We investigate the properties of local minima energy landscape a continuous non-convex optimization problem, spherical perceptron with piecewise linear cost function and show that they are critical, marginally stable displaying set pseudogaps, singularities non-linear excitations whose appear to be in same universality class jammed packings hard spheres. The problem appears as an evolution pure...

The solution path of the 1D fused lasso for an ndimensional input is piecewise linear with O(n) segments [1], [2]. However, existing proofs of this bound do not hold for the weighted fused lasso. At the same time, results for the generalized lasso, of which the weighted fused lasso is a special case, allow Ω(3) segments [3]. In this paper, we prove that the number of segments in the solution pa...

For each piecewise linear Lorenz map that expand on average, we show that it admits a dichotomy: it is either periodic renormalizable or prime. As a result, such a map is conjugate to a β-transformation.

Life-logging video streams, financial time series, and Twitter tweets are a few examples of high-dimensional signals over practically unbounded time. We consider the problem of computing optimal segmentation of such signals by a k-piecewise linear function, using only one pass over the data by maintaining a coreset for the signal. The coreset enables fast further analysis such as automatic summ...

We report tests of CPLP, a piecewise-linear simplex implementation based on the XMP subroutine library. Using test problems of various shapes and origins, we judge CPLP against a comparable linear bounded-variable simplex code that is applied to equivalent linear programs. Our evidence indicates that CPLP is typically 2 to 3 times faster in solving the test problems that are most signiicantly p...

By adopting the technique of pre-regulator, a high PSRR and low temperature coefficient piecewise-linear bandgap reference (BGR) is designed for analog and mixed-signal application in this paper. The piecewise-linear BGR with pre-regulator, which is analyzed and simulated in SMIC 0.18μm CMOS process, has simple circuit architecture. Simulation results show that piecewise-linear BGR with pre-reg...

Recently Braga and Mello conjectured that for a given n ∈ N there is a piecewise linear system with two zones in the plane with exactly n limit cycles. In this paper we prove a result from which the conjecture is an immediate consequence. Several explicit examples are given where location and stability of limit cycles are provided.

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in repre...

An approach to radiance calculation of scenes of surfaces which are reflecting light, incident from extended anisotropic light sources, directional-diffusely or specularly is presented. The resulting light field is represented as a piecewise linear function over an adaptive, hierarchical cell decomposition of the linespace. Versions with exact and approximated visibility are worked out. The lin...