Fast Spectral Clustering Using Autoencoders and Landmarks

In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we first build the adjacency matrix of the corresponding graph of the dataset. To build this matrix, we only consider a limited number of points, called landmarks, and compute the similarity of all data points with the landmarks. Then, we present a definition of the Laplacian matrix of the graph that enable us to perform eigen decomposition efficiently, using a deep autoencoder. The overall complexity of the algorithm for eigen decomposition is $O(np)$, where $n$ is the number of data points and $p$ is the number of landmarks. At last, we evaluate the performance of the algorithm in different experiments.Comment: 8 Pages- Accepted in 14th International Conference on Image Analysis and Recognitio

Approximate Consensus in Highly Dynamic Networks: The Role of Averaging Algorithms

In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate consensus is solvable if and only if the communication graph in each round has a rooted spanning tree, i.e., there is a coordinator at each time. The striking point in this result is that the coordinator is not required to be unique and can change arbitrarily from round to round. Interestingly, the class of averaging algorithms, which are memoryless and require no process identifiers, entirely captures the solvability issue of approximate consensus in that the problem is solvable if and only if it can be solved using any averaging algorithm. Concerning the time complexity of averaging algorithms, we show that approximate consensus can be achieved with precision of $\varepsilon$ in a coordinated network model in $O(n^{n+1} \log\frac{1}{\varepsilon})$ synchronous rounds, and in $O(\Delta n^{n\Delta+1} \log\frac{1}{\varepsilon})$ rounds when the maximum round delay for a message to be delivered is $\Delta$. While in general, an upper bound on the time complexity of averaging algorithms has to be exponential, we investigate various network models in which this exponential bound in the number of nodes reduces to a polynomial bound. We apply our results to networked systems with a fixed topology and classical benign fault models, and deduce both known and new results for approximate consensus in these systems. In particular, we show that for solving approximate consensus, a complete network can tolerate up to 2n-3 arbitrarily located link faults at every round, in contrast with the impossibility result established by Santoro and Widmayer (STACS '89) showing that exact consensus is not solvable with n-1 link faults per round originating from the same node

Baryon Washout, Electroweak Phase Transition, and Perturbation Theory

We analyze the conventional perturbative treatment of sphaleron-induced baryon number washout relevant for electroweak baryogenesis and show that it is not gauge-independent due to the failure of consistently implementing the Nielsen identities order-by-order in perturbation theory. We provide a gauge-independent criterion for baryon number preservation in place of the conventional (gauge-dependent) criterion needed for successful electroweak baryogenesis. We also review the arguments leading to the preservation criterion and analyze several sources of theoretical uncertainties in obtaining a numerical bound. In various beyond the standard model scenarios, a realistic perturbative treatment will likely require knowledge of the complete two-loop finite temperature effective potential and the one-loop sphaleron rate.Comment: 25 pages, 9 figures; v2 minor typos correcte

Alpha-fetoprotein kinetics in patients with hepatocellular carcinoma receiving ramucirumab or placebo: An analysis of the phase 3 REACH study

Background: Post-hoc analyses of AFP response and progression and their relationship with objective measures of response and survival were performed in patients from REACH. Methods: Serum AFP was measured at baseline and every 3 cycles (2 weeks/cycle). Associations between AFP and radiographic progression and efficacy end points were analysed. Results: Median percent AFP increase from baseline was smaller in the ramucirumab than in the placebo arm throughout treatment. Time to AFP progression (HR 0.621; P < 0.0001) and to radiographic progression (HR 0.613; P < 0.0001) favoured ramucirumab. Association between AFP and radiographic progression was shown at 6 (OR 6.44, 95% CI 4.03, 10.29; P < 0.0001) and 12 weeks (OR 2.28, 95% CI 1.47, 3.53; P = 0.0002). AFP response was higher with ramucirumab compared with placebo (P < 0.0001). More patients in the ramucirumab arm experienced tumour shrinkage and AFP response compared with placebo. Survival was longer in patients with AFP response (13.6 months) than in patients without (6.2 months), irrespective of treatment (HR 0.457, P < 0.0001). Conclusions: Treatment with ramucirumab prolonged time to AFP progression, slowed AFP increase and was more likely to induce AFP response. Similar benefits in radiographic progression and response correlated with AFP changes

The Sphaleron Rate in SU(N) Gauge Theory

The sphaleron rate is defined as the diffusion constant for topological number NCS = int g^2 F Fdual/32 pi^2. It establishes the rate of equilibration of axial light quark number in QCD and is of interest both in electroweak baryogenesis and possibly in heavy ion collisions. We calculate the weak-coupling behavior of the SU(3) sphaleron rate, as well as making the most sensible extrapolation towards intermediate coupling which we can. We also study the behavior of the sphaleron rate at weak coupling at large Nc.Comment: 18 pages with 3 figure

Left sided inferior vena cava duplication and venous thromboembolism: case report and review of literature

The etiology of venous thromboembolism in young patients is frequently associated with hereditary coagulation abnormalities, immunologic diseases, and neoplasia. The advent of radiological advances, namely Computed Tomography (CT) scans and venography has identified vena cava malformations as a new etiologic factor worthy of consideration. In this case report, we describe the unusual occurrence of venous thromboembolism in association with a duplicated inferior vena cava. Duplications of the inferior vena cava (IVC) are seen with an incidence of 0.2% to 3.0% in the general population. Embryogenesis of the IVC is a complex process involving the intricate formation and regression of numerous anastomoses, potentially leading to various anomalies. We present a 23-year-old Caucasian woman with IVC duplication who developed a deep venous thrombosis and multiple pulmonary emboli. Anomaly of the IVC is a rare example of a congenital condition that predisposes to thromboembolism, presumably by favoring venous stasis. This diagnosis should be considered in patients under the age of 30 with spontaneous occurrence of blood clots

High apex predator biomass on remote Pacific islands

Author Posting. © The Author(s), 2006. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Coral Reefs 26 (2007): 47-51, doi:10.1007/s00338-006-0158-x.On coral reefs in Palmyra—a central Pacific atoll with limited fishing pressure—total fish biomass is 428 and 299% greater than on reefs in nearby Christmas and Fanning Islands. Large apex predators –groupers, sharks, snappers, and jacks larger than 50 cm in length- account for 56% of total fish biomass in Palmyra on average, but only 7% and 3% on Christmas and Fanning. These biomass proportions are remarkably similar to those previously reported for the remote and uninhabited Northwest Hawaiian Islands (NWHI) and densely populated Main Hawaiian Islands (MHI), although Palmyra’s reefs are dominated in biomass by sharks (44% of the total), whereas the NWHI by jacks (39%). Herbivorous fish biomass was also greater on Palmyra than on Christmas and Fanning (343% and 207%, respectively). These results and previous findings indicate that remote, uninhabited islands support high levels of consumers, and highlight the importance of healthy coral reef ecosystems as reference points for assessment of human impacts and establishment of restoration goals

The physics of spreading processes in multilayer networks

The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (i.e., "multiplexity") among their constituent components and/or multiple interacting subsystems. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent "multilayer" approach for modeling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. On one hand, it allows one to couple different structural relationships by encoding them in a convenient mathematical object. On the other hand, it also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation. Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure.Comment: 25 pages, 4 figure

Excluding Electroweak Baryogenesis in the MSSM

In the context of the MSSM the Light Stop Scenario (LSS) is the only region of parameter space that allows for successful Electroweak Baryogenesis (EWBG). This possibility is very phenomenologically attractive, since it allows for the direct production of light stops and could be tested at the LHC. The ATLAS and CMS experiments have recently supplied tantalizing hints for a Higgs boson with a mass of ~ 125 GeV. This Higgs mass severely restricts the parameter space of the LSS, and we discuss the specific predictions made for EWBG in the MSSM. Combining data from all the available ATLAS and CMS Higgs searches reveals a tension with the predictions of EWBG even at this early stage. This allows us to exclude EWBG in the MSSM at greater than (90) 95% confidence level in the (non-)decoupling limit, by examining correlations between different Higgs decay channels. We also examine the exclusion without the assumption of a ~ 125 GeV Higgs. The Higgs searches are still highly constraining, excluding the entire EWBG parameter space at greater than 90% CL except for a small window of m_h ~ 117 - 119 GeV.Comment: 24 Pages, 4 Figures (v3: fixed typos, minor corrections, added references