Narrow Results

The problem of negative design of DNA languages is addressed, that is, properties and construction methods of large sets of words that prevent undesired bonds when used in DNA computations. We recall a few existing formalizations of the problem and then define the property of sim-bond-freedom, where sim is a similarity relation between words. We show that this property is decidable for context-free languages and polynomial-time decidable for regular languages. The maximality of this property also turns out to be decidable for regular languages and polynomial-time decidable for an important case of the Hamming similarity. Then we consider various construction methods for Hamming bond-free languages, including the recently introduced method of templates, and obtain a complete structural characterization of all maximal Hamming bond-free languages. This result is applicable to the θ-k-code property introduced by Jonoska and Mahalingam.

We study the trajectories of photons in modified Hayward black hole spacetime. Three kinds of horizons are distinguished by analyzing the lapse function of modified Hayward black hole spacetime. Through plotting the effective potential with different values of parameters, it is found that the parameter $b$ has more conspicuous effects than parameters $\alpha$ ($\alpha$ is associated with the time-delay) and $\beta$ ($\beta$ is related to the 1-loop quantum corrections) for the effective potential. The change of the parameters ($\alpha$, $\beta$ and $b$) has an obvious influence on unstable circular orbits. The structure of null geodesic is simpler than that of time-like geodesic. The stable circular orbits and the bound orbits are not included for the photon trajectories. By analyzing the corresponding effective potential, all possible orbits of null geodesic are found. The radius of unstable circular orbit equals 2.8790 for fixed $\ell =0.60M$, $b=4.00M$, $\alpha =0.50$, $\beta =1.00$ and $M=1.00$.

This paper presents a new approach for the estimation of motion trajectories from image sequences. This approach is seen to be similar to both "token tracking" feature-based methods, and "block based" region-matching approaches. Initially, a parametric motion trajectory model is formulated, and the motion trajectory estimation problem is conveniently cast into a Markov Random Field (MRF) framework which allows a priori motion constraints to be expressed. A three-stage optimization algorithm is presented, and a recursive estimation approach is developed. A method for the robust detection of areas of occlusion is presented, as are comparative results to show the relative success of this motion estimation approach. Although robustly computed motion trajectories show great promise in many motion-related areas of computer vision, this paper illustrates their use in the context of motion compensated prediction as part of a video compression algorithm.

Widespread availability of location aware devices (such as GPS receivers) promotes capture of detailed movement trajectories of people, animals, vehicles and other moving objects. We investigate spatio-temporal movement patterns in large tracking data sets, i.e. in large sets of polygonal paths. Specifically, we study so-called 'popular places', that is, regions that are visited by many entities.

Given a set of polygonal paths with a total of vertices, we look at the problem of computing such popular places in two different settings. For the discrete model, where only the vertices of the polygonal paths are considered, we propose an algorithm; and for the continuous model, where also the straight line segments between the vertices of a polygonal path are considered, we develop an algorithm. We also present lower bounds and hardness results.

In this paper we consider the problem of detecting commuting patterns in a trajectory. For this we search for similar subtrajectories. To measure spatial similarity we choose the Fréchet distance and the discrete Fréchet distance between subtrajectories, which are invariant under differences in speed. We give several approximation algorithms, and also show that the problem of finding the 'longest' subtrajectory cluster is as hard as MaxClique to compute and approximate.

One of the important tasks in the analysis of spatio-temporal data collected from moving entities is to find a group: a set of entities that travel together for a sufficiently long period of time. Buchin et al.² introduce a formal definition of groups, analyze its mathematical structure, and present efficient algorithms for computing all maximal groups in a given set of trajectories. In this paper, we refine their definition and argue that our proposed definition corresponds better to human intuition in certain cases, particularly in dense environments.

We present algorithms to compute all maximal groups from a set of moving entities according to the new definition. For a set of $n$ moving entities in ${ℝ}^1$, specified by linear interpolation in a sequence of $\tau$ time stamps, we show that all maximal groups can be computed in $O({\tau }^2{n}^4)$ time. A similar approach applies if the time stamps of entities are not the same, at the cost of a small extra factor of $\alpha (n)$ in the running time, where $\alpha$ denotes the inverse Ackermann function. In higher dimensions, we can compute all maximal groups in $O({\tau }^2{n}^{5}logn)$ time (for any constant number of dimensions), regardless of whether the time stamps of entities are the same or not.

We also show that one $\tau$ factor can be traded for a much higher dependence on $n$ by giving a $O(\tau n^4{2}^n)$ algorithm for the same problem. Consequently, we give a linear-time algorithm when the number of entities is constant and the input size relates to the number of time stamps of each entity. Finally, we provide a construction to show that it might be difficult to develop an algorithm with polynomial dependence on $n$and linear dependence on $\tau$.

This paper presents a multiscale comparison method for three-dimensional trajectories. In order to deal with the problem that zero-crossings of curvature cannot be determined for space curve, we utilize the maxima of curvature. The method first traces the positions of curvature maxima across scales for recognizing the hierarchy of partial trajectories. Then it performs cross-scale matching of partial trajectories derived from two input trajectories, and obtains the structurally best matches. Finally, it calculates the value-based dissimilarity for each pair of the matched partial trajectories and output as the final dissimilarity between trajectories that can be further used for clustering or classification tasks. In experiments on the UCI character trajectory dataset we demonstrate that reasonable correspondences were captured successfully and the derived dissimilarity yielded good clustering results comparable to DTW. We also demonstrate using real medical data that the method could generate interesting clusters that might reflect distribution of fibrotic stages.

Recent improvements in positioning technology have led to a much wider availability of massive moving object data. A crucial task is to find the moving objects that travel together. In common, these object sets are called object movement patterns. Due to the emergence of many different kinds of object movement patterns in recent years, different approaches have been proposed to extract them. However, each approach only focuses on mining a specific kind of patterns. It is costly and time consuming to mine and manage various number of patterns, since we have to execute a large number of different pattern mining algorithms. Moreover, we have to execute these algorithms again whenever new data are added to the existing database. To address these issues, we first redefine movement patterns in the itemset context. Second, we propose a unifying approach, named GeT_Move, which uses a frequent closed itemset-based object movement pattern-mining algorithm to mine and manage different patterns. GeT_Move is developed in two versions which are GeT_Move and Incremental GeT_Move. To optimize the efficiency and to free the parameters setting, we further propose a Parameter Free Incremental GeT_Move algorithm. Comprehensive experiments are performed on real and large synthetic datasets to demonstrate the effectiveness and efficiency of our approaches.

In earlier models, synaptic plasticity forms the basis for cellular signaling underlying learning and memory. However, synaptic computation of learning and memory in the brain remains controversial. In this paper, we discuss ways in which synaptic plasticity remodels subcellular networks by deflecting trajectories in neuronal state-space as regulating patterns for the synthesis of dynamic continuity that form cognitive networks of associable representations through endogenous dendritic coding to consolidate memory.

In the north of Chile three of the five pre-selected candidate sites to host TMT are located; namely, these were Cerro Armazones, Cerro Tolar and Cerro Tolonchar. The TMT site testing program conducted measurements of the meteorological conditions and the optical turbulence strength throughout the atmosphere (the turbulence profiles) above these sites. A peculiar case of turbulence occurrence above these sites happened during the night of August 13, 2006. We will show a study on the meteorological conditions above these sites adressing the origin of this particular turbulence behaviour.

A synoptic analysis for this night shows anticyclonic predominance (AP) and Jet Stream (JS) activity at the high levels of the atmosphere. Simulations using the MM5 mesoscale model are performed and compared to the measured meteorological site conditions. Turbulence above Tolonchar seems be associated to the Jet Stream, but the turbulence above Tolar can not clearly be associated to the synoptic conditions. Also trajectories were calculated for each site at altitude levels of the turbulence profiles. The low level trajectories for Tolar show the origin of air during this night being South-East of the central valley, following the orography. For Armazones the low level trajectories originate from North-East. The flow which affects Tolonchar is strongly influenced by the western circulation which is present at these intermediate altitudes at around 500 hPa. Simulations based on MM5 show clear signs of a local circulation for each site, but to improve the results it will be necessary to increase the spatial resolution of the models in order to trace turbulent processes, follow their evolution and investigate their relation with good and bad seeing.

We study the property that trajectories on real hypersurfaces of type (B) in a complex hyperbolic space are tangentially of order two. By investigating the image of the moduli space of such trajectories in the moduli space of circles on a complex hyperbolic space, we give some characterizations of homogeneous Hopf hypersurfaces.

We study whether trajectories for Kähler magnetic fields on a complex hyperbolic space are obtained as extrinsic shapes of trajectories on some real hypersurface of type (A). We show that bounded trajectories are expressed by geodesics and by trajectories on some real hypersurfaces but unbounded trajectories are not expressed by them if strengths of Kähler magnetic fields are small compared with the absolute value of the holomorphic sectional curvature.

We define magnetic mean operators which are generators of random walks under action of magnetic fields. We calculate their formal Taylor expansions and show that the influence of magnetic fields first appears on the third term in general and on the fourth term for Kähler magnetic fields.

We give a survey on constructing real surfaces associated with trajectories for Kähler magnetic fields and on comparing sectors and crescents on these surfaces.

This paper presents a new approach for the estimation of motion trajectories from image sequences. This approach is seen to be similar to both “token tracking” feature-based methods, and “block based” region-matching approaches. Initially, a parametric motion trajectory model is formulated, and the motion trajectory estimation problem is conveniently cast into a Markov Random Field (MRF) framework which allows a priori motion constraints to be expressed. A three-stage optimization algorithm is presented, and a recursive estimation approach is developed. A method for the robust detection of areas of occlusion is presented, as are comparative results to show the relative success of this motion estimation approach. Although robustly computed motion trajectories show great promise in many motion-related areas of computer vision, this paper illustrates their use in the context of motion compensated prediction as part of a video compression algorithm.

In this article we propose discrete models of trajectories for Kähler magnetic fields. We consider regular graphs whose edges are colored by 2 colors and compare the asymptotic behaviors of the number of prime cycles on them with those of prime trajectory-cycles on compact quatients of complex hyperbolic spaces.

In this paper we improve the comparison theorem on magnetic Jacobi fields for Kähler magnetic fields under an assumption that sectional curvatures are bounded from above or from below by some constants.

On a real hypersurface in a Kähler manifold we have a natural closed 2-form associated with the induced almost contact metric structure. Constant multiples of this form are called Sasakian magnetic fields. In this article we explain the behavior of trajectories for these magnetic fields which are also circles or curves of order 2 on homogeneous Hopf real hypersurfaces of constant principal curvatures in a complex hyperbolic space.

In this note we attempt to reconsider circles of positive geodesic curvature on a complex hyperbolic space by use of magnetic fields on real hypersurfaces. In particular, we show that every horocyclic circle is a trajectory for some Sasakian magnetic field on a horosphere. We show also that the same property holds for horocyclic helices of proper order 3 each of which is an orbit of one parameter family of isometries and lies on a totally geodesic complex hyperbolic plane.

In this paper we study balls and spheres formed by trajectories for Kähler magnetic fields on a Kähler manifold and give estimates of their volume elements under some assumptions on sectional curvatures.