A Compact Camera with a Reconfigurable Real-time Embedded Image Processor for Pharmaceutical Capsule Inspections

The following thesis presents the system requirements, design methodology, final hardware design and system integration of a custom digital camera for high-speed pharmaceutical capsule inspections. The primary goals of the camera design were to minimize the cost of the device and to have a flexible design that could be easily upgraded in the future. For this application, a 3.1 mega pixel CMOS image sensor was used with a USB 2.0 interface. In addition, the custom camera can pre-process image data in an embedded, reconfigurable real-time image processor implemented in a FPGA. All data processing in the camera occurs with only buffering four rows of an image, eliminating the need for RAM on the device and lowering the overall cost. The final design was manufactured and implemented into a complete inspection system which used 16 of these cameras to inspect up to 60 000 capsules per second

Lower Bounds for Linear Locally Decodable Codes and Private Information Retrieval

We prove that if a linear error-correcting code C: {0, 1}^n → {0, 1}^m is such that a bit of the message can be probabilistically reconstructed by looking at two entries of a corrupted codeword, then m = 2^(Ω(n)). We also present several extensions of this result. We show a reduction from the complexity, of one-round, information-theoretic private information retrieval systems (with two servers) to locally decodable codes, and conclude that if all the servers' answers are linear combinations of the database content, then t = Ω(n/2^a), where t is the length of the user's query and a is the length of the servers' answers. Actually, 2^a can be replaced by O(a^k), where k is the number of bit locations in the answer that are actually inspected in the reconstruction

On Parsimonious Explanations For 2-D Tree- and Linearly-Ordered Data

This paper studies the ``explanation problem\u27\u27 for tree- and linearly-ordered array data, a problem motivated by database applications and recently solved for the one-dimensional tree-ordered case. In this paper, one is given a matrix A=(a_{ij}) whose rows and columns have semantics: special subsets of the rows and special subsets of the columns are meaningful, others are not. A submatrix in A is said to be meaningful if and only if it is the cross product of a meaningful row subset and a meaningful column subset, in which case we call it an ``allowed rectangle.\u27\u27 The goal is to ``explain\u27\u27 A as a sparse sum of weighted allowed rectangles. Specifically, we wish to find as few weighted allowed rectangles as possible such that, for all i,j, a_ij equals the sum of the weights of all rectangles which include cell (i,j). In this paper we consider the natural cases in which the matrix dimensions are tree-ordered or linearly-ordered. In the tree-ordered case, we are given a rooted tree $T_1$ whose leaves are the rows of $A$ and another, $T_2$, whose leaves are the columns. Nodes of the trees correspond in an obvious way to the sets of their leaf descendants. In the linearly-ordered case, a set of rows or columns is meaningful if and only if it is contiguous. For tree-ordered data, we prove the explanation problem NP-Hard and give a randomized $2$-approximation algorithm for it. For linearly-ordered data, we prove the explanation problem NP-Har and give a $2.56$-approximation algorithm. To our knowledge, these are the first results for the problem of sparsely and exactly representing matrices by weighted rectangles

Improved Approximation Algorithms for PRIZE-COLLECTING STEINER TREE and TSP

Abstract — We study the prize-collecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a. PATH-TSP) problems (PCST, PCTSP, and PCS, respectively): given a graph (V, E) with costs on each edge and a penalty (a.k.a. prize) on each node, the goal is to find a tree (for PCST), cycle (for PCTSP), or stroll (for PCS) that minimizes the sum of the edge costs in the tree/cycle/stroll and the penalties of the nodes not spanned by it. In addition to being a useful theoretical tool for helping to solve other optimization problems, PCST has been applied fruitfully by AT&T to the optimization of real-world telecommunications networks. The most recent improvements for the first two problems, giving a 2-approximation algorithm for each, appeared first in 1992. (A 2-approximation for PCS appeared in 2003.) The natural linear programming (LP) relaxation of PCST has an integrality gap of 2, which has been a barrier to further improvements for this problem. We present (2 − ɛ)-approximation algorithms for all three problems, connected by a unified technique for improving prizecollecting algorithms that allows us to circumvent the integrality gap barrier. 1

Real-time Expulsion Detection and Characterization in Ultrasound M-scans of the Resistance Spot Welding Process

In this work, ultrasound is used as a non-destructive method of monitoring the welding process in real-time to detect expulsion events. During spot welding, a single element ultrasound transducer placed behind one of the welding electrodes operates in pulse-echo mode and probes the axial center of the welded zone. Acoustic reflections from the electrodes, plate interfaces and liquid metal weld nugget are recorded as A-scans. During welding, the A-Scan reflections change with time, since the material properties of steel (e.g. density and elasticity) change with temperature. Imaging successive A-scans in time forms an M-Scan image of the welding process from which the dynamic formation of the spot weld can be depicted and analyzed. This thesis focuses on taking a brand new approach to the problem of expulsion detection by identifying and characterizing expulsion events in M-scan data. Expulsion occurs when molten material is ejected from the welded zone as a result of overheating due to: poor electrical/thermal contact, coating thickness and/or excessive weld current. An expulsion can have a significant impact on the final yield strength of the weld, and thus the detection and characterization of expulsion events is significant to the quality assurance of resulting spot welds. The main contribution of this work was the discovery of M-scan features that provide a means of detecting, predicting and classifying the event. These include: 1) Detection by sudden phase delay change of the workpiece surface reflection. 2) Prediction by ultrasonically measuring the heating rate prior to expulsion. 3) Classification of the weld quality by ultrasonically measuring indentation in the heated workpiece. In addition, new methods for automatically detecting and measuring these features were developed that utilize a new efficient Hough transform variant proposed in this work. It was shown using both lab experiments and industrial data that not only does the automatic detection of these features provide a new and robust means of identifying expulsions in a wide range of welding setups, but this research can also be used in the future to provide real-time feedback to dynamic weld controllers and eliminate expulsions from occurring altogether

Lessons from the Congested Clique Applied to MapReduce

The main results of this paper are (I) a simulation algorithm which, under quite general constraints, transforms algorithms running on the Congested Clique into algorithms running in the MapReduce model, and (II) a distributed $O(\Delta)$-coloring algorithm running on the Congested Clique which has an expected running time of (i) $O(1)$ rounds, if $\Delta \geq \Theta(\log^4 n)$; and (ii) $O(\log \log n)$ rounds otherwise. Applying the simulation theorem to the Congested-Clique $O(\Delta)$-coloring algorithm yields an $O(1)$-round $O(\Delta)$-coloring algorithm in the MapReduce model. Our simulation algorithm illustrates a natural correspondence between per-node bandwidth in the Congested Clique model and memory per machine in the MapReduce model. In the Congested Clique (and more generally, any network in the $\mathcal{CONGEST}$ model), the major impediment to constructing fast algorithms is the $O(\log n)$ restriction on message sizes. Similarly, in the MapReduce model, the combined restrictions on memory per machine and total system memory have a dominant effect on algorithm design. In showing a fairly general simulation algorithm, we highlight the similarities and differences between these models.Comment: 15 page

EVOLUTIONARY ALGORITHMS FOR OVERLAPPING CORRELATION CLUSTERING

Abstract. In Overlapping Correlation Clustering (OCC), a number of objects are assigned to clusters. Two objects in the same cluster have correlated characteristics. As opposed to traditional clustering where objects are assigned to a single cluster, in OCC objects may be assigned to one or more clusters. since an object can have characteristics that are correlated with objects in more than one cluster. In this paper, we present Biased Random-Key Genetic Algorithms for OCC. Computational experiments are presented. 1

Competitive Algorithms for Layered Graph Traversal

A layered graph is a connected graph whose vertices are partitioned into sets L0=s, L1, L2,..., and whose edges, which have nonnegative integral weights, run between consecutive layers. Its width is {|Li|}. In the on-line layered graph traversal problem, a searcher starts at s in a layered graph of unknown width and tries to reach a target vertex t; however, the vertices in layer i and the edges between layers i-1 and i are only revealed when the searcher reaches layer i-1. We give upper and lower bounds on the competitive ratio of layered graph traversal algorithms. We give a deterministic on-line algorithm which is O(9w)-competitive on width-w graphs and prove that for no w can a deterministic on-line algorithm have a competitive ratio better than 2w-2 on width-w graphs. We prove that for all w, w/2 is a lower bound on the competitive ratio of any randomized on-line layered graph traversal algorithm. For traversing layered graphs consisting of w disjoint paths tied together at a common source, we give a randomized on-line algorithm with a competitive ratio of O(log w) and prove that this is optimal up to a constant factor