186,470 research outputs found
Efficient integration of the variational equations of multi-dimensional Hamiltonian systems: Application to the Fermi-Pasta-Ulam lattice
We study the problem of efficient integration of variational equations in
multi-dimensional Hamiltonian systems. For this purpose, we consider a
Runge-Kutta-type integrator, a Taylor series expansion method and the so-called
`Tangent Map' (TM) technique based on symplectic integration schemes, and apply
them to the Fermi-Pasta-Ulam (FPU-) lattice of nonlinearly
coupled oscillators, with ranging from 4 to 20. The fast and accurate
reproduction of well-known behaviors of the Generalized Alignment Index (GALI)
chaos detection technique is used as an indicator for the efficiency of the
tested integration schemes. Implementing the TM technique--which shows the best
performance among the tested algorithms--and exploiting the advantages of the
GALI method, we successfully trace the location of low-dimensional tori.Comment: 14 pages, 6 figure
Phase-Retrieved Tomography enables imaging of a Tumor Spheroid in Mesoscopy Regime
Optical tomographic imaging of biological specimen bases its reliability on
the combination of both accurate experimental measures and advanced
computational techniques. In general, due to high scattering and absorption in
most of the tissues, multi view geometries are required to reduce diffuse halo
and blurring in the reconstructions. Scanning processes are used to acquire the
data but they inevitably introduces perturbation, negating the assumption of
aligned measures. Here we propose an innovative, registration free, imaging
protocol implemented to image a human tumor spheroid at mesoscopic regime. The
technique relies on the calculation of autocorrelation sinogram and object
autocorrelation, finalizing the tomographic reconstruction via a three
dimensional Gerchberg Saxton algorithm that retrieves the missing phase
information. Our method is conceptually simple and focuses on single image
acquisition, regardless of the specimen position in the camera plane. We
demonstrate increased deep resolution abilities, not achievable with the
current approaches, rendering the data alignment process obsolete.Comment: 21 pages, 5 figure
Kernel Manifold Alignment
We introduce a kernel method for manifold alignment (KEMA) and domain
adaptation that can match an arbitrary number of data sources without needing
corresponding pairs, just few labeled examples in all domains. KEMA has
interesting properties: 1) it generalizes other manifold alignment methods, 2)
it can align manifolds of very different complexities, performing a sort of
manifold unfolding plus alignment, 3) it can define a domain-specific metric to
cope with multimodal specificities, 4) it can align data spaces of different
dimensionality, 5) it is robust to strong nonlinear feature deformations, and
6) it is closed-form invertible which allows transfer across-domains and data
synthesis. We also present a reduced-rank version for computational efficiency
and discuss the generalization performance of KEMA under Rademacher principles
of stability. KEMA exhibits very good performance over competing methods in
synthetic examples, visual object recognition and recognition of facial
expressions tasks
Sample positioning in neutron diffraction experiments using a multi-material fiducial marker
An alternative sample positioning method is reported for use in conjunction with sample positioning and experiment planning software systems deployed on some neutron diffraction strain scanners. In this approach, the spherical fiducial markers and location trackers used with optical metrology hardware are replaced with a specifically designed multi-material fiducial marker that requires one diffraction measurement. In a blind setting, the marker position can be determined within an accuracy of ±164 µm with respect to the instrument gauge volume. The scheme is based on a pre-determined relationship that links the diffracted peak intensity to the absolute positioning of the fiducial marker with respect to the instrument gauge volume. Two methods for establishing the linking relationship are presented, respectively based on fitting multi-dimensional quadratic functions and a cross-correlation artificial neural network
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