Pairs of Noncrossing Free Dyck Paths and Noncrossing Partitions

Using the bijection between partitions and vacillating tableaux, we establish a correspondence between pairs of noncrossing free Dyck paths of length $2n$ and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the number of up steps at odd positions, we find a characterization of Dyck paths constructed from pairs of noncrossing free Dyck paths by using the Labelle merging algorithm.Comment: 9 pages, 5 figures, revised version, to appear in Discrete Mathematic

Testing and demonstration of model predictive control applied to a radiant slab cooling system in a building test facility

Radiant slab systems have the potential to significantly reduce energy consumption in buildings. However, control of radiant slab systems is challenging. Classical feedback control is inadequate due to the large thermal inertia of the systems and heuristic feed-forward control often leads to unacceptable indoor comfort and may not achieve the full energy savings potential. Model predictive control (MPC) is now attracting increasing interest in the building industry and holds promise for radiant systems. However, an often-cited barrier to its implementation in the building industry is the high computational cost and complexity relative to the feedback controls used in conventional systems. The objectives of this study were to (i) verify the correct operation of an open source MPC toolchain developed for radiant slab systems, and (ii) demonstrate its efficacy in a test facility. A matched pair of cells in the FLEXLAB building test facility at the Lawrence Berkeley National Laboratory was used in the study. The proposed MPC toolchain was implemented in one cell and the performance compared to that of the other cell, which used a conventional heuristic control strategy. The results showed that the simplified MPC approach applied in the toolchain worked as expected and realized energy savings over the conventional control strategy. The MPC yielded 42% chilled water pump power reduction and 16% cooling thermal energy savings, while maintaining equal or better indoor comfort

Normal families and fixed points of iterates

Let F be a family of holomorphic functions and let K be a constant less than 4. Suppose that for all f in F the second iterate of f does not have fixed points for which the modulus of the multiplier is greater than K. We show that then F is normal. This is deduced from a result about the multipliers of iterated polynomials.Comment: 5 page

Adaptive obstacle detection for mobile robots in urban environments using downward-looking 2D LiDAR

Environment perception is important for collision-free motion planning of outdoor mobile robots. This paper presents an adaptive obstacle detection method for outdoor mobile robots using a single downward-looking LiDAR sensor. The method begins by extracting line segments from the raw sensor data, and then estimates the height and the vector of the scanned road surface at each moment. Subsequently, the segments are divided into either road ground or obstacles based on the average height of each line segment and the deviation between the line segment and the road vector estimated from the previous measurements. A series of experiments have been conducted in several scenarios, including normal scenes and complex scenes. The experimental results show that the proposed approach can accurately detect obstacles on roads and could effectively deal with the different heights of obstacles in urban road environments

Chinese herbal medicine for atopic eczema

Background: Traditional Chinese herbal mixtures have been used to treat atopic eczema for many years. Their efficacy has attracted public attention and recently some clinical trials have been undertaken. Objectives: To assess the effects of Chinese herbal mixtures in the treatment of atopic eczema. Search strategy: We searched the Cochrane Central Register of Controlled Trials (CENTRAL) ( January 2004), the Cochrane Skin Group Specialised Register (January 2004), MEDLINE (1966 to January 2004), EMBASE (1980 to January 2004), CINHL (1980 to January 2004) and a number of complementary medicine databases. In addition, the cited references of all trials identified and key review articles were searched. Pharmaceutical companies involved in oral traditional Chinese herbs and experts in the field were contacted. Selection criteria: Randomised controlled trials of Chinese herbal mixtures used in the treatment of atopic eczema. Data collection and analysis: Two authors independently applied eligibility criteria, assessed the quality of the trials and extracted data. Any discrepancies were discussed to achieve consensus. Main results: Four randomised controlled trials, with eight weeks for each phase, met the inclusion criteria. The trials randomised 159 participants aged from 1 to 60 years. The withdrawal rates ranged from 7.5 to 22.5% and no trial used intention to treat analysis