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We propose a technique that we call HodgeRank for ranking data that may be incomplete and imbalanced, characteristics common in modern datasets coming from e-commerce and internet applications. We are primarily interested in cardinal data based on scores or ratings though our methods also give specific insights on ordinal data. From raw ranking data, we construct pairwise rankings, represented as edge flows on an appropriate graph. Our statistical ranking method exploits the graph Helmholtzian, which is the graph theoretic analogue of the Helmholtz operator or vector Laplacian, in much the same way the graph Laplacian is an analogue of the Laplace operator or scalar Laplacian. We shall study the graph Helmholtzian using combinatorial Hodge theory, which provides a way to unravel ranking information from edge flows. In particular, we show that every edge flow representing pairwise ranking can be resolved into two orthogonal components, a gradient flow that represents the l 2 -optimal global ranking and a divergence-free flow (cyclic) that measures the validity of the global ranking obtained-if this is large, then it indicates that the data does not have a good global ranking. This divergence-free flow can be further decomposed orthogonally into a curl flow (locally cyclic) and a harmonic flow (locally acyclic but globally cyclic); these provides information on whether inconsistency in the ranking data arises locally or globally. When applied to statistical ranking problems, Hodge decomposition sheds light on whether a given dataset may be globally ranked in a meaningful way or if the data is inherently inconsistent and thus could not have any reasonable global ranking; in the latter case it provides information on the nature of the inconsistencies. An obvious advantage over the NP-hardness of Kemeny optimization is that HodgeRank may be easily computed via a linear least squares regression. We also discuss connections with well-known ordinal ranking techniques such as Kemeny optimization and Borda count from social choice theory.

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Motivated by the increasing availability of large collections of noisy GPS traces, we present a new data-driven framework for smoothing trajectory data. The framework, which can be viewed of as a generalization of the classical moving average technique, naturally leads to ecient algorithms for various smoothing objectives. We analyze an algorithm based on this framework and provide connections to previous smoothing techniques. We implement a variation of the algorithm to smooth an entire collection of trajectories and show that it perform well on both synthetic data and massive collections of GPS traces.

Synthesis of a series of novel dual-acting levofloxacin–HDACi conjugates, which show potent inhibitory activities against HDACs, tubulin polymerization, and significant antiproliferative effect on MCF-7 cells.

In this paper, we have proposed efficient admission control algorithms for multimedia storage servers that are providers of variable-bit-rate media streams. The proposed schemes are based on a slicing technique and use aggressive methods for admission control. We have developed two types of admission control schemes: Future-Max (FM) and Interval Estimation (IE). The FM algorithm uses the maximum bandwidth requirement of the future to estimate the bandwidth requirement. The IE algorithm defines a class of admission control schemes that use a combination of the maximum and average bandwidths within each interval to estimate the bandwidth requirement of the interval. The performance evaluations done through simulations show that the server utilization is improved by using the FM and IE algorithms. Furthermore, the quality of service is also improved by using the FM and IE algorithms. Several results depicting the trade-off between the implementation complexity, the desired accuracy, the number of accepted requests, and the quality of service are presented.

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PurposeThis study aimed to evaluate two modes of Rigiscan for predicting tadalafil response, and to identify which Rigiscan variables are the most efficient at making these predictions.MethodsAll patients received at least two rounds of nocturnal penile tumescence and rigidity (NPTR) testing and/or audiovisual sexual stimulation (AVSS), then completed the International Index of Erectile Function-5 (IIEF-5) questionnaire, followed by oral 5 mg tadalafil daily for 4 weeks. After a 4-week washout period, all respondents underwent an the IIEF-5 questionnaire again. ED patients were then categorized into tadalafil responders and tadalafil non-responders, who were then further divided into cured patients and uncured patients.ResultsWhen predicting tadalafil responders, the area under the curve (AUC) of NPTR was superior to that of AVSS (0.68~0.84 VS 0.69~0.73), and the predicted optimal cut-off values were DOEE60≥17.75 min in NPTR, compared to other parameters regardless of AVSS or NPTR (P<0.05). When predicting which patients would be cured, the AUC of AVSS was superior to NPTR parameters (0.77~0.81 vs 0.61~0.76), and the determined best diagnostic cut-off values were DOEE≥4.125min in AVSS, compared to other parameters regardless of AVSS or NPTR (P < 0.05).ConclusionRigiscan was able to predict the efficacy of daily tadalafil accurately and efficiently. Its diagnostic value was at maximum when DOEE60 ≥17.75 min of NPTR in tadalafil responders and DOEE ≥ 4.125 min of AVSS in cured patients.