5,389 research outputs found
Cyclic derangements
A classic problem in enumerative combinatorics is to count the number of
derangements, that is, permutations with no fixed point. Inspired by a recent
generalization to facet derangements of the hypercube by Gordon and McMahon, we
generalize this problem to enumerating derangements in the wreath product of
any finite cyclic group with the symmetric group. We also give q- and (q,
t)-analogs for cyclic derangements, generalizing results of Brenti and Gessel.Comment: 14 page
Sensemaking Practices in the Everyday Work of AI/ML Software Engineering
This paper considers sensemaking as it relates to everyday software engineering (SE) work practices and draws on a multi-year ethnographic study of SE projects at a large, global technology company building digital services infused with artificial intelligence (AI) and machine learning (ML) capabilities. Our findings highlight the breadth of sensemaking practices in AI/ML projects, noting developers' efforts to make sense of AI/ML environments (e.g., algorithms/methods and libraries), of AI/ML model ecosystems (e.g., pre-trained models and "upstream"models), and of business-AI relations (e.g., how the AI/ML service relates to the domain context and business problem at hand). This paper builds on recent scholarship drawing attention to the integral role of sensemaking in everyday SE practices by empirically investigating how and in what ways AI/ML projects present software teams with emergent sensemaking requirements and opportunities
Formation of caustics in Dirac-Born-Infeld type scalar field systems
We investigate the formation of caustics in Dirac-Born-Infeld type scalar
field systems for generic classes of potentials, viz., massive rolling scalar
with potential, and inverse
power-law potentials with . We find that in the case
of\texttt{} exponentially decreasing rolling massive scalar field potential,
there are multi-valued regions and regions of likely to be caustics in the
field configuration. However there are no caustics in the case of exponentially
increasing potential. We show that the formation of caustics is inevitable for
the inverse power-law potentials under consideration in Minkowski space time
whereas caustics do not form in this case in the FRW universe.Comment: 16 pages, 14 figures, major revision, conclusions strengthen, to
appear in PR
Inflation and dark energy arising from geometrical tachyons
We study the motion of a BPS D3-brane in the NS5-brane ring background. The
radion field becomes tachyonic in this geometrical set up. We investigate the
potential of this geometrical tachyon in the cosmological scenario for
inflation as well as dark energy. We evaluate the spectra of scalar and tensor
perturbations generated during tachyon inflation and show that this model is
compatible with recent observations of Cosmic Microwave Background (CMB) due to
an extra freedom of the number of NS5-branes. It is not possible to explain the
origin of both inflation and dark energy by using a single tachyon field, since
the energy density at the potential minimum is not negligibly small because of
the amplitude of scalar perturbations set by CMB anisotropies. However
geometrical tachyon can account for dark energy when the number of NS5-branes
is large, provided that inflation is realized by another scalar field.Comment: 11 pages, 8 figure
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