Graphene as a Novel Single Photon Counting Optical and IR Photodetector

Bilayer graphene has many unique optoelectronic properties , including a tuneable band gap, that make it possible to develop new and more efficient optical and nanoelectronic devices. We have developed a Monte Carlo simulation for a single photon counting photodetector incorporating bilayer graphene. Our results show that, conceptually it would be feasible to manufacture a single photon counting photodetector (with colour sensitivity) from bilayer graphene for use across both optical and infrared wavelengths. Our concept exploits the high carrier mobility and tuneable band gap associated with a bilayer graphene approach. This allows for low noise operation over a range of cryogenic temperatures, thereby reducing the cost of cryogens with a trade off between resolution and operating temperature. The results from this theoretical study now enable us to progress onto the manufacture of prototype photon counters at optical and IR wavelengths that may have the potential to be groundbreaking in some scientific research applications.Comment: Conference Proceeding in Graphene-Based Technologies, 201

Finding the Minimum-Weight k-Path

Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k M). If the weights are reals in $[1,M]$, we provide a $(1+\varepsilon)$-approximation which has a running time of \tilde{O}(2^k \poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem of $k$-tree, in which we wish to find a minimum-weight copy of a $k$-node tree $T$ in a given weighted graph $G$, under the same restrictions on edge weights respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k) M n^3) and a $(1+\varepsilon)$-approximate solution of running time \tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201

Fast Witness Extraction Using a Decision Oracle

The gist of many (NP-)hard combinatorial problems is to decide whether a universe of $n$ elements contains a witness consisting of $k$ elements that match some prescribed pattern. For some of these problems there are known advanced algebra-based FPT algorithms which solve the decision problem but do not return the witness. We investigate techniques for turning such a YES/NO-decision oracle into an algorithm for extracting a single witness, with an objective to obtain practical scalability for large values of $n$. By relying on techniques from combinatorial group testing, we demonstrate that a witness may be extracted with $O(k\log n)$ queries to either a deterministic or a randomized set inclusion oracle with one-sided probability of error. Furthermore, we demonstrate through implementation and experiments that the algebra-based FPT algorithms are practical, in particular in the setting of the $k$-path problem. Also discussed are engineering issues such as optimizing finite field arithmetic.Comment: Journal version, 16 pages. Extended abstract presented at ESA'1

Eliciting Risk and Time Preferences Using Field Experiments: Some Methodological Issues

We design experiments to jointly elicit risk and time preferences for the adult Danish population. The experimental procedures build on laboratory experiments that have been evaluated using traditional subject pools. The field experiments utilize field sampling designs that we developed, and procedures that were chosen to be relatively transparent in the field with non-standard subject pools. Our overall design was also intended to be a general template for such field experiments in other countries. We examine the characterization of risk over a wider domain for each subject than previous experiments, allowing more precise estimates of risk attitudes. We also examine individual discount rates over six time horizons, as the first stage in a panel experiment in which we revisit subjects to test consistency and stability of responses over time. Risk and time preferences are heterogeneous, varying by observable individual characteristics. On a methodological level, we implement a refinement of existing procedures which elicits much more precise estimates, and also mitigates framing effects.