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Submission note: This thesis is submitted in total fulfilment of the requirements for the degree of Doctor of Philosophy to the Department of Politics and Philosophy, School of Humanities and Social Sciences, College of Arts, Social Sciences and Commerce, La Trobe University, Victoria, Australia.

Over the past decade, tremendous progress has been made to extend the tools of laser cooling and trapping to molecules. Those same tools have recently been applied to polyatomic molecules (molecules containing three or more atoms). In this review, we discuss the scientific drive to bring larger molecules to ultralow temperatures, the features of molecular structure that provide the most promising molecules for this pursuit, and some technical aspects of how lasers can be used to control the motion and quantum states of polyatomic molecules. We also present opportunities for and challenges to the use of polyatomic molecules for science and technology., Comment: 112 pages, 32 figures; review article prepared for Advances in Atomic, Molecular and Optical Physics

Ultracold polyatomic molecules are promising candidates for experiments in quantum science, quantum sensing, ultracold chemistry, and precision measurements of physics beyond the Standard Model. A key, yet unrealized, requirement of these experiments is the ability to achieve full quantum control over the complex internal structure of the molecules. Here, we establish coherent control of individual quantum states in a polyatomic molecule, calcium monohydroxide (CaOH), and use these techniques to demonstrate a method for searching for the electron electric dipole moment (eEDM). Optically trapped, ultracold CaOH molecules are prepared in a single quantum state, polarized in an electric field, and coherently transferred into an eEDM sensitive state where an electron spin precession measurement is performed. To extend the coherence time of the measurement, we utilize eEDM sensitive states with tunable, near-zero magnetic field sensitivity. The spin precession coherence time is limited by AC Stark shifts and uncontrolled magnetic fields. These results establish a path for eEDM searches with trapped polyatomic molecules, towards orders-of-magnitude improved experimental sensitivity to time-reversal-violating physics.

We present D-Phi iteration: an algorithm for distributed, localized, and scalable robust control of systems with structured uncertainties. This algorithm combines the System Level Synthesis (SLS) parametrization for distributed control with stability criteria from L1, LInf, and nu robust control. We show in simulation that this algorithm achieves good nominal performance while greatly increasing the robust stability margin compared to the LQR controller. To the best of our knowledge, this is the first distributed and localized algorithm for structured robust control; furthermore, algorithm complexity depends only on the size of local neighborhoods and is independent of global system size. We additionally characterize the suitability of different robustness criteria for distributed and localized computation., Comment: To appear in CDC 2022

We present a new, scalable alternative to the structured singular value, which we call $ν$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the relationship between robust control of dynamical systems and non-negative constant matrices., Submitted to CDC2022, six pages. Companion article: arXiv:2204.02493

The best limit on the electron electric dipole moment (eEDM) comes from the ACME II experiment [Nature \textbf{562} (2018), 355-360] which probes physics beyond the Standard Model at energy scales well above 1 TeV. ACME II measured the eEDM by monitoring electron spin precession in a cold beam of the metastable H$^3Δ_1$ state of thorium monoxide (ThO) molecules, with an observation time $τ\approx 1$ ms for each molecule. We report here a new measurement of the lifetime of the ThO (H$^3Δ_1$) state, $τ_H = 4.2\pm 0.5$ ms. Using an apparatus within which $τ\approx τ_H$ will enable a substantial reduction in uncertainty of an eEDM measurement., 6 pages, 5 figures

Animals can move reliably in unpredictable environments. The study of sensorimotor control has assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single, unidirectional perception-action loop. This loop contains internal delays in sensory and motor pathways, which can lead to unstable control. We show here that these delays can be compensated by internal feedback signals that flow backwards, which are ubiquitous in neural sensorimotor systems. Recent advances in control theory show that internal feedback plays a key role in compensating internal delays. Based on these theoretical advances, we use a basic, mathematically tractable control model to show that internal feedback has an indispensable role in state estimation, can explain localization of function -- why different parts of cortex control different parts of the body -- and how attention can improve motor performance, all of which are crucial for effective sensorimotor control. Control theory can explain anatomical, physiological and behavioral observations, including motor signals in visual cortex, heterogeneous kinetics of sensory receptors and the presence of giant Betz cells in motor cortex.

Rapid and repeated photon cycling has enabled precision metrology and the development of quantum information systems using a variety of atoms and simple molecules. Extending optical cycling to structurally complex molecules would provide new capabilities in these areas, as well as in ultracold chemistry. Increased molecular complexity, however, makes realizing closed optical transitions more difficult. Building on the already established strong optical cycling of diatomic, linear triatomic, and symmetric top molecules, recent theoretical and experimental work has indicated that cycling will be extendable to phenol containing molecules, as well as other asymmetric species. The paradigm for these systems is the use of an optical cycling center bonded to a molecular ligand. Theory has suggested that cycling may be extended to even larger ligands, like naphthalene, pyrene and coronene. Here, we study the optical excitation and vibrational branching of the molecules CaO-2-naphthyl, SrO-2-naphthyl and CaO-1-naphthyl and find only weak decay to excited vibrational states, indicating a promising path to full quantum control and laser cooling of large arene-based molecules., Comment: 9 pages, 3 figures, 2 tables

In this paper we study two questions related to exceptional behavior of preperiodic points of polynomials in $\mathbb{Q}[x]$. We show that for all $d\geq 2$, there exists a polynomial $f_d(x) \in \mathbb{Q}[x]$ with $2\leq \mathrm{deg}(f_d) \leq d$ such that $f_d(x)$ has at least $d + \lfloor \log_2(d)\rfloor$ rational preperiodic points. Furthermore, we show that for infinitely many integers $d$, the polynomials $f_d(x)$ and $f_d(x) + 1$ have at least $d^2 + d\lfloor \log_2(d)\rfloor - 2d + 1$ common complex preperiodic points., Comment: Strengthened results, added new references

We study the dynamics of stochastic families of rational maps on the projective line. As such families can be infinite and may not typically be defined over a single number field, we introduce the concept of generalized adelic measures, generalizing previous notions introduced by Favre and Rivera-Letelier and Mavraki and Ye. Generalized adelic measures are defined over the measure space of places of an algebraic closure of the rationals, using a framework established by Allcock and Vaaler. This turns our heights from sums over places into integrals. We prove an equidistribution result for generalized adelic measures, and use this result to prove an equidistribution result for random backwards orbits in stochastic arithmetic dynamics., Comment: 54 pages

Feedback is ubiquitous in both biological and engineered control systems. In biology, in addition to typical feedback between plant and controller, we observe feedback pathways within control systems, which we call internal feedback pathways (IFPs), that are often very complex. IFPs are most familiar in neural systems, our primary motivation, but they appear everywhere from bacterial signal transduction to the human immune system. In this paper, we describe these very different motivating examples and introduce the concepts necessary to explain their complex IFPs, particularly the severe speed-accuracy tradeoffs that constrain the hardware in biology. We also sketch some minimal theory for extremely simplified toy models that nevertheless highlight the importance of diversity-enabled sweet spots (DESS) in mitigating the impact of hardware tradeoffs. For more realistic models, standard modern and robust control theory can give some insights into previously cryptic IFPs, and the new System Level Synthesis theory expands this substantially. These additional theories explaining IFPs will be explored in more detail in several companion papers., Comment: This paper is a companion to arXiv:2109.11752 and arXiv:2109.11757. v3: updated title + author metadata to match PDF

Given a generic polynomial $f(x)$, the generalized dynatomic polynomial $\Phi_{f,c,d}(x)$ vanishes at precisely those $\alpha$ such that $f^c(\alpha)$ has period exactly $d$ under iteration of $f(x)$. We show that the shifted dynatomic polynomials $\Phi_{f,c,d}(x) - 1$ often have generalized dynatomic factors, and that these factors are in correspondence with certain cyclotomic factors of necklace polynomials. These dynatomic factors of $\Phi_{f,c,d}(x) - 1$ have an interpretation in terms of new multiplicative relations between dynamical units which are uniform in the polynomial $f(x)$., Comment: 19 pages, comments welcome!

We demonstrate the direct loading of a D$_2$ MOT of potassium-39 atoms from a cryogenic buffer gas beam source. We load $10^8$ atoms in a 10 ms pulse, with no degradation in performance up to a 10 Hz repetition rate. Observed densities reach $\sim10^{11}$ atoms/cm$^3$ in a single pulse, achieved with no sub-Doppler cooling or transverse compression. This system produces an ideal starting point for ultracold atom experiments where high experimental repetition rates are desirable and initial high densities are critical. Extension to other atomic species (e.g., refractory metals) that present technical challenges to high-yield production using oven-based sources is straightforward., Comment: 7 pages, 4 figures

Descending predictive feedback (DPF) is an ubiquitous yet unexplained phenomenon in the central nervous system. Motivated by recent observations on motor-related signals in the visual system, we approach this problem from a sensorimotor standpoint and make use of optimal controllers to explain DPF. We define and analyze DPF in the optimal control context, revisiting several control problems (state feedback, full control, and output feedback) to explore conditions that necessitate DPF. We find that even small deviations from the unconstrained state feedback problem (e.g. incomplete sensing, communication delay) necessitate DPF in the optimal controller. We also discuss parallels between controller structure and observations from neuroscience. In particular, the system level (SLS) controller displays DPF patterns compatible with predictive coding theory and easily accommodates signaling restrictions (e.g. delay) typical to neurons, making it a candidate for use in sensorimotor modeling.

Given a set $S=\{x^2+c_1,\dots,x^2+c_s\}$ defined over a field and an infinite sequence $\gamma$ of elements of $S$, one can associate an arboreal representation to $\gamma$, generalizing the case of iterating a single polynomial. We study the probability that a random sequence $\gamma$ produces a ``large-image'' representation, meaning that infinitely many subquotients in the natural filtration are maximal. We prove that this probability is positive for most sets $S$ defined over $\mathbb{Z}[t]$, and we conjecture a similar positive-probability result for suitable sets over $\mathbb{Q}$. As an application of large-image representations, we prove a density-zero result for the set of prime divisors of some associated quadratic sequences. We also consider the stronger condition of the representation being finite-index, and we classify all $S$ possessing a particular kind of obstruction that generalizes the post-critically finite case in single-polynomial iteration., Comment: 22 pages

This paper develops empirical mathematical models for physiological responses to exercise. We first find single-input single-output models describing heart rate variability, ventilation, oxygen consumption and carbon dioxide production in response to workload changes and then identify a single-input multi-output model from workload to these physiological variabilities. We also investigate the possibility of the existence of a universal model for physiological variability in different individuals during treadmill running. Simulations based on real data substantiate that the obtained models accurately capture the physiological responses to workload variations. In particular, it is observed that (i) different physiological responses to exercise can be captured by low-order linear or mildly nonlinear models; and (ii) there may exist a universal model for oxygen consumption that works for different individuals.

The best upper limit for the electron electric dipole moment was recently set by the ACME collaboration. This experiment measures an electron spin-precession in a cold beam of ThO molecules in their metastable $H~(^3��_1)$ state. Improvement in the statistical and systematic uncertainties is possible with more efficient use of molecules from the source and better magnetometry in the experiment, respectively. Here, we report measurements of several relevant properties of the long-lived $Q~(^3��_2)$ state of ThO, and show that this state is a very useful resource for both these purposes. The $Q$ state lifetime is long enough that its decay during the time of flight in the ACME beam experiment is negligible. The large electric dipole moment measured for the $Q$ state, giving rise to a large linear Stark shift, is ideal for an electrostatic lens that increases the fraction of molecules detected downstream. The measured magnetic moment of the $Q$ state is also large enough to be used as a sensitive co-magnetometer in ACME. Finally, we show that the $Q$ state has a large transition dipole moment to the $C~(^1��_1)$ state, which allows for efficient population transfer between the ground state $X~(^1��^+)$ and the $Q$ state via $X-C-Q$ Stimulated Raman Adiabatic Passage (STIRAP). We demonstrate $90\,$% STIRAP transfer efficiency. In the course of these measurements, we also determine the magnetic moment of $C$ state, the $X\rightarrow C$ transition dipole moment, and branching ratios of decays from the $C$ state., 21 pages, 6 figures, 5 pages appendices

We present an overview of K2 short cadence observations for 34 M dwarfs observed in Campaigns 1 - 9 which have spectral types between M0 - L1. All of the stars in our sample showed flares with the most energetic reaching $3\times10^{34}$ ergs. As previous studies have found, we find rapidly rotating stars tend to show more flares, with evidence for a decline in activity in stars with rotation periods longer than approximately 10 days. We determined the rotational phase of each flare and performed a simple statistical test on our sample to determine whether the phase distribution of the flares is random or if there is a preference for phase. We find, with the exception of one star which is in a known binary system, that none show a preference for the rotational phase of the flares. This is unexpected and all stars in our sample show flares at all rotational phases, suggesting these flares are not all originating from one dominant starspot on the surface of the stars. We outline three scenarios which could explain the lack of a correlation between the number of flares and the stellar rotation phase. In addition we also highlight preliminary observations of DP Cnc, observed in campaigns 16 and 18, and is one of the stars in our extended sample from K2Campaigns 10 -18 which are still to be examined., {"references":["Bopp, B. W. & Moett, T. 1973, ApJ, 185, 239.","Davenport, J. R., Hawley, S. L., Hebb, L., Wisniewski, J. P., Kowalski, A. F., et al. 2014, ApJ, 797, 122.","Doyle, L., Ramsay, G., Doyle, J. G., Wu, K., & Scullion, E. 2018, Monthly Notices of the Royal Astronomical Society, 480, 2153.","Gaia Collaboration, Brown, A. G. A., Vallenari, A., Prusti, T., de Bruijne, J. H. J., et al. 2018, ArXiv e-prints.","Gershberg, R. 1972, Astrophysics and Space Science, 19, 75.","Gershberg, R. & Shakhovskaya, N. 1983, ApSS, 95, 235.","Gershberg, R. E. 2005, Solar-type activity in main-sequence Stars (Springer Science & Business Media).","Hawley, S. L., Davenport, J. R., Kowalski, A. F., Wisniewski, J. P., Hebb, L., et al. 2014, ApJ, 797, 121.","Huber, D., Bryson, S., Haas, M., Barclay, T., Barentsen, G., et al. 2016, VizieR Online Data Catalog, 222.","Kowalski, A. F., Hawley, S. L., Wisniewski, J. P., Osten, R. A., Hilton, E. J., et al. 2013, The Astrophysical Journal Supple- ment Series, 207, 15.","Luger, R., Agol, E., Kruse, E., Barnes, R., Becker, A., et al. 2016, AJ, 152, 100.","Lurie, J. C., Davenport, J. R., Hawley, S. L., Wilkinson, T. D., Wisniewski, J. P., et al. 2015, The Astrophysical Journal, 800, 95.","Ramsay, G. & Doyle, J. G. 2015, Monthly Notices of the Royal Astronomical Society, 449, 3015.","Ramsay, G., Doyle, J. G., Hakala, P., Garcia-Alvarez, D., Brooks, A., et al. 2013, MNRAS, 434, 2451.","Stelzer, B., Damasso, M., Scholz, A., & Matt, S. P. 2016, MN- RAS, 463, 1844."]}

We report non-destructive imaging of optically trapped calcium monofluoride (CaF) molecules using in-situ $��$-enhanced gray molasses cooling. $200$ times more fluorescence is obtained compared to destructive on-resonance imaging, and the trapped molecules remain at a temperature of $20\,��\text{K}$. The achieved number of scattered photons makes possible non-destructive single-shot detection of single molecules with high fidelity., 6 pages, 4 figures

Let $f:\mathbb{P}^N\to\mathbb{P}^N$ be an endomorphism of degree $d\ge2$ defined over $\overline{\mathbb{Q}}$ or $\overline{\mathbb{Q}}_p$, and let $K$ be the field of moduli of $f$. We prove that there is a field of definition $L$ for $f$ whose degree $[L:K]$ is bounded solely in terms of $N$ and $d$., Comment: 22 pages

Motivated by the dynamical uniform boundedness conjecture of Morton and Silverman, specifically in the case of quadratic polynomials, we give a formal construction of a certain class of dynamical analogues of classical modular curves. The preperiodic points for a quadratic polynomial map may be endowed with the structure of a directed graph satisfying certain strict conditions; we call such a graph admissible. Given an admissible graph $G$, we construct a curve $X_1(G)$ whose points parametrize quadratic polynomial maps -- which, up to equivalence, form a one-parameter family -- together with a collection of marked preperiodic points that form a graph isomorphic to $G$. Building on work of Bousch and Morton, we show that these curves are irreducible in characteristic zero, and we give an application of irreducibility in the setting of number fields. We end with a discussion of the Galois theory associated to the preperiodic points of quadratic polynomials, including a certain Galois representation that arises naturally in this setting., Comment: 26 pages

The existence of the Sun’s hot atmosphere and the solar wind acceleration continues to be an outstanding problem in solar-astrophysics. Although magnetohydrodynamic (MHD) modes and dissipation of magnetic energy contribute to heating and the mass cycle of the solar atmosphere, yet direct evidence of such processes often generates debate. Ground-based 1-m Swedish Solar Telescope (SST)/CRISP, Hα 6562.8 Å observations reveal, for the first time, the ubiquitous presence of high frequency (~12–42 mHz) torsional motions in thin spicular-type structures in the chromosphere. We detect numerous oscillating flux tubes on 10 June 2014 between 07:17 UT to 08:08 UT in a quiet-Sun field-of-view of 60” × 60” (1” = 725 km). Stringent numerical model shows that these observations resemble torsional Alfvén waves associated with high frequency drivers which contain a huge amount of energy (~105 W m−2) in the chromosphere. Even after partial reflection from the transition region, a significant amount of energy (~103 W m−2) is transferred onto the overlying corona. We find that oscillating tubes serve as substantial sources of Alfvén wave generation that provide sufficient Poynting flux not only to heat the corona but also to originate the supersonic solar wind.

Robust control theory studies the effect of noise, disturbances, and other uncertainty on system performance. Despite growing recognition across science and engineering that robustness and efficiency tradeoffs dominate the evolution and design of complex systems, the use of robust control theory remains limited, partly because the mathematics involved is relatively inaccessible to nonexperts, and the important concepts have been inexplicable without a fairly rich mathematics background. This paper aims to begin changing that by presenting the most essential concepts in robust control using human stick balancing, a simple case study popular in both the sensorimotor control literature and extremely familiar to engineers. With minimal and familiar models and mathematics, we can explore the impact of unstable poles and zeros, delays, and noise, which can then be easily verified with simple experiments using a standard extensible pointer. Despite its simplicity, this case study has extremes of robustness and fragility that are initially counter-intuitive but for which simple mathematics and experiments are clear and compelling. The theory used here has been well-known for many decades, and the cart-pendulum example is a standard in undergrad controls courses, yet a careful reconsidering of both leads to striking new insights that we argue are of great pedagogical value., Comment: Submitted to Conference on Decisions and Control 2016

Let $K$ be an algebraically closed field of characteristic zero, and let $\mathcal{K} := K(t)$ be the rational function field over $K$. For each $d \ge 2$, we consider the unicritical polynomial $f_d(z) := z^d + t \in \mathcal{K}[z]$, and we ask the following question: If we fix $\alpha \in \mathcal{K}$ and integers $M \ge 0$, $N \ge 1$, and $d \ge 2$, does there exist a place $\mathfrak{p} \in \operatorname{Spec} K[t]$ such that, modulo $\mathfrak{p}$, the point $\alpha$ enters into an $N$-cycle after precisely $M$ steps under iteration by $f_d$? We answer this question completely, concluding that the answer is generally affirmative and explicitly giving all counterexamples. This extends previous work by the author in the case that $\alpha$ is a constant point., Comment: 18 pages + references

Natural selection provides feedback through which information about the environment and its recurring challenges is captured, inherited, and accumulated within genomes in the form of variations that contribute to survival. The variation upon which natural selection acts is generally described as "random." Yet evidence has been mounting for decades, from such phenomena as mutation hotspots, horizontal gene transfer, and highly mutable repetitive sequences, that variation is far from the simplifying idealization of random processes as white (uniform in space and time and independent of the environment or context). This paper focuses on what is known about the generation and control of mutational variation, emphasizing that it is not uniform across the genome or in time, not unstructured with respect to survival, and is neither memoryless nor independent of the (also far from white) environment. We suggest that, as opposed to frequentist methods, Bayesian analysis could capture the evolution of nonuniform probabilities of distinct classes of mutation, and argue not only that the locations, styles, and timing of real mutations are not correctly modeled as generated by a white noise random process, but that such a process would be inconsistent with evolutionary theory. Keywords: Darwin;randommutation;naturalselection;evolution;feedback

We measure inelastic collisional cross sections for the ground $^3$F$_2$ state and the excited $^3$P$_0$ state of atomic thorium in cold collisions with $^3$He. We determine for Th ($^3$F$_2$) at 800 mK the ratio $\gamma \approx 500$ of the momentum-transfer to Zeeman relaxation cross sections for collisions with $^3$He. For Th ($^3$P$_0$), we study electronic inelastic processes and find no quenching even after $10^6$ collisions. We also determine the radiative lifetime of Th ($^3$P$_0$) to be $\tau > 130$ ms. This great stability of the metastable state opens up the possibility for further study, including trapping.

This paper gives a new solution to the output feedback H_2 model matching problem for a large class of delayed information sharing patterns. Existing methods for such problems typically reduce the decentralized problem to a centralized problem of higher state dimension. In contrast, the controller given in this paper is constructed from the solutions to the centralized control and estimation Riccati equations for the original system. The problem is solved by decomposing the controller into two components. One is centralized, but delayed, while the other is decentralized with finite impulse response (FIR). It is then shown that the optimal controller can be constructed through a combination of centralized spectral factorization and quadratic programming., Comment: Preliminary draft of conference paper

The metastable $H \ {}^3��_1$ state in the thorium monoxide (ThO) molecule is highly sensitive to the presence of a CP-violating permanent electric dipole moment of the electron (eEDM). The magnetic dipole moment $��_H$ and the molecule-fixed electric dipole moment $D_H$ of this state are measured in preparation for a search for the eEDM. The small magnetic moment $��_H = 8.5(5) \times 10^{-3} \ ��_B$ displays the predicted cancellation of spin and orbital contributions in a ${}^3 ��_1$ paramagnetic molecular state, providing a significant advantage for the suppression of magnetic field noise and related systematic effects in the eEDM search. In addition, the induced electric dipole moment is shown to be fully saturated in very modest electric fields ($, 4 pages, 3 figures

Republished as a chapter in The Best Writing on Mathematics 2010, M. Pitici, Ed., Princeton University Press, Princeton, NJ, 2010. The objective of this study was to calculate the effectiveness of a pedestrian injury mitigation system that autonomously brakes the car prior to impact at reducing fatal and severe injuries. The database from the German In-Depth Accident Study (GIDAS) was queried for pedestrians hit by the front of cars from 1999 to 2007. Information on vehicle and pedestrian velocities and trajectories were used to estimate the field of view needed for a vehicle-based sensor to detect the pedestrians one second prior to the actual crash. The pre-impact braking system was assumed to provide a braking deceleration up to the limit of the road surface conditions, but never to exceed 0.6g. New impact speeds were calculated for pedestrians that would have been detected by the sensor. These calculations assumed that all pedestrians that were within the given field of view and not hidden by surrounding objects would be detected. The changes in fatality and severe injury risks were quantified using risk curves derived by logistic regression of the accident data. Summing the risks for all pedestrians, new casualty numbers were obtained. The study documents that the effectiveness of reducing fatally (severely) injured pedestrians reached 40% (27%) at a field of view of 40°. Increasing the field of view further led to only marginal improvements in effectiveness.

We measure and theoretically determine the effect of molecular rotational splitting on Zeeman relaxation rates in collisions of cold 3Sigma molecules with helium atoms in a magnetic field. All four stable isotopomers of the imidogen (NH) molecule are magnetically trapped and studied in collisions with 3He and 4He. The 4He data support the predicted 1/B_{e};{2} dependence of the collision-induced Zeeman relaxation rate coefficient on the molecular rotational constant B_{e}. The measured 3He rate coefficients are much larger than the 4He coefficients, depend less strongly on B_{e}, and theoretical analysis indicates they are strongly affected by a shape resonance. The results demonstrate the influence of molecular structure on collisional energy transfer at low temperatures.

We observe magnetic trapping of atomic nitrogen (N14) and cotrapping of ground-state imidogen (N14 H, X Σ-3). Both are loaded directly from a room-temperature beam via buffer gas cooling. We trap approximately 1× 1011 N14 atoms at a peak density of 5× 1011 cm-3 at 550 mK. The 12±4 s 1/e lifetime of atomic nitrogen in the trap is consistent with a model for loss of atoms over the edge of the trap in the presence of helium buffer gas. Cotrapping of N14 and N14 H is accomplished, with 108 NH trapped molecules at a peak density of 108 cm-3. © 2008 The American Physical Society.

We observe magnetic trapping of atomic nitrogen (14^N) and cotrapping of ground state imidogen (14^NH, X-triplet-Sigma-). Both are loaded directly from a room temperature beam via buffer gas cooling. We trap approximately 1 * 10^11 14^N atoms at a peak density of 5 * 10^11 cm^-3 at 550 mK. The 12 +5/-3 s 1/e lifetime of atomic nitrogen in the trap is limited by elastic collisions with the helium buffer gas. Cotrapping of 14^N and 14^NH is accomplished, with 10^8 NH trapped molecules at a peak density of 10^8 cm^-3. We observe no spin relaxation of nitrogen in collisions with helium.

NH radicals are magnetically trapped and their Zeeman relaxation and energy transport collision cross sections with helium are measured. Continuous buffer-gas loading of the trap is direct from a room-temperature molecular beam. The Zeeman relaxation (inelastic) cross section of magnetically trapped electronic, vibrational, and rotational ground state NH molecules in collisions with 3He is measured to be 3.8+/-1.1 x 10(-19) cm(2) at 710 mK. The NH-He energy transport cross section is also measured, indicating a ratio of diffusive to inelastic cross sections of gamma=7 x 10(4), in agreement with recent theory [R. V. Krems, H. R. Sadeghpour, A. Dalgarno, D. Zgid, J. Kłos, and G. Chałasiński, Phys. Rev. A 68, 051401 (2003)10.1103/PhysRevA.68.051401].

Proc. 2007 IEEE Internat. Conf. Systems, Man and Cybernetics. Montreal, Canada, October 7-10, 2007. Considerable attention is now being devoted to the study of “complexity science” with the intent of discovering and applying universal laws of highly interconnected and evolved systems. This paper considers several issues related to the use of these theories in the context of critical infrastructures, particularly the Internet. Specifically, we revisit the notion of “organized complexity” and suggest that it is fundamental to our ability to understand, operate, and design next-generation infrastructure networks.We comment on the role of engineering in defining an architecture to support networked infrastructures and highlight recent advances in the theory of distributed control driven by network technologies.

Hashimoto's encephalopathy (HE) has been described as an encephalopathy, with acute or subacute onset, accompanied by seizures, tremor, myoclonus, ataxia, psychosis, and stroke-like episodes, with a relapsing/remitting or progressive course. HE patients have positive antithyroid antibodies, are usually in a subclinical hypothyroid state, have elevated cerebral spinal fluid (CSF) protein, and have nonspecific electroencephalogram (EEG) and imaging abnormalities in the absence of CNS infection, tumor, or stroke. The authors present two cases of HE, demonstrating an excellent response to high dose steroids acutely followed by long-term treatment with steroids and other immunomodulatory agents. A review of the literature is also provided.

One feature of many naturally occurring or engineered complex systems is tremendous variability in event sizes. To account for it, the behavior of these systems is often described using power law relationships or scaling distributions, which tend to be viewed as "exotic" because of their unusual properties (e.g., infinite moments). An alternate view is based on mathematical, statistical, and data-analytic arguments and suggests that scaling distributions should be viewed as "more normal than normal". In support of this latter view that has been advocated by Mandelbrot for the last 40 years, we review in this paper some relevant results from probability theory and illustrate a powerful statistical approach for deciding whether the variability associated with observed event sizes is consistent with an underlying Gaussian-type (finite variance) or scaling-type (infinite variance) distribution. We contrast this approach with traditional model fitting techniques and discuss its implications for future modeling of complex systems.

The motivation for this paper is to contribute to a unified approach to modeling, realization, approximation and analysis for systems with a rich class of uncertainty structures. The specific focus is on what is the appropriate framework to model components with uncertainty, and what is the appropriate notion of approximation for such components. Components and systems are conceptualized in terms of their behaviors, which can be specified by parametrized equations. More questions are posed than are answered.

We introduce highly optimized tolerance (HOT), a mechanism that connects evolving structure and power laws in interconnected systems. HOT systems arise, e.g., in biology and engineering, where design and evolution create complex systems sharing common features, including (1) high efficiency, performance, and robustness to designed-for uncertainties, (2) hypersensitivity to design flaws and unanticipated perturbations, (3) nongeneric, specialized, structured configurations, and (4) power laws. We introduce HOT states in the context of percolation, and contrast properties of the high density HOT states with random configurations near the critical point. While both cases exhibit power laws, only HOT states display properties (1-3) associated with design and evolution., Comment: 4 pages, 2 figures

It is shown that, in the case of joint real parametric and complex uncertainty, Doyle's structured singular value can be obtained as the solution of a smooth constrained optimization problem. While this problem may have local maxima, an improved computable upper bound to the structured singular value is derived, leading to a sufficient condition for robust stability and performance.

A comprehensive study of track/track dynamics was undertaken, utilizing analytical, laboratory test, and field test techniques to develop a better understanding of track dynamics and performance. Analytical techniques were developed to predict track vibration modes, chordal action effects, dynamic tension and path, energy dissipation, tension going over obstacles, tension distribution, pin/bushing stresses and deflections, temperature buildup, and end connector tightening effectiveness. Double-pin track for heavy tanks was analyzed with these techniques, and designs for improved track suitable for the XM-1 tank were developed. A laboratory bushing research machine was designed, and a track-mounted telemetry system was built. (Author)

Apparent increases in sales and price of rural land, recent changes in land taxing procedure and proposed land-use legislation have brought forth a number of land questions among legislators, public officials and the general citizenry of Utah. This study is directed at questions pertaining to land purchases and land buyers in rural Utah counties. A random sample was taken of the land transfer cards on file at the Utah State Tax Commission. Land buyers whose names appeared on the transfer cards and the returned questionnaires were used in the analysis and are the sole basis of the conclusions of the study. General conclusions from the study were: Land-use at the time of the transaction was most frequently agricultural or vacant or idle for acreages and was most frequently nonagricultural for lots. Following the transaction there was a tendency on the part of buyers to change agricultural and vacant or idle land to a different land use. Buyer characteristics such as annual income, buyer age and residence varied among the regions of the state and were important factors in land transfers. About 50 percent of the total dollars spent for land parcels included in the sample went for residential land. Land located near city limits, improved or unimproved, averaged the highest price per acre or lot. The study's conclusions apply only to recorded land transfers on file at the Utah State Tax Commission for the years 1969 through 1971.

The paper introduces a general approach for analysing linear systems with structured uncertainty based on a new generalised spectral theory for matrices. The results of the paper naturally extend techniques based on singular values and eliminate their most serious difficulties.

This chapter explores ‘engagement without recognition’, a widespread practice whereby states and non-state actors interact with entities that they do not formally recognise as states. The chapter addresses the practical consequences of the plurivocal use of the engagement without recognition formula for EU policies. It gives particular attention to the EU’s ‘non-recognition and engagement’ with Abkhazia and South Ossetia, a policy which has framed the EU’s continued support for communities in these regions, and which is aimed at conflict resolution while maintaining the opposition of EU members to the secession of these territories from Georgia. The chapter argues that a precise distinction needs to be drawn between the formula of ‘non-recognition and engagement’ and that of ‘engagement without recognition’: the first is appropriate for describing the EU’s engagement policies where its member states are united in defending a position of non-recognition as a primary objective; the second formula, on the other hand, is appropriate for analysing these policies where, in order to overcome divisions between member states on the question of recognition, the EU has to defend a status-neutral position.