other vertebrates. Another neural crest marker, the transcription factor AP-2, is expressed by premigratory neural crest cells within the neural folds and migrating neural crest cells en route to and within the branchial arches. Rotations of the cranial neural folds suggest that premigratory neural crest cells are not committed to a specific branchial arch fate, but can compensate when displaced short distances from their targets by migrating to a new target arch. In contrast, when cells are displaced far from their original location, they appear unable to respond appropriately to their new milieu such that they fail to migrate or appear to migrate randomly. When trunk neural folds are grafted heterotopically into the head, trunk neural crest cells migrate in a highly disorganized fashion and fail to follow normal cranial neural crest pathways. Importantly, we find incorporation of some trunk cells into branchial arch cartilage despite the random nature of their migration. This is the first demonstration that trunk neural crest cells can form cartilage when transplanted to the head. Our results indicate that, although cranial and trunk neural crest cells have inherent differences in ability to recognize migratory pathways, trunk neural crest can differentiate into cranial cartilage when given proper instructive cues