Related papers: A short note on Hauser's Kangaroo phenomena and we…

Higher criticism is a method for detecting signals that are both sparse and weak. Although first proposed in cases where the noise variables are independent, higher criticism also has reasonable performance in settings where those variables…

Cold interstellar gas clouds provide an exciting new method to discover dark matter. Their immense size makes them uniquely sensitive to interactions from the heaviest, most rarefied dark matter models. Using gas cloud observations, we…

The existence of several exotic phenomena, such as duality and spectral anholonomy is pointed out in one-dimensional quantum wire with a single defect. The topological structure in the spectral space which is behind these phenomena is…

Many optimal control problems exhibit a peculiar behavior that is not completely understood, the Fuller Phenomenon. In a naive way, this phenomenon can be described as the accumulation of discontinuities in the control function. In this…

An example is given of an interaction that produces an infinite amount of entanglement in an infinitely short time, but only a finite amount in longer times. The interaction arises from a standard Kerr nonlinearity and a 50/50 beamsplitter,…

The dissipative Hofstadter model describes the quantum mechanics of a charged particle in two dimensions subject to a periodic potential, uniform magnetic field, and dissipative force. Its phase diagram exhibits an SL(2,Z) duality symmetry…

This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these…

Many random phenomena, including life-testing and environmental data, show positive values and excess zeros, which pose modeling challenges. In life testing, immediate failures result in zero lifetimes, often due to defects or poor quality,…

We study the problem of testing whether the missing values of a potentially high-dimensional dataset are Missing Completely at Random (MCAR). We relax the problem of testing MCAR to the problem of testing the compatibility of a collection…

We consider the fourth-order differential theory of gravitation to treat the problem of singularity avoidance: studying the short-distance behaviour in the case of black-holes and the big-bang we are going to see a way to attack the issue…

We introduce a class of self-interacting scalar theories in which the various coupling contants obey a recursive relation. These imply a particularly simple form for the generating function of the Feynman amplitudes with vanishing external…

We provide a mini-guide to some of the possible manifestations of weak scale supersymmetry. For each of six scenarios we provide a brief description of the theoretical underpinnings, the adjustable parameters, a qualitative description of…

This note presents an analytic construction of the optimal unit-norm direction hat(x) = x/|x| that maximizes or minimizes the objective linear expression, B . hat(x), subject to a system of linear constraints of the form [A] . x = 0, where…

We study the limiting behavior of $r$-maximum distance minimizers and the asymptotics of their $1$-dimensional Hausdorff measures as $r$ tends to zero in several contexts, including situations involving objects of fractal nature.

If there is new physics associated with the top quark, it could show up as anomalous couplings of the top quark to weak gauge bosons, such as $Z\ttbar$ and $W\tbbar$ vector and axial-vector couplings. We use the processes $\ttbar\to…

The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…

We discuss whether the future extrapolation of the present cosmological state may lead to a singularity even in case of "conventional" (negative) pressure of the dark energy field, namely $w=p/\rho \geq -1$. The discussion is based on an…

Using weakly nonlinear conditional PDF for the density field around an overdense region we find that the expected density contrast around a peak is always smaller while its rms fluctuation larger than in the linear case. We apply these…

For two particles in a disordered chain of length $L$ with on-site interaction $U$, a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the…

We develop a theory describing neutral atoms scattering at low energies in an optical lattice. We show that for a repulsive interaction, as the microscopic scattering length increases, the effective scattering amplitude approaches a…