Instabilities and the roton spectrum of a quasi-1D Bose-Einstein condensed gas with dipole-dipole interactions

We point out the possibility of having a roton-type excitation spectrum in a quasi-1D Bose-Einstein condensate with dipole-dipole interactions. Normally such a system is quite unstable due to the attractive portion of the dipolar interaction. However, by reversing the sign of the dipolar interaction using either a rotating magnetic field or a laser with circular polarization, a stable cigar-shaped configuration can be achieved whose spectrum contains a `roton' minimum analogous to that found in helium II. Dipolar gases also offer the exciting prospect to tune the depth of this `roton' minimum by directly controlling the interparticle interaction strength. When the minimum touches the zero-energy axis the system is once again unstable, possibly to the formation of a density wave.Comment: 7 pages, 6 figures. Special Issue: "Ultracold Polar Molecules: Formation and Collisions

Introduction to orbital flight planning (1)

This workbook is designed for students interested in space flight planning, who after training, may serve as flight planning aides. Routine flight planning activities requiring engineering-type calculations and analysis are covered. Practice exercises and brief instructions are given for the programming and use of the hand calculator as well as the calculation of position and velocity in the orbital plane. Calculation of relative orbital position is also covered with emphasis upon celestial coordinates and time measurement

Counting edge-injective homomorphisms and matchings on restricted graph classes

We consider the $\#\mathsf{W}[1]$-hard problem of counting all matchings with exactly $k$ edges in a given input graph $G$; we prove that it remains $\#\mathsf{W}[1]$-hard on graphs $G$ that are line graphs or bipartite graphs with degree $2$ on one side. In our proofs, we use that $k$-matchings in line graphs can be equivalently viewed as edge-injective homomorphisms from the disjoint union of $k$ length-$2$ paths into (arbitrary) host graphs. Here, a homomorphism from $H$ to $G$ is edge-injective if it maps any two distinct edges of $H$ to distinct edges in $G$. We show that edge-injective homomorphisms from a pattern graph $H$ can be counted in polynomial time if $H$ has bounded vertex-cover number after removing isolated edges. For hereditary classes $\mathcal{H}$ of pattern graphs, we complement this result: If the graphs in $\mathcal{H}$ have unbounded vertex-cover number even after deleting isolated edges, then counting edge-injective homomorphisms with patterns from $\mathcal{H}$ is $\#\mathsf{W}[1]$-hard. Our proofs rely on an edge-colored variant of Holant problems and a delicate interpolation argument; both may be of independent interest.Comment: 35 pages, 9 figure

A structural approach to kernels for ILPs: Treewidth and Total Unimodularity

Kernelization is a theoretical formalization of efficient preprocessing for NP-hard problems. Empirically, preprocessing is highly successful in practice, for example in state-of-the-art ILP-solvers like CPLEX. Motivated by this, previous work studied the existence of kernelizations for ILP related problems, e.g., for testing feasibility of Ax <= b. In contrast to the observed success of CPLEX, however, the results were largely negative. Intuitively, practical instances have far more useful structure than the worst-case instances used to prove these lower bounds. In the present paper, we study the effect that subsystems with (Gaifman graph of) bounded treewidth or totally unimodularity have on the kernelizability of the ILP feasibility problem. We show that, on the positive side, if these subsystems have a small number of variables on which they interact with the remaining instance, then we can efficiently replace them by smaller subsystems of size polynomial in the domain without changing feasibility. Thus, if large parts of an instance consist of such subsystems, then this yields a substantial size reduction. We complement this by proving that relaxations to the considered structures, e.g., larger boundaries of the subsystems, allow worst-case lower bounds against kernelization. Thus, these relaxed structures can be used to build instance families that cannot be efficiently reduced, by any approach.Comment: Extended abstract in the Proceedings of the 23rd European Symposium on Algorithms (ESA 2015

Mechanical characteristics of filter structures for MEMS adaptive infrared detectors

This paper reports the mechanical design and optimization of tunable Fabry-Perot (FP) filter structures for the development of MEMS adaptive infrared detectors using finite element modeling and experimental investigations. The results indicate that the mechanical characteristics of the FP filters are significantly influenced by the structural designs, which eventually affect the filter performance and device integrity

Finding detours is fixed-parameter tractable

We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s,t)-path in G that is at least k longer than a shortest (s,t)-path. Using insights into structural graph theory, we prove that Longest Detour is fixed-parameter tractable (FPT) on undirected graphs and actually even admits a single-exponential algorithm, that is, one of running time exp(O(k)) poly(n). This matches (up to the base of the exponential) the best algorithms for finding a path of length at least k. Furthermore, we study the related problem Exact Detour that asks whether a graph G contains an (s,t)-path that is exactly k longer than a shortest (s,t)-path. For this problem, we obtain a randomized algorithm with running time about 2.746^k, and a deterministic algorithm with running time about 6.745^k, showing that this problem is FPT as well. Our algorithms for Exact Detour apply to both undirected and directed graphs.Comment: Extended abstract appears at ICALP 201

Strongly Constrained Discrete Hashing

Learning to hash is a fundamental technique widely used in large-scale image retrieval. Most existing methods for learning to hash address the involved discrete optimization problem by the continuous relaxation of the binary constraint, which usually leads to large quantization errors and consequently suboptimal binary codes. A few discrete hashing methods have emerged recently. However, they either completely ignore some useful constraints (specifically the balance and decorrelation of hash bits) or just turn those constraints into regularizers that would make the optimization easier but less accurate. In this paper, we propose a novel supervised hashing method named Strongly Constrained Discrete Hashing (SCDH) which overcomes such limitations. It can learn the binary codes for all examples in the training set, and meanwhile obtain a hash function for unseen samples with the above-mentioned constraints preserved. Although the model of SCDH is fairly sophisticated, we are able to find closed-form solutions to all of its optimization subproblems and thus design an efficient algorithm that converges quickly. In addition, we extend SCDH to a kernelized version SCDH_K. Our experiments on three large benchmark datasets have demonstrated that not only can SCDH and SCDH_K achieve substantially higher MAP scores than state-of-the-art baselines, but they run much faster than those that are also supervised

Cooling effects of urban vegetation: The role of golf courses

Increased heat in urban environments, from the combined effects of climate change and land use/land cover change, is one of the most severe problems confronting cities and urban residents worldwide, and requires urgent resolution. While large urban green spaces such as parks and nature reserves are widely recognized for their benefits in mitigating urban heat islands (UHIs), the benefit of urban golf courses is less established. This is the first study to combine remote sensing of golf courses with Morphological Spatial Pattern Analysis (MSPA) of vegetation cover. Using ArborCamTM multispectral, high-resolution airborne imagery (0.3 × 0.3 m), this study develops an approach that assesses the role of golf courses in reducing urban land surface temperature (LST) relative to other urban land-uses in Perth, Australia, and identifies factors that influence cooling. The study revealed that urban golf courses had the second lowest LST (around 31 °C) after conservation land (30 °C), compared to industrial, residential, and main road land uses, which ranged from 35 to 37 °C. They thus have a strong capacity for summer urban heat mitigation. Within the golf courses, distance to water bodies and vegetation structure are important factors contributing to cooling effects. Green spaces comprising tall trees (>10 m) and large vegetation patches have strong effects in reducing LST. This suggests that increasing the proportion of large trees, and increasing vegetation connectivity within golf courses and with other local green spaces, can decrease urban LST, thus providing benefits for urban residents. Moreover, as golf courses are useful for biodiversity conservation, planning for new golf course development should embrace the retention of native vegetation and linkages to conservation corridors

Nosocomial infections: A further assault on patients in a high-volume urban trauma centre in South Africa

Background. Hospital-acquired infections (HAIs) are a major cause of morbidity and mortality. Surgical site infection (SSI) rates are reported to range from 2.5% to 41%. HAI increases the risk of death by 2 - 11%, and three-quarters of these deaths are directly attributable to SSIs.Objectives. To determine the incidence of HAI and to identify risk factors amenable to modification with a resultant reduction in infection rates.Methods. An analysis of HAIs was performed between January and April 2018 in the trauma centre surgical wards at Groote Schuur Hospital, Cape Town, South Africa.Results. There were 769 admissions during the study period. Twenty-two patients (0.03%) developed an HAI. The majority were men, and the mean age was 32 years (range 18 - 57). The mean length of hospital stay (LoS) was 9 days, higher than the mean LoS for the hospital of 6 days. Fourteen patients underwent emergency surgery, 3 patients underwent abbreviated damage control surgery, and 9 patients were admitted to the critical care unit. Most patients with nosocomial sepsis were treated with appropriate culture-based antibiotics (82%). Four patients were treated with amoxicillin/clavulanic acid presumptively prior to culture and sensitivity results, after which antibiotic therapy was tailored. All but 1 patient received antibiotics.Conclusions. A combination of measures is required to prevent trauma-related infections. By determining the incidence of nosocomial infections in our trauma patients, uniform policies to reduce infection rates further could be determined. Our low incidence of infection may be explained by established preventive care bundles already in place.