Induced Matchings and the Algebraic Stability of Persistence Barcodes

We define a simple, explicit map sending a morphism $f:M \rightarrow N$ of pointwise finite dimensional persistence modules to a matching between the barcodes of $M$ and $N$. Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of $\ker f$ and $\mathop{\mathrm{coker}} f$. As an immediate corollary, we obtain a new proof of the algebraic stability of persistence, a fundamental result in the theory of persistent homology. In contrast to previous proofs, ours shows explicitly how a $\delta$-interleaving morphism between two persistence modules induces a $\delta$-matching between the barcodes of the two modules. Our main result also specializes to a structure theorem for submodules and quotients of persistence modules, and yields a novel "single-morphism" characterization of the interleaving relation on persistence modules.Comment: Expanded journal version, to appear in Journal of Computational Geometry. Includes a proof that no definition of induced matching can be fully functorial (Proposition 5.10), and an extension of our single-morphism characterization of the interleaving relation to multidimensional persistence modules (Remark 6.7). Exposition is improved throughout. 11 Figures adde

One in Eight Oregonians Needs Congress to Halt the Erosion in Food Stamps

The purchasing power of food stamps has declined because Congress has not updated the value of food stamp benefits to keep up with the rising cost of food. The U.S. House of Representatives will soon decide whether to put a stop to this erosion of food stamp benefits when they vote on the 2007 Farm Bill.This short paper discusses the reasons behind the erosion in food stamp benefits and how it impacts Oregonians

Punishing Food Stamp Program Success: The Bush's Administration's Farm Bill would reverse Oregon's progress against hunger

The Bush Administration has proposed eliminating $543 million in food stamp benefits for about 329,000 low-income Americans over the next five years. The Agriculture Committee of the U.S. House of Representatives may soon vote on this proposal as an amendment to the 2007 Farm Bill

Term premia and the news

How do monetary policy expectations and term premia respond to news? This paper provides new answers to this question by means of a dynamic term structure model (DTSM) in which risk prices are restricted. This leads to more precise and more reliable estimates of expectations and term premium components. I provide a new econometric framework for DTSM estimation that allows the researcher to select plausible constraints from a large set of restrictions, to correctly quantify statistical uncertainty, and to incorporate model uncertainty in the inference about risk pricing. The main empirical result is that under the restrictions favored by the data the expectations component, and not the term premium, accounts for the majority of high-frequency movements of long-term interest rates and for essentially all of their procyclical response to macroeconomic news. At both high and low frequencies, term premia are more stable than implied by a DTSM with unconstrained risk prices. The apparent disconnect between long-term rates and policy rates that has puzzled macroeconomists for some time is resolved by appropriately restricting the risk adjustment in models for bond pricing.Bonds - Prices ; Interest rates

Signals from unconventional monetary policy

Federal Reserve announcements of future purchases of longer-term bonds may affect asset prices by changing market expectations of the future supply of targeted securities. Such announcements may also affect asset prices by signaling that the stance of conventional monetary policy is likely to remain loose for longer than previously anticipated. Research suggests that these signaling effects were a major contributor to the cumulative declines in Treasury security yields following the eight Fed announcements in 2008 and 2009 about its first round of large-scale asset purchases.Monetary policy ; Open market operations

Universality of single quantum gates

We supply a rigorous proof that an open dense set of all possible 2-qubit gates G has the property that if the quantum circuit model is restricted to only permit swap of qubits lines and the application of G to pairs of lines, then the model is still computationally universal.Comment: 6 pages, 1 figure; added references to previous proof