3,385 research outputs found
Investigation of the Roughness of the Australian Gravity Field Using Statistical, Graphical, Fractal and Fourier Power Spectrum Techniques
Exploring the Detailed Structure of the Local Earth's Gravity Field Using Fractal and Fourier Power Spectrum Techniques
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EFAB: Batch Production of Functional, Fully-Dense Metal Parts with Micron-Scale Features
EFAB (Electrochemical FABrication) is a new SFF process with the potential to economically fabricate
prototypes or mass production quantities of functional, mesoscale-microscale parts and mechanisms. EFAB
generates an entire layer simultaneously-versus serially, as with most SFF. Based on electrodeposition,
EFAB allows ultra-thin layers (2-10 microns, or even submicron) that minimize stairsteps, and generates a
net-shape, fully-dense metal structure that can be homogeneous and isotropic. Minimum feature width is
approximately 25 microns, and can be reduced further. EFAB can be used to manufacture micromachines
and microelectromechanical systems (MEMS), offering significant advantages over current processes: e.g.,
true 3-D geometry, IC compatibility, low capital investment, and process automation.Mechanical Engineerin
NOUS: Construction and Querying of Dynamic Knowledge Graphs
The ability to construct domain specific knowledge graphs (KG) and perform
question-answering or hypothesis generation is a transformative capability.
Despite their value, automated construction of knowledge graphs remains an
expensive technical challenge that is beyond the reach for most enterprises and
academic institutions. We propose an end-to-end framework for developing custom
knowledge graph driven analytics for arbitrary application domains. The
uniqueness of our system lies A) in its combination of curated KGs along with
knowledge extracted from unstructured text, B) support for advanced trending
and explanatory questions on a dynamic KG, and C) the ability to answer queries
where the answer is embedded across multiple data sources.Comment: Codebase: https://github.com/streaming-graphs/NOU
Tight Guarantees for Multi-unit Prophet Inequalities and Online Stochastic Knapsack
Prophet inequalities are a useful tool for designing online allocation
procedures and comparing their performance to the optimal offline allocation.
In the basic setting of -unit prophet inequalities, the magical procedure of
Alaei (2011) with its celebrated performance guarantee of
has found widespread adoption in mechanism design and
other online allocation problems in online advertising, healthcare scheduling,
and revenue management. Despite being commonly used for implementing online
allocation, the tightness of Alaei's procedure for a given has remained
unknown. In this paper we resolve this question, characterizing the tight bound
by identifying the structure of the optimal online implementation, and
consequently improving the best-known guarantee for -unit prophet
inequalities for all . We also consider a more general online stochastic
knapsack problem where each individual allocation can consume an arbitrary
fraction of the initial capacity. We introduce a new "best-fit" procedure for
implementing a fractionally-feasible knapsack solution online, with a
performance guarantee of , which we also show
is tight. This improves the previously best-known guarantee of 0.2 for online
knapsack. Our analysis differs from existing ones by eschewing the need to
split items into "large" or "small" based on capacity consumption, using
instead an invariant for the overall utilization on different sample paths.
Finally, we refine our technique for the unit-density special case of knapsack,
and improve the guarantee from 0.321 to 0.3557 in the multi-resource
appointment scheduling application of Stein et al. (2020). All in all, our
results imply \textit{tight} Online Contention Resolution Schemes for
-uniform matroids and the knapsack polytope, respectively, which has further
implications in mechanism design
A Stability Timescale for Non-Hierarchical Three-Body Systems
The gravitational three-body problem is a fundamental problem in physics and
has significant applications to astronomy. Three-body configurations are often
considered stable as long the system is hierarchical; that is, the two orbital
distances are well-separated. However, instability, which is often associated
with significant energy exchange between orbits, takes time to develop.
Assuming two massive objects in a circular orbit and a test particle in an
eccentric orbit, we develop an analytical formula estimating the time it takes
for the test particle's orbital energy to change by an order of itself. We show
its consistency with results from N-body simulations. For eccentric orbits in
particular, the instability is primarily driven not by close encounters of the
test particle with one of the other bodies, but by the fundamental
susceptibility of eccentric orbits to exchange energy at their periapsis.
Motivated by recent suggestions that the galactic center may host an
intermediate-mass black hole (IMBH) as a companion to the massive black hole
Sgr A*, we use our timescale to explore the parameter space that could harbor
an IMBH for the lifetime of the S-cluster of stars surrounding Sgr A*.
Furthermore, we show that the orbit of an S-star can be stable for long
timescales in the presence of other orbital crossing stars, thus suggesting
that the S-cluster may be stable for the lifetimes of its member stars.Comment: 16 pages, 8 figure
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