Distance Problem Research Articles

A new linear time algorithm to compute the genomic distance via the double cut and join distance

The genomic distance problem in the Hannenhalli–Pevzner (HP) theory is the following: Given two genomes whose chromosomes are linear, calculate the minimum number of translocations, fusions, fissions and inversions that transform one genome into the other. This paper presents a new distance formula based on a simple tree structure that captures all the delicate features of this problem in a unifying way, and a linear time algorithm for computing this distance.

Bandh Syndrome and its Impact on Trade and Commerce in North-East India

The North-East India (NEI) consists of eight states and it is a ‘mixed bag’ of several ethnic groups. The region is known for its unexploited natural and human resources which are the basic factors of economic development. So, the energetic entrepreneurs are necessary if we want to harness it properly. With the emergence of Globalization and more recently with the inception of ‘Look East Policy’, trade and commerce has become an important tool in linking this region with the Asian and South East Asian countries. Look-East Policy is expected to provide an opportunity to overcome the problem of distance from big markets. It is apparent that NE India as a whole needs a big push or a kick starts to launch the economy on the development path through trade and commerce. But, it is greatly handicapped by law and order situation or bandh and blockade in the region. Economic development of a region is quite illusive agenda without developing trade and commerce in the region. Peaceful environment in the region is the pre-requisite condition for economic development. Keeping this in mind, the question that arises is who will be the active agents in bringing peace in the region?

Flexibility of Contactless Power Transfer using Magnetic Resonance Coupling to Air Gap and Misalignment for EV

Nowadays, the establishment of the technologies of contactless power transfer (CPT) for electric vehicles (EVs) are needed. The system can provide people with a convenient charging system which can powers their EVs wirelessly and automatically when they park. Traditional CPT solutions have the problem of distance between transmitting antennas and receiving antennas (air gap), as well as from the misalignment of the antennas. Those systems cannot power at a great distance and the efficiency is very low. In this paper, CPT by magnetic resonance couplings and small antennas are proposed. These techniques more easily span air gaps and are more forgiving to antennas misalignments than traditional solutions. The Efficiencies are still high when the air gaps are longer than the diameter of the antennas. As well, the efficiencies are over 90% when the antennas are half a diameter out of alignment. For example, when the air gap and the displacement is 150mm, the efficiency is about 96%. The magnetic resonant couplings can power wirelessly even if there is a weak connection. Thus, a large air gaps with high efficiency are possible. The relation between two resonant frequencies and the coupling coefficient are described using the method of equivalent circuits. As well, the relation between resonant frequencies and the efficiencies, especially the moment of decreasing, are described.

Multichromosomal median and halving problems under different genomic distances.

BackgroundGenome median and genome halving are combinatorial optimization problems that aim at reconstructing ancestral genomes as well as the evolutionary events leading from the ancestor to extant species. Exploring complexity issues is a first step towards devising efficient algorithms. The complexity of the median problem for unichromosomal genomes (permutations) has been settled for both the breakpoint distance and the reversal distance. Although the multichromosomal case has often been assumed to be a simple generalization of the unichromosomal case, it is also a relaxation so that complexity in this context does not follow from existing results, and is open for all distances.ResultsWe settle here the complexity of several genome median and halving problems, including a surprising polynomial result for the breakpoint median and guided halving problems in genomes with circular and linear chromosomes, showing that the multichromosomal problem is actually easier than the unichromosomal problem. Still other variants of these problems are NP-complete, including the DCJ double distance problem, previously mentioned as an open question. We list the remaining open problems.ConclusionThis theoretical study clears up a wide swathe of the algorithmical study of genome rearrangements with multiple multichromosomal genomes.

FREIMAN THEOREM, FOURIER TRANSFORM AND ADDITIVE STRUCTURE OF MEASURES

AbstractWe use the Freiman theorem in arithmetic combinatorics to show that if the Fourier transform of certain measures satisfies sufficiently bad estimates, then the support of the measure possesses an additive structure. The result is then discussed in light of the Falconer distance problem.

A Coarsened Network Model Reveals Allosteric Machinery

The past decade has witnessed the development and success of coarse-grained network models of proteins for predicting many equilibrium properties related to collective modes of motion(1,2). We first use a systematic approach on a large set of globular proteins to find a basis for why the network models work well to define certain properties of the system. The analysis is based on the radial distribution function and the spectral dimensions(3) of proteins as well as newly defined quantities, the angular distribution function, and the contact order per mean path length of individual residues. We prove that the network construction is free of the cut-off distance problem if one is interested in the collective motions of the residues.We next undertake a linear response analysis. If the collection of forces applied on a specific residue is independent and large in number, they will appear in a spherically symmetric set of directions. With the aid of responses deviating from such a spherically symmetric distribution, we rigorously determine the residues involved in the remote control of the ligand. These are usually charged surface loop residues, providing binding locations for ions which are known to influence ligand release kinetics(4). We prove that by perturbing any one of these residues, the tip of the cap that opens the exit of the ligand is made to operate coherently, irrespective of the direction of the perturbation. We thereby provide a mechanism on how proteins remotely modulate bound ligands to create preferred kinetic pathways(5,6).1. Bahar, I., A.J. Rader. 2005. Curr Opin Str Biol 15:586.2. Yang, L. et al. 2007. Biophys J 93:920.3. Reuveni, S. et al. 2008. Phys Rev Lett 100:4.4. Hamilton D.H. et al. 2004. J Biol Inorganic Chem 9:936.5. Vendruscolo M.,C.M.Dobson. 2006. Science 313:1586.6. Boehr D.D. et al. 2006. Science 313:1638.

Relationships among different SOS-based relaxations for quadratic distance problems

The objective of the paper is to investigate relationships among different convex relaxations for quadratic distance problems. The main motivation is that a number of problems in robust control can be cast as minimum distance problems from a point to a polynomial surface. It is proven that two families of relaxations proposed in the literature, both based on sum of squares, are equivalent: the former exploits properties of homogeneous forms, while the latter relies on the Positivstellensatz theorem. It is also shown that two different relaxations based on Positivstellensatz present different levels of conservativeness. The results presented in the paper provide useful insights on the trade off between computational burden and conservativeness of the considered relaxations.

The Erdös–Falconer Distance Problem, Exponential Sums, and Fourier Analytic Approach to Incidence Theorems in Vector Spaces over Finite Fields

We study the Erdös–Falconer distance problem in vector spaces over finite fields with respect to the cubic metric. Estimates for discrete Airy sums and Adolphson–Sperber estimates for exponential sums in terms of Newton polyhedra play a crucial role. Similar techniques are used to study the incidence problem between points and cubic and quadratic curves. As a result we obtain a nontrivial range of exponents that appear to be difficult to attain using combinatorial methods.

最適レギュレータによる位置決め整定と残留振動抑制の一手法

Positioning control of vibration systems such as flexible structures is one of the most fundamental technologies for mechanical structures. Different from feedforward control based methods, the use of LQ optimal regulator realizes the feedback control of vibrating parts of a controlled object. However, if the standard LQ optimal regulator is applied to long distance positioning problems, it requires much control energy in motion starting and the positioning error becomes large in settling. Therefore, its use is suitable for positioning settling and residual vibration reduction control in short distance problems. Taking such a background into account, this study proposes a control method switching from a simple feedforward access control technique to the LQ optimal regulator. Especially, this paper mentions a proper switching method of the two control modes. The proposed method does not require much computational load in comparison with the author's conventional methods and is practical for many industry applications. The effectiveness of the proposed method is verified by numerical calculations and experiments.

Improved algorithms for approximate string matching (extended abstract)

BackgroundThe problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share.ResultsWe designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s - |n - m|)·min(m, n, s) + m + n) and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm also excels in practice, especially in cases where the two strings compared differ significantly in length.ConclusionWe have provided the design, analysis and implementation of a new algorithm for calculating the edit distance of two strings with both theoretical and practical implications. Source code of our algorithm is available online.

Flexibility of Programme Delivery in Providing Effective Family-centred Intervention for Remote Families

Equity of service delivery to families of children with hearing loss is an important outcome that is sometimes difficult to achieve. With the current philosophy of family centred practice, questions arise as to how service can be delivered, how equitable that service might be, and how the quality of service may or may not be affected. There were two aims of this study. The first was to investigate beliefs and values around family-centred practice through examining professional beliefs about children, parents and how they could work with families. The second was to investigate how the mode of programme delivery might be associated with outcomes for families. This was done through measuring families' ratings of their own family functioning. Participants included 27 professionals from an early intervention programme for children with hearing loss and 24 families receiving services from the same programme (n = 16 metro; n = 8 rural). Results showed that professionals showed evidence of strong beliefs in most aspects of family-centred practice. They reported that they believed in practice that fostered partnerships, and that they were most effective when they worked with parents rather than directly providing child therapy. All families were satisfied with the intervention they had received and rated themselves highly on family functioning. For rural families the problem of distance from the centre was not an issue since the programme had adopted a flexible service delivery approach. Copyright © 2008 John Wiley & Sons, Ltd.

On distinct distances among points in general position and other related problems

A set of points in the plane is said to be in general position if no three of them are collinear and no four of them are cocircular. If a point set determines only distinct vectors, it is called parallelogram free. We show that there exist n-element point sets in the plane in general position, and parallelogram free, that determine only O(n 2/√log n) distinct distances. This answers a question of Erdős, Hickerson and Pach. We then revisit an old problem of Erdős: given any n points in the plane (or in d dimensions), how many of them can one select so that the distances which are determined are all distinct? — and provide (make explicit) some new bounds in one and two dimensions. Other related distance problems are also discussed.

On the Alexandrov problem of distance preserving mapping

In this paper the author has studied the Alexandrov problem of area preserving mappings in linear 2-normed spaces and has provided some remarks for the generalization of earlier results of H.Y. Chu, C.G. Park and W.G. Park.In addition the author has introduced the concept of linear ( 2 , p ) -normed spaces and for such spaces he has solved the Alexandrov problem.

Pattern matching with pair correlation distance

In pattern matching with the pair correlation distance problem, the goal is to find all occurrences of a pattern P of length m , in a text T of length n , where the distance between them is less than a threshold k . For each text location i , the distance is defined as the number of different kinds of mismatched pairs ( α , β ) , between P and T [ i … i + m ] . We present an algorithm with running time of O ( min { | Σ P | 2 n log m , n ( m log m ) 2 3 } ) for this problem. Another interesting problem is the one-side pair correlation distance where it is desired to find all occurrences of P where the number of mismatched characters in P is less than k . For this problem, we present an algorithm with running time of O ( min { | Σ P | n log m , n m log m } ) .

Protection distance of surge protective devices in low voltage distribution systems

Protection distance of surge protective devices (SPDs) is an important problem in designing a good location scheme of SPDs in low voltage distribution systems for protecting electrical equipments against over-voltage caused by lightning stroke. The simplified lumped-parameter circuit model and the circuit method were used to study the protection distance problem of SPDs. The analytical solutions of the load voltage and general equations of the protection distance of SPDs under different load conditions were given. Simulation results of examples proved the validity of the proposed analytical method.

Optimal recombination algorithms for generalized chains

The problem of sequence recombination has important applications in computational molecular biology. Recently, a distance problem involving recombination consisting of a single crossover was proposed. The problem is to generate a given set of sequences 𝒜 from a given pair of sequences 𝒮 in a minimum number of recombination (i.e., crossover) operations. For an arbitrary class 𝒜 of sequences, the computational complexity of the problem has not yet been settled so it is interesting to find polynomially solvable cases for this kind of recombination distance problem. In recent papers [Y. He and T. Chen, Optimal algorithms for recombination distance problem, Optim. Methods and Soft. 18 (2003), pp. 647–655], [S. Wu and X. Gu, A greedy algorithm for optimal recombination. Proceedings of COCOON2001, Lecture Notes in Computer Science 2108, 2001, 86–90], special classes of sequences called ‘tree’ and ‘chain’ were proposed, and polynomial time algorithms were designed for optimally generating tree and chain classes, respectively. In this paper, we define a new class 𝒜 of sequences, called generalized chain, which greatly extends the definition of chain class by ignoring some restrictive conditions. We distinguish a generalized chain into three cases: continuous chain, discontinuous chain and mixed chain. Then we present optimal algorithms for dealing with all cases of a generalized chain. All algorithms run in polynomial time.

Faster algorithms for guided tree edit distance

The guided tree edit distance problem is to find a minimum cost series of edit operations that transforms two input forests F and G into isomorphic forests F ′ and G ′ such that a third input forest H is included in F ′ (and G ′ ). The edit operations are relabeling a vertex and deleting a vertex. We show efficient algorithms for this problem that are faster than the previous algorithm for this problem of Peng and Ting [Z. Peng, H. Ting, Guided forest edit distance: Better structure comparisons by using domain-knowledge, in: Proc. 18th Symposium on Combinatorial Pattern Matching (CPM), 2007, pp. 28–39].

Multi-break rearrangements and chromosomal evolution

Most genome rearrangements (e.g., reversals and translocations) can be represented as 2- breaks that break a genome at 2 points and glue the resulting fragments in a new order. Multi-break rearrangements break a genome into multiple fragments and further glue them together in a new order. While multi-break rearrangements were studied in depth for k = 2 breaks, the k -break distance problem for arbitrary k remains unsolved. We prove a duality theorem for multi-break distance problem and give a polynomial algorithm for computing this distance.

On the subgroup distance problem

We investigate the computational complexity of finding an element of a permutation group H ⊆ S n with minimal distance to a given π ∈ S n , for different metrics on S n . We assume that H is given by a set of generators. In particular, the size of H might be exponential in the input size, so that in general the problem cannot be solved in polynomial time by exhaustive enumeration. For the case of the Cayley Distance, this problem has been shown to be NP-hard, even if H is abelian of exponent two [R.G.E. Pinch, The distance of a permutation from a subgroup of S n , in: G. Brightwell, I. Leader, A. Scott, A. Thomason (Eds.), Combinatorics and Probability, Cambridge University Press, 2007, pp. 473–479]. We present a much simpler proof for this result, which also works for the Hamming Distance, the l p distance, Lee’s Distance, Kendall’s tau, and Ulam’s Distance. Moreover, we give an NP-hardness proof for the l ∞ distance using a different reduction idea. Finally, we discuss the complexity of the corresponding fixed-parameter and maximization problems.

A numerically stable least squares solution to the quadratic programming problem

Abstract The strictly convex quadratic programming problem is transformed to the least distance problem — finding the solution of minimum norm to the system of linear inequalities. This problem is equivalent to the linear least squares problem on the positive orthant. It is solved using orthogonal transformations, which are memorized as products. Like in the revised simplex method, an auxiliary matrix is used for computations. Compared to the modified-simplex type methods, the presented dual algorithm QPLS requires less storage and solves ill-conditioned problems more precisely. The algorithm is illustrated by some difficult problems.