24,526 research outputs found
Complex spherical codes with three inner products
Let be a finite set in a complex sphere of dimension. Let be
the set of usual inner products of two distinct vectors in . A set is
called a complex spherical -code if the cardinality of is and
contains an imaginary number. We would like to classify the largest
possible -codes for given dimension . In this paper, we consider the
problem for the case . Roy and Suda (2014) gave a certain upper bound for
the cardinalities of -codes. A -code is said to be tight if
attains the bound. We show that there exists no tight -code except for
dimensions , . Moreover we make an algorithm to classify the largest
-codes by considering representations of oriented graphs. By this algorithm,
the largest -codes are classified for dimensions , , with a
current computer.Comment: 26 pages, no figur
Generic rigidity with forced symmetry and sparse colored graphs
We review some recent results in the generic rigidity theory of planar
frameworks with forced symmetry, giving a uniform treatment to the topic. We
also give new combinatorial characterizations of minimally rigid periodic
frameworks with fixed-area fundamental domain and fixed-angle fundamental
domain.Comment: 21 pages, 2 figure
Ghetto of Venice: Access to the Target Node and the Random Target Access Time
Random walks defined on undirected graphs assign the absolute scores to all
nodes based on the quality of path they provide for random walkers. In city
space syntax, the notion of segregation acquires a statistical interpretation
with respect to random walks. We analyze the spatial network of Venetian canals
and detect its most segregated part which can be identified with canals
adjacent to the Ghetto of Venice.Comment: 14 pages, 3 figure
Three dimensional loop quantum gravity: coupling to point particles
We consider the coupling between three dimensional gravity with zero
cosmological constant and massive spinning point particles. First, we study the
classical canonical analysis of the coupled system. Then, we go to the
Hamiltonian quantization generalizing loop quantum gravity techniques. We give
a complete description of the kinematical Hilbert space of the coupled system.
Finally, we define the physical Hilbert space of the system of self-gravitating
massive spinning point particles using Rovelli's generalized projection
operator which can be represented as a sum over spin foam amplitudes. In
addition we provide an explicit expression of the (physical) distance operator
between two particles which is defined as a Dirac observable.Comment: Typos corrected and references adde
Transport Networks Revisited: Why Dual Graphs?
Deterministic equilibrium flows in transport networks can be investigated by
means of Markov's processes defined on the dual graph representations of the
network. Sustained movement patterns are generated by a subset of automorphisms
of the graph spanning the spatial network of a city naturally interpreted as
random walks. Random walks assign absolute scores to all nodes of a graph and
embed space syntax into Euclidean space.Comment: 12 page
On Quantum Field Theory with Nonzero Minimal Uncertainties in Positions and Momenta
We continue studies on quantum field theories on noncommutative geometric
spaces, focusing on classes of noncommutative geometries which imply
ultraviolet and infrared modifications in the form of nonzero minimal
uncertainties in positions and momenta. The case of the ultraviolet modified
uncertainty relation which has appeared from string theory and quantum gravity
is covered. The example of euclidean -theory is studied in detail and
in this example we can now show ultraviolet and infrared regularisation of all
graphs.Comment: LaTex, 32 page
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