On approximate and algebraic computability over the real numbers

AbstractWe consider algebraic and approximate computations of (partial) real functions ƒ:Rd ↣ R. Algebraic computability is defined by means of (parameter-free) finite algorithmic procedures. The notion of approximate computability is a straightforward generalization of the Ko-Friedman approach, based on oracle Turing machines, to functions with not necessarily recursively open domains.The main results of the paper give characterizations of approximate computability by means of the passing sets of finite algorithmic procedures, i.e., characterizations from the algebraic point of view. Some consequences and also modifications of the concepts are discussed. Finally, two variants of arithmetical hierarchies over the reals are considered and used to classify and mutually compare the domains, graphs and ranges of algebraically resp. approximately computable real functions

Inhale, Exhale: Promoting Mindfulness in the Elementary Classroom

When students have the ability to regulate their emotions, they encounter more positive peer-to-peer interactions, improved decision-making skills, and they are more likely to be engaged in their learning. Unfortunately, teachers are entering the classroom ill-prepared and unequipped to help their students self-regulate. In response to this, an instructional website was developed and evaluated to provide K-2 teachers with knowledge and tools to be comfortable with incorporating meditative breathing / yoga in the classroom to improve student mindfulness. The introduction section of the instruction included an overview of self-regulation, emotional intelligence, and yoga. The three modules covered information about meditative breathing, chair yoga, and standing yoga. The instruction was designed based on the ADDIE framework, with the incorporation of the ARCS model, Gagne’s Nine Events, Merrill’s Principles of Instruction and Mayer’s Multimedia Design Principles. The website, Inhale, Exhale: Mindfulness in the Elementary Classroom, was evaluated for its usability, as well as how effective it was for learning. The usability was tested by three participants and the learning effectiveness was measured through the participation of 17 current or former teachers. The usability testing focused on the visual design, navigation, and overall content within the website, while the learning effectiveness participants were asked to go through the instruction by watching videos, engaging in learning activities then completing pre and post tests. Participant feedback was primarily positive, and informed design changes.The designer concluded that the instruction was effective in that all participants showed growth between the pre and post assessment. More importantly, the participants’ knowledge, confidence and motivation to try meditative breathing and yoga in their classroom also increased. Relevant conclusions and recommendations will be discussed during the presentation

Observations on complete sets between linear time and polynomial time

AbstractThere is a single set that is complete for a variety of nondeterministic time complexity classes with respect to related versions of m-reducibility. This observation immediately leads to transfer results for determinism versus nondeterminism solutions. Also, an upward transfer of collapses of certain oracle hierarchies, built analogously to the polynomial-time or the linear-time hierarchies, can be shown by means of uniformly constructed sets that are complete for related levels of all these hierarchies. A similar result holds for difference hierarchies over nondeterministic complexity classes. Finally, we give an oracle set relative to which the nondeterministic classes coincide with the deterministic ones, for several sets of time bounds, and we prove that the strictness of the tape-number hierarchy for deterministic linear-time Turing machines does not relativize

Spectroscopy On Aluminum Monochloride (alcl) For Laser Cooling And Trapping

Cooling atoms to the ultracold regime has allowed for studies of physics, ranging from many-body physics of quantum degenerate gases, quantum computing, precision measurements and tests of fundamental symmetries. Extending these experiments to polar molecules has the prospect of enhancing the sensitivity of such tests and of enabling novel studies, such as cold controlled chemistry. However, applying traditional laser cooling techniques to molecules is rendered difficult due their additional degrees of freedom which result in a limited photon scattering budget. Here we study aluminum monochloride (AlCl) as a promising candidate for laser cooling and trapping. The cooling transition at 261 nm ($A^{1} \Pi - X^{1} \Sigma^{+}$) has a theoretical Franck-Condon factor of 99.88\% which allows for scattering ~800 photons with a single laser before the molecule enters an excited vibrational state. We use a frequency-tripled (SHG + SFG) Titanium-Sapphire laser and generate AlCl via laser ablation in a cryogenic helium buffer gas beam source. We will present our spectroscopy results on AlCl and the measured molecular constants of the $A^{1}\Pi$ state and compare them with ab-initio calculations. We will also discuss our estimates on the Franck-Condon factors

Algebraic synthesis of time-optimal unitaries in SU(2) with alternating controls

We present an algebraic framework to study the time-optimal synthesis of arbitrary unitaries in SU(2), when the control set is restricted to rotations around two non-parallel axes in the Bloch sphere. Our method bypasses commonly used control-theoretical techniques, and easily imposes necessary conditions on time-optimal sequences. In a straightforward fashion, we prove that time-optimal sequences are solely parametrized by three rotation angles and derive general bounds on those angles as a function of the relative rotation speed of each control and the angle between the axes. Results are substantially different whether both clockwise and counterclockwise rotations about the given axes are allowed, or only clockwise rotations. In the first case, we prove that any finite time-optimal sequence is composed at most of five control concatenations, while for the more restrictive case, we present scaling laws on the maximum length of any finite time-optimal sequence. The bounds we find for both cases are stricter than previously published ones and severely constrain the structure of time-optimal sequences, allowing for an efficient numerical search of the time-optimal solution. Our results can be used to find the time-optimal evolution of qubit systems under the action of the considered control set, and thus potentially increase the number of realizable unitaries before decoherence

Environmental equity in southeast Louisiana: oil, people, policy, and the geography of industrial hazards

This dissertation explores issues and concepts underlying the creation of Louisiana’s rural-industrial petrochemical complex as they relate to environmental equity and industrial development’s deleterious consequences. Cumulative hazards models examine the distribution of technological hazards associated with petroleum extraction and processing and explores how this varies among different socioeconomic groups in three coastal Louisiana parishes. Considerable onshore oil extraction occurs in Jefferson Parish. Lafourche Parish is the primary land-based supply center for the majority of the offshore oil activity in the Gulf of Mexico. The refineries of Saint Bernard Parish represent the endpoint of the flow of raw product and the staging point from which the refined product is transported to the wider market. Transportation infrastructure and a web of oil and gas pipelines connect these three parishes to each other and the areas beyond. The hazards models found a range of potential impacts affecting a wide swath of communities. Chalmette, for example, faces the greatest immediate risk from Saint Bernard Parish’s two large refineries and has the lowest proportion of minority residents within the study area. Conversely, Houma Indians residing on the wetland fringe stand at risk from the petroleum industry, both directly, through potential residential exposure, and indirectly, through potentially impacted hunting and fishing grounds. These results highlight the importance of using a fine grained localized environmental equity model. Historic process-based analyses examined the development of environmental inequity in communities identified by the hazards models. The historical development of environmental inequity is an extremely dynamic process. Generally, industry arrived first followed by population. After the initial siting, industry and population grew concomitantly. Industry growth continued even after the communities became predominantly minority or low-income. This research examined regional migration patterns over the last decade to explore why people move into potentially hazardous areas. Statistical analysis reveals that historic segregation patterns are a primary factor in most population movement. Additionally, populations are moving into neighborhoods proximate to their place of employment. Finally, this dissertation describes how the results achieved compare to those of other environmental equity studies and identifies six tenets of a practical, attainable, place-specific model of environmental equity