43,601 research outputs found
Constructing a Distance Sensitivity Oracle in O(n^2.5794 M) Time
Get PDFWe continue the study of distance sensitivity oracles (DSOs). Given a directed graph G with n vertices and edge weights in {1, 2, … , M}, we want to build a data structure such that given any source vertex u, any target vertex v, and any failure f (which is either a vertex or an edge), it outputs the length of the shortest path from u to v not going through f. Our main result is a DSO with preprocessing time O(n^2.5794 M) and constant query time. Previously, the best preprocessing time of DSOs for directed graphs is O(n^2.7233 M), and even in the easier case of undirected graphs, the best preprocessing time is O(n^2.6865 M) [Ren, ESA 2020]. One drawback of our DSOs, though, is that it only supports distance queries but not path queries.
Our main technical ingredient is an algorithm that computes the inverse of a degree-d polynomial matrix (i.e. a matrix whose entries are degree-d univariate polynomials) modulo x^r. The algorithm is adapted from [Zhou, Labahn and Storjohann, Journal of Complexity, 2015], and we replace some of its intermediate steps with faster rectangular matrix multiplication algorithms.
We also show how to compute unique shortest paths in a directed graph with edge weights in {1, 2, … , M}, in O(n^2.5286 M) time. This algorithm is crucial in the preprocessing algorithm of our DSO. Our solution improves the O(n^2.6865 M) time bound in [Ren, ESA 2020], and matches the current best time bound for computing all-pairs shortest paths
Rationally designed Magnetic Particles enable Capturing and Detection of Bacterial Pathogens
No full textIn this work we highlight magnetic blood purification as possible therapy for blood stream infections [1-2], where circulating pathogens are at first removed from the bodily fluid and subsequently recovered and analyzed. (Fig. 1) This process would result in an immediate therapeutic benefit for the patient, while also considerably shortening the diagnosis process, a critical step which heavily affects the final outcome of the treatment. Finally, the use of a newly developed human IgG1 monoclonal antibody against poly-N-acetylglucosamine (PNAG) as targeting moiety extends this therapy to the majority of the pathogens responsible for the most frequent nosocomial infections. We show an experimental proof-of-concept study along with an optimization of carrier-pathogen interactions based on a mathematical model and an investigations on the process safety [3].
[1] I. K. Herrmann, M. Urner, F. M. Koehler, M. Hasler, B. Roth-Z’Graggen, R. N. Grass, U. Ziegler, B. Beck-Schimmer, and W. J. Stark, Small, 2010, 6, 1388
[2] I. K. Herrmann , M. Urner, S. Graf , C. M. Schumacher , B. Roth-Z’graggen , M. Hasler , W. J. Stark , and B. Beck-Schimmer, Adv. Healthcare Mater., 2013, 2, 829–835
[3] M. Lattuada, Q. Ren, F. Zuber, M. Galli, N. Bohmer, A. Wichser, S. Bertazzo, G. B. Pier and I. K. Herrmann, J. Mater Chem. B, under review
Getting Started as a Medical Teacher in Times of Change
No full textMedical school teaching is a skill that is very often learned on the job. The faculty comprised of researchers and clinicians are expert in many biomedical disciplines, but familiarity with learning theories and pedagogy are usually not included in their knowledge and skill sets. The pressure to see patients and acquire extramural funding leaves little time for faculty to learn how to teach. When coupled with the natural attrition of senior faculty it is necessary to start junior faculty on the correct path to being effective medical educators who are capable of lecturing and facilitating. Institutions cannot afford to have medical educators learn through trial and error. The standards set by the Liaison Committee on Medical Education (LCME) are also creating an urgency to produce competent teachers as quickly as possible. Novice teachers need to be able to use these standards to align their teaching with goals, objectives and the appropriate pedagogy. This article is designed to be a self-directed guide describing some essentials that a newly hired faculty member can quickly use to get started. An institutional faculty development program can then serve to build upon and enrich the experience for the new faculty member.This is the authors' accepted manuscript of the article. The final publication is available at Springer via http://dx.doi.org/doi:10.1007/s40670-014-0098-y.Peer reviewe
Regularity for anisotropic elliptic equations with degenerate coercivity
No full textThis paper deals with boundary value problems of the form −∑i=1nDi(ai(x,u(x),Du(x)))=f(x),x∈Ω,u(x)=0,x∈∂Ω. Assume that there exist c1,ν,θ>0 such that for almost all x∈Ω and all (s,z)∈R×Rn, |ai(x,s,z)|≤c11+|zi|pjavax.xml.bind.JAXBElement@6841a49a−1,i=1,...,n, and [Formula presented] We let f∈Lm(Ω) and we derive regularity results for weak solutions
Sous-facteurs de L(F∞) d'indice 4cos2π/n,n≥3
No full textLet Q be a factor of type II1, λ a number in the Jones discrete series {4cosπ/m:m≥3}, and {ei} the Jones projections associated with λ. Denote by A2n and A1n the finite-dimensional von Neumann algebras generated, respectively, by {1,e2,⋯,en} and {1,e1,⋯,en}, with the corresponding traces. The author shows that, for n sufficiently large, the index of the inclusion An=(Q⊗A2n)∗A2nA1n⊂(Q⊗A2n+1)∗A2n+1A1n+1=An+1 is equal to λ (here ∗ denotes the reduced, amalgamated free product of the algebras in question). Using the random matrix model of Voiculescu, he proves that if Q is the von Neumann algebra L(F∞) of the free group with infinitely many generators, then An is isomorphic to L(F∞).
The two facts together imply the existence, for any λ in the Jones discrete series, of an irreducible subfactor of L(F∞) of index λ. This constitutes the first example of a nonhyperfinite, non-Γ II1 factor such that its Jones invariant is fully computable (the existence of nonirreducible subfactors of L(F∞) for any index ≥4 is a simple consequence of known results)
Bioramix (Leipopleura) impressithorax Bai & Ren 2020, sp. nov.
No full textBioramix (Leipopleura) impressithorax sp. nov. (Figs 10, 80–81, 240–241) Description. Body black-brown, weakly shining, antennae, palpi and tarsi brown, elytral surface with weakly metallic sheen. Male (Figs 10, 80–81, 240). Head. Anterior margin of epistome straight, surface with dense and coarse punctures. Frons and genae weakly convex, surface with dense and coarse punctures. Dorsal surface of head with dense and coarse punctures. Eyes transverse, anterior margin shallowly emarginate. Antennae (Fig. 10: A) reaching pronotal base, antennomeres II–VIII short cylindrical and thicker at apex, IX–X nearly spherical, XI sharped-oval. Length (width)ratio of antennomeresII–XI 29 (17): 32(16):26 (16): 24 (16): 22(16):25 (17): 28 (22): 26(23):24 (23): 35 (25). Prothorax. Pronotum (Fig. 10: B) transverse and strongly convex, 1.5 times as wide as long and 2.0 times as wide as head. Lateral sides widest anterior to base, arcuately narrowing toward base and apex. Ratio of width at anterior margin to widest part and base 26: 44: 42. Anterior margin emarginate, posterior one straight. Anterior and posterior angles obtuse. Anterior and posterior margins edged laterally, entire lateral margins edged. Dorsal surface with sparse and fine punctures on disc, dense and coarse at sides. Lateral sides widely flattened. Prothoracic hypomera with longitudinal wrinkles and sparse yellow setae. Prosternum anterior to procoxae with yellow setae, prosternal process sharply sloping behind procoxae, apex not projecting beyond level of procoxae in lateral view. Pterothorax. Elytra elongate-oval and strongly convex, 1.1 times as long as wide and 1.1 times as wide as pronotum, base slightly wider than pronotum and widest at middle. Surface smooth, with shallowly sparse, fine punctures and fine wrinkles. Lateral margins of elytra not reaching sutural angle, interrupted anterior to apex of elytra, visible anterior 1/ 3 in dorsal view. Abdomen with dense yellow setae, ventrites 1–2 depressed at middle. Legs. Profemora stout, with sparse punctures and yellow setae. Protibiae (Fig. 10: D) gradually widened toward apex, underside concave at apex, apical margin foliate extended, inner side with dense yellow hairbrush from middle to apex. Protarsi (Fig. 10: C) narrower than apex of protibiae. Meso- and metafemora longer than profemora. Mesotibiae (Fig. 10: E) gradually widened toward apex, with rufous thick setae, inner side with dense yellow hairbrush from middle to apex. Mesotarsi (Fig. 10: F) narrower than apex of mesotibiae. Metatibiae (Fig. 10: G) straight, with rufous thick setae, inner side with dense yellow hairbrush from middle to apex. Length (width) ratio of pro-, meso- and metafemora 19 (8): 23 (7): 26 (7), that of corresponding tibiae 19 (8): 19 (5): 27 (6), and protarsi 26 (27): 34 (54): 32 (53): 20 (39): 53 (18), mesotarsi 32 (27): 30 (45): 30 (39): 22 (26): 59 (18), metatarsi (Fig. 10: H) 67 (22): 40 (21): 31 (19): 54 (19). Aedeagus (Figs 10: I–J, 80–81) 2.7 mm long and 0.7 mm wide. Parameres 1.0 mm long and 0.5 mm wide, widest at base and narrowing toward apex, base strongly wider than apex, distal part curved dorsally in lateral view. Female (Fig. 241). Body wider, antennae not reaching pronotal base, abdominal ventrites 1–2 neither depressed nor flattened at middle, pro- and mesotarsi not widened, other characters similar to male. Measurements. Body length: ♂ 7.7–9.4 mm, ♀ 7.9–8.8 mm and width: ♂ 4.2–4.9 mm, ♀ 4.4–4.7 mm. Type material. Holotype: ♂ (MHBU), CHINA : Qinghai: Gyobrag Township, Nangqên County, 1.VII.2014, Zhi-Jun Zhou leg. Paratypes: 1♂, 5♀♀ (MHBU), same data as holotype; 4♂♂, 4♀♀ (MHBU), Nangqên County, 4000 m, 5.VII.2008, Guo-Dong Ren et al. leg.; 3♂♂ (MHBU), Nangqên County, 27–29.VII.2014, Zhi-Jun Zhou leg.; 1♂ (MHBU), Zadoi County, 20.VII.1963, Xiang-Chu Yin leg., coll. NWIPB; 21♂♂, 18♀♀ (MHBU), Zadoi County, 4400 m, 4.VII.2008, Guo-Dong Ren et al. leg.; 1♂, 5♀♀ (MHBU), Sai Qu, Zadoi County, 32°50.783′ N, 95°28.634′ E, 4045 m, 22.VII.2012, Guo-Dong Ren et al. leg.; 1♂ (MHBU), Sahuteng Town, Zadoi County, 32°53.641′ N, 95°19.062′ E, 4292 m, 22.VII.2012, Guo-Dong Ren et al. leg.; 1♀ (MHBU), Namsai Township, Za- doi County, 3–5.VII.2014, Zhi-Jun Zhou leg.; 1♀ (MHBU), Qumarlêb County, 8.IX.1966, Zhang leg., coll. IZCAS; 1♂, 2♀♀ (MHBU), Yushu County, 4350 m, 4.VII.2008, Guo-Dong Ren et al. leg.; 1♂, 1♀ (MHBU), Shanglaxiu Township, Yushu County, 32°57.479′ N, 96°06.856′ E, 4227 m, 21.VII.2012, Guo-Dong Ren et al. leg.; 1♂, 1♀ (MHBU), Chenwen Town, Chindu County, 33.3416° N, 97.1782° E, 3996 m, 17.VII.2009, Guo-Dong Ren et al. leg.; 1♀ (MHBU), Chenwen Town, Chindu County, 33.3416° N, 97.1782° E, 3996 m, 17.VII.2009, Guo-Dong Ren, Yi-Bin Ba & Yong Zhou leg. Distribution. China: Qinghai. Diagnosis. This new species is similar to Bioramix (Leipopleura) reinigi (Kaszab, 1940), but can be distinguished from the latter by the following characters (based on male): (1) pronotum and elytra strongly convex (more weakly in B. reinigi); (2) lateral sides of pronotum widely flattened, posterior angles widely obtuse (narrowly depressed, rectangular or weakly obtuse in B. reinigi). Etymology. This species name is derived from its widely flattened lateral sides of pronotum.Published as part of Bai, Xing-Long & Ren, Guo-Dong, 2020, Revision of the genus Bioramix Bates, 1879 (Coleoptera: Tenebrionidae: Platyscelidini) from China, pp. 1-102 in Zootaxa 4815 (1) on pages 29-30, DOI: 10.11646/zootaxa.4815.1.1, http://zenodo.org/record/394431
Bioramix (Leipopleura) subcarinata Bai & Ren 2020, sp. nov.
No full text<i>Bioramix</i> (<i>Leipopleura</i>) <i>subcarinata</i> sp. nov. <p>(Figs 21, 182–183, 313–314)</p> <p> <b>Description.</b> Body brown, weakly shining, antennae, palpi and legs red-brown, elytral surface with weakly metallic sheen.</p> <p> <b>Male</b> (Figs 21, 182–183, 313). <i>Head</i>. Anterior margin of epistome straight, surface with dense and coarse punctures. Frons and genae weakly convex, surface with dense and coarse punctures. Dorsal surface of head flattened, with dense and coarse punctures. Anterior margin of gena protruding outward anterior to eyes, distance between genae almost as long as that of eyes. Eyes transverse, anterior margin shallowly emarginate. Antennae (Fig. 21: A) not reaching pronotal base, antennomeres II–VIII short cylindrical and thicker at apex, IX–X nearly spherical, XI sharped-oval. Length (width) ratio of antennomeres II–XI 25 (17): 47 (20): 28 (20): 27 (18): 26 (18): 29 (19): 29 (24): 25 (25): 26 (25): 28 (22).</p> <p> <i>Prothorax</i>. Pronotum (Fig. 21: B) transverse and convex, 1.4 times as wide as long and 1.7 times as wide as head. Lateral sides widest nearly at middle, nearly straight or arcuately narrowing toward base and apex. Ratio of width at anterior margin to widest part and base 19: 30: 29. Anterior margin weakly emarginate or nearly straight, posterior one weakly protruding backward. Anterior and posterior angles obtuse. Anterior and posterior margins edged laterally, entire lateral margins edged. Dorsal surface with sparse and fine punctures on disc, denser and coarser at sides. Lateral sides narrowly depressed from base to middle. Prothoracic hypomera with longitudinal wrinkles and sparse yellow setae. Prosternum anterior to procoxae with yellow setae, prosternal process sharply sloping behind procoxae, apex not projecting beyond level of procoxae in lateral view.</p> <p> <i>Pterothorax.</i> Elytra elongate-oval and convex, 1.2 times as long as wide and 1.2 times as wide as pronotum, base wider than pronotum and widest at middle. Surface with sparse, fine punctures and wrinkles, traces of longitudinal carinae. Lateral margins of elytra not reaching sutural angle, interrupted at middle, visible at base in dorsal view.</p> <p> <i>Abdomen</i> with dense yellow setae, ventrites 1–2 flattened at middle.</p> <p> <i>Legs.</i> Profemora stout, with sparse punctures and yellow setae. Protibiae (Fig. 21: D) gradually widened toward apex, underside concave at apex, apical margin foliate extended, inner side with dense yellow hairbrush from middle to apex. Protarsi (Fig. 21: C) narrower than apex of protibiae. Meso- and metafemora longer than profemora. Mesotibiae (Fig. 21: E) gradually widened toward apex, with rufous thick setae, inner side with dense yellow hairbrush from middle to apex. Mesotarsi (Fig. 21: F) narrower than apex of mesotibiae. Metatibiae (Fig. 21: G) weakly curved, with rufous thick setae, inner side with dense yellow hairbrush from middle to apex. Length (width) ratio of pro-, meso- and metafemora 20 (6): 22 (6): 28 (7), that of corresponding tibiae 20 (7): 20 (6): 30 (7), and protarsi 20 (21): 38 (51): 28 (51): 21 (37): 57 (18), mesotarsi 18 (27): 37 (43): 32 (40): 22 (27): 60 (19), metatarsi (Fig. 21: H) 66 (24): 43 (23): 33 (22): 65 (20).</p> <p> <i>Aedeagus</i> (Figs 21: I–J, 182–183) 2.4 mm long and 0.7 mm wide. Parameres 0.8 mm long and 0.6 mm wide, widest at base and narrowing toward apex, distal part strongly curved dorsally in lateral view.</p> <p> <b>Female</b> (Fig. 314). Body wider, abdominal ventrites 1–2 not flattened at middle, pro- and mesotarsi not widened, other characters similar to male.</p> <p> <b>Measurements.</b> Body length: ♂ 8.1–10.1 mm, ♀ 7.8–9.6 mm and width: ♂ 4.4–5.5 mm, ♀ 4.6–5.5 mm.</p> <p> <b>Type material.</b> <b>Holotype:</b> ♂ (MHBU), <b>CHINA</b> <b>:</b> <b>Xizang:</b> Qulho Township, Coqên County, 30°08.116′ N, 85°41.630′ E, 5351 m, 21.VIII.2015, Guo-Dong Ren, Xing-Long Bai & Jun-Sheng Shan leg. <b>Paratypes:</b> 15♂♂, 9♀♀ (MHBU), same data as holotype; 2♂♂, 2♀♀ (MHBU), Gyangrang Township, Coqên County, 30°23.071′ N, 85°37.860′ E, 4850 m, 21.VIII.2015, Guo-Dong Ren, Xing-Long Bai & Jun-Sheng Shan leg.; 8♂♂, 3♀♀ (MHBU), Daxung Township, Coqên County, 31°37.756′ N, 85°10.225′ E, 5134 m, 22.VIII.2015, Guo-Dong Ren, Xing-Long Bai & Jun-Sheng Shan leg.; 2♂♂, 2♀♀ (ZIN), Coqên County, 30°51′ N, 85°09′ E, 4615 m, 18.VII.2012, Ai-Min Shi & Yi-Bin Ba; 3♂♂, 3♀♀ (MCWNU), 2♂♂, 2♀♀ (MRCSPU), Coqên County, 30°51′ N, 85°09′ E, 4615 m, 18.VII.2004, Yun-Chun Li & Yong-Ping Lai leg.; 8♂♂, 15♀♀ (MHBU), Eluo, Xainza County, 30.5580° N, 88.9305° E, 4850 m, 3.VIII.2009, Guo-Dong Ren <i>et al</i>. leg.; 36♂♂, 31♀♀ (MHBU), Tüna Township, Yadong County, Xigazê City, 28°02.990′ N, 89°10.164′ E, 4506 m, 1.VIII.2011, Guo-Dong Ren <i>et al</i>. leg.; 28♂♂, 29♀♀ (MHBU), Tüna Township, Yadong County, 28°03.518′ N, 89°16.215′ E, 4510 m, 19.VIII.2015, Guo-Dong Ren, Xing-Long Bai & Jun-Sheng Shan leg.; 14♂♂, 10♀♀ (MHBU), Tüna Township, Yadong County, 27°52.440′ N, 89°11.471′ E, 4519 m, 19.VIII.2015, Guo-Dong Ren, Xing-Long Bai & Jun-Sheng Shan leg.; 1♂, 3♀♀ (MHBU), Pagri Town, Yadong County, 27°48.237′ N, 89°08.766′ E, 4413 m, 18.VIII.2015, Guo-Dong Ren, Xing-Long Bai & Jun-Sheng Shan leg.; 11♂♂, 6♀♀ (MHBU), N Pagri Town, Yadong County, 27°47.778′ N, 89°08.803′ E, 4359 m, 11.VI.2018, Xing- Long Bai leg.; 118♂♂, 76♀♀ (MHBU), Zhahujue Shan, Yadong County, 27°51′30.9′′ N, 88°57′46.8′′ E, 4591 m, 20.VIII.2019, Zhao Pan, Xiu-Min Li, Ming Wen & Lan-Rui Wang leg.; 2♂♂ (MHBU), Riazhi, Bangoin County, 31°15.619′ N, 90°21.162′ E, 4657 m, 11.VIII.2011, Guo-Dong Ren <i>et al</i>. leg.; 16♂♂, 10♀♀ (MHBU), Lamucuo Shan, Maintang Township, Bangoin County, 31°28.876′ N, 89°51.916′ E, 4772 m, 17.VIII.2018, Xing-Long Bai, Zi- Yuan Hu & Ming-Min Ma leg.; 1♂, 1♀ (MHBU), Moxiu, Pubu Town, Bangoin County, 31°27.316′ N, 89°59.023′ E, 4872 m, 17.VIII.2018, Xing-Long Bai, Zi-Yuan Hu & Ming-Min Ma leg.; 8♂♂, 3♀♀ (MHBU), Songduoke, Chigu Town, Comai County, 28°35.158′ N, 91°30.319′ E, 4727 m, 8.VIII.2014, Guo-Dong Ren, Xing-Long Bai & Jun-Sheng Shan leg.; 35♂♂, 38♀♀ (MHBU), Bowu, Songduoke, Comai County, 28°34′23′′ N, 91°29′55.45′′ E, 4973 m, 31.VII.2019, Zhao Pan, Xiu-Min Li, Ming Wen & Lan-Rui Wang leg.; 3♂♂, 3♀♀ (ZIN), Comai County, 28º34.946′ N, 91º30.397′ E, 4834 m, 8.VIII.2014, Yun-Chun Li leg.; 6♂♂, 1♀ (MHBU), Daggyai Co, Ngamring County, 29°45.595′ N, 85°44.574′ E, 5230 m, 21.VIII.2015, Guo-Dong Ren, Xing-Long Bai & Jun-Sheng Shan leg.; 4♂♂, 3♀♀ (MHBU), Xuege La Shan, Damxung County, 29°55′26.4′′ N, 90°08′19.4′′ E, 5147 m, 9.VIII.2019, Zhao Pan, Xiu-Min Li, Ming Wen & Lan-Rui Wang leg.</p> <p> <b>Distribution.</b> China: Xizang.</p> <p> <b>Diagnosis.</b> This new species is similar to <i>Bioramix</i> (<i>Leipopleura</i>) <i>rugelytra</i> sp. nov., but can be distinguished from the latter by the following characters (based on male): (1) pronotum widest nearly at middle, surface with fine punctures on disc, denser and coarser at sides (at base, coarse on disc, dense at sides in <i>B. rugelytra</i>); (2) elytra with traces of longitudinal carinae (without in <i>B. rugelytra</i>); (3) metatibiae weakly curved (straight in <i>B. rugelytra</i>); (4) distal part of parameres strongly curved dorsally in lateral view (more weakly in <i>B. rugelytra</i>).</p> <p> <b>Etymology.</b> This species name is derived from its traces of longitudinal carinae on elytra.</p>Published as part of <i>Bai, Xing-Long & Ren, Guo-Dong, 2020, Revision of the genus Bioramix Bates, 1879 (Coleoptera: Tenebrionidae: Platyscelidini) from China, pp. 1-102 in Zootaxa 4815 (1)</i> on pages 53-55, DOI: 10.11646/zootaxa.4815.1.1, <a href="http://zenodo.org/record/3944316">http://zenodo.org/record/3944316</a>
Kai meng yao xun 開 蒙 要 訓 [par Ma Ren shou 馬 仁 壽].
No full textKai meng yao xun 開 蒙 要 訓. Ma Ren shou 馬 仁 壽. Ouvrages de pédagogie et de morale populaireContient : Xia nü fu ci 下 女 夫 詞Numérisation effectuée à partir d'un document original.En 1 j. fin manque, Quelques variantes par rapport au Pelliot chinois 2578, éd, in THTS , n° 76, fasc. 3, pp. 305-311. Écr. kai. Encre foncée. 1 car. ajouté (col. 3) ; car. taboué min 民 col. 8, ye 葉) ; 1 trait épais à la col. 3. Quelques ratures. 30 col. en tout (f. 1 : 10 col.), 14 à 18 car. par col. Marges sup. et inf. 0,1 cm
Postać n-tej iteracji operatora q = f d/dx
No full textArtykuł nie zawiera streszczeniaMotivated by applications in linear dynamical systems, the author studies q^n(f), where q is the operator f●(d/dx) and qn is its n-th iteration. q^n(f) is a polynomial F(f(0),f(1),...,f(n)) in the derivatives f(0)=f,...,f(n) of f with integer coefficients. Special attention is paid to determining the coefficients of F. The author presents algorithms for computing the coefficients and also shows that the sum of all coefficients of F equals n!. The paper ends with some remarks on the number of coefficients of F, which is related to the number-theoretic unrestricted partition function
Optimal Communication Complexity of Authenticated Byzantine Agreement
Get PDFByzantine Agreement (BA) is one of the most fundamental problems in distributed computing, and its communication complexity is an important efficiency metric. It is well known that quadratic communication is necessary for BA in the worst case due to a lower bound by Dolev and Reischuk. This lower bound has been shown to be tight for the unauthenticated setting with f < n/3 by Berman et al. but a considerable gap remains for the authenticated setting with n/3 ≤ f < n/2.
This paper provides two results towards closing this gap. Both protocols have a quadratic communication complexity and have different trade-offs in resilience and assumptions. The first protocol achieves the optimal resilience of f < n/2 but requires a trusted setup for threshold signature. The second protocol achieves near optimal resilience f ≤ (1/2 - ε)n in the standard PKI model
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