34,480 research outputs found
Bounding Embeddings of VC Classes into Maximum Classes
One of the earliest conjectures in computational learning theory-the Sample
Compression conjecture-asserts that concept classes (equivalently set systems)
admit compression schemes of size linear in their VC dimension. To-date this
statement is known to be true for maximum classes---those that possess maximum
cardinality for their VC dimension. The most promising approach to positively
resolving the conjecture is by embedding general VC classes into maximum
classes without super-linear increase to their VC dimensions, as such
embeddings would extend the known compression schemes to all VC classes. We
show that maximum classes can be characterised by a local-connectivity property
of the graph obtained by viewing the class as a cubical complex. This geometric
characterisation of maximum VC classes is applied to prove a negative embedding
result which demonstrates VC-d classes that cannot be embedded in any maximum
class of VC dimension lower than 2d. On the other hand, we show that every VC-d
class C embeds in a VC-(d+D) maximum class where D is the deficiency of C,
i.e., the difference between the cardinalities of a maximum VC-d class and of
C. For VC-2 classes in binary n-cubes for 4 <= n <= 6, we give best possible
results on embedding into maximum classes. For some special classes of Boolean
functions, relationships with maximum classes are investigated. Finally we give
a general recursive procedure for embedding VC-d classes into VC-(d+k) maximum
classes for smallest k.Comment: 22 pages, 2 figure
Meteorite cloudy zone formation as a quantitative indicator of paleomagnetic field intensities and cooling rates on planetesimals
Metallic microstructures in slowly-cooled iron-rich meteorites reflect the
thermal and magnetic histories of their parent planetesimals. Of particular
interest is the cloudy zone, a nanoscale intergrowth of Ni-rich islands within
a Ni-poor matrix that forms below 350{\deg}C by spinodal decomposition. The
sizes of the islands have long been recognized as reflecting the
low-temperature cooling rates of meteorite parent bodies. However, a model
capable of providing quantitative cooling rate estimates from island sizes has
been lacking. Moreover, these islands are also capable of preserving a record
of the ambient magnetic field as they grew, but some of the key physical
parameters required for recovering reliable paleointensity estimates from
magnetic measurements of these islands have been poorly constrained. To address
both of these issues, we present a numerical model of the structural and
compositional evolution of the cloudy zone as a function of cooling rate and
local composition. Our model produces island sizes that are consistent with
present-day measured sizes. This model enables a substantial improvement in the
calibration of paleointensity estimates and associated uncertainties. In
particular, we can now accurately quantify the statistical uncertainty
associated with the finite number of islands and the uncertainty on their size
at the time of the record. We use this new understanding to revisit
paleointensities from previous pioneering paleomagnetic studies of cloudy
zones. We show that these could have been overestimated but nevertheless still
require substantial magnetic fields to have been present on their parent
bodies. Our model also allows us to estimate absolute cooling rates for
meteorites that cooled slower than 10000{\deg}C My-1. We demonstrate how these
cooling rate estimates can uniquely constrain the low-temperature thermal
history of meteorite parent bodies.Comment: Manuscript resubmitted after revision
Connectivity Explains Local Ant Community Structure in A Neotropical Forest Canopy: A LargeāScale Experimental Approach
Understanding how habitat structure and resource availability affect local species distributions is a key goal of community ecology. Where habitats occur as a mosaic, variation in connectivity among patches influences both local species richness and composition, and connectivity is a key conservation concern in fragmented landscapes. Similarly, availability of limiting resources frequently determines species coexistence or exclusion. For primarily cursorial arthropods like ants, gaps between neighboring trees are a significant barrier to movement through the forest canopy. Competition for limited resources such as nest sites also promotes antagonistic interactions. Lianas (woody vines) connect normally isolated neighboring tree crowns and often have hollow stems inhabited by ants. We used two largeāscale lianaāremoval experiments to determine how connectivity and nest site availability provided by lianas affect arboreal ant species richness, species composition, and Ī²ādiversity in a lowland tropical forest in Panama. Removing lianas from a tree crown reduced ant species richness up to 35%, and disproportionately affected species that require large foraging areas. Adding artificial connectivity to trees mitigated the effects of liana removal. Ant colonization of artificial nests was higher (73% occupied) in trees without lianas vs. trees with lianas (28% occupied). However, artificial nests typically were colonized by existing polydomous, resident ant species. As a result, nest addition did not affect ant community structure. Collectively, these results indicate that lianas are important to the maintenance of arboreal ant diversity specifically by providing connectivity among neighboring tree crowns. Anticipated increases in liana abundance in this forest could increase the local (treeālevel) species richness of arboreal ants, with a compositional bias toward elevating the density of broadāranging specialist predators
Classical Rules in Quantum Games
We consider two aspects of quantum game theory: the extent to which the
quantum solution solves the original classical game, and to what extent the new
solution can be obtained in a classical model.Comment: The previous title, "Quantum games are no fun (yet)", was too
whimsical for Physical Review. This is a comment on most, but not all, papers
on quantum game theor
Parameter space metric for 3.5 post-Newtonian gravitational-waves from compact binary inspirals
We derive the metric on the parameter space of 3.5 post-Newtonian (3.5PN)
stationary phase compact binary inspiral waveforms for a single detector,
neglecting spin, eccentricity, and finite-body effects. We demonstrate that
this leads to better template placement than the current practice of using the
2PN metric to place 3.5PN templates: The recovered event rate is improved by
about 10% at a cost of nearly doubling the number of templates. The
cross-correlations between mass parameters are also more accurate, which will
result in better coincidence tests.Comment: 10 pages, 7 figure
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