Half Dimension Research Articles

Parabolic Hitchin maps and their generic fibers

We set up a BNR correspondence for moduli spaces of Higgs bundles over a curve with a parabolic structure over any algebraically closed field. This leads to a concrete description of generic fibers of the associated strongly parabolic Hitchin map. We also show that the global nilpotent cone is equi-dimensional with half dimension of the total space. As a result, we prove the flatness and surjectivity of this map and the existence of very stable parabolic vector bundles.

Proof of Simultaneous Conditional Exponential Stabilization and Destabilization of Linear Hamiltonian Systems

It is proved that any linear Hamiltonian system is simultaneously conditionally (with respect to a subspace of half dimension) exponentially stabilizable and destabilizable by uniformly small Hamiltonian perturbations.

A review of methods of cartographic presentation of urban space

The aim of the article is to present selected solutions applied in urban planning, which, even contemporarily, can be used as models. The paper presents a review of selected concepts of model cities from the antiquity to contemporary times. The article presents methods of creating three-dimensional city models (or their flat presentations in so-called two and a half dimensions), including the historical conceptualization, portraying both the practical and aesthetical features of former map projections. Referring to historical examples, the article also includes historical and contemporary urban 3D models corresponding to analyzed conceptions.

The proof of simultaneous conditional stabilization and destabilization of linear Hamiltonian systems

It is proved that each linear Hamiltonian system is simultaneously conditionally (with respect to a subspace of half dimension) stabilizable and destabilizable by infinitesimal Hamiltonian perturbation.

The Relative Contribution of Features and Dimensions to Semantic Similarity

Similarity governs our perception and reasoning, helping us to relate new stimuli to their long-established category labels and to generalize learned behaviors to novel situations. Similarity has often been explained as arising from commonality of features and parts (Attneave, 1950; Tversky & Hemmenway, 1984) and as a defining metric for categorization processes (Ashby & William 1991; McClelland & Rogers 2004). However, it remains unclear how feature-based (implicit) and explicit components of similarity combine to give rise to perceptual similarity for real-world objects. Here, we collected pairs of explicit unconstrained ('How similar are these two animals?') and dimension-cued similarity judgments, as well as feature ratings used to derive an implicit measure of similarity, for ten basic-level animals across twelve similarity dimensions (six objective: e.g. size; six subjective: e.g. cuteness), presented as either text labels or short videos. Participants' reported explicit similarity judgments were virtually unaffected by presentation modality (r=0.95). Feature-based similarity significantly predicted dimension-cued similarity (top half dimensions: r=0.63--0.92,p< 0.001) and dimension-cued similarity significantly predicted unconstrained similarity (top half dimensions: r=0.78--0.96,p< 0.001). However, feature-based similarity could not explain unconstrained similarity on a dimension-by-dimension basis, but only by linearly combining all implicit similarity dimensions into an aggregate measure (equal-weight: r=0.35,p< 0.05; optimal-weight: r=0.65,p< 0.001). Furthermore, we observed an interaction between subjectivity and explicitness: subjective implicit dimensions explained more variance for explicit similarity, while objective explicit dimensions explained more variance for unconstrained similarity (subjectivity main effect p< 0.01, interaction p< 0.01). Together, our results suggest that feature-based and dimension-cued similarity may combine in a non-trivial way based on feature subjectivity to help generate similarity judgments. Given recent work showing interaction of cognitive control and infero-temporal regions in computing similarity judgments (Keung et al., 2016), our results provide an interesting hypothesis for elucidating the neural components of similarity and its susceptibility to attention and other sources of bias. Meeting abstract presented at VSS 2017

The product of octahedra is badly approximated in the ℓ 2,1-metric

We prove that the Cartesian product of octahedra B1,∞n,m = B1n ×···× B1n (m factors) is poorly approximated by spaces of half dimension in the mixed norm: dN/2(B1,∞n,m, l2,1n,m) ≥ cm, N = mn. As a corollary, we find the order of linear widths of the Holder–Nikol’skii classes Hpr(Td) in the metric of Lq in certain domains of variation of the parameters (p, q).

Stochastic Hall-Magneto-hydrodynamics System in Three and Two and a Half Dimensions

We introduce the stochastic Hall-magneto-hydrodynamics (Hall-MHD) system in three and two and a half dimensions with infinite-dimensional multiplicative noise, white in time, and prove the global existence of a martingale solution via a stochastic Galerkin approximation and applications of Prokhorov’s, Skorokhod’s and martingale representation theorems, as well as the pressure term through de Rham’s theorem adapted to processes. The Hall term represents mathematically a very singular nonlinear term, unprecedented in the previous work. The results extend many others on the deterministic Hall-MHD and stochastic MHD systems and Navier–Stokes equations. In contrast to the stochastic MHD system, the path-wise uniqueness in the two and a half dimensional case is an open problem.

Visual Understanding of Metabolic Pathways Across Organisms using Layout in Two and a Half Dimensions

1 Summary We propose a method for visualizing a set of related metabolic pathways across organisms using 21/2 dimensional graph visualization. Interdependent, twodimensional layouts of each pathway are stacked on top of each other so that biologists get a full picture of subtle and significant dierences among the pathways. The (dis)similarities between pathways are expressed by the Hamming distances of the underlying graphs which are used to compute a stacking order for the pathways. Layouts are determined by a global layout of the union of all pathway graphs using a variant of the proven Sugiyama approach for layered graph drawing. Our variant layout approach allows edges to cross if they appear in dierent graphs.

Interpolation with symmetric polynomials

The Lagrange interpolation problem on spaces of symmetric bivariate polynomials is considered to reduce the interpolation problem to problems of approximately half dimension. The Berzolari-Radon construction is adapted to these kinds of problems by considering nodes placed on symmetric lines or symmetric pairs of lines. A Newton formula for the symmetric interpolant using the Berzolari-Radon construction is proposed.

Compact descriptor for local feature using dominating centre‐symmetric local binary pattern

The authors propose a terse texture feature, called the dominant centre-symmetric local binary pattern (DCSLBP), which has similar distinctiveness and half dimension compared against original centre-symmetric local binary pattern (CS-LBP). On the basis of DCSLBP histogram and an improved construction, a compact descriptor for local feature is presented. To assess the proposed descriptor with the state-of-the-art in performance and dimension, the authors extend it to two variants with different dimensions using the existing method. These descriptors are compared with scale-invariant feature transform (SIFT), multisupport region rotation and intensity monotonic invariant descriptor (MRRID), orthagonal combination local binary pattern (OC-LBP) in interest region matching and in the application of object recognition. The experiments demonstrate the proposed descriptor's compactness and robustness to various image transformations, especially to large illumination change.

Fractal dimension variability in ULF magnetic field with reference to local earthquakes at MPGO, Ghuttu

ABSTRACTUltra-low frequency (ULF) geomagnetic data recorded during 1 January 2010 to 31 December 2010 at multi-parametric geophysical observatory (30.53°N, 78.74°E) in Garhwal Himalaya region of Uttarakhand, India, are analyzed. From the temporal variation of polarization ratio, the presence of seismo-magnetic disturbances superposed upon background geomagnetic variations are inferred. Considering earthquake process as a self-organized critical system based on flicker noise characteristics, fractal dimension for each day is estimated using two methods namely power spectral (FFT) method and Higuchi method. Variability in fractal dimension is studied in the background of local earthquakes (M ≥ 3.5) within a zone of radius 150 km from observing station multi-parametric geophysical observatory (MPGO), Ghuttu. Fractal dimension variability indicates that average fractal dimension for first half of the year is increased as compared to average fractal dimension of second half of the year and there is gradual increase in the fractal dimension before earthquakes. It is also observed that during the first half of the year, there is seismic activity within zone of 150 Km radius centred at around MPGO, Ghuttu. There are no earthquakes during the second half of the year. Gradual increase in the fractal dimension before earthquakes, observed elsewhere in the world, is considered precursory signature of seismo-electromagnetic field emissions.

Effect of base elongation of circular cylinder on its wake characteristics

The present numerical study aims at the control of vortex shedding and drag reduction by shaping the rear geometry of a circular cylinder. The ratio of the semi-major/minor axis dimension (A) of the rear half to the radius of the circular part (R) is varied over a range of values between 0.0 and 4.0. A two-dimensional flow solver has been developed using body-fitting coordinate transformation with Cartesian velocity components as dependent variables and solved using a modified MAC algorithm. The flow solver offers a fast and accurate procedure for modelling viscous incompressible flows in complex geometries. The effect of elongation on the wake characteristics and hydrodynamic coefficients has been investigated for different values of Reynolds number (Re) ranging from 40 to 200. The predicted results indicate that vortex suppression occurs primarily due to reduction in the amplitude of fluctuation than by reduction in the vortex shedding frequency. The critical value of Re for the onset of vortex shedding has been correlated with elongation ratio ER, based on the numerical predictions.

Analysis of stability and stabilization of nonlinear systems via decomposition

We establish necessary and sufficient conditions for the solvability of a Lyapunov-type system of PDEs in the class of homogeneous functions. Using these, we propose an approach to studying the stability of an equilibrium of an essentially nonlinear system of ODEs in the critical case of n zero roots and n pure imaginary roots. The approach bases on decomposition of the system in question into two separate subsystems of half dimension.

Fractional Topological Insulators: A Pedagogical Review

Fractional topological insulators (FTIs) are electronic systems that carry fractionally charged excitations, conserve charge, and are symmetric to reversal of time. In this review, we introduce the basic essential concepts of the field and then survey theoretical understanding of FTIs in two and three dimensions. In between, we discuss the case of “two and a half dimensions,” the FTIs that may form on the two-dimensional surface of an unfractionalized three-dimensional topological insulator. We focus on electronic systems and emphasize properties of edges and surfaces, most notably the stability of gapless edge modes to perturbations.

On the simultaneous conditional stabilizability and destabilizability of linear Hamiltonian systems

Every linear Hamiltonian system is simultaneously conditionally stabilizable (with respect to a subspace of half dimension) and destabilizable by infinitesimal Hamiltonian perturbations; it is also simultaneously conditionally exponentially stabilizable and destabilizable by uniformly small perturbations.

Mechanical and Electrical Reliability Assessment of Stacking of Ultrathin Chips on Si Interposer Using Back-to-Face Architecture

Chip-to-wafer stacking is a key enabling technology for two and half dimension (2.5D) as well as for three dimension (3D), with technological challenges driven by the increase of the die surface and the number of input/outputs (I/Os) and the reduction of the vertical dimensions. In our investigation, chips were assembled using a back-to-face approach on a silicon interposer containing copper through-silicon vias (TSVs). This technology is based on the realization of a high-topology redistribution layer passing over the dies bonded with the active face up on the interposer by using a polymer layer. This architecture is attractive because of the reduction of the chip thickness to an ultrathin dimension, and can offer substantial advantages in terms of design flexibility and technology cost. In this architecture, chip bonding strategies are compared: several bonding materials were tested either on the die side using die-attach film or on the bottom side of the interposer using wafer-level spin-coated polymers. Then, a novel brick (sequence) of processes consisting of high-topology encapsulation and metallization was fully developed to connect the top dies to the bottom wafer. The resulting structure has been modeled through the temperature cycles seen during fabrication using a thermomechanical finite element modeling (FEM) simulation for different geometries and materials. The results indicate a moderate level of stress in the stacked film layers with some concentration in localized regions of the topology. Electrical tests have also been completed at the wafer level, showing low resistances and high yield at front-side and at the back-side level after TSV exposure. Successful reliability tests have also been carried out and support the good mechanical behavior of this integration.

Magnetic Translation Symmetry on the Lattice

Magnetic translation symmetry on a finite periodic square lattice is investigated for an arbitrary uniform magnetic field in arbitrary dimensions. It can be used to classify eigenvectors of the Hamiltonian. The system can be converted to another system of half or lower dimensions. A higher dimensional generalization of Harper equation is obtained for tight-binding systems.

COMMENTARY. tooth‐ and tissue‐supported provisional restorations for the treatment of patients with extended edentulous spans

The loss of even a single tooth is often a psychologically traumatic event. Going from a position where one can claim to have some of his or her “own teeth” to a state of complete edentulism is devastating in a number of ways. The common satisfaction and joy of being able to eat a variety of foods with various textures, tastes, and consistencies is now lost. The patients’ self-image suffers from their inability to smile, speak, and chew with confidence. In addition, the soft-tissue facial drape is now negatively affected by the loss of supporting teeth and a profound decrease in the vertical dimension of the lower half of their face. This significant change in facial appearance becomes most noticeable during the very frequent act of swallowing. A rapidly aged appearance is now how they see themselves in the mirror. The sequela of seeing this, if even for a short time, is a lasting negative effect on their psyche, often difficult to later overcome. Dentistry has always been aware of these intimate relationships and has sought to provide endodontic and periodontal care with the goal of maintaining and prolonging the retention of teeth. Failing that, prosthodontics has provided solutions from fixed bridgework to immediately delivered complete dentures. Whereas immediate dentures could partially mitigate the patients’ feeling of loss and satisfy their esthetic needs, they fell short in the functional and psychological aspects that patients desired. The advent of implant dentistry gave us new modalities with which to eventually satisfy these needs. However, for the newly edentulous patient, a complete denture was usually the interim prosthesis used during the period of osseointegration. Occasionally, during the immediate postsurgical period, he or she was even asked to go without it to allow for optimal soft-tissue healing, worsening the psychological trauma. The authors of this article have painstakingly developed a protocol using teeth with a poor or hopeless prognosis and relatively stable soft-tissue anatomic landmarks to retain and stabilize a provisional fixed prosthesis, their goal being to overcome that awkward phase between tooth loss and restoration of the integrated implants. They have given us a fresh way of looking at a failing dentition and should be applauded for an innovative concept that adds another tool for our use in trying to provide optimum treatment for our patients. However, as shown in this article, a meticulous regimen involving significant laboratory participation with multiple castings, and considerable clinical chair time to develop, deliver, and maintain this interim prosthesis are required. While this technique appears well suited for an institutional practice where teaching is the objective, the costs involved, from both a monetary and clinical time perspective, may make this procedure beyond the reach of most patients in a private practice. As such, it may find limited application in everyday dentistry, especially given the availability of diagnostic three-dimensional digital imaging with its capability to both virtually design implant placements and develop and fabricate the necessary surgical guides, models, and immediately placed implant-supported provisional prostheses.

Integral Formula of Isotonic Functions over Unbounded Domain in Clifford Analysis

In this paper we mainly study the so-called isotonic Dirac system over more general types of unbounded domains in Euclidean space of even dimension. In such systems different Dirac operators in the half dimension act from the left and from the right on the functions considered. We obtain the integral representation of isotonic functions satisfying the decay condition over the unbounded domains, and show that the integral representation formula over the unbounded domains for holomorphic functions of several complex variables and for Hermitean monogenic functions may be derived from it.

Anisotropic viscous dissipation in compressible magnetic X-points

Context. Visco-resistive damping in line-tied magnetic X-points is examined. Aims. The goal is to determine whether fast, Alfvenic energy dissipation is possible for X-point disturbances damped by the plasma resistivity and non-isotropic viscosity. Methods. The response of X-points to planar and axial perturbations is explored numerically by solving the linearized compressible MHD equations in two and a half dimensions. Results. It is demonstrated that fast dissipation is possible in the case of non-reconnective planar disturbances damped by anisotropic viscosity in weakly resistive plasmas. Although perturbations which change the initial X-point topology decay slowly at large times when viscous effects are dominant, there is an initial phase in which a significant fraction of the disturbance energy is removed on an Alfvenic timescale. The decay of incompressive axial field disturbances occurs by a different mechanism, however, that is always formally slow (i.e. dependent on the small viscous and resistive damping coefficients). Conclusions. Computations suggest that fast, visco-resistive energy release in coronal plasmas is possible for compressive X-point disturbances. This result could have important implications for understanding rapid energy release in coronal active regions.