On Logical Depth and the Running Time of Shortest Programs

The logical depth with significance $b$ of a finite binary string $x$ is the shortest running time of a binary program for $x$ that can be compressed by at most $b$ bits. There is another definition of logical depth. We give two theorems about the quantitative relation between these versions: the first theorem concerns a variation of a known fact with a new proof, the second theorem and its proof are new. We select the above version of logical depth and show the following. There is an infinite sequence of strings of increasing length such that for each $j$ there is a $b$ such that the logical depth of the $j$th string as a function of $j$ is incomputable (it rises faster than any computable function) but with $b$ replaced by $b+1$ the resuling function is computable. Hence the maximal gap between the logical depths resulting from incrementing appropriate $b$'s by 1 rises faster than any computable function. All functions mentioned are upper bounded by the Busy Beaver function. Since for every string its logical depth is nonincreasing in $b$, the minimal computation time of the shortest programs for the sequence of strings as a function of $j$ rises faster than any computable function but not so fast as the Busy Beaver function.Comment: 12 pages LaTex (this supercedes arXiv:1301.4451

Conservation of Orbital Angular Momentum in Stimulated Down-Conversion

We report on an experiment demonstrating the conservation of orbital angular momentum in stimulated down-conversion. The orbital angular momentum is not transferred to the individual beams of the spontaneous down-conversion, but it is conserved when twin photons are taken individually. We observe the conservation law for an individual beam of the down-conversion through cavity-free stimulated emission.Comment: Submitted for publication in Phys. Rev. Let

Precoded generalized spatial modulation for downlink MIMO transmissions in beyond 5G networks

The design of multiple input multiple output (MIMO) schemes capable of achieving both high spectral and energy efficiency constitutes a challenge for next-generation wireless networks. MIMO schemes based on generalized spatial modulations (GSM) have been widely considered as a powerful technique to achieve that purpose. In this paper, a multi-user (MU) GSM MIMO system is proposed, which relies on the transmission of precoded symbols from a base station to multiple receivers. The precoder’s design is focused on the removal of the interference between users and allows the application of single-user GSM detection at the receivers, which is accomplished using a low-complexity iterative algorithm. Link level and system level simulations of a cloud radio access network (C-RAN) comprising several radio remote units (RRUs) were run in order to evaluate the performance of the proposed solution. Simulation results show that the proposed GSM MU-MIMO approach can exploit efficiently a large number of antennas deployed at the transmitter. Moreover, it can also provide large gains when compared to conventional MU-MIMO schemes with identical spectral efficiencies. In fact, regarding the simulated C-RAN scenario with perfect channel estimation, system level results showed potential gains of up to 155% and 139% in throughput and coverage, respectively, compared to traditional cellular networks. The introduction of imperfect channel estimation reduces the throughput gain to 125%.info:eu-repo/semantics/publishedVersio

Characterization of bespoke force sensors for tailored applications

Bespoke force sensors made with active polymer composites are inexpensive, thin and flexible, hence popular in wearable electronics, however their wider application is limited due to the lack of literature studying their voltage response related errors. We present the voltage response characterization of bespoke force sensors made with an active polymer composite, silver coated fabric, stainless steel thread and silver epoxy. Characterization of the effects of static and dynamic loading was completed with a mechanical testing machine. Static tests consisted of loading and unloading at 0.01, 0.1, 0.5 and 1 N/s, and drift tests for 120 minutes up to 10 N every 1 N. Dynamic tests consisted of a sinusoidal load of 5 N ± 1 N applied at 0.05, 0.1 and 0.5 Hz for 60 minutes. The force-voltage relationships were modelled using an exponential function. Maximum mean drift error was observed when applying different static loads for 120 minutes each. Drift error is minimal at 5 s (<1%)and at 60 (< 5%) minutes with loads under 1 N. Maximum hysteresis of 18% was observed at a 1 N/s loading rate. The maximum drift error after one hour of dynamic loading was observed at 0.5 Hz and is minimal (-0.00004%). The cost of fabricating these sensors is very low compared with commercially available options. These sensors can be fabricated in any shape and size with the added advantage of being able to set the location of the electronic connections as desired