Abstract:
Epidemiology studies are often overlooked in the current world of evidence-based medicine. The studies do not rank in the hierarchy of clinical trial data, they are not often considered to influence clinical care and they may be considered merely 'descriptive' of a medical problem. Despite the limitations of epidemiology studies, they remain a critical component of biomedical research without which the remaining 'higher order' studies, such as cohort studies and controlled trials, could not be effectively conducted.Critical care epidemiology studies, of which the current study from the Intensive Care National Audit and Research Center database is a good example [1], serve a variety of purposes that advance the mission of both practicing intensive care unit (ICU) physicians and scientific researchers. At the most basic level, epidemiology studies convey important information about disease characteristics, the type of patients affected, and the frequency and outcomes of the disease. Importantly, these studies keep medical events in perspective. Epidemiology studies report and reinforce the frequency of deaths related to atherosclerotic disease, cancer and sepsis in developed countries, and of deaths from a variety of infectious diseases and sepsis in developing countries. These reminders are essential in an era of increasing media attention on diseases such as severe acute respiratory syndrome and avian influenza that are less immediate public health concerns.Descriptive epidemiology studies also inform intensivists about the type of conditions they should expect to encounter in their ICU (i.e. the frequency of disease) and they guide clinicians in treating patients by reporting information on relative causality (such as Streptococcus pneumoniae being the most common cause of community-acquired pneumonia). Local and regional epidemiology data have long been disseminated to tailor therapy for infectious diseases based on local organism resistance patterns. In contrast,

Abstract:
The interpretation of clinical trial data is the cornerstone of both evidence-based medicine and medical practice [1,2]. The level of evidence that we apply to study results depends on the type of trial being reported. For example, randomized, controlled trials (RCTs) represent a higher level of evidence than observational trials. Thus, RCTs more appropriately guide the practice of medicine. Observational trials are statistically and financially efficient, however, and almost invariably precede results from an RCT. Can we base the care of critically ill patients on the results of observational data?The 'Sepsis Occurrence in Acutely Ill Patients' (SOAP) study represents an observational trial conducted in intensive care units (ICUs) from 24 European countries during a two-week period. In this issue of Critical Care, Vincent and colleagues [3] present SOAP study data related to albumin therapy in these patients. From this perspective, 11.2% of study subjects received albumin during their ICU stay, and those who received albumin were more frequently surgical patients and more likely to have cancer, liver cirrhosis, and sepsis. Patients who received albumin were more severely ill, confounding the findings of greater length of ICU stay and mortality. However, even after adjustment for these differences (either by proportional hazards regression or by subject pairs matched by propensity scores), albumin use remained associated with a higher risk of death.Does this mean that albumin either causes or contributes to the death of critically ill patients? Because the data presented are observational in nature, it is impossible to draw that conclusion. Inherent to their nature, observational trials have one crucial deficiency: their design is not experimental. Each patient's treatment is chosen rather than randomly assigned, creating an unavoidable risk of selection bias and systematic differences in outcomes that are not due to the treatment itself. Although statistical adjust

Abstract:
Firstly: Globalization is reshaping the social geography within which we might strive to create health or prevent disease. The determinants of health – be they a SARS virus or a predilection for fatty foods – have joined us in our global mobility. Driven by economic liberalization and changing technologies, the phenomenon of 'access' is likely to dominate to an increasing extent the unfolding experience of human disease and wellbeing.Secondly: Understanding globalization as a subject matter itself needs certain benchmarks and barometers of its successes and failings. Health is one such barometer. It is a marker of social infrastructure and social welfare and as such can be used to either sound an alarm or give a victory cheer as our interconnectedness hurts and heals the populations we serve.And lastly: In as much as globalization can have an effect on health, it is also true that health and disease has an effect on globalization as exemplified by the existence of quarantine laws and the devastating economic effects of the AIDS pandemic.A balanced view would propose that the effects of globalization on health (and health systems) are neither universally good nor bad, but rather context specific. If the dialogue pertaining to globalization is to be directed or biased in any direction, then it must be this: that we consider the poor first.I am pleased to introduce 'Globalization and Health', a peer reviewed, open access (free to the end user) journal. In this, the début editorial, I will briefly outline the purpose and scope of this journal highlighting our intention to publish a balanced mixture of opinion on the subject.That the journal be 'Open Access' is entirely appropriate. Knowledge, at its best utility, is a 'public good' i.e. non-rival, non-excludable. While this journal will deal with the subject matter of creating 'global public goods for health', it will also by virtue of its very existence, contribute toward that process. Globalization and Health's 'Open

Abstract:
Four and a half billion years of evolution has left the microbes that cause disease in humans, with a remarkable capacity for adaptation to changes in their micro chemical environment. This month Globalization and Health published a paper, "Antibiotic resistance as a global threat: Evidence from China, Kuwait and the United States" which explores the possibility of a global spread in antimicrobial resistance (AMR) and a novel technique for monitoring such a phenomenon. Whether or not AMR spread will become a global phenomenon still remains to be seen, the monitoring thereof will however be a valuable exercise, (figure 1).The problem of AMR need to be addressed on three fronts. Firstly, on a bio-molecular level, antimicrobial development needs to be aggressive and target aspects of the pathogens which are least likely to have variable phenotypes. While research along these lines is being done, our failing is perhaps in the pace of it. Research and development for diseases in the poorest countries – those that are most affected by infectious disease – is sorely lacking and innovative mechanisms to provide incentives for the pharmaceutical industry to develop drugs which are in the global public interest need to be devised. Public Private Partnerships (PPPs) have shown some promise but are yet to represent a definitive solution. It is quite remarkable that, until last year, despite 1.5 million people dying of the disease annually, we had failed to produce a single novel TB treatment for 30 years.Secondly, and perhaps most importantly, mechanisms need to be put in place to ensure responsible antimicrobial usage by clinicians. Overuse, under-use, poor diagnostic techniques and inappropriate choice of antimicrobial account for the bulk of resistant strains emerging world wide. The WHO has taken the lead in this regard with its recommendations under the 'widely and wisely' approach to AMR control.The overuse of medication is often a response to demanding patients receiving

Abstract:
This paper concerns the values of the Euler phi-function evaluated simultaneously on k arithmetic progressions a_1 n + b_1, a_2 n + b_2, ..., a_k n + b_k. Assuming the necessary condition that no two of the polynomials a_i x + b_i are constant multiples of each other, we show that there are infinitely many integers n for which phi(a_1 n + b_1) > phi(a_2 n + b_2) > ... > phi(a_k n + b_k). In particular, there exist infinitely many strings of k consecutive integers whose phi-values are arranged from largest to smallest in any prescribed manner. Also, under the necessary condition ad \ne bc, any inequality of the form phi(an+b) < phi(cn+d) infinitely often has k consecutive solutions. In fact, we prove that the sets of solutions to these inequalities have positive lower density.

Abstract:
In this note, we review some facts about polynomials representing functions modulo primes p. In addition we prove that the polynomial f(x) = x^{p-2} + x^{p-3} + ... + x^3 + x^2 + 2x + 1 represents the transposition (0 1) modulo p, that is, f(0) \equiv 1 (mod p), f(1) \equiv 0 (mod p), and f(a) \equiv a (mod p) for all 2 \le a \le p-1.

Abstract:
Let D(n) be the set of all fractions in the unit interval whose denominator in lowest terms equals $n$. We evaluate the product of the values of the Gamma function at the points of D(n), as a function of $n$; the answer depends on whether or not $n$ is a prime power.

Abstract:
Moser asked whether the collection of rectangles of dimensions 1 x 1/2, 1/2 x 1/3, 1/3 x 1/4, ..., whose total area equals 1, can be packed into the unit square without overlap, and whether the collection of squares of side lengths 1/2, 1/3, 1/4, ... can be packed without overlap into a rectangle of area pi^2/6-1. Computational investigations have been made into packing these collections into squares of side length 1+epsilon and rectangles of area pi^2/6-1+epsilon, respectively, and one can consider the apparently weaker question whether such packings are possible for every positive number epsilon. In this paper we establish a general theorem on sequences of geometrical packings that implies in particular that the ``for every epsilon'' versions of these two problems are actually equivalent to the original tiling problems.

Abstract:
In this paper we correct an analysis of the two-player perfect-information game Dukego given in Berlekamp, Conway, and Guy's Winning Ways for your Mathematical Plays (Chapter 19). In particular, we characterize the board dimensions that are fair, i.e., those for which the first player to move has a winning strategy.

Abstract:
It has been well-observed that an inequality of the type $\pi(x;q,a) > \pi(x;q,b)$ is more likely to hold if $a$ is a non-square modulo $q$ and $b$ is a square modulo $q$ (the so-called ``Chebyshev Bias''). For instance, each of $\pi(x;8,3)$, $\pi(x;8,5)$, and $\pi(x;8,7)$ tends to be somewhat larger than $\pi(x;8,1)$. However, it has come to light that the tendencies of these three $\pi(x;8,a)$ to dominate $\pi(x;8,1)$ have different strengths. A related phenomenon is that the six possible inequalities of the form $\pi(x;8,a_1) > \pi(x;8,a_2) > \pi(x;8,a_3)$ with $\{a_1,a_2,a_3\}=\{3,5,7\}$ are not all equally likely---some orderings are preferred over others. In this paper we discuss these phenomena, focusing on the moduli $q=8$ and $q=12$, and we explain why the observed asymmetries (as opposed to other possible asymmetries) occur.