Treatment of fractures of the tibial diaphysis using external fixator compared with locked intramedullary nails Tratamento das fraturas diafisárias da tíbia com fixador externo com... by Rodrigo Tavares Cardozo, Luís Gustavo Silva, Leandro Augusto Bragante, Murilo Antônio Rocha

“…OBJECTIVE: To compare efficiency of external fixator in modular form with unilateral and uniplanar intramedullary locked seeking definitive treatment of fractures of the tibia diaphysis. …”
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SBML Level 3: an extensible format for the exchange and reuse of biological models by Sarah M Keating, Dagmar Waltemath, Matthias König, Fengkai Zhang, Andreas Dräger, Claudine Chaouiya, Frank T Bergmann, Andrew Finney, Colin S Gillespie, Tomáš Helikar, Stefan Hoops, Rahuman S Malik‐Sheriff, Stuart L Moodie, Ion I Moraru, Chris J Myers, Aurélien Naldi, Brett G Olivier, Sven Sahle, James C Schaff, Lucian P Smith, Maciej J Swat, Denis Thieffry, Leandro Watanabe, Darren J Wilkinson, Michael L Blinov, Kimberly Begley, James R Faeder, Harold F Gómez, Thomas M Hamm, Yuichiro Inagaki, Wolfram Liebermeister, Allyson L Lister, Daniel Lucio, Eric Mjolsness, Carole J Proctor, Karthik Raman, Nicolas Rodriguez, Clifford A Shaffer, Bruce E Shapiro, Joerg Stelling, Neil Swainston, Naoki Tanimura, John Wagner, Martin Meier‐Schellersheim, Herbert M Sauro, Bernhard Palsson, Hamid Bolouri, Hiroaki Kitano, Akira Funahashi, Henning Hermjakob, John C Doyle, Michael Hucka, SBML Level 3 Community members

“…A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction‐based models and packages that extend the core with features suited to other model types including constraint‐based models, reaction‐diffusion models, logical network models, and rule‐based models. …”
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Neutrino masses and mixing from double covering of finite modular groups by Xiang-Gan Liu, Gui-Jun Ding

“…Abstract We extend the even weight modular forms of modular invariant approach to general integral weight modular forms. …”
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Performance Engineering of Modular Symbols by Boonsiriseth, Krit

“…We present a new program MFSplit which computes information about newform subspaces for modular forms of weight 2 and trivial character. Modular forms are certain functions in mathematics that appear in many different subfields of mathematics, including number theory and complex analysis; newform subspaces are spaces spanned by a special type of modular forms and are, in some sense, building blocks of spaces of modular forms. …”
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sl(2)ˆ Decomposition of denominator formulae of some BKM Lie superalgebras - II by Suresh Govindarajan, Mohammad Shabbir

“…The square-root of Siegel modular forms of CHL ZN orbifolds of type II compactifications are denominator formulae for some Borcherds-Kac-Moody Lie superalgebras for N=1,2,3,4. …”
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Mock modularity and a secondary elliptic genus by Davide Gaiotto, Theo Johnson-Freyd

“…Abstract The theory of Topological Modular Forms suggests the existence of deformation invariants for two-dimensional supersymmetric field theories that are more refined than the standard elliptic genus. …”
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Examples of abelian surfaces with everywhere good reduction by Dembélé, Lassina, Kumar, Abhinav

“…These examples provide evidence for the Eichler–Shimura conjecture for Hilbert modular forms over a real quadratic field. Several of the examples also support a conjecture of Brumer and Kramer on abelian varieties associated to Siegel modular forms with paramodular level structures.…”
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3d modularity by Miranda C.N. Cheng, Sungbong Chun, Francesca Ferrari, Sergei Gukov, Sarah M. Harrison

“…These modular structures include: mock modular forms, SL(2,ℤ) Weil representations, quantum modular forms, non-semisimple modular tensor categories, and chiral algebras of logarithmic CFTs.…”
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Towards unification of quark and lepton flavors in $$A_4$$ A 4 modular invariance by Hiroshi Okada, Morimitsu Tanimoto

“…Abstract We study quark and lepton mass matrices in the $$A_4$$ A 4 modular symmetry towards the unification of the quark and lepton flavors. We adopt modular forms of weights 2 and 6 for quarks and charged leptons, while we use modular forms of weight 4 for the neutrino mass matrix which is generated by the Weinberg operator. …”
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Double cover of modular S4 for flavour model building by P.P. Novichkov, J.T. Penedo, S.T. Petcov

“…The integer weight k>0 of the level 4 modular forms indispensable for the formalism can be even or odd. …”
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Iterated primitives of meromorphic quasimodular forms for SL2(Z) by Matthes, N

“…We also study spaces of meromorphic modular forms with restricted poles, generalizing results of Guerzhoy in the weakly holomorphic case. …”

Modular A 5 symmetry for flavour model building by P. P. Novichkov, J. T. Penedo, S. T. Petcov, A. V. Titov

“…We explicitly construct a basis for the 11 modular forms of weight 2 and level 5. We show how these forms arrange themselves into two triplets and a quintet of A 5. …”
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Bounding Selmer groups for the Rankin–Selberg convolution of Coleman families by Graham, A, Gulotta, DR, Xu, Y

“…Let f and g be two cuspidal modular forms and let F be a Coleman family passing through f, defined over an open affinoid subdomain V of weight space W . …”

Modular graph forms from equivariant iterated Eisenstein integrals by Daniele Dorigoni, Mehregan Doroudiani, Joshua Drewitt, Martijn Hidding, Axel Kleinschmidt, Nils Matthes, Oliver Schlotterer, Bram Verbeek

“…Abstract The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown’s alternative construction of non-holomorphic modular forms in the recent mathematics literature from so-called equivariant iterated Eisenstein integrals. …”
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Modular inflation observables and j-inflation phenomenology by Rolf Schimmrigk

“…It is shown that the nonmodular nature of derivatives of modular forms leads to CMB observables in modular invariant inflation theories that are in general constructed from almost holomorphic modular forms. …”
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THE KATZ–KLEMM–VAFA CONJECTURE FOR $K3$ SURFACES by R. PANDHARIPANDE, R. P. THOMAS

“…We prove the KKV conjecture expressing Gromov–Witten invariants of $K3$ surfaces in terms of modular forms. Our results apply in every genus and for every curve class. …”
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Computing p-adic L-functions of totally real fields by Lauder, A, Vonk, J

“…We describe an algorithm for computing -adic L-functions of characters of totally real fields, using the Fourier expansions of diagonal restrictions of Hilbert modular forms.…”

Modularity of Galois representations and Langlands functoriality by Newton, J

“…This survey reports on some of the recent developments in the area of Galois representations and automorphic forms, with a particular focus on the author and Thorne’s work on symmetric power functoriality for modular forms.…”

BKM Lie superalgebras from counting twisted CHL dyons – II by Suresh Govindarajan, Sutapa Samanta

“…We show the modularity of some Siegel modular forms that appear in umbral moonshine associated with Niemeier lattices constructed from A-type root systems and further show that the same Siegel modular forms appear for generalized Mathieu moonshine in some cases. …”
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ℓ-Adic properties of partition functions by Belmont, Eva, Lee, Holden, Musat, Alexandra, Trebat-Leder, Sarah

“…Folsom, Kent, and Ono used the theory of modular forms modulo ℓ to establish remarkable “self-similarity” properties of the partition function and give an overarching explanation of many partition congruences. …”
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