Trace Map Research Articles

New quantum codes from dual-containing cyclic codes over finite rings

Let $R=\mathbb{F}_{2^{m}}+u\mathbb{F}_{2^{m}}+\cdots+u^{k}\mathbb{F}_{2^{m}}$ , where $\mathbb{F}_{2^{m}}$ is a finite field with $2^{m}$ elements, $m$ is a positive integer, $u$ is an indeterminate with $u^{k+1}=0.$ In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over $R$. A new Gray map over $R$ is defined and a sufficient and necessary condition for the existence of dual-containing cyclic codes over $R$ is given. A new family of $2^{m}$-ary quantum codes is obtained via the Gray map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over $R.$ Furthermore, a new family of binary quantum codes is obtained via the Gray map, the trace map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over $R.$

Transition from collision to subduction in Western Greece: the Katouna–Stamna active fault system and regional kinematics

Transition from subduction to collision occurs in Western Greece and is accommodated along the downgoing plate by the Kefalonia right-lateral fault that transfers the Hellenic subduction front to the Apulian collision front. Here we present an active tectonic study of Aitolo-Akarnania (Western Greece) that highlights how such a transition is accommodated in the overriding plate. Based on new multi-scale geomorphic and tectonic observations, we performed an accurate active fault trace mapping in the region, and provide evidence for active normal and left-lateral faulting along the Katouna–Stamna Fault (KSF), a 65-km-long NNW-striking fault system connecting the Amvrakikos Gulf to the Patras Gulf. We further show that the Cenozoic Hellenide thrusts located west of the KSF are no longer active, either in field observation or in GPS data, leading us to propose that the KSF forms the northeastern boundary of a rigid Ionian Islands-Akarnania Block (IAB). Cosmic ray exposure measurements of 10Be and 36Cl were performed on a Quaternary alluvial fan offset along the KSF (~50 m left-lateral offset). A maximum abandonment age of ~12–14 ka for the alluvial fan surface can be determined, giving an estimated KSF minimum geological left-lateral slip rate of ~4 mm year−1, in agreement with high GPS slip rates (~10 mm year−1). Despite this high slip rate, the KSF is characterized by subdued morphological evidence of tectonic activity, a gypsum-breccia bedrock and a low level of seismicity, suggesting a dominantly creeping behavior for this fault. Finally, we discuss how the IAB appears to have been progressively individualized during the Pleistocene (younger than ~1.5 Ma).

Improvements to field and remote sensing methods for mapping discontinuity persistence and intact rock bridges in rock slopes

Discontinuity persistence and intact rock bridges are critical factors that influence the stability of rock slopes. Persistence influences the extent of pre-existing potential failure surfaces, and intact rock bridges can add cohesion and tensile strength to an incipient failure surface, which must be destroyed before slope failure can occur. Despite continued research and improvements in mapping technology, computing power, and numerical modelling codes, there is no standard recommended methodology for field characterisation of intact rock bridges, or their incorporation into stability analysis. We use observations from remote sensing and field mapping investigations at three open pit mines and one natural rock slope to recommend improvements to field and remote sensing methods for mapping discontinuity persistence and intact rock bridges in rock slopes.We apply a fracture network engineering approach to discontinuity trace mapping, using new intensity factors to describe intact rock bridge trace intensity R21, and blast-induced fracture intensity B21. We emphasize the importance of multi-scale characterisation of discontinuity persistence and rock bridges in rock slopes, and we distinguish between different classes of intact rock bridges based on scale and geometry, with particular attention given to the distinction between laboratory sample scale intact rock bridges on incipient discontinuities, and larger rock mass bridges, which represent metre or larger scale intervals of fractured rock mass that may exist between very high persistence joints and faults.

침수흔적도 작성 방법 개선을 위한 무인항공기 적용 연구

침수흔적도 작성 방법 개선을 위한 무인항공기 적용 연구

CT-Mapper: Mapping sparse multimodal cellular trajectories using a multilayer transportation network

Mobile phone data have recently become an attractive source of information about mobility behavior. Since cell phone data can be captured in a passive way for a large user population, they can be harnessed to collect well-sampled mobility information. In this paper, we propose CT-Mapper, an unsupervised algorithm that enables the mapping of mobile phone traces over a multimodal transport network. One of the main strengths of CT-Mapper is its capability to map noisy sparse cellular multimodal trajectories over a multilayer transportation network where the layers have different physical properties and not only to map trajectories associated with a single layer. Such a network is modeled by a large multilayer graph in which the nodes correspond to metro/train stations or road intersections and edges correspond to connections between them. The mapping problem is modeled by an unsupervised HMM where the observations correspond to sparse user mobile trajectories and the hidden states to the multilayer graph nodes. The HMM is unsupervised as the transition and emission probabilities are inferred using respectively the physical transportation properties and the information on the spatial coverage of antenna base stations. To evaluate CT-Mapper we collected cellular traces with their corresponding GPS trajectories for a group of volunteer users in Paris and vicinity (France). We show that CT-Mapper is able to accurately retrieve the real cell phone user paths despite the sparsity of the observed trace trajectories. Furthermore our transition probability model is up to 20% more accurate than other naive models.

Intrinsic Astrocyte Heterogeneity Influences Tumor Growth in Glioma Mouse Models.

The influence of cellular origin on glioma pathogenesis remains elusive. We previously showed that mutations inactivating Rb and Pten and activating Kras transform astrocytes and induce tumorigenesis throughout the adult mouse brain. However, it remained unclear whether astrocyte subpopulations were susceptible to these mutations. We therefore used genetic lineage tracing and fate mapping in adult conditional, inducible genetically engineered mice to monitor transformation of glial fibrillary acidic protein (GFAP) and glutamate aspartate transporter (GLAST) astrocytes and immunofluorescence to monitor cellular composition of the tumor microenvironment over time. Because considerable regional heterogeneity exists among astrocytes, we also examined the influence of brain region on tumor growth. GFAP astrocyte transformation induced uniformly rapid, regionally independent tumor growth, but transformation of GLAST astrocytes induced slowly growing tumors with significant regional bias. Transformed GLAST astrocytes had reduced proliferative response in culture and in vivo and malignant progression was delayed in these tumors. Recruited glial cells, including proliferating astrocytes, oligodendrocyte progenitors and microglia, were the majority of GLAST, but not GFAP astrocyte-derived tumors and their abundance dynamically changed over time. These results suggest that intrinsic astrocyte heterogeneity, and perhaps regional brain microenvironment, significantly contributes to glioma pathogenesis.

The Fibonacci Hamiltonian

We consider the Fibonacci Hamiltonian, the central model in the study of electronic properties of one-dimensional quasicrystals, and provide a detailed description of its spectrum and spectral characteristics (namely, the optimal H\"older exponent of the integrated density of states, the dimension of the density of states measure, the dimension of the spectrum, and the upper transport exponent) for all values of the coupling constant (in contrast to all previous quantitative results, which could be established only in the regime of small or large coupling). In particular, we show that the spectrum of this operator is a dynamically defined Cantor set and that the density of states measure is exact-dimensional; this implies that all standard fractal dimensions coincide in each case. We show that all the gaps of the spectrum allowed by the gap labeling theorem are open for all values of the coupling constant. Also, we establish strict inequalities between the four spectral characteristics in question, and provide the exact large coupling asymptotics of the dimension of the density of states measure (for the other three quantities, the large coupling asymptotics were known before). A crucial ingredient of the paper is the relation between spectral properties of the Fibonacci Hamiltonian and dynamical properties of the Fibonacci trace map (such as dimensional characteristics of the non-wandering hyperbolic set and its measure of maximal entropy as well as other equilibrium measures, topological entropy, multipliers of periodic orbits). We establish exact identities relating the spectral and dynamical quantities, and show the connection between the spectral quantities and the thermodynamic pressure function.

A Study on the Watershed Analysis of the Expected Flood Inundation Area in South Han River

Flood risk map, flood damage map, disaster information map, inundation trace map are involved with the cartographic analysis of flood inundation based on prevention, preparation, restoration, response from natural disasters such as flood, flooding, etc. In this study, the analysis for channel and basin characteristics Chungju dam to Paldang dam of South han river after four river project. Flood scenario is selected to take advantage of design flood level of schematic design for river. Flood inundation of one dimensional non-uniform flow by using HEC-RAS with basin characteristics is accomplished and two dimensional unsteady flow was interpreted by using FLUMEN. Frequency analysis is carried out about each abundance of South han river for 100 year period, 200 year period and 500 year period. Flooding disaster area of 100 year period on 0.5m damage functions is 2378.8ha, 200 year period on 0.5m damage functions is 3155.2ha, 500 year period on 0.5m damage functions is 3995.3ha respectively. It will be significant data for decision making to establish inundation trace map for providing basic plan for river maintenance, land use plan, flood protection plan, application plan and getting information of flood expectation area.

Nontrivial algebraic cycles in the Jacobian varieties of some quotients of Fermat curves

We obtain the trace map images of the values of certain harmonic volumes for some cyclic quotients of [Formula: see text]th Fermat curves. These provide the algorithm showing that the algebraic cycles, called [Formula: see text]th Ceresa cycles, are not algebraically equivalent to zero in their Jacobian varieties. We apply the method to curves for prime [Formula: see text] with [Formula: see text] modulo [Formula: see text], [Formula: see text] and [Formula: see text] [Formula: see text].

Phylogenomic exploration of the relationships between strains of Mycobacterium avium subspecies paratuberculosis.

BackgroundMycobacterium avium subspecies paratuberculosis (Map) is an infectious enteric pathogen that causes Johne’s disease in livestock. Determining genetic diversity is prerequisite to understanding the epidemiology and biology of Map. We performed the first whole genome sequencing (WGS) of 141 global Map isolates that encompass the main molecular strain types currently reported. We investigated the phylogeny of the Map strains, the diversity of the genome and the limitations of commonly used genotyping methods.ResultsSingle nucleotide polymorphism (SNP) and phylogenetic analyses confirmed two major lineages concordant with the former Type S and Type C designations. The Type I and Type III strain groups are subtypes of Type S, and Type B strains are a subtype of Type C and not restricted to Bison species.We found that the genome-wide SNPs detected provided greater resolution between isolates than currently employed genotyping methods. Furthermore, the SNP used for IS1311 typing is not informative, as it is likely to have occurred after Type S and C strains diverged and does not assign all strains to the correct lineage. Mycobacterial Interspersed Repetitive Unit-Variable Number Tandem Repeat (MIRU-VNTR) differentiates Type S from Type C but provides limited resolution between isolates within these lineages and the polymorphisms detected do not necessarily accurately reflect the phylogenetic relationships between strains.WGS of passaged strains and coalescent analysis of the collection revealed a very high level of genetic stability, with the substitution rate estimated to be less than 0.5 SNPs per genome per year.ConclusionsThis study clarifies the phylogenetic relationships between the previously described Map strain groups, and highlights the limitations of current genotyping techniques. Map isolates exhibit restricted genetic diversity and a substitution rate consistent with a monomorphic pathogen. WGS provides the ultimate level of resolution for differentiation between strains. However, WGS alone will not be sufficient for tracing and tracking Map infections, yet importantly it can provide a phylogenetic context for affirming epidemiological connections.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-015-2234-5) contains supplementary material, which is available to authorized users.

Rupture complexity and the supershear transition on rough faults

AbstractField investigations suggest that supershear earthquakes occur on geometrically simple, smooth fault segments. In contrast, dynamic rupture simulations show how heterogeneity of stress, strength, and fault geometry can trigger supershear transitions, as well as other complex rupture styles. Here we examine the Fang and Dunham (2013) ensemble of 2‐D plane strain dynamic ruptures on fractally rough faults subject to strongly rate weakening friction laws to document the effect of fault roughness and prestress on rupture behavior. Roughness gives rise to extremely diverse rupture styles, such as rupture arrests, secondary slip pulses that rerupture previously slipped fault sections, and supershear transitions. Even when the prestress is below the Burridge‐Andrews threshold for supershear on planar faults with uniform stress and strength conditions, supershear transitions are observed. A statistical analysis of the rupture velocity distribution reveals that supershear transients become increasingly likely at higher stress levels and on rougher faults. We examine individual ruptures and identify recurrent patterns for the supershear transition. While some transitions occur on fault segments that are favorably oriented in the background stress field, other transitions happen at the initiation of or after propagation through an unfavorable bend. We conclude that supershear transients are indeed favored by geometric complexity. In contrast, sustained supershear propagation is most common on segments that are locally smoother than average. Because rupture style is so sensitive to both background stress and small‐scale details of the fault geometry, it seems unlikely that field maps of fault traces will provide reliable deterministic predictions of supershear propagation on specific fault segments.

Fast Many-Lights Rendering with Temporal Shadow Maps

We present an effcient method for computing shadows of many light sources (e.g. 1,024). Our work is based on the observation that conventional shadow mapping becomes redundant as the number of lights increases. First, we sample the scene with a constant number of depth images (e.g. 10), which we call temporal shadow maps. Then the shadow map for each light is approximated through rendering triangles reconstructed from all the temporal shadow maps. The cost of rendering the triangles reconstructed from the temporal shadow maps is much smaller than rendering the entire scene when the geometry is complex. The algorithm supports fully dynamic scenes. The experiment results show that our method can produce comparable soft shadows with much higher speed than ray tracing and shadow mapping methods.

A new method for automated discontinuity trace mapping on rock mass 3D surface model

This paper presents an automated discontinuity trace mapping method on a 3D surface model of rock mass. Feature points of discontinuity traces are first detected using the Normal Tensor Voting Theory, which is robust to noisy point cloud data. Discontinuity traces are then extracted from feature points in four steps: (1) trace feature point grouping, (2) trace segment growth, (3) trace segment connection, and (4) redundant trace segment removal. A sensitivity analysis is conducted to identify optimal values for the parameters used in the proposed method. The optimal triangular mesh element size is between 5cm and 6cm; the angle threshold in the trace segment growth step is between 70° and 90°; the angle threshold in the trace segment connection step is between 50° and 70°, and the distance threshold should be at least 15 times the mean triangular mesh element size. The method is applied to the excavation face trace mapping of a drill-and-blast tunnel. The results show that the proposed discontinuity trace mapping method is fast and effective and could be used as a supplement to traditional direct measurement of discontinuity traces.

Morita, Galois, and the trace map: a survey

Let A be a \({\mathcal {K}}\)-algebra and H a \({\mathcal {K}}\)-bialgebra (\({\mathcal {K}}\) being a field). Any action \(\beta \) of H on A gives rise to two new \({\mathcal {K}}\)-algebras, namely, the algebra \(A^\beta \) of the invariants of A under \(\beta \) and the smash product \(A\#_\beta H\), as well as a canonical Morita context connecting them. Such a context keeps a close relation with the notion of Galois extension. Indeed, in some cases where it makes sense the strictness of this context is equivalent to exactly say that A is a \(H^*\)-Galois extension of \(A^\beta \). In general, such an equivalence depends also on the surjectivity of a certain trace map from A to \(A^\beta \). This paper is a survey about the strictness of this context in the setting of partial actions of groups and of Hopf algebras.

The Review of Nuclear Microscopy Techniques: An Approach for Nondestructive Trace Elemental Analysis and Mapping of Biological Materials.

The properties of many biological materials often depend on the spatial distribution and concentration of the trace elements present in a matrix. Scientists have over the years tried various techniques including classical physical and chemical analyzing techniques each with relative level of accuracy. However, with the development of spatially sensitive submicron beams, the nuclear microprobe techniques using focused proton beams for the elemental analysis of biological materials have yielded significant success. In this paper, the basic principles of the commonly used microprobe techniques of STIM, RBS, and PIXE for trace elemental analysis are discussed. The details for sample preparation, the detection, and data collection and analysis are discussed. Finally, an application of the techniques to analysis of corn roots for elemental distribution and concentration is presented.

Constructions of negabent functions over finite fields

Bent functions are actively investigated for their various applications in cryptography, coding theory and combinatorial design. As one of their generalizations, negabent functions are also quite useful, and they are originally defined via nega-Hadamard transforms for boolean functions. In this paper, we look at another equivalent definition of them. It allows us to investigate negabent functions f on F2n$\mathbb {F}_{2^{n}}$, which can be written as a composition of a univariate polynomial over F2n$\mathbb {F}_{2^{n}}$ and the trace mapping from F2n$\mathbb {F}_{2^{n}}$ to F2$\mathbb {F}_{2}$. In particular, when this polynomial is a monomial, we call f a monomial negabent function. Families of quadratic and cubic monomial negabent functions are constructed, together with several sporadic examples. To obtain more interesting negabent functions in special forms, we also look at certain negabent polynomials. We obtain several families of cubic negabent functions by using the theory of projective polynomials over finite fields.

Compression of local slant stacks by the estimation of multiple local slopes and the matching pursuit decomposition

Because local slant stacking increases the data dimension in beam migration, the volume of local slant stacks can be enormous and can obstruct efficient data processing. In addition, a proper beam compression algorithm can reduce the computation of ray tracing and beam mapping. Thus, compressing the local slant stacks with high fidelity can improve the efficiency of beam migration. A new approach is proposed to efficiently compress the local slant stacks. This approach combines the estimation of multiple local slopes based on the structure tensor to reduce the number of slopes, and the sparse representation for the slant stacked data via the matching pursuit decomposition to reduce the number of temporal samples. Furthermore, a new algorithm to estimate multiple local slopes based on the second-order structure tensor is proposed to handle the intersecting events efficiently. Several data examples indicated that the new compression algorithm required much less storage. Meanwhile, the new algorithm can restore the significant events and tolerate some random noise. The migration results determined that this compression algorithm does not obviously degrade the quality of the beam migration result, and it even makes the migration result more clear by suppressing the random noise smearing.

A note on the distribution of self-dual normal bases generators of finite fields under trace map

Let \(\mathbb {F}_{q^n}\) be an extension of the field \(\mathbb {F}_q\) of degree \(n=mp^l,~l\ge 1\) where p is the characteristic of the field \(\mathbb {F}_q.\) It is proved that the number of self-dual normal bases generators of \({\mathbb {F}_{q^n}}\) over \(\mathbb {F}_q\) in \((Tr_{\mathbb {F}_{q^n}|\mathbb {F}_{q^m}})^{-1}(\beta ),\) for any self-dual normal basis generator \(\beta \) of \(\mathbb {F}_{q^m}\) over \(\mathbb {F}_q,\) is independent of the choice of \(\beta \).

Twisted Frobenius Extensions of Graded Superrings

We define twisted Frobenius extensions of graded superrings. We develop equivalent definitions in terms of bimodule isomorphisms, trace maps, bilinear forms, and dual sets of generators. The motivation for our study comes from categorification, where one is often interested in the adjointness properties of induction and restriction functors. We show that $A$ is a twisted Frobenius extension of $B$ if and only if induction of $B$-modules to $A$-modules is twisted shifted right adjoint to restriction of $A$-modules to $B$-modules. A large (non-exhaustive) class of examples is given by the fact that any time $A$ is a Frobenius graded superalgebra, $B$ is a graded subalgebra that is also a Frobenius graded superalgebra, and $A$ is projective as a left $B$-module, then $A$ is a twisted Frobenius extension of $B$.

Grundlagen und Technik der diffusionsgewichteten MR‑Bildgebung und der Diffusions‑Tensor‑Bildgebung

Due to their thermal energy, water molecules in tissue are in continuous random motion called diffusion. Water diffusion in pathologically modified tissue (e. g. ischemia, inflammation and neoplasia) is different from normal conditions. Diffusion-weighted magnetic resonance (MR) imaging (DWI) can measure the local strength and main direction of the diffusional motion in any picture element, thus providing diagnostic tissue information exceeding the morphological depiction. Diffusion-weighted MR sequences are based on the echo planar imaging (EPI) technique which is very rapid but also susceptible to artefacts. Using especially strong magnetic field gradient pulses the MR signal is sensitized to microscopic motion of water molecules resulting in a unique image contrast in addition to T1 and T2. Local deviations of the diffusion strength from normal values indicate pathological processes. The DWI sequences can measure diffusion along any direction; however, in the clinical routine only directionally averaged DWI images (trace maps) are used. Diffusion tensor imaging (DTI) represents an advanced DWI method which specifically explores diffusional anisotropy in order to obtain additional information about tissue microstructure. Diffusion-weighted MRI is an established technique for the assessment of pathological processes. Although DWI is mainly applied in stroke diagnostics, it is increasingly being used to detect and characterize various lesions in the brain as well as in the whole body. With new sequence techniques imaging artefacts can be significantly reduced. In addition, DTI allows the reconstruction and 3-dimensional visualization of tissue fibre structure. This method has proven to be clinically important primarily for the depiction of nerve tracts in the brain and spinal cord when planning surgical interventions and radiation therapy.