Approximate Sparse Recovery: Optimizing Time and Measurements

An approximate sparse recovery system consists of parameters $k,N$, an $m$-by-$N$ measurement matrix, $\Phi$, and a decoding algorithm, $\mathcal{D}$. Given a vector, $x$, the system approximates $x$ by $\widehat x =\mathcal{D}(\Phi x)$, which must satisfy $\| \widehat x - x\|_2\le C \|x - x_k\|_2$, where $x_k$ denotes the optimal $k$-term approximation to $x$. For each vector $x$, the system must succeed with probability at least 3/4. Among the goals in designing such systems are minimizing the number $m$ of measurements and the runtime of the decoding algorithm, $\mathcal{D}$. In this paper, we give a system with $m=O(k \log(N/k))$ measurements--matching a lower bound, up to a constant factor--and decoding time $O(k\log^c N)$, matching a lower bound up to $\log(N)$ factors. We also consider the encode time (i.e., the time to multiply $\Phi$ by $x$), the time to update measurements (i.e., the time to multiply $\Phi$ by a 1-sparse $x$), and the robustness and stability of the algorithm (adding noise before and after the measurements). Our encode and update times are optimal up to $\log(N)$ factors

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that that when each agent's signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate common-knowledge. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.Common learning, common belief, private signals, private beliefs

Common Learning

Consider two agents who learn the value of an unknown parameter by observing a sequence of private signals. The signals are independent and identically distributed across time but not necessarily across agents. We show that that when each agent's signal space is finite, the agents will commonly learn its value, i.e., that the true value of the parameter will become approximate common-knowledge. In contrast, if the agents' observations come from a countably infinite signal space, then this contraction mapping property fails. We show by example that common learning can fail in this case.Common learning, Common belief, Private signals, Private beliefs

Using UAV acquired photography and structure from motion techniques for studying glacier landforms: application to the glacial flutes at Isfallsglaciären

Glacier and ice sheet retreat exposes freshly deglaciated terrain which often contains small-scale fragile geomorphological features which could provide insight into subglacial or submarginal processes. Subaerial exposure results in potentially rapid landscape modification or even disappearance of the minor-relief landforms as wind, weather, water and vegetation impact on the newly exposed surface. Ongoing retreat of many ice masses means there is a growing opportunity to obtain high resolution geospatial data from glacier forelands to aid in the understanding of recent subglacial and submarginal processes. Here we used an unmanned aerial vehicle to capture close-range aerial photography of the foreland of Isfallsglaciären, a small polythermal glacier situated in Swedish Lapland. An orthophoto and a digital elevation model with ~2 cm horizontal resolution were created from this photography using structure from motion software. These geospatial data was used to create a geomorphological map of the foreland, documenting moraines, fans, channels and flutes. The unprecedented resolution of the data enabled us to derive morphological metrics (length, width and relief) of the smallest flutes, which is not possible with other data products normally used for glacial landform metrics mapping. The map and flute metrics compare well with previous studies, highlighting the potential of this technique for rapidly documenting glacier foreland geomorphology at an unprecedented scale and resolution. The vast majority of flutes were found to have an associated stoss-side boulder, with the remainder having a likely explanation for boulder absence (burial or erosion). Furthermore, the size of this boulder was found to strongly correlate with the width and relief of the lee-side flute. This is consistent with the lee-side cavity infill model of flute formation. Whether this model is applicable to all flutes, or multiple mechanisms are required, awaits further study

Masculinity at work: The experiences of men in female dominated occupations

This paper presents the findings of a research project on the implications of men's non-traditional career choices for their experiences within the organization and for gender identity. The research is based on 40 in-depth interviews with male workers from four occupational groups: librarian-ship, cabin crew, nurses and primary school teachers. Results suggest a typology of male workers in female dominated occupations: seekers (who actively seek the career), finders (who find the occupation in the process of making general career decisions) and settlers (who settle into the career after periods of time in mainly male dominated occupations). Men benefit from their minority status through assumptions of enhanced leadership (the assumed authority effect), by being given differential treatment (the special consideration effect) and being associated with a more careerist attitude to work (the career effect). At the same time, they feel comfortable working with women (the zone of comfort effect). Despite this comfort, men adopt a variety of strategies to re-establish a masculinity that has been undermined by the 'feminine' nature of their work. These include re-labeling, status enhancement and distancing from the feminine. The dynamics of maintaining and reproducing masculinities within the non-traditional work setting are discussed in the light of recent theorising around gender, masculinity and work