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A cross-correlation technique of lensing tomography is presented to measure the evolution of dark energy in the universe. The variation of the weak lensing shear with redshift around massive foreground objects like bright galaxies and…
Type Ia supernovae have provided fundamental observational data in the discovery of the late acceleration of the expansion of the Universe in cosmology. However, this analysis has relied on the assumption of a Gaussian distribution for the…
As weak lensing surveys become deeper, they reveal more non-Gaussian aspects of the convergence field which can only be extracted using statistics beyond the power spectrum. In Cheng et al. (2020) we showed that the scattering transform, a…
Let $n$ be an integer with $3 \leq n \leq 7$, and let $g$ be a Riemannian metric on $B^2 \times T^{n-2}$ with scalar curvature at least $-n(n-1)$. We establish an inequality relating the systole of the boundary to the infimum of the mean…
A generalized Langevin equation is suggested to describe a system with memory($u(t,t') = \frac{1}{\Gamma (\nu )}(t - t')^\nu $) as well as with positive and negative damping. The equation can be transformed into the Fokker-Planck equation…
A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary…
In quintessence models, the dark energy content of the universe is described by a slowly rolling scalar field whose pressure and energy density obey an equation of state of the form p=w $\rho$; w is in general a function of time such that…
Free-space propagation can be described as a shearing of the Wigner distribution function in the spatial coordinate; this shearing is linear in paraxial approximation but assumes a more complex shape for wide-angle propagation. Integration…
If dark matter has strong self-interactions, future astrophysical and cosmological observations, together with a clearer understanding of baryonic feedback effects, might be used to extract the velocity dependence of the dark matter…
We present a comprehensive full-sky 3-dimensional analysis of the weak-lensing fields and their corresponding power spectra. Using the formalism of spin-weight spherical harmonics and spherical Bessel functions, we relate the two-point…
In this paper we introduce an optical approximation into the theory of impedance calculation, one valid in the limit of high frequencies. This approximation neglects diffraction effects in the radiation process, and is conceptually…
We derive the joint distribution of the moments $\mathrm{Tr}\, Q^{\kappa}$ ($\kappa\geq0$) of the Wigner-Smith matrix for a chaotic cavity supporting a large number of scattering channels $n$. This distribution turns out to be…
Large-scale structure distorts the images of background galaxies, which allows one to measure directly the projected distribution of dark matter in the universe and determine its power spectrum. Here we address the question of how to…
Accurately calculating time delays between signals is pivotal in many modern physics applications. One approach to estimating these delays is computing the cross-spectrum in the time-frequency domain. Linear time-frequency representations,…
We explore various pitfalls and challenges in determining the equation-of-state (w) of dark energy component that dominates the universe and causes the current accelerated expansion. We demonstrated in an earlier paper the existence of a…
This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the…
Ergodic optimization and discrete weak KAM theory are two parallel theories with several results in common. For instance, the Mather set is the locus of orbits which minimize the ergodic averages of a given observable. In the favorable…
Based on the canonical formalism, the dilatation symmetry is implemented to the Fokker-Planck equation for the Wigner distribution function that describes atomic motion in an optical lattice. This reveals the symmetry principle underlying…
The dark-matter candidates of particle physics invariably possess electromagnetic interactions, if only via quantum fluctuations. Taken en masse, dark matter can thus engender an index of refraction which deviates from its vacuum value. Its…
Since microscopic velocity diffusion can be incorporated into general relativity in a consistent way, we study cosmological background solutions when the diffusion phenomena takes place in an expanding universe. Our focus here relies on the…