On the dual-cone nature of the conical refraction phenomenon

In conical refraction (CR), a focused Gaussian input beam passing through a biaxial crystal and parallel to one of the optic axes is transformed into a pair of concentric bright rings split by a dark (Poggendorff) ring at the focal plane. Here, we show the generation of a CR transverse pattern that does not present the Poggendorff fine splitting at the focal plane, i.e., it forms a single light ring. This light ring is generated from a nonhomogeneously polarized input light beam obtained by using a spatially inhomogeneous polarizer that mimics the characteristic CR polarization distribution. This polarizer allows modulating the relative intensity between the two CR light cones in accordance with the recently proposed dual-cone model of the CR phenomenon. We show that the absence of interfering rings at the focal plane is caused by the selection of one of the two CR cones. (C) 2015 Optical Society of America

Development of Swept Source Optical Coherence Tomography and Adaptive Optics Scanning Laser Ophthalmoscopy: Improved Imaging Speed and Handheld Applications

Optical coherence tomography (OCT) is a noninvasive three-dimensional interferometric imaging technique capable of achieving micrometer scale resolution. It is now a standard of care in ophthalmology, where it is used to improve the accuracy of early diagnosis, to better understand the source of pathophysiology, and to monitor disease progression and response to therapy. In particular, retinal imaging has been the most prevalent clinical application of OCT, but researchers and companies alike are developing OCT systems for cardiology, dermatology, dentistry, and many other medical and industrial applications.

Adaptive optics (AO) is a technique used to reduce monochromatic aberrations in optical instruments. It is used in astronomical telescopes, laser communications, high-power lasers, retinal imaging, optical fabrication and microscopy to improve system performance. Scanning laser ophthalmoscopy (SLO) is a noninvasive confocal imaging technique that produces high contrast two-dimensional retinal images. AO is combined with SLO (AOSLO) to compensate for the wavefront distortions caused by the optics of the eye, providing the ability to visualize the living retina with cellular resolution. AOSLO has shown great promise to advance the understanding of the etiology of retinal diseases on a cellular level.

Broadly, we endeavor to enhance the vision outcome of ophthalmic patients through improved diagnostics and personalized therapy. Toward this end, the objective of the work presented herein was the development of advanced techniques for increasing the imaging speed, reducing the form factor, and broadening the versatility of OCT and AOSLO. Despite our focus on applications in ophthalmology, the techniques developed could be applied to other medical and industrial applications. In this dissertation, a technique to quadruple the imaging speed of OCT was developed. This technique was demonstrated by imaging the retinas of healthy human subjects. A handheld, dual depth OCT system was developed. This system enabled sequential imaging of the anterior segment and retina of human eyes. Finally, handheld SLO/OCT systems were developed, culminating in the design of a handheld AOSLO system. This system has the potential to provide cellular level imaging of the human retina, resolving even the most densely packed foveal cones.

Pollen and macrofossil profiles from six cores in Illinois, U.S.A

Pollen analysis of Wisconsinan sediments from eleven localities in northern and central Illinois, combined with the results of older studies, allows a first general survey of the vegetational changes in Illinois during the last glaciation. In the late Altonian (after 40,000 B.P.), pine was already the most prevalent tree type in northern Illinois. Probably because of the influence of the last Altonian ice advance to northern Illinois, pine migrated to the south and reached south-central Illinois, which was at that time a region of prairie, with oak and hickory trees in favorable sites. Likewise in the late Altonian, spruce appeared in northern Illinois. Spruce also expanded its area to the south during the Wisconsinan, reaching south-central Illinois only after 21,000 B.P., in the early Woodfordian. Deciduous trees (predominantly oak) were present in south-central Illinois throughout the Wisconsinan. Their prevalence decreased to the north. The vegetation during the different subdivisions of the last glacial period in Illinois was approximately as follows: Late Altonian: Pine/spruce forest with some deciduous trees in northern and central Illinois; prairie and oak/hickory stands in south-central Illinois; immigration of pine. Farmdalian: Pine/spruce forest in central Illinois; deciduous trees and pine in south-central Illinois, with areas of open vegetation, perhaps similar to the present-day transition of prairie to forest in the northern Great Plains. Woodfordian: Northern and central Illinois ice covered; in south central Illinois, spruce and oak as dominant tree types, but also pine and grassland. During the Woodfordian, pine and spruce disappeared again from south-central Illinois, and oak/hickory forest and prairie again prevailed. The ice-free areas of northern Illinois become populated temporarily with spruce, but later there is proof of deciduous forest in this region. Pollen investigations in south-central Illinois have shown convincingly that deciduous trees could survive relatively close (less than 60 km) to the ice margin. Therefore the frequently presented view that arctic climatic conditions prevailed in North America during the last glaciation far south of the ice margin can be refuted for the Illinois area, confirming the opinion of other authors resulting from investigations of fossil mollusks and frost-soil features. The small number of localities investigated still permits no complete reconstruction of the vegetation zones and their possible movements in Illinois. During the Altonian and Farmdalian in Illinois, a vegetational zonation probably existed similar to that of today in North America. As the ice pushed southward as far as 39° 20' N. lat in the early Woodfordian, this zonation was apparently broken up under the influence of a relatively moderate climate. In any case, the Vandalia area, which was only about 60 km south of the ice, was at that time neither in a tundra zone nor in a zone of boreal coniferous forest.

Results of the pollen analysis of the Dyanushka peat sediments K7/P2

A 415cm thick permafrost peat section from the Verkhoyansk Mountains was radiocarbon-dated and studied using palaeobotanical and sedimentological approaches. Accumulation of organic-rich sediment commenced in a former oxbow lake, detached from a Dyanushka River meander during the Younger Dryas stadial, at ~12.5 kyr BP. Pollen data indicate that larch trees, shrub alder and dwarf birch were abundant in the vegetation at that time. Local presence of larch during the Younger Dryas is documented by well-preserved and radiocarbon-dated needles and cones. The early Holocene pollen assemblages reveal high percentages of Artemisia pollen, suggesting the presence of steppe-like communities around the site, possibly in response to a relatively warm and dry climate ~11.4-11.2 kyr BP. Both pollen and plant macrofossil data demonstrate that larch woods were common in the river valley. Remains of charcoal and pollen of Epilobium indicate fire events and mark a hiatus ~11.0-8.7 kyr BP. Changes in peat properties, C31/C27 alkane ratios and radiocarbon dates suggest that two other hiatuses occurred ~8.2-6.9 and ~6.7-0.6 kyr BP. Prior to 0.6 kyr BP, a major fire destroyed the mire surface. The upper 60 cm of the studied section is composed of aeolian sands modified in the uppermost part by the modern soil formation. For the first time, local growth of larch during the Younger Dryas has been verified in the western foreland of the Verkhoyansk Mountains (~170km south of the Arctic Circle), thus increasing our understanding of the quick reforestation of northern Eurasia by the early Holocene.

Biblioteca Digital de Teses e Dissertações: grau de utilização pelos mestrandos do curso de Ciência da Informação das Universidades Públicas Brasileiras

A pesquisa aborda o uso das Tecnologias de Informação e Comunicação, que vem revolucionando as atividades e ocasionando muitas mudanças relacionadas ao acesso e uso de informações. O objetivo foi analisar o grau de utilização do conhecimento científico produzido pelos Programas de Pós-Graduação das Universidades Públicas Brasileiras, através da BDTD, pelos mestrandos dos referidos programas. Nos procedimentos metodológicos realizados, procurou-se inicialmente analisar o amplo espectro da população do corpus da pesquisa. Em razão da impossibilidade de trabalhar com os Programas de Pós-Graduação como um todo, optou-se por fazer um recorte, elegendo os cursos de Pós-Graduação em Ciência da Informação, vez que estes representam o principal segmento social de interesse da pesquisa. Foi utilizado o método de estudo de usuários, onde se optou por adotar o grupo, “estudos orientados aos usuários”, que identifica as necessidades e comportamento de acesso e uso da informação. Para coletar os dados, elaborou-se um questionário semi-estruturado com 25 questões, que versavam sobre o uso, dificuldades de acesso e recuperação da informação, bem como a satisfação na utilização dessa fonte informacional. Dentre os vários resultados obtidos, podemos destacar o fato de que a maioria dos mestrandos (71,8%) só teve contato com a BDTD somente no momento em que se encontrava cursando o mestrado e, somente 24,3%, tiveram contato durante a graduação. Estes resultados representam um problema, que pode afetar o bom desempenho do projeto BDTD, o qual consiste em disseminar e divulgar a produção científica dos Programas de Pós-Graduação das Universidades Públicas Brasileiras para a sua comunidade. Foi observado também, que os mestrandos oriundos do curso de Biblioteconomia tende a ter contato com a BDTD bem mais cedo do que mestrandos de outros cursos de graduação. A fim de minimizar o problema detectado, propõe-se uma divulgação mais eficaz na graduação através de dois procedimentos: Primeiro, o docente deve fazer uma divulgação mais eficaz da BDTD junto aos discentes de todos os cursos de graduação; segundo: deverá ser feita a divulgação na mídia eletrônica, através da inserção de ícones da BDTD, nos portais dos Departamentos dos Cursos de Graduação das Universidades Públicas Brasileiras. Acredita-se que com estes procedimentos seja possível aperfeiçoar o uso dessa fonte de informação científica.

The synthetic progestin norgestrel modulates Nrf2 signaling and acts as an antioxidant in a model of retinal degeneration

Retinitis pigmentosa (RP) is one of the most common retinal degenerative conditions affecting people worldwide, and is currently incurable. It is characterized by the progressive loss of photoreceptors, in which the death of rod cells leads to the secondary death of cone cells; the cause of eventual blindness. As rod cells die, retinal-oxygen metabolism becomes perturbed, leading to increased levels of reactive oxygen species (ROS) and thus oxidative stress; a key factor in the secondary death of cones. In this study, norgestrel, an FDA-approved synthetic analog of progesterone, was found to be a powerful neuroprotective antioxidant, preventing light-induced ROS in photoreceptor cells, and subsequent cell death. Norgestrel also prevented light-induced photoreceptor morphological changes that were associated with ROS production, and that are characteristic of RP. Further investigation showed that norgestrel acts via post-translational modulation of the major antioxidant transcription factor Nrf2; bringing about its phosphorylation, subsequent nuclear translocation, and increased levels of its effector protein superoxide dismutase 2 (SOD2). In summary, these results demonstrate significant protection of photoreceptor cells from oxidative stress, and underscore the potential of norgestrel as a therapeutic option for RP.

Yes, nós temos arquitetura moderna! Reconstituição e análise da arquitetura residencial moderna em Natal das décadas de 50 e 60

Brazilian architecture was recognized because of the consecration of the icons of the Carioca and Paulista schools which are represented nationally and internationally by names like Niemeyer, Lucio Costa and Vilanova Artigas, among others. Because of this, classic studies dedicated to the Brazilian case look to present the Southeastern region with the title of father of modern Brazil, at the cost of subjugating various other modern movements and peripheral sayings, whether their values are known or forgotten. On the other hand, there has been an effort, in the sense of registering and analyzing these regional productions of modern Brazilian architecture, an assignment that DOCOMOMO Brasil participates firmly through initiatives like the creation of a Library to aid in the documentation and registration of modernity in Brazil. Inside this context of insertions of the National-Modern scheme, this work has as its objective to present modern potiguar (northern Brazil) architecture through its contemporary residential examples, investigating specifically its constructive, formal aspects, that together that together demonstrate one more architectural emphasis of modern Brazilian architecture: the potiguar. This way, by contributing to the work of the register and the documentation of the Modern Movement and attributing to the modern architecture of Natal it s real worth, we can say: Yes, we have modern architecture

Security through Obscurity: Layout Obfuscation of Digital Integrated Circuits using Don't Care Conditions

Contemporary integrated circuits are designed and manufactured in a globalized environment leading to concerns of piracy, overproduction and counterfeiting. One class of techniques to combat these threats is circuit obfuscation which seeks to modify the gate-level (or structural) description of a circuit without affecting its functionality in order to increase the complexity and cost of reverse engineering. Most of the existing circuit obfuscation methods are based on the insertion of additional logic (called “key gates”) or camouflaging existing gates in order to make it difficult for a malicious user to get the complete layout information without extensive computations to determine key-gate values. However, when the netlist or the circuit layout, although camouflaged, is available to the attacker, he/she can use advanced logic analysis and circuit simulation tools and Boolean SAT solvers to reveal the unknown gate-level information without exhaustively trying all the input vectors, thus bringing down the complexity of reverse engineering. To counter this problem, some ‘provably secure’ logic encryption algorithms that emphasize methodical selection of camouflaged gates have been proposed previously in literature [1,2,3]. The contribution of this paper is the creation and simulation of a new layout obfuscation method that uses don't care conditions. We also present proof-of-concept of a new functional or logic obfuscation technique that not only conceals, but modifies the circuit functionality in addition to the gate-level description, and can be implemented automatically during the design process. Our layout obfuscation technique utilizes don’t care conditions (namely, Observability and Satisfiability Don’t Cares) inherent in the circuit to camouflage selected gates and modify sub-circuit functionality while meeting the overall circuit specification. Here, camouflaging or obfuscating a gate means replacing the candidate gate by a 4X1 Multiplexer which can be configured to perform all possible 2-input/ 1-output functions as proposed by Bao et al. [4]. It is important to emphasize that our approach not only obfuscates but alters sub-circuit level functionality in an attempt to make IP piracy difficult. The choice of gates to obfuscate determines the effort required to reverse engineer or brute force the design. As such, we propose a method of camouflaged gate selection based on the intersection of output logic cones. By choosing these candidate gates methodically, the complexity of reverse engineering can be made exponential, thus making it computationally very expensive to determine the true circuit functionality. We propose several heuristic algorithms to maximize the RE complexity based on don’t care based obfuscation and methodical gate selection. Thus, the goal of protecting the design IP from malicious end-users is achieved. It also makes it significantly harder for rogue elements in the supply chain to use, copy or replicate the same design with a different logic. We analyze the reverse engineering complexity by applying our obfuscation algorithm on ISCAS-85 benchmarks. Our experimental results indicate that significant reverse engineering complexity can be achieved at minimal design overhead (average area overhead for the proposed layout obfuscation methods is 5.51% and average delay overhead is about 7.732%). We discuss the strengths and limitations of our approach and suggest directions that may lead to improved logic encryption algorithms in the future. References: [1] R. Chakraborty and S. Bhunia, “HARPOON: An Obfuscation-Based SoC Design Methodology for Hardware Protection,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 28, no. 10, pp. 1493–1502, 2009. [2] J. A. Roy, F. Koushanfar, and I. L. Markov, “EPIC: Ending Piracy of Integrated Circuits,” in 2008 Design, Automation and Test in Europe, 2008, pp. 1069–1074. [3] J. Rajendran, M. Sam, O. Sinanoglu, and R. Karri, “Security Analysis of Integrated Circuit Camouflaging,” ACM Conference on Computer Communications and Security, 2013. [4] Bao Liu, Wang, B., "Embedded reconfigurable logic for ASIC design obfuscation against supply chain attacks,"Design, Automation and Test in Europe Conference and Exhibition (DATE), 2014 , vol., no., pp.1,6, 24-28 March 2014.

História eruptiva do sistema vulcânico fissural dos picos e avaliação da susceptibilidade a escoadas lávicas (ilha de S. Miguel - Açores)

Tese de Doutoramento, Geologia (Vulcanologia), 18 de Julho 2013, Universidade dos Açores.

Biblioteca Digital de Teses e Dissertações: grau de utilização pelos mestrandos do curso de Ciência da Informação das Universidades Públicas Brasileiras

A pesquisa aborda o uso das Tecnologias de Informação e Comunicação, que vem revolucionando as atividades e ocasionando muitas mudanças relacionadas ao acesso e uso de informações. O objetivo foi analisar o grau de utilização do conhecimento científico produzido pelos Programas de Pós-Graduação das Universidades Públicas Brasileiras, através da BDTD, pelos mestrandos dos referidos programas. Nos procedimentos metodológicos realizados, procurou-se inicialmente analisar o amplo espectro da população do corpus da pesquisa. Em razão da impossibilidade de trabalhar com os Programas de Pós-Graduação como um todo, optou-se por fazer um recorte, elegendo os cursos de Pós-Graduação em Ciência da Informação, vez que estes representam o principal segmento social de interesse da pesquisa. Foi utilizado o método de estudo de usuários, onde se optou por adotar o grupo, “estudos orientados aos usuários”, que identifica as necessidades e comportamento de acesso e uso da informação. Para coletar os dados, elaborou-se um questionário semi-estruturado com 25 questões, que versavam sobre o uso, dificuldades de acesso e recuperação da informação, bem como a satisfação na utilização dessa fonte informacional. Dentre os vários resultados obtidos, podemos destacar o fato de que a maioria dos mestrandos (71,8%) só teve contato com a BDTD somente no momento em que se encontrava cursando o mestrado e, somente 24,3%, tiveram contato durante a graduação. Estes resultados representam um problema, que pode afetar o bom desempenho do projeto BDTD, o qual consiste em disseminar e divulgar a produção científica dos Programas de Pós-Graduação das Universidades Públicas Brasileiras para a sua comunidade. Foi observado também, que os mestrandos oriundos do curso de Biblioteconomia tende a ter contato com a BDTD bem mais cedo do que mestrandos de outros cursos de graduação. A fim de minimizar o problema detectado, propõe-se uma divulgação mais eficaz na graduação através de dois procedimentos: Primeiro, o docente deve fazer uma divulgação mais eficaz da BDTD junto aos discentes de todos os cursos de graduação; segundo: deverá ser feita a divulgação na mídia eletrônica, através da inserção de ícones da BDTD, nos portais dos Departamentos dos Cursos de Graduação das Universidades Públicas Brasileiras. Acredita-se que com estes procedimentos seja possível aperfeiçoar o uso dessa fonte de informação científica.

APP RERMS enriched matrix as an adhesion substrate for neuritic outgrowth

Specific domains can determine protein structural functional relationships. For the Alzheimer’s Amyloid Precursor Protein (APP) several domains have been described, both in its intracellular and extracellular fragments. Many functions have been attributed to APP including an important role in cell adhesion and cell to cell recognition. This places APP at key biological responses, including synaptic transmission. To fulfil these functions, extracellular domains take on added significance. The APP extracellular domain RERMS is in fact a likely candidate to be involved in the aforementioned physiological processes. A multidisciplinary approach was employed to address the role of RERMS. The peptide RERMS was crosslinked to PEG (Polyethylene glycol) and the reaction validated by FTIR (Fourier transform infrared spectrometry). FTIR proved to be the most efficient at validating this reaction because it requires only a drop of sample, and it gives information about the reactions occurred in a mixture. The data obtained consist in an infrared spectra of the sample, where peaks positions give information about the structure of the molecules, and the intensity of peaks is related to the concentration of the molecules. Subsequently substrates of PEG impregnated with RERMS were prepared and SH-SY5Y (human neuroblastoma cell line) cells were plated and differentiated on the latter. Several morphological alterations were clearly evident. The RERMS peptide provoked cells to take on a flatter appearance and the cytoskeletal architecture changed, with the appearance of stress fibres, a clear indicator of actin reorganization. Given that focal adhesions play a key role in determining cellular structure the latter were directly investigated. Focal adhesion kinase (FAK) is one of the most highly expressed proteins in the CNS (central nervous system) during development. It has been described to be crucial for radial migration of neurons. FAK can be localized in growth cones and mediated the response to attractive and repulsive cues during migration. One of the mechanisms by which FAK becomes active is by auto phosphorylation at tyrosine 397. It became clearly evident that in the presence of the RERMS peptide pFAK staining at focal adhesions intensified and more focal adhesions became apparent. Furthermore speckled structures in the nucleus, putatively corresponding to increased expression activity, also increased with RERMS. Taken together these results indicate that the RERMS domain in APP plays a critical role in determining cellular physiological responses. Here is suggested a model by which RERMS domain is recognized by integrins and mediate intracellular responses involving FAK, talin, actin filaments and vinculin. This mechanism probably is responsible for mediating cell adhesion and neurite outgrowth on neurons.

Desenvolvimento de protótipo de aplicativo móvel em Android® para o controle e acompanhamento nutricional da saúde óssea em mulheres menopáusicas

Following a drop in estrogen in the period of menopause some women begin to lose bone mass more than 1% per year reaching the end of five years with loss greater than 25%. In this regard, factors such as older age, low calcium intake and premature menopause favor the onset of osteoporosis. Preventive methods such as nutritional counseling to a proper diet and the support of technology through applications that assess dietary intake are essential. Thus, this study aimed to develop an application for Android® platform focused on the evaluation of nutritional and organic conditions involved in bone health and risks for developing osteoporosis in postmenopausal women. To achieve this goal we proceeded to a study of 72 women aged 46-79 years, from the physical exercise for bone health of the Laboratory for Research in Biochemistry and Densitometry the Federal Technological University of Paraná program. Data were collected in the second half of 2014 through tests Bone Densitometry and Body Composition, Blood Tests, Anthropometric data and Nutrition Assessment. The study included women with a current diagnosis of osteopenia or osteoporosis primary, aged more than 45 years postmenopausal. For the assessment of bone mineral density and body composition used the device Absorptiometry Dual Energy X-ray (DXA) brand Hologic Discovery TM Model A. For anthropometric assessment was included to body mass, height, abdominal circumference, Waist circumference and hip circumference. The instrument for assessing food consumption was used Recall 24 hours a day (24HR). The estimated intake of energy and nutrients was carried from the tabulation of the food eaten in the Software Diet Pro 4®. In a sub sample of 30 women with osteopenia / osteoporosis serum calcium and alkaline phosphatase tests were performed. The results demonstrated a group of women (n = 30) average calcium intake of 570mg / day (± 340). The analysis showed a mean serum calcium within the normal range (10,20mg / dl ± 0.32) and average values and slightly increased alkaline phosphatase (105.40 U / L ± 23.70). Furthermore, there was a significant correlation between the consumption of protein and the optimal daily intake of calcium (0.375 p-value 0.05). Based on these findings, we developed an application early stage in Android® platform operating system Google®, being called OsteoNutri. We chose to use Java Eclipse® where it was executed Android® version of the project; choice of application icons and setting the visual editor for building the application layouts. The DroidDraw® was used for development of the three application GUIs. For practical tests we used a cell compatible with the version that was created (4.4 or higher). The prototype was developed in conjunction with the Group and Instrumentation Applications Development (GDAI) of the Federal Technological University of Paraná. So this application can be considered an important tool in dietary control, allowing closer control consumption of calcium and dietary proteins.

Intraplate versus ridge volcanism on the Pacific-Antarctic Ridge near 37°S -111°W

Exploration of the Foundation Volcanic Chain (33 degrees S-131 degrees W; 37 degrees S-111 degrees W) revealed the existence of different magmatic provinces with relation to their geological settings. (1) The Pacific-Antarctic Ridge (PAR) is made up of several en echelon segments where both glassy midocean ridge basalts (MORBs) with low incompatible elements (K2O<200 ppm, Zr<120 ppm and Ce <20 ppm) as well as andesites and dacites have erupted, (2) Oblique Ridges located up to 300 lan from the PAR axis are topped with seamounts made up essentially of transitional (T) and enriched (E) MORBs with intermediate incompatible elements (K2O=0.11-0.40 %, Zr=70-140 ppm and Ce=15-30 ppm), (3) the Foundation Seamounts (FS) consisting essentially of isolated volcanoes which have erupted alkalic lavas (alkali basalt, trachybasalt and trachyandesite) with high incompatible elements (K2O (0.50-1.1 %, Zr (>150 ppm) and Ce (>48 ppm)) at about 306-1300 km from the PAR axis, (4) The Old Pacific Seamounts built on a crust older than 23 m. y. located west of longitude 124 degrees W (> 1300 km from the PAR axis) consist of T and EMORB. On the PAR axis, extensive crystal fractionation (>65%) produced the silicic lavas. On the basis of Pacific plate reconstruction using a half spreading rate of about 50 mm/yr and integrating the observed compositional changes with respect to the structural settings, it is inferred that the last volcanic events giving rise to the FS took place at about 110 km from the PAR axis about 5 m. y. ago. The Oblique Ridges built between 5 m. y. and <1 m. y. are believed to represent ancient leaky transforms and/or large discontinuities between accreting ridge segments filled by volcanic cones during the interaction (mixing) of the enriched plume components of the FS with PAR depleted (MORB type) magmatism. The Old Pacific Seamounts built on ancient crust (>23 m. y.) with MORB volcanics comparable to those of the the Oblique Ridge-PAR provinces, could also have been formed by an interaction between the Foundation Seamount (dredge site 28) hotspot magmatism and that of an ancient accreting ridge magmatism precursor of the PAR.

Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.