Making sense out of massive data by going beyond differential expression

With the rapid growth of publicly available high-throughput transcriptomic data, there is increasing recognition that large sets of such data can be mined to better understand disease states and mechanisms. Prior gene expression analyses, both large and small, have been dichotomous in nature, in which phenotypes are compared using clearly defined controls. Such approaches may require arbitrary decisions about what are considered “normal” phenotypes, and what each phenotype should be compared to. Instead, we adopt a holistic approach in which we characterize phenotypes in the context of a myriad of tissues and diseases. We introduce scalable methods that associate expression patterns to phenotypes in order both to assign phenotype labels to new expression samples and to select phenotypically meaningful gene signatures. By using a nonparametric statistical approach, we identify signatures that are more precise than those from existing approaches and accurately reveal biological processes that are hidden in case vs. control studies. Employing a comprehensive perspective on expression, we show how metastasized tumor samples localize in the vicinity of the primary site counterparts and are overenriched for those phenotype labels. We find that our approach provides insights into the biological processes that underlie differences between tissues and diseases beyond those identified by traditional differential expression analyses. Finally, we provide an online resource (http://concordia.csail.mit.edu) for mapping users’ gene expression samples onto the expression landscape of tissue and disease

Counting dark matter particles in LHC events

We suggest trying to count the number of invisible particles produced in missing energy events at the LHC, arguing that multiple production of such particles provides evidence that they constitute stable Dark Matter and that counting them could yield further insights into the nature of Dark Matter. We propose a method to count invisible particles, based on fitting the shapes of certain transverse- or invariant-mass distributions, discuss various effects that may affect the measurement, and simulate the use of the method to count neutrinos in Standard Model processes and Dark Matter candidates in new physics processes.Comment: 18 pages, 13 figures, revtex4 forma

Cosmological perturbations of brane-induced gravity and the vDVZ discontinuity on FLRW space-times

We investigate the cosmological perturbations of the brane-induced (Dvali-Gabadadze-Porrati) model which exhibits a van Dam-Veltman-Zakharov (vDVZ) discontinuity when linearized over a Minkowski background. We show that the linear brane scalar cosmological perturbations over an arbitrary Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time have a well defined limit when the radius of transition between 4D and 5D gravity is sent to infinity with respect to the background Hubble radius. This radius of transition plays for the brane-induced gravity model a role equivalent to the Compton wavelength of the graviton in a Pauli-Fierz theory, as far as the vDVZ discontinuity is concerned. This well defined limit is shown to obey the linearized 4D Einstein's equations whenever the Hubble factor is non vanishing. This shows the disappearance of the vDVZ discontinuity for general FLRW background, and extends the previously know result for maximally-symmetric space-times of non vanishing curvature. Our reasoning is valid for matter with simple equation of state such as a scalar field, or a perfect fluid with adiabatic perturbations, and involves to distinguish between space-times with a vanishing scalar curvature and space-times with a non vanishing one. We also discuss the validity of the linear perturbation theory, in particular for those FLRW space-times where the Ricci scalar is vanishing only on a set of zero measure. In those cases, we argue that the linear perturbation theory breaks down when the Ricci scalar vanishes (and the radius of transition is sent to infinity), in a way similar to what has been found to occur around sources on a Minkowski background.Comment: 36 pages, v.2, typos correcte

Massless Flows I: the sine-Gordon and O(n) models

The massless flow between successive minimal models of conformal field theory is related to a flow within the sine-Gordon model when the coefficient of the cosine potential is imaginary. This flow is studied, partly numerically, from three different points of view. First we work out the expansion close to the Kosterlitz-Thouless point, and obtain roaming behavior, with the central charge going up and down in between the UV and IR values of $c=1$. Next we analytically continue the Casimir energy of the massive flow (i.e. with real cosine term). Finally we consider the lattice regularization provided by the O(n) model in which massive and massless flows correspond to high- and low-temperature phases. A detailed discussion of the case $n=0$ is then given using the underlying N=2 supersymmetry, which is spontaneously broken in the low-temperature phase. The ``index'' \tr F(-1)^F follows from the Painleve III differential equation, and is shown to have simple poles in this phase. These poles are interpreted as occuring from level crossing (one-dimensional phase transitions for polymers). As an application, new exact results for the connectivity constants of polymer graphs on cylinders are obtained.Comment: 39 pages, 7 uuencoded figures, BUHEP-93-5, USC-93/003, LPM-93-0

Measuring stochastic gravitational-wave energy beyond general relativity

Gravity theories beyond general relativity (GR) can change the properties of gravitational waves: their polarizations, dispersion, speed, and, importantly, energy content are all heavily theory- dependent. All these corrections can potentially be probed by measuring the stochastic gravitational- wave background. However, most existing treatments of this background beyond GR overlook modifications to the energy carried by gravitational waves, or rely on GR assumptions that are invalid in other theories. This may lead to mistranslation between the observable cross-correlation of detector outputs and gravitational-wave energy density, and thus to errors when deriving observational constraints on theories. In this article, we lay out a generic formalism for stochastic gravitational- wave searches, applicable to a large family of theories beyond GR. We explicitly state the (often tacit) assumptions that go into these searches, evaluating their generic applicability, or lack thereof. Examples of problematic assumptions are: statistical independence of linear polarization amplitudes; which polarizations satisfy equipartition; and which polarizations have well-defined phase velocities. We also show how to correctly infer the value of the stochastic energy density in the context of any given theory. We demonstrate with specific theories in which some of the traditional assumptions break down: Chern-Simons gravity, scalar-tensor theory, and Fierz-Pauli massive gravity. In each theory, we show how to properly include the beyond-GR corrections, and how to interpret observational results.Comment: 18 pages (plus appendices), 1 figur