On uniform relationships between combinatorial problems

The enterprise of comparing mathematical theorems according to their logical strength is an active area in mathematical logic, with one of the most common frameworks for doing so being reverse mathematics. In this setting, one investigates which theorems provably imply which others in a weak formal theory roughly corresponding to computable mathematics. Since the proofs of such implications take place in classical logic, they may in principle involve appeals to multiple applications of a particular theorem, or to nonuniform decisions about how to proceed in a given construction. In practice, however, if a theorem Q implies a theorem P, it is usually because there is a direct uniform translation of the problems represented by P into the problems represented by Q, in a precise sense formalized by Weihrauch reducibility. We study this notion of uniform reducibility in the context of several natural combinatorial problems, and compare and contrast it with the traditional notion of implication in reverse mathematics. We show, for instance, that for all n; j; k 1, if j < k then Ramsey's theorem for n-tuples and k many colors is not uniformly, or Weihrauch, reducible to Ramsey's theorem for n-tuples and j many colors. The two theorems are classically equivalent, so our analysis gives a genuinely ner metric by which to gauge the relative strength of mathematical propositions. We also study Weak K�onig's Lemma, the Thin Set Theorem, and the Rainbow Ramsey's Theorem, along with a number of their variants investigated in the literature. Weihrauch reducibility turns out to be connected with sequential forms of mathematical principles, where one wishes to solve in nitely many instances of a particular problem simultaneously. We exploit this connection to uncover new points of di erence between combinatorial problems previously thought to be more closely related

An order-theoretic characterization of the Howard-Bachmann-hierarchy

In this article we provide an intrinsic characterization of the famous Howard-Bachmann ordinal in terms of a natural well-partial-ordering by showing that this ordinal can be realized as a maximal order type of a class of generalized trees with respect to a homeomorphic embeddability relation. We use our calculations to draw some conclusions about some corresponding subsystems of second order arithmetic. All these subsystems deal with versions of light-face Π₁¹-comprehension

Reverse mathematics of matroids

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles and statements about vector spaces. Finally, we formalize some of the Weihrauch reductions to extract related reverse mathematics results. In particular, we show that the existence of bases for vector spaces of bounded dimension is equivalent to the induction scheme for \Sigma^0_2 formulas

Aortic dissection at the University hospital of the West Indies: A 20-year clinicopathological study of autopsy cases

<p>Abstract</p> <p>Background</p> <p>An autopsy study of aortic dissection (AD) at our institution was previously reported. In the approximately 20 years since then, however, many aspects of diagnosis and treatment of this disease have changed, with a fall in mortality reported in many centers around the world. An impression amongst our pathologists that, there might be an increase in the prevalence of AD in the autopsy service at our hospital, since that earlier report, led to this repeated study, in an attempt to validate that notion. We also sought to identify any changes in clinicopathological features between the two series or any occurring during this study period itself.</p> <p>Findings</p> <p>All cases of AD identified at autopsy, during the 20-year period since the conclusion of the last study, were collected and pertinent clinical and pathological data were analyzed and compared, both within the two decades of this study period and against the results of the last study.</p> <p>Fifty-six cases comprised this study group including 36 males and 20 females, with a mean age of 63.9 years. There were, more patients in the second decade (n = 33; 59%) compared with the first decade (n = 23; 41%). Hypertension as a risk factor was identified in 52 (93%) cases and rupture occurred in 49 (88%) cases. A clinical diagnosis of AD was considered prior to surgery or autopsy in 25 (45%) cases overall, more during the second decade. Surgery was attempted in 25% of all cases with an increase in the second decade compared with the first.</p> <p>Conclusions</p> <p>Compared with the earlier review, a variety of changes in the profile of patients with AD in the autopsy service has been noted, including a reversal in the female predominance seen previously. Other observations include an increase in cases where the correct clinical diagnosis was considered and in which surgical treatment was attempted, changes also evident when the second decade of the present study was compared with the earlier decade. Overall, there were many positive trends. However, areas that could still be improved include an increased index of suspicion for the diagnosis of AD and perhaps in the initiation of treatment, earlier, in those cases where the correct diagnosis was considered.</p

High-throughput imaging of ATG9A distribution as a diagnostic functional assay for adaptor protein complex 4-associated hereditary spastic paraplegia

Adaptor protein complex 4-associated hereditary spastic paraplegia is caused by biallelic loss-of-function variants in AP4B1, AP4M1, AP4E1 or AP4S1, which constitute the four subunits of this obligate complex. While the diagnosis of adaptor protein complex 4-associated hereditary spastic paraplegia relies on molecular testing, the interpretation of novel missense variants remains challenging. Here, we address this diagnostic gap by using patient-derived fibroblasts to establish a functional assay that measures the subcellular localization of ATG9A, a transmembrane protein that is sorted by adaptor protein complex 4. Using automated high-throughput microscopy, we determine the ratio of the ATG9A fluorescence in the trans-Golgi-network versus cytoplasm and ascertain that this metric meets standards for screening assays (Z'-factor robust >0.3, strictly standardized mean difference >3). The 'ATG9A ratio' is increased in fibroblasts of 18 well-characterized adaptor protein complex 4-associated hereditary spastic paraplegia patients [mean: 1.54 ± 0.13 versus 1.21 ± 0.05 (standard deviation) in controls] and receiver-operating characteristic analysis demonstrates robust diagnostic power (area under the curve: 0.85, 95% confidence interval: 0.849-0.852). Using fibroblasts from two individuals with atypical clinical features and novel biallelic missense variants of unknown significance in AP4B1, we show that our assay can reliably detect adaptor protein complex 4 function. Our findings establish the 'ATG9A ratio' as a diagnostic marker of adaptor protein complex 4-associated hereditary spastic paraplegia

Splenectomy for solitary splenic metastasis of ovarian cancer

BACKGROUND: Splenic metastases occur in rare cases with a few case reports of patients in the literature. Generally, splenic metastases mean late dissemination of a disease. Solitary splenic metastases from solid tumors are extremely unusual. CASE PRESENTATION: We report a case of a patient with ovarian mucinous cystadenocarcinoma who underwent splenectomy for isolated parenchymal metastasis. CONCLUSION: Ovarian epithelial tumors comprised most of isolated splenic metastases from gynecologic tumor. When isolated splenic recurrence is suspected on image studies and serum tumor markers, intraabdominal gross findings should be examined to exclude peritoneal carcinomatosis. If only spleen was under suspicion of recurrence of ovarian cancer, splenectomy may play a therapeutic role

A plague on five of your houses - statistical re-assessment of three pneumonic plague outbreaks that occurred in Suffolk, England, between 1906 and 1918

<p>Abstract</p> <p>Background</p> <p>Plague is a re-emerging disease and its pneumonic form is a high priority bio-terrorist threat. Epidemiologists have previously analysed historical outbreaks of pneumonic plague to better understand the dynamics of infection, transmission and control. This study examines 3 relatively unknown outbreaks of pneumonic plague that occurred in Suffolk, England, during the first 2 decades of the twentieth century.</p> <p>Methods</p> <p>The Kolmogorov-Smirnov statistical test is used to compare the symptomatic period and the length of time between successive cases (i.e. the serial interval) with previously reported values. Consideration is also given to the case fatality ratio, the average number of secondary cases resulting from each primary case in the observed minor outbreaks (termed <it>R</it>_{<it>minor</it>}), and the proportion of individuals living within an affected household that succumb to pneumonic plague via the index case (i.e. the household secondary attack rate (SAR)).</p> <p>Results</p> <p>2 of the 14 cases survived giving a case fatality ratio of 86% (95% confidence interval (CI) = {57%, 98%}). For the 12 fatal cases, the average symptomatic period was 3.3 days (standard deviation (SD) = 1.2 days) and, for the 11 non index cases, the average serial interval was 5.8 days (SD = 2.0 days). <it>R</it>_{<it>minor </it>}was calculated to be 0.9 (SD = 1.0) and, in 2 households, the SAR was approximately 14% (95% CI = {0%, 58%}) and 20% (95% CI = {1%, 72%}), respectively.</p> <p>Conclusions</p> <p>The symptomatic period was approximately 1 day longer on average than in an earlier study but the serial interval was in close agreement with 2 previously reported values. 2 of the 3 outbreaks ended without explicit public health interventions; however, non-professional caregivers were particularly vulnerable - an important public health consideration for any future outbreak of pneumonic plague.</p

Parents' Experiences of Receiving the Initial Positive Newborn Screening (NBS) Result for Cystic Fibrosis and Sickle Cell Disease

The clinical advantages of the newborn screening programme (NBS) in the UK are well described in the literature. However, there has been little exploration of the psychosocial impact on the family. This study followed the principles of grounded theory to explore parents' experiences of receiving the initial positive NBS result for their child with cystic fibrosis (CF) or sickle cell disease (SCD). Semi-structured, qualitative interviews were conducted with 22 parents (12 mothers and 10 fathers) whose children had been diagnosed with CF or SCD via NBS and were under the age of 1 year at the time of interview. The main themes that arose from the data were; parents previous knowledge of the condition and the NBS programme, the method of delivery and parental reactions to the result, sharing the results with others, the impact on parental relationships and support strategies. Study conclusions indicate that most parents thought initial positive NBS results should be delivered by a health professional with condition specific knowledge, preferably with both parents present. Genetic counselling needs to include a focus on the impact of NBS results on parental relationships. Careful consideration needs to be given to strategies to support parents of babies who have positive NBS results both in terms of the psychological health and to assist them in sharing the diagnosis

Ischaemic accumulation of succinate controls reperfusion injury through mitochondrial ROS.

Ischaemia-reperfusion injury occurs when the blood supply to an organ is disrupted and then restored, and underlies many disorders, notably heart attack and stroke. While reperfusion of ischaemic tissue is essential for survival, it also initiates oxidative damage, cell death and aberrant immune responses through the generation of mitochondrial reactive oxygen species (ROS). Although mitochondrial ROS production in ischaemia reperfusion is established, it has generally been considered a nonspecific response to reperfusion. Here we develop a comparative in vivo metabolomic analysis, and unexpectedly identify widely conserved metabolic pathways responsible for mitochondrial ROS production during ischaemia reperfusion. We show that selective accumulation of the citric acid cycle intermediate succinate is a universal metabolic signature of ischaemia in a range of tissues and is responsible for mitochondrial ROS production during reperfusion. Ischaemic succinate accumulation arises from reversal of succinate dehydrogenase, which in turn is driven by fumarate overflow from purine nucleotide breakdown and partial reversal of the malate/aspartate shuttle. After reperfusion, the accumulated succinate is rapidly re-oxidized by succinate dehydrogenase, driving extensive ROS generation by reverse electron transport at mitochondrial complex I. Decreasing ischaemic succinate accumulation by pharmacological inhibition is sufficient to ameliorate in vivo ischaemia-reperfusion injury in murine models of heart attack and stroke. Thus, we have identified a conserved metabolic response of tissues to ischaemia and reperfusion that unifies many hitherto unconnected aspects of ischaemia-reperfusion injury. Furthermore, these findings reveal a new pathway for metabolic control of ROS production in vivo, while demonstrating that inhibition of ischaemic succinate accumulation and its oxidation after subsequent reperfusion is a potential therapeutic target to decrease ischaemia-reperfusion injury in a range of pathologies