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Weak gravitational lensing provides a unique method to directly measure the distribution of mass in the universe. Because the distortions induced by lensing in the shape of background galaxies are small, the measurement of weak lensing…
We develop a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our approach is an adaptation of Burnett's formulation of the "shortwave approximation",…
In this paper, we develop a new gravitational lensing inversion technique. While traditional approaches assume that the lensing field varies little across a galaxy image, we note that this variation in the field can give rise to a…
Training a sparse neural network from scratch requires optimizing connections at the same time as the weights themselves. Typically, the weights are redistributed after a predefined number of weight updates, removing a fraction of the…
Weak gravitational lensing surveys are rapidly becoming important tools to probe directly the mass density fluctuations in the universe and its background dynamics. Earlier studies have shown that it is possible to model the statistics of…
We present a novel method for image anomaly detection, where algorithms that use samples drawn from some distribution of "normal" data, aim to detect out-of-distribution (abnormal) samples. Our approach includes a combination of encoder and…
The relationship between the metric and nonrelativistic matter distribution depends on the theory of gravity and additional fields, providing a possible way of distinguishing competing theories. With the assumption that the geometry and…
We present a new method for recovering the cosmological density, velocity, and potential fields from all-sky redshift catalogues. The method is based on an expansion of the fields in orthogonal radial (Bessel) and angular (spherical…
Visual anomaly detection is common in several applications including medical screening and production quality check. Although a definition of the anomaly is an unknown trend in data, in many cases some hints or samples of the anomaly class…
Modeling the mass distribution of galaxy-scale strong gravitational lenses is a task of increasing difficulty. The high-resolution and depth of imaging data now available render simple analytical forms ineffective at capturing lens…
We present an analytic method for rapidly forecasting the accuracy of gravitational potential reconstruction possible from measurement of radial peculiar velocities of every galaxy cluster with M > M_th in solid angle \theta^2 and over…
Weak gravitational lensing is the slight distortion of galaxy shapes caused primarily by the gravitational effects of dark matter in the universe. In our work, we seek to invert the weak lensing signal from 2D telescope images to…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
We discuss how to model the surface of celestial bodies (such as stars) in quantum gravity to ensure the regularity of quantum corrections to classical solutions of general relativity at the surface of such bodies. Specifically, we use the…
A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the…
We describe a new method for analyzing gravitational lens images, for the case where the source light distribution is pixelized. The method is suitable for high resolution, high S/N data of a multiply-imaged extended source. For a given…
A possibility of geophysical measurements using the large scale laser interferometrical gravitational wave antenna is discussed. An interferometer with suspended mirrors can be used as a gradiometer measuring variations of an angle between…
Whilst the underlying assumption of the Friedman-Lema\^itre-Robertson-Walker (FLRW) cosmological model is that matter is homogeneously distributed throughout the universe, gravitational influences over the life of the universe have resulted…
The problem of reconstructing non-harmonic internal gravity wave packets generated by a source moving in a stratified ocean is considered. The uniform asymptotic form of the internal gravity waves field generated by a source moving above…
When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are…