No division implies chaos

Motion of vortices implies chaos in Bohmian mechanics

– Bohmian mechanics is a causal interpretation of quantum mechanics in which particles describe trajectories guided by the wave function. The dynamics in the vicinity of nodes of the wave function, usually called vortices, is regular if they are at rest. However, vortices generically move during time evolution of the system. We show that this movement is the origin of chaotic behavior of quantu...

Few distinct distances implies no heavy lines or circles

We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set P of n points determines o(n) distinct distances, then no line contains Ω(n) points of P and no circle contains Ω(n) points of P . We rely on the bipartite and partial variant of the Elekes-Sharir framework that was presented by Sharir, Sheffer, and Solymosi in [2...

No non-uniform lower bounds implies PIT is hard and no derandomization

We consider arithmetic circuits. In this model, inputs are variables or constants from a field and the computation is performed using + and ×. Formally: Definition 1. An arithmetic circuit C over the field F and the set of variables X = x1, . . . , xn is a directed acyclic graph as follows. The vertices of C are called gates. Every gate in C of in-degree 0 is labeled by either a variable from X...

Chaos -- no randomness in cardiac physiology.

Svoboda-Tung division with no compensation

The development of a new general radix-b division algorithm, based on the Svoboda-Tung division, suitable for VLSI implementation is presented. The new algorithm overcomes the drawbacks of the Svoboda-Tung techniques that have prevented the VLSI implementation. First of all, the proposed algorithm is valid for any radix b ≥ 2; and next, it avoids the possible compensation due to overflow on the...