Where Have We Failed? Asks New York Paper in Race Crisis

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Codes for Graph Erasures

Motivated by systems where the information is represented by a graph, such as neural networks, associative memories, and distributed systems, we present in this work a new class of codes, called codes over graphs. Under this paradigm, the information is stored on the edges of an undirected graph, and a code over graphs is a set of graphs. A node failure is the event where all edges in the neighborhood of the failed node have been erased. We say that a code over graphs can tolerate $\rho$ node failures if it can correct the erased edges of any $\rho$ failed nodes in the graph. While the construction of such codes can be easily accomplished by MDS codes, their field size has to be at least $O(n^2)$, when $n$ is the number of nodes in the graph. In this work we present several constructions of codes over graphs with smaller field size. In particular, we present optimal codes over graphs correcting two node failures over the binary field, when the number of nodes in the graph is a prime number. We also present a construction of codes over graphs correcting $\rho$ node failures for all $\rho$ over a field of size at least $(n+1)/2-1$, and show how to improve this construction for optimal codes when $\rho=2,3$.Comment: To appear in IEEE International Symposium on Information Theor

Failed Supernovae Explain the Compact Remnant Mass Function

One explanation for the absence of higher mass red supergiants (16.5 Msun < M < 25Msun) as the progenitors of Type IIP supernovae (SNe) is that they die in failed SNe creating black holes. Simulations show that such failed SNe still eject their hydrogen envelopes in a weak transient, leaving a black hole with the mass of the star's helium core (5-8Msun). Here we show that this naturally explains the typical masses of observed black holes and the gap between neutron star and black hole masses without any fine-tuning of the SN mechanism beyond having it fail in a mass range where many progenitor models have density structures that make the explosions more likely to fail. There is no difficulty including this ~20% population of failed SNe in any accounting of SN types over the progenitor mass function. And, other than patience, there is no observational barrier to either detecting these black hole formation events or limiting their rates to be well below this prediction.Comment: Submitted to Ap

Informal water suppliers meeting water needs in the peri-urban areas of Mumbai, India

This paper is based on fieldwork on the small-scale water providers in the peri-urban areas of Mumbai. It tries to explain why small-scale water providers have appeared there, what type of service they provide and why they have succeeded, where the municipalities have failed. The objective is to examine to what extent small-scale water providers activities are sustainable and wheter they constitute a temporary or a permanent phenomenon in these territories ; to examine whether we are heading towards new forms of urban governance, where informal actors no longer compete with each other, but cooperate with public utilities and emerge as an extension of the public utility.INDIA ; INFORMAL ACTOR ; URBAN GOVERNANCE ; WATER