Circuit and fractional circuit covers of matroids

AbstractLet M be a connected matroid having a ground set E. Lemos and Oxley proved that |E(M)|≤12c(M)c∗(M) where c(M) (resp. c∗(M)) is the circumference (resp. cocircumference) of M. In addition, they conjectured that one can find a collection of at most c∗(M) circuits which cover the elements of M at least twice. In this paper, we verify this conjecture for regular matroids. Moreover, we show that a version of this conjecture is true for fractional circuit covers

Serial Exchanges in Random Bases

It was conjectured by Kotlar and Ziv that for any two bases $B_1$ and $B_2$ in a matroid $M$ and any subset $X \subset B_1$, there is a subset $Y$ and orderings $x_1 \prec x_2 \prec \cdots \prec x_k$ and $y_1 \prec y_2 \prec \cdots \prec y_k$ of $X$ and $Y$, respectively, such that for $i = 1, \dots ,k$, $B_1 - \{ x_1, \dots ,x_i\} + \{y_1, \dots ,y_k \}$ and $B_2 - \{ y_1, \dots ,y_i\} + \{x_1, \dots ,x_k \}$ are bases; that is, $X$ is serially exchangeable with $Y$. Let $M$ be a rank-$n$ matroid which is representable over $\mathbb{F}_q.$ We show that for $q>2,$ if bases $B_1$ and $B_2$ are chosen randomly amongst all bases of $M$, and if a subset $X$ of size $k \le \ln(n)$ is chosen randomly in $B_1$, then with probability tending to one as $n \rightarrow \infty$, there exists a subset $Y\subset B_2$ such that $X$ is serially exchangeable with $Y.

A Dichotomy Theorem for Circular Colouring Reconfiguration

The "reconfiguration problem" for circular colourings asks, given two $(p,q)$-colourings $f$ and $g$ of a graph $G$, is it possible to transform $f$ into $g$ by changing the colour of one vertex at a time such that every intermediate mapping is a $(p,q)$-colouring? We show that this problem can be solved in polynomial time for $2\leq p/q <4$ and is PSPACE-complete for $p/q\geq 4$. This generalizes a known dichotomy theorem for reconfiguring classical graph colourings.Comment: 22 pages, 5 figure

Cycle and Cocycle Coverings of Graphs

Abstract: In this article, we show that for any simple, bridgeless graph G on n vertices, there is a family C of at most n−1 cycles which cover the edges of G at least twice. A similar, dual result is also proven for cocycles namely: for any loopless graph G on n vertices and edges having cogirth g * ≥ 3 and k(G) components, there is a family of at most −n+k(G) cocycles which cover the edges of G at least twice

Penoscrotal Transposition: A Cadaveric Review

Introduction: With only 20 documented cases, the congenital malformation known as complete extreme penoscrotal transposition with an intact scrotum, midline raphe, and absence of hypospadias is an extremely rare abnormality. Penoscrotal transposition occurs when the scrotum fuses above the penis for a complete abnormality or does not fuse at all for an incomplete abnormality. This failure of the scrotum to descend below the penis occurs during development, when the genital swellings fail to descend below the penis and fuse. The irregularity has been known to follow an X-linked recessive pattern in some cases. In others, it results from a defect of chromosome 13. This disease would have significant clinical implications for a patient in day to day activities, as well as sexually. However, little is known as to whether this transposition impacts spermatogenesis. Method: Dissection and observations were made from a 72-year-old male as part of a gross anatomy course at Philadelphia College of Osteopathic Medicine, utilizing the methods of the dissection manual. Biopsy of the testes were taken and without further fixation processed for light microscopy, using standard techniques. Results: Upon dissection, the individual exhibited a complete extreme penoscrotal transposition, with the scrotum fused above the penis in a shawl fashion, with no hypospadias. The tunica albuginea was thickened, fused in the midline, and adhered to the testis. Histology of the testis supports that spermatogenesis was not altered. The organization of the seminiferous tubules and developing germ cells appeared to be normal. Discussion: Along with the penoscrotal transposition, many abnormalities are typically also present. It was observed that the patient had several hernias, mega colon, and many abdominal adhesions. One interesting anomaly observed during dissection was bilateral fused adductor magnus/adductor longus muscles. As a senior computer analyst, this individual likely had no cognitive or mental impairment, however, his cause of death was due to end stage Parkinson’s disease. Living with this disease would have been very difficult because the patient has virtually no protection of the testis as they are positioned superior to the penis. It would have had significant psychosocial implications for the patient, especially with regard to reproduction and sexual intercourse

An experimental comparison of knowledge transfer algorithms in deep neural networks

Neural knowledge transfer methods aim to constrain the hidden representation of one neural network to be similar, or have similar properties, to another by applying specially designed loss functions between the two networks hidden layers. In this way the intangible knowledge encoded by the network's weights is transferred without having to replicate exact weight structures or alter the knowledge representation from its natural highly distributed form. Motivated by the need to enable greater transparency in evaluating such methods by bridging the gap between different experimental setups in the existing literature, the need to cast a wider net in comparing each method to a greater number of its peers and a desire to explore novel combinations of existing methods we conduct an experimental comparison of eight contemporary neural knowledge transfer algorithms and further explore the performance of some combinations. We conduct our experiments on an image classification task and measure relative performance gains over non-knowledge enhanced baseline neural networks in terms of classification accuracy. We observed (i) some interesting contradictions between our results and those reported in original papers, (ii) a general lack of correlation between any given methods standalone performance vs performance when used in combination with knowledge distillation, (iii) a general trend of older simpler methods outperforming newer ones and (iv) Contrastive Representation Distillation (CRD) achieving best performance

Design of a releasable snowboard binding system to prevent upper body injury

The objective of this project was to design, build, and test a snowboard binding system that prevents upper body injury to snowboarders due to the flyswatter effect . This effect occurs when the user catches the longitudinal edge of the snowboard during turns, swinging the user\u27s upper body towards the terrain. The system was designed to release under shear stress caused by the effect, and a moment lock mechanism activated by normal riding forces was integrated to prevent inadvertent release

Total Fluorine Analysis to Screen for PFAS in Personal Care Products

A series of commercially available personal care products have been screened for the presence of fluorine, as a surrogate for the presence of per- and polyfluorinated alkyl substances (PFAS). The novel total fluorine method used is Particle-Induced Gamma-ray Emission (PIGE) spectroscopy, which has been previously used in prevalence studies of PFAS in consumer goods such as food packaging and textiles. As in other industries, a significant fraction of personal care products was found to contain large quantities of total fluorine, although because of the presence of some inorganic fluoride compounds used in cosmetics (synthetic mica, for example), it is more difficult to distinguish which products use PFAS. However, an organofluorine analysis was performed as well as traditional LC-MS/MS measurements to identify likely PFAS compounds present. Preliminary data about the two forms of personal care products that are likely to represent significant PFAS exposure risks to the wearer (water-proof mascara and water-proof lip-stick) will be presented.Ope

Treatment interventions to maintain abstinence from alcohol in primary care:Systematic review and network meta-analysis

OBJECTIVE: To determine the most effective interventions in recently detoxified, alcohol dependent patients for implementation in primary care. DESIGN: Systematic review and network meta-analysis. DATA SOURCES: Medline, Embase, PsycINFO, Cochrane CENTRAL, ClinicalTrials.gov, and the World Health Organization's International Clinical Trials Registry Platform. STUDY SELECTION: Randomised controlled trials comparing two or more interventions that could be used in primary care. The population was patients with alcohol dependency diagnosed by standardised clinical tools and who became detoxified within four weeks. DATA EXTRACTION: Outcomes of interest were continuous abstinence from alcohol (effectiveness) and all cause dropouts (as a proxy for acceptability) at least 12 weeks after start of intervention. RESULTS: 64 trials (43 interventions) were included. The median probability of abstinence across placebo arms was 25%. Compared with placebo, the only intervention associated with increased probability of abstinence and moderate certainty evidence was acamprosate (odds ratio 1.86, 95% confidence interval 1.49 to 2.33, corresponding to an absolute probability of 38%). Of the 62 included trials that reported all cause dropouts, interventions associated with a reduced number of dropouts compared with placebo (probability 50%) and moderate certainty of evidence were acamprosate (0.73, 0.62 to 0.86; 42%), naltrexone (0.70, 0.50 to 0.98; 41%), and acamprosate-naltrexone (0.30, 0.13 to 0.67; 17%). Acamprosate was the only intervention associated with moderate confidence in the evidence of effectiveness and acceptability up to 12 months. It is uncertain whether other interventions can help maintain abstinence and reduce dropouts because of low confidence in the evidence. CONCLUSIONS: Evidence is lacking for benefit from interventions that could be implemented in primary care settings for alcohol abstinence, other than for acamprosate. More evidence from high quality randomised controlled trials is needed, as are strategies using combined interventions (combinations of drug interventions or drug and psychosocial interventions) to improve treatment of alcohol dependency in primary care. SYSTEMATIC REVIEW REGISTRATION: PROSPERO CRD42016049779