Optimal Sparsification for Some Binary CSPs Using Low-degree Polynomials

This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization. Existing results show that if NP is not contained in coNP/poly, no efficient preprocessing algorithm can reduce n-variable instances of CNF-SAT with d literals per clause, to equivalent instances with $O(n^{d-e})$ bits for any e > 0. For the Not-All-Equal SAT problem, a compression to size $\~O(n^{d-1})$ exists. We put these results in a common framework by analyzing the compressibility of binary CSPs. We characterize constraint types based on the minimum degree of multivariate polynomials whose roots correspond to the satisfying assignments, obtaining (nearly) matching upper and lower bounds in several settings. Our lower bounds show that not just the number of constraints, but also the encoding size of individual constraints plays an important role. For example, for Exact Satisfiability with unbounded clause length it is possible to efficiently reduce the number of constraints to n+1, yet no polynomial-time algorithm can reduce to an equivalent instance with $O(n^{2-e})$ bits for any e > 0, unless NP is a subset of coNP/poly.Comment: Updated the cross-composition in lemma 18 (minor update), since the previous version did NOT satisfy requirement 4 of lemma 18 (the proof of Claim 20 was incorrect

Legislative and executive translation of the right to have access to health care services

It is the task of government to turn the basic rights contained in the Constitution into lived reality for South Africa's people by means of legislation and policy. Marius Pieterse focuses on the crucially important right of access to health care services, examining the extent to which the legislature and executive have translated this right into concrete, claimable individual entitlements. The author draws links between the creation of statutory or policy-based socio-economic entitlements, the establishment of processes through which they may be enforced and the extent to which beneficiaries are able to access them. Contrary to the conventional wisdom that non-enjoyment of the right to have access to health care services is due to lack of implementation of laws and policies rather than weaknesses in the laws and policies themselves, the author argues that legislative and executive "translation failures" are impacting detrimentally on access to treatment, especially by the most vulnerable. Against this background the article considers whether the current judicial approach to socio-economic adjudication is adequate to perceive and correct such "translation failures"

Rapid deconvolution of low-resolution time-of-flight data using Bayesian inference

The deconvolution of low-resolution time-of-flight data has numerous advantages, including the ability to extract additional information from the experimental data. We augment the well-known Lucy-Richardson deconvolution algorithm using various Bayesian prior distributions and show that a prior of second-differences of the signal outperforms the standard Lucy-Richardson algorithm, accelerating the rate of convergence by more than a factor of four, while preserving the peak amplitude ratios of a similar fraction of the total peaks. A novel stopping criterion and boosting mechanism are implemented to ensure that these methods converge to a similar final entropy and local minima are avoided. Improvement by a factor of two in mass resolution allows more accurate quantification of the spectra. The general method is demonstrated in this paper through the deconvolution of fragmentation peaks of the 2,5-dihydroxybenzoic acid matrix and the benzyltriphenylphosphonium thermometer ion, following femtosecond ultraviolet laser desorption

Photovoice as a critical reflection methodology for a service learning module

The article examines the value of using photovoice to assist reflection in a service learning module. Students were required to complete a reflective assignment in order to facilitate critical reflection on experiences during their community-based projects. They had to identify a specific incident during the execution of their project which they experienced as a challenge. They had to take a photograph to depict the challenge and at the end of their project, complete a reflective questionnaire about the identified challenge. The concepts of photovoice as a methodology tool were used to determine the value of such a reflective assignment for students.The study shows that identifying the challenge during the execution of their project enhanced the students’ creativity during the project and assisted reflection after completing the project. Furthermore, the photographic reminder of the incident they had identified as a challenge, helped the students to recall their experiences and resulted in a more meaningful reflection.Keywords: service learning, photovoice, reflectio

A Bird Survey of Gunung Lumut Protection Forest, East Kalimantan and a Recommendation for its Designation as an Important Bird Area - Part 1

We report on a bird survey in and near Gunung Lumut Protection Forest in East Kalimantan, and evaluate our results against the BirdLife International criteria for recognition as an Important Bird Area. Five globally threatened species (Storm 's Stork Ciconia stormi, Bomean Peacock-pheasant Polyplectron schleiermacheri, Large Green Pigeon Treron capellei, Short-toed Coucal Centropus rectunguis and Blue-headed Pitta Pitta baudii) were encountered, as well as 91 species endemic to the Sundaic Lowland Forest biome, and up to 1% of the biogeographic population of the congregatory Storm's Stork. Based on these observations, we recommend Gunung Lumut Protection Forest to be included in Birdlife International 's Important Bird Area network

Optimal Data Reduction for Graph Coloring Using Low-Degree Polynomials

The theory of kernelization can be used to rigorously analyze data reduction for graph coloring problems. Here, the aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural properties, such as the size of a minimum vertex cover. In this paper we settle two open problems about data reduction for q-Coloring. First, we use a recent technique of finding redundant constraints by representing them as low-degree polynomials, to obtain a kernel of bitsize O(k^(q-1) log k) for q-Coloring parameterized by Vertex Cover for any q >= 3. This size bound is optimal up to k^o(1) factors assuming NP is not a subset of coNP/poly, and improves on the previous-best kernel of size O(k^q). Our second result shows that 3-Coloring does not admit non-trivial sparsification: assuming NP is not a subset of coNP/poly, the parameterization by the number of vertices n admits no (generalized) kernel of size O(n^(2-e)) for any e > 0. Previously, such a lower bound was only known for coloring with q >= 4 colors

Sparsification Upper and Lower Bounds for Graphs Problems and Not-All-Equal SAT

We present several sparsification lower and upper bounds for classic problems in graph theory and logic. For the problems 4-Coloring, (Directed) Hamiltonian Cycle, and (Connected) Dominating Set, we prove that there is no polynomial-time algorithm that reduces any n-vertex input to an equivalent instance, of an arbitrary problem, with bitsize O(n^{2-epsilon}) for epsilon > 0, unless NP is a subset of coNP/poly and the polynomial-time hierarchy collapses. These results imply that existing linear-vertex kernels for k-Nonblocker and k-Max Leaf Spanning Tree (the parametric duals of (Connected) Dominating Set) cannot be improved to have O(k^{2-epsilon}) edges, unless NP is a subset of NP/poly. We also present a positive result and exhibit a non-trivial sparsification algorithm for d-Not-All-Equal-SAT. We give an algorithm that reduces an n-variable input with clauses of size at most d to an equivalent input with O(n^{d-1}) clauses, for any fixed d. Our algorithm is based on a linear-algebraic proof of Lovász that bounds the number of hyperedges in critically 3-chromatic d-uniform n-vertex hypergraphs by binom{n}{d-1}. We show that our kernel is tight under the assumption that NP is not a subset of NP/poly

Reduction of Coxiella burnetii prevalence by vaccination of goats and sheep, the Netherlands

Recently, the number of human Q fever cases in the Netherlands increased dramatically. In response to this increase, dairy goats and dairy sheep were vaccinated against Coxiella burnetii. All pregnant dairy goats and dairy sheep in herds positive for Q fever were culled. We identified the effect of vaccination on bacterial shedding by small ruminants. On the day of culling, samples of uterine fluid, vaginal mucus, and milk were obtained from 957 pregnant animals in 13 herds. Prevalence and bacterial load were reduced in vaccinated animals compared with unvaccinated animals. These effects were most pronounced in animals during their first pregnancy. Results indicate that vaccination may reduce bacterial load in the environment and human exposure to C. burnetii