Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

Bias adjustment of satellite precipitation estimation using ground-based measurement: A case study evaluation over the southwestern United States

Reliable precipitation measurement is a crucial component in hydrologic studies. Although satellite-based observation is able to provide spatial and temporal distribution of precipitation, the measurements tend to show systematic bias. This paper introduces a grid-based precipitation merging procedure in which satellite estimates from the Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks-Cloud Classification System (PERSIANN-CCS) are adjusted based on the Climate Prediction Center (CPC) daily rain gauge analysis. To remove the bias, the hourly CCS estimates were spatially and temporally accumulated to the daily 1°×1° scale, the resolution of CPC rain gauge analysis. The daily CCS bias was then downscaled to the hourly temporal scale to correct hourly CCS estimates. The bias corrected CCS estimates are called the adjusted CCS (CCSA) product. With the adjustment from the gauge measurement, CCSA data have been generated to provide more reliable high temporal/spatial-resolution precipitation estimates. In the case study, the CCSA precipitation estimates from the proposed approach are compared against ground-based measurements in high-density gauge networks located in the southwestern United States. © 2009 American Meteorological Society

On maximizing the throughput of opportunistic multicast in wireless cellular networks with erasure codes

In this paper, we discuss the opportunistic multicast scheduling (OMS) in a wireless network using erasure codes. Originally proposed for channels with erasures such as internet, erasure codes are found useful in wireless multicast to achieve better tradeoff between multiuser diversity and the multicast gain. In this work we investigated how to design an opportunistic multicast scheduling scheme which can efficiently improve the per user throughput capacity in a wireless network using erasure codes. Aiming at maximize the throughput, we proposed a maximal OMS (M-OMS) scheme which is inspired by the unicast maximal opportunistic scheduling. We build a system model and provide theoretical analysis on proposed M-OMS scheme. The proposed scheme shows substantial improvement over existing fixed selection ratio opportunistic multicast scheduling schemes (F-OMS). © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Conference on Communications (ICC 2011), Kyoto, Japan, 5-9 June 2011. In Proceedings of the IEEE ICC, 2011, p. 1-

A new phase for screening redundant broadcast nodes in source-independent broadcasting protocols

Following the distributed approach, source-independent broadcasting protocols select a subset of nodes in a network as broadcasting nodes to cover the entire network. The selection of broadcasting nodes is performed prior to actual message transmission. These broadcasting nodes collectively form a connected dominating set or CDS. Aiming at finding a minimum CDS, existing source-independent broadcasting protocols consist of two phases. In this paper, we propose to add a third phase to eliminate unnecessary nodes in a CDS while ensuring all remaining nodes are still connected. We call it the redundant node screening phase. This paper shows that this new phase is a very important element that has been ignored by existing source-independent broadcasting protocols. When applying the new phase on existing broadcasting protocols, the savings in terms of number of nodes in the CDS could be as high as 21% in a 1000m x 1000m network of 20 nodes. © 2011 IEEE.published_or_final_versionThe 2011 IEEE International Conference on Communications (ICC 2011), Kyoto, Japan, 5-9 June 2011. In Proceedings of the IEEE ICC, 2011, p. 1-

Variable power broadcasting based on local information for source-dependent broadcasting protocols

A typical broadcasting protocol for wireless network usually involves fixed transmission power that covers, for example an area within 250 meters (m). However, it is often unnecessary to broadcast using fixed power because a node that needs to be covered may just be 100m away. By reducing the transmission power enough to cover this node, energy expenditure would be reduced, thus, prolonging the lifetime of battery-powered wireless networks such as Mobile Ad Hoc Networks (MANETs) and Wireless Sensor Networks (WSNs). Existing source-dependent broadcasting protocols do not have any mechanisms for adjusting the transmission power of nodes. Therefore, this paper proposes some effective mechanisms based on local neighborhood knowledge, while ensuring the overall network is still covered. Results of extensive simulations confirm the effectiveness of the proposed protocols in reducing energy consumption. © 2011 IEEE.published_or_final_versionThe 2011 IEEE Wireless Communications and Networking Conference (WCNC), Cancun, Mexico, 28-31 March 2011. In Proceedings of IEEE WCNC, 2011, p. 796-80

Self-pruning broadcasting for mobile ad hoc networks

The IEEE Global Telecommunications Conference (GLOBECOM 2009), Honolulu, HI., 30 November-4 December 2009, p. 1-6Broadcasting is a process of delivering a message to all nodes in a network. While it is important to ensure that all nodes get a copy of the broadcast message, minimizing the number of sending nodes is equally important especially in resource-constrained wireless networks. Existing broadcasting protocols based on self-pruning are ineffective in achieving these objectives. Therefore this paper proposes two protocols based on simple timer mechanisms to prioritize broadcasting of messages such that node with most uncovered neighbors rebroadcast first. Additionally a timer suppression mechanism is proposed to further enhance the effectiveness of the broadcasting protocol. Compared with an existing protocol, extensive simulation experiments confirm that the proposed protocols achieve better performance.published_or_final_versio

Enhanced termination condition for deterministic broadcasting protocols in mobile ad hoc networks

Deterministic approach to broadcasting in Mobile Ad Hoc Networks (MANETs) is effective in reducing redundant broadcasting. In this approach, a transmitting node selects a subset of its immediate or 1-hop neighbors to rebroadcast the message such that all its 2-hop neighbors will receive the message, or being covered. In order to reduce redundant broadcasting, the set of 1-hop neighbors to be covered should be reduced as much as possible. Another important aspect that affects the effectiveness of a deterministic broadcasting protocol is the termination condition that inhibits a node from transmitting a particular message unnecessarily. However, existing termination conditions are not optimized. We propose a new covered/uncovered termination condition where each node is assigned with covered/uncovered status. In this paper, we show that our covered/uncovered termination condition ensures full network coverage, does not incur any control message overhead, and yet requires the least number of rebroadcasting nodes. When we apply the termination condition to some existing deterministic broadcasting protocols, the saving in the number of broadcasting nodes can be as significant as 45% when there are 100 nodes randomly distributed in an area of 1000 x 1000 m2. ©2010 IEEE.published_or_final_versionThe 72nd IEEE Vehicular Technology Conference (VTC 2010-Fall), Ottawa, ON., 6-9 September 2010. In Proceedings of the IEEE-VTS Vehicular Technology Conference, 2010, p. 1-

Enhanced variable power broadcasting based on local information in mobile ad hoc networks

Broadcasting in mobile ad hoc networks (MANETs) usually involve fixed transmission power that covers, for example an area within 250 meters. However, it is often unnecessary to broadcast using fixed power because a node that needs to be covered may just be 100 meters away. By reducing the transmission power enough to cover this node, energy expenditure would be reduced, thus, prolonging the lifetime of a battery-powered MANET. Existing works on variable power broadcasting based on local information are effective in achieving this objective. However, they are not optimized and can be improved by dynamically adjusting the transmission power based on where a broadcast message comes from. This paper proposes simple mechanisms based on local knowledge to adjust the transmission power dynamically and incorporates a timer suppression mechanism to further enhance the effectiveness of the protocols in reducing energy expenditure. Results of simulation studies confirm the effectiveness of the proposed enhancements. ©2010 IEEE.published_or_final_versionThe 2010 IEEE Wireless Communications and Networking Conference (WCNC), Sydney, Australia, 18-21 April 2010. In Proceedings of IEEE-WCNC, 2010, p. 1-

Levi umbilical surfaces in complex space

We define a complex connection on a real hypersurface of \C^{n+1} which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in \C^{n+1}, $n\ge 2$, which are Levi umbilical and have non zero constant Levi curvature. It turns out that such surfaces are contained either in a sphere or in the boundary of a complex tube domain with spherical section.Comment: 18 page