Amortized Rotation Cost in AVL Trees

An AVL tree is the original type of balanced binary search tree. An insertion in an $n$-node AVL tree takes at most two rotations, but a deletion in an $n$-node AVL tree can take $\Theta(\log n)$. A natural question is whether deletions can take many rotations not only in the worst case but in the amortized case as well. A sequence of $n$ successive deletions in an $n$-node tree takes $O(n)$ rotations, but what happens when insertions are intermixed with deletions? Heaupler, Sen, and Tarjan conjectured that alternating insertions and deletions in an $n$-node AVL tree can cause each deletion to do $\Omega(\log n)$ rotations, but they provided no construction to justify their claim. We provide such a construction: we show that, for infinitely many $n$, there is a set $E$ of {\it expensive} $n$-node AVL trees with the property that, given any tree in $E$, deleting a certain leaf and then reinserting it produces a tree in $E$, with the deletion having done $\Theta(\log n)$ rotations. One can do an arbitrary number of such expensive deletion-insertion pairs. The difficulty in obtaining such a construction is that in general the tree produced by an expensive deletion-insertion pair is not the original tree. Indeed, if the trees in $E$ have even height $k$, $2^{k/2}$ deletion-insertion pairs are required to reproduce the original tree

Decoding the `Nature Encoded' Messages for Distributed Energy Generation Control in Microgrid

The communication for the control of distributed energy generation (DEG) in microgrid is discussed. Due to the requirement of realtime transmission, weak or no explicit channel coding is used for the message of system state. To protect the reliability of the uncoded or weakly encoded messages, the system dynamics are considered as a `nature encoding' similar to convolution code, due to its redundancy in time. For systems with or without explicit channel coding, two decoding procedures based on Kalman filtering and Pearl's Belief Propagation, in a similar manner to Turbo processing in traditional data communication systems, are proposed. Numerical simulations have demonstrated the validity of the schemes, using a linear model of electric generator dynamic system.Comment: It has been submitted to IEEE International Conference on Communications (ICC

OPTIMAL POST-HARVEST GRAINS STORAGE BY RISK AVERSE FARMERS

Most previous research on post-harvest grain storage by farmers has assumed risk-neutral behavior and/or made restrictive assumptions about underlying price probability distributions. In this study we solve the optimal post-harvest storage problem for a risk averse farmer under more general assumptions about underlying price distributions. The resulting model is applied to Michigan corn farmers and results show that, contrary to the sell all-or-nothing risk-neutral rule, risk averse farmers will spread sales out over the storage season. The optimal pattern for sales by Michigan corn farmers is to sell approximately 50% of corn at harvest in November (a risk-reduction strategy) and approximately 40% in May (a return-enhancing strategy).Crop Production/Industries,

Dynamics of confined water reconstructed from inelastic x-ray scattering measurements of bulk response functions

Nanoconfined water and surface-structured water impacts a broad range of fields. For water confined between hydrophilic surfaces, measurements and simulations have shown conflicting results ranging from “liquidlike” to “solidlike” behavior, from bulklike water viscosity to viscosity orders of magnitude higher. Here, we investigate how a homogeneous fluid behaves under nanoconfinement using its bulk response function: The Green's function of water extracted from a library of S(q,ω) inelastic x-ray scattering data is used to make femtosecond movies of nanoconfined water. Between two confining surfaces, the structure undergoes drastic changes as a function of surface separation. For surface separations of ≈9 Å, although the surface-associated hydration layers are highly deformed, they are separated by a layer of bulklike water. For separations of ≈6 Å, the two surface-associated hydration layers are forced to reconstruct into a single layer that modulates between localized “frozen’ and delocalized “melted” structures due to interference of density fields. These results potentially reconcile recent conflicting experiments. Importantly, we find a different delocalized wetting regime for nanoconfined water between surfaces with high spatial frequency charge densities, where water is organized into delocalized hydration layers instead of localized hydration shells, and are strongly resistant to `freezing' down to molecular distances (<6 Å)

Eliciting Stakeholders’ Requirements for Future Energy Systems: A Case Study of Heat Decarbonisation in the UK

It is a truism that whole energy system models underpin the development of policies for energy system decarbonisation. However, recent reviews have thrown doubt on the appropriateness of such models for addressing the multiple goals for future energy systems, in the face of emergent real-world complexity and the evolution of stakeholder’s priorities. Without an understanding of the changing priorities of policy makers and expectations of stakeholders for future systems, system objectives and constraints are likely to be ill-defined, and there is a risk that models may be inadvertently instrumentalised. Adopting a system architecture perspective, the authors have undertaken a three-year programme of research to explore strategies for decarbonising heat in the UK, with interaction with and elicitation of needs from stakeholders at its heart. This paper presents the procedure, methods, and results of an exercise in which experts from stakeholder organisations across the energy system were interviewed. Analysis of interview data reveals two broad approaches to heat decarbonisation which can be defined as either adaptive or transformative. Specific insights gained from these interviews enabled our modelling teams to refocus their work for exploration with a wider circle of stakeholders. Results suggests that this iterative approach to formalising model-policy interaction could improve the transparency and legitimacy of modelling and enhance its impact on policy making

Chemical Abundances For Evolved Stars In M5: Lithium Through Thorium

We present analysis of high-resolution spectra of a sample of stars in the globular cluster M5 (NGC 5904). The sample includes stars from the red giant branch (RGB; seven stars), the red horizontal branch (two stars), and the asymptotic giant branch (AGB; eight stars), with effective temperatures ranging from 4000 K to 6100 K. Spectra were obtained with the HIRES spectrometer on the Keck I telescope, with a wavelength coverage from 3700 angstrom to 7950 angstrom for the HB and AGB sample, and 5300 angstrom to 7600 angstrom for the majority of the RGB sample. We find offsets of some abundance ratios between the AGB and the RGB branches. However, these discrepancies appear to be due to analysis effects, and indicate that caution must be exerted when directly comparing abundance ratios between different evolutionary branches. We find the expected signatures of pollution from material enriched in the products of the hot hydrogen burning cycles such as the CNO, Ne-Na, and Mg-Al cycles, but no significant differences within these signatures among the three stellar evolutionary branches especially when considering the analysis offsets. We are also able to measure an assortment of neutron-capture element abundances, from Sr to Th, in the cluster. We find that the neutron-capture signature for all stars is the same, and shows a predominately r-process origin. However, we also see evidence of a small but consistent extra s-process signature that is not tied to the light-element variations, pointing to a pre-enrichment of this material in the protocluster gas.National Science Foundation AST-0802292NSF AST-0406988, AST-0607770, AST-0607482DFGW. M. Keck FoundationAstronom

A Critical Examination of Hypernova Remnant Candidates in M101. II. NGC 5471B

NGC 5471B has been suggested to contain a hypernova remnant because of its extraordinarily bright X-ray emission. To assess its true nature, we have obtained high-resolution images in continuum bands and nebular lines with the Hubble Space Telescope, and high-dispersion long-slit spectra with the Kitt Peak National Observatory 4-m echelle spectrograph. The images reveal three supernova remnant (SNR) candidates in the giant HII region NGC 5471, with the brightest one being the 77x60 pc shell in NGC 5471B. The Ha velocity profile of NGC 5471B can be decomposed into a narrow component (FWHM = 41 km/s) from the background HII region and a broad component (FWHM = 148 km/s) from the SNR shell. Using the brightness ratio of the broad to narrow components and the Ha flux measured from the WFPC2 Ha image, we derive an Ha luminosity of (1.4+-0.1)x10^39 ergs/s for the SNR shell. The [SII]6716,6731 doublet ratio of the broad velocity component is used to derive an electron density of ~700 cm^-3 in the SNR shell. The mass of the SNR shell is thus 4600+-500 Mo. With a \~330 km/s expansion velocity implied by the extreme velocity extent of the broad component, the kinetic energy of the SNR shell is determined to be 5x10^51 ergs. This requires an explosion energy greater than 10^52 ergs, which can be provided by one hypernova or multiple supernovae. Comparing to SNRs in nearby active star formation regions, the SNR shell in NGC 5471B appears truly unique and energetic. We conclude that the optical observations support the existence of a hypernova remnant in NGC 5471B.Comment: 27 pages, 9 figures, to appear in May 2002 issue of The Astronomical Journa

Exploring the Relationship between Whole vs. Part Destination Images: A Case Study

This study attempted to explore the relationship between the destination image of one region (whole destination image) and those of its inner areas (part destination images) via a core-periphery structural perspective. To date, empirical studies on this topic remain rare. By content analyzing online reviews, the relationship of memory associations in the whole and part destination images was analyzed. Our results show that whole destination image shares a number of associations with part destination images. Yet the percentages of shared image associations on whole destination image are not equal among part destination images. The status (core/periphery) of shared associations may not be the same in whole and part destination images. Besides, core associations of part destination images are more likely to be found in whole destination image compared to periphery associations of part destination images. Conceptual and managerial implications of the findings were discussed

Communicating Socially Acceptable Risk Judgments: The Role of Impression Information Insufficiency in The Risk Information Seeking and Processing Model

The COVID-19 pandemic has created uncertainty and controversy around risk-related issues such as vaccine mandates. People expressing their opinions on these issues to important others, such as employers, may face significant consequences, such as rewards or rejection. Therefore, people may try to find, avoid, or use information in a way that helps them express risk judgments that are socially acceptable in different social situations. This study investigated how people seek, avoid, and process risk information when they are concerned about their impression management. It also introduced the concept of impression information insufficiency (the perceived gap between the information one has and the information one needs to convey socially acceptable judgments and meet interpersonal needs in social situations) and examined its antecedents and outcomes within the risk information seeking and processing model. We conducted an online survey with 1673 Hong Kong adults during the COVID-19 pandemic. The results showed that fear and social norms related to greater impression information insufficiency, which thereby was associated with biased risk information seeking, avoidance, and processing