On Approximating the Number of kk-cliques in Sublinear Time

We study the problem of approximating the number of $k$-cliques in a graph when given query access to the graph. We consider the standard query model for general graphs via (1) degree queries, (2) neighbor queries and (3) pair queries. Let $n$ denote the number of vertices in the graph, $m$ the number of edges, and $C_k$ the number of $k$-cliques. We design an algorithm that outputs a $(1+\varepsilon)$-approximation (with high probability) for $C_k$, whose expected query complexity and running time are O\left(\frac{n}{C_k^{1/k}}+\frac{m^{k/2}}{C_k}\right)\poly(\log n,1/\varepsilon,k). Hence, the complexity of the algorithm is sublinear in the size of the graph for $C_k = \omega(m^{k/2-1})$. Furthermore, we prove a lower bound showing that the query complexity of our algorithm is essentially optimal (up to the dependence on $\log n$, $1/\varepsilon$ and $k$). The previous results in this vein are by Feige (SICOMP 06) and by Goldreich and Ron (RSA 08) for edge counting ($k=2$) and by Eden et al. (FOCS 2015) for triangle counting ($k=3$). Our result matches the complexities of these results. The previous result by Eden et al. hinges on a certain amortization technique that works only for triangle counting, and does not generalize for larger cliques. We obtain a general algorithm that works for any $k\geq 3$ by designing a procedure that samples each $k$-clique incident to a given set $S$ of vertices with approximately equal probability. The primary difficulty is in finding cliques incident to purely high-degree vertices, since random sampling within neighbors has a low success probability. This is achieved by an algorithm that samples uniform random high degree vertices and a careful tradeoff between estimating cliques incident purely to high-degree vertices and those that include a low-degree vertex

External Sampling

36th International Colloquium, ICALP 2009, Rhodes, Greece, July 5-12, 2009, Proceedings, Part IWe initiate the study of sublinear-time algorithms in the external memory model [1]. In this model, the data is stored in blocks of a certain size B, and the algorithm is charged a unit cost for each block access. This model is well-studied, since it reflects the computational issues occurring when the (massive) input is stored on a disk. Since each block access operates on B data elements in parallel, many problems have external memory algorithms whose number of block accesses is only a small fraction (e.g. 1/B) of their main memory complexity. However, to the best of our knowledge, no such reduction in complexity is known for any sublinear-time algorithm. One plausible explanation is that the vast majority of sublinear-time algorithms use random sampling and thus exhibit no locality of reference. This state of affairs is quite unfortunate, since both sublinear-time algorithms and the external memory model are important approaches to dealing with massive data sets, and ideally they should be combined to achieve best performance. In this paper we show that such combination is indeed possible. In particular, we consider three well-studied problems: testing of distinctness, uniformity and identity of an empirical distribution induced by data. For these problems we show random-sampling-based algorithms whose number of block accesses is up to a factor of 1/√B smaller than the main memory complexity of those problems. We also show that this improvement is optimal for those problems. Since these problems are natural primitives for a number of sampling-based algorithms for other problems, our tools improve the external memory complexity of other problems as well.David & Lucile Packard Foundation (Fellowship)Center for Massive Data Algorithmics (MADALGO)Marie Curie (International Reintegration Grant 231077)National Science Foundation (U.S.) (Grant 0514771)National Science Foundation (U.S.) (Grant 0728645)National Science Foundation (U.S.) (Grant 0732334)Symantec Research Labs (Research Fellowship

Demonstration of the histopathological and immunohistochemical effects of a novel hemostatic agent, ankaferd blood stopper, on vascular tissue in a rat aortic bleeding model

Background: Ankaferd Blood Stopper®(ABS) is a folkloric medicinal plant extract used as a hemostatic agent in traditional Turkish medicine. This experimental study investigated the histopathological and immunohistochemical effects of ABS on vascular tissue in a rat model of aortic bleeding.Methods: Four groups of 11 Wistar albino rats were used. The abdominal aortas of the rats were wounded; an ABS-soaked tampon was applied to rats in Groups 1 and 3, and a plain gauze tampon was applied to rats in Groups 2 and 4 until the bleeding stopped. The bleeding time was recorded. Immediately following sacrificing, the arteriotomy sites from Groups 1 and 2 were removed. The abdominal incisions in Groups 3 and 4 were closed following hemostasis. On Day 7 of the study, Group 3 and 4 rats were sacrificed and the abdominal aorta arteriotomy sites were removed for histopathological and immunohistochemical evaluation.Results: The mean bleeding time in 15 animals in Groups 2 and 4 was 4.9 ± 0.6 s, and in 22 animals in Groups 1 and 3 was 3.1 ± 0.6 s. Distal aortic occlusion was not observed on either Day 1 or 7 in any group. Significantly more widespread and dense endothelial nitric oxide synthase (eNOS) staining was observed in Group 1 animals than Group 2. On Days 1 and 7 after application of ABS, histopathological changes, consisting of necrosis, inflammation, and endothelial cell loss, in the rat abdominal aortas did not differ between Groups 1 and 2. The basophilic discoloration in the ABS group on the operation day was a result of a foreign body reaction and hemosiderin-loaded histiocyte accumulation, which occurred on Day 7.Conclusions: In this study, hemostasis was successfully achieved with ABS in rat abdominal aortas. No histopathological change was found in the rat abdominal aortas between the ABS and control groups on Days 1 and 7. Further studies on the long-term effects of foreign body reactions and hemosiderin-loaded histiocyte accumulation are required. © 2010 Kandemir et al; licensee BioMed Central Ltd

Intrauterine growth restriction and placental angiogenesis

Background: Vascular endothelial growth factor (VEGF), basic-fibroblast growth factor (b-FGF), and endothelial nitric oxide synthase (eNOS) are factors that take part in placental angiogenesis. They are highly expressed during embryonic and fetal development, especially in the first trimester. In this study, we aimed to investigate the role of placental angiogenesis in the development of intrauterine growth restriction (IUGR) by comparing the levels of expression of VEGF-A, b-FGF, and eNOS in normal-term pregnancy and IUGR placentas.Methods: The expression of VEGF-A, b-FGF, and eNOS was studied using the avidin-biotin-peroxidase method in placental tissues diagnosed as normal (n = 55) and IUGR (n = 55). Results were evaluated in a semi-quantitative manner.Results: The expression of all the markers was significantly higher (p < 0.001) in cytotrophoblasts, syncytiotrophoblasts, extravillous trophoblasts, vascular smooth muscle cells, chorionic villous stromal cells, and villous vascular endothelial cells of the IUGR placentas when compared with those collected from normal-term pregnancies.Conclusion: Increased expression of VEGF-A, b-FGF, and eNOS may be the result of inadequate uteroplacental perfusion, supporting the proposal that abnormal angiogenesis plays a role in the pathophysiology of IUGR. © 2010 Barut et al; licensee BioMed Central Ltd

Adhesion and proliferation of living cell on surface functionalized with glycine nanostructures

This research presents the application of glycine amino acid for establishing firm cell-substrate interaction instead of expensive adhesion proteins, peptides and peptide derivatives. The glycine amino acid is chemically functionalized on the coverslip to achieve self-assembled nanostructure. Glycine self-assembly on NaCl treated coverslips is initiated with SiONa+:COO− linkage while their nanostructure is achieved with formation of glycine chain through NH3+:COO− covalent linkage between the adjacent molecules. The functionalization steps are confirmed by Fourier-transform infrared spectroscopy (FTIR) investigation. The atomic force microscopy (AFM) and scanning electron microscopy (SEM) investigations reveal that glycine growth initiates at 4 Hours (H) post-treatment while maximum growth appears after 8H-10H. Both the vertical and horizontal growth of nanostructures show dependence on functionalization periods. Various levels of glycine functionalized surface show different levels of baby hamster kidney (BHK-21) cell adhesion and proliferation efficiency with maximum performance for 10H functionalized surface. The adhesion and proliferation performance of 10H glycine functionalized surface shows negligible difference when compared with glycine-aspartic acid (RGD) functionalized surface. Finally, growth curves obtained from both glycine and RGD functionalized surface reveal exponential growth phage up to 48H followed by stationary phage between 48H and 72H while death of many cells appears from 72H to 96H. Thus, this research concluded that glycine functionalized surface is equally effective for cell adhesion and proliferation

The Oil Searching Problem

Abstract. Given n potential oil locations, where each has oil at a certain depth, we seek good trade-offs between the number of oil sources found and the total amount of drilling performed. The cost of exploring a location is proportional to the depth to which it is drilled. The algorithm has no clue about the depths of the oil sources at the different locations or even if there are any. Abstraction of the oil searching problem applies naturally to several life contexts. Consider a researcher who wants to decide which research problems to invest time into. A natural dilemma whether to invest all the time into a few problems, or share time across many problems. When you have spent a lot of time on one problem with no success, should you continue or move to another problem? One could study this problem using a competitive analysis that compares the cost of an algorithm to that of an adversary that knows the depths of the oil sources, but the competitive ratio of the best algorithm for this problem is Ω(n). Instead we measure the performance of a strategy by comparing it to a weaker adversary that knows the set of depths of the oil sources but does not know which location has what depth. Surprisingly, we find that to find k oil sources there is a strategy whose cost is close to that of any adversary that has this limited knowledge of only the set of depths. In particular, we show that if any adversary can find k oil sources with drilling cost B while knowing the set of depths, our strategy finds k − Õ(k5/6) sources with drilling cost B(1+o(1)). This proves that our strategy is very close to the best possible strategy in the total absence of information.

Primary intestinal diffuse large B-cell lymphoma forming multiple lymphomatous polyposis

Multifocal and skip involvement is quite a rare developmental pattern for primary gastrointestinal lymphomas. A 25-year-old male patient with diffuse large B-cell lymphoma of the small intestine, with macroscopic features and clinical aspects imitating Crohn's disease and attracting attention with cobblestone-like appearance, is presented herein together with the clinical and pathological features. Multiple ulcerated lesions were also observed infiltrating the serosa with polypoid appearance, 2.5 cm in largest diameter, within the resected jejunoileal specimen, which displayed patchy, healthy-appearing mucosal areas. In microscopic examination, a tumoral infiltration was observed comprised of pleomorphic, atypical lymphoid cells with abundant eosinophilic cytoplasm, marked nucleoli and vesicular nuclei. A B-cell phenotype immunoreaction was observed by vimentin, LCA, CD20, and CD79a in those atypical cells. The diagnosis of the case was diffuse large B-cell lymphoma.The possibility of the presence of this disorder, although rare, is emphasized here for patients applying to the hospital with the signs and symptoms of Crohn's disease