1,464 research outputs found
LR characterization of chirotopes of finite planar families of pairwise disjoint convex bodies
We extend the classical LR characterization of chirotopes of finite planar
families of points to chirotopes of finite planar families of pairwise disjoint
convex bodies: a map \c{hi} on the set of 3-subsets of a finite set I is a
chirotope of finite planar families of pairwise disjoint convex bodies if and
only if for every 3-, 4-, and 5-subset J of I the restriction of \c{hi} to the
set of 3-subsets of J is a chirotope of finite planar families of pairwise
disjoint convex bodies. Our main tool is the polarity map, i.e., the map that
assigns to a convex body the set of lines missing its interior, from which we
derive the key notion of arrangements of double pseudolines, introduced for the
first time in this paper.Comment: 100 pages, 73 figures; accepted manuscript versio
On The Phase Structure and Thermodynamic Geometry of R-Charged Black Holes
We study the phase structure and equilibrium state space geometry of
R-charged black holes in , 4 and 7 and the corresponding rotating ,
and branes. For various charge configurations of the compact black
holes in the canonical ensemble we demonstrate new liquid-gas like phase
coexistence behaviour culminating in second order critical points. The critical
exponents turn out to be the same as that of four dimensional asymptotically
AdS black holes in Einstein Maxwell theory. We further establish that the
regions of stability for R-charged black holes are, in some cases, more
constrained than is currently believed, due to properties of some of the
response coefficients. The equilibrium state space scalar curvature is
calculated for various charge configurations, both for the case of compact as
well as flat horizons and its asymptotic behaviour with temperature is
established.Comment: 1 + 33 pages, LaTeX, 25 figures. References adde
On the Thermodynamic Geometry and Critical Phenomena of AdS Black Holes
In this paper, we study various aspects of the equilibrium thermodynamic
state space geometry of AdS black holes. We first examine the
Reissner-Nordstrom-AdS (RN-AdS) and the Kerr-AdS black holes. In this context,
the state space scalar curvature of these black holes is analysed in various
regions of their thermodynamic parameter space. This provides important new
insights into the structure and significance of the scalar curvature. We
further investigate critical phenomena, and the behaviour of the scalar
curvature near criticality, for KN-AdS black holes in two mixed ensembles,
introduced and elucidated in our earlier work arXiv:1002.2538 [hep-th]. The
critical exponents are identical to those in the RN-AdS and Kerr-AdS cases in
the canonical ensemble. This suggests an universality in the scaling behaviour
near critical points of AdS black holes. Our results further highlight
qualitative differences in the thermodynamic state space geometry for electric
charge and angular momentum fluctuations of these.Comment: 1 + 37 Pages, LaTeX, includes 31 figures. A figure and a
clarification added
The International-Trade Network: Gravity Equations and Topological Properties
This paper begins to explore the determinants of the topological properties
of the international - trade network (ITN). We fit bilateral-trade flows using
a standard gravity equation to build a "residual" ITN where trade-link weights
are depurated from geographical distance, size, border effects, trade
agreements, and so on. We then compare the topological properties of the
original and residual ITNs. We find that the residual ITN displays, unlike the
original one, marked signatures of a complex system, and is characterized by a
very different topological architecture. Whereas the original ITN is
geographically clustered and organized around a few large-sized hubs, the
residual ITN displays many small-sized but trade-oriented countries that,
independently of their geographical position, either play the role of local
hubs or attract large and rich countries in relatively complex
trade-interaction patterns
Regular Incidence Complexes, Polytopes, and C-Groups
Regular incidence complexes are combinatorial incidence structures
generalizing regular convex polytopes, regular complex polytopes, various types
of incidence geometries, and many other highly symmetric objects. The special
case of abstract regular polytopes has been well-studied. The paper describes
the combinatorial structure of a regular incidence complex in terms of a system
of distinguished generating subgroups of its automorphism group or a
flag-transitive subgroup. Then the groups admitting a flag-transitive action on
an incidence complex are characterized as generalized string C-groups. Further,
extensions of regular incidence complexes are studied, and certain incidence
complexes particularly close to abstract polytopes, called abstract polytope
complexes, are investigated.Comment: 24 pages; to appear in "Discrete Geometry and Symmetry", M. Conder,
A. Deza, and A. Ivic Weiss (eds), Springe
How citation boosts promote scientific paradigm shifts and Nobel Prizes
Nobel Prizes are commonly seen to be among the most prestigious achievements
of our times. Based on mining several million citations, we quantitatively
analyze the processes driving paradigm shifts in science. We find that
groundbreaking discoveries of Nobel Prize Laureates and other famous scientists
are not only acknowledged by many citations of their landmark papers.
Surprisingly, they also boost the citation rates of their previous
publications. Given that innovations must outcompete the rich-gets-richer
effect for scientific citations, it turns out that they can make their way only
through citation cascades. A quantitative analysis reveals how and why they
happen. Science appears to behave like a self-organized critical system, in
which citation cascades of all sizes occur, from continuous scientific progress
all the way up to scientific revolutions, which change the way we see our
world. Measuring the "boosting effect" of landmark papers, our analysis reveals
how new ideas and new players can make their way and finally triumph in a world
dominated by established paradigms. The underlying "boost factor" is also
useful to discover scientific breakthroughs and talents much earlier than
through classical citation analysis, which by now has become a widespread
method to measure scientific excellence, influencing scientific careers and the
distribution of research funds. Our findings reveal patterns of collective
social behavior, which are also interesting from an attention economics
perspective. Understanding the origin of scientific authority may therefore
ultimately help to explain, how social influence comes about and why the value
of goods depends so strongly on the attention they attract.Comment: 6 pages, 6 figure
Size Dependence of Metal-Insulator Transition in Stoichiometric Fe3O4 Nanocrystals
Magnetite (Fe3O4) is one of the most actively studied materials with a famous
metal-insulator transition (MIT), so-called the Verwey transition at around 123
K. Despite the recent progress in synthesis and characterization of Fe3O4
nanocrystals (NCs), it is still an open question how the Verwey transition
changes on a nanometer scale. We herein report the systematic studies on size
dependence of the Verwey transition of stoichiometric Fe3O4 NCs. We have
successfully synthesized stoichiometric and uniform-sized Fe3O4 NCs with sizes
ranging from 5 to 100 nm. These stoichiometric Fe3O4 NCs show the Verwey
transition when they are characterized by conductance, magnetization, cryo-XRD,
and heat capacity measurements. The Verwey transition is weakly size-dependent
and becomes suppressed in NCs smaller than 20 nm before disappearing completely
for less than 6 nm, which is a clear, yet highly interesting indication of a
size effect of this well-known phenomena. Our current work will shed new light
on this ages-old problem of Verwey transition.Comment: 18 pages, 4 figures, Nano Letters (accepted
Some Experiments on the influence of Problem Hardness in Morphological Development based Learning of Neural Controllers
Natural beings undergo a morphological development process of their bodies
while they are learning and adapting to the environments they face from infancy
to adulthood. In fact, this is the period where the most important learning
pro-cesses, those that will support learning as adults, will take place.
However, in artificial systems, this interaction between morphological
development and learning, and its possible advantages, have seldom been
considered. In this line, this paper seeks to provide some insights into how
morphological development can be harnessed in order to facilitate learning in
em-bodied systems facing tasks or domains that are hard to learn. In
particular, here we will concentrate on whether morphological development can
really provide any advantage when learning complex tasks and whether its
relevance towards learning in-creases as tasks become harder. To this end, we
present the results of some initial experiments on the application of
morpho-logical development to learning to walk in three cases, that of a
quadruped, a hexapod and that of an octopod. These results seem to confirm that
as task learning difficulty increases the application of morphological
development to learning becomes more advantageous.Comment: 10 pages, 4 figure
Climate Change and invasibility of the Antarctic benthos
Benthic communities living in shallow-shelf habitats in Antarctica (<100-m depth) are archaic in their structure and function. Modern predators, including fast-moving, durophagous (skeleton-crushing) bony fish, sharks, and crabs, are rare or absent; slow-moving invertebrates are the top predators; and epifaunal suspension feeders dominate many soft substratum communities. Cooling temperatures beginning in the late Eocene excluded durophagous predators, ultimately resulting in the endemic living fauna and its unique food-web structure. Although the Southern Ocean is oceanographically isolated, the barriers to biological invasion are primarily physiological rather than geographic. Cold temperatures impose limits to performance that exclude modern predators. Global warming is now removing those physiological barriers, and crabs are reinvading Antarctica. As sea temperatures continue to rise, the invasion of durophagous predators will modernize the shelf benthos and erode the indigenous character of marine life in Antarctica
Aortic bypass and orthotopic right renal autotransplantation for midaortic syndrome: a case report
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