DISTANCE PRESERVING SUBTREES IN MINIMUM AVERAGE DISTANCE SPANNING TREES

We are developing a decision support system for treatment response assessment of bladder cancer in CT urography (CTU). Accurate segmentation of bladder cancer is a critical and challenging task. We previously developed a bladder cancer segmentation method using a deep learning convolutional neural network and level set (DL-CNN+LS) approach. In this study we investigated the application of a U-Net based deep learning (U-Net) model for bladder cancer segmentation. Our new U-Net method did not require the second-stage level set refinement, greatly simplifying the overall segmentation pipeline. The proposed U-Net model utilized a user-defined box to direct the attention of the U-Net to the lesion region by masking out the structured background outside the box. We trained and evaluated the performance of the U-Net segmentations by using hand-drawn 3D contours from a radiologist as reference standard. The segmentation accuracy was evaluated by the average volume intersection ratio (AVI), average percent volume error (AVE), average absolute volume error (AAVE), average minimum distance (AMD), and the Jaccard index (JI). On the validation set, the cropped U-Net achieved values of AVI = 65.5±20.2%, AVE = 3.7±44.4%, AAVE = 30.9±30.8%, AMD = 2.9±1.5 mm, and JI = 51.4±16.8%. The previous DL-CNN+LS approach achieved values of AVI = 36.2±28.4%, AVE = 51.1±39.3%, AAVE = 52.0±38.0%, AMD = 4.1±1.7 mm, and JI = 32.9±27.2%. On the independent test set, the cropped U-Net achieved values of AVI = 66.0±22.8%, AVE = -3.7±39.4%, AAVE = 28.1±27.3%, AMD = 4.5±3.3 mm, and JI = 49.2±20.0%. The DL-CNN+LS achieved values of AVI = 31.2±24.3%, AVE = 59.9±30.9%, AAVE = 60.8±29.0%, AMD = 5.5±2.2 mm, and JI = 27.9±20.8%, respectively. The results demonstrated that the U-Net model could achieve a higher accuracy than the previous DL-CNN+LS model while reducing the complexity of the segmentation pipeline.

A subgraph H of a given graph G is isometric if the distances between every pair of vertices in H are the same as the distances of those vertices in G. We say a graph G is distance preserving if there exists an isometric subgraph of every possible order up to the order of G. Distance preserving property has been applied to many real world problems such as route recommendation systems and all kinds of shortest-path-related applications. Here, we propose a biologically-inspired search algorithm to address the problem of finding isometric subgraphs that consequently determines if a given graph is distance preserving. In this algorithm, using a well defined fitness function, selection operator selects isometric subgraphs to generate the offspring for the next generation. There is a trade-off between the population size and searching speed. On one hand, the larger the population size is, the slower the search algorithm would be. On the other hand, by increasing the population size, we increase the likelihood of finding an existing isometric subgraph. Experimental results depict the performance of the proposed algorithm in finding isometric subgraphs even for challenging problems, and interestingly by these results one can see that almost all graphs are distance preserving. In closing, we show the smallest distance preserving graph whose product factors are not distance preserving. This graph has 80 vertices, and can be used as benchmark for algorithms in this concept.

We are developing a U-Net based deep learning (U-DL) model for bladder segmentation in CT urography (CTU) as a part of a computer-assisted bladder cancer detection and treatment response assessment pipeline. We previously developed a bladder segmentation method that used a deep-learning convolution neural network and level sets (DCNNLS) within a user-input bounding box. The new method does not require a user-input box nor the level sets for postprocessing. To identify the best model for this task, we compared a number of U-DL models: 1) 2D CTU slices or 3D volume as input, 2) different image resolutions, and 3) preprocessing with and without automated cropping on each slice. We evaluated the segmentation performance of the different U-DL models using 3D hand-segmented contours as reference standard. The segmentation accuracy was quantified by the average volume intersection ratio (AVI), average percent volume error (AVE), average absolute volume error (AAVE), average minimum distance (AMD), and the Jaccard index (JI) for a data set of 81 training/validation and 92 independent test cases. For the test set, the best 2D UDL model achieved AVI, AVE, AAVE, AMD, and JI values of 93.4±9.5%, -4.2±14.2%, 9.2±11.5%, 2.7±2.5 mm, 85.0±11.3%, respectively, while the best 3D U-DL achieved 90.6±11.9%, -2.3±21.7%, 11.5±18.5%, 3.1±3.2 mm, and 82.6±14.2%, respectively. For comparison, the corresponding values obtained with our previous DCNN-LS method were 81.9±12.1%, 10.2±16.2%, 14.0±13.0%, 3.6±2.0 mm, and 76.2±11.8%, respectively, for the same test set. The UDL model provided highly accurate bladder segmentation and was more automated than the previous approach.

We make improvements to the upper bounds on several popular types of distance preserving graph sketches. These sketches are all various restrictions of the {\em additive pairwise spanner} problem, in which one is given an undirected unweighted graph $G$, a set of node pairs $P$, and an error allowance $+\beta$, and one must construct a sparse subgraph $H$ satisfying $\delta_H(u, v) \le \delta_G(u, v) + \beta$ for all $(u, v) \in P$. The first part of our paper concerns {\em pairwise distance preservers}, which make the restriction $\beta=0$ (i.e. distances must be preserved {\em exactly}). Our main result here is an upper bound of $|H| = O(n^{2/3}|P|^{2/3} + n|P|^{1/3})$ when $G$ is undirected and unweighted. This improves on existing bounds whenever $|P| = \omega(n^{3/4})$, and it is the first such improvement in the last ten years. We then devise a new application of distance preservers to graph clustering algorithms, and we apply this algorithm to {\em subset spanners}, which require $P = S \times S$ for some node subset $S$, and {\em (standard) spanners}, which require $P = V \times V$. For both of these objects, our construction generalizes the best known bounds when the error allowance is constant, and we obtain the strongest polynomial error/sparsity tradeoff that has yet been reported (in fact, for subset spanners, ours is the {\em first} nontrivial construction that enjoys improved sparsity from a polynomial error allowance). We leave open a conjecture that $O(n^{2/3}|P|^{2/3} + n)$ pairwise distance preservers are possible for undirected unweighted graphs. Resolving this conjecture in the affirmative would improve and simplify our upper bounds for all the graph sketches mentioned above.

For an undirected graph G¿=¿(V,E), we say that for l,u,v¿¿¿V, l separates u from v if the distance between u and l differs from the distance from v to l. A set of vertices L¿¿¿V is a feasible solution if for every pair of vertices u,v¿¿¿V there is l¿¿¿L that separates u from v. The metric dimension of a graph is the minimum cardinality of such a feasible solution. Here, we extend this well-studied problem to the case where each vertex v has a non-negative cost, and the goal is to find a feasible solution with a minimum total cost. This weighted version is NP-hard since the unweighted variant is known to be NP-hard. We show polynomial time algorithms for the cases where G is a path, a tree, a cycle, a cograph, a k-edge-augmented tree (that is, a tree with additional k edges) for a constant value of k, and a (not necessarily complete) wheel. The results for paths, trees, cycles, and complete wheels extend known polynomial time algorithms for the unweighted version, whereas the other results are the first known polynomial time algorithms for these classes of graphs even for the unweighted version. Next, we extend the set of graph classes for which computing the unweighted metric dimension of a graph is known to be NPC by showing that for split graphs, bipartite graphs, co-bipartite graphs, and line graphs of bipartite graphs, the problem of computing the unweighted metric dimension of the graph is NPC.

A locating-dominating set of an undirected graph is a subset of vertices S such that S is dominating and for every u,v∉S, the neighbourhood of u and v on S are distinct (i.e. N(u)∩S≠N(v)∩S). Locating-dominating sets have received a considerable attention in the last decades. In this paper, we consider the oriented version of the problem. A locating-dominating set in an oriented graph is a set S such that for each w∈V∖S, N−(w)∩S≠∅ and for each pair of distinct vertices u,v∈V∖S, N−(u)∩S≠N−(v)∩S. We consider the following two parameters. Given an undirected graph G, we look for γ→LD(G) (Γ→LD(G)) which is the size of the smallest (largest) optimal locating-dominating set over all orientations of G. In particular, if D is an orientation of G, then γ→LD(G)≤γLD(D)≤Γ→LD(G) where γLD(D) is the minimum size of a locating-dominating set of D.For the best orientation, we prove that, for every twin-free graph G on n vertices, γ→LD(G)≤n/2 which proves a “directed version” of a widely studied conjecture on the location-domination number. As a side result we obtain a new improved upper bound for the location-domination number in undirected trees. Moreover, we give some bounds for γ→LD(G) on many graph classes and drastically improve the value n/2 for (almost) d-regular graphs by showing that γ→LD(G)∈O(log⁡d/d⋅n) using a probabilistic argument.While γ→LD(G)≤γLD(G) holds for every graph G, we give some graph classes such as outerplanar graphs for which Γ→LD(G)≥γLD(G) and some for which Γ→LD(G)≤γLD(G) such as complete graphs. We also give general bounds for Γ→LD(G) such as Γ→LD(G)≥α(G). Finally, we show that for many graph classes Γ→LD(G) is polynomial on n but we leave open the question whether there exist graphs with Γ→LD(G)∈O(log⁡n).

Performance analysis of a cache-based multiprocessor system using data movement policies

In the first of this two-part cadaver investigation, we inserted a specially designed, pointed device (simulating a 12-mm nail) in an antegrade fashion in each of eight fresh-frozen cadaver tibial specimens; the tibial isthmus was used as a centralizing guide. The exit point was noted, and the specimen was dissected to identify the structures at risk. In all specimens, we found that the device placed the lateral plantar artery and nerve at risk (average minimal distance from device to structure, 0 mm) and that damage to the flexor hallucis brevis and plantar fascia occurred. In addition, in six of the eight specimens, the device skewered or skived the flexor hallucis longus tendon. We also noted that in each specimen the exit point was the sustentaculum tali, not the body of the calcaneus as expected. Thus, there was less calcaneal bone-to-rod interface for stability, and distal locking would be less effective in the lateral-to-medial direction because of the lack of medial bone stock. On the basis of the results of the first portion of the study, we investigated an alternative approach to retrograde tibial nailing to reduce the risk of injury to the plantar and medial structures of the foot. We performed a medial malleolar resection, medially displaced the talus, inserted the device in an antegrade fashion, and dissected the specimens to analyze the structures at risk. We found that malleolar resection and medial translation of the distal extremity an average of 9.3 mm (range, 7-11 mm) increased the average minimal distance from the tip of the device to the neurovascular bundle to 18.4 mm (range, 14-32 mm). We also found that there was no damage to the flexor hallucis longus and that all eight specimens demonstrated bony contact completely surrounding the nail device within the tuberosity portion of the calcaneus (assessed by postoperative radiographs). The results of this study suggest that malleolar resection and medial translation of the distal extremity before retrograde nailing of the tibia may reduce the risk of vital structure injury and enhance the rigidity of the fixation.

In his pioneering paper on matroids in 1935, Whitney obtained a characterization for binary matroids and left a comment at end of the paper that the problem of characterizing graphic matroids is the same as that of characterizing matroids which correspond to matrices (mod 2) with exactly two ones in each column. Later on Tutte obtained a characterization of graphic matroids in terms of forbidden minors in 1959. It is clear that Whitney indicated about incidence matrices of simple undirected graphs. Here we introduce the concept of a segment binary matroid which corresponds to matrices over $\mathbb{Z}_2$ which has the consecutive $1$'s property (i.e., $1$'s are consecutive) for columns and obtained a characterization of graphic matroids in terms of this. In fact, we introduce a new representation of simple undirected graphs in terms of some vectors of finite dimensional vector spaces over $\mathbb{Z}_2$ which satisfy consecutive $1$'s property. The set of such vectors is called a coding sequence of a graph $G$. Among all such coding sequences we identify the one which is unique for a class of isomorphic graphs. We call it the code of the graph. We characterize several classes of graphs in terms of coding sequences. It is shown that a graph $G$ with $n$ vertices is a tree if and only if any coding sequence of $G$ is a basis of the vector space $\mathbb{Z}_2^{n-1}$ over $\mathbb{Z}_2$. Moreover considering coding sequences as binary matroids, we obtain a characterization for simple graphic matroids and found a necessary and sufficient condition for graph isomorphism in terms of a special matroid isomorphism between their corresponding coding sequences. For this, we introduce the concept of strong isomorphisms of segment binary matroids and show that two simple (undirected) graphs are isomorphic if and only if their canonical sequences are strongly isomorphic segment binary matroids.

Simulated annealing algorithm is adopted to detect the parameters of lines, circles, ellipses, and hyperbolic patterns. We define the distance from a point to a pattern such that the detection becomes feasible, especially in hyperbola. The proposed simulated annealing parameter detection system has the capability to find a set of parameter vectors with global minimal error to the input data. Using average minimum distance, we propose a method to determine the number of patterns automatically. Experiments on the detection of lines, circles, ellipses, and hyperbolas in images are quite successful. The detection system is also applied to detect the line pattern of direct wave and the hyperbolic pattern of reflection wave in the simulated one-shot seismogram. The results are good and can improve seismic interpretations and further seismic data processing.

Various methods for automatic building extraction from remote sensing data including light detection and ranging (LiDAR) data have been proposed over the last two decades but a standard metric for evaluation of the extracted building boundary has not been found yet. An extracted building boundary from LiDAR data usually has a zigzag pattern with missing detail, which makes it hard to compare the boundary with its reference. The existing metrics do not consider the significant point (e.g., corner) correspondences, therefore, cannot identify individual extralap and underlap areas in the extracted boundary. This article proposes an evaluation metric for the extracted boundary based on a newly proposed robust corner correspondence algorithm that finds one-to-one true corner correspondences between the reference and extracted boundaries. Assuming a building has a rectilinear shape, corners and lines are first detected for the extracted boundary. Then, corner correspondences are obtained between the extracted and reference boundaries. Each corner has two corresponding lines on its two sides that ideally are perpendicular to each other. The corner correspondences are finally ranked based on their distance, angle, and parallelism of corresponding lines. The metric is defined as the average minimum distance $d_{\mathrm{avg}}$ from the extracted boundary points to their corresponding reference lines. Extralap and underlap areas are identified by comparing the point distances with $d_{\mathrm{avg}}$ . In experiments, the proposed metric performs more realistic than the existing metrics and finds the individual extralap and underlap areas effectively.

Many recent applications require text segmentation for born-digital compound images. To this end, we propose a coarse-to-fine framework for segmenting texts of arbitrary scales and orientations in born-digital compound images. In the coarse stage, the local image activity measure is designed based upon the variation distribution of characters, to highlight the difference between textual and pictorial regions. This stage outputs a coarse textual layer including textual regions as well as a few pictorial regions with high activity. In the fine stage, a textual connected component (TCC) based refinement is proposed to eliminate the survived pictorial regions. In particular, a scale and orientation invariant grouping algorithm is proposed to adaptively generate TCCs with uniform statistical features. The minimum average distance and morphological operations are employed to assist the formation of candidate TCCs. Then, three string-level features (i.e., shapeness, color similarity, and mean activity level) are designed to distinguish the true TCCs from the false positive ones that are formed by connecting the high activity pictorial components. Extensive experiments show that the proposed framework can segment textual regions precisely from born-digital compound images, while preserving the integrity of texts with varied scales and orientations, and avoiding over-connection of textual regions.

Twelve colonies where the Red-legged Cormorant (Phalacrocorax gaimardi) breeds in Argentina were visited. Physical and biological characteristics were recorded at 29 nesting cliffs and at different sectors within cliffs. Forty-five percent of the cliffs were located on continental shores, the rest were on islands. Cliff height and length varied (mean height = 14 ± 5 m, length range = 12 to 3,000 m) but their slope was commonly 80 to 90°. Most cliffs had more than 50% of the total available area with apparent suitable breeding sites. Cliff length and available area was positively correlated with the number of nests. Forty-nine different sectors used by Red-legged Cormorant on the cliffs were identified. In those sectors, number of active nests was positively correlated and nest density negatively correlated with area. Highest median density of nests was NE in orientation, protected from predominant winds. Minimum average distance from the tide line to the closest nest group was positively correlat...

This paper presents a novel method for isolated English word recognition based on energy and zero crossing features with vector quantization. This isolated word recognition method consists of two phases, feature extraction phase and recognition phase. In feature extraction, end points are detected and noise is removed using end point detection algorithm, a feature vector is obtained by combining the energy and zero cross rate into a single vector of twenty dimensions. Recognition phase consists of two steps, feature training and testing, in feature training, codebooks for each reference samples are generated using LBG Vector Quantization algorithm. For testing Euclidean distance is calculated between test sample feature vector and codebook of all reference speech samples. Speech sample with minimum average distance is selected. Experimental results showed that the maximum recognition rate of 85% is obtained for codebook size of 4.

A new compact pattern based dynamic channel assignment strategy called CP-based DCA is proposed. The strategy aims at dynamically keeping the cochannel cells of any channel to a compact pattern. A compact pattern of a channel is defined as the pattern with minimum average distance between cochannel cells. CP-based DCA consists of two phases: channel allocation and channel packing. Channel allocation is used to assign an optimal idle channel to a new call. Channel packing is responsible for the restoration of the compact patterns and is performed only when a compact channel is released. Simulation results indicate that the CP-based DCA always performs better than the borrowing with directional channel locking (BDCL) strategy. In our designed example, CP-based DCA is shown to have 2% more traffic-carrying capacity than that of the BDCL in case of uniform traffic, and 8% more traffic-carrying capacity in case of nonuniform traffic, both at a blocking rate of 0.02. Besides, the number of channels reassigned per released call in CP-based DCA is at most one and is, therefore, another advantage over BDCL.