Exact steady-state velocity of ratchets driven by random sequential adsorption

We solve the problem of discrete translocation of a polymer through a pore, driven by the irreversible, random sequential adsorption of particles on one side of the pore. Although the kinetics of the wall motion and the deposition are coupled, we find the exact steady-state distribution for the gap between the wall and the nearest deposited particle. This result enables us to construct the mean translocation velocity demonstrating that translocation is faster when the adsorbing particles are smaller. Monte-Carlo simulations also show that smaller particles gives less dispersion in the ratcheted motion. We also define and compare the relative efficiencies of ratcheting by deposition of particles with different sizes and we describe an associated "zone-refinement" process.Comment: 11 pages, 4 figures New asymptotic result for low chaperone density added. Exact translocation velocity is proportional to (chaperone density)^(1/3

A Cosmological No-Hair Theorem

A generalisation of Price's theorem is given for application to Inflationary Cosmologies. Namely, we show that on a Schwarzschild--de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.Comment: 9 pages, NCL94 -TP4, (Revtex

Boundary definition of a multiverse measure

We propose to regulate the infinities of eternal inflation by relating a late time cut-off in the bulk to a short distance cut-off on the future boundary. The light-cone time of an event is defined in terms of the volume of its future light-cone on the boundary. We seek an intrinsic definition of boundary volumes that makes no reference to bulk structures. This requires taming the fractal geometry of the future boundary, and lifting the ambiguity of the conformal factor. We propose to work in the conformal frame in which the boundary Ricci scalar is constant. We explore this proposal in the FRW approximation for bubble universes. Remarkably, we find that the future boundary becomes a round three-sphere, with smooth metric on all scales. Our cut-off yields the same relative probabilities as a previous proposal that defined boundary volumes by projection into the bulk along timelike geodesics. Moreover, it is equivalent to an ensemble of causal patches defined without reference to bulk geodesics. It thus yields a holographically motivated and phenomenologically successful measure for eternal inflation.Comment: 39 pages, 4 figures; v2: minor correction

Asynchronous Training of Word Embeddings for Large Text Corpora

Word embeddings are a powerful approach for analyzing language and have been widely popular in numerous tasks in information retrieval and text mining. Training embeddings over huge corpora is computationally expensive because the input is typically sequentially processed and parameters are synchronously updated. Distributed architectures for asynchronous training that have been proposed either focus on scaling vocabulary sizes and dimensionality or suffer from expensive synchronization latencies. In this paper, we propose a scalable approach to train word embeddings by partitioning the input space instead in order to scale to massive text corpora while not sacrificing the performance of the embeddings. Our training procedure does not involve any parameter synchronization except a final sub-model merge phase that typically executes in a few minutes. Our distributed training scales seamlessly to large corpus sizes and we get comparable and sometimes even up to 45% performance improvement in a variety of NLP benchmarks using models trained by our distributed procedure which requires $1/10$ of the time taken by the baseline approach. Finally we also show that we are robust to missing words in sub-models and are able to effectively reconstruct word representations.Comment: This paper contains 9 pages and has been accepted in the WSDM201

Kasner and Mixmaster behavior in universes with equation of state w \ge 1

We consider cosmological models with a scalar field with equation of state $w\ge 1$ that contract towards a big crunch singularity, as in recent cyclic and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to anisotropy and curvature are suppressed, and the contraction is described by a homogeneous and isotropic Friedmann equation if $w>1$. We generalize the results to theories where the scalar field couples to p-forms and show that there exists a finite value of $w$, depending on the p-forms, such that chaotic oscillations are suppressed. We show that $Z_2$ orbifold compactification also contributes to suppressing chaotic behavior. In particular, chaos is avoided in contracting heterotic M-theory models if $w>1$ at the crunch.Comment: 25 pages, 2 figures, minor changes, references adde

A uniqueness theorem for the adS soliton

The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the AdS soliton, a globally static, asymptotically toroidal $\Lambda<0$ spacetime with negative mass. Nonetheless, arguing from the AdS/CFT correspondence, Horowitz and Myers (hep-th/9808079) proposed a new positive energy conjecture, which asserts that the AdS soliton is the unique state of least energy in its asymptotic class. We give a new structure theorem for static $\Lambda<0$ spacetimes and use it to prove uniqueness of the AdS soliton. Our results offer significant support for the new positive energy conjecture and add to the body of rigorous results inspired by the AdS/CFT correspondence.Comment: Revtex, 4 pages; Matches published version. More detail in Abstract and one equation corrected. For details of proofs and further results, see hep-th/020408

A Cosmological Constant Limits the Size of Black Holes

In a space-time with cosmological constant $\Lambda>0$ and matter satisfying the dominant energy condition, the area of a black or white hole cannot exceed $4\pi/\Lambda$. This applies to event horizons where defined, i.e. in an asymptotically deSitter space-time, and to outer trapping horizons (cf. apparent horizons) in any space-time. The bound is attained if and only if the horizon is identical to that of the degenerate `Schwarzschild-deSitter' solution. This yields a topological restriction on the event horizon, namely that components whose total area exceeds $4\pi/\Lambda$ cannot merge. We discuss the conjectured isoperimetric inequality and implications for the cosmic censorship conjecture.Comment: 10 page

One-dimensional fermions with incommensuration

We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from pi, and delta, the strength of the incommensuration, are small. For free fermions, we use a continuum Dirac theory to show that there are an infinite number of bands which meet at zero energy as q approaches zero. In the limit that the ratio q/ \delta --> 0, the number of states lying inside the q=0 gap is nonzero and equal to 2 \delta /\pi^2. Thus the limit q --> 0 differs from q=0; this can be seen clearly in the behavior of the specific heat at low temperature. For interacting fermions or the XXZ spin-1/2 chain close to dimerization, we use bosonization to argue that similar results hold; as q --> 0, we find a nontrivial density of states near zero energy. However, the limit q --> 0 and q=0 give the same results near commensurate wave numbers which are different from pi. We apply our results to the Azbel-Hofstadter problem of electrons hopping on a two-dimensional lattice in the presence of a magnetic field. Finally, we discuss the complete energy spectrum of noninteracting fermions with incommensurate hopping by going up to higher orders in delta.Comment: Revtex, 23 pages including 7 epsf figures; this is a greatly expanded version of cond-mat/981133