3,025 research outputs found
Semipurity of tempered Deligne cohomology
In this paper we define the formal and tempered Deligne cohomology groups,
that are obtained by applying the Deligne complex functor to the complexes of
formal differential forms and tempered currents respectively. We then prove the
existence of a duality between them, a vanishing theorem for the former and a
semipurity property for the latter. The motivation of these results comes from
the study of covariant arithmetic Chow groups. The semi-purity property of
tempered Deligne cohomology implies, in particular, that several definitions of
covariant arithmetic Chow groups agree for projective arithmetic varieties
Strategy updating rules and strategy distributions in dynamical multiagent systems
In the evolutionary version of the minority game, agents update their
strategies (gene-value ) in order to improve their performance. Motivated by
recent intriguing results obtained for prize-to-fine ratios which are smaller
than unity, we explore the system's dynamics with a strategy updating rule of
the form (). We find that the strategy
distribution depends strongly on the values of the prize-to-fine ratio , the
length scale , and the type of boundary condition used. We show that
these parameters determine the amplitude and frequency of the the temporal
oscillations observed in the gene space. These regular oscillations are shown
to be the main factor which determines the strategy distribution of the
population. In addition, we find that agents characterized by
(a coin-tossing strategy) have the best chances of survival at asymptotically
long times, regardless of the value of and the boundary conditions
used.Comment: 4 pages, 7 figure
Thermal treatment of the minority game
We study a cost function for the aggregate behavior of all the agents
involved in the Minority Game (MG) or the Bar Attendance Model (BAM). The cost
function allows to define a deterministic, synchronous dynamics that yields
results that have the main relevant features than those of the probabilistic,
sequential dynamics used for the MG or the BAM. We define a temperature through
a Langevin approach in terms of the fluctuations of the average attendance. We
prove that the cost function is an extensive quantity that can play the role of
an internal energy of the many agent system while the temperature so defined is
an intensive parameter. We compare the results of the thermal perturbation to
the deterministic dynamics and prove that they agree with those obtained with
the MG or BAM in the limit of very low temperature.Comment: 9 pages in PRE format, 6 figure
SOLUTION OF 1D AND 2D POISSON'S EQUATION BY USING WAVELET SCALING FUNCTIONS
The use of multiresolution techniques and wavelets has become increasingly popular in the development of numerical schemes for the solution of partial differential equations (PDEs). Therefore, the use of wavelet scaling functions as a basis in computational analysis holds some promise due to their compact support, orthogonality and localization properties. Daubechies and Deslauriers-Dubuc functions have been successfully used as basis functions in several schemes like the Wavelet- Galerkin Method (WGM) and the Wavelet Finite Element Method (WFEM). Another possible advantage of their use is the fact that the calculation of integrals of inner products of wavelet scaling functions and their derivatives can be made by solving a linear system of equations, thus avoiding the problem of using approximations by some numerical method. These inner products were defined as connection coefficients and they are employed in the calculation of stiffness matrices and load vectors. In this work, some mathematical foundations regarding wavelet scaling functions, their derivatives and connection coefficients are reviewed. A scheme based on the Galerkin Method is proposed for the direct solution of Poisson's equation (potential problems) in a meshless formulation using interpolating wavelet scaling functions (Interpolets). The applicability of the proposed method and some convergence issues are illustrated by means of a few examples
Synthesis of Positron Emission Tomography (PET) Images via Multi-channel Generative Adversarial Networks (GANs)
Positron emission tomography (PET) image synthesis plays an important role,
which can be used to boost the training data for computer aided diagnosis
systems. However, existing image synthesis methods have problems in
synthesizing the low resolution PET images. To address these limitations, we
propose multi-channel generative adversarial networks (M-GAN) based PET image
synthesis method. Different to the existing methods which rely on using
low-level features, the proposed M-GAN is capable to represent the features in
a high-level of semantic based on the adversarial learning concept. In
addition, M-GAN enables to take the input from the annotation (label) to
synthesize the high uptake regions e.g., tumors and from the computed
tomography (CT) images to constrain the appearance consistency and output the
synthetic PET images directly. Our results on 50 lung cancer PET-CT studies
indicate that our method was much closer to the real PET images when compared
with the existing methods.Comment: 9 pages, 2 figure
Spin transfer torques due to the bulk states of topological insulators
Spin torques at topological insulator (TI)/ferromagnet interfaces have
received considerable attention in recent years with a view towards achieving
full electrical manipulation of magnetic degrees of freedom. The most important
question in this field concerns the relative contributions of bulk and surface
states to the spin torque, a matter that remains incompletely understood.
Whereas the surface state contribution has been extensively studied, the
contribution due to the bulk states has received comparatively little
attention. Here we study spin torques due to TI bulk states and show that: (i)
There is no spin-orbit torque due to the bulk states on a homogeneous
magnetisation, in contrast to the surface states, which give rise to a
spin-orbit torque via the well-known Edelstein effect. (ii) The bulk states
give rise to a spin transfer torque (STT) due to the inhomogeneity of the
magnetisation in the vicinity of the interface. This spin transfer torque,
which has not been considered in TIs in the past, is somewhat unconventional
since it arises from the interplay of the bulk TI spin-orbit coupling and the
gradient of the monotonically decaying magnetisation inside the TI. Whereas we
consider an idealised model in which the magnetisation gradient is small and
the spin transfer torque is correspondingly small, we argue that in real
samples the spin transfer torque should be sizable and may provide the dominant
contribution due to the bulk states. We show that an experimental smoking gun
for identifying the bulk states is the fact that the field-like component of
the spin transfer torque generates a spin density with the same size but
opposite sign for in-plane and out-of-plane magnetisations. This distinguishes
them from the surface states, which are expected to give a spin density of a
similar size and the same sign for both an in-plane and out-of-plane
magnetisations
New Superhard Phases for 3D C60-based Fullerites
We have explored new possible phases of 3D C60-based fullerites using
semiempirical potentials and ab-initio density functional methods. We have
found three closely related structures - two body centered orthorhombic and one
body centered cubic - having 52, 56 and 60 tetracoordinated atoms per molecule.
These 3D polymers result in semiconductors with bulk moduli near 300 GPa, and
shear moduli around 240 GPa, which make them good candidates for new low
density superhard materials.Comment: To be published in Physical Review Letter
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