Partial Adjustment Without Apology

Many kinds of economic behavior appear to be governed by discrete and occasional individual choices. Despite this, econometric partial adjustment models perform relatively well at the aggregate level. Analyzing the classic employment adjustment problem, we show how discrete and occasional microeconomic adjustment is well described by a new form of partial adjustment model that aggregates the actions of a large number of heterogeneous producers. We begin by describing a basic model of discrete and occasional adjustment at the micro level, where production units are essentially restricted to either operate with a fixed number of workers or shut down. We show that this simple model is observationally equivalent at the market level to the standard rational expectations partial adjustment model. We then construct a related, but more realistic, model that incorporates the idea that increases or decreases in the size of an establishment’s workforce are subject to fixed adjustment costs. In the market equilibrium of this model, employment responses to aggregate disturbances include changes both in employment selected by individual establishments and in the measure of establishments actively undertaking adjustment. Yet the model retains a partial adjustment flavor in its aggregate responses. Moreover, in contrast to existing models of discrete adjustment, our generalized partial adjustment model is sufficiently tractable to allow extension to general equilibrium.

Axion-like-particle decay in strong electromagnetic backgrounds

The decay of a massive pseudoscalar, scalar and U(1) boson into an electron-positron pair in the presence of strong electromagnetic backgrounds is calculated. Of particular interest is the constant-crossed-field limit, relevant for experiments that aim to measure high-energy axion-like-particle conversion into electron-positron pairs in a magnetic field. The total probability depends on the quantum nonlinearity parameter - a product of field and lightfront momentum invariants. Depending on the seed particle mass, different decay regimes are identified. In the below-threshold case, we find the probability depends on a non-perturbative tunnelling exponent depending on the quantum parameter and the particle mass. In the above-threshold case, we find that when the quantum parameter is varied linearly, the probability oscillates nonlinearly around the spontaneous decay probability. A strong-field limit is identified in which the threshold is found to disappear. In modelling the fall-off of a quasi-constant-crossed magnetic field, we calculate probabilities beyond the constant limit and investigate when the decay probability can be regarded as locally constant.Comment: 22 pages, 7 figure

Ion engine thrust vector study, phase 2 Quarterly report

Performance prediction for expected thrust misalignment in electron bombardment ion thruste

Proof of Luck: an Efficient Blockchain Consensus Protocol

In the paper, we present designs for multiple blockchain consensus primitives and a novel blockchain system, all based on the use of trusted execution environments (TEEs), such as Intel SGX-enabled CPUs. First, we show how using TEEs for existing proof of work schemes can make mining equitably distributed by preventing the use of ASICs. Next, we extend the design with proof of time and proof of ownership consensus primitives to make mining energy- and time-efficient. Further improving on these designs, we present a blockchain using a proof of luck consensus protocol. Our proof of luck blockchain uses a TEE platform's random number generation to choose a consensus leader, which offers low-latency transaction validation, deterministic confirmation time, negligible energy consumption, and equitably distributed mining. Lastly, we discuss a potential protection against up to a constant number of compromised TEEs.Comment: SysTEX '16, December 12-16, 2016, Trento, Ital

POTENTIAL PITFALLS IN RENEWABLE RESOURCE DECISION MAKING THAT UTILIZES CONVEX COMBINATIONS OF DISCRETE ALTERNATIVES

Decision makers in renewable resource planning are often unable to specify their objective function a priori, and are presented with a discrete set of alternatives reflecting a range of options that are actually much more continuous. It is common for the decision maker to be interested in some other alternative than those originally developed. An iterative process thus often takes place between decision maker an analyst as they search for a satisfactory alternative. This paper analyzes the economic tenability of simply interpolating (taking convex combinations of) initial alternatives to generate new alternatives in this process. It is shown that convex combinations of outputs will be producible (feasible) with the interpolated input levels, under very common conditions. In fact, the cost estimate resulting from interpolating the cost of two (or more) alternatives will generally be an overestimate. The magnitude of this overestimate is investigated in a test case. It is concluded that this cost overestimate can be rather large, and is not systematically predictable. Only when the output sets in the original alternatives are very similar are the interpolated cost estimates fairly accurate.Resource /Energy Economics and Policy,

Average output entropy for quantum channels

We study the regularized average Renyi output entropy \bar{S}_{r}^{\reg} of quantum channels. This quantity gives information about the average noisiness of the channel output arising from a typical, highly entangled input state in the limit of infinite dimensions. We find a closed expression for \beta_{r}^{\reg}, a quantity which we conjecture to be equal to \Srreg. We find an explicit form for \beta_{r}^{\reg} for some entanglement-breaking channels, and also for the qubit depolarizing channel $\Delta_{\lambda}$ as a function of the parameter $\lambda$. We prove equality of the two quantities in some cases, in particular we conclude that for $\Delta_{\lambda}$ both are non-analytic functions of the variable $\lambda$.Comment: 32 pages, several plots and figures; positivity condition added for Theorem on entanglement breaking channels; new result for entrywise positive channel

Rationale for windshield glass system specification requirements for shuttle orbiter

A preliminary procurement specification for the space shuttle orbiter windshield pane, and some of the design considerations and rationale leading to its development are presented. The windshield designer is given the necessary methods and procedures for assuring glass pane structural integrity by proof test. These methods and procedures are fully developed for annealed and thermally tempered aluminosilicate, borosilicate, and soda lime glass and for annealed fused silica. Application of the method to chemically tempered glass is considered. Other considerations are vision requirements, protection against bird impact, hail, frost, rain, and meteoroids. The functional requirements of the windshield system during landing, ferrying, boost, space flight, and entry are included

Ion engine thrust vector study

Probability of thrust vector misalignment in ion thrustor arra

Precision measurement of the 5 2S1/2 - 4 2D5/2 quadrupole transition isotope shift between 88Sr+ and 86Sr+

We have measured the isotope shift of the narrow quadrupole-allowed 5 2S1/2 - 4 2D5/2 transition in 86Sr+ relative to the most abundant isotope 88Sr+. This was accomplished using high-resolution laser spectroscopy of individual trapped ions, and the measured shift is Delta-nu_meas^(88,86) = 570.281(4) MHz. We have also tested a recently developed and successful method for ab-initio calculation of isotope shifts in alkali-like atomic systems against this measurement, and our initial result of Delta-nu_calc^(88,86) = 457(28) MHz is also presented. To our knowledge, this is the first high precision measurement and calculation of that isotope shift. While the measurement and the calculation are in broad agreement, there is a clear discrepancy between them, and we believe that the specific mass shift was underestimated in our calculation. Our measurement provides a stringent test for further refinements of theoretical isotope shift calculation methods for atomic systems with a single valence electron

Notes on multiplicativity of maximal output purity for completely positive qubit maps

A problem in quantum information theory that has received considerable attention in recent years is the question of multiplicativity of the so-called maximal output purity (MOP) of a quantum channel. This quantity is defined as the maximum value of the purity one can get at the output of a channel by varying over all physical input states, when purity is measured by the Schatten $q$-norm, and is denoted by $\nu_q$. The multiplicativity problem is the question whether two channels used in parallel have a combined $\nu_q$ that is the product of the $\nu_q$ of the two channels. A positive answer would imply a number of other additivity results in QIT. Very recently, P. Hayden has found counterexamples for every value of $q>1$. Nevertheless, these counterexamples require that the dimension of these channels increases with $1-q$ and therefore do not rule out multiplicativity for $q$ in intervals $[1,q_0)$ with $q_0$ depending on the channel dimension. I argue that this would be enough to prove additivity of entanglement of formation and of the classical capacity of quantum channels. More importantly, no counterexamples have as yet been found in the important special case where one of the channels is a qubit-channel, i.e. its input states are 2-dimensional. In this paper I focus attention to this qubit case and I rephrase the multiplicativity conjecture in the language of block matrices and prove the conjecture in a number of special cases.Comment: Manuscript for a talk presented at the SSPCM07 conference in Myczkowce, Poland, 10/09/2007. 12 page