Conditional Reliability in Uncertain Graphs

Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of existence. Many approaches and problem variants have been considered in the literature, all assuming that edge-existence probabilities are fixed. Nevertheless, in real-world graphs, edge probabilities typically depend on external conditions. In metabolic networks a protein can be converted into another protein with some probability depending on the presence of certain enzymes. In social influence networks the probability that a tweet of some user will be re-tweeted by her followers depends on whether the tweet contains specific hashtags. In transportation networks the probability that a network segment will work properly or not might depend on external conditions such as weather or time of the day. In this paper we overcome this limitation and focus on conditional reliability, that is assessing reliability when edge-existence probabilities depend on a set of conditions. In particular, we study the problem of determining the k conditions that maximize the reliability between two nodes. We deeply characterize our problem and show that, even employing polynomial-time reliability-estimation methods, it is NP-hard, does not admit any PTAS, and the underlying objective function is non-submodular. We then devise a practical method that targets both accuracy and efficiency. We also study natural generalizations of the problem with multiple source and target nodes. An extensive empirical evaluation on several large, real-life graphs demonstrates effectiveness and scalability of the proposed methods.Comment: 14 pages, 13 figure

IMMEDIATE EFFECT OF INCENTIVE SPIROMETRY ON ARTERIAL BLOOD GASES ANALYSIS AFTER CORONARY BYPASS GRAFT SURGERY PATIENTS

Background: The patients who have done CABG are prone to pulmonary complications. Various physiotherapy management is present for prevention of lung complication. Literature shows lots of technique as treatment of choice, incentive spirometry is one of them. AIM: To asses immediate effect of incentive spirometry on arterial blood gas analysis in patient recently underwent coronary artery bypass surgery. Method: There was 30 patients. Blood was drawn from arterial line for pre-treatment ABG. Incentive spirometry was given 10 reps and 3 sets. Patient was prop up 30-40 degree. Romsons tri colour volume spirometry is used. Mouthpiece was placed in patient's mouth and made a good seal over the mouthpiece with lips. Exhaled through nose normally then breathe in slowly through mouth. Ball in the incentive spirometer will go up. The patient to hold or rise the ball as high as possible and hold it for 3 or 5 seconds the slowly exhale. This was done for 10 to 15 times. Blood was drawn from arterial line for post treatment ABG. Result: There was statistically extremely significant change in value of PaO2 (112.54 ±39.46 vs133.01 ±42.13) p value <0.0001, PaCO2 (38.75 ±4.2 vs 36.9 ±3.7) p value 0.0003 and SaO2 (96.8 ±1.84 vs 98.93 ±1.11) p value <0.0001 Conclusion: This study shows that there is immediate effect of Incentive Spirometry on ABG analysis in CABG surgery patient by significant improvement of PaO2 and SaO2 and decrease in PaCO2. Keywords: Incentive spirometry; Arterial blood gas analysis; Coronary artery bypass graft surgery

IMMEDIATE EFFECT OF INCENTIVE SPIROMETRY ON ARTERIAL BLOOD GASES ANALYSIS AFTER CORONARY BYPASS GRAFT SURGERY PATIENTS

Background: The patients who have done CABG are prone to pulmonary complications. Various physiotherapy management is present for prevention of lung complication. Literature shows lots of technique as treatment of choice, incentive spirometry is one of them. AIM: To asses immediate effect of incentive spirometry on arterial blood gas analysis in patient recently underwent coronary artery bypass surgery. Method: There was 30 patients. Blood was drawn from arterial line for pre-treatment ABG. Incentive spirometry was given 10 reps and 3 sets. Patient was prop up 30-40 degree. Romsons tri colour volume spirometry is used. Mouthpiece was placed in patient\u27s mouth and made a good seal over the mouthpiece with lips. Exhaled through nose normally then breathe in slowly through mouth. Ball in the incentive spirometer will go up. The patient to hold or rise the ball as high as possible and hold it for 3 or 5 seconds the slowly exhale. This was done for 10 to 15 times. Blood was drawn from arterial line for post treatment ABG. Result: There was statistically extremely significant change in value of PaO2 (112.54 ±39.46 vs133.01 ±42.13) p value <0.0001, PaCO2 (38.75 ±4.2 vs 36.9 ±3.7) p value 0.0003 and SaO2 (96.8 ±1.84 vs 98.93 ±1.11) p value <0.0001 Conclusion: This study shows that there is immediate effect of Incentive Spirometry on ABG analysis in CABG surgery patient by significant improvement of PaO2 and SaO2 and decrease in PaCO2. Keywords: Incentive spirometry; Arterial blood gas analysis; Coronary artery bypass graft surgery

Classification, reduction and stability of toric principal bundles

Let $X$ be a complex toric variety equipped with the action of an algebraic torus $T$, and let $G$ be a complex linear algebraic group. We classify all $T$-equivariant principal $G$-bundles $\mathcal{E}$ over $X$ and the morphisms between them. When $G$ is connected and reductive, we characterize the equivariant automorphism group $\text{Aut}_T(\mathcal{E} )$ of $\mathcal{E}$ as the intersection of certain parabolic subgroups of $G$ that arise naturally from the $T$-action on $\mathcal{E}$. We then give a criterion for the equivariant reduction of the structure group of $\mathcal{E}$ to a Levi subgroup of $G$ in terms of $\text{Aut}_T(\mathcal{E} )$. We use it to prove a principal bundle analogue of Kaneyama's theorem on equivariant splitting of torus equivariant vector bundles of small rank over a projective space. When $X$ is projective and $G$ is connected and reductive, we show that the notions of stability and equivariant stability are equivalent for any $T$-equivariant principal $G$-bundle over $X$.Comment: 47 page

Distributed Graph Embedding with Information-Oriented Random Walks

Graph embedding maps graph nodes to low-dimensional vectors, and is widely adopted in machine learning tasks. The increasing availability of billion-edge graphs underscores the importance of learning efficient and effective embeddings on large graphs, such as link prediction on Twitter with over one billion edges. Most existing graph embedding methods fall short of reaching high data scalability. In this paper, we present a general-purpose, distributed, information-centric random walk-based graph embedding framework, DistGER, which can scale to embed billion-edge graphs. DistGER incrementally computes information-centric random walks. It further leverages a multi-proximity-aware, streaming, parallel graph partitioning strategy, simultaneously achieving high local partition quality and excellent workload balancing across machines. DistGER also improves the distributed Skip-Gram learning model to generate node embeddings by optimizing the access locality, CPU throughput, and synchronization efficiency. Experiments on real-world graphs demonstrate that compared to state-of-the-art distributed graph embedding frameworks, including KnightKing, DistDGL, and Pytorch-BigGraph, DistGER exhibits 2.33x-129x acceleration, 45% reduction in cross-machines communication, and > 10% effectiveness improvement in downstream tasks