Cache-Oblivious Selection in Sorted X+Y Matrices

Let X[0..n-1] and Y[0..m-1] be two sorted arrays, and define the mxn matrix A by A[j][i]=X[i]+Y[j]. Frederickson and Johnson gave an efficient algorithm for selecting the k-th smallest element from A. We show how to make this algorithm IO-efficient. Our cache-oblivious algorithm performs O((m+n)/B) IOs, where B is the block size of memory transfers

Adaptive neuro-fuzzy technique for autonomous ground vehicle navigation

This article proposes an adaptive neuro-fuzzy inference system (ANFIS) for solving navigation problems of an autonomous ground vehicle (AGV). The system consists of four ANFIS controllers; two of which are used for regulating both the left and right angular velocities of the AGV in order to reach the target position; and other two ANFIS controllers are used for optimal heading adjustment in order to avoid obstacles. The two velocity controllers receive three sensor inputs: front distance (FD); right distance (RD) and left distance (LD) for the low-level motion control. Two heading controllers deploy the angle difference (AD) between the heading of AGV and the angle to the target to choose the optimal direction. The simulation experiments have been carried out under two different scenarios to investigate the feasibility of the proposed ANFIS technique. The simulation results have been presented using MATLAB software package; showing that ANFIS is capable of performing the navigation and path planning task safely and efficiently in a workspace populated with static obstacles

Fat Polygonal Partitions with Applications to Visualization and Embeddings

Let $\mathcal{T}$ be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in $\mathcal{T}$ is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in $\mathbb{R}^d$. We use these partitions with slack for embedding ultrametrics into $d$-dimensional Euclidean space: we give a $\mathop{\rm polylog}(\Delta)$-approximation algorithm for embedding $n$-point ultrametrics into $\mathbb{R}^d$ with minimum distortion, where $\Delta$ denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in $n$. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.Comment: 26 page

Models of Non-Well-Founded Sets via an Indexed Final Coalgebra Theorem

The paper uses the formalism of indexed categories to recover the proof of a standard final coalgebra theorem, thus showing existence of final coalgebras for a special class of functors on categories with finite limits and colimits. As an instance of this result, we build the final coalgebra for the powerclass functor, in the context of a Heyting pretopos with a class of small maps. This is then proved to provide a model for various non-well-founded set theories, depending on the chosen axiomatisation for the class of small maps

Can we always sweep the details of RNA-processing under the carpet?

RNA molecules follow a succession of enzyme-mediated processing steps from transcription until maturation. The participating enzymes, for example the spliceosome for mRNAs and Drosha and Dicer for microRNAs, are also produced in the cell and their copy-numbers fluctuate over time. Enzyme copy-number changes affect the processing rate of the substrate molecules; high enzyme numbers increase the processing probability, low enzyme numbers decrease it. We study different RNA processing cascades where enzyme copy-numbers are either fixed or fluctuate. We find that for fixed enzyme-copy numbers the substrates at steady-state are Poisson-distributed, and the whole RNA cascade dynamics can be understood as a single birth-death process of the mature RNA product. In this case, solely fluctuations in the timing of RNA processing lead to variation in the number of RNA molecules. However, we show analytically and numerically that when enzyme copy-numbers fluctuate, the strength of RNA fluctuations increases linearly with the RNA transcription rate. This linear effect becomes stronger as the speed of enzyme dynamics decreases relative to the speed of RNA dynamics. Interestingly, we find that under certain conditions, the RNA cascade can reduce the strength of fluctuations in the expression level of the mature RNA product. Finally, by investigating the effects of processing polymorphisms we show that it is possible for the effects of transcriptional polymorphisms to be enhanced, reduced, or even reversed. Our results provide a framework to understand the dynamics of RNA processing

Using Entropy-Based Methods to Study General Constrained Parameter Optimization Problems

In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use on the quest for optimal solutions of an optimization problem. Moreover, the entropy, and its associated density of states, give us information concerning the feasibility of solutions.Comment: 10 pages, 3 figures, references correcte

Snapping Graph Drawings to the Grid Optimally

In geographic information systems and in the production of digital maps for small devices with restricted computational resources one often wants to round coordinates to a rougher grid. This removes unnecessary detail and reduces space consumption as well as computation time. This process is called snapping to the grid and has been investigated thoroughly from a computational-geometry perspective. In this paper we investigate the same problem for given drawings of planar graphs under the restriction that their combinatorial embedding must be kept and edges are drawn straight-line. We show that the problem is NP-hard for several objectives and provide an integer linear programming formulation. Given a plane graph G and a positive integer w, our ILP can also be used to draw G straight-line on a grid of width w and minimum height (if possible).Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

The Homogeneous Broadcast Problem in Narrow and Wide Strips

Let $P$ be a set of nodes in a wireless network, where each node is modeled as a point in the plane, and let $s\in P$ be a given source node. Each node $p$ can transmit information to all other nodes within unit distance, provided $p$ is activated. The (homogeneous) broadcast problem is to activate a minimum number of nodes such that in the resulting directed communication graph, the source $s$ can reach any other node. We study the complexity of the regular and the hop-bounded version of the problem (in the latter, $s$ must be able to reach every node within a specified number of hops), with the restriction that all points lie inside a strip of width $w$. We almost completely characterize the complexity of both the regular and the hop-bounded versions as a function of the strip width $w$.Comment: 50 pages, WADS 2017 submissio