Luca Foschini

On the complexity of time-dependent shortest paths

We investigate the complexity of shortest paths in time-dependent graphs where the costs of edges (that is, edge travel times) vary as a function of time, and as a result the shortest path between two nodes s and d can change over time. Our main result is that when the edge cost functions are (polynomial-size) piecewise linear, the shortest path from s to d can change nΘ(logn) times, settling a several-year-old conjecture of Dean (Technical Reports, 1999, 2004). However, despite the fact that the arrival time function may have superpolynomial complexity, we show that a minimum delay path for any departure time interval can be computed in polynomial time. We also show that the complexity is polynomial if the slopes of the linear function come from a restricted class and describe an efficient scheme for computing a (1+ϵ)-approximation of the travel time function.

A Parallel Architecture for Stateful, High-Speed Intrusion Detection

The increase in bandwidth over processing power has made stateful intrusion detection for high-speed networks more difficult, and, in certain cases, impossible. The problem of real-time stateful intrusion detection in high-speed networks cannot easily be solved by optimizing the packet matching algorithm utilized by a centralized process or by using custom-developed hardware. Instead, there is a need for a parallel approach that is able to decompose the problem into subproblems of manageable size. We present a novel parallel matching algorithm for the signature-based detection of network attacks. The algorithm is able to perform stateful signature matching and has been implemented only using off-the-shelf components. Our initial experiments confirm that, by making the rule matching process parallel, it is possible to achieve a scalable implementation of a stateful, network-based intrusion detection system.

Space-efficient online approximation of time series data: Streams, amnesia, and out-of-order

In this paper, we present an abstract framework for online approximation of time-series data that yields a unified set of algorithms for several popular models: data streams, amnesic approximation, and out-of-order stream approximation. Our framework essentially develops a popular greedy method of bucket-merging into a more generic form, for which we can prove space-quality approximation bounds. When specialized to piecewise linear bucket approximations and commonly used error metrics, such as L2 or L∞, our framework leads to provable error bounds where none were known before, offers new results, or yields simpler and unified algorithms. The conceptual simplicity of our scheme translates into highly practical implementations, as borne out in our simulation studies: the algorithms produce near-optimal approximations, require very small memory footprints, and run extremely fast.

Complexity reduction of Mamdani Fuzzy Systems through multi-valued logic minimization

In this paper, we propose an approach to complexity reduction of Mamdani-type fuzzy rule-based systems (FRBSs) based on removing logical redundancies. We first generate an FRBS from data by applying a simplified version of the well-known Wang and Mendel method. Then, we represent the FRBS as a multi-valued logic relation. Finally, we apply MVSIS, a tool for circuit minimization and simulation, to minimize the relation and consequently to reduce complexity of the associated FRBS. Unlike similar previous approaches proposed in the literature, the use of MVSIS let us deal with nondeterminism, that is, let us manage rules with the same antecedent but different consequents. To allow nondeterminism guarantees to achieve a higher (or at least not worse) complexity reduction than the one achievable from removing nondeterminism as soon as it appears. We apply our approach to six popular benchmarks. Results show a considerable complexity reduction associated only sporadically with consistent accuracy degradation. Moreover, quite surprisingly, the complexity reduction often comes together with an improvement in the classification accuracy.

Efficiently selecting spatially distributed keypoints for visual tracking

We describe an algorithm dubbed Suppression via Disk Covering (SDC) to efficiently select a set of strong, spatially distributed key-points, and we show that selecting keypoint in this way significantly improves visual tracking. We also describe two efficient implementation schemes for the popular Adaptive Non-Maximal Suppression algorithm, and show empirically that SDC is significantly faster while providing the same improvements with respect to tracking robustness. In our particular application, using SDC to filter the output of an inexpensive (but, by itself, less reliable) keypoint detector (FAST) results in higher tracking robustness at significantly lower total cost than using a computationally more expensive detector.

TC-SocialRank: Ranking the Social Web

Web search is extensively adopted for accessing information on the web, and recent development in personalized search, social bookmarking and folksonomy systems has tremendously eased the users path towards the desired information. In this paper, we discuss TC-SocialRank , a novel link-based algorithm which extends state-of-the-art algorithms for folksonomy systems. The algorithm leverages the importance of users in the social community, the importance of the bookmarks/resource they share, and additional temporal information and clicks information. Temporal information has a primary importance in social bookmarking search since users continuously post new and fresh information. The importance of this information may decay after a while, if it is no longer tagged or clicked. As a case study for testing the effectiveness of TC-SocialRank , we discuss JammingSearch a novel folksonomy system that unifies web search and social bookmarking by transparently leveraging a Wiki-based collaborative editing system. When an interesting search result is found, a user can share it with the JammingSearch community by simply clicking a button. This information is implicitly tagged with the query submitted to any commodity search engine. Later on, additional tags can be added by the user community. Currently, our system interacts with Ask.com , Google , Microsoft Live , Yahoo! , and AOL .

The union of probabilistic boxes: maintaining the volume

Suppose we have a set of n axis-aligned rectangular boxes in d-space, {B1, B2, ..., Bn}, where each box Bi is active (or present) with an independent probability pi. We wish to compute the expected volume occupied by the union of all the active boxes. Our main result is a data structure for maintaining the expected volume over a dynamic family of such probabilistic boxes at an amortized cost of O(n(d-1)/2 log n) time per insert or delete. The core problem turns out to be one-dimensional: we present a new data structure called an anonymous segment tree, which allows us to compute the expected length covered by a set of probabilistic segments in logarithmic time per update. Building on this foundation, we then generalize the problem to d dimensions by combining it with the ideas of Overmars and Yap [13]. Surprisingly, while the expected value of the volume can be efficiently maintained, we show that the tail bounds, or the probability distribution, of the volume are intractable-- specifically, it is NP-hard to compute the probability that the volume of the union exceeds a given value V even when the dimension is d = 1.

The Spread of Physical Activity Through Social Networks

Many behaviors that lead to worsened health outcomes are modifiable, social, and visible. Social influence has thus the potential to foster adoption of habits that promote health and improve disease management. In this study, we consider the evolution of the physical activity of 44.5 thousand Fitbit users as they interact on the Fitbit social network, in relation to their health status. The users collectively recorded 9.3 million days of steps over the period of a year through a Fitbit device. 7,515 of the users also self-reported whether they were diagnosed with a major chronic condition. A time-aggregated analysis shows that ego net size, average alter physical activity, gender, and body mass index (BMI) are significantly predictive of ego physical activity. For users who self-reported chronic conditions, the direction and effect size of associations varied depending on the condition, with diabetic users specifically showing almost a 6-fold increase in additional daily steps for each additional social tie. Subsequently, we consider the co-evolution of activity and friendship longitudinally on a month by month basis. We show that the fluctuations in average alter activity significantly predict fluctuations in ego activity. By leveraging a class of novel non-parametric statistical tests we investigate the causal factors in these fluctuations. We find that under certain stationarity assumptions, non-null causal dependence exists between ego and alters activity, even in the presence of unobserved stationary individual traits. We believe that our findings provide evidence that the study of online social networks have the potential to improve our understanding of factors affecting adoption of positive habits, especially in the context of chronic condition management.

Observation Time vs. Performance in Digital Phenotyping

Mobile health (mHealth) technologies enable frequent sampling of physiological and psychological signals over time. In our recent work we used a convolutional neural network (CNN) model to predict self-reported phenotypes of chronic conditions from step and sleep data recorded from passive trackers in free living conditions. We investigated the impact of the time-granularity of the collected data and showed that training the models on higher- resolution (minute-level) data improved classification performance on conditions related to mental health and nervous system disorders, as compared to using only day-level totals. In the present work we shift the focus from the time resolution of the observation window to its duration. We study how the performance of the best-performing model on the highest-resolution data changes as the length of the data collection window is varied from 3 to 147 days for each user. We found that for mental health and nervous system disorders, a model trained on 30 days of mHealth data attains the same performance as using the full 147-day window of data, in terms of AUC increase over a baseline model that uses only demographics, height, and weight. Additionally, for the same cluster of conditions, only 7 days of data are sufficient to realize 62% of the maximum increase in AUC over baseline attainable using the full window. The results suggest that for some conditions health-related digital phenotyping in free-living conditions can potentially be performed in a relatively short amount of time, imposing minimal disruptions on user habits.

Spatial coherence of oriented white matter microstructure: Applications to white matter regions associated with genetic similarity

&NA; We present a method to discover differences between populations with respect to the spatial coherence of their oriented white matter microstructure in arbitrarily shaped white matter regions. This method is applied to diffusion MRI scans of a subset of the Human Connectome Project dataset: 57 pairs of monozygotic and 52 pairs of dizygotic twins. After controlling for morphological similarity between twins, we identify 3.7% of all white matter as being associated with genetic similarity (35.1 k voxels, Symbol, false discovery rate 1.5%), 75% of which spatially clusters into twenty‐two contiguous white matter regions. Furthermore, we show that the orientation similarity within these regions generalizes to a subset of 47 pairs of non‐twin siblings, and show that these siblings are on average as similar as dizygotic twins. The regions are located in deep white matter including the superior longitudinal fasciculus, the optic radiations, the middle cerebellar peduncle, the corticospinal tract, and within the anterior temporal lobe, as well as the cerebellum, brain stem, and amygdalae. Symbol. No caption available. These results extend previous work using undirected fractional anisotrophy for measuring putative heritable influences in white matter. Our multidirectional extension better accounts for crossing fiber connections within voxels. This bottom up approach has at its basis a novel measurement of coherence within neighboring voxel dyads between subjects, and avoids some of the fundamental ambiguities encountered with tractographic approaches to white matter analysis that estimate global connectivity. HighlightsA method associating regions of white matter with a population is proposed.Regions contain more coherent neighboring voxels within the population than expected.Nearly all deep white matter is associated with genetic similarity.