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We explore alternative descriptions of the charged lepton sector in modular invariant models of lepton masses and mixing angles. In addition to the modulus, the symmetry breaking sector of our models includes ordinary flavons. Neutrino mass…
For most aspherical Seifert-fibered 3-manifolds $M$, the space of Seifert fiberings $SF(M)$ is known to have contractible components. It is also known that the space of Hopf fiberings of the three-sphere is noncontractible. We provide the…
We classify a class of 2-step nilpotent Lie algebras related to the representations of the Clifford algebras in the following way. Let $J\colon \Cl(\mathbb R^{r,s})\toU$ be a representation of the Clifford algebra $\Cl(\mathbb R^{r,s})$…
By a well-known theorem of Viterbo, the symplectic homology of the cotangent bundle of a closed manifold is isomorphic to the homology of its loop space. In this paper we extend the scope of this isomorphism in several directions. First, we…
We decompose linear $\mathrm{G}_2$-structure in canonical ways adapted to 3-dimensional subspaces, in terms of certain natural 1-forms and definite triple of 2-forms, and apply the decompositions to the study of $\mathrm{G}_2$-structure…
We review various aspects of cluster algebras and the ways in which they appear in the study of loop-level amplitudes in planar ${\cal N} = 4$ supersymmetric Yang-Mills theory. In particular, we highlight the different forms of…
A natural construction of the logarithmic extension of the M(2,p) minimal models is presented, which generalises our previous model [0708.0802] of percolation (p=3). Its key aspect is the replacement of the minimal model irreducible modules…
We study the global topology of the space $\mathcal L$ of loops of contactomorphisms of a non-orderable closed contact manifold $(M^{2n+1}, \alpha)$. We filter $\mathcal L$ by a quantitative measure of the ``positivity'' of the loops and…
We construct a loop induced seesaw model in a TeV scale theory with gauged U(1)_{B-L} symmetry. Light neutrino masses are generated at two-loop level and right-handed neutrinos also obtain their masses by one-loop effect. Multi-component…
Construction C (also known as Forney's multi-level code formula) forms a Euclidean code for the additive white Gaussian noise (AWGN) channel from $L$ binary code components. If the component codes are linear, then the minimum distance is…
Vector-like leptons (VLLs) as one kind of the most intriguing particles, have been widely concerned in several extensions of the Standard Model (SM). In this work, we explore the discovery potential of VLLs via pair production in the…
Let $p\neq3$ be any prime and $l\neq3$ be any odd prime with $gcd(p,l)=1$. $F_{q}^{*}=\langle\xi\rangle$ is decomposed into mutually disjoint union of $gcd(q-1,3lp^{s})$ coset over the subgroup $\langle\xi^{3lp^{s}}\rangle$, where $\xi$ is…
Circular-shift linear network coding (LNC) is a class of vector LNC with local encoding kernels selected from cyclic permutation matrices, so that it has low coding complexities. However, it is insufficient to exactly achieve the capacity…
Let p, ell be distinct primes and let q be a power of p. Let G be a connected compact Lie group. We show that there exists an integer b such that the mod ell cohomology of the classifying space of a finite Chevalley group G(F_q) is…
We propose an extension of the 3-3-1 model with an additional symmetry group $Z_{2}\times Z_{4} \times U(1)_{L_g}$ and an extended scalar sector. To our best knowledge this is the first example of a renormalizable 3-3-1 model, which allows…
In the setting of homotopy type theory, each type can be interpreted as a space. Moreover, given an element of a type, i.e. a point in the corresponding space, one can define another type which encodes the space of loops based at this…
We perform a systematic study of the $d=5$ Weinberg operator at the one-loop level. We identify three different categories of neutrino mass generation: (1) finite irreducible diagrams; (2) finite extensions of the usual seesaw mechanisms at…
Opening up the Weinberg operator at 1-loop level using a scalar triplet, two scalar doublets and one fermion gives rise to T4-2-i one-loop topology. Neutrino masses generated from this topology are always accompanied by the tree level Type…
The NAFIL is a finite loop in which every element has a unique (two-sided)inverse. NAFIL loops can be classified into two types: composite (with at least one non-trivial subsystem) and non-composite or plain (without any non-trivial…
Circular-shift linear network coding (LNC) is a class of vector LNC with low encoding and decoding complexities, and with local encoding kernels chosen from cyclic permutation matrices. When $L$ is a prime with primitive root $2$, it was…