Ovidiu Daescu

The Human Red Blood Cell Proteome and Interactome

The red blood cell or erythrocyte is easily purified, readily available, and has a relatively simple structure. Therefore, it has become a very well studied cell in terms of protein composition and function. RBC proteomic studies performed over the last five years, by several laboratories, have identified 751 proteins within the human erythrocyte. As RBCs contain few internal structures, the proteome will contain far fewer proteins than nucleated cells. In this minireview, we summarize the current knowledge of the RBC proteome, discuss alterations in this partial proteome in varied human disease states, and demonstrate how in silico studies of the RBC interactome can lead to considerable insight into disease diagnosis, severity, and drug or gene therapy response. To make these latter points we focus on what is known concerning changes in the RBC proteome in Sickle Cell Disease.

The proteomics and interactomics of human erythrocytes

In this minireview, we focus on advances in our knowledge of the human erythrocyte proteome and interactome that have occurred since our seminal review on the topic published in 2007. As will be explained, the number of unique proteins has grown from 751 in 2007 to 2289 as of today. We describe how proteomics and interactomics tools have been used to probe critical protein changes in disorders impacting the blood. The primary example used is the work done on sickle cell disease where biomarkers of severity have been identified, protein changes in the erythrocyte membranes identified, pharmacoproteomic impact of hydroxyurea studied and interactomics used to identify erythrocyte protein changes that are predicted to have the greatest impact on protein interaction networks.

Determining an Optimal Penetration among Weighted Regions in Two and Three Dimensions

We present efficient algorithms for solving the problem of computing an optimal penetration (a ray or a semi-ray) among weighted regions in 2-D and 3-D spaces. This problem finds applications in several areas, such as radiation therapy, geological exploration, and environmental engineering. Our algorithms are based on a combination of geometric techniques and optimization methods. Our geometric analysis shows that the d-D (d = 2, 3) optimal penetration problem can be reduced to solving O(n2(d−1)) instances of certain special types of non-linear optimization problems, where n is the total number of vertices of the regions. We also give implementation results of our 2-D algorithms.

SPACE-EFFICIENT ALGORITHMS FOR APPROXIMATING POLYGONAL CURVES IN TWO-DIMENSIONAL SPACE

Given an n-vertex polygonal curve P = [p1, p2, …, pn] in the 2-dimensional space R2, we consider the problem of approximating P by finding another polygonal curve such that the vertex sequence of P′ is an ordered subsequence of the vertices along P. The goal is to either minimize the size m of P′ for a given error tolerance ∊ (called the min-# problem), or minimize the deviation error ∊ between P and P′ for a given size m of P′ (called the min-∊ problem). We present useful techniques and develop efficient algorithms for solving the 2-D min-# and min-∊ problems under two commonly-used error criteria for curve approximations. Our algorithms improve substantially the space bounds of the previously best known results on the same problems while maintain the same time bounds as those of the best known algorithms. We further show that our 2-D techniques can be used to improve the time and space bounds for a special case of the 3-D min-# and min-∊ problems.

Efficient algorithms and implementations for optimizing the sum of linear fractional functions, with applications

This paper presents an improved algorithm for solving the sum of linear fractional functions (SOLF) problem in 1-D and 2-D. A key subproblem to our solution is the off-line ratio query (OLRQ) problem, which asks to find the optimal values of a sequence of m linear fractional functions (called ratios), each ratio subject to a feasible domain defined by O(n) linear constraints. Based on some geometric properties and the parametric linear programming technique, we develop an algorithm that solves the OLRQ problem in O((m+n)log (m+n)) time. The OLRQ algorithm can be used to speed up every iteration of a known iterative SOLF algorithm, from O(m(m+n)) time to O((m+n)log (m+n)), in 1-D and 2-D. Implementation results of our improved 1-D and 2-D SOLF algorithm have shown that in most cases it outperforms the commonly-used approaches for the SOLF problem. We also apply our techniques to some problems in computational geometry and other areas, improving the previous results.

CUTTING OUT POLYGONS WITH LINES AND RAYS

We present approximation algorithms for cutting out a polygon P with n vertices from another convex polygon Q with m vertices by line cuts and ray cuts. For line cuts we require both P and Q are convex while for ray cuts we require Q is convex and P is ray cuttable. Our results answer a number of open problems and are either the first solutions or significantly improve over previously known solutions. For the line cutting version, we prove a key property that leads to a simple, constant factor approximation algorithm. For the ray cutting version, we prove it is possible to compute in almost linear time a cutting sequence that is an O(log2 n)-factor approximation of an optimal cutting sequence. No algorithms were previously known for the ray cutting version.

Space-Efficient Algorithms for Approximating Polygonal Curves in Two Dimensional Space

Given an n-vertexp olygonal curve P = [p1, p2,..., pn] in the 2-dimensional space R2, we consider the problem of approximating P by finding another polygonal curve P′ = [p′1, p′2,..., p′m] of m vertices in R2 such that the vertexs equence of P′ is an ordered subsequence of the vertices along P. The goal is to either minimize the size m of P′ for a given error tolerance ∈ (called the min-# problem), or minimize the deviation error ∈ between P and P′ for a given size m of P′ (called the min-∈ problem). We present useful techniques and develop a number of efficient algorithms for solving the 2-D min-# and min-∈ problems under two commonly-used error criteria for curve approximations. Our algorithms improve substantially the space bounds of the previously best known results on the same problems while maintain the same time bounds as those of the best known algorithms.

Farthest-point queries with geometric and combinatorial constraints

In this paper we discuss farthest-point problems in which a set or sequence S of n points in the plane is given in advance and can be preprocessed to answer various queries efficiently. First, we give a data structure that can be used to compute the point farthest from a query line segment in O(log2 n) time. Our data structure needs O(n log n) space and preprocessing time. To the best of our knowledge no solution to this problem has been suggested yet. Second, we show how to use this data structure to obtain an output-sensitive query-based algorithm for polygonal path simplification. Both results are based on a series of data structures for fundamental farthest-point queries that can be reduced to each other.

k -link shortest paths in weighted subdivisions

We study the shortest path problem in weighted polygonal subdivisions of the plane, with the additional constraint of an upper bound, k, on the number of links (segments) in the path. We prove structural properties of optimal paths and utilize these results to obtain approximation algorithms that yield a path having O(k) links and weighted length at most (1+e) times the weighted length of an optimal k-link path, for any fixed e>0. Some of our results make use of a new solution for the 1-link case, based on computing optimal solutions for a special sum-of-fractionals (SOF) problem. We have implemented a system, based on the CORE library, for computing optimal 1-link paths; we experimentally compare our new solution with a previous method for 1-link optimal paths based on a prune-and-search scheme.

Applying parallel design techniques to template matching with GPUs

Designing algorithms for data parallelism can create significant gains in performance on SIMD architectures. The performance of General Purpose GPUs can also benefit from careful analysis of memory usage and data flow due to their large throughput and system memory bottlenecks. In this paper we present an algorithm for template matching that is designed from the beginning for the GPU architecture and achieves greater than an order of magnitude speedup over traditional algorithms designed for the CPU and reimplemented on the GPU. This shows that it is not only desirable to adapt existing algorithms to run on GPUs, but also that future algorithms should be designed with the GPU architecture in mind.