Plurality preference digraphs realized by trees, II: on realization numbers

AbstractA digraph D with vertex set X = {x1, x2,…, xn} is realizable by a connected graph G if there exists a subset C = {c1, c2,…, cn} of vertices of G so that for all distinct i and j in {1, 2,…, n}, xixj is an arc of D if and only if more vertices of G are closer to ci than to cj. For a positive integer n, let Fn denote the family of digraphs of order n which are realizable by trees. For a fixed D∈Fn, the realization number of D, denoted α(itD), is the smallest order of a tree which realizes D. Let α(Fn)=max{α(D):D∈Fn}. In this paper α(Fn) is determined explicitly

Exterior Vertices in Graphs and Realization of Plurality Preference Digraphs.

Part I: Peripheral and eccentric vertices of graphs. For a connected graph G, let P(G) and EC(G) denote the sets of peripheral vertices and eccentric vertices of G, respectively. In 1988 F. Buckley initiated the study of the class S of graphs G for which P(G) = EC(G). We provide several families of graphs which are in S. For certain graphs G with diameter equal to 2r(G) or 2r(G) or 2r(G) $-$ 1, we give criteria for P(G) and EC(G) to be equal. Also, for certain products, we characterize those pairs of graphs so that their product is in S. We present graphs which are then used to show that all possible set-inclusion relations between P(G) and EC(G) may occur. Additionally, we estimate the smallest order of a graph H having a given graph G as an induced subgraph so that P(H) = EC(H) (or P(H) = V(G)). Part II: Realization of plurality preference digraphs. A digraph D with vertex set \{x\sb1,x\sb2,\...,x\sb{k}\} is (n,h,k)-realizable if there exists a connected graph G of order n, a subset V $\subseteq$ V(G) with $\vert V\vert$ = h, and a subset C = \{c\sb1,c\sb2,\...,c\sb{k}\}\subseteq V(G) so that for all distinct i and j in $\{1,2,\...,k\}$, (x\sb{i},x\sb{j}) is an arc of D if and only if more vertices in V are closer to c\sb{j} in G. In particular, if h = n, then we simply say that D is realizable by G or that G realizes D. In 1988, Johnson and Slater proved that any oriented graph is realizable by a graph. We provide two constructions of graphs which realize a given oriented graph and show that each of these has a smaller order than the example due to Johnson and Slater. The best known construction, due recently to by W. Schnyder is also provided. Secondly, we characterize digraphs which are realizable by trees. Additionally, we derive some properties of a digraph which is (n,n,n)-realizable by a tree and describe a class of such digraphs. Finally, let {\cal F}\sb{n} denote the family of digraphs of order n which are realizable by trees. For a fixed D $\in$ {\cal F}\sb{n}, let $\alpha$(D) be the smallest order of a tree which realizes D. We determine the value of $\alpha$({\cal F}\sb{n} = $max\{\alpha(D)$: D \in\ {\cal F}\sb{n}\} explicitly

Manufacturing with light – micro-assembly of opto-electronic microstructures

Optical micromanipulation allows the movement and patterning of discrete micro-particles within a liquid environment. However, for manufacturing applications it is desirable to remove the liquid, leaving the patterned particles in place. In this work, we have demonstrated the use of optoelectronic tweezers (OET) to manipulate and accurately assemble Sn62Pb36Ag2 solder microspheres into tailored patterns. A technique based on freeze-drying technology was then developed that allows the assembled patterns to be well preserved and fixed in place after the liquid medium in the OET device is removed. After removing the liquid from the OET device and subsequently heating the assembled pattern and melting the solder microspheres, electrical connections between the microspheres were formed, creating a permanent conductive bridge between two isolated metal electrodes. Although this method is demonstrated with 40 µm diameter solder beads arranged with OET, it could be applied to a great range of discrete components from nanowires to optoelectronic devices, thus overcoming one of the basic hurdles in using optical micromanipulation techniques in a manufacturing micro-assembly setting

Atomic-layered Au clusters on α-MoC as catalysts for the low-temperature water-gas shift reaction

The water-gas shift (WGS) reaction (where carbon monoxide plus water yields dihydrogen and carbon dioxide) is an essential process for hydrogen generation and carbon monoxide removal in various energy-related chemical operations. This equilibrium-limited reaction is favored at a low working temperature. Potential application in fuel cells also requires a WGS catalyst to be highly active, stable, and energy-efficient and to match the working temperature of on-site hydrogen generation and consumption units. We synthesized layered gold (Au) clusters on a molybdenum carbide (α-MoC) substrate to create an interfacial catalyst system for the ultralow-temperature WGS reaction. Water was activated over α-MoC at 303 kelvin, whereas carbon monoxide adsorbed on adjacent Au sites was apt to react with surface hydroxyl groups formed from water splitting, leading to a high WGS activity at low temperatures

TRQ3DNet: A 3D Quasi-Recurrent and Transformer Based Network for Hyperspectral Image Denoising

We propose a new deep neural network termed TRQ3DNet which combines convolutional neural network (CNN) and transformer for hyperspectral image (HSI) denoising. The network consists of two branches. One is built by 3D quasi-recurrent blocks, including convolution and quasi-recurrent pooling operation. Specifically, the 3D convolution can extract the spatial correlation within a band, and spectral correlation between different bands, while the quasi-recurrent pooling operation is able to exploit global correlation along the spectrum. The other branch is composed of a series of Uformer blocks. The Uformer block uses window-based multi-head self-attention (W-MSA) mechanism and the locally enhanced feed-forward network (LeFF) to exploit the global and local spatial features. To fuse the features extracted by the two branches, we develop a bidirectional integration bridge (BI bridge) for better preserving the image feature information. Experimental results on synthetic and real HSI data show the superiority of our proposed network. For example, in the case of Gaussian noise with sigma 70, the PSNR value of our method significantly increases about 0.8 compared with other state-of-the-art methods

TRQ3DNet: A 3D Quasi-Recurrent and Transformer Based Network for Hyperspectral Image Denoising

We propose a new deep neural network termed TRQ3DNet which combines convolutional neural network (CNN) and transformer for hyperspectral image (HSI) denoising. The network consists of two branches. One is built by 3D quasi-recurrent blocks, including convolution and quasi-recurrent pooling operation. Specifically, the 3D convolution can extract the spatial correlation within a band, and spectral correlation between different bands, while the quasi-recurrent pooling operation is able to exploit global correlation along the spectrum. The other branch is composed of a series of Uformer blocks. The Uformer block uses window-based multi-head self-attention (W-MSA) mechanism and the locally enhanced feed-forward network (LeFF) to exploit the global and local spatial features. To fuse the features extracted by the two branches, we develop a bidirectional integration bridge (BI bridge) for better preserving the image feature information. Experimental results on synthetic and real HSI data show the superiority of our proposed network. For example, in the case of Gaussian noise with sigma 70, the PSNR value of our method significantly increases about 0.8 compared with other state-of-the-art methods

Evolutionary particle filter : re-sampling from the genetic algorithm perspective

The sample impoverishment problem in particle filters is investigated from the perspective of genetic algorithms. The contribution of this paper is in the proposal of a hybrid technique to mitigate sample impoverishment such that the number of particles required and hence the computation complexities are reduced. Studies are conducted through the use of Chebyshev inequality for the number of particles required. The relationship between the number of particles and the time for impoverishment is examined by considering the takeover phenomena as found in genetic algorithms. It is revealed that the sample impoverishment problem is caused by the resampling scheme in implementing the particle filter with a finite number of particles. The use of uniform or roulette-wheel sampling also contributes to the problem. Crossover operators from genetic algorithms are adopted to tackle the finite particle problem by re-defining or re-supplying impoverished particles during filter iterations. Effectiveness of the proposed approach is demonstrated by simulations for a monobot simultaneous localization and mapping application

AUSTRALASIAN JOURNAL OF COMBINATORICS Volume 32 (2005), Pages 117–124 Chords in Graphs

We characterize all simple graphs such that each edge is a chord of some cycle. As a consequence, we characterize all simple 2-connected graphs such that, for any two adjacent vertices x and y, the local connectivity k(x, y) ≥ 3. We also make a conjecture about chords for 3-connected graphs.

Water Level Change of Qinghai Lake from ICESat and ICESat-2 Laser Altimetry

Long-term satellite observations of the water levels of lakes are crucial to our understanding of lake hydrological basin systems. The Ice, Cloud, and Land Elevation satellite (ICESat) and ICESat-2 were employed to monitor the water level of Qinghai Lake in the hydrological basin. The median of absolute deviation (MAD) method was exploited to remove the outliers. The results confirmed that the MAD range of ICESat was from 0.0525 to 0.2470 m, and the range of σ was from 0.0778 to 0.3662 m; the MAD range of ICESat-2 was from 0.0291 to 0.0490 m, and the range of σ was from 0.0431 to 0.0726 m; ICESat-2 was less than that of ICESat. The reference ellipsoid and geoid transfer equations were applied to convert the water level to the World Geodetic System (WGS84) and Earth Gravitational Model 2008 (EGM2008) geoid. The water level, as derived from laser altimeters, was validated by the Xiashe Hydrological Station; with ICESat, the coefficient of association (R) was 0.8419, the root mean square error (RMSE) was 0.1449 m, and the mean absolute error (MAE) was 0.1144 m; with ICESat-2, the R was 0.6917, the RMSE was 0.0531 m, and the MAE was 0.0647 m. The water levels from ICESat-2 are much more accurate than those from ICESat. The two combined laser altimeters showed that the R was 0.9931, the RMSE was 0.1309 m, and the MAE was 0.1035 m. The water level rise was 3.6584 m from 2004 to 2020. The rising rate was 0.2287 m/a. The collaborative use of the ICESat-2 and ICESat satellites made it easier to obtain the lake water levels

Clinical risk factors for peritoneal dialysis withdrawal at different dialysis duration

AbstractBackground The duration of patients maintained on peritoneal dialysis (PD) varied. This study investigated the clinical risk factors for PD withdrawal at different dialysis duration.Methods Patients who initiated PD from 1994 to 2011 were recruited and followed for at least 10 years until 2021. Patients were grouped into four groups according to dialysis duration or time on treatment (TOT) when withdrew PD.Results A cohort of 586 patients were enrolled (mean age of 54.9 years, median dialysis duration or TOT of 47.9 months). Patients who maintained PD for longer than 10 years were younger, with lower prevalence of diabetes, lower serum C-reactive protein (CRP) level and white blood cell (WBC) count, higher serum albumin and pre-albumin level, higher normalized protein catabolic rate (nPCR) and residual kidney function, and more common use of renin–angiotensin system inhibitors (RASi) at baseline (p < 0.05 for all). Peritonitis related death and ultrafiltration failure related HD transferring increased along with time on PD (p < 0.001). Old age, diabetes, low serum albumin, high WBC count, hypertensive nephropathy, and nonuse of RASi were associated with increased risk of non-transplantation related PD withdrawal (p < 0.05 for all). Low baseline CRP and use of RASi were independent predictors for long-term PD maintenance (p < 0.05 for all).Conclusions Long-term PD patients demonstrated young age, low prevalence of diabetes, better nutrition status, absence of inflammation, better residual kidney function, and higher proportion of RASi usage at baseline. Absence of inflammation and use of RASi were independently associated with long-term PD maintenance