Testing read-once formula satisfaction

We study the query complexity of testing for properties defined by read once formulas, as instances of {\em massively parametrized properties}, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in $\epsilon$, doubly exponential in the arity, and independent of all other parameters. When the gates are limited to being monotone, we prove that there is an {\em estimation} algorithm, that outputs an approximation of the distance of the input from satisfying the property. For formulas only involving And/Or gates, we provide a more efficient test whose query complexity is only quasipolynomial in $\epsilon$. On the other hand, we show that such testability results do not hold in general for formulas over non-Boolean alphabets; specifically we construct a property defined by a read-once arity $2$ (non-Boolean) formula over an alphabet of size $4$, such that any $1/4$-test for it requires a number of queries depending on the formula size. We also present such a formula over an alphabet of size $5$ that additionally satisfies a strong monotonicity condition

Supertwistors as Quarks of SU(2,2|4)

The GS superstring on AdS_5 x S^5 has a nonlinearly realized, spontaneously broken SU(2,2|4) symmetry. Here we introduce a two-dimensional model in which the unbroken SU(2,2|4) symmetry is linearly realized. The basic variables are supertwistors, which transform in the fundamental representation of this supergroup. The quantization of this supertwistor model leads to the complete oscillator construction of the unitary irreducible representations of the centrally extended SU(2,2|4). They include the states of d=4 SYM theory, massless and KK states of AdS_5 supergravity, and the descendants on AdS_5 of the standard massive string states, which form intermediate and long supermultiplets. We present examples of such multiplets and discuss possible states of solitonic and (p,q) strings.Comment: 12 pages, LaTeX, 1 EPS figur

Balancing speed and accuracy of polyclonal T cell activation: a role for extracellular feedback

Background: Extracellular feedback is an abundant module of intercellular communication networks, yet a detailed understanding of its role is still lacking. Here, we study interactions between polyclonal activated T cells that are mediated by IL-2 extracellular feedback as a model system. Results: Using mathematical modeling we show that extracellular feedback can give rise to opposite outcomes: competition or cooperation between interacting T cells, depending on their relative levels of activation. Furthermore, the outcome of the interaction also depends on the relative timing of activation of the cells. A critical time window exists after which a cell that has been more strongly activated nevertheless cannot exclude an inferior competitor. Conclusions: In a number of experimental studies of polyclonal T-cell systems, outcomes ranging from cooperation to competition as well as time dependent competition were observed. Our model suggests that extracellular feedback can contribute to these observed behaviors as it translates quantitative differences in T cells’ activation strength and in their relative activation time into qualitatively different outcomes. We propose extracellular feedback as a general mechanism that can balance speed and accuracy – choosing the most suitable responders out of a polyclonal population under the clock of an escalating threat

Self-assembly of collagen bundles and enhanced piezoelectricity induced by chemical crosslinking.

The piezoelectricity of collagen is purported to be linked to many biological processes including bone formation and wound healing. Although the piezoelectricity of tissue-derived collagen has been documented across the length scales, little work has been undertaken to characterise the local electromechanical properties of processed collagen, which is used as a base for tissue-engineering implants. In this work, three chemically distinct treatments used to form structurally and mechanically stable scaffolds-EDC-NHS, genipin and tissue transglutaminase-are investigated for their effect on collagen piezolectricity. Crosslinking with EDC-NHS is noted to produce a distinct self-assembly of the fibres into bundles roughly 300 nm in width regardless of the collagen origin. These fibre bundles also show a localised piezoelectric response, with enhanced vertical piezoelectricity of collagen. Such topographical features are not observed with the other two chemical treatments, although the shear piezoelectric response is significantly enhanced upon crosslinking. These observations are reconciled by a proposed effect of the crosslinking mechanisms on the molecular and nanostructure of collagen. These results highlight the ability to modify the electromechanical properties of collagen using chemical crosslinking methods.ERC, Bill and Melinda Gates Foundation, Geistlich Pharma A

Why Matrix theory works for oddly shaped membranes

We give a simple proof of why there is a Matrix theory approximation for a membrane shaped like an arbitrary Riemann surface. As corollaries, we show that noncompact membranes cannot be approximated by matrices and that the Poisson algebra on any compact phase space is U(infinity). The matrix approximation does not appear to work properly in theories such as IIB string theory or bosonic membrane theory where there is no conserved 3-form charge to which the membranes couple.Comment: 8 pages, 4 figures, revtex; references adde

Chew-Bites, Jaw Movement Allocation and Bite Rate in Grazing Cattle as Identified by Acoustic Monitoring

Bite rate derives from the time budget of the biting and chewing processes of intake, which are both performed by jaw movements. A new type of jaw movement was revealed by acoustic monitoring in cattle - the chew-bite -which chews herbage already in the mouth and harvests fresh herbage with the same jaw movement (Laca et al., 1992). Chew-biting should enable the animal to reduce the total number of jaw movements performed per bite without reducing the number of chews per bite. We examined the variation among individuals in the allocation of jaw movements between the three types, and its relation to bite rate

The Importance of Patch Size in Estimating Steady-State Bite Rate in Grazing Cattle

Since the pioneering work of Black and Kenney (1984), various intake studies have been conducted at the spatial scale of a single feeding station ( patch ) to elucidate the processes that determine instantaneous intake rate (e.g. Laca et al., 1994). While these are well-suited for patch depletion studies, it is less clear how well they represent non-patchy and relatively homogeneous environments (Ungar & Griffiths, 2002). Clearly, grazing should be restricted to the upper grazing horizon (i.e. layer of bites), but sample duration may be insufficient to characterize steady-state behaviour, especially when grazing commences on an empty mouth. We examined the impact of feeding station size on bite rate and jaw movement allocation between bites and chews

GRB 051221A and Tests of Lorentz Symmetry

Various approaches to quantum gravity suggest the possibility of violation of Lorentz symmetry at very high energies. In these cases we expect a modification at low energies of the dispersion relation of photons that contains extra powers of the momentum suppressed by a high energy scale. These terms break boost invariance and can be tested even at relatively low energies. We use the light curves of the very bright short Gamma-Ray Burst GRB 051221A and compare the arrival times of photons at different energies with the expected time delay due to a modified dispersion relation. As no time delay was observed, we set a lower bound of 0.0066 E_{pl} \sim 0.66 10^{17} GeV on the scale of Lorentz invariance violation.Comment: 9 pages, 2 figure

Development of a 2-Dimensional Video-Acoustic Tool for Monitoring Bite Placement

Studies of grazing behaviour conducted at the spatial scale of a feeding station demonstrate that intake rate declines with increasing depletion, a response attributed to an increase in bite overlap (Ginnett et al., 1999; Ungar et al., 2001). In order to understand the rules that govern bite placement, a methodology is required that can map the sequential placement of bites on the sward surface. We developed a video-acoustic tool to achieve this and report the findings of using the tool on small uniform patches of herbage