9,055 research outputs found
Efficiency of Truthful and Symmetric Mechanisms in One-sided Matching
We study the efficiency (in terms of social welfare) of truthful and
symmetric mechanisms in one-sided matching problems with {\em dichotomous
preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are
particularly interested in the well-known {\em Random Serial Dictatorship}
mechanism. For dichotomous preferences, we first show that truthful, symmetric
and optimal mechanisms exist if intractable mechanisms are allowed. We then
provide a connection to online bipartite matching. Using this connection, it is
possible to design truthful, symmetric and tractable mechanisms that extract
0.69 of the maximum social welfare, which works under assumption that agents
are not adversarial. Without this assumption, we show that Random Serial
Dictatorship always returns an assignment in which the expected social welfare
is at least a third of the maximum social welfare. For normalized von
Neumann-Morgenstern preferences, we show that Random Serial Dictatorship always
returns an assignment in which the expected social welfare is at least
\frac{1}{e}\frac{\nu(\opt)^2}{n}, where \nu(\opt) is the maximum social
welfare and is the number of both agents and items. On the hardness side,
we show that no truthful mechanism can achieve a social welfare better than
\frac{\nu(\opt)^2}{n}.Comment: 13 pages, 1 figur
Eulerian and modified Lagrangian approaches to multi-dimensional condensation and collection
Turbulence is argued to play a crucial role in cloud droplet growth. The
combined problem of turbulence and cloud droplet growth is numerically
challenging. Here, an Eulerian scheme based on the Smoluchowski equation is
compared with two Lagrangian superparticle (or su- perdroplet) schemes in the
presence of condensation and collection. The growth processes are studied
either separately or in combination using either two-dimensional turbulence, a
steady flow, or just gravitational acceleration without gas flow. Good
agreement between the differ- ent schemes for the time evolution of the size
spectra is observed in the presence of gravity or turbulence. Higher moments of
the size spectra are found to be a useful tool to characterize the growth of
the largest drops through collection. Remarkably, the tails of the size spectra
are reasonably well described by a gamma distribution in cases with gravity or
turbulence. The Lagrangian schemes are generally found to be superior over the
Eulerian one in terms of computational performance. However, it is shown that
the use of interpolation schemes such as the cloud-in-cell algorithm is
detrimental in connection with superparticle or superdroplet approaches.
Furthermore, the use of symmetric over asymmetric collection schemes is shown
to reduce the amount of scatter in the results.Comment: 36 pages, 17 figure
Social welfare in one-sided matchings: Random priority and beyond
We study the problem of approximate social welfare maximization (without
money) in one-sided matching problems when agents have unrestricted cardinal
preferences over a finite set of items. Random priority is a very well-known
truthful-in-expectation mechanism for the problem. We prove that the
approximation ratio of random priority is Theta(n^{-1/2}) while no
truthful-in-expectation mechanism can achieve an approximation ratio better
than O(n^{-1/2}), where n is the number of agents and items. Furthermore, we
prove that the approximation ratio of all ordinal (not necessarily
truthful-in-expectation) mechanisms is upper bounded by O(n^{-1/2}), indicating
that random priority is asymptotically the best truthful-in-expectation
mechanism and the best ordinal mechanism for the problem.Comment: 13 page
Extending the range of error estimates for radial approximation in Euclidean space and on spheres
We adapt Schaback's error doubling trick [R. Schaback. Improved error bounds
for scattered data interpolation by radial basis functions. Math. Comp.,
68(225):201--216, 1999.] to give error estimates for radial interpolation of
functions with smoothness lying (in some sense) between that of the usual
native space and the subspace with double the smoothness. We do this for both
bounded subsets of R^d and spheres. As a step on the way to our ultimate goal
we also show convergence of pseudoderivatives of the interpolation error.Comment: 10 page
Quasi-thermal Comptonization and gamma-ray bursts
Quasi-thermal Comptonization in internal shocks formed between relativistic
shells can account for the high energy emission of gamma-ray bursts. This is in
fact the dominant cooling mechanism if the typical energy of the emitting
particles is achieved either through the balance between heating and cooling or
as a result of electron-positron pair production. Both processes yield sub or
mildly relativistic energies. In this case the synchrotron spectrum is
self-absorbed, providing the seed soft photons for the Comptonization process,
whose spectrum is flat [F(v) ~ const], ending either in an exponential cutoff
or a Wien peak, depending on the scattering optical depth of the emitting
particles. Self-consistent particle energy and optical depth are estimated and
found in agreement with the observed spectra.Comment: 10 pages, ApJ Letters, accepted for publicatio
Effect of turbulence on collisional growth of cloud droplets
We investigate the effect of turbulence on the collisional growth of um-sized
droplets through high- resolution numerical simulations with well resolved
Kolmogorov scales, assuming a collision and coalescence efficiency of unity.
The droplet dynamics and collisions are approximated using a superparticle
approach. In the absence of gravity, we show that the time evolution of the
shape of the droplet-size distribution due to turbulence-induced collisions
depends strongly on the turbulent energy-dissipation rate, but only weakly on
the Reynolds number. This can be explained through the energy dissipation rate
dependence of the mean collision rate described by the Saffman-Turner collision
model. Consistent with the Saffman-Turner collision model and its extensions,
the collision rate increases as the square root of the energy dissipation rate
even when coalescence is invoked. The size distribution exhibits power law
behavior with a slope of -3.7 between a maximum at approximately 10 um up to
about 40 um. When gravity is invoked, turbulence is found to dominate the time
evolution of an initially monodisperse droplet distribution at early times. At
later times, however, gravity takes over and dominates the collisional growth.
We find that the formation of large droplets is very sensitive to the turbulent
energy dissipation rate. This is due to the fact that turbulence enhances the
collisional growth between similar sized droplets at the early stage of
raindrop formation. The mean collision rate grows exponentially, which is
consistent with the theoretical prediction of the continuous collisional growth
even when turbulence-generated collisions are invoked. This consistency only
reflects the mean effect of turbulence on collisional growth
Social Welfare in One-sided Matching Markets without Money
We study social welfare in one-sided matching markets where the goal is to
efficiently allocate n items to n agents that each have a complete, private
preference list and a unit demand over the items. Our focus is on allocation
mechanisms that do not involve any monetary payments. We consider two natural
measures of social welfare: the ordinal welfare factor which measures the
number of agents that are at least as happy as in some unknown, arbitrary
benchmark allocation, and the linear welfare factor which assumes an agent's
utility linearly decreases down his preference lists, and measures the total
utility to that achieved by an optimal allocation. We analyze two matching
mechanisms which have been extensively studied by economists. The first
mechanism is the random serial dictatorship (RSD) where agents are ordered in
accordance with a randomly chosen permutation, and are successively allocated
their best choice among the unallocated items. The second mechanism is the
probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which
computes a fractional allocation that can be expressed as a convex combination
of integral allocations. The welfare factor of a mechanism is the infimum over
all instances. For RSD, we show that the ordinal welfare factor is
asymptotically 1/2, while the linear welfare factor lies in the interval [.526,
2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the
linear welfare factor is roughly 2/3. To our knowledge, these results are the
first non-trivial performance guarantees for these natural mechanisms
On the Approximability of Digraph Ordering
Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute
a labeling maximizing the number of forward edges, i.e.
edges (u,v) such that (u) < (v). For different values of k, this
reduces to Maximum Acyclic Subgraph (k=n), and Max-Dicut (k=2). This work
studies the approximability of Max-k-Ordering and its generalizations,
motivated by their applications to job scheduling with soft precedence
constraints. We give an LP rounding based 2-approximation algorithm for
Max-k-Ordering for any k={2,..., n}, improving on the known
2k/(k-1)-approximation obtained via random assignment. The tightness of this
rounding is shown by proving that for any k={2,..., n} and constant
, Max-k-Ordering has an LP integrality gap of 2 -
for rounds of the
Sherali-Adams hierarchy.
A further generalization of Max-k-Ordering is the restricted maximum acyclic
subgraph problem or RMAS, where each vertex v has a finite set of allowable
labels . We prove an LP rounding based
approximation for it, improving on the
approximation recently given by Grandoni et al.
(Information Processing Letters, Vol. 115(2), Pages 182-185, 2015). In fact,
our approximation algorithm also works for a general version where the
objective counts the edges which go forward by at least a positive offset
specific to each edge.
The minimization formulation of digraph ordering is DAG edge deletion or
DED(k), which requires deleting the minimum number of edges from an n-vertex
directed acyclic graph (DAG) to remove all paths of length k. We show that
both, the LP relaxation and a local ratio approach for DED(k) yield
k-approximation for any .Comment: 21 pages, Conference version to appear in ESA 201
Emission Spectra from Internal Shocks in Gamma-Ray-Burst Sources
Unsteady activity of gamma-ray burst sources leads to internal shocks in
their emergent relativistic wind. We study the emission spectra from such
shocks, assuming that they produce a power-law distribution of relativistic
electrons and posses strong magnetic fields. The synchrotron radiation emitted
by the accelerated electrons is Compton up-scattered multiple times by the same
electrons. A substantial component of the scattered photons acquires high
energies and produces e+e- pairs. The pairs transfer back their kinetic energy
to the radiation through Compton scattering. The generic spectral signature
from pair creation and multiple Compton scattering is highly sensitive to the
radius at which the shock dissipation takes place and to the Lorentz factor of
the wind. The entire emission spectrum extends over a wide range of photon
energies, from the optical regime up to TeV energies. For reasonable values of
the wind parameters, the calculated spectrum is found to be in good agreement
with the burst spectra observed by BATSE.Comment: 12 pages, latex, 2 figures, submitted to ApJ
Dairy farmer and farm staff attitudes and perceptions regarding daily milk allowance to calves
The benefits of feeding calves more milk are increasingly being recognized by dairy farmers. However, most producers have still not implemented higher feeding plans. The aim of the present study was to gain a deeper understanding of farmer and farm staff attitudes, and the perceptions and factors considered in their decision-making regarding daily milk allowances. We collected data through focus group interviews with dairy farm-ers, farm managers, and calf-care workers who were selected using purposive and snowball sampling. In total, 40 persons (24 women and 16 men) joined a focus group interview (6 in all, each with 5-8 participants). Interviews were recorded, and recordings were tran-scribed and analyzed thematically. Participants had contrasting opinions about the minimum, maximum, and recommended daily milk allowances to their calves. Their suggested lowest daily milk allowance to sustain animal welfare ranged from 4 to 8-10 L and the maxi-mum allowance from 6 to 15 L. We found that farmers' and farm staff's choices and recommendations of milk-feeding protocols were influenced by a large number of factors that could be grouped into 4 themes: (1) Life beyond work, (2) Farm facilities and equipment, (3) Care of the calves, and (4) Profitability and pro-duction. Participants' considerations were similar and aimed to maximize daily milk allowance based on farm conditions. However, the allowances they described as optimal for their calves often differed from what they considered practically feasible. We found that the care of the calves and the well-being of the owners and the staff was central in the participants' decision-making, but that this care perspective was challenged by the social and economic sustainability of the farm. Most participants fed their calves twice daily and did not think that increasing that number would be practically feasible. Our results indicate that the participants' viewpoints regarding calves were important for their decision-making about milk allowances. We suggest that a more holistic perspective should be used when advising farmers about milk allowances, putting particular emphasis on the caring and social sustainability aspects of the individual farm
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