Being Good in a World of Need: Some Empirical Worries and an Uncomfortable Philosophical Possibility

In this article, I present some worries about the possible impact of global efforts to aid the needy in some of the world’s most desperate regions. Among the worries I address are possible unintended negative consequences that may occur elsewhere in a society when aid agencies hire highly qualified local people to promote their agendas; the possibility that foreign interests and priorities may have undue influence on a country’s direction and priorities, negatively impacting local authority and autonomy; and the related problem of outside interventions undermining the responsiveness of local and national governments to their citizens. Another issue I discuss is the possibility that efforts to aid the needy may involve an Each-We Dilemma, in which case conflicts may arise between what is individually rational or moral, and what is collectively rational or moral. Unfortunately, it is possible that if each of us does what we have most reason to do, morally, in aiding the needy, we together will bring about an outcome which is worse, morally, in terms of its overall impact on the global needy. The article ends by briefly noting a number of claims and arguments that I made in my 2017 Uehiro Lectures regarding how good people should respond in a world of need. As I have long argued, I have no doubt that those who are well off are open to serious moral criticism if they ignore the plight of the needy. Unfortunately, however, for a host of both empirical and philosophical reasons, what one should do in light of that truth is much more complex, and murky, than most people have realized

Endomorphisms of power series fields and residue fields of Fargues-Fontaine curves

We show that for k a perfect field of characteristic p, there exist endomorphisms of the completed algebraic closure of k((t)) which are not bijective. As a corollary, we resolve a question of Fargues and Fontaine by showing that for p a prime and C_p a completed algebraic closure of Q_p, there exist closed points of the Fargues-Fontaine curve associated to C_p whose residue fields are not (even abstractly) isomorphic to C_p as topological fields.Comment: 6 pages; v7: refereed version; added reference to Matignon-Reversa

Relative Riemann-Zariski spaces

In this paper we study relative Riemann-Zariski spaces attached to a morphism of schemes and generalizing the classical Riemann-Zariski space of a field. We prove that similarly to the classical RZ spaces, the relative ones can be described either as projective limits of schemes in the category of locally ringed spaces or as certain spaces of valuations. We apply these spaces to prove the following two new results: a strong version of stable modification theorem for relative curves; a decomposition theorem which asserts that any separated morphism between quasi-compact and quasi-separated schemes factors as a composition of an affine morphism and a proper morphism. (In particular, we obtain a new proof of Nagata's compactification theorem.)Comment: 30 pages, the final version, to appear in Israel J. of Mat

National Foreclosure Mitigation Counseling Program Evaluation: Final Report, Rounds 3 Through 5

The Urban Institute completed a four-year evaluation of Rounds 3 through 5 of the National Foreclosure Mitigation Counseling (NFMC) program. Using a representative NFMC sample of 137,000 loans and a comparison non-NFMC sample of 103,000 loans, the Urban Institute was able to employ robust statistical techniques to isolate the impact of NFMC counseling on loan performance through June 2013.The final evaluation of Rounds 3 through 5 conducted by Urban Institute indicates that the NFMC program continues to have positive effects for homeowners participating in the program Counseled homeowners were more likely to cure a serious delinquency or foreclosure with a modification or other type cure, stay current after obtaining a cure, and for NFMC clients who cured a serious delinquency, avoid foreclosure altogether

Coexistence of localized and extended states in the Anderson model with long-range hopping

We study states arising from fluctuations in the disorder potential in systems with long-range hopping. Here, contrary to systems with short-range hopping, the optimal fluctuations of disorder responsible for the formation of the states in the gap, are not rendered shallow and long-range when $E$ approaches the band edge ($E\to 0$). Instead, they remain deep and short-range. The corresponding electronic wave functions also remain short-range-localized for all $E<0$. This behavior has striking implications for the structure of the wave functions slightly above $E=0$. By a study of finite systems, we demonstrate that the wave functions $\Psi_E$ transform from a localized to a quasi-localized type upon crossing the $E=0$ level, forming resonances embedded in the $E>0$ continuum. The quasi-localized $\Psi_{E>0}$ consists of a short-range core that is essentially the same as $\Psi_{E=0}$ and a delocalized tail extending to the boundaries of the system. The amplitude of the tail is small, but it decreases with $r$ slowly. Its contribution to the norm of the wave function dominates for sufficiently large system sizes, $L\gg L_c(E)$; such states behave as delocalized ones. In contrast, in small systems, $L\ll L_c(E)$, quasi-localized states are overwhelmingly dominated by the localized cores and are effectively localized.Comment: 18+1 pages, 9+1 figure

Onsager approach to 1D solidification problem and its relation to phase field description

We give a general phenomenological description of the steady state 1D front propagation problem in two cases: the solidification of a pure material and the isothermal solidification of two component dilute alloys. The solidification of a pure material is controlled by the heat transport in the bulk and the interface kinetics. The isothermal solidification of two component alloys is controlled by the diffusion in the bulk and the interface kinetics. We find that the condition of positive-definiteness of the symmetric Onsager matrix of interface kinetic coefficients still allows an arbitrary sign of the slope of the velocity-concentration line near the solidus in the alloy problem or of the velocity-temperature line in the case of solidification of a pure material. This result offers a very simple and elegant way to describe the interesting phenomenon of a possible non-single-value behavior of velocity versus concentration which has previously been discussed by different approaches. We also discuss the relation of this Onsager approach to the thin interface limit of the phase field description.Comment: 5 pages, 1 figure, submitted to Physical Review

On the role of confinement on solidification in pure materials and binary alloys

We use a phase-field model to study the effect of confinement on dendritic growth, in a pure material solidifying in an undercooled melt, and in the directional solidification of a dilute binary alloy. Specifically, we observe the effect of varying the vertical domain extent ($\delta$) on tip selection, by quantifying the dendrite tip velocity and curvature as a function of $\delta$, and other process parameters. As $\delta$ decreases, we find that the operating state of the dendrite tips becomes significantly affected by the presence of finite boundaries. For particular boundary conditions, we observe a switching of the growth state from 3-D to 2-D at very small $\delta$, in both the pure material and alloy. We demonstrate that results from the alloy model compare favorably with those from an experimental study investigating this effect.Comment: 13 pages, 9 figures, 3 table