We explain how idempotents in homotopy groups give rise to splittings of homotopy categories of modules over commutative S-algebras, and we observe that there are naturally occurring equivariant examples involving idempotents in Burnside rings. We then give a version of the Landweber exact functor theorem that applies to MU -modules. In 1997, not long after [6] was written, I gave an April Fool...

Image deconvolution is an important problem which has seen plenty of progress in the last decades. Due to its ill-posedness, a common approach is to formulate the reconstruction as an optimisation problem, regularised by an additional sparsityenforcing term. This term is often modeled as an l1 norm measured in the domain of a suitable signal transform. The resulting optimisation problem can be ...

Church’s Problem asks for the construction of a procedure which, given a logical specification φ on sequence pairs, realizes for any input sequence I an output sequenceO such that (I,O) satisfies φ. McNaughton reduced Church’s Problem to a problem about two-player ω-games. Büchi and Landweber gave a solution for Monadic Second-Order Logic of Order (MLO) specifications in terms of finite-state s...

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected N...

Let p > 3 be a prime. In the ring of modular forms with q-expansions defined over Z(p), the Eisenstein function Ep+1 is shown to satisfy (Ep+1) p−1 ≡ − −1 p ∆ 2−1)/12 mod (p, Ep−1). This is equivalent to a result conjectured by de Shalit on the polynomial satisfied by all the j-invariants of supersingular elliptic curves over Fp. It is also closely related to a result of Gross and Landweber use...

1389-1286/$ see front matter 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.bjp.2013.12.037 q GENI is funded by the U.S. National Science Foundation. Any opinions, findings, conclusions or recommendations expressed in this material are the authors’ and do not necessarily reflect the views of the National Science Foundation. ⇑ Corresponding author. Tel.: +1 617 873 3675. E-m...

We consider the ill-posed inverse problem of identifying a nonlinearity in time-dependent PDE model. The is approximated by neural network, and needs to be determined alongside other unknown physical parameters state. Hence, it not possible construct input-output data pairs perform supervised training process. Proposing an all-at-once approach, we bypass need for recover all unknowns simultaneo...