"Uniform Measures On Inverse Limit Spaces"

Motivated by problems from dynamic economic models, we consider the problem of defining a uniform measure on inverse limit spaces. Let f be a function from a compact metric space X into itself where f is continuous, onto and piecewise one-to-one. Let Y be the inverse limit of (X,f). Then starting with a measure m1 on the Borel sets of X, we recursively construct a sequence of probability measures (m1,m2,...) on the Borel sets of X satisfying mn(A)=mn+1[B] for each Borel set A and n=1,2,... and B is the preimage of A under f. This sequence of probability measures is then uniquely extended to a probability measure on the inverse limit space Y. If m1 is a uniform measure, we argue that the measure induced on the inverse limit space by the recursively constructed sequence of measures is a uniform measure. As such, the measure has uses in economic theory for policy evaluation and in dynamical systems in providing an ambient measure (when Lebesgue measure is not available) with which to define an SRB measure or a metric attractor for the shift map on the inverse limit space.Inverse Limits, probability measure, multiple equilibria, global indeterminancy

Chaos and Sector-specific Externalities

Benhabib and Farmer (1996) explore the possibility of local indeterminacy in a twosector model with sector-speci c externalities. They nd that very small sector-specific externalities are su cient for local indeterminacy. In this case, it is possible to construct sunspot equilibria where extrinsic uncertainty matters. In this paper, I provide a global analysis of their model revealing the existence of Euler equation branching. This branching allows for regime switching equilibria with cycles and chaotic behavior. These equilibria occur whether the \local dynamics" are determinate or indeterminate.two-sector model, regime switching, global indeterminacy, cycles and chaos

Sources of business cycles in Korea and the United States

The authors estimate common and nation-specific components of technology shocks, real demand shocks, and combined (common and nation-specific) monetary shocks using quarterly data for Korea and the United States.Business cycles ; Korea

"Euler Equation Branching"

Some macroeconomic models exhibit a type of global indeterminacy known as Euler equation branching (e.g., the one-sector growth model with a production externality). The dynamics in such models are governed by a differential inclusion. In this paper, we show that in models with Euler equation branching there are multiple equilibria and that the dynamics are chaotic. In particular, we provide sufficient conditions for a dynamical system on the plane with Euler equation branching to be chaotic and show analytically that in a neighborhood of a steady state, these sufficient conditions will typically be satisfied. We also extend the results of Christiano and Harrison (JME, 1999) for the one-sector growth model with a production externality. In a more general setting, we provide necessary and sufficient conditions for Euler equation branching in this model. We show that chaotic and cyclic equilibria are possible and that this behavior is not dependent on the steady state being "locally" determinate or indeterminate.global indeterminacy, Euler equation branching, multiple equilibria, cycles,chaos, increasing returns to scale, externality, regime switching

Expected Utility in Models with Chaos

In this paper, we provide a framework for calculating expected utility in models with chaotic equilibria and consequently a framework for ranking chaos. Suppose that a dynamic economic model’s equilibria correspond to orbits generated by a chaotic dynamical system f : X ! X where X is a compact metric space and f is continuous. The map f could represent the forward dynamics xt+1 = f(xt) or the backward dynamics xt = f(xt+1). If f represents the forward/backward dynamics, the set of equilibria forms a direct/inverse limit space. We use a natural f-invariant measure on X to induce a measure on the direct/inverse limit space and show that this induced measure is a natural ¾-invariant measure where ¾ is the shift operator. We utilize this framework in the cash-in-advance model of money where f is the backward map to calculate expected utility when equilibria are chaotic.chaos, inverse limits, direct limits, natural invariant measure, cash-in-advance

CAD enabled trajectory optimization and accurate motion control for repetitive tasks

As machine users generally only define the start and end point of the movement, a large trajectory optimization potential rises for single axis mechanisms performing repetitive tasks. However, a descriptive mathematical model of the mecha- nism needs to be defined in order to apply existing optimization techniques. This is usually done with complex methods like virtual work or Lagrange equations. In this paper, a generic technique is presented to optimize the design of point-to-point trajectories by extracting position dependent properties with CAD motion simulations. The optimization problem is solved by a genetic algorithm. Nevertheless, the potential savings will only be achieved if the machine is capable of accurately following the optimized trajectory. Therefore, a feedforward motion controller is derived from the generic model allowing to use the controller for various settings and position profiles. Moreover, the theoretical savings are compared with experimental data from a physical set-up. The results quantitatively show that the savings potential is effectively achieved thanks to advanced torque feedforward with a reduction of the maximum torque by 12.6% compared with a standard 1/3-profil

The Relationship between Cost Analysis and Program Management

Cost analysis if often viewed as applying basic principles and cost methodologies to determine total system cost. These finished estimates then flow into a decision making process and the cost estimator leaves the stage. Reality shows that the cost estimator is actually one of the main contributors to the decision making process. Our introduction to this special issue explores the areas where cost estimating plays a major role in program management in areas beyond the normal program estimate. We have included articles that show the key role estimators can play in source selection strategies and evaluation; cost of delay analysis for management decisions, earned value management methods to predict program costs; decision criteria to rank competing projects that complement traditional cost-based methods; and a new methodology for determining research and development budget profiles

Optimal load angle learning algorithm for sensorless closed-loop stepping motor control

Stepping motors are well suited for open-loop positioning tasks at low-power. The rotor position of the machine is simply controlled by the user. Every time the user sends a next pulse, the stepping motor driver excites the correct stator phases to rotate the rotor over a pre-defined discrete angular position. In this way, counting the step command pulses enables open-loop positioning. However, when the motor is overloaded or stuck, the relation between the expected rotor position based on the number of step command pulses and the actual rotor position is lost. To avoid this, the bulk of the widely used full-step open-loop stepping motor drive algorithms are driven at maximum current. This non-optimal way of control leads to low efficiency. To use stepping motors more optimally, closed-loop control is needed. A previously described sensorless load angle estimation algorithm, solely based on voltage and current measurements, is used to provide sensorless feedback. A closed-loop load angle controller adapts the current level to reach the setpoint load angle to obtain the optimal torque/current ratio. The difficulty is that the optimal load angle depends on the mechanical dynamics. To avoid the requirement of knowledge of the mechanical parameters, a practical learning algorithm to determine the optimal load angle is presented in this paper. Measurements validate the proposed approach

Grindr Users Take More Risks, but Are More Open to Human Immunodeficiency Virus (HIV) Pre-exposure Prophylaxis: Could This Dating App Provide a Platform for HIV Prevention Outreach?

BackgroundTechnology has changed the way that men who have sex with men (MSM) seek sex. More than 60% of MSM in the United States use the internet and/or smartphone-based geospatial networking apps to find sex partners. We correlated use of the most popular app (Grindr) with sexual risk and prevention behavior among MSM.MethodsA nested cohort study was conducted between September 2018 and June 2019 among MSM receiving community-based human immunodeficiency virus (HIV) and sexually transmitted infection (STI) screening in central San Diego. During the testing encounter, participants were surveyed for demographics, substance use, risk behavior (previous 3 months), HIV pre-exposure prophylaxis (PrEP) use, and Grindr usage. Participants who tested negative for HIV and who were not on PrEP were offered immediate PrEP.ResultsThe study included 1256 MSM, 1090 of whom (86.8%) were not taking PrEP. Overall, 580 of 1256 (46%) participants indicated that they used Grindr in the previous 7 days. Grindr users reported significantly higher risk behavior (greater number of male partners and condomless sex) and were more likely to test positive for chlamydia or gonorrhea (8.6% vs 4.7% of nonusers; P = .005). Grindr users were also more likely to be on PrEP (18.7% vs 8.7% of nonusers; P < .001) and had fewer newly diagnosed HIV infections (9 vs 26 among nonusers; P = .014). Grindr users were also nearly twice as likely as nonusers to initiate PrEP (24.6% vs 14%; P < .001).ConclusionsGiven the higher risk behavior and greater acceptance of PrEP among MSM who used Grindr, Grindr may provide a useful platform to promote HIV and STI testing and increase PrEP uptake

Evidence-Based Progressive Passage to Reopening American Societies Post COVID-19

In the United States, the total number of confirmed reported cases of Covid-19 had reached  1.36 million with a total death of 80,574 and a total confirmed recoveries of 210,000 cases. Significant efforts have been invested to flatten the curve and control new cases appearing in the societies. Meanwhile, the governments has imposed a lockdown with the objective of controlling the transmission of the virus. The re-opening of societies is challenging and might involve threats, many of them remain unseen. We describe here a dynamic scenario to un-locking and re-opening societies using an evidence-based design, suggested by an algorithm of screening using RT-PCR and antibodies in a large population