Real-time interference analysis between a tool and an environment

Spatial data structures form a core ingredient of many geometric algorithms, both in theory and in practice. Many of these data structures, especially the ones used in practice, are based on partitioning the underlying space (examples are binary space partitions and decompositions of polygons) or partitioning the set of objects (examples are bounding-volume hierarchies). The efficiency of such data structures---and, hence, of the algorithms that use them---depends on certain characteristics of the partitioning. For example the performance of many algorithms that use binary space partitions (BSPs) depends on the size of the BSPs. Similarly, the performance of answering range queries using bounding-volume hierarchies (BVHs) depends on the so-called crossing number that can be associated with the partitioning on which the BVH is based. Much research has been done on the problem of computing partitioning whose characteristics are good in the worst case. In this thesis, we studied the problem from a different point of view, namely instance-optimality. In particular, we considered the following question: given a class of geometric partitioning structures---like BSPs, simplicial partitions, polygon triangulations, …---and a cost function---like size or crossing number---can we design an algorithm that computes a structure whose cost is optimal or close to optimal for any input instance (rather than only worst-case optimal). We studied the problem of finding optimal data structures for some of the most important spatial data structures. As an example having a set of n points and an input parameter r, It has been proved that there are input sets for which any simplicial partitions has crossing number ¿(vr). It has also been shown that for any set of n input points and the parameter r one can make a simplicial partition with stabbing number O(vr). However, there are input point sets for which one can make simplicial partition with lower stabbing number. As an example when the points are on a diagonal, one can always make a simplicial partition with stabbing number 1. We started our research by studying BSPs for line segments in the plane, where the cost function is the size of the BSPs. A popular type of BSPs for line segments are the so-called auto-partitions. We proved that finding an optimal auto-partition is NP-hard. In fact, finding out if a set of input segments admits an auto-partition without any cuts is already NP-hard. We also studied the relation between two other types of BSPs, called free and restricted BSPs, and showed that the number of cuts of an optimal restricted BSP for a set of segments in R2 is at most twice the number of cuts of an optimal free BSP for that set. The details are being represented in Chapter 1 of the thesis. Then we turned our attention to so-called rectilinear r-partitions for planar point sets, with the crossing number as cost function. A rectilinear r-partition of a point set P is a partitioning of P into r subsets, each having roughly |P|/r points. The crossing number of the partition is defined using the bounding boxes of the subsets; in particular, it is the maximum number of bounding boxes that can be intersected by any horizontal or vertical line. We performed some theoretical as well as experimental studies on rectilinear r-partitions. On the theoretical side, we proved that computing a rectilinear r-partition with optimal stabbing number for a given set of points and parameter r is NP-hard. We also proposed an exact algorithm for finding optimal rectilinear r-partitions whose running time is polynomial when r is a constant, and a faster 2-approximation algorithm. Our last theoretical result showed that considering only partitions whose bounding boxes are disjoint is not sufficient for finding optimal rectilinear r-partitions. On the experimental side, we performed a comparison between four different heuristics for constructing rectilinear r-partitions. The so-called windmill KD-tree gave the best results. Chapter 2 of the thesis describes all the details of our research on rectilinear r-partitions. We studied another spatial data structure in Chapter 3 of the thesis. Decomposition of the interior of polygons is one of the fundamental problems in computational geometry. In case of a simple polygon one usually wants to make a Steiner triangulation of it, and when we have a rectilinear polygon at hand, one typically wants to make a rectilinear decomposition for it. Due to this reason there are algorithms which make Steiner triangulations and rectangular decompositions with low stabbing number. These algorithms are worst-case optimal. However, similar to the two previous data structures, there are polygons for which one can make decompositions with lower stabbing numbers. In 3 we proposed a 3-approximation for finding an optimal rectangular decomposition of a rectilinear polygon. We also proposed an O(1)-approximation for finding optimal Steiner triangulation of a simple polygon. Finally, in Chapter 4 of the thesis, we considered another optimization problem, namely how to approximate a piecewise-linear function F: R ¿R with another piecewise-linear function with fewer pieces. Here one can distinguish two versions of the problem. The first one is called the min-k problem; the goal is then to approximate the function within a given error e such that the resulting function has the minimum number of links. The second one is called the min-e problem; here the goal is to find an approximation with at most k links (for a given k) such that the error is minimized. These problems have already been studied before. Our contribution is to consider the problem for so-called uncertain functions, where the value of the input function F at its vertices is given as a discrete set of different values, each with an associated probability. We show how to compute an approximation that minimizes the expected error.

We describe a new and simple method for constructing binary space partitions (BSPs) in arbitrary dimensions. We also introduce the concept of uncluttered scenes, which are scenes with a certain property that we suspect many realistic scenes exhibit, and we show that our method constructs a BSP of size O(n) for an uncluttered scene consisting of n objects. The construction time is O(n log n) . Because any set of disjoint fat objects is uncluttered, our result implies an efficient method to construct a linear size BSP for fat objects. We use our BSP to develop a data structure for point location in uncluttered scenes. The query time of our structure is O( log n) , and the amount of storage is O(n) . This result can in turn be used to perform range queries with not-too-small ranges in scenes consisting of disjoint fat objects or, more generally, in so-called low-density scenes.

New results on binary space partitions in the plane

We show that there is always a binary space partition (BSP) of size O(n log k) and an autopartition of size O(nk) for n disjoint line segments in the plane, assuming that the segments have k distinct orientations. In particular, if k is a constant, these bounds imply that there is a linear-size BSP and autopartition. Our proof is constructive and can be turned into algorithms computing such a BSP or autopartition in O(n2 ) and O(n2k ) times.

We revisit the notion of kinetic efficiency for noncanonically defined discrete attributes of moving data, like binary space partitions and triangulations. Under reasonable computational models, we obtain lower bounds on the minimum amount of work required to maintain any binary space partition of moving segments in the plane or any Steiner triangulation of moving points in the plane. Such lower bounds—the first to be obtained in the kinetic context—are necessary to evaluate the efficiency of kinetic data structures when the attribute to be maintained is not canonically defined.

We provide a variety of new results, including upper and lower bounds, as well as simpler proof techniques for the efficient construction of binary space partitions (BSP's) of axis-parallel segments, rectangles, and hyperrectangles. (a) A consequence of the analysis in \cite{dAF} is that any set of $n$ axis-parallel and pairwise-disjoint line segments in the plane admits a binary space partition of size at most $2n-1$. We establish a worst-case lower bound of $2n-o(n)$ for the size of such a BSP, thus showing that this bound is almost tight in the worst case. (b) We give an improved worst-case lower bound of $\frac{9}{4}n-o(n)$ on the size of a BSP for isothetic pairwise disjoint rectangles. (c) We present simple methods, with equally simple analysis, for constructing BSP's for axis-parallel segments in higher dimensions, simplifying the technique of \cite{PY2} and improving the constants. (d) We obtain an alternative construction (to that in \cite{PY2}) of BSP's for collections of axis-parallel rectangles in 3-space. (e) We present a construction of BSP's of size $O(n^{5/3})$ for $n$ axis-parallel pairwise disjoint 2-rectangles in $\reals^4$, and give a matching worst-case lower bound of $\Omega(n^{5/3})$ for the size of such a BSP. (f) We extend the results of \cite{PY2} to axis-parallel $k$-dimensional rectangles in $\reals^d$, for $k

Spoken accents severely degrade the performance of automatic speech recognition (ASR) systems. Domain adversarial training (DAT) is widely adopted for generating domain-invariant features to reduce the influence of accents. However, the generated features trained by DAT are still maintaining some accent discrimination information, limiting the ASR performance. In addition, the features generated by DAT of each accent have different degrees of residual accent discriminant information. In this paper, we propose an adaptive attention network with DAT to further eliminate the influence of retaining accent information in features generated by DAT. We employ the adaptive attention module to transform the encoder output to a more general representation. Experiments on the AESRC2020 dataset show that the proposed method can achieve satisfactory performance improvements on seen and unseen accent when the correct accent information is still preserved in the output of the encoder.

Structural magnetic resonance imaging (sMRI) reveals the structural organization of the brain. Learning general brain representations from sMRI is an enduring topic in neuroscience. Previous deep learning models neglect that the brain, as the core of cognition, is distinct from other organs whose primary attribute is anatomy. Capturing the high-level representation associated with inter-individual cognitive variability is key to appropriately represent the brain. Given that this cognition-related information is subtle, mixed, and distributed in the brain structure, sMRI-based models need to both capture fine-grained details and understand how they relate to the overall global structure. Additionally, it is also necessary to explicitly express the cognitive information that implicitly embedded in local-global image features. Therefore, we propose MCPATS, a brain representation learning framework that combines Multi-task Collaborative Pre-training (MCP) and Adaptive Token Selection (ATS). First, we develop MCP, including mask-reconstruction to understand global context, distort-restoration to capture fine-grained local details, adversarial learning to integrate features at different granularities, and age-prediction, using age as a surrogate for cognition to explicitly encode cognition-related information from local-global image features. This co-training allows progressive learning of implicit and explicit cognition-related representations. Then, we develop ATS based on mutual attention for downstream use of the learned representation. During fine-tuning, the ATS highlights discriminative features and reduces the impact of irrelevant information. MCPATS was validated on three different public datasets for brain disease diagnosis, outperforming competing methods and achieving accurate diagnosis. Further, we performed detailed analysis to confirm that the MCPATS-learned representation captures cognition-related information.

We propose in this paper a new method based on binary space partitions to simultaneously mesh and compress a depth map. The method divides the map adaptively into a mesh that has the form of a binary triangular tree (tritree). The nodes of the mesh are the sparse non-uniform samples of the depth map and are able to interpolate the other pixels with minimal error. We apply differential coding after that to represent the sparse disparities at the mesh nodes. We then use entropy coding to compress the encoded disparities. We finally benefit from the binary tree and compress the mesh via binary tree coding to condense its representation. The results we obtained on various depth images show that the proposed scheme leads to lower depth error rate at higher compression ratios when compared to standard compression techniques like JPEG 2000. Moreover, using our method, a depth map is represented with a compressed adaptive mesh that can be directly applied to render the 3D scene.

The focus of this paper is a novel Intelligent Distribution Panel (IDP) for controlling and monitoring power quality in small-scale ac power grids. A prototype ten-channel IDP capable of managing up to 38 kW is demonstrated. Each channel includes a relay and supports high-frequency current monitoring for smart metering. The ac current's fundamental and harmonic content up to the 7th harmonic are precisely measured and the state of each channel can be controlled. A low-power single-board computer is used to perform data acquisition and facilitate energy management. Tasks such as frequency locking and real-time power monitoring are implemented using a digital Multiple Second Order General Integrator - Frequency Locked Loop (MSOGI-FLL) algorithm. The measured frequency and the extracted real and reactive power have an accuracy within 1% for the majority of the operating conditions.