1,308 research outputs found
Manipulating the transmission matrix of scattering media for nonlinear imaging beyond the memory effect
The measurement of the Transmission Matrix (TM) of a scattering medium is of
great interest for imaging. It can be acquired directly by interferometry using
an internal reference wavefront. Unfortunately, internal reference fields are
scattered by the medium which results in a speckle that makes the TM
measurement heterogeneous across the output field of view. We demonstrate how
to correct for this effect using the intrinsic properties of the TM. For thin
scattering media, we exploit the memory effect of the medium and the reference
speckle to create a corrected TM. For highly scattering media where the memory
effect is negligible, we use complementary reference speckles to compose a new
TM, not compromised by the speckled reference anymore. Using this correction,
we demonstrate large field of view second harmonic generation imaging through
thick biological media
Interpolation of characteristic classes of singular hypersurfaces
We show that the Chern-Schwartz-MacPherson class of a hypersurface X in a
nonsingular variety M `interpolates' between two other notions of
characteristic classes for singular varieties, provided that the singular locus
of X is smooth and that certain numerical invariants of X are constant along
this locus. This allows us to define a lift of the Chern-Schwartz-MacPherson
class of such `nice' hypersurfaces to intersection homology. As another
application, the interpolation result leads to an explicit formula for the
Chern-Schwartz-MacPherson class of X in terms of its polar classes.Comment: 10 page
Sizing the length of complex networks
Among all characteristics exhibited by natural and man-made networks the
small-world phenomenon is surely the most relevant and popular. But despite its
significance, a reliable and comparable quantification of the question `how
small is a small-world network and how does it compare to others' has remained
a difficult challenge to answer. Here we establish a new synoptic
representation that allows for a complete and accurate interpretation of the
pathlength (and efficiency) of complex networks. We frame every network
individually, based on how its length deviates from the shortest and the
longest values it could possibly take. For that, we first had to uncover the
upper and the lower limits for the pathlength and efficiency, which indeed
depend on the specific number of nodes and links. These limits are given by
families of singular configurations that we name as ultra-short and ultra-long
networks. The representation here introduced frees network comparison from the
need to rely on the choice of reference graph models (e.g., random graphs and
ring lattices), a common practice that is prone to yield biased interpretations
as we show. Application to empirical examples of three categories (neural,
social and transportation) evidences that, while most real networks display a
pathlength comparable to that of random graphs, when contrasted against the
absolute boundaries, only the cortical connectomes prove to be ultra-short
An elementary proof of Euler formula using Cauchy's method
The use of Cauchy's method to prove Euler's well-known formula is an object
of many controversies. The purpose of this paper is to prove that Cauchy's
method applies for convex polyhedra and not only for them, but also for
surfaces such as the torus, the projective plane, the Klein bottle and the
pinched torus
Enhanced nonlinear imaging through scattering media using transmission matrix based wavefront shaping
Despite the tremendous progresses in wavefront control through or inside
complex scattering media, several limitations prevent reaching practical
feasibility for nonlinear imaging in biological tissues. While the optimization
of nonlinear signals might suffer from low signal to noise conditions and from
possible artifacts at large penetration depths, it has nevertheless been
largely used in the multiple scattering regime since it provides a guide star
mechanism as well as an intrinsic compensation for spatiotemporal distortions.
Here, we demonstrate the benefit of Transmission Matrix (TM) based approaches
under broadband illumination conditions, to perform nonlinear imaging. Using
ultrashort pulse illumination with spectral bandwidth comparable but still
lower than the spectral width of the scattering medium, we show strong
nonlinear enhancements of several orders of magnitude, through thicknesses of a
few transport mean free paths, which corresponds to millimeters in biological
tissues. Linear TM refocusing is moreover compatible with fast scanning
nonlinear imaging and potentially with acoustic based methods, which paves the
way for nonlinear microscopy deep inside scattering media
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