52 research outputs found
Access to Opportunity Project: Final Report
This project’s goal is to lift up promising approaches, suggest new strategies and encourage honest conversations that result in public policy solutions to income and racial segregation and poverty. The overarching question that motivates this work is: What are effective policies and strategies that promote access to high-opportunity amenities for low-income families?
As a first step, the researchers surveyed efforts on the ground in the metropolitan areas encompassing Seattle, Washington; Portland, Oregon; and San Diego, California, to determine whether there were any candidates for deeper study. We selected these three metropolitan areas for several reasons. First, prior interaction revealed that attention had been given to this question and that parties in each had embarked on purposeful efforts to make progress. Second, they represent a diverse array of communities that vary in significant ways, including along key economic, demographic, and social dimensions, and in some regards are bellwethers for changes beginning to take place in many parts of the country. As a consequence, experiences and successes in these places could potentially be applied to a diverse set of other urban areas across the United States.
The three regions are among the largest in the United States, with Seattle and Portland being the largest in their respective states and San Diego third in California (behind Los Angeles and the Bay Area). Despite their size, they differ in important ways that result in different social and political dynamics prevailing in each location.
In considering access to opportunity, one must understand the opportunities that are available in order to tailor skill-building efforts and investments in “connective infrastructure,” such as mass transit and suburban affordable housing, so that they are maximally effective. From an economic perspective, the three regions are quite different, which means that the approaches observed across the regions will potentially vary in measurable ways.
In each metropolitan area, we sought the counsel of key governmental, practitioner, academic, and philanthropic players. During the course of our initial visits to each region, we met with and interviewed almost 80 people—28 in Seattle, 26 in Portland, and 24 in San Diego. Through these conversations, we identified 27 projects—nine in each metropolitan area—as being promising examples of cases where lower-income families may have achieved increased access to high-opportunity amenities.
Given time, available funding, and the presence of partners willing to support our research effort by providing access to program data and program participants, we chose three projects for examination:
• The San Diego Housing Commission’s Achievement Academy
• Seattle/King County’s A Regional Coalition for Housing (ARCH)
• Humboldt Gardens in Northeast Portlan
Asymptotic Limits and Zeros of Chromatic Polynomials and Ground State Entropy of Potts Antiferromagnets
We study the asymptotic limiting function , where is the chromatic polynomial for a graph
with vertices. We first discuss a subtlety in the definition of
resulting from the fact that at certain special points , the
following limits do not commute: . We then
present exact calculations of and determine the corresponding
analytic structure in the complex plane for a number of families of graphs
, including circuits, wheels, biwheels, bipyramids, and (cyclic and
twisted) ladders. We study the zeros of the corresponding chromatic polynomials
and prove a theorem that for certain families of graphs, all but a finite
number of the zeros lie exactly on a unit circle, whose position depends on the
family. Using the connection of with the zero-temperature Potts
antiferromagnet, we derive a theorem concerning the maximal finite real point
of non-analyticity in , denoted and apply this theorem to
deduce that and for the square and
honeycomb lattices. Finally, numerical calculations of and
are presented and compared with series expansions and bounds.Comment: 33 pages, Latex, 5 postscript figures, published version; includes
further comments on large-q serie
Lower Bounds and Series for the Ground State Entropy of the Potts Antiferromagnet on Archimedean Lattices and their Duals
We prove a general rigorous lower bound for
, the exponent of the ground state
entropy of the -state Potts antiferromagnet, on an arbitrary Archimedean
lattice . We calculate large- series expansions for the exact
and compare these with our lower bounds on
this function on the various Archimedean lattices. It is shown that the lower
bounds coincide with a number of terms in the large- expansions and hence
serve not just as bounds but also as very good approximations to the respective
exact functions for large on the various lattices
. Plots of are given, and the general dependence on
lattice coordination number is noted. Lower bounds and series are also
presented for the duals of Archimedean lattices. As part of the study, the
chromatic number is determined for all Archimedean lattices and their duals.
Finally, we report calculations of chromatic zeros for several lattices; these
provide further support for our earlier conjecture that a sufficient condition
for to be analytic at is that is a regular
lattice.Comment: 39 pages, Revtex, 9 encapsulated postscript figures, to appear in
Phys. Rev.
Spanning forests and the q-state Potts model in the limit q \to 0
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta
J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially,
this limit gives rise to the generating polynomial of spanning forests;
physically, it provides information about the Potts-model phase diagram in the
neighborhood of (q,v) = (0,0). We have studied this model on the square and
triangular lattices, using a transfer-matrix approach at both real and complex
values of w. For both lattices, we have computed the symbolic transfer matrices
for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves
of partition-function zeros in the complex w-plane. For real w, we find two
distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp.
w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w >
w_0 we find a non-critical disordered phase, while for w < w_0 our results are
compatible with a massless Berker-Kadanoff phase with conformal charge c = -2
and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w =
w_0 we find a "first-order critical point": the first derivative of the free
energy is discontinuous at w_0, while the correlation length diverges as w
\downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0
seems to be the same for both lattices and it differs from that of the
Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1,
the leading thermal scaling dimension is x_{T,1} = 0, and the critical
exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65
Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and
forests_tri_2-9P.m. Final journal versio
Exact Potts Model Partition Functions on Ladder Graphs
We present exact calculations of the partition function of the -state
Potts model and its generalization to real , the random cluster model, for
arbitrary temperature on -vertex ladder graphs with free, cyclic, and
M\"obius longitudinal boundary conditions. These partition functions are
equivalent to Tutte/Whitney polynomials for these graphs. The free energy is
calculated exactly for the infinite-length limit of these ladder graphs and the
thermodynamics is discussed.Comment: 73 pages, Latex, 20 postscript figures, Physica A, in pres
A Little Statistical Mechanics for the Graph Theorist
In this survey, we give a friendly introduction from a graph theory
perspective to the q-state Potts model, an important statistical mechanics tool
for analyzing complex systems in which nearest neighbor interactions determine
the aggregate behavior of the system. We present the surprising equivalence of
the Potts model partition function and one of the most renowned graph
invariants, the Tutte polynomial, a relationship that has resulted in a
remarkable synergy between the two fields of study. We highlight some of these
interconnections, such as computational complexity results that have alternated
between the two fields. The Potts model captures the effect of temperature on
the system and plays an important role in the study of thermodynamic phase
transitions. We discuss the equivalence of the chromatic polynomial and the
zero-temperature antiferromagnetic partition function, and how this has led to
the study of the complex zeros of these functions. We also briefly describe
Monte Carlo simulations commonly used for Potts model analysis of complex
systems. The Potts model has applications as widely varied as magnetism, tumor
migration, foam behaviors, and social demographics, and we provide a sampling
of these that also demonstrates some variations of the Potts model. We conclude
with some current areas of investigation that emphasize graph theoretic
approaches.
This paper is an elementary general audience survey, intended to popularize
the area and provide an accessible first point of entry for further
exploration.Comment: 30 pages, 3 figure
Estimation of Sobolev-type embedding constant on domains with minimally smooth boundary using extension operator
Determining relative bulk viscosity of kilometre-scale crustal units using field observations and numerical modelling
Though the rheology of kilometre-scale polymineralic rock units is crucial for reliable large-scale, geotectonic models, this information is difficult to obtain. In geotectonic models, a layer is defined as an entity at the kilometre scale, even though it is heterogeneous at the millimetre to metre scale. Here, we use the shape characteristics of the boundaries between rock units to derive the relative bulk viscosity of those units at the kilometre scale. We examine the shape of a vertically oriented ultramafic, harzburgitic-lherzolitic unit, which developed a kilometre-scale pinch and swell structure at mid-crustal conditions (~ 600 °C, ~ 8.5 kbar), in the Anita Shear Zone, New Zealand. The ultramafic layer is embedded between a typical polymineralic paragneiss to the west, and a feldspar-quartz-hornblende orthogneiss, to the east. Notably, the boundaries on either side of the ultramafic layer give the ultramafics an asymmetric shape. Microstructural analysis shows that deformation was dominated by dislocation creep (n = 3). Based on the inferred rheological behaviour from the field, a series of numerical simulations are performed. Relative and absolute values are derived for bulk viscosity of the rock units by comparing boundary tortuosity difference measured on the field example and the numerical series. Our analysis shows that during deformation at mid-crustal conditions, paragneisses can be ~ 30 times less viscous than an ultramafic unit, whereas orthogneisses have intermediate viscosity, ~ 3 times greater than the paragneisses. If we assume a strain rate of 10⁻ ¹⁴ s⁻ ¹ the ultramafic, orthogneiss and paragneiss have syn-deformational viscosities of 3 × 10²², 2.3 × 10²¹ and 9.4 × 10²⁰ Pa s, respectively. Our study shows pinch and swell structures are useful as a gauge to assess relative bulk viscosity of rock units based on shape characteristics at the kilometre scale and in non-Newtonian flow regimes, even where heterogeneity occurs within the units at the outcrop scale
A coordinate-based ALE functional MRI meta-analysis of brain activation during verbal fluency tasks in healthy control subjects
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