In an implicit combinatorial optimization problem, the constraints are not enumerated explicitly but rather stated implicitly through equations, other constraints or auxiliary algorithms. An important subclass of such problems is the implicit set cover (or, equivalently, hitting set) problem in which the sets are not given explicitly but rather defined implicitly. For example, the well-known minimum feedback arc set problem is such a problem. In this paper, we consider such a cover problem that arises in the study of wild populations in biology in which the sets are defined implicitly via the Mendelian constraints and prove approximability results for this problem.
Background Since biological systems are complex and often involve multiple types of genomic relationships, tensor analysis methods can be utilized to elucidate these hidden complex relationships. There is a pressing need for this, as the interpretation of the results of high‐throughput experiments has advanced at a much slower pace than the accumulation of data. Results In this review we provide an overview of some tensor analysis methods for biological systems. Conclusions Tensors are natural and powerful generalizations of vectors and matrices to higher dimensions and play a fundamental role in physics, mathematics and many other areas. Tensor analysis methods can be used to provide the foundations of systematic approaches to distinguish significant higher order correlations among the elements of a complex systems via finding ensembles of a small number of reduced systems that provide a concise and representative summary of these correlations.
We show that neural networks with three-times continuously differentiable activation functions are capable of computing a certain family of n-bit Boolean functions with two gates, whereas networks composed of binary threshold functions require at least Ω(log n) gates. Thus, for a large class of activation functions, analog neural networks can be more powerful than discrete neural networks, even when computing Boolean functions.
The understanding of molecular cell biology requires insight into the structure and dynamics of networks that are made up of thousands of interacting molecules of DNA, RNA, proteins, metabolites, and other components. One of the central goals of systems biology is the unraveling of the as yet poorly characterized complex web of interactions among these components. This work is made harder by the fact that new species and interactions are continuously discovered in experimental work, necessitating the development of adaptive and fast algorithms for network construction and updating. Thus, the "reverse-engineering" of networks from data has emerged as one of the central concern of systems biology research. A variety of reverse-engineering methods have been developed, based on tools from statistics, machine learning, and other mathematical domains. In order to effectively use these methods, it is essential to develop an understanding of the fundamental characteristics of these algorithms. With that in mind, this chapter is dedicated to the reverse-engineering of biological systems. Specifically, we focus our attention on a particular class of methods for reverse-engineering, namely those that rely algorithmically upon the so-called "hitting-set" problem, which is a classical combinatorial and computer science problem, Each of these methods utilizes a different algorithm in order to obtain an exact or an approximate solution of the hitting set problem. We will explore the ultimate impact that the alternative algorithms have on the inference of published in silico biological networks.
REVIEWS OF BOOKS CLINICAL RHEUMATOLOGY ILLUSTRATED. Edited by Frank Dudley Hart. Pp. 409. £54.50. Baltimore: Williams and Wilkins. 1987. B. DASGUPTA B. DASGUPTA Search for other works by this author on: Oxford Academic PubMed Google Scholar Rheumatology, Volume 28, Issue 1, February 1989, Pages 91–92, https://doi.org/10.1093/rheumatology/28.1.91-b Published: 01 February 1989
In this paper we consider the problem of cooperative motion planning for redundant mobile manipulator on uneven terrains. This approach involves formulating the trajectory planning as non-linear constrained minimization problem of joint angle movement of mobile manipulator at each instance. The main problem is to solve (i) the redundancy exist in the system considering parameters of wheel-terrain interactions, (ii) the cooperative behavior of the mobile manipulator while performing the task, and (iii) the manipulability issues. To perform task the manipulator moves towards desired location, while the mobile robot moves to enhance the manipulator task space. A weighting factors has been introduced to define the level of importance of movement of each joint of the mobile manipulator. A quality measure has been computed to measure the ability of mobile manipulator for a particular configuration. The problem of trajectory planning and redundancy resolution has been solved by Augmented Lagrangian Method (ALM). To evaluate the method several simulations have been performed. The simulation and experimental results have been presented, which shows that the method provides feasible trajectories and successfully tracks the desired end-effector path.
Steinhaus graphs are simple undirected graphs in which the first row of the adjacency matrix A=(a_{r,s}) (excluding the very first entry which is always 0) is an arbitrary sequence of zeros and ones and the remaining entries in the upper triangular part of A are defined by a_{r,s} = ((a_{r-1,s-1} + a_{r-1,s})) mod 2 (for 2 >= r > s >= n). Such graphs have already been studied for their various properties. In this paper we characterize bipartite Steinhaus graphs, and use this characterization to give an exact count as well as linear upper and lower bounds for the number of such graphs on n vertices. These results answer affirmatively some questions posed by W.M. Dymacek (Discrete Mathematics, 59 (1986) pp. 9-20).
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