On dynamical bit sequences

Let X^{(k)}(t) = (X_1(t), ..., X_k(t)) denote a k-vector of i.i.d. random variables, each taking the values 1 or 0 with respective probabilities p and 1-p. As a process indexed by non-negative t, $X^{(k)}(t)$ is constructed--following Benjamini, Haggstrom, Peres, and Steif (2003)--so that it is strong Markov with invariant measure ((1-p)\delta_0+p\delta_1)^k. We derive sharp estimates for the probability that ``X_1(t)+...+X_k(t)=k-\ell for some t in F,'' where F \subset [0,1] is nonrandom and compact. We do this in two very different settings: (i) Where \ell is a constant; and (ii) Where \ell=k/2, k is even, and p=q=1/2. We prove that the probability is described by the Kolmogorov capacitance of F for case (i) and Howroyd's 1/2-dimensional box-dimension profiles for case (ii). We also present sample-path consequences, and a connection to capacities that answers a question of Benjamini et. al. (2003)Comment: 25 pages. This a substantial revision of an earlier paper. The material has been reorganized, and Theorem 1.3 is ne

Vibrating soap films: An analog for quantum chaos on billiards

We present an experimental setup based on the normal modes of vibrating soap films which shows quantum features of integrable and chaotic billiards. In particular, we obtain the so-called scars -narrow linear regions with high probability along classical periodic orbits- for the classically chaotic billiards. We show that these scars are also visible at low frequencies. Finally, we suggest some applications of our experimental setup in other related two-dimensional wave phenomena.Comment: 5 pages, 7 figures. Better Postscript figures available on reques

Obtrusiveness of smartphone applications for sleep health

Unobtrusiveness is one of the main issues concerning health-related systems. Many developers affirm that their systems do not burden users; however, this is not always achieved. This article evaluates the obtrusiveness of various systems developed to improve sleep quality. The systems analyzed are related to sleep hygiene, since it has become an interesting topic for researchers, physicians and people in general, mainly because it has become part of the methods used to estimate a persons’ health status A set of design elements are presented as keys to achieving unobtrusiveness. We propose a scale to measure the level of unobtrusiveness and use it to evaluate several systems, with a focus on smartphone applications.

Design and Evaluation of a Virtual Quadrant Receiver for 4-ary Pulse Position Modulation/Optical Code Division Multiple Access (4-ary PPM/O-CDMA)

M-ary pulse position modulation (M-ary PPM) is an alternative to on-off-keying (OOK) that transmits multiple bits as a single symbol occupying a frame of M slots. PPM does not require thresholding as in OOK signaling, instead performing a comparison test among all slots in a frame to make the slot decision. Combining PPM with optical code division multiple access (PPM/O-CDMA) adds the benefit of supporting multiple concurrent, asynchronous bursty PPM users. While the advantages of PPM/O-CDMA are well known, implementing a receiver that performs comparison test can be difficult. This paper describes the design of a novel array receiver for M-ary PPM/O-CDMA (M = 4) where the received signal is mapped onto an xy-plane whose quadrants define the PPM slot decision by means of an associated control law. The receiver does not require buffering or nonlinear operations. In this paper we describe a planar lightwave circuit (PLCs) implementation of the receiver. We give detailed numerical simulations that test the concept and investigate the effects of multi-access interference (MAI) and optical beat interference (OBI) on the slot decisions. These simulations provide guidelines for subsequent experimental measurements that will be described

Development of Pulse Position Modulation/Optical CDMA (PPM/O-CDMA) for Gb/s Fiber Optic Networking

Pulse position modulation (PPM) in lasercom systems is known to provide potential advantages over other modulation schemes. [1]. In PPM, a periodic time frame is established and data is transmitted by placing a pulse in any one of several subintervals (or ''slots'') within each frame. In PPM/O-CDMA all users use the same frame structure and each transmits its unique address code in place of the PPM pulse. The advantage of PPM as a pulsed signal format is that (1) a single pulse can transmit multiple bits during each frame; (2) decoding (determining which subinterval contains the pulse) is by comparison rather than threshold tests (as in on-off-keying); (3) each user transmits in only a small fraction of the frame, hence the multi-access interference (MAI) of any user statistically spreads over the entire frame time, reducing the chance of overlap with any other user; and (4) under an average power constraint, increasing frame time increases the peak pulse power (i.e., PPM trades average power for peak power). The most straightforward approach to implementing PPM/O-CDMA data modulator inserts the PPM pulse modulation first, then imposes the O-CDMA coding. A pulsed PPM modulator converts bits (words) into pulse positions. In the case of wavelength/time (W/T) matrix codes, multi-wavelength pulses are generated at the beginning of each frame, at the frame rate. For M-ary PPM, a block of k bits represents M = 2{sup k} unique interval positions in the frame corresponding to M-l specific time delays (the zero delay is also a position). PPM modulation is achieved by shifting the initial pulse into an interval position with delay D(i) (i=0,1,2,..,M-1). The location of a pulse position (selection of a delay) therefore identifies a unique k-bit word in the frame. At the receiver, determining which delay occurs relative to the frame start time decodes the data word. The probability of pulse overlap between two users decreases with M, which therefore decreases the probability of MAI buildup. Spreadsheet simulations suggest that a slot-synchronous M-ary PPM/O-CDMA system will support more concurrent users than a chip-synchronous or frame-synchronous system

Design of a Virtual Quadrant Receiver for 4-ary Pulse Position Modulation/Optical CDMA (4-ary PPM/O-CDMA)

We describe a receiver that performs optical code division multiple access (O-CDMA) decoding followed by pulse position modulation (PPM) symbol detection that behaves like a radar quadrant receiver. Simulations determine the impact of multi-access interference on symbol detection for up to 32 users