We construct a new harmonic family: dielectric flow solutions with maximal supersymmetry in eleven-dimensional supergravity. These solutions are asymptotically AdS4 ×S7, while in the infra-red the M2 branes are dielectrically polarized into M5 branes. These solutions are holographically dual to vacua of the mass deformed theory on M2 branes. They also provide an interesting insight on the super...

As mentioned before, the success of CASE relies on two noteworthy properties: the Sure Screening (SS) property and the Separable After Screening (SAS) property. In this section, we discuss the two properties in detail, and illustrate how these properties enable us to decompose the original regression problem to many small-size regression problems which can be fit separately. We then use these p...

I describe a modification to Shanks’ baby-step giant-step algorithm for computing the order n of an element g of a group G, assuming n is finite. My method has the advantage of being able to compute n quickly, which Shanks’ method fails to do when the order of G is infinite, unknown, or much larger than n. I describe the algorithm in detail. I also present the results of implementations of my a...

For each type of classical Lie algebra, we list the dominant highest weights ζ for which (ζ;μi) is not a primitive pair and the weight space Vμi has dimension one where μi are the highest long and short roots in each case. These dimension one weight spaces lead to examples of nilmanifolds for which we cannot prove or disprove the density of closed geodesics.

In this paper we study the asymptotic behaviour under dilations of probability measures supported on smooth curves in nilmanifolds. We prove, under some mild conditions, effective equidistribution of such measures to the Haar measure. We also formulate a mean ergodic theorem for Rn-representations on Hilbert spaces, restricted to a moving phase of low dimension. Furthermore, we bound the necess...

The relative Lefschetz and Nielsen fixed-point theorems are generalized for compact absorbing contractions on ANR-spaces and nilmanifolds. The nontrivial Lefschetz number implies the existence of a fixedpoint in the closure of the complementary domain. The relative Nielsen numbers improve the lower estimate of the number of coincidences on the total space or indicate the location of fixed-point...