Distributed Approximation Algorithms for Weighted Shortest Paths

A distributed network is modeled by a graph having $n$ nodes (processors) and diameter $D$. We study the time complexity of approximating {\em weighted} (undirected) shortest paths on distributed networks with a $O(\log n)$ {\em bandwidth restriction} on edges (the standard synchronous \congest model). The question whether approximation algorithms help speed up the shortest paths (more precisely distance computation) was raised since at least 2004 by Elkin (SIGACT News 2004). The unweighted case of this problem is well-understood while its weighted counterpart is fundamental problem in the area of distributed approximation algorithms and remains widely open. We present new algorithms for computing both single-source shortest paths (\sssp) and all-pairs shortest paths (\apsp) in the weighted case. Our main result is an algorithm for \sssp. Previous results are the classic $O(n)$-time Bellman-Ford algorithm and an $\tilde O(n^{1/2+1/2k}+D)$-time $(8k\lceil \log (k+1) \rceil -1)$-approximation algorithm, for any integer $k\geq 1$, which follows from the result of Lenzen and Patt-Shamir (STOC 2013). (Note that Lenzen and Patt-Shamir in fact solve a harder problem, and we use $\tilde O(\cdot)$ to hide the O(\poly\log n) term.) We present an $\tilde O(n^{1/2}D^{1/4}+D)$-time $(1+o(1))$-approximation algorithm for \sssp. This algorithm is {\em sublinear-time} as long as $D$ is sublinear, thus yielding a sublinear-time algorithm with almost optimal solution. When $D$ is small, our running time matches the lower bound of $\tilde \Omega(n^{1/2}+D)$ by Das Sarma et al. (SICOMP 2012), which holds even when $D=\Theta(\log n)$, up to a \poly\log n factor.Comment: Full version of STOC 201

Summer Camp as a Force for 21st Century Learning: Exploring Divergent Thinking and Activity Selection in a Residential Camp Setting

This study investigated change in divergent thinking (DT), an indicator of creative potential, at two gender-specific residential summer camps. Additionally, this study examined whether the change in DT varied by gender and by the type of activities campers self-select. Quantitative methods, using a quasi-experimental design was used in order to understand differences in camper scores. A total of 189 youth, 100 girls, 89 boys, between the ages of 9 and 14 years participated in the current study. Participants were administered a modified version of Guilford\u27s (1967) alternate uses task, a measure of DT, in which respondents were asked questions such as name all of the uses for a brick or name all of the uses for a plate before the camp session started, and then again at the end of the two-week session. Results indicate overall mean significant increases in DT across all scoring methods of fluency, flexibility, and originality. Participants who self-selected one or more artistic activities (e.g., drama, arts and crafts, dance) had significant increases on the tasks as opposed to participants who did not select any artistic activities (e.g., basketball, baseball, archery). Finally, girls significantly increased across all scoring methods, whereas boys slightly increased in fluency and flexibility but not in originality. These results indicate residential summer camp may provide a creativity benefit for youth in attendance, especially those who participate in certain activities. Practitioners should use this study to understand their own programming in terms of creativity, activity offerings, and camp cultur

Compression of Martian atmosphere for production of oxygen

The compression of CO2 from the Martian atmosphere for production of O2 via an electrochemical cell is addressed. Design specifications call for an oxygen production rate of 10 kg per day and for compression of 50 times that mass of CO2. Those specifications require a compression rate of over 770 cfm at standard Martian temperature and pressure (SMTP). Much of the CO2 being compressed represents waste, unless it can be recycled. Recycling can reduce the volume of gas that must be compressed to 40 cfm at SMTP. That volume reduction represents significant mass savings in the compressor, heating equipment, filters, and energy source. Successful recycle of the gas requires separation of CO (produced in the electrochemical cell) from CO2, N2, and Ar found in the Martian atmosphere. That aspect was the focus of this work

Unlocking the riddles of Imperial Greek melodies : the ‘Lydian’ metamorphosis of the classical harmonic system

Building upon Lynch 2022a and 2022b, this article offers the first account of the historical evolution of the Greek harmonic system and notation keys (tónoi) that bridges the gap between Classical and Imperial music. This new solution allows us to reconstruct, for the first time, a continuous, if evolving, tradition that stretches from Euripides’ Orestes to late antiquity, reconciling key theoretical insights provided by Ptolemy, Porphyry and others with documentary evidence that illustrates the structure of the Imperial harmonic system and its use in the Imperial musical documents (dDAGM). This approach also enables us to trace the gradual expansion of the Greek notation system from an initial set of symbols (Α—Ω) to the full array recorded by Aristides and Alypius, mapping its development onto key historical milestones including the revolutionary innovations of the New Musicians and Damon of Oa’s inclusion of the Lydian mode into the Greek modulation system.Peer reviewe

10-30-eV optical properties of GaN

The reflectance of basal-plane epitaxial layers of GaN has been measured between 5 and 30 eV, and Kramers-Kronig analyzed to get the dielectric function and the electron-energy-loss function. The second derivative of the reflectance with respect to energy was obtained in the region of Ga 3d→ conduction-band excitations. The latter show weak structure from transitions to Γ final states and stronger structures to final states along U, both split by the 0.40-eV Ga 3d spin-orbit splitting. The loss function exhibits two peaks, the stronger one at 19.0 eV, below the expected 23.3 eV, while the weaker one is at 23.2 eV

Ce-catalyzed oxidation of Ta(110)

Photoemission spectroscopy was used to investigate the initial oxidation of the Ce/Ta(110) interface at room temperature. The oxidation of Ta(110) is dramatically enhanced by a thin Ce overlayer. A Ta suboxide TaOχ (0.5≤χ≤1) is formed first in the interface, followed by the rapid formation of Ta2O5 upon further oxygen exposure. A weak interface reaction exists in Ce/Ta(110), but is excluded as the main cause of the catalytic oxidation. An earlier suggestion is reconfirmed that the Ce layer converts O2 to oxygen ions and thus promotes the oxidation of the substrate

Submicrosecond comparisons of time standards via the Navigation Technology Satellites (NTS)

An interim demonstration was performed of the time transfer capability of the NAVSTAR GPS system using a single NTS satellite. Measurements of time difference (pseudo-range) are made from the NTS tracking network and at the participating observatories. The NTS network measurements are used to compute the NTS orbit trajectory. The central NTS tracking station has a time link to the Naval Observatory UTC (USNO,MC1) master clock. Measurements are used with the NTS receiver at the remote observatory, the time transfer value UTC (USNO,MC1)-UTC (REMOTE, VIA NTS) is calculated. Intercomparisons were computed using predicted values of satellite clock offset and ephemeus

Does a Carbonatite Deposit Influence Its Surrounding Ecosystem?

Carbonatites are unusual alkaline rocks with diverse compositions. Although previous work has characterized the effects these rocks have on soils and plants, little is known about their impacts on local ecosystems. Using a deposit within the Great Lakes–St. Lawrence forest in northern Ontario, Canada, we investigated the effect of a carbonatite on soil chemistry and on the structure of plant and soil microbial communities. This was done using a vegetation survey conducted above and around the deposit, with corresponding soil samples collected for determining soil nutrient composition and for assessing microbial community structure using 16S/ITS Illumina Mi-Seq sequencing. In some soils above the deposit a soil chemical signature of the carbonatite was found, with the most important effect being an increase in soil pH compared with the non-deposit soils. Both plants and microorganisms responded to the altered soil chemistry: the plant communities present in carbonatite-impacted soils were dominated by ruderal species, and although differences in microbial communities across the surveyed areas were not obvious, the abundances of specific bacteria and fungi were reduced in response to the carbonatite. Overall, the deposit seems to have created microenvironments of relatively basic soil in an otherwise acidic forest soil. This study demonstrates for the first time how carbonatites can alter ecosystems in situ