1,156 research outputs found
Budget Imbalance Criteria for Auctions: A Formalized Theorem
We present an original theorem in auction theory: it specifies general
conditions under which the sum of the payments of all bidders is necessarily
not identically zero, and more generally not constant. Moreover, it explicitly
supplies a construction for a finite minimal set of possible bids on which such
a sum is not constant. In particular, this theorem applies to the important
case of a second-price Vickrey auction, where it reduces to a basic result of
which a novel proof is given. To enhance the confidence in this new theorem, it
has been formalized in Isabelle/HOL: the main results and definitions of the
formal proof are re- produced here in common mathematical language, and are
accompanied by an informal discussion about the underlying ideas.Comment: 6th Podlasie Conference on Mathematics 2014, 11 page
Proving soundness of combinatorial Vickrey auctions and generating verified executable code
Using mechanised reasoning we prove that combinatorial Vickrey auctions are
soundly specified in that they associate a unique outcome (allocation and
transfers) to any valid input (bids). Having done so, we auto-generate verified
executable code from the formally defined auction. This removes a source of
error in implementing the auction design. We intend to use formal methods to
verify new auction designs. Here, our contribution is to introduce and
demonstrate the use of formal methods for auction verification in the familiar
setting of a well-known auction
Probing the LMC age gap at intermediate cluster masses
The LMC has a rich star cluster system spanning a wide range of ages and
masses. One striking feature of the LMC cluster system is the existence of an
age gap between 3-10 Gyrs. But this feature is not as clearly seen among field
stars. Three LMC fields containing relatively poor and sparse clusters whose
integrated colours are consistent with those of intermediate age simple stellar
populations have been imaged in BVI with the Optical Imager (SOI) at the
Southern Telescope for Astrophysical Research (SOAR). A total of 6 clusters, 5
of them with estimated initial masses M < 10^4M_sun, were studied in these
fields. Photometry was performed and Colour-Magnitude Diagrams (CMD) were built
using standard point spread function fitting methods. The faintest stars
measured reach V ~ 23. The CMD was cleaned from field contamination by making
use of the three-dimensional colour and magnitude space available in order to
select stars in excess relative to the field. A statistical CMD comparison
method was developed for this purpose. The subtraction method has proven to be
successful, yielding cleaned CMDs consistent with a simple stellar population.
The intermediate age candidates were found to be the oldest in our sample, with
ages between 1-2 Gyrs. The remaining clusters found in the SOAR/SOI have ages
ranging from 100 to 200 Myrs. Our analysis has conclusively shown that none of
the relatively low-mass clusters studied by us belongs to the LMC age-gap.Comment: 9 pages, 8 figures. Accepted to MNRA
Bridge over troubled gas: clusters and associations under the SMC and LMC tidal stresses
We obtained SOAR telescope B and V photometry of 14 star clusters and 2
associations in the Bridge tidal structure connecting the LMC and SMC. These
objects are used to study the formation and evolution of star clusters and
associations under tidal stresses from the Clouds. Typical star clusters in the
Bridge are not richly populated and have in general relatively large diameters
(~30-35 pc), being larger than Galactic counterparts of similar age. Ages and
other fundamental parameters are determined with field-star decontaminated
photometry. A self-consistent approach is used to derive parameters for the
most-populated sample cluster NGC 796 and two young CMD templates built with
the remaining Bridge clusters. We find that the clusters are not coeval in the
Bridge. They range from approximately a few Myr (still related to optical HII
regions and WISE and Spitzer dust emission measurements) to about 100-200 Myr.
The derived distance moduli for the Bridge objects suggests that the Bridge is
a structure connecting the LMC far-side in the East to the foreground of the
SMC to the West. Most of the present clusters are part of the tidal dwarf
candidate D 1, which is associated with an H I overdensity. We find further
evidence that the studied part of the Bridge is evolving into a tidal dwarf
galaxy, decoupling from the Bridge.Comment: 15 pages, 15 figures, MNRAS, Accepted 2015 July 2
Sparse Higher Order ?ech Filtrations
For a finite set of balls of radius r, the k-fold cover is the space covered by at least k balls. Fixing the ball centers and varying the radius, we obtain a nested sequence of spaces that is called the k-fold filtration of the centers. For k = 1, the construction is the union-of-balls filtration that is popular in topological data analysis. For larger k, it yields a cleaner shape reconstruction in the presence of outliers. We contribute a sparsification algorithm to approximate the topology of the k-fold filtration. Our method is a combination and adaptation of several techniques from the well-studied case k = 1, resulting in a sparsification of linear size that can be computed in expected near-linear time with respect to the number of input points
Mass segregation in rich LMC clusters from modelling of deep HST colour-magnitude diagrams
We used the deep colour-magnitude diagrams (CMDs) of five rich LMC clusters (NGC1805, 1818, 1831, 1868, and Hodge14) observed with HST/WFPC2 to derive their present day mass function (PDMF) and its variation with position within the cluster. The PDMF was parameterized as a power law in the available main-sequence mass range of each cluster, typically 0.9 <~ m/M_sun <~ 2.5; its slope was determined at different positions spanning from the very centre out to several core radii. The CMDs in the central regions of the clusters were carefully studied earlier, resulting in accurate age, metallicity, distance modulus, and reddening values. The slope alpha (where Salpeter is 2.35) was determined in annuli by following two distinct methods: 1) a power law fit to the PDMF obtained from the systemic luminosity function (LF); 2) a statistical comparison between observed and model CMDs. In all clusters, significant mass segregation is found from the positional dependence of the PDMF slope: alpha <~ 1.8 for R <= 1.0 R_core and alpha ~ Salpeter inside R=2~3 R_core (except for Hodge 14, where alpha ~ Salpeter for R ~ 4 R_core). The results are robust in the sense that they hold true for both methods used. The CMD method reveals that unresolved binaries flatten the PDMF obtained form the systemic LF, but this effect is smaller than the uncertainties in the alpha determination. For each cluster we estimated dynamical ages inside the core and for the entire system. In both cases we found a trend in the sense that older clusters have flatter PDMF, consistent with a dynamical mass segregation and stellar evaporation
Magic, Religion, and Science: Secularization Trends and Continued Coexistence
While multiple studies have applied cultural evolutionary perspectives to the study of religion, few studies have examined the cultural evolutionary dynamics of a more secretive but equally ubiquitous form of supernatural belief: magic. We conducted two studies, an American nationally representative survey and a comparative phylogenetic analysis of religious traditions, to test three hypothesized cultural evolutionary drivers for beliefs in magic. We find the greatest support for the hypothesis that magic is employed when it provides its users benefits that are distinct from those provided by either science or religion, some support for secularization (broadly conceived) trends applying to magic, and no evidence that innate and unavoidable features of human cognition are primary drivers of the cultural evolution of magical beliefs. We conclude by suggesting specific hypothesized benefits for magic that may account for the evolution of humanity's facultative (i.e., context‐dependent) use of magical beliefs
Self-adjoint symmetry operators connected with the magnetic Heisenberg ring
We consider symmetry operators a from the group ring C[S_N] which act on the
Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We
investigate such symmetry operators a which are self-adjoint (in a sence
defined in the paper) and which yield consequently observables of the
Heisenberg model. We prove the following results: (i) One can construct a
self-adjoint idempotent symmetry operator from every irreducible character of
every subgroup of S_N. This leads to a big manifold of observables. In
particular every commutation symmetry yields such an idempotent. (ii) The set
of all generating idempotents of a minimal right ideal R of C[S_N] contains one
and only one idempotent which ist self-adjoint. (iii) Every self-adjoint
idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k
which are also self-adjoint and pairwise orthogonal. We give a computer
algorithm for the calculation of such decompositions. Furthermore we present 3
additional algorithms which are helpful for the calculation of self-adjoint
operators by means of discrete Fourier transforms of S_N. In our investigations
we use computer calculations by means of our Mathematica packages PERMS and
HRing.Comment: 13 page
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