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Journal articles on the topic 'Proof reconstruction'

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Author: Grafiati

Published: 25 May 2024

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1

Bundy, Alan, Mateja Jamnik, and Andrew Fugard. "What is a proof?" Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1835 (September 14, 2005): 2377–91. http://dx.doi.org/10.1098/rsta.2005.1651.

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To those brought up in a logic-based tradition there seems to be a simple and clear definition of proof. But this is largely a twentieth century invention; many earlier proofs had a different nature. We will look particularly at the faulty proof of Euler's Theorem and Lakatos' rational reconstruction of the history of this proof. We will ask: how is it possible for the errors in a faulty proof to remain undetected for several years—even when counter-examples to it are known? How is it possible to have a proof about concepts that are only partially defined? And can we give a logic-based account of such phenomena? We introduce the concept of schematic proofs and argue that they offer a possible cognitive model for the human construction of proofs in mathematics. In particular, we show how they can account for persistent errors in proofs.

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2

Francez, Nissim, and Gilad Ben-Avi. "Proof-Theoretic Reconstruction of Generalized Quantifiers." Journal of Semantics 32, no. 3 (March 20, 2014): 313–71. http://dx.doi.org/10.1093/jos/ffu001.

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3

Fasan, Oluwasola Mary, and Martin S. Olivier. "Correctness proof for database reconstruction algorithm." Digital Investigation 9, no. 2 (November 2012): 138–50. http://dx.doi.org/10.1016/j.diin.2012.09.002.

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4

Iványi, Antal. "Reconstruction of score sets." Acta Universitatis Sapientiae, Informatica 6, no. 2 (December 1, 2014): 210–29. http://dx.doi.org/10.1515/ausi-2015-0005.

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Abstract The score set of a tournament is defined as the set of its different outdegrees. In 1978 Reid [15] published the conjecture that for any set of nonnegative integers D there exists a tournament T whose degree set is D. Reid proved the conjecture for tournaments containing n = 1, 2, and 3 vertices. In 1986 Hager [4] published a constructive proof of the conjecture for n = 4 and 5 vertices. In 1989 Yao [18] presented an arithmetical proof of the conjecture, but general polynomial construction algorithm is not known. In [6] we described polynomial time algorithms which reconstruct the score sets containing only elements less than 7. In [5] we improved this bound to 9. In this paper we present and analyze new algorithms Hole-Map, Hole-Pairs, Hole-Max, Hole-Shift, Fill-All, Prefix-Deletion, and using them improve the above bound to 12, giving a constructive partial proof of Reid’s conjecture.

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5

Banach, R. "Sequent reconstruction in LLM—A sweepline proof." Annals of Pure and Applied Logic 73, no. 3 (June 1995): 277–95. http://dx.doi.org/10.1016/0168-0072(94)00033-y.

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6

Krajewski, Stanisław. "Anti-foundationalist Philosophy of Mathematics and Mathematical Proofs." Studia Humana 9, no. 3-4 (October 1, 2020): 154–64. http://dx.doi.org/10.2478/sh-2020-0034.

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Abstract The Euclidean ideal of mathematics as well as all the foundational schools in the philosophy of mathematics have been contested by the new approach, called the “maverick” trend in the philosophy of mathematics. Several points made by its main representatives are mentioned – from the revisability of actual proofs to the stress on real mathematical practice as opposed to its idealized reconstruction. Main features of real proofs are then mentioned; for example, whether they are convincing, understandable, and/or explanatory. Therefore, the new approach questions Hilbert’s Thesis, according to which a correct mathematical proof is in principle reducible to a formal proof, based on explicit axioms and logic.

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7

D’Alpaos, Diana, Giovanni Badiali, Francesco Ceccariglia, and Achille Tarsitano. "Delayed Orbital Floor Reconstruction Using Mirroring Technique and Patient-Specific Implants: Proof of Concept." Journal of Personalized Medicine 14, no. 5 (April 26, 2024): 459. http://dx.doi.org/10.3390/jpm14050459.

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Enophthalmos is a severe complication of primary reconstruction following orbital floor fractures, oncological resections, or maxillo-facial syndromes. The goal of secondary orbital reconstruction is to regain a symmetrical globe position to restore function and aesthetics. In this article, we present a method of computer-assisted orbital floor reconstruction using a mirroring technique and a custom-made titanium or high-density polyethylene mesh printed using computer-aided manufacturing techniques. This reconstructive protocol involves four steps: mirroring of the healthy orbit computer tomography files at the contralateral affected site, virtual design of a customized implant, computer-assisted manufacturing (CAM) of the implant using Direct Metal Laser Sintering (DMLS) or Computer Numerical Control (CNC) methods, and surgical insertion of the device. Clinical outcomes were assessed using 3dMD photogrammetry and computed tomography measures in 13 treated patients and compared to a control group treated with stock implants. An improvement of 3.04 mm (range 0.3–6 mm) in globe protrusion was obtained for the patients treated with patient-specific implants (PSI), and no major complications have been registered. The technique described here appears to be a viable method for correcting complex orbital floor defects needing delayed reconstruction.

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8

RUMBERG, ANTJE. "BOLZANO’S CONCEPT OF GROUNDING (ABFOLGE) AGAINST THE BACKGROUND OF NORMAL PROOFS." Review of Symbolic Logic 6, no. 3 (July 3, 2013): 424–59. http://dx.doi.org/10.1017/s1755020313000154.

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AbstractIn this paper, I provide a thorough discussion and reconstruction of Bernard Bolzano’s theory of grounding and a detailed investigation into the parallels between his concept of grounding and current notions of normal proofs. Grounding (Abfolge) is an objective ground-consequence relation among true propositions that is explanatory in nature. The grounding relation plays a crucial role in Bolzano’s proof-theory, and it is essential for his views on the ideal buildup of scientific theories. Occasionally, similarities have been pointed out between Bolzano’s ideas on grounding and cut-free proofs in Gentzen’s sequent calculus. My thesis is, however, that they bear an even stronger resemblance to the normal natural deduction proofs employed in proof-theoretic semantics in the tradition of Dummett and Prawitz.

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9

Klima, Gyula. "Aquinas’s Real Distinction and Its Role in a Causal Proof of God’s Existence." Roczniki Filozoficzne 67, no. 4 (December 23, 2019): 7–26. http://dx.doi.org/10.18290/rf.2019.67.4-1.

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This paper is not going to offer any criticism of the way Gaven Kerr treats Aquinas’ argument. Instead, it offers an alternative way of reconstructing Aquinas’ argument, intending to strengthen especially those controversial aspects of it that Kerr’s reconstruction left untreated or in relative obscurity. Accordingly, although the paper’s treatment will have to have some overlaps with Kerr’s (such as the critique of Kenny’s critique of Aquinas), it will deal with issues essential to adequate replies to certain competent criticisms of his argument untreated by Kerr (such as Buridan’s critique). For the sake of the “formally inclined” reader, the paper’s treatment will also include an Appendix offering a formal reconstruction of both the main argument and its sub-arguments to demonstrate the formal rigor of Aquinas’ original.

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10

Godino-Moya, Alejandro, Rosa-María Menchón-Lara, Marcos Martín-Fernández, Claudia Prieto, and Carlos Alberola-López. "Elastic AlignedSENSE for Dynamic MR Reconstruction: A Proof of Concept in Cardiac Cine." Entropy 23, no. 5 (April 29, 2021): 555. http://dx.doi.org/10.3390/e23050555.

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Numerous methods in the extensive literature on magnetic resonance imaging (MRI) reconstruction exploit temporal redundancy to accelerate cardiac cine. Some of them include motion compensation, which involves high computational costs and long runtimes. In this work, we proposed a method—elastic alignedSENSE (EAS)—for the direct reconstruction of a motion-free image plus a set of nonrigid deformations to reconstruct a 2D cardiac sequence. The feasibility of the proposed approach was tested in 2D Cartesian and golden radial multi-coil breath-hold cardiac cine acquisitions. The proposed approach was compared against parallel imaging compressed sense (sPICS) and group-wise motion corrected compressed sense (GWCS) reconstructions. EAS provides better results on objective measures with considerable less runtime when an acceleration factor is higher than 10×. Subjective assessment of an expert, however, invited proposing the combination of EAS and GWCS as a preferable alternative to GWCS or EAS in isolation.

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11

Hinestroza G., Doris, Carlos E. Mejia, Lijia Guo, and Diego A. Murio. "Rigorous Proofs For Cone-Beam Reconstruction." Revista de Ciencias 8 (November 8, 2011): 95–110. http://dx.doi.org/10.25100/rc.v8i0.616.

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Cone beam reconstruction is a three-dimensional tomographic reconstruction technique with the potential capability of producing images with temporal contrast, and three-dimensional spatial resolution.In this paper we present a rigorous proof of the novel three-dimensional inversion formula developed by B. Smith and derive strict tipper bound« for the error

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12

Myasnikov, A., S. Merts, K. Gertsenberger, A. Driuk, and S. Nemnyugin. "Parallel Event Reconstruction in BmnRoot Using the Proof System." Physics of Particles and Nuclei Letters 19, no. 5 (October 2022): 577–79. http://dx.doi.org/10.1134/s1547477122050302.

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13

Sanchez, J., and H. Benaroya. "Asymptotic approximation method of force reconstruction: Proof of concept." Mechanical Systems and Signal Processing 92 (August 2017): 39–63. http://dx.doi.org/10.1016/j.ymssp.2017.01.022.

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14

Gupta, S. K., Pankaj Mangal, and Vineet Paliwal. "Some work towards the proof of the reconstruction conjecture." Discrete Mathematics 272, no. 2-3 (November 2003): 291–96. http://dx.doi.org/10.1016/s0012-365x(03)00198-5.

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15

RICCA, RENZO L., and BERNARDO NIPOTI. "GAUSS' LINKING NUMBER REVISITED." Journal of Knot Theory and Its Ramifications 20, no. 10 (October 2011): 1325–43. http://dx.doi.org/10.1142/s0218216511009261.

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In this paper we provide a mathematical reconstruction of what might have been Gauss' own derivation of the linking number of 1833, providing also an alternative, explicit proof of its modern interpretation in terms of degree, signed crossings and intersection number. The reconstruction presented here is entirely based on an accurate study of Gauss' own work on terrestrial magnetism. A brief discussion of a possibly independent derivation made by Maxwell in 1867 completes this reconstruction. Since the linking number interpretations in terms of degree, signed crossings and intersection index play such an important role in modern mathematical physics, we offer a direct proof of their equivalence. Explicit examples of its interpretation in terms of oriented area are also provided.

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16

Stoyanova, Ani, Ann-Kathrin Berg, and Katharina Beyer. "A Robotic Completely Intercorporeal Jejunal Pouch Reconstruction after Gastrectomy." Current Oncology 29, no. 11 (November 12, 2022): 8600–8608. http://dx.doi.org/10.3390/curroncol29110678.

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Robotic surgery is increasingly gaining importance. While initial results suggest an advantage of the robotic over the minimally invasive approach in patients with gastric cancer, definitive proof of its superiority has yet to be provided. There are numerous approaches to recreate a gastric reservoir after a total gastrectomy. However, a major disadvantage of most conventional reconstructions are long term effects such as dumping syndrome, afferent loop syndrome and poor nutrition intake with severe impact on the patient quality of life. The jejunal pouch reconstruction is a beneficial reconstruction, which provides a larger reservoir capacity after gastrectomy and prevents anastomotic stenosis and dumping syndrome. The completely intercorporeal approach with a Pfannenstiel incision instead of an unfavorable midline incision can potentially decrease delayed complications such as incision hernias. With the increased deployment of robotic surgery, a complete intercorporeal reconstruction is now possible without major increase in operating time or further technical weak points. We provide for the first time a detailed technical explanation of the completely intercorporeal robotic jejunal pouch reconstruction after gastrectomy.

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17

Abaci, Uygar. "Kant's Only Possible Argument and Chignell's Real Harmony." Kantian Review 19, no. 1 (January 31, 2014): 1–25. http://dx.doi.org/10.1017/s1369415413000277.

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AbstractAndrew Chignell recently proposed an original reconstruction of Kant's ‘Only Possible Argument’ for the existence of God. Chignell claims that what motivates the ‘Grounding Premise’ of Kant's proof, ‘real possibility must be grounded in actuality’, is the requirement that the predicates of a really possible thing must be ‘really harmonious’, i.e. compatible in an extra-logical or metaphysical sense. I take issue with Chignell's reconstruction. First, the pre-Critical Kant does not present ‘real harmony’ as a general condition of real possibility. Second, the real harmony requirement is not what motivates the ‘Grounding Premise’ of the proof. Instead, this premise is sufficiently motivated by what Chignell labels the ‘content’ requirement. Finally, Kant's downgrading of the proof in his Critical period is not based on a concern regarding the real harmony of the predicates of God, but on his Critical restrictions on cognition in general and modal cognition in particular.

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18

Lodder, Elmer, and Maarten van der Elst. "Chest Wall Reconstruction with Precontoured Locking Plate Proof of Concept." Journal of Cancer Therapy 01, no. 03 (2010): 131–33. http://dx.doi.org/10.4236/jct.2010.13021.

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19

Fortun, Denis, Paul Guichard, Ning Chu, and Michael Unser. "Reconstruction From Multiple Poses in Fluorescence Imaging: Proof of Concept." IEEE Journal of Selected Topics in Signal Processing 10, no. 1 (February 2016): 61–70. http://dx.doi.org/10.1109/jstsp.2015.2493884.

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20

Scherf, N., J. Einenkel, L. C. Horn, N. Wentzensen, M. Loeffler, J. P. Kuska, and U. D. Braumann. "Large Histological Serial Sections for Computational Tissue Volume Reconstruction." Methods of Information in Medicine 46, no. 05 (2007): 614–22. http://dx.doi.org/10.1160/me9065.

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Summary Objectives: A proof of principle study was conducted for microscopic tissue volume reconstructions using a new image processing chain operating on alternately stained large histological serial sections. Methods: Digital histological images were obtained from conventional brightfield transmitted light microscopy. A powerful nonparametric nonlinear optical flow-based registration approach was used. In order to apply a simple but computationally feasible sum-of-squared-differences similarity measure even in case of differing histological stainings, a new consistent tissue segmentation procedure was placed upstream. Results: Two reconstructions from uterine cervix carcinoma specimen were accomplished, one alternately stained with p16INK4a (surrogate tumor marker) and H&E (routine reference), and another with three different alternate stainings, H&E, p16INK4a, and CD3 (a T-lymphocyte marker). For both cases, due to our segmentation-based reference-free nonlinear registration procedure, resulting tissue reconstructions exhibit utmost smooth image-to-image transitions without impairing warpings. Conclusions: Our combination of modern nonparametric nonlinear registration and consistent tissue segmentation has turned out to provide a superior tissue reconstruction quality.

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21

MILLER, DALE E. "On Millgram on Mill." Utilitas 16, no. 1 (February 11, 2004): 96–108. http://dx.doi.org/10.1017/s0953820803001080.

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In a recent article in Ethics, Elijah Millgram presents a novel reconstruction of J. S. Mill's ‘proof’ of the principle of utility. Millgram's larger purpose is to critique instrumentalist approaches to practical reasoning. His reading of the proof makes Mill out to be an instrumentalist, and Millgram thinks that the ultimate failure of Mill's argument usefully illustrates an inconsistency inherent in instrumentalism. Yet Millgram's interpretation of the proof does not succeed. Mill is not an instrumentalist. Millgram may be right that instrumentalism is incoherent, but he has chosen the wrong figure to illustrate the point.

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22

Dalla Rosa, Davide. "On the Formal Validity of Proof by Contradiction in Kant’s Logic." History of Philosophy & Logical Analysis 25, no. 1 (June 10, 2022): 95–114. http://dx.doi.org/10.30965/26664275-bja10015.

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Abstract The paper provides a reconstruction of proof by contradiction in Kant’s pure general logic. A seemingly less-explored point of view on this topic is how apagogical proof can account for the formal truth of a judgement. Integrating the argument held by Kjosavik (2019), I intend to highlight how one can use proof by contradiction, conceived as a modus tollens, to establish the logical actuality (logical or formal truth) of a cognition. Although one might agree on the capacity of the proof to prove formal falsity, the logical actuality of a judgement is assessable based on a logically grounded judgement and, as for transcendental logic, this cognitive operation has to presuppose the real possibility of an object.

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23

Pafitanis, Georgios, Alexandros Vris, Dimitris Reissis, Amir Sadri, Reza Alamouti, Simon Myers, and Parviz Sadigh. "Recycling of flap pedicle in complex lower extremity reconstruction: A proof of free muscle flap neovascularization." Archives of Plastic Surgery 47, no. 6 (November 15, 2020): 619–21. http://dx.doi.org/10.5999/aps.2018.00171.

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This article portrays the authors’ clinical experience of a complex case of lower extremity reconstruction using a recycled pedicle from 10 years old free latissimus dorsi musculocutaneous flap to supply a new free anterolateral thigh flap for proximal tibia wound defect reconstruction. It provides clinical evidence that muscle neovascularization occurs and supports the dogma peripheral tissue neovascularization. This case stipulates that recycling of pedicle is feasible, when used with appropriate strategy and safety and also provides evidence for the long-term survival of greater saphenous vein grafts in lower extremity reconstruction.

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24

Aspden, Suzanne. "‘An infinity of factions’: Opera in eighteenth-century Britain and the undoing of society." Cambridge Opera Journal 9, no. 1 (March 1997): 1–19. http://dx.doi.org/10.1017/s0954586700005139.

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It seems fair to say that we are enmeshed in an Age of Reconstruction. Whatever groans the shibboleth of ‘authenticity’ may elicit from musicians and musicologists, the film industry's leap for the bandwagon is proof of the principle that Period Pieces Pay. Of the recent spate of feature films set in the eighteenth century, one in particular has marketed itself through its reconstructive credentials. The technologies that allow us to remodel our bodies, and revive old recordings on compact disc, also allowed the makers of Farinelli, Il Castrato to reach back and breathe new life into the voice of the long-dead castrati.

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25

Borys, Andrzej. "Definition of Sampled Signal Spectrum and Shannon’s Proof of Reconstruction Formula." TransNav, the International Journal on Marine Navigation and Safety of Sea Transportation 16, no. 3 (2022): 473–78. http://dx.doi.org/10.12716/1001.16.03.08.

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26

Bocher, Marie, Alexandre Fournier, and Nicolas Coltice. "Ensemble Kalman filter for the reconstruction of the Earth's mantle circulation." Nonlinear Processes in Geophysics 25, no. 1 (February 16, 2018): 99–123. http://dx.doi.org/10.5194/npg-25-99-2018.

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Abstract. Recent advances in mantle convection modeling led to the release of a new generation of convection codes, able to self-consistently generate plate-like tectonics at their surface. Those models physically link mantle dynamics to surface tectonics. Combined with plate tectonic reconstructions, they have the potential to produce a new generation of mantle circulation models that use data assimilation methods and where uncertainties in plate tectonic reconstructions are taken into account. We provided a proof of this concept by applying a suboptimal Kalman filter to the reconstruction of mantle circulation (Bocher et al., 2016). Here, we propose to go one step further and apply the ensemble Kalman filter (EnKF) to this problem. The EnKF is a sequential Monte Carlo method particularly adapted to solve high-dimensional data assimilation problems with nonlinear dynamics. We tested the EnKF using synthetic observations consisting of surface velocity and heat flow measurements on a 2-D-spherical annulus model and compared it with the method developed previously. The EnKF performs on average better and is more stable than the former method. Less than 300 ensemble members are sufficient to reconstruct an evolution. We use covariance adaptive inflation and localization to correct for sampling errors. We show that the EnKF results are robust over a wide range of covariance localization parameters. The reconstruction is associated with an estimation of the error, and provides valuable information on where the reconstruction is to be trusted or not.

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27

Kövesdi, Balázs, Dénes Kollár, and László Dunai. "Temporary Structural Health Monitoring of Historical Széchenyi Chain Bridge." Buildings 14, no. 2 (February 17, 2024): 535. http://dx.doi.org/10.3390/buildings14020535.

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A temporary monitoring system was installed on the 175-year-old historical Széchenyi Chain Bridge during its reconstruction. The bridge is in the downtown area in the capital city of Hungary and plays a significant role in the city life of Budapest. Six-month-long measurements were conducted during the reconstruction process of the bridge, yielding crucial insights into the structural behaviour of the historical structure. The measurement results were evaluated; the findings encompass the rotation capacity of the pins between the chain elements and the structural response to temperature changes. This information helped the decision-making between 2021 and 2023 by the designers and construction company during the reconstruction. For instance, daily temperature fluctuations resulted in increased bending moments in the chain elements, rising up to 158% compared to the values observed during a proof load test in 2018. Furthermore, the measurements reveal an approximate 42% increase in normal forces compared to the proof load test, which highlights the high sensitivity of chain bridges to temperature fluctuations, where geometric stiffness plays a crucial role. Reconstruction, namely reducing self-weight, notably intensifies the impact on normal forces and bending moments. These outcomes strongly emphasize the dominance of the dead load and self-weight in the case of chain bridges.

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28

Zhou, Meng, and Yi Mao. "Reconstruction of Cosmological Initial Density Field with Observations from the Epoch of Reionization." Astrophysical Journal 965, no. 1 (April 1, 2024): 31. http://dx.doi.org/10.3847/1538-4357/ad2991.

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Abstract The initial density distribution provides a basis for understanding the complete evolution of cosmological density fluctuations. While reconstruction in our local Universe exploits the observations of galaxy surveys with large volumes, observations of high-redshift galaxies are performed with a small field of view and therefore can hardly be used for reconstruction. Here, we propose reconstructing the initial density field using the H i 21 cm and CO line intensity maps from the epoch of reionization. Observations of these two intensity maps provide complementary information on the density field—the H i 21 cm field is a proxy of matter distributions in the neutral regions, while the CO line intensity maps are sensitive to the high-density, star-forming regions that host the sources for reionization. Technically, we employ the conjugate gradient method and develop the machinery for minimizing the cost function for the intensity mapping observations. Analytical expressions for the gradient of cost function are derived explicitly. We show that the resimulated intensity maps match the input maps of mock observations using semi-numerical simulations of reionization with an rms error ≲7% at all stages of reionization. This reconstruction is also robust with an rms error of ∼10% when an optimistic level of shot noise is applied to the CO map or white noise at the level of ≲10% of the standard deviation is applied to each map. Our proof-of-concept work demonstrates the robustness of the reconstruction method, thereby providing an effective technique for reconstructing the cosmological initial density distribution from high-redshift observations.

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29

Castagna, Giuseppe, Mickaël Laurent, Kim Nguyễn, and Matthew Lutze. "On type-cases, union elimination, and occurrence typing." Proceedings of the ACM on Programming Languages 6, POPL (January 16, 2022): 1–31. http://dx.doi.org/10.1145/3498674.

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We extend classic union and intersection type systems with a type-case construction and show that the combination of the union elimination rule of the former and the typing rules for type-cases of our extension encompasses occurrence typing . To apply this system in practice, we define a canonical form for the expressions of our extension, called MSC-form. We show that an expression of the extension is typable if and only if its MSC-form is, and reduce the problem of typing the latter to the one of reconstructing annotations for that term. We provide a sound algorithm that performs this reconstruction and a proof-of-concept implementation.

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Asaadi, Jonathan, Martin Auger, Antonio Ereditato, Damian Goeldi, Umut Kose, Igor Kreslo, David Lorca, et al. "First Demonstration of a Pixelated Charge Readout for Single-Phase Liquid Argon Time Projection Chambers." Instruments 4, no. 1 (March 23, 2020): 9. http://dx.doi.org/10.3390/instruments4010009.

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Traditional charge readout technologies of single-phase Liquid Argon Time projection Chambers (LArTPCs) based on projective wire readout introduce intrinsic ambiguities in event reconstruction. Combined with the slow response inherent in LArTPC detectors, reconstruction ambiguities have limited their performance, until now. Here, we present a proof of principle of a pixelated charge readout that enables the full 3D tracking capabilities of LArTPCs. We characterize the signal-to-noise ratio of charge readout chain to be about 14, and demonstrate track reconstruction on 3D space points produced by the pixel readout. This pixelated charge readout makes LArTPCs a viable option for high-multiplicity environments.

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31

Xi, Hongguang, and Jianzhong Su. "A harmonic function method for EEG source reconstruction." Electronic Research Archive 30, no. 2 (2022): 492–514. http://dx.doi.org/10.3934/era.2022026.

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<abstract><p>In this paper we study a harmonic function method for dipolar source reconstruction, and implemented the numerical simulations. We propose a new error estimate and provide a rigorous proof of the estimate. Then, we validate our method in computer-simulated data and study its numerical stability in different noise levels. It is shown that the harmonic function method can be used to quickly and accurately locate the active regions in EEG source reconstruction.</p></abstract>

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AMENTA, NINA, SUNGHEE CHOI, TAMAL K. DEY, and NAVEEN LEEKHA. "A SIMPLE ALGORITHM FOR HOMEOMORPHIC SURFACE RECONSTRUCTION." International Journal of Computational Geometry & Applications 12, no. 01n02 (February 2002): 125–41. http://dx.doi.org/10.1142/s0218195902000773.

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The problem of computing a piecewise linear approximation to a surface from a set of sample points is important in solid modeling, computer graphics and computer vision. A recent algorithm1 using the Voronoi diagram of the sample points gave a guarantee on the distance of the output surface from the original sampled surface assuming that the sample was sufficiently dense. We give a similar algorithm, simplifying the computation and the proof of the geometric guarantee. In addition, we guarantee that our output surface is homeomorphic to the original surface; to our knowledge this is the first such topological guarantee for this problem.

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33

Roch, S. "A Short Proof that Phylogenetic Tree Reconstruction by Maximum Likelihood Is Hard." IEEE/ACM Transactions on Computational Biology and Bioinformatics 3, no. 1 (January 2006): 92–94. http://dx.doi.org/10.1109/tcbb.2006.4.

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34

Vershik, A. M. "A bijective proof of the Jacobi identity and reconstruction of Young diagrams." Journal of Soviet Mathematics 41, no. 2 (April 1988): 889–91. http://dx.doi.org/10.1007/bf01247084.

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35

Mbuku, R. B., C. Sanchez, R. Evrard, A. Englebert, J. Manon, V. Henriet, G. Nolens, et al. "A NEW TISSUE-ENGINEERED PRODUCT INDICATED FOR BONE RECONSTRUCTION: PROOF OF CONCEPT." Orthopaedic Proceedings 106-B, SUPP_2 (January 2, 2024): 125. http://dx.doi.org/10.1302/1358-992x.2024.2.125.

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To design slow resorption patient-specific bone graft whose properties of bone regeneration are increased by its geometry and composition and to assess it in in-vitro and in-vivo models.A graft composed by hydroxyapatite (HA) and β-TCP was designed as a cylinder with 3D gyroid porosities and 7 mm medullary space based on swine's anatomy. It was produced using a stereolithography 3D-printing machine (V6000, Prodways).Sterile bone grafts impregnated with or without a 10µg/mL porcine BMP-2 (pBMP-2) solution were implanted into porcine femurs in a bone loss model. Bone defect was bi-weekly evaluated by X-ray during 3 months. After sacrifice, microscanner and non-decalcified histology analysis were conducted on biopsies.Finally, osteoblasts were cultured inside the bone graft or in monolayer underneath the bone graft. Cell viability, proliferation, and gene expression were assessed after 7 and 14 days of cell culture (n=3 patients).3D scaffolds were successfully manufactured with a composition of 80% HA and 20% β-TCP ±5% with indentation compressive strength of 4.14 MPa and bending strength of 11.8MPa.In vivo study showed that bone regeneration was highly improved in presence of pBMP-2. Micro-CT shows a filling of the gyroid sinuses of the implant (Figure 1).In vitro, the presence of BMP2 did not influence the viability of the osteoblasts and the mortality remained below 3%. After 7 days, the presence of BMP2 in the scaffold significantly increased by 85 and 65% the COL1A1 expression and by 8 and 33-fold the TNAP expression by osteoblasts in the monolayer or in the scaffold, respectively. This BMP2 effect was transient in monolayer and did not modify gene expression at day 14.BMP2-impregnated bone graft is a promising patient-personalized 3D-printed solution for bone defect regeneration, by promoting neighboring host cells recruitment and solid new bone formation.For any figures and tables, please contact the authors directly.

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Schäfer, Jörg. "A Note on Ultrametric Spaces, Minimum Spanning Trees and the Topological Distance Algorithm." Information 11, no. 9 (August 28, 2020): 418. http://dx.doi.org/10.3390/info11090418.

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We relate the definition of an ultrametric space to the topological distance algorithm—an algorithm defined in the context of peer-to-peer network applications. Although (greedy) algorithms for constructing minimum spanning trees such as Prim’s or Kruskal’s algorithm have been known for a long time, they require the complete graph to be specified and the weights of all edges to be known upfront in order to construct a minimum spanning tree. However, if the weights of the underlying graph stem from an ultrametric, the minimum spanning tree can be constructed incrementally and it is not necessary to know the full graph in advance. This is possible, because the join algorithm responsible for joining new nodes on behalf of the topological distance algorithm is independent of the order in which the nodes are added due to the property of an ultrametric. Apart from the mathematical elegance which some readers might find interesting in itself, this provides not only proofs (and clearer ones in the opinion of the author) for optimality theorems (i.e., proof of the minimum spanning tree construction) but a simple proof for the optimality of the reconstruction algorithm omitted in previous publications too. Furthermore, we define a new algorithm by extending the join algorithm to minimize the topological distance and (network) latency together and provide a correctness proof.

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Vovin, Alexander. "Proto-K(r)adai ‘hand’, ‘eye’, and ‘bird’ revisited." Cahiers de Linguistique Asie Orientale 47, no. 1 (October 11, 2018): 150–64. http://dx.doi.org/10.1163/19606028-04701003.

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Abstract This article revisits the traditional comparisons for K(r)adai and Austronesian ‘hand’, ‘eye’, and ‘bird’. In the case of ‘hand’ it attempts to improve the comparison by offering an unorthodox solution for Proto-K(r)adai reconstruction that, in my opinion, should be *lima, virtually identical to proto-Austronesian. It also provides additional evidence for reconstructing ‘eye’ and ‘bird’ as disyllabic words in K(r)adai, showing that these two were also very close to (with minor differences) to proto-Austronesian. Although these facts alone cannot be used as ultimate proof of K(r)adai and Austronesian genetic relationship, I believe that they constitute a further step in refining the arguments in this direction.

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Aftab, N., P. Boonpornprasert, G. Georgiev, J. Good, M. Gross, W. Hillert, A. Hoffmann, et al. "Improvements in longitudinal phase space tomography at PITZ." Journal of Physics: Conference Series 2687, no. 7 (January 1, 2024): 072017. http://dx.doi.org/10.1088/1742-6596/2687/7/072017.

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Abstract Methodical studies to improve the existing e-beam Longitudinal Phase Space (LPS) tomography were performed at the Photo Injector Test facility at DESY in Zeuthen. Proof-of-principle simulations were done to address some core concerns e.g. booster phase range, space charge effects and noisy artefacts in results. Phase advance analysis was done with the help of an analytical model that determined the booster phase range and step size. A slit was introduced before the booster to truncate the beam and reduce space charge forces. The reconstruction method adopted was image space reconstruction algorithm owing to its assurance of non-negative solution. An initial scientific presumption of LPS from low energy momentum measurements was established to reduce artefacts in the phase space. This paper will explain the proof-of-principle simulations highlighting the key aspects to obtain accurate results. Reconstructed LPS for different experimental cases will be presented to demonstrate the diagnostic capability.

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Hinst, Peter. "A Logical Analysis of the Main Argument in Chapter 2 of the Proslogion by Anselm of Canterbury." History of Philosophy and Logical Analysis 17, no. 1 (April 5, 2014): 22–44. http://dx.doi.org/10.30965/26664275-01701003.

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The primary aim is the reconstruction of the main argument of the second chapter of Anselm’s Proslogion. To be proved is the statement that God, or something than which nothing greater can be thought, exists in reality. I proceed by a piecemeal analysis of every sentence of the Latin original and its subsequent translation into a formal second-order language with choice operator. Reconstructing Anselm’s reasoning demands interpretative input and additions. For example, the formula ‘quod maius est’ has to be suitably interpreted and expanded. Furthermore, I try to explicate Anselm’s maius predicate in terms of a perfection predicate and to develop a general proof for Anselm’s theorem, i.e. the statement that something/that than which something greater cannot be thought has all greater-making attributes.

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Qin, Mengyuan. "Optimization of Intersection in Construction at Low Cost- A Case Study of the Intersection of Youyi Road and Luojiagang Road." Highlights in Science, Engineering and Technology 37 (March 18, 2023): 182–95. http://dx.doi.org/10.54097/hset.v37i.6073.

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Intersections in construction are common in China when roads in plenty of Chinese cities are under reconstruction and expansion in a large scale. As intersections are traffic hub where big traffic flows passing by, smoothness and efficiency are ought to be guaranteed in order to reduce effect caused by construction. However, plans at lower cost and more effective are appreciated because reconstructing an intersection is costly. The research analysis the current situation and raise a complete optimize plan for the crossing of Youyi Road and Luojiagang Road in order to proof there is possibility to optimize an intersection at lower cost. The research raises a feasible optimize plan for a crossing. It is feasible to cheaply optimize a crossing which still allows vehicles running while under construction.

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Hintz, Peter, and Gunther Uhlmann. "Reconstruction of Lorentzian Manifolds from Boundary Light Observation Sets." International Mathematics Research Notices 2019, no. 22 (February 2, 2017): 6949–87. http://dx.doi.org/10.1093/imrn/rnx320.

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Abstract On a time-oriented Lorentzian manifold (M, g) with nonempty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets S ⊂ M of sources is uniquely determined by measurements of the intersection of future light cones from points in S with a fixed open subset of the boundary of M; here, light rays are reflected at ∂M according to Snell’s law. Our proof is constructive, and allows for interior conjugate points as well as multiply reflected and self-intersecting light cones.

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Ginthör, Stephan J., Judith Schlagnitweit, Matthias Bechmann, and Norbert Müller. "Nuclear spin noise tomography in three dimensions with iterative simultaneous algebraic reconstruction technique (SART) processing." Magnetic Resonance 1, no. 2 (August 6, 2020): 165–73. http://dx.doi.org/10.5194/mr-1-165-2020.

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Abstract. We report three-dimensional spin noise imaging (SNI) of nuclear spin density from spin noise data acquired by Faraday detection. Our approach substantially extends and improves the two-dimensional SNI method for excitation-less magnetic resonance tomography reported earlier (Müller and Jerschow, 2006). This proof of principle was achieved by taking advantage of the particular continuous nature of spin noise acquired in the presence of constant magnitude magnetic field gradients and recent advances in nuclear spin noise spectroscopy acquisition as well as novel processing techniques. In this type of projection–reconstruction-based spin noise imaging the trade-off between signal-to-noise ratio (or image contrast) and resolution can be adjusted a posteriori during processing of the original time-domain data by iterative image reconstruction in a unique way not possible in conventional rf-pulse-dependent magnetic resonance imaging (MRI). The 3D SNI is demonstrated as a proof of concept on a commercial 700 MHz high-resolution NMR spectrometer, using a 3D-printed polymeric phantom immersed in water.

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Chen, P., Z. Chen, E. Landao, T. Leys, T. Wang, Q. Zheng, Y. Ding, and M. Zheng. "FABRICATION OF BIOACTIVE COLLAGEN ROPE FOR ANTERIOR CRUCIATE LIGAMENT RECONSTRUCTION." Orthopaedic Proceedings 105-B, SUPP_7 (April 4, 2023): 137. http://dx.doi.org/10.1302/1358-992x.2023.7.137.

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To address the current challenge of anterior cruciate ligament (ACL) reconstruction, this study is the first to fabricate a braided collagen rope (BCR) which mimics native hamstring for ACL reconstruction. The study aims to evaluate the biological and biomechanical properties of BCR both in vivo and vitro.Rabbit ACL reconstruction model using collagen rope and autograft (hamstring tendon) was conducted. The histological and biomechanical evaluations were conducted at 6-, 12-, 18, 26-week post-operation. In vitro study included cell morphology analysis, cell function evaluation and RNA sequencing of the tenocytes cultured on BCR. A cadaver study was also conducted to verify the feasibility of BCR for ACL reconstruction.BCR displays satisfactory mechanical strength similar to hamstring graft for ACL reconstruction in rabbit. Histological assessment showed BCR restore ACL morphology at 26 weeks similar to native ACL. The superior dynamic ligamentization in BCR over autograft group was evidenced by assessment of cell and collagen morphology and orientation. The in vitro study showed that the natural collagen fibres within BCR enables to signal the morphology adaptation and orientation of human tenocytes in bioreactor. BCR enables to enhance cell proliferation and tenogenic expression of tenocytes as compared to hydrolysed collagen. We performed an RNA-Sequencing (RNA-seq) experiment where RNA was extracted from tenocyte seeded with BCR. Analysis of enriched pathways of the up-regulated genes revealed that the most enriched pathways were the Hypoxia-inducible factor 1-alpha (HIF1A) regulated networks, implicating the possible mechanism BCR induced ACL regeneration. The subsequent cadaver study was conducted to proof the feasibility of BCR for ACL reconstruction.This study demonstrated the proof-of-concept of bio-textile braided collagen rope for ACL reconstruction, and the mechanism by which BCR induces natural collagen fibres that positively regulate morphology and function of tenocytes.

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Soemarto, Soehartono. "The Reconstruction of the Reversal of the Burden of Proof Verificationin Corruption Delict." International Journal of English Literature and Social Sciences 3, no. 5 (2018): 732–45. http://dx.doi.org/10.22161/ijels.3.5.7.

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Pietruski, Piotr, Marcin Majak, Ewelina Światek-Najwer, Magdalena Żuk, Michał Popek, Maciej Mazurek, Marta Świecka, and Janusz Jaworowski. "Navigation-guided fibula free flap for mandibular reconstruction: A proof of concept study." Journal of Plastic, Reconstructive & Aesthetic Surgery 72, no. 4 (April 2019): 572–80. http://dx.doi.org/10.1016/j.bjps.2019.01.026.

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Kereković, Davorin. "Project “proof of the identity of reconstruction project of the city of Vukovar”." Computers, Environment and Urban Systems 18, no. 2 (March 1994): 143–46. http://dx.doi.org/10.1016/0198-9715(94)90009-4.

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Peng, Hanchuan, Fuhui Long, Ting Zhao, and Eugene Myers. "Proof-editing is the Bottleneck Of 3D Neuron Reconstruction: The Problem and Solutions." Neuroinformatics 9, no. 2-3 (December 18, 2010): 103–5. http://dx.doi.org/10.1007/s12021-010-9090-x.

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Cureton, Adam. "A Contractualist Reading of Kant's Proof of the Formula of Humanity." Kantian Review 18, no. 3 (October 7, 2013): 363–86. http://dx.doi.org/10.1017/s1369415413000150.

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AbstractKant offers the following argument for the formula of humanity (FH): Each rational agent necessarily conceives of her own rational nature as an end in itself and does so on the same grounds as every other rational agent, so all rational agents must conceive of one another's rational nature as an end in itself. As it stands, the argument appears to be question-begging and fallacious. Drawing on resources from the formula of universal law (FUL) and Kant's claims about the primacy of duties to oneself, I propose a contractualist reconstruction of this puzzling line of reasoning.

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Altenkort, Luis, Alexander M. Eller, Olaf Kaczmarek, Lukas Mazur, Guy D. Moore, and Hai-Tao Shu. "Spectral reconstruction details of a gradient-flowed color-electric correlator." EPJ Web of Conferences 259 (2022): 10004. http://dx.doi.org/10.1051/epjconf/202225910004.

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In a recently published work we provide a proof-of-concept of a novel method to extract the heavy quark momentum diffusion coefficient from color-electric correlators on the lattice using gradient flow. The transport coefficient can be found in the infrared limit of the corresponding spectral function which is reconstructed through perturbative model fits of the correlator data. In this proceedings report we want to give more detailed insights into the systematic uncertainties of this procedure and compare our results with other studies.

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AMBARTSOUMIAN, GAIK, RIM GOUIA-ZARRAD, VENKATESWARAN P. KRISHNAN, and SOUVIK ROY. "Image reconstruction from radially incomplete spherical Radon data." European Journal of Applied Mathematics 29, no. 3 (September 11, 2017): 470–93. http://dx.doi.org/10.1017/s0956792517000250.

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We study inversion of the spherical Radon transform with centres on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of radially incomplete data, we show that the spherical Radon transform can be uniquely inverted recovering the image function in spherical shells. Our result is valid when the support of the image function is inside the data acquisition sphere, outside that sphere, as well as on both sides of the sphere. Furthermore, in addition to the uniqueness result, our method of proof provides reconstruction formulas for all those cases. We present a robust computational algorithm and demonstrate its accuracy and efficiency on several numerical examples.

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