We study general methods to build forking-like notions in the framework of tame abstract elementary classes (AECs) with amalgamation. We show that whenever such classes are categorical in a high-enough cardinal, they admit a good frame: a forking-like notion for types of singleton elements. Theorem 0.1 (Superstability from categoricity). Let K be a (< κ)-tame AEC with amalgamation. If κ = iκ > ...

We study regression M-estimates in the setting where p, the number of covariates, and n, the number of observations, are both large, but p ≤ n. We find an exact stochastic representation for the distribution of β = argmin(β∈ℝ(p)) Σ(i=1)(n) ρ(Y(i) - X(i')β) at fixed p and n under various assumptions on the objective function ρ and our statistical model. A scalar random variable whose determinist...

For a two-dimensional surface M in the four-dimensional Euclidean space E we introduce an invariant linear map of Weingarten type in the tangent space of the surface, which generates two invariants k and κ. The condition k = κ = 0 characterizes the surfaces consisting of flat points. The minimal surfaces are characterized by the equality κ − k = 0. The class of the surfaces with flat normal con...

In this study, we introduce a primal-dual prediction-correction algorithm framework for convex optimization problems with known saddle-point structure. Our unified frame adds the proximal term with a positive definite weighting matrix. Moreover, different proximal parameters in the frame can derive some existing well-known algorithms and yield a class of new primal-dual schemes. We prove the co...

Light chain proximal tubulopathy is a rarely reported entity associated with plasma cell dyscrasia that classically manifests as acquired Fanconi syndrome and is characterized by the presence of κ-restricted crystals in the proximal tubular cytoplasm. We herein present a case of multiple myeloma with Fanconi syndrome and acute kidney injury due to light chain proximal tubulopathy with light cha...

In this paper, we extend the geometric descent method recently proposed by Bubeck, Lee and Singh [5] to solving nonsmooth and strongly convex composite problems. We prove that the resulting algorithm, GeoPG, converges with a linear rate (1− 1/√κ), thus achieves the optimal rate among first-order methods, where κ is the condition number of the problem. Numerical results on linear regression and ...

We show that when correctly formulated the equation ∇ × a = κa does not exhibit some inconsistencies atributed to it, so that its solutions can represent physical fields. We want to look for solutions of Maxwell equations which describe stationary electromagnetic configurations – in the sense that the energy of the field does not propagate. In order to obtain one such stationary solution it is ...

This report contains revision and extension of some results about RBO from [14]. RBO is a simple and efficient broadcast scheduling of n = 2 uniform frames for battery powered radio receivers. Each frame contains a key from some arbitrary linearly ordered universe. The broadcast cycle – a sequence of frames sorted by the keys and permuted by k-bit reversal – is transmitted in a round robin fash...