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251. A study of truncation effects in boundary flows of the Ising model on a strip

Author

Toth, Gabor Zsolt

Subjects
High Energy Physics - Theory, Condensed Matter - Other Condensed Matter
Abstract

We investigate the idea that the effect of the truncation applied in the TCSA method on the spectrum coincides with the effect of a suitable changing of the coefficients of the terms in the Hamiltonian operator. The investigation is done in the case of the critical Ising model on a strip with an external magnetic field on one of the boundaries. A detailed quantum field theoretical description of this model is also given, and we propose a description as a perturbation of the infinite coupling limit. The investigation is also carried out for a truncation method which preserves the solvability of the model. The results of perturbative and numerical calculations presented support the above idea and show that the qualitative behaviour of the truncated spectrum as a function of the coupling constant depends on the truncation method., Comment: 39 pages

Published
2006
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252. A Renormalisation group for TCSA

Author

Feverati, Giovanni, Graham, Kevin, Pearce, Paul A., Toth, Gabor Zs., and Watts, Gerard

Subjects
High Energy Physics - Theory
Abstract

We discuss the errors introduced by level truncation in the study of boundary renormalisation group flows by the Truncated Conformal Space Approach. We show that the TCSA results can have the qualitative form of a sequence of RG flows between different conformal boundary conditions. In the case of a perturbation by the field phi(13), we propose a renormalisation group equation for the coupling constant which predicts a fixed point at a finite value of the TCSA coupling constant and we compare the predictions with data obtained using TBA equations., Comment: 11 pages, 7 figures, talk presented by G Watts at the workshop "Integrable Models and Applications: from Strings to Condensed Matter", Santiago de Compostela, Spain, 12-16 September 2005

Published
2006

256. Targeted therapy with a localised abluminal groove, low-dose sirolimus-eluting, biodegradable polymer coronary stent (TARGET All Comers): a multicentre, open-label, randomised non-inferiority trial

Author

Lansky, Alexandra, Wijns, William, Xu, Bo, Kelbæk, Henning, van Royen, Niels, Zheng, Ming, Morel, Marie-angèle, Knaapen, Paul, Slagboom, Ton, Johnson, Thomas W, Vlachojannis, Georgios, Arkenbout, Karin E, Holmvang, Lene, Janssens, Luc, Ochala, Andrzej, Brugaletta, Salvatore, Naber, Christoph K, Anderson, Richard, Rittger, Harald, Berti, Sergio, Barbato, Emanuele, Toth, Gabor G, Maillard, Luc, Valina, Christian, Buszman, Paweł, Thiele, Holger, Schächinger, Volker, and Baumbach, Andreas

Published
2018
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262. A nonperturbative study of phase transitions in the multi-frequency sine-Gordon model

Author

Toth, Gabor Zsolt

Subjects
High Energy Physics - Theory, Condensed Matter - Other Condensed Matter
Abstract

The phase spaces of the two- and three-frequency sine-Gordon models are examined in the framework of truncated conformal space approach. The focus is mainly on a tricritical point in the phase space of the three-frequency model. We give substantial evidence that this point exists. We also find the critical line in the phase space and present TCSA data showing the change of the spectrum on the critical line as the tricritical endpoint is approached. We find a few points of the line of first order transition as well., Comment: 26 pages, LaTeX, minor modification

Published
2004
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263. BREAKING THE EQUILIBRIUM: FROM DISTRUST OF REPRESENTATIVE GOVERNMENT TO AN AUTHORITARIAN EXECUTIVE.

Author

Toth, Gabor Attila

Subjects
Populism -- Analysis -- Models, Equilibrium (Economics) -- Analysis -- Political aspects, Authoritarianism -- Analysis -- Models, Constitutional law -- Evaluation -- Models -- Political aspects
Abstract

I. THE RISE OF POPULIST AUTHORITARIANISM In the twenty-first century, more than half of the countries in the world are far from what we would consider "normal" constitutional democracies. (1) [...], Although contemporary populist authoritarians have not entirely abandoned the aims and methods of their ancestors, authoritarianism has been undergoing a reinvention in recent years. Behind a facade of constitutionalism, new authoritarianism claims to abide by democratic principles. Populist authoritarians legitimize themselves through popular elections and maintain the entire set of formal institutions associated with constitutional democracy, using them as both an appearance of representation and a tool of authoritarian imposition. The article focuses on the concepts of trust and distrust of representative government to afford a better understanding of populist authoritarianism. The paper describes two rival theoretical conceptions of government, known as Hobbesian (sovereign government) and Lockean (limited government). The Hobbesian conception rests on the idea of an effective and efficient executive that is able to protect the safety of the people and avoid anarchy. In contrast, the Lockean tradition requires checks and balances in the constitutional design in order to prevent the rise of a tyrannical executive. In the former conception, trust in the authority is a substitute for constitutional constraints, whereas in the latter, constitutional limitations presuppose that public officials and institutions should be distrusted. The article argues that constitutionalism is better served when the characterizing traits of the two theories are balanced. A comparison of some of the elements of modern constitutionalism supports the idea that under certain circumstances, a relatively stable equilibrium between trustful constitutional cooperation and constitutional mechanisms of distrust can be achieved. However, the executive may gain unrestrained power when a constitutional system loses this balance. The article shows how a divergence from equilibrium can be a marker of populist authoritarianism. Cite as: Gabor Attila Toth, Breaking the Equilibrium: From Distrust of Representative Government to an Authoritarian Executive, 28 WASH. INT'L L.J. 317 (2019).

Published
2019

264. Mean Minkowski Measures

Author

Toth, Gabor, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Toth, Gabor

Published
2015
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265. First Things First on Convex Sets

Author

Toth, Gabor, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Toth, Gabor

Published
2015
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266. Affine Diameters and the Critical Set

Author

Toth, Gabor, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Toth, Gabor

Published
2015
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267. Measures of Symmetry and Stability

Author

Toth, Gabor, Axler, Sheldon, Series editor, Capasso, Vincenzo, Series editor, Casacuberta, Carles, Series editor, MacIntyre, Angus, Series editor, Ribet, Kenneth, Series editor, Sabbah, Claude, Series editor, Süli, Endre, Series editor, Woyczyński, Wojbor A., Series editor, and Toth, Gabor

Published
2015
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268. HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

Author

Gammie, Charles F., McKinney, Jonathan C., and Tóth, Gábor

Subjects
Astrophysics
Abstract

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, and van Leer scheme. A variant of constrained transport, proposed earlier by T\'oth, is used to maintain a divergence free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole., Comment: 38 pages, 18 figures, submitted to ApJ

Published
2003
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270. On the role of mass in the mathematical structure of Newtonian and special relativistic mechanics

Author

Toth, Gabor Zsolt

Subjects
Mathematical Physics
Abstract

We consider five-dimensional real linear spaces with a (otherwise well-known) linear action of the Galilei and the Poincare group on them, describe the geometry of these two spaces, and show, that these geometries comprise the notions of space-time, mass, momentum, force and physical dimensions in a natural way. In this way we geometrize the quantity of mass and integrate it together with space-time into two geometries in a natural way, so that these geometries are perfectly suitable for underlying the Newtonian and special relativistic mechanics of pointlike bodies., Comment: plain tex, 25 pages

Published
1999

271. Correction to: New Trends in Intuitive Geometry

Author

Ambrus, Gergely, Bárány, Imre, Böröczky, Károly J., Fejes Tóth, Gábor, Pach, János, Fejes Tóth, Gabor, Editor-in-Chief, Ambrus, Gergely, Series Editor, Katona, Gyula, Editorial Board Member, Lovász, László, Editorial Board Member, Miklós, Dezső, Editorial Board Member, Pálfy, Péter Pal, Editorial Board Member, Recski, Andras, Editorial Board Member, Stipsicz, András, Editorial Board Member, Szász, Domokos, Editorial Board Member, Bárány, Imre, editor, Böröczky, Károly J., editor, Fejes Tóth, Gábor, editor, and Pach, János, editor

Published
2018
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273. Biodegradable-Polymer or Durable-Polymer Stents in Patients at High Bleeding Risk: A Randomized, Open-Label Clinical Trial

Author

Valgimigli, Marco, primary, Wlodarczak, Adrian, additional, Tölg, Ralph, additional, Merkely, Béla, additional, Kelbæk, Henning, additional, Legutko, Jacek, additional, Galli, Stefano, additional, Godin, Matthieu, additional, Toth, Gabor G., additional, Lhermusier, Thibault, additional, Honton, Benjamin, additional, Dietrich, Peter Laurenz, additional, Stammen, Francis, additional, Ferdinande, Bert, additional, Silvain, Johanne, additional, Capodanno, Davide, additional, Cayla, Guillaume, additional, Valgimigli, Marco, additional, Moccetti, Marco, additional, Toth-Gayor, Gabor G., additional, Sanguineti, Francesca, additional, Birkemeyer, Ralf, additional, Schneider, Steffen, additional, Büllesfeld, Lutz, additional, Witzenbichler, Bernhard, additional, Hochadel, Matthias, additional, Collins, Nicolas, additional, Shiekh, Imran, additional, Van Gaal, William, additional, Brandt, Mathias-Christoph, additional, Kefer, Joëlle, additional, Coussement, Patrick, additional, Olsen, Niels Thue, additional, Puymirat, Etienne, additional, Lemesle, Gilles, additional, Romain, Didier, additional, Haude, Michael, additional, Schmitz, Thomas, additional, Sherif, Mohammad, additional, Wöhrle, Jochen, additional, Arthur Yung, See Yue, additional, Yan, Bryan, additional, Vorobcsuk, András, additional, Horvath, Ivan, additional, Ferlini, Marco, additional, Nicolini, Elisa, additional, Erglis, Andrejs, additional, Kalnins, Artis, additional, Azmi, Shaiful, additional, Somi, Samer, additional, Somaratne, Jithendra, additional, Zhi Lin, Deanna Khoo, additional, de la Torre Hernandez, Jose Maria, additional, Bosco, Alfonso Torres, additional, Fores, Juan Sanchis, additional, Fournier, Stéphane, additional, Iglesias, Juan, additional, Rubimbura, Vladimir, additional, and Kehasukcharoen, Wirash, additional

Published
2023
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274. Clinical and Vessel Characteristics Associated With Hard Outcomes After PCI and Their Combined Prognostic Implications

Author

Yang, Seokhun, primary, Hwang, Doyeon, additional, Zhang, Jinlong, additional, Park, Jiesuck, additional, Yun, Jun Pil, additional, Lee, Joo Myung, additional, Nam, Chang‐Wook, additional, Shin, Eun‐Seok, additional, Doh, Joon‐Hyung, additional, Chen, Shao‐Liang, additional, Kakuta, Tsunekazu, additional, Toth, Gabor G., additional, Piroth, Zsolt, additional, Johnson, Nils P., additional, Hakeem, Abdul, additional, Uretsky, Barry F, additional, Hokama, Yohei, additional, Tanaka, Nobuhiro, additional, Lim, Hong‐Seok, additional, Ito, Tsuyoshi, additional, Matsuo, Akiko, additional, Azzalini, Lorenzo, additional, Leesar, Massoud A., additional, Neleman, Tara, additional, van Mieghem, Nicolas M, additional, Diletti, Roberto, additional, Daemen, Joost, additional, Collison, Damien, additional, Collet, Carlos, additional, De Bruyne, Bernard, additional, and Koo, Bon‐Kwon, additional

Published
2023
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277. Phylogeographic evolution of horseshoe bat sarbecoviruses in Vietnam and implications for the origins of SARS-CoV and SARS-CoV-2

Author

HASSANIN, Alexandre, primary, Tu, Vuong, additional, Görföl, Tamás, additional, Ngon, Lam, additional, Pham, Phu, additional, Hang, Chu, additional, Tuan, Tran, additional, Prot, Matthieu, additional, SIMON-LORIERE, Etienne, additional, Kemenesi, Gabor, additional, Toth, Gabor, additional, Moulin, Laurent, additional, and Wurtzer, Sébastien, additional

Published
2023
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278. Flow diversion for the treatment of intracranial bifurcation aneurysms: a systematic review and meta-analysis

Author

Kashkoush, Ahmed, primary, El-Abtah, Mohamed Ehab, additional, Petitt, Jordan C, additional, Glauser, Gregory, additional, Winkelman, Robert, additional, Achey, Rebecca L, additional, Davison, Mark, additional, Abdulrazzak, Mohammad A, additional, Hussain, Shazam M, additional, Toth, Gabor, additional, Bain, Mark, additional, and Moore, Nina, additional

Published
2023
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279. Applied coronary physiology for planning and guidance of percutaneous coronary interventions. A clinical consensus statement from the European Association of Percutaneous Cardiovascular Interventions (EAPCI) of the European Society of Cardiology

Author

Escaned, Javier, primary, Berry, Colin, additional, De Bruyne, Bernard, additional, Shabbir, Asad, additional, Collet, Carlos, additional, Lee, Joo Myung, additional, Appelman, Yolande, additional, Barbato, Emanuele, additional, Biscaglia, Simone, additional, Buszman, Piotr P., additional, Campo, Gianluca, additional, Chieffo, Alaide, additional, Jeremias, Allen, additional, Paradies, Valeria, additional, Piróth, Zsolt, additional, Raposo, Luís, additional, Roguin, Ariel, additional, Rudolph, Tanja, additional, Sarno, Giovanna, additional, Sen, Sayan, additional, Toth, Gabor G., additional, Van Belle, Eric, additional, Zimmermann, Frederick M., additional, Dudek, Dariusz, additional, Stefanini, Giulio, additional, and Tarantini, Giuseppe, additional

Published
2023
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280. A new resorbable magnesium scaffold for de novo coronary lesions (DREAMS 3): one-year results of the BIOMAG-I first-in-human study

Author

Haude, Michael, primary, Wlodarczak, Adrian, additional, van der Schaaf, René J., additional, Torzewski, Jan, additional, Ferdinande, Bert, additional, Escaned, Javier, additional, Iglesias, Juan F, additional, Bennett, Johan, additional, Toth, Gabor G., additional, Joner, Michael, additional, Toelg, Ralph, additional, Wiemer, Marcus, additional, Olivecrano, Göran, additional, Vermeersch, Paul, additional, Garcia-Garcia, Hector M., additional, and Waksman, Ron, additional

Published
2023
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282. Optical Coherence Tomography Characteristics of the Novel Resorbable Magnesium Scaffold at 6 Months: An Intravascular Imaging Analysis of the First-in-Human Trial on DREAMS 3G

Author

Seguchi, Masaru, primary, Aytekin, Alp, additional, Xhepa, Erion, additional, Haude, Michael, additional, Wlodarczak, Adrian, additional, van der Schaaf, René J., additional, Torzewski, Jan, additional, Ferdinande, Bert, additional, Escaned, Javier, additional, Iglesias, Juan F., additional, Bennett, Johan, additional, Toth, Gabor, additional, Toelg, Ralph, additional, Wiemer, Marcus, additional, Olivecrona, Göran, additional, Verheye, Stefan, additional, Garcia Garcia, Hector M., additional, and Joner, Michael, additional

Published
2023
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283. Are There Coronary Plaque Characteristics Associated With Late Lumen Loss? Artificial Intelligence-Based Optical Coherence Tomography (OCT) Study From the First-in-Human Trial on DREAMS 3G Scaffold

Author

Garcia Garcia, Hector M., primary, Beyene, Solomon, additional, Melaku, Gebremedhin D., additional, Levine, Molly B., additional, Haude, Michael, additional, Wlodarczak, Adrian, additional, van der Schaaf, René J., additional, Torzewski, Jan, additional, Ferdinande, Bert, additional, Escaned, Javier, additional, Iglesias, Juan F., additional, Bennett, Johan, additional, Toth, Gabor, additional, Toelg, Ralph, additional, Wiemer, Marcus, additional, Olivecrona, Göran, additional, Verheye, Stefan, additional, Joner, Michael, additional, Romero, Jose Antonio Sorolla, additional, and Waksman, Ron, additional

Published
2023
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288. Intelligence

Author

Kanai, Chieko, Toth, Gabor, Itahashi, Takashi, Hashimoto, Ryuichiro, Kato, Nobumasa, and Matson, Johnny L., Series Editor

Published
2016
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289. On the Azimuthal Stability of Shock Waves around Black Holes

Author

Molteni, Diego, Toth, Gabor, and Kuznetsov, Oleg A.

Subjects
Astrophysics
Abstract

Analytical studies and numerical simulations of time dependent axially symmetric flows onto black holes have shown that it is possible to produce stationary shock waves with a stable position both for ideal inviscid and for moderately viscous accretion disks. We perform several two dimensional numerical simulations of accretion flows in the equatorial plane to study shock stability against non-axisymmetric azimuthal perturbations. We find a peculiar new result. A very small perturbation seems to produce an instability as it crosses the shock, but after some small oscillations, the shock wave suddenly transforms into an asymmetric closed pattern, and it stabilizes with a finite radial extent, despite the inflow and outflow boundary conditions are perfectly symmetric. The main characteristics of the final flow are: 1) The deformed shock rotates steadily without any damping. It is a permanent feature and the thermal energy content and the emitted energy vary periodically with time. 2) This behavior is also stable against further perturbations. 3) The average shock is still very strong and well defined, and its average radial distance is somewhat larger than that of the original axially symmetric circular shock. 4) Shocks obtained with larger angular momentum exhibit more frequencies and beating phenomena. 5) The oscillations occur in a wide range of parameters, so this new effect may have relevant observational consequences, like (quasi) periodic oscillations, for the accretion of matter onto black holes. Typical time scales for the periods are 0.01 and 1000 seconds for black holes with 10 and 1 million solar mass, respectively., Comment: 15 pages, 7 figures, accepted by the Astrophysical Journal

Published
1998
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296. Thrombectomy Outcomes With General vs Nongeneral Anesthesia

Author

Sarraj, Amrou, Albers, Gregory W., Mitchell, Peter J., Hassan, Ameer E., Abraham, Michael G., Blackburn, Spiros, Sharma, Gagan, Yassi, Nawaf, Kleinig, Timothy J., Shah, Darshan G., Wu, Teddy Y., Hussain, Muhammad Shazam, Tekle, Wondwoseen G., Gutierrez, Santiago Ortega, Aghaebrahim, Amin Nima, Haussen, Diogo C., Toth, Gabor, Pujara, Deep, Budzik, Ronald F., Hicks, William, Vora, Nirav, Edgell, Randall C., Slavin, Sabreena, Lechtenberg, Colleen G., Maali, Laith, Qureshi, Abid, Rosterman, Lee, Abdulrazzak, Mohammad Ammar, AlMaghrabi, Tareq, Shaker, Faris, Mir, Osman, Arora, Ashish, Martin-Schild, Sheryl, Sitton, Clark W., Churilov, Leonid, Gupta, Rishi, Lansberg, Maarten G., Nogueira, Raul G., Grotta, James C., Donnan, Geoffrey Alan, Davis, Stephen M., and Campbell, Bruce C. V.

Subjects
Neurology (clinical), Research Article
Abstract

Background and ObjectivesThe effect of anesthesia choice on endovascular thrombectomy (EVT) outcomes is unclear. Collateral status on perfusion imaging may help identify the optimal anesthesia choice.MethodsIn a pooled patient-level analysis of EXTEND-IA, EXTEND-IA TNK, EXTEND-IA TNK part II, and SELECT, EVT functional outcomes (modified Rankin Scale score distribution) were compared between general anesthesia (GA) vs non-GA in a propensity-matched sample. Furthermore, we evaluated the association of collateral flow on perfusion imaging, assessed by hypoperfusion intensity ratio (HIR) – Tmax > 10 seconds/Tmax > 6 seconds (good collaterals – HIR < 0.4, poor collaterals – HIR ≥ 0.4) on the association between anesthesia type and EVT outcomes.ResultsOf 725 treated with EVT, 299 (41%) received GA and 426 (59%) non-GA. The baseline characteristics differed in presentation National Institutes of Health Stroke Scale score (median [interquartile range] GA: 18 [13–22], non-GA: 16 [11–20],p< 0.001) and ischemic core volume (GA: 15.0 mL [3.2–38.0] vs non-GA: 9.0 mL [0.0–31.0],p< 0.001). In addition, GA was associated with longer last known well to arterial access (203 minutes [157–267] vs 186 minutes [138–252],p= 0.002), but similar procedural time (35.5 minutes [23–59] vs 34 minutes [22–54],p= 0.51). Of 182 matched pairs using propensity scores, baseline characteristics were similar. In the propensity score–matched pairs, GA was independently associated with worse functional outcomes (adjusted common odds ratio [adj. cOR]: 0.64, 95% CI: 0.44–0.93,p= 0.021) and higher neurologic worsening (GA: 14.9% vs non-GA: 8.9%, aOR: 2.10, 95% CI: 1.02–4.33,p= 0.045). Patients with poor collaterals had worse functional outcomes with GA (adj. cOR: 0.47, 95% CI: 0.29–0.76,p= 0.002), whereas no difference was observed in those with good collaterals (adj. cOR: 0.93, 95% CI: 0.50–1.74,p= 0.82),pinteraction: 0.07. No difference was observed in infarct growth overall and in patients with good collaterals, whereas patients with poor collaterals demonstrated larger infarct growth with GA with a significant interaction between collaterals and anesthesia type on infarct growth rate (pinteraction: 0.020).DiscussionGA was associated with worse functional outcomes after EVT, particularly in patients with poor collaterals in a propensity score–matched analysis from a pooled patient-level cohort from 3 randomized trials and 1 prospective cohort study. The confounding by indication may persist despite the doubly robust nature of the analysis. These findings have implications for randomized trials of GA vs non-GA and may be of utility for clinicians when making anesthesia type choice.Classification of EvidenceThis study provides Class III evidence that use of GA is associated with worse functional outcome in patients undergoing EVT.Trial Registration InformationEXTEND-IA: ClinicalTrials.gov (NCT01492725); EXTEND-IA TNK: ClinicalTrials.gov (NCT02388061); EXTEND-IA TNK part II: ClinicalTrials.gov (NCT03340493); and SELECT: ClinicalTrials.gov (NCT02446587).

Published
2022
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298. Algorithm of differential diagnosis of anemia involving laboratory medicine specialists to advance diagnostic excellence.

Author

Hevessy, Zsuzsanna, Toth, Gabor, Antal-Szalmas, Peter, Tokes-Fuzesi, Margit, Kappelmayer, Janos, Karai, Bettina, and Ajzner, Eva

Subjects
*MEDICAL specialties & specialists, *DIFFERENTIAL diagnosis, *MEDICAL personnel, *CLINICAL pathology, *DELAYED diagnosis, *TESTING laboratories, *PATHOLOGICAL laboratories
Abstract

Anemia is a severe global public health issue. Testing practices for anemia suggest overuse of screening laboratory tests and misinterpretation of studies even in "easy-to-diagnose" underlying causes, leading to late diagnoses and missed treatment opportunities. We aimed to develop a complete and efficient algorithm for clinical pathologists and laboratory medicine physicians for the differential diagnosis of anemia. Comprehensive literature search encompassing original articles, studies, reviews, gold standard books, and other evidence. We created a complex algorithm, primarily for clinical pathology/laboratory use, that explores all major and several rare causes of anemia in an efficient and evidence-based manner. The algorithm includes gold-standard diagnostic laboratory tests available in most clinical laboratories and indices that can be easily calculated to provide an evidence-based differential diagnosis of anemia. The diagnostic strategy combines previously available diagnostic tests and protocols in an efficient order. Clinical pathologists following the algorithm can independently provide valuable diagnostic support for healthcare providers. Clinical pathologists providing complete differential diagnostic services with the proposed algorithm may create an opportunity for an advanced diagnostic service that supports diagnostic excellence and helps patients receive a timely diagnosis and early treatment opportunities. [ABSTRACT FROM AUTHOR]

Published
2024
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299. Highly saturated packings and reduced coverings

Author

Tóth, Gabor Fejes, Kuperberg, Greg, and Kuperberg, Włodzimierz

Subjects
Mathematics - Metric Geometry
Abstract

We introduce and study certain notions which might serve as substitutes for maximum density packings and minimum density coverings. A body is a compact connected set which is the closure of its interior. A packing $\cal P$ with congruent replicas of a body $K$ is $n$-saturated if no $n-1$ members of it can be replaced with $n$ replicas of $K$, and it is completely saturated if it is $n$-saturated for each $n\ge 1$. Similarly, a covering $\cal C$ with congruent replicas of a body $K$ is $n$-reduced if no $n$ members of it can be replaced by $n-1$ replicas of $K$ without uncovering a portion of the space, and it is completely reduced if it is $n$-reduced for each $n\ge 1$. We prove that every body $K$ in $d$-dimensional Euclidean or hyperbolic space admits both an $n$-saturated packing and an $n$-reduced covering with replicas of $K$. Under some assumptions on $K\subset \mathbb{E}^d$ (somewhat weaker than convexity), we prove the existence of completely saturated packings and completely reduced coverings, but in general, the problem of existence of completely saturated packings and completely reduced coverings remains unsolved. Also, we investigate some problems related to the the densities of $n$-saturated packings and $n$-reduced coverings. Among other things, we prove that there exists an upper bound for the density of a $d+2$-reduced covering of $\mathbb{E}^d$ with congruent balls, and we produce some density bounds for the $n$-saturated packings and $n$-reduced coverings of the plane with congruent circles.

Published
1995

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