4,611 research outputs found
Ground state energy of -state Potts model: the minimum modularity
A wide range of interacting systems can be described by complex networks. A
common feature of such networks is that they consist of several communities or
modules, the degree of which may quantified as the \emph{modularity}. However,
even a random uncorrelated network, which has no obvious modular structure, has
a finite modularity due to the quenched disorder. For this reason, the
modularity of a given network is meaningful only when it is compared with that
of a randomized network with the same degree distribution. In this context, it
is important to calculate the modularity of a random uncorrelated network with
an arbitrary degree distribution. The modularity of a random network has been
calculated [Phys. Rev. E \textbf{76}, 015102 (2007)]; however, this was limited
to the case whereby the network was assumed to have only two communities, and
it is evident that the modularity should be calculated in general with communities. Here, we calculate the modularity for communities by
evaluating the ground state energy of the -state Potts Hamiltonian, based on
replica symmetric solutions assuming that the mean degree is large. We found
that the modularity is proportional to regardless of and that only the coefficient depends on . In
particular, when the degree distribution follows a power law, the modularity is
proportional to . Our analytical results are
confirmed by comparison with numerical simulations. Therefore, our results can
be used as reference values for real-world networks.Comment: 14 pages, 4 figure
Cheryl's Birthday
We present four logic puzzles and after that their solutions. Joseph Yeo
designed 'Cheryl's Birthday'. Mike Hartley came up with a novel solution for
'One Hundred Prisoners and a Light Bulb'. Jonathan Welton designed 'A Blind
Guess' and 'Abby's Birthday'. Hans van Ditmarsch and Barteld Kooi authored the
puzzlebook 'One Hundred Prisoners and a Light Bulb' that contains other
knowledge puzzles, and that can also be found on the webpage
http://personal.us.es/hvd/lightbulb.html dedicated to the book.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Unsupervised Fiber Bundles Registration using Weighted Measures Geometric Demons
International audienceBrain image registration aims at reducing anatomical variability across subjects to create a common space for group analysis. Multi-modal approaches intend to minimize cortex shape variations along with internal structures, such as fiber bundles. A di ficulty is that it requires a prior identi fication of these structures, which remains a challenging task in the absence of a complete reference atlas. We propose an extension of the log-Geometric Demons for jointly registering images and fi ber bundles without the need of point or ber correspondences. By representing fi ber bundles as Weighted Measures we can register subjects with di fferent numbers of fiber bundles. The ef ficacy of our algorithm is demonstrated by registering simultaneously T1 images and between 37 and 88 ber bundles depending on each of the ten subject used. We compare results with a multi-modal T1 + Fractional Anisotropy (FA) and a tensor-based registration algorithms and obtain superior performance with our approach
Detection of Gravitational Wave - An Application of Relativistic Quantum Information Theory
We show that a passing gravitational wave may influence the spin entropy and
spin negativity of a system of massive spin-1/2 particles, in a way that is
characteristic of the radiation. We establish the specific conditions under
which this effect may be nonzero. The change in spin entropy and negativity,
however, is extremely small. Here, we propose and show that this effect may be
amplified through entanglement swapping. Relativistic quantum information
theory may have a contribution towards the detection of gravitational wave.Comment: 9 page
Joint T1 and Brain Fiber Log-Demons Registration Using Currents to Model Geometry
International audienceWe present an extension of the diffeomorphic Geometric Demons algorithm which combines the iconic registration with geometric constraints. Our algorithm works in the log-domain space, so that one can efficiently compute the deformation field of the geometry. We represent the shape of objects of interest in the space of currents which is sensitive to both location and geometric structure of objects. Currents provides a distance between geometric structures that can be defined without specifying explicit point-to-point correspondences. We demonstrate this framework by registering simultaneously T1 images and 65 fiber bundles consistently extracted in 12 subjects and compare it against non-linear T1, tensor, and multi-modal T1+ Fractional Anisotropy (FA) registration algorithms. Results show the superiority of the Log-domain Geometric Demons over their purely iconic counterparts
Self-healing efficiency study of thermoset-thermoplastic polymer material
This study is focused on exploring intrinsic self-healing polymer material development, where the inclusion of thermoplastic additives into thermoset polymer material as healing agents. Intrinsic self-healing thermoset-thermoplastic development is involving the material formulation of thermoset liquid resin (Poly Bisphenol A-co-epichlorohydrin) and thermoplastic (polycaprolactone). The material formulation ratio is up to 30% polycaprolactone with respect to thermoset weight. The mixture is heated and stirred to saturate at 80oC before the hardener is added. The mixture is cured and further finishing as Charpy impact test specimen. The specimen is fractured and absorbed impact energy property characterised through the Charpy impact test. The heat treatment is then performed to trigger the self-healing reaction in the polymer. The self-healing efficiency of the thermoset thermoplastic is investigated based on the absorbed impact energy before and after the heat treatment. The 20% or higher thermoplastic concentration in the polymer caused the polymer to possess high self-healing efficiency and faster healing time as compared to the low thermoplastic concentration polymer. However, the high concentration polymer has a disadvantage on the overall structural strength instead. On the contrary, 10% to 15% thermoplastic composition will result in lower and slower self-healing performance but higher initial structural strength
Conditions for the freezing phenomena of geometric measure of quantum discord for arbitrary two-qubit X states under non-dissipative dephasing noises
We study the dynamics of geometric measure of quantum discord (GMQD) under
the influences of two local phase damping noises. Consider the two qubits
initially in arbitrary X-states, we find the necessary and sufficient
conditions for which GMQD is unaffected for a finite period. It is further
shown that such results also hold for the non-Markovian dephasing process.Comment: 4 pages, 2 figure
Reentrant Melting of Soliton Lattice Phase in Bilayer Quantum Hall System
At large parallel magnetic field , the ground state of bilayer
quantum Hall system forms uniform soliton lattice phase. The soliton lattice
will melt due to the proliferation of unbound dislocations at certain finite
temperature leading to the Kosterlitz-Thouless (KT) melting. We calculate the
KT phase boundary by numerically solving the newly developed set of Bethe
ansatz equations, which fully take into account the thermal fluctuations of
soliton walls. We predict that within certain ranges of , the
soliton lattice will melt at . Interestingly enough, as temperature
decreases, it melts at certain temperature lower than exhibiting
the reentrant behaviour of the soliton liquid phase.Comment: 11 pages, 2 figure
Nonparametric nonlinear model predictive control
Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC
- …