Incremental closure for systems of two variables per inequality

Subclasses of linear inequalities where each inequality has at most two vari- ables are popular in abstract interpretation and model checking, because they strike a balance between what can be described and what can be efficiently computed. This paper focuses on the TVPI class of inequalities, for which each coefficient of each two variable inequality is unrestricted. An implied TVPI in- equality can be generated from a pair of TVPI inequalities by eliminating a given common variable (echoing resolution on clauses). This operation, called result , can be applied to derive TVPI inequalities which are entailed (implied) by a given TVPI system. The key operation on TVPI is calculating closure: satisfiability can be observed from a closed system and a closed system also simplifies the calculation of other operations. A closed system can be derived by repeatedly applying the result operator. The process of adding a single TVPI inequality to an already closed input TVPI system and then finding the closure of this augmented system is called incremental closure. This too can be calcu- lated by the repeated application of the result operator. This paper studies the calculus defined by result , the structure of result derivations, and how deriva- tions can be combined and controlled. A series of lemmata on derivations are presented that, collectively, provide a pathway for synthesising an algorithm for incremental closure. The complexity of the incremental closure algorithm is analysed and found to be O (( n 2 + m 2 )lg( m )), where n is the number of variables and m the number of inequalities of the input TVPI system

Steady-state probability density function of the phase error for a DPLL with an integrate-and-dump device

The steady-state behavior of a particular type of digital phase-locked loop (DPLL) with an integrate-and-dump circuit following the phase detector is characterized in terms of the probability density function (pdf) of the phase error in the loop. Although the loop is entirely digital from an implementation standpoint, it operates at two extremely different sampling rates. In particular, the combination of a phase detector and an integrate-and-dump circuit operates at a very high rate whereas the loop update rate is very slow by comparison. Because of this dichotomy, the loop can be analyzed by hybrid analog/digital (s/z domain) techniques. The loop is modeled in such a general fashion that previous analyses of the Real-Time Combiner (RTC), Subcarrier Demodulator Assembly (SDA), and Symbol Synchronization Assembly (SSA) fall out as special cases

DSA's subcarrier demodulation losses

The degradation in bit error rate performance due to imperfect subcarrier tracking by the Demodulation Synchronization Assembly (DSA) is investigated. Results apply to any type of digital loop and received signal dynamics. A type four loop causes the least amount of loss, because it tracks phase jerk with zero steady-state error. However, when frequency rate and frequency acceleration are as large as in the extended Magellan mission, it will be necessary to decrease the loop update time in order to minimize the losses

Real-time combiner loss

Telemetry signals from several channels are aligned in time and combined by the Real-Time Combiner (RTC) in order to increase the strength of the total signal. In this article, the impact of the timing jitter in the RTC on the bit/symbol error rate is investigated. Equations are derived for the timing jitter loss associated with the coded and uncoded channels. Included are curves that depict the bit-symbol error rate vs. E sub b/N sub 0 and E sub s/N sub 0 for some typical telemetry conditions. The losses are typically below 0.1 dB

Performance analysis of the DSN baseband assembly (Bba) Real-Time Combiner (RTC)

The operation of the BBA Real Time Combiner (RTC) is discussed and its performance investigated in detail. It is shown that each channel of the RTC can be modelled by a simple block diagram in the z-transform domain from which all pertinent transient and steady state behavioral characteristics can be determined. In particular, the characteristic equation of the tracking loop and its equivalent noise bandwidth are found and used to evaluate the closed loop transient response and steady-state mean squared timing jitter. The impact of the totality of these loop jitter contributions on the combiner output SNR is evaluated and illustrated numerically. These results show that for parameters of interest to various space missions, the RTC is capable of providing significant SNR improvement relative to a single receiving antenna

Physics of randomness and regularities for cities, languages, and their lifetimes and family trees

Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size distribution of the cities and for that of the languages, respectively. The cities and the languages are treated differently (and as connected; for example, the languages split in terms of splitting the cities, etc.) and thus two distributions are obtained in the same computation at the same time. Evolutions of lifetimes and families for the cities and the languages are also studied. We suggest that the regularities may be evolving out of randomness, in terms of the relevant processes.Comment: 22 pages including all figures; for Int. J. Mod. Phys. C 18 (2007

IUE observations of the chromospheric activity-age relation in young solar-type stars

Ultraviolet data obtained with the IUE spacecraft are presented for a dozen solar-type stars in the field. The stars are of spectral type F6 V - G1 V; on the basis of their high Li content, they range in age from 0.1 to 2.8 Gyr. The evolution of transition regions and chromospheric emission with stellar age is studied along with the surface distribution of magnetically active regions as revealed by rotational modulation of UV emission line fluxes