Lower Bounds for the Graph Homomorphism Problem

The graph homomorphism problem (HOM) asks whether the vertices of a given $n$-vertex graph $G$ can be mapped to the vertices of a given $h$-vertex graph $H$ such that each edge of $G$ is mapped to an edge of $H$. The problem generalizes the graph coloring problem and at the same time can be viewed as a special case of the $2$-CSP problem. In this paper, we prove several lower bound for HOM under the Exponential Time Hypothesis (ETH) assumption. The main result is a lower bound $2^{\Omega\left( \frac{n \log h}{\log \log h}\right)}$. This rules out the existence of a single-exponential algorithm and shows that the trivial upper bound $2^{{\mathcal O}(n\log{h})}$ is almost asymptotically tight. We also investigate what properties of graphs $G$ and $H$ make it difficult to solve HOM$(G,H)$. An easy observation is that an ${\mathcal O}(h^n)$ upper bound can be improved to ${\mathcal O}(h^{\operatorname{vc}(G)})$ where $\operatorname{vc}(G)$ is the minimum size of a vertex cover of $G$. The second lower bound $h^{\Omega(\operatorname{vc}(G))}$ shows that the upper bound is asymptotically tight. As to the properties of the "right-hand side" graph $H$, it is known that HOM$(G,H)$ can be solved in time $(f(\Delta(H)))^n$ and $(f(\operatorname{tw}(H)))^n$ where $\Delta(H)$ is the maximum degree of $H$ and $\operatorname{tw}(H)$ is the treewidth of $H$. This gives single-exponential algorithms for graphs of bounded maximum degree or bounded treewidth. Since the chromatic number $\chi(H)$ does not exceed $\operatorname{tw}(H)$ and $\Delta(H)+1$, it is natural to ask whether similar upper bounds with respect to $\chi(H)$ can be obtained. We provide a negative answer to this question by establishing a lower bound $(f(\chi(H)))^n$ for any function $f$. We also observe that similar lower bounds can be obtained for locally injective homomorphisms.Comment: 19 page

Empirical Analysis of Factors Affecting Confirmation Bias Levels of Software Engineers

Confirmation bias is defined as the tendency of people to seek evidence that verifies a hypothesis rather than seeking evidence to falsify it. Due to the confirmation bias, defects may be introduced in a software product during requirements analysis, design, implementation and/or testing phases. For instance, testers may exhibit confirmatory behavior in the form of a tendency to make the code run rather than employing a strategic approach to make it fail. As a result, most of the defects that have been introduced in the earlier phases of software development may be overlooked leading to an increase in software defect density. In this paper, we quantify confirmation bias levels in terms of a single derived metric. However, the main focus of this paper is the analysis of factors affecting confirmation bias levels of software engineers. Identification of these factors can guide project managers to circumvent negative effects of confirmation bias, as well as providing guidance for the recruitment and effective allocation of software engineers. In this empirical study, we observed low confirmation bias levels among participants with logical reasoning and hypothesis testing skills

Quantifying Privacy: A Novel Entropy-Based Measure of Disclosure Risk

It is well recognised that data mining and statistical analysis pose a serious treat to privacy. This is true for financial, medical, criminal and marketing research. Numerous techniques have been proposed to protect privacy, including restriction and data modification. Recently proposed privacy models such as differential privacy and k-anonymity received a lot of attention and for the latter there are now several improvements of the original scheme, each removing some security shortcomings of the previous one. However, the challenge lies in evaluating and comparing privacy provided by various techniques. In this paper we propose a novel entropy based security measure that can be applied to any generalisation, restriction or data modification technique. We use our measure to empirically evaluate and compare a few popular methods, namely query restriction, sampling and noise addition.Comment: 20 pages, 4 figure

Racial/ethnic differences in job loss for women with breast cancer

IntroductionWe examined race/ethnic differences in treatment-related job loss and the financial impact of treatment-related job loss, in a population-based sample of women diagnosed with breast cancer.MethodsThree thousand two hundred fifty two women with non-metastatic breast cancer diagnosed (August 2005-February 2007) within the Los Angeles County and Detroit Metropolitan Surveillance Epidemiology and End Results registries, were identified and asked to complete a survey (mean time from diagnosis = 8.9 months). Latina and African American women were over-sampled (n = 2268, eligible response rate 72.1%).ResultsOne thousand one hundred eleven women (69.6%) of working age (<65 years) were working for pay at time of diagnosis. Of these women, 10.4% (24.1% Latina, 10.1% African American, 6.9% White, p < 0.001) reported that they lost or quit their job since diagnosis due to breast cancer or its treatment (defined as job loss). Latina women were more likely to experience job loss compared to White women (OR = 2.0, p = 0.013)), independent of sociodemographic factors. There were no significant differences in job loss between African American and White women, independent of sociodemographic factors. Additional adjustments for clinical and treatment factors revealed a significant interaction between race/ethnicity and chemotherapy (p = 0.007). Among women who received chemotherapy, Latina women were more likely to lose their job compared to White women (OR = 3.2, p < 0.001), however, there were no significant differences between Latina and White women among those who did not receive chemotherapy. Women who lost their job were more likely to experience financial strain (e.g. difficulty paying bills 27% vs. 11%, p < 0.001).ConclusionJob loss is a serious consequence of treatment for women with breast cancer. Clinicians and staff need to be aware of aspects of treatment course that place women at higher risk for job loss, especially ethnic minorities receiving chemotherapy

Trigger finger: etiology, evaluation, and treatment

Trigger finger is a common finger aliment, thought to be caused by inflammation and subsequent narrowing of the A1 pulley, which causes pain, clicking, catching, and loss of motion of the affected finger. Although it can occur in anyone, it is seen more frequently in the diabetic population and in women, typically in the fifth to sixth decade of life. The diagnosis is usually fairly straightforward, as most patients complain of clicking or locking of the finger, but other pathological processes such as fracture, tumor, or other traumatic soft tissue injuries must be excluded. Treatment modalities, including splinting, corticosteroid injection, or surgical release, are very effective and are tailored to the severity and duration of symptoms

Cooling athletes with a spinal cord injury

Cooling strategies that help prevent a reduction in exercise capacity whilst exercising in the heat have received considerable research interest over the past 3 decades, especially in the lead up to a relatively hot Olympic and Paralympic Games. Progressing into the next Olympic/Paralympic cycle, the host, Rio de Janeiro, could again present an environmental challenge for competing athletes. Despite the interest and vast array of research into cooling strategies for the able-bodied athlete, less is known regarding the application of these cooling strategies in the thermoregulatory impaired spinal cord injured (SCI) athletic population. Individuals with a spinal cord injury (SCI) have a reduced afferent input to the thermoregulatory centre and a loss of both sweating capacity and vasomotor control below the level of the spinal cord lesion. The magnitude of this thermoregulatory impairment is proportional to the level of the lesion. For instance, individuals with high-level lesions (tetraplegia) are at a greater risk of heat illness than individuals with lower-level lesions (paraplegia) at a given exercise intensity. Therefore, cooling strategies may be highly beneficial in this population group, even in moderate ambient conditions (~21 °C). This review was undertaken to examine the scientific literature that addresses the application of cooling strategies in individuals with an SCI. Each method is discussed in regards to the practical issues associated with the method and the potential underlying mechanism. For instance, site-specific cooling would be more suitable for an athlete with an SCI than whole body water immersion, due to the practical difficulties of administering this method in this population group. From the studies reviewed, wearing an ice vest during intermittent sprint exercise has been shown to decrease thermal strain and improve performance. These garments have also been shown to be effective during exercise in the able-bodied. Drawing on additional findings from the able-bodied literature, the combination of methods used prior to and during exercise and/or during rest periods/half-time may increase the effectiveness of a strategy. However, due to the paucity of research involving athletes with an SCI, it is difficult to establish an optimal cooling strategy. Future studies are needed to ensure that research outcomes can be translated into meaningful performance enhancements by investigating cooling strategies under the constraints of actual competition. Cooling strategies that meet the demands of intermittent wheelchair sports need to be identified, with particular attention to the logistics of the sport

Volcanic impacts on the Holocene vegetation history of Britain and Ireland? A review and meta-analysis of the pollen evidence

Volcanic ash layers show that the products of Icelandic volcanism reached Britain and Ireland many times during the Holocene. Historical records suggest that at least one eruption, that of Laki in a.d. 1783, was associated with impacts on vegetation. These results raise the question: did Icelandic volcanism affect the Holocene vegetation history of Britain and Ireland? Several studies have used pollen data to address this issue but no clear consensus has been reached. We re-analyse the palynological data using constrained ordination with various representations of potential volcanic impacts. We find that the palynological evidence for volcanic impacts on vegetation is weak but suggest that this is a case of absence of evidence and is not necessarily evidence of absence of impact. To increase the chances of identifying volcanic impacts, future studies need to maximise temporal resolution, replicate results, and investigate a greater number of tephras in a broader range of locations, including more studies from lake sediments

Worsening of Cardiomyopathy Using Deflazacort in an Animal Model Rescued by Gene Therapy

We have previously demonstrated that gene therapy can rescue the phenotype and extend lifespan in the delta-sarcoglycan deficient cardiomyopathic hamster. In patients with similar genetic defects, steroids have been largely used to slow down disease progression. Aim of our study was to evaluate the combined effects of steroid treatment and gene therapy on cardiac function. We injected the human delta-sarcoglycan cDNA by adeno-associated virus (AAV) 2/8 by a single intraperitoneal injection into BIO14.6 Syrian hamsters at ten days of age to rescue the phenotype. We then treated the hamsters with deflazacort. Treatment was administered to half of the hamsters that had received the AAV and the other hamsters without AAV, as well as to normal hamsters. Both horizontal and vertical activities were greatly enhanced by deflazacort in all groups. As in previous experiments, the AAV treatment alone was able to preserve the ejection fraction (70±7% EF). However, the EF value declined (52±14%) with a combination of AAV and deflazacort. This was similar with all the other groups of affected animals. We confirm that gene therapy improves cardiac function in the BIO14.6 hamsters. Our results suggest that deflazacort is ineffective and may also have a negative impact on the cardiomyopathy rescue, possibly by boosting motor activity. This is unexpected and may have significance in terms of the lifestyle recommendations for patients