Simple Geometric Transformations Research Articles

DOCLASP - Docking ligands to target proteins using spatial and electrostatic congruence extracted from a known holoenzyme and applying simple geometrical transformations.

The ability to accurately and effectively predict the interaction between proteins and small drug-like compounds has long intrigued researchers for pedagogic, humanitarian and economic reasons. Protein docking methods (AutoDock, GOLD, DOCK, FlexX and Glide to name a few) rank a large number of possible conformations of protein-ligand complexes using fast algorithms. Previously, it has been shown that structural congruence leading to the same enzymatic function necessitates the congruence of electrostatic properties (CLASP). The current work presents a methodology for docking a ligand into a target protein, provided that there is at least one known holoenzyme with ligand bound - DOCLASP (Docking using CLASP). The contact points of the ligand in the holoenzyme defines a motif, which is used to query the target enzyme using CLASP. If there are no significant matches, the ligand cannot be docked in the protein. Otherwise, the holoenzyme and the target protein are superimposed based on congruent atoms. The same linear and rotational transformations are also applied to the ligand, thus creating a unified coordinate framework having the holoenzyme, the ligand and the target enzyme. This provides the docked ligand in the target enzyme. Previously, CLASP was used to predict and validate (in vivo) the inhibition of phosphoinositide-specific phospholipase C (PI-PLC) from Bacillus cereus by two dipeptidyl peptidase-IV (DPP4) inhibitors - vildagliptin and K-579. In the current work, vildagliptin was docked to the PI-PLC structure complexed with myo-inositol using DOCLASP. The docked ligand is free from steric clashes and interacts with the same side chain residues that bind myo-inositol, providing corroboration of the validity of the proposed methodology.

DOCLASP - Docking ligands to target proteins using spatial and electrostatic congruence extracted from a known holoenzyme and applying simple geometrical transformations.

The ability to accurately and effectively predict the interaction between proteins and small drug-like compounds has long intrigued researchers for pedagogic, humanitarian and economic reasons. Protein docking methods (AutoDock, GOLD, DOCK, FlexX and Glide to name a few) rank a large number of possible conformations of protein-ligand complexes using fast algorithms. Previously, it has been shown that structural congruence leading to the same enzymatic function necessitates the congruence of electrostatic properties (CLASP). The current work presents a methodology for docking a ligand into a target protein, provided that there is at least one known holoenzyme with ligand bound - DOCLASP (Docking using CLASP). The contact points of the ligand in the holoenzyme defines a motif, which is used to query the target enzyme using CLASP. If there are no significant matches, the ligand cannot be docked in the protein. Otherwise, the holoenzyme and the target protein are superimposed based on congruent atoms. The same linear and rotational transformations are also applied to the ligand, thus creating a unified coordinate framework having the holoenzyme, the ligand and the target enzyme. This provides the docked ligand in the target enzyme. Previously, CLASP was used to predict and validate (in vivo) the inhibition of phosphoinositide-specific phospholipase C (PI-PLC) from Bacillus cereus by two dipeptidyl peptidase-IV (DPP4) inhibitors - vildagliptin and K-579. In the current work, vildagliptin was docked to the PI-PLC structure complexed with myo-inositol using DOCLASP. The docked ligand is free from steric clashes and interacts with the same side chain residues that bind myo-inositol, providing corroboration of the validity of the proposed methodology.

Design of Pyramid Column Sensor with Photodiodes for Measuring Solar Power

In this study, five photodiode detectors are used to constitute a solar power sensor that can measure both the directly incident and undisciplined power of solar light. The solar power sensor is composed of four trapezoidal facets along with an upper rectangular facet formed on top to constitute a rectangular pyramid column sensor. On each facet, a photodiode sensor is implemented to collect solar light power coming from different orientations including the directly incident and undisciplined power. By applying a perpetual calendar to obtain the corresponding azimuth angle and elevation angle of sunlight, the collected power data of the five detectors are employed to estimate the maximum directly incident power and undisciplined power of solar light by simple geometric transformation. Therefore, the proposed rectangular pyramid column sensor can effectively provide the detailed solar power data including directly incident and undisciplined power.

A Geometric Mapping Cross Approximation method

Abstract The matrices of Boundary Element Method (BEM) are fully populated and require special compression techniques for the efficient treatment. In this article, the H-matrix representation is used to approximate the dense stiffness matrix in admissible blocks by low-rank matrices. This paper presents a Geometric Mapping Cross Approximation (GMCA) algorithm to compute the low-rank matrices. Compared with the Adaptive Cross Approximation (ACA), the GMCA determines the skeleton points from the two interacting groups of nodes by their spacing characteristics directly and, thus, has a remarkable non-iterative nature and requires some simple geometric transformations, only. Numerical examples show that the new algorithm is feasible.

Improved iris localization by using wide and narrow field of view cameras for iris recognition

Biometrics is a method of identifying individuals by their physiological or behavioral characteristics. Among other biometric identifiers, iris recognition has been widely used for various applications that require a high level of security. When a conventional iris recognition camera is used, the size and position of the iris region in a captured image vary according to the X , Y positions of a user’s eye and the Z distance between a user and the camera. Therefore, the searching area of the iris detection algorithm is increased, which can inevitably decrease both the detection speed and accuracy. To solve these problems, we propose a new method of iris localization that uses wide field of view (WFOV) and narrow field of view (NFOV) cameras. Our study is new as compared to previous studies in the following four ways. First, the device used in our research acquires three images, one each of the face and both irises, using one WFOV and two NFOV cameras simultaneously. The relation between the WFOV and NFOV cameras is determined by simple geometric transformation without complex calibration. Second, the Z distance (between a user’s eye and the iris camera) is estimated based on the iris size in the WFOV image and anthropometric data of the size of the human iris. Third, the accuracy of the geometric transformation between the WFOV and NFOV cameras is enhanced by using multiple matrices of the transformation according to the Z distance. Fourth, the searching region for iris localization in the NFOV image is significantly reduced based on the detected iris region in the WFOV image and the matrix of geometric transformation corresponding to the estimated Z distance. Experimental results showed that the performance of the proposed iris localization method is better than that of conventional methods in terms of accuracy and processing time.

IMPROVED POINTER MACHINE AND I/O LOWER BOUNDS FOR SIMPLEX RANGE REPORTING AND RELATED PROBLEMS

We investigate one of the fundamental areas in computational geometry: lower bounds for range reporting problems in the pointer machine and the external memory models. We develop new techniques that lead to new and improved lower bounds for simplex range reporting as well as some other geometric problems. Simplex range reporting is the problem of storing n points in the d-dimensional space in a data structure such that the k points that lie inside a query simplex can be found efficiently. This is one of the fundamental and extensively studied problems in computational geometry. Currently, the best data structures for the problem achieve Q(n) + O(k) query time using [Formula: see text] space in which the [Formula: see text] notation either hides a polylogarithmic or an nε factor for any constant ε > 0, (depending on the data structure and Q(n)). The best lower bound on this problem is due to Chazelle and Rosenberg who showed any pointer machine data structure that can answer queries in O(nγ + k) time must use Ω(nd-ε-dγ) space. Observe that this bound is a polynomial factor away from the best known data structures. In this article, we improve the space lower bound to [Formula: see text]. Not only this bridges the gap from polynomial to sub-polynomial, it also offers a smooth trade-off curve. For instance, for polylogarithmic values of Q(n), our space lower bound almost equals Ω((n/Q(n))d); the latter is generally believed to be the “right” bound. By a simple geometric transformation, we also improve the best lower bounds for the halfspace range reporting problem. Furthermore, we study the external memory model and offer a new simple framework for proving lower bounds in this model. We show that answering simplex range reporting queries with Q(n)+O(k/B) I/Os requires [Formula: see text]) space or [Formula: see text] blocks, in which B is the block size.

The geometric element transformation method for tetrahedral mesh smoothing

The geometric element transformation method (GETMe) has been introduced as a new element driven approach to mesh smoothing. It is based on simple geometric transformations, which, if applied iteratively, lead to the regularization of mesh elements. Global mesh smoothing can be accomplished by successively improving the worst elements or by averaging node positions obtained by the simultaneous transformation of all elements. GETMe smoothing has been successfully applied in the case of surface meshes. As shown in this paper, this approach also naturally extends to tetrahedral mesh smoothing without major conceptual modifications. A regularizing transformation for tetrahedra is presented and a combined approach of simultaneous and sequential GETMe smoothing is described. First numerical examples yield high quality meshes superior to those obtained by other geometry-based methods. In fact, the presented results are in a majority of cases at least comparable to those obtained by a state of the art global optimization-based method.

The geometric element transformation method for mixed mesh smoothing

The geometric element transformation method (GETMe) is a geometry-based smoothing method for mixed and non-mixed meshes. It is based on a simple geometric transformation applicable to elements bounded by polygons with an arbitrary number of nodes. The transformation, if applied iteratively, leads to a regularization of the polygons. Global mesh smoothing is accomplished by averaging the new node positions obtained by local element transformations. Thereby, the choice of transformation parameters as well as averaging weights can be based on the element quality which leads to high quality results. In this paper, a concept of an enhanced transformation approach is presented and a proof for the regularizing effect of the transformation based on eigenpolygons is given. Numerical examples confirm that the GETMe approach leads to superior mesh quality if compared to other geometry-based methods. In terms of quality it can even compete with optimization-based techniques, despite being conceptually significantly simpler.

Interest Points for Hyperspectral Image Data

Interest points are widely used as point-features for image matching. This paper describes robust and efficient algorithms to extract multiscale interest points in hyperspectral images in which structural information is distributed across several spectral bands. The formulation is based on a Gaussian scale-space representation of the hyperspectral data cube, and the use of a principal components decomposition to combine information efficiently across spectral bands. A spectral distance measure is used to characterize spatial relations between neighboring hyperspectral pixels. In addition, we describe methods for preprocessing a pair of hyperspectral images, clustering the spectral signatures of interest points, and using the resulting data for matching points under simple geometric transformations. The stability of the resulting interest points in time-lapse satellite images was determined to be in the range of 52% to 75% in the testing data set that were acquired from variety of landforms like coastal islands of La Parguera, Chesapeake Bay, the Cuprite Mining District of Nevada, and agricultural field images of Kansas and Oklahoma, and thus, they can be used as a foundation for image matching and related image analysis tasks.

Precise Modeling Framework for Short-Channel Double-Gate and Gate-All-Around MOSFETs

A precise modeling framework for short-channel nanoscale double-gate (DG) and gate-all-around (GAA) MOSFETs is presented. For the DG MOSFET, the modeling is based on a conformal mapping analysis of the potential distribution in the device body arising from the interelectrode capacitive coupling, combined with a self-consistent procedure to include the effects of the inversion charge. The DG interelectrode coupling, which dominates the subthreshold behavior of the device, can also be applied with a high degree of precision to the cylindrical GAA MOSFET by performing a simple geometric scaling transformation to account for the difference in gate control in the two devices. Near threshold, self-consistent procedures invoking Poisson's equation in combination with boundary conditions and suitable modeling expressions for the potential are applied to the two devices. In strong inversion, these solutions converge to those of the respective long-channel devices. The drain current is calculated as part of the self-consistent treatment. The results for both the electrostatics and the current are in excellent agreement with numerical simulations.

Capacities of certain plane condensers and sets under simple geometric transformations

In this article, we investigate the behaviour of conformal capacities of several plane condensers and logarithmic capacities of some compact sets under the following types of geometric transformations: a gap moving in one or two plates, translation, and rotation of plates and breaking plates. Main motivating examples are provided by parallel plate condensers although the majority of our results are true for more general condensers. We prove monotonicity theorems in most cases and find extremal configurations with maximal capacity in more difficult ones. Our main tools are polarization and direct application of the extended Dirichlet principle. The last section of this article contains several open problems and conjectures.

Unwrapping Curves from Cylinders and Cones

Now imagine the elliptical cross section replaced by any curve lying on the surface of a right circular cylinder. What happens to this curve when the cylinder is unwrapped? Consider also the inverse problem, which you can experiment with by yourself: Start with a plane curve (line, circle, parabola, sine curve, etc.) drawn with a felt pen on a rectangular sheet of transparent plastic, and roll the sheet into cylinders of different radii. What shapes does the curve take on these cylinders? How do they appear when viewed from different directions? A few trials reveal an enormous number of possibilities, even for the simple case of a circle. This paper formulates these somewhat vague questions more precisely, in terms of equations, and shows that they can be answered with surprisingly simple twodimensional geometric transformations, even when the cylinder is not circular. For a circular cylinder, a sinusoidal influence is always present, as exhibited in Figures

Employing genetic ‘moments’ in the history of mathematics in classroom activities

The integration of history into educational practice can lead to the development of activities through the use of genetic ‘moments’ in the history of mathematics. In the present paper, we utilize Oresme’s genetic ideas – developed during the fourteenth century, including ideas on the velocity–time graphical representation as well as geometric transformations and reconfigurations – to develop mathematical models that can be employed for the solution of problems relating to linear motion. The representation of distance covered as the area of the figure between the graph of velocity and the time axis employed in these activities, leads on naturally to the study of problems on motion by means of functions, as well as allowing for the use of tools (concepts and propositions) from Euclidean geometry of relevance to such problems. By employing simple geometric transformations, equivalent real life problems are obtained which lead, in turn, to a simple classification of all linear motion-related problems. When applied to a wider range of motion problems, this approach prepares the way for the introduction of basic Calculus concepts (such as integral, derivative and their interrelation); in fact, we would argue that it could be beneficial to teach the basic concepts and results of Calculus from an early grade by employing natural extensions of the teaching methods considered in this paper.

Influence of Geometry and Edge Cooling on Thermal Spreading Resistance

This paper presents a simple geometric transformation for predicting thermal spreading resistance in isotropic and compound rectangular flux channels using the solution for an isotropic or compound circular flux tube. It is shown that the results are valid for a wide range of channel aspect ratios and source to base coverage ratio. Because the circular disk solution requires a single series summation, it is preferable to the rectangular flux channel solution, which requires the evaluation of two single-series and one double-series summation. The effect of edge cooling is also addressed in flux tubes and flux channels. A new analytical solution is obtained for thermal spreading resistance in a rectangular flux channel with edge cooling. This solution contains many limiting cases, including a previously published solution for adiabatic edges. Comparisons are made with the circular flux tube with edge cooling and with adiabatic edges. Simple relationships are developed for edge-cooled systems to assess the importance of edge cooling. This alleviates the issue of computing or recomputing eigenvalues when the edge-cooling conditions change or have no impact. It is shown that this simple approach provides good results for a wide range of dimensionless parameters.

High-Frequency Operation of the Coils for Standard Magnetic-Field Generation Using the Bulk-Current Technique

The sum of the currents in the individual wires of a multiturn coil (here referred to as the bulk current) possesses properties that can extend the useful operating range of the device to frequencies substantially higher that those obtainable through the traditional control of the terminal current. This paper theoretically analyzes and experimentally confirms some basic results about the high-frequency behavior of coils. The analysis is initially based on the multiconductor transmission line theory applied to an equivalent line model obtained through a simple geometrical transformation of the coil; then closed-form formulas predicting the essential deviations from ideal at high frequencies (well beyond the first resonance) are presented. The response to different types of feed (balanced or single ended) is also described. The "bunch" or "bulk" current concept is a new finding, not existing in the previous literature. The analysis of the bulk current reveals that the magnetic field remains constant and predictable up to frequencies many times higher than the resonant frequency of the coil. Experimental results confirming the theoretical predictions are presented and discussed.

Watermarking schema for digital still images based on geometrical transformation

In real time watermarking applications robustness and computational complexity are playing very important role. In this paper we focus on new algorithm for inserting of watermark in digital still images. This algorithm is based on simple but efficient geometrical transformation of image and has fast embedding and extracting watermark pattern with acceptable robustness. Proposed method is illustrated on one example. It has been shown that it is possible to confirm existing of the watermark also in JPEG compressed image.

Local and global visual grouping: tuning for spatial frequency and contrast.

Glass patterns are visual textures composed of a field of dot pairs (dipoles) whose orientations are determined by a simple geometrical transformation, such as a rotation. Detection of structure in these patterns requires the observer to perform local grouping (to find dipoles) and global grouping to combine their orientations into a percept of overall shape. We estimated the spatial frequency tuning of these grouping processes by measuring signal-to-noise detection thresholds for Glass patterns composed of spatially narrow-band elements. Local tuning was probed by varying the spatial frequency difference between the two elements comprising each dipole. Global tuning was estimated using dipoles containing one spatial frequency and then estimating masking as a function of the spatial frequency of randomly positioned noise elements. We report that the tuning of local grouping is band-pass (ie, it is responsive to a narrow range of spatial frequencies), but that tuning of global grouping is broad and low-pass (ie, it integrates across a broader range of lower spatial frequencies). Control experiments examined how the contrast and visibility of elements might contribute to these findings. Local grouping proved to be more resistant to local contrast variation than global grouping. We conclude that local grouping is consistent with the use of simple-oriented filtering mechanisms. Global grouping seems to depend more on the visibility of elements that can be affected by both spatial frequency and contrast.

The Involvement of Recurrent Connections in Area CA3 in Establishing the Properties of Place Fields: a Model

Strong constraints on the neural mechanisms underlying the formation of place fields in the rodent hippocampus come from the systematic changes in spatial activity patterns that are consequent on systematic environmental manipulations. We describe an attractor network model of area CA3 in which local, recurrent, excitatory, and inhibitory interactions generate appropriate place cell representations from location- and direction-specific activity in the entorhinal cortex. In the model, familiarity with the environment, as reflected by activity in neuromodulatory systems, influences the efficacy and plasticity of the recurrent and feedforward inputs to CA3. In unfamiliar, novel, environments, mossy fiber inputs impose activity patterns on CA3, and the recurrent collaterals and the perforant path inputs are subject to graded Hebbian plasticity. This sculpts CA3 attractors and associates them with activity patterns in the entorhinal cortex. In familiar environments, place fields are controlled by the way that perforant path inputs select among the attractors. Depending on the training experience provided, the model generates place fields that are either directional or nondirectional and whose changes when the environment undergoes simple geometric transformations are in accordance with experimental data. Representations of multiple environments can be stored and recalled with little interference, and these have the appropriate degrees of similarity in visually similar environments.

On Rational Geometry of Conic Sections

Simple geometric objects and transformations appear in representations and algorithms of geometric facilities in computer applications such as modelling, robotics, or graphics. Usually, these applications only support objects and transformations fully describable by rational parameters, and a computer display of points of the objects at least implicitly requires points with rational coordinates. In this setting we investigate some basic questions of the geometry of rational conic sections, when the geometry is defined by the group of rational projective transformations, the group of rational affine transformations, or the group of rational rigid transformations. Some results follow classical results, while others turn out to be quite different. In particular, we obtain a complete classification scheme for nondegenerate rational conics for rational affine geometry and a constructive method for production of a minimal set of representatives of all equivalence classes.

The use of video sample rate converters to achieve three-dimensional effects

This paper presents a method of performing high-quality video scaling and advanced video juggling to achieve three-dimensional video effects. This method does not rely on an expensive three-dimensional graphics rendering unit but smartly combines simple geometric and perspective transformations with advanced video sample rate conversion. The key is to start from two-dimensional video sample rate conversion, instead of graphics accelerators, for these three-dimensional effects. Results show that the picture quality using this method greatly exceeds that with state-of-the-art 3D graphics rendering units. Furthermore, the complexity is only in the order of video sample rate converters, which are usually already part of a high-end TV set.