Improved Bounds for the Excluded-Minor Approximation of Treedepth

Treedepth, a more restrictive graph width parameter than treewidth and pathwidth, plays a major role in the theory of sparse graph classes. We show that there exists a constant C such that for every integers a,b >= 2 and a graph G, if the treedepth of G is at least Cab log a, then the treewidth of G is at least a or G contains a subcubic (i.e., of maximum degree at most 3) tree of treedepth at least b as a subgraph. As a direct corollary, we obtain that every graph of treedepth Omega(k^3 log k) is either of treewidth at least k, contains a subdivision of full binary tree of depth k, or contains a path of length 2^k. This improves the bound of Omega(k^5 log^2 k) of Kawarabayashi and Rossman [SODA 2018]. We also show an application for approximation algorithms of treedepth: given a graph G of treedepth k and treewidth t, one can in polynomial time compute a treedepth decomposition of G of width O(kt log^{3/2} t). This improves upon a bound of O(kt^2 log t) stemming from a tradeoff between known results. The main technical ingredient in our result is a proof that every tree of treedepth d contains a subcubic subtree of treedepth at least d * log_3 ((1+sqrt{5})/2)

The role of MMP-12 gene polymorphism - 82 A-to-G (rs2276109) in immunopathology of COPD in polish patients : a case control study

Table 1S. Logistic regression analysis of association between -82 A-to-G SNP of MMP12 gene (rs2276109) and COPD – the multiple inheritance models. Description of data: This table contains the logistic regression results of modeled association between SNP rs2276109 of MMP12 gene and COPD. (DOCX 16 kb

The development of a minimally invasive zygoma fracture repair technique

Zygoma fractures are common and may potentially lead to negative aesthetic and functional consequences: cheek asymmetry, ocular globe asymmetry, infra-orbital nerve dysfunction. There has been a significant evolution in the treatment of zygoma fractures, with general transition from older, closed techniques to newer methods that involve greater exposure, more visualized reduction and increased stability of fixation. Little objective data is present to demonstrate the superiority of either technique. It is our hypothesis that each technique has significant disadvantages and the ultimate objective of this thesis was to develop and quantitatively demonstrate the superiority of a novel method of repair.First, we developed a quantitative method of zygoma position evaluation and demonstrated its validity and reliability in a clinical setting. Second, we quantitatively compared the accuracy and complication rates of closed and ORIF methods, demonstrating that although increased exposure improves accuracy, it carries a significant risk of access related complications. Third, we showed that routine orbital floor exploration is not necessary in the majority of zygoma fractures and thus the relatively high-risk incision required to perform it may typically be avoided. Fourth, we developed a c-arm imaging technique that allows for visualization of the zygoma and comparison of its position to the contra-lateral, uninjured side. The accuracy of the technique was shown in a cadaver zygoma fracture model. The technique was modified for clinical use by the addition of an intra-oral incision allowing fracture reduction with the c-arm in-situ as well as miniplate placement in an inconspicuous location. Last, the accuracy of the technique, its low complication profile and practicality were demonstrated in a clinical patient series.Les fractures du zygoma sont communes et peuvent potentiellement mener à desconséquences esthétiques et fonctionnelles négatives: asymétries des joues, globeoculaire asymétrique, nerf infra-orbital dysfonctionnel. Il y a eut une évolutionsignificative dans le traitement des fractures du zygoma, avec une transition générale detechniques plus anciennes et fermées, à de nouvelles méthodes qui impliquent une plusgrande exposition, une réduction plus visualisée et une augmentation de la stabilité defixation. Peu de données objectives sont aujourd’hui présentes qui pourraient démontrerla supériorité de l’une ou de l’autre technique. C’est notre hypothèse que chaquetechnique a des inconvénients importants et l’ultime objectif de cette thèse était dedévelopper et de démontrer de manière quantitative la supériorité d’une méthode deréparation innovante.D’abord, nous avons développé une méthode quantitative d’évaluation de laposition du zygoma et avons démontré sa validité et sa fiabilité dans un cadre médical. Ensecond lieu, nous avons comparé de manière quantitative la précision et les taux decomplications de méthodes fermées et ORIF, démontrant que bien que l’augmentation del’exposition permette d’augmenter le niveau de précision, elle porte un risque importantde complications dues à l’accession. Troisièmement, nous avons démontré quel’exploration routinière du plancher orbital n’est pas nécessaire dans la majorité desfractures du zygoma et donc que l’incision à relativement hauts-risques nécessaire pourl’exécuter peut être généralement évitée. Quatrièmement, nous avons développé unetechnique d’imagerie avec arceau « c-arm » qui permet une visualisation du zygoma etune comparaison de sa position par rapport au côté contra-latéral non blessé. La précisionde la technique a été démontrée sur un modèle cadavérique d’une fracture du zygoma. Latechnique a été modifiée pour son utilisation médicale en y ajoutant une incision intraoralpermettant la réduction de la fracture avec l’arceau « c-arm » in-situ ainsi que leplacement d’une mini plaque a un endroit discret. Enfin, la précision de la technique, sonpeu de risques au niveau des complications et son aspect pratique ont tous été démontrésdans une série de patients médicaux

Error Mitigation Methods for FSM Using Triple Modular Redundancy

In many areas of operation, application-specific logic implemented in FPGAs (Field Programmable Gate Arrays) is critical. In these situations, various mitigation methods are used to reduce or completely eliminate malfunctions in the circuit resulting from undesired physical phenomena (e.g., ionizing radiation). Such phenomena may occur, among others, in medicine, the military, nuclear power, and space systems. One of the most popular methods is the use of triple modular redundancy (TMR). Here, the FPGA provides a good basis for building TMR-based safety-critical systems due to its concurrent processing. This paper presents an overview of the implementation of logic structures using TMR. In this paper, the authors focus on different concepts for the implementation of FSMs. The different concepts differ in the way TMR voters are attached and the extent of redundancy of the individual FSM components. The article compares the efficiency of the different solutions. In order to evaluate this efficiency, it is crucial to determine the logic utilization or the power consumption of a given implementation. In the experimental part of the article, the authors show the results of the synthesis of FSM benchmarks, for different mitigation models. The synthesis was carried out for both commercial and academic tools

Performance Testing of the Triple Modular Redundancy Mitigation Circuit Test Environment Implementation in Field Programmable Gate Array Structures

The logic structures implemented in Field Programmable Gate Arrays (FPGAs) are often critical and their correct operation is vital. FPGA devices are often used in areas where there is increased ionising radiation (space, medical diagnostics, aviation or nuclear power). There is therefore a need for mechanisms to correct radiation-induced errors. A common approach is the redundant implementation of particularly critical parts of the logic structure. By triplicating selected fragments, it is possible not only to detect potential errors but also to correct them. Such an approach is called triple modular redundancy (TMR), and its essence lies in the use of specialised voting circuits called voters, which allow the erroneous results of individual subcircuits to be eliminated by voting. The triplicate circuit under consideration, together with the voter, constitutes the mitigation structure. It becomes necessary to develop a test environment to assess the correct operation of these circuits. Also key is the efficiency of the implementation of these structures, which can be related to the occupation of logical resources or the power consumption of a given implementation. This paper demonstrates the essence of implementing a test environment to test the correctness of the mitigation of logic structures using TMR voters. An error injector mechanism using the Pseudo-Random Bit Sequence (PRBS) register is proposed, which introduces an element of randomness into the testing process. The aim of this research is to determine the implementation efficiency of the proposed test environment. In the experimental part, the implementation costs of the proposed solution were examined. The results indicate that between 66 and 109 LUT blocks were required to implement the error injector, corresponding to a relatively small increase in dynamic power consumption: by 22% for combinational circuits and by 37% for sequential circuits