Necessary and sufficient conditions of solution uniqueness in ℓ1\ell_1 minimization

This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leq\sigma$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining I=\supp(x^*) and s=\sign(x^*_I), $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.Comment: 6 pages; revised version; submitte

The Off-Shell Electromagnetic T-matrix: momentum-dependent scattering from spherical inclusions with both dielectric and magnetic contrast

The momentum- and frequency-dependent T-matrix operator for the scattering of electromagnetic waves by a dielectric/conducting and para- or diamagnetic sphere is derived as a Mie-type series, and presented in a compact form emphasizing various symmetry properties, notably the unitarity identity. This result extends to magnetic properties one previously obtained for purely dielectric contrasts by other authors. Several situations useful to spatially-dispersive effective-medium approximations to one-body order are examined. Partial summation of the Mie series is achieved in the case of elastic scattering.Comment: 22 pages. Preprint of a paper to appear in `Waves in Complex And Random Media' ((c) Taylor and Francis, 2011

Relevant Deformations in Open String Field Theory: a Simple Solution for Lumps

We propose a remarkably simple solution of cubic open string field theory which describes inhomogeneous tachyon condensation. The solution is in one-to-one correspondence with the IR fixed point of the RG-flow generated in the two--dimensional world-sheet theory by integrating a relevant operator with mild enough OPE on the boundary. It is shown how the closed string overlap correctly captures the shift in the closed string one point function between the UV and the IR limits of the flow. Examples of lumps in non-compact and compact transverse directions are given.Comment: 45 pages. v2: typos and minor improvements. v3: submitted to jhe

Researching with Twitter timeline data: A demonstration via “everyday” socio-political talk around welfare provision

Increasingly, social media platforms are understood by researchers to be valuable sites of politically-relevant discussions. However, analyses of social media data are typically undertaken by focusing on ‘snapshots’ of issues using query-keyword search strategies. This paper develops an alternative, less issue-based, mode of analysing Twitter data. It provides a framework for working qualitatively with longitudinally-oriented Twitter data (user-timelines), and uses an empirical case to consider the value and the challenges of doing so. Exploring how Twitter users place “everyday” talk around the socio-political issue of UK welfare provision, we draw on digital ethnography and narrative analysis techniques to analyse 25 user-timelines and identify three distinctions in users’ practices: users’ engagements with welfare as TV entertainment or as a socio-political concern; the degree of sustained engagement with said issues, and; the degree to which users’ tweeting practices around welfare were congruent with or in contrast to their other tweets. With this analytic orientation, we demonstrate how a longitudinal analysis of user-timelines provides rich resources that facilitate a more nuanced understanding of user engagement in everyday socio-political discussions online

Conservation laws and tachyon potentials in the sliver frame

Conservation laws have provided an elegant and efficient tool to evaluate the open string field theory interaction vertex, they have been originally implemented in the case where the string field is expanded in the Virasoro basis. In this work we derive conservation laws in the case where the string field is expanded in the so-called sliver $\mathcal{L}_0$-basis. As an application of these conservation laws derived in the sliver frame, we compute the open string field action relevant to the tachyon condensation and in order to present not only an illustration but also an additional information, we evaluate the action without imposing a gauge choice.Comment: 26 pages, some typos fixed, comments added, references adde

Exploring hypotheses of the actions of TGF-beta 1 in epidermal wound healing using a 3D computational multiscale model of the human epidermis

In vivo and in vitro studies give a paradoxical picture of the actions of the key regulatory factor TGF-beta 1 in epidermal wound healing with it stimulating migration of keratinocytes but also inhibiting their proliferation. To try to reconcile these into an easily visualized 3D model of wound healing amenable for experimentation by cell biologists, a multiscale model of the formation of a 3D skin epithelium was established with TGF-beta 1 literature-derived rule sets and equations embedded within it. At the cellular level, an agent-based bottom-up model that focuses on individual interacting units ( keratinocytes) was used. This was based on literature-derived rules governing keratinocyte behavior and keratinocyte/ECM interactions. The selection of these rule sets is described in detail in this paper. The agent-based model was then linked with a subcellular model of TGF-beta 1 production and its action on keratinocytes simulated with a complex pathway simulator. This multiscale model can be run at a cellular level only or at a combined cellular/subcellular level. It was then initially challenged ( by wounding) to investigate the behavior of keratinocytes in wound healing at the cellular level. To investigate the possible actions of TGF-beta 1, several hypotheses were then explored by deliberately manipulating some of these rule sets at subcellular levels. This exercise readily eliminated some hypotheses and identified a sequence of spatial-temporal actions of TGF-beta 1 for normal successful wound healing in an easy-to-follow 3D model. We suggest this multiscale model offers a valuable, easy-to-visualize aid to our understanding of the actions of this key regulator in wound healing, and provides a model that can now be used to explore pathologies of wound healing

High energy emission from microquasars

The microquasar phenomenon is associated with the production of jets by X-ray binaries and, as such, may be associated with the majority of such systems. In this chapter we briefly outline the associations, definite, probable, possible, and speculative, between such jets and X-ray, gamma-ray and particle emission.Comment: Contributing chapter to the book Cosmic Gamma-Ray Sources, K.S. Cheng and G.E. Romero (eds.), to be published by Kluwer Academic Publishers, Dordrecht, 2004. (19 pages

Magnetic vortex oscillator driven by dc spin-polarized current

Transfer of angular momentum from a spin-polarized current to a ferromagnet provides an efficient means to control the dynamics of nanomagnets. A peculiar consequence of this spin-torque, the ability to induce persistent oscillations of a nanomagnet by applying a dc current, has previously been reported only for spatially uniform nanomagnets. Here we demonstrate that a quintessentially nonuniform magnetic structure, a magnetic vortex, isolated within a nanoscale spin valve structure, can be excited into persistent microwave-frequency oscillations by a spin-polarized dc current. Comparison to micromagnetic simulations leads to identification of the oscillations with a precession of the vortex core. The oscillations, which can be obtained in essentially zero magnetic field, exhibit linewidths that can be narrower than 300 kHz, making these highly compact spin-torque vortex oscillator devices potential candidates for microwave signal-processing applications, and a powerful new tool for fundamental studies of vortex dynamics in magnetic nanostructures.Comment: 14 pages, 4 figure

Genomic structure and alternative splicing of murine R2B receptor protein tyrosine phosphatases (PTPκ, μ, ρ and PCP-2)

BACKGROUND: Four genes designated as PTPRK (PTPκ), PTPRL/U (PCP-2), PTPRM (PTPμ) and PTPRT (PTPρ) code for a subfamily (type R2B) of receptor protein tyrosine phosphatases (RPTPs) uniquely characterized by the presence of an N-terminal MAM domain. These transmembrane molecules have been implicated in homophilic cell adhesion. In the human, the PTPRK gene is located on chromosome 6, PTPRL/U on 1, PTPRM on 18 and PTPRT on 20. In the mouse, the four genes ptprk, ptprl, ptprm and ptprt are located in syntenic regions of chromosomes 10, 4, 17 and 2, respectively. RESULTS: The genomic organization of murine R2B RPTP genes is described. The four genes varied greatly in size ranging from ~64 kb to ~1 Mb, primarily due to proportional differences in intron lengths. Although there were also minor variations in exon length, the number of exons and the phases of exon/intron junctions were highly conserved. In situ hybridization with digoxigenin-labeled cRNA probes was used to localize each of the four R2B transcripts to specific cell types within the murine central nervous system. Phylogenetic analysis of complete sequences indicated that PTPρ and PTPμ were most closely related, followed by PTPκ. The most distant family member was PCP-2. Alignment of RPTP polypeptide sequences predicted putative alternatively spliced exons. PCR experiments revealed that five of these exons were alternatively spliced, and that each of the four phosphatases incorporated them differently. The greatest variability in genomic organization and the majority of alternatively spliced exons were observed in the juxtamembrane domain, a region critical for the regulation of signal transduction. CONCLUSIONS: Comparison of the four R2B RPTP genes revealed virtually identical principles of genomic organization, despite great disparities in gene size due to variations in intron length. Although subtle differences in exon length were also observed, it is likely that functional differences among these genes arise from the specific combinations of exons generated by alternative splicing

Borrelia recurrentis employs a novel multifunctional surface protein with anti-complement, anti-opsonic and invasive potential to escape innate immunity

Borrelia recurrentis, the etiologic agent of louse-borne relapsing fever in humans, has evolved strategies, including antigenic variation, to evade immune defence, thereby causing severe diseases with high mortality rates. Here we identify for the first time a multifunctional surface lipoprotein of B. recurrentis, termed HcpA, and demonstrate that it binds human complement regulators, Factor H, CFHR-1, and simultaneously, the host protease plasminogen. Cell surface bound factor H was found to retain its activity and to confer resistance to complement attack. Moreover, ectopic expression of HcpA in a B. burgdorferi B313 strain, deficient in Factor H binding proteins, protected the transformed spirochetes from complement-mediated killing. Furthermore, HcpA-bound plasminogen/plasmin endows B. recurrentis with the potential to resist opsonization and to degrade extracellular matrix components. Together, the present study underscores the high virulence potential of B. recurrentis. The elucidation of the molecular basis underlying the versatile strategies of B. recurrentis to escape innate immunity and to persist in human tissues, including the brain, may help to understand the pathological processes underlying louse-borne relapsing fever