Some New Bounds For Cover-Free Families Through Biclique Cover

An $(r,w;d)$ cover-free family $(CFF)$ is a family of subsets of a finite set such that the intersection of any $r$ members of the family contains at least $d$ elements that are not in the union of any other $w$ members. The minimum number of elements for which there exists an $(r,w;d)-CFF$ with $t$ blocks is denoted by $N((r,w;d),t)$. In this paper, we show that the value of $N((r,w;d),t)$ is equal to the $d$-biclique covering number of the bipartite graph $I_t(r,w)$ whose vertices are all $w$- and $r$-subsets of a $t$-element set, where a $w$-subset is adjacent to an $r$-subset if their intersection is empty. Next, we introduce some new bounds for $N((r,w;d),t)$. For instance, we show that for $r\geq w$ and $r\geq 2$ $$N((r,w;1),t) \geq c{{r+w\choose w+1}+{r+w-1 \choose w+1}+ 3 {r+w-4 \choose w-2} \over \log r} \log (t-w+1),$$ where $c$ is a constant satisfies the well-known bound $N((r,1;1),t)\geq c\frac{r^2}{\log r}\log t$. Also, we determine the exact value of $N((r,w;d),t)$ for some values of $d$. Finally, we show that $N((1,1;d),4d-1)=4d-1$ whenever there exists a Hadamard matrix of order 4d

D’égal à égal ? Herméneutique critique du dialogue initié par l’État avec les musulmans d’Allemagne

Cet article analyse le dialogue interculturel en Allemagne grâce à l’outil conceptuel que représente l’herméneutique critique de Gadamer. Le point de départ en est le Deutsche Islam Konferenz (DIK), une initiative de dialogue avec les musulmans menée par l’État en Allemagne. À partir de l’idée de Gadamer du caractère processuel du dialogue et d’une ouverture principielle à la différence de l’autre, je souhaite montrer que le DIK trouve ses origines bien plus dans une politique d’intégration que dans une idée de « compréhension » mutuelle. Plutôt que de délinéer une réflexion critique sur les prémisses d’un « travail de l’histoire » (Wirkungsgeschichte) propre à un individu et d’une révision potentielle de ces prémisses à travers la rencontre, cet article suggère qu’un tel événement dialogique se base sur l’assomption d’une normalité de soi et d’une déviance d’autrui à transformer. En donnant la parole à certains représentants musulmans et à leur refus de se transformer unilatéralement, j’avance que les retombées de telles mesures de dialogue n’en sont pas moins ouvertes et ambivalentes.This article analyses intercultural dialogue in Germany through the conceptual tool of Gadamer’s critical hermeneutics. The starting point is the Deutsche Islam Konferenz (DIK), a state-led dialogue initiative with Muslims in Germany. Starting from Gadamer’s idea of the procedural character of dialogue and a principled openness towards the difference of the other, I argue that the DIK is in the first place anchored in politics of integration and less in the ideal of mutual « understanding ». Instead of encompassing a critical reflection upon the premises of one’s own « history of effect » (Wirkungsgeschichte) and a potential revision of these through the encounter, the article suggests that this dialogical event is based on the assumption of the normalcy of the self and the deviation of the other to be transformed. Introducing the voices of some Muslim representatives and their refusal to one-sidedly transform, I claim that the outcomes of such dialogue measures are nonetheless open and ambivalent.Este artículo analiza el diálogo intercultural en Alemania gracias a la herramienta conceptual que representa la hermenéutica crítica de Gadamer. El punto de partida es la Deutsche Islam Konferenz (DIK), una iniciativa de diálogo con los musulmanes dirigida por el Estado en Alemania. Partiendo de la idea de Gadamer del carácter procesual del diálogo y de una apertura principial a la diferencia del otro, este artículo desea mostrar que la DIK encuentra sus orígenes más bien en una política de integración que en una idea de “comprensión” mutua. Más que delinear una reflexión crítica acerca de las premisas de un “trabajo de la historia” (Wirkungsgeschichte) propia a un individuo y de una revisión potencial de sus premisas a través del encuentro, este artículo sugiere que tal evento dialógico se basa en la asunción de una normalidad de sí mismo y una desviación del otro que debe ser transformada. Al dar la palabra a ciertos representantes musulmanes y su rechazo a transformarse unilateralmente, el artículo señala que los resultados de tales medidas de diálogo no son menos abiertos y ambivalentes

Alpha-tocotrienol as a possible indicator for monitoring the presence of palm mid-fraction in dark chocolate

The compositional variations of tocopherols and tocotrienols composition of the genuine CB and PMF were investigated to introduce a more reliable indicator in detecting as well as quantifying the PMF in CB. The results suggested that the α-tocotrienol data presented could be utilized for the detection of the PMF admixture to CB. Detection and of PMF admixture to CB in a chocolate model system was conducted using α-tocotrienol as an indicator. This study focused on mono-addition of PMF to CB. The PMF was added to CB at 1, 2, 3, 4, 5, 10, 15, 20 and 25% levels. HPLC was used to detect the presence of PMF admixture to CB. The results derived from the model system indicated that by increasing the PMF amount at 0 to 15% to CB resulted in an increase in the concentration of the α-tocotrienol significantly (P<0.05). However, the addition of PMF amount more than 15% did not have any effect on the α-tocotrienol concentration. A linear plot with a high correlation of 0.9967 was obtained with standard error (SE) of 1.527. The PMF amount in chocolate was at 1.4, 2.8, 4.2, 5.6, 5.9, 6.2, 6.4, 6.7 and 7% levels. There was a significant difference (P<0.05) between the detected concentrations of the α-tocotrienol when the amount of the PMF was increased from 1.4% to 5.6%. However, the addition of PMF amount at 5.6 to 6.4% level did not have any effect on α-tocotrienol concentration. The interesting results were obtained when the amount of the PMF was increased from 6.4 to 7% where a significant difference was observed. A linear plot (R2 = 0.9837) was obtained with SE of 1.986. A validation test was conducted to verify the equation obtained from the regression analysis. The high correlation obtained indicated a good accuracy, reflecting a close relationship between the predicted and actual values obtained by theoretical and experimental, respectively. From these studies the use of α-tocotrienol as a promising indicator for detection and quantification of PMF in chocolate was demonstrated. The results suggested that the amount of the added PMF in the CB in chocolate was predictable in the condition when smaller and more than 5% PMF was added. Therefore, it can be concluded that the identification of the foreign fat added was made possible because only one type of the foreign fat was added in this experiment scheme

Characterization of Cardiomyopathy in a Mouse Model of Duchenne Muscular Dystrophy (DMD) Using Echocardiography, DCE-CT, and PET-FDG

Duchenne muscular dystrophy (DMD) is an X-linked recessive neuromuscular disease that is the result of a loss of functional dystrophin, which causes cardiomyocyte fibrosis and death, leading to cardiomyopathy. In this thesis, I have utilized dynamic contrast-enhanced computed tomography (DCE-CT), positron emission tomography-fluorodeoxyglucose (PET-FDG), echocardiography, and traditional histology to longitudinally assess disease progression and degree of cardiomyopathy in a murine model of DMD (mdx:utrn-/-). No significant changes were observed in the blood flow, blood volume, or cardiac volume measured via DCE-CT, nor in standard uptake value (SUV) of glucose as measured by PET-FDG in the left myocardium between and within the two study groups (of mdx:utrn -/- mice and healthy wild-type mice) over time. Our pilot echocardiography study and histological results show possible morphological/architectural and functional changes in affected myocardia of mdx:utrn-/- mice. These findings may provide us with an avenue to longitudinally characterize the progression of cardiomyopathy in the murine model of DMD, mdx:utrn -/- , in addition to providing a potential baseline for a comparison with future therapeutics