Random trees between two walls: Exact partition function

We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that adjacent vertices have labels differing by +1 or -1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p-function with constrained periods. These results are used to analyze the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs.Comment: 25 pages, 7 figures, tex, harvmac, epsf; accepted version; main modifications in Sect. 5-6 and conclusio

Force distributions in a triangular lattice of rigid bars

We study the uniformly weighted ensemble of force balanced configurations on a triangular network of nontensile contact forces. For periodic boundary conditions corresponding to isotropic compressive stress, we find that the probability distribution for single-contact forces decays faster than exponentially. This super-exponential decay persists in lattices diluted to the rigidity percolation threshold. On the other hand, for anisotropic imposed stresses, a broader tail emerges in the force distribution, becoming a pure exponential in the limit of infinite lattice size and infinitely strong anisotropy.Comment: 11 pages, 17 figures Minor text revisions; added references and acknowledgmen

Controls on the CO2 seasonal cycle

Surface pressure measurement performed by the Viking landers show substantial variations in pressure on seasonal timescales that are characterized by two local minima and two local maxima. These variations have widely been attributed to the seasonal condensation and sublimation of CO2 in the two polar regions. It has been somewhat of a surprise that the amplitude of the minimum and maximum that is dominated by the CO2 cycle in the north was much weaker than the corresponding amplitude of the south-dominated extrema. Another surprise was that the seasonal pressure cycle during years 2 and 3 of the Viking mission was so similar to that for year 1, despite the occurrence of two global dust storms during year 1 and none during years 2 and 3. An energy balance model that incorporates dynamical factors from general circulation model (GCM) runs in which the atmospheric dust opacity and seasonal date were systematically varied was used to model the observed seasonal pressure variations. The energy balance takes account of the following processes in determining the rates of CO2 condensation and sublimation at each longitudinal and latitudinal grid point: solar radiation, infrared radiation from the atmosphere and surface, subsurface heat conduction, and atmospheric heat advection. Condensation rates are calculated both at the surface and in the atmosphere. In addition, the energy balance model also incorporates information from the GCM runs on seasonal redistribution of surface pressure across the globe. Estimates of surface temperature of the seasonal CO2 caps were used to define the infrared radiative losses from the seasonal polar caps. The seasonal pressure variations measured at the Viking lander sites were closely reproduced

The impact of climate change on incomes and convergence in Africa

© 2019 Elsevier Ltd Climate change is projected to detrimentally affect African countries’ economic development, while income inequalities across economies is among the highest on the planet. However, it is projected that income levels would converge on the continent. Hitherto there is limited evidence on how climate change could affect projected income convergence, accelerating, slowing down, or even reversing this process. Here, we analyze convergence considering climate-change damages, by employing an economic model embedding the three dimensions of risks at the country-level: exposure, vulnerability and hazards. The results show (1) with historical mean climate-induced losses between 10 and 15 percent of GDP per capita growth, the majority of African economies are poorly adapted to their current climatic conditions, (2) Western and Eastern African countries are projected to be the most affected countries on the continent and (3) As a consequence of these heightened impacts on a number of countries, inequalities between countries are projected to widen in the high warming scenario compared to inequalities in the low and without warming scenarios. To mitigate the impacts of economic development and inequalities across countries, we stress (1) the importance of mitigation ambition and Africa's leadership in keeping global mean temperature increase below 1.5 °C, (2) the need to address the current adaptation deficit as soon as possible, (3) the necessity to integrate quantitatively climate risks in economic and development planning and finally (4) we advocate for the generalization of a special treatment for the most vulnerable countries to access climate-related finance. The analysis raises issues on the ability of African countries to reach their SDGs targets and the potential increasing risk of instability, migration across African countries, of decreased trade and economic cooperation opportunities as a consequence of climate change – exacerbating its negative consequences

The impact of climate change on incomes and convergence in Africa

© 2019 Elsevier Ltd Climate change is projected to detrimentally affect African countries’ economic development, while income inequalities across economies is among the highest on the planet. However, it is projected that income levels would converge on the continent. Hitherto there is limited evidence on how climate change could affect projected income convergence, accelerating, slowing down, or even reversing this process. Here, we analyze convergence considering climate-change damages, by employing an economic model embedding the three dimensions of risks at the country-level: exposure, vulnerability and hazards. The results show (1) with historical mean climate-induced losses between 10 and 15 percent of GDP per capita growth, the majority of African economies are poorly adapted to their current climatic conditions, (2) Western and Eastern African countries are projected to be the most affected countries on the continent and (3) As a consequence of these heightened impacts on a number of countries, inequalities between countries are projected to widen in the high warming scenario compared to inequalities in the low and without warming scenarios. To mitigate the impacts of economic development and inequalities across countries, we stress (1) the importance of mitigation ambition and Africa's leadership in keeping global mean temperature increase below 1.5 °C, (2) the need to address the current adaptation deficit as soon as possible, (3) the necessity to integrate quantitatively climate risks in economic and development planning and finally (4) we advocate for the generalization of a special treatment for the most vulnerable countries to access climate-related finance. The analysis raises issues on the ability of African countries to reach their SDGs targets and the potential increasing risk of instability, migration across African countries, of decreased trade and economic cooperation opportunities as a consequence of climate change – exacerbating its negative consequences

The receptor guanylyl cyclase Npr2 is essential for sensory axon bifurcation within the spinal cord

Sensory axonal projections into the spinal cord display a highly stereotyped pattern of T- or Y-shaped axon bifurcation at the dorsal root entry zone (DREZ). Here, we provide evidence that embryonic mice with an inactive receptor guanylyl cyclase Npr2 or deficient for cyclic guanosine monophosphate-dependent protein kinase I (cGKI) lack the bifurcation of sensory axons at the DREZ, i.e., the ingrowing axon either turns rostrally or caudally. This bifurcation error is maintained to mature stages. In contrast, interstitial branching of collaterals from primary stem axons remains unaffected, indicating that bifurcation and interstitial branching are processes regulated by a distinct molecular mechanism. At a functional level, the distorted axonal branching at the DREZ is accompanied by reduced synaptic input, as revealed by patch clamp recordings of neurons in the superficial layers of the spinal cord. Hence, our data demonstrate that Npr2 and cGKI are essential constituents of the signaling pathway underlying axonal bifurcation at the DREZ and neuronal connectivity in the dorsal spinal cord

Response of a Hexagonal Granular Packing under a Localized External Force: Exact Results

We study the response of a two-dimensional hexagonal packing of massless, rigid, frictionless spherical grains due to a vertically downward point force on a single grain at the top layer. We use a statistical approach, where each mechanically stable configuration of contact forces is equally likely. We show that this problem is equivalent to a correlated $q$-model. We find that the response is double-peaked, where the two peaks, sharp and single-grain diameter wide, lie on the two downward lattice directions emanating from the point of the application of the external force. For systems of finite size, the magnitude of these peaks decreases towards the bottom of the packing, while progressively a broader, central maximum appears between the peaks. The response behaviour displays a remarkable scaling behaviour with system size $N$: while the response in the bulk of the packing scales as $\frac{1}{N}$, on the boundary it is independent of $N$, so that in the thermodynamic limit only the peaks on the lattice directions persist. This qualitative behaviour is extremely robust, as demonstrated by our simulation results with different boundary conditions. We have obtained expressions of the response and higher correlations for any system size in terms of integers corresponding to an underlying discrete structure.Comment: Accepted for publication in JStat; 33 pages, 10 figures; Section 2.2 reorganized and rewritten; Details about the simulation procedure added in Sec.3.1. ; A new section, summarizing the final results and the calculation procedure adde

A New Approach to Analyzing Patterns of Collaboration in Co-authorship Networks - Mesoscopic Analysis and Interpretation

This paper focuses on methods to study patterns of collaboration in co-authorship networks at the mesoscopic level. We combine qualitative methods (participant interviews) with quantitative methods (network analysis) and demonstrate the application and value of our approach in a case study comparing three research fields in chemistry. A mesoscopic level of analysis means that in addition to the basic analytic unit of the individual researcher as node in a co-author network, we base our analysis on the observed modular structure of co-author networks. We interpret the clustering of authors into groups as bibliometric footprints of the basic collective units of knowledge production in a research specialty. We find two types of coauthor-linking patterns between author clusters that we interpret as representing two different forms of cooperative behavior, transfer-type connections due to career migrations or one-off services rendered, and stronger, dedicated inter-group collaboration. Hence the generic coauthor network of a research specialty can be understood as the overlay of two distinct types of cooperative networks between groups of authors publishing in a research specialty. We show how our analytic approach exposes field specific differences in the social organization of research.Comment: An earlier version of the paper was presented at ISSI 2009, 14-17 July, Rio de Janeiro, Brazil. Revised version accepted on 2 April 2010 for publication in Scientometrics. Removed part on node-role connectivity profile analysis after finding error in calculation and deciding to postpone analysis

Wall Crossing, Quivers and Crystals

We study the spectrum of BPS D-branes on a Calabi-Yau manifold using the 0+1 dimensional quiver gauge theory that describes the dynamics of the branes at low energies. The results of Kontsevich and Soibelman predict how the degeneracies change. We argue that Seiberg dualities of the quiver gauge theories, which change the basis of BPS states, correspond to crossing the "walls of the second kind." There is a large class of examples, including local del Pezzo surfaces, where the BPS degeneracies of quivers corresponding to one D6 brane bound to arbitrary numbers of D4, D2 and D0 branes are counted by melting crystal configurations. We show that the melting crystals that arise are a discretization of the Calabi-Yau geometry. The shape of the crystal is determined by the Calabi-Yau geometry and the background B-field, and its microscopic structure by the quiver Q. We prove that the BPS degeneracies computed from Q and Q' are related by the Kontsevich Soibelman formula, using a geometric realization of the Seiberg duality in the crystal. We also show that, in the limit of infinite B-field, the combinatorics of crystals arising from the quivers becomes that of the topological vertex. We thus re-derive the Gromov-Witten/Donaldson-Thomas correspondence