Efficient digital-to-analog encoding

An important issue in analog circuit design is the problem of digital-to-analog conversion, i.e., the encoding of Boolean variables into a single analog value which contains enough information to reconstruct the values of the Boolean variables. A natural question is: what is the complexity of implementing the digital-to-analog encoding function? That question was answered by Wegener (see Inform. Processing Lett., vol.60, no.1, p.49-52, 1995), who proved matching lower and upper bounds on the size of the circuit for the encoding function. In particular, it was proven that [(3n-1)/2] 2-input arithmetic gates are necessary and sufficient for implementing the encoding function of n Boolean variables. However, the proof of the upper bound is not constructive. In this paper, we present an explicit construction of a digital-to-analog encoder that is optimal in the number of 2-input arithmetic gates. In addition, we present an efficient analog-to-digital decoding algorithm. Namely, given the encoded analog value, our decoding algorithm reconstructs the original Boolean values. Our construction is suboptimal in that it uses constants of maximum size n log n bits; the nonconstructive proof uses constants of maximum size 2n+[log n] bits

Efficient Digital to Analog Encoding

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract included in .pdf document. An important issue in analog circuit design is the problem of digital to analog conversion, namely, the encoding of Boolean variables into a single analog value which contains enough information to reconstruct the values of the Boolean variables. A natural question is: What is the complexity of implementing the digital to analog encoding function? That question was recently answered in (5), where matching lower and upper bounds on the size of the circuit for the encoding function were proven. In particular, it was proven that [...] 2-input arithmetic gates are necessary and sufficient for implementing the encoding function of n Boolean variables. However, the proof of the upper bound is not constructive. In this paper, we present an explicit construction of a digital to analog encoder that is optimal in the number of 2-input arithmetic gates. In addition, we present an efficient analog to digital decoding algorithm. Namely, given the encoded analog value, our decoding algorithm reconstructs the original Boolean values. Our construction is suboptimal in that it uses constants [...] bits

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels

There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more common, systems with very small numbers of molecules are important in some applications, e.g., in small biological cells or in surface processes. In both views, most complicated systems with multiple reaction channels and multiple chemical species cannot be solved analytically. There are exact numerical simulation methods to simulate trajectories of discrete, stochastic systems, methods that are rigorously equivalent to the Master Equation approach, but they do not scale well to systems with many reaction pathways. This paper presents the Next Reaction Method, an exact algorithm to simulate coupled chemical reactions that is also efficient: it (a) uses only a single random number per simulation event, and (b) takes time proportional to the logarithm of the number of reactions, not to the number of reactions itself. The Next Reaction Method is extended to include time-dependent rate constants and non-Markov processes and it is applied to a sample application in biology: the lysis/lysogeny decision circuit of lambda phage. When run on lambda the Next Reaction Method requires approximately 1/15th as many operations as a standard implementation of the existing methods

A Mixed Methods Approach to Identifying Administration Issues Pertinent in Interscholastic Sports

The purpose of this study was to investigate three propositions: a) What are the administration issues most pertinent to interscholastic sport today, as well as the next five years?, b) How important are those administration issues to athletic administrators?, and c) What are the potential implications of those pertinent administration issues to practicing athletic administrators? The literature provides a general overview of relevant issues surrounding interscholastic athletics. However, the importance and implications of relevant issues to practicing high school athletic administrators are difficult to discern. To answer the first proposition, the Minnesota State High School League (MSHSL) provided 10 contemporary administration issues that were most pertinent to interscholastic sport today, as well as the next five years. To answer the second proposition, a Likert-Scale was created so that practicing athletic administrators could rate each issue on a scale of 5 = extremely important to 1 = very little importance. A national study was conducted with athletic directors from the National Interscholastic Athletic Administrators Association (N = 170) annual conference. A one-tailed ANOVA was executed to determine significant differences among the 10 administration issues identified by the MSHSL. Four issues were found to be significant; Athletic Facilities, Athletic Training, Health Issues and Travel Teams. A Games-Howell post hoc was executed to determine significant differences across geographical regions of the United States. For the third proposition, semi-structured interviews were completed to provide insight on the implications for practicing athletic administrators. The results offer insight from which further investigations could be conducted to continue building on policies that influence interscholastic athletic administrators’ day-to-day accountability when overseeing their athletic programs

Integrated lunar materials manufacturing process

A manufacturing plant and process for production of oxygen on the moon uses lunar minerals as feed and a minimum of earth-imported, process materials. Lunar feed stocks are hydrogen-reducible minerals, ilmenite and lunar agglutinates occurring in numerous, explored locations mixed with other minerals in the pulverized surface layer of lunar soil known as regolith. Ilmenite (FeTiO.sub.3) and agglutinates contain ferrous (Fe.sup.+2) iron reducible by hydrogen to yield H.sub.2 O and metallic Fe at about 700.degree.-1,200.degree. C. The H.sub.2 O is electrolyzed in gas phase to yield H.sub.2 for recycle and O.sub.2 for storage and use. Hydrogen losses to lunar vacuum are minimized, with no net hydrogen (or any other earth-derived reagent) consumption except for small leaks. Feed minerals are surface-mined by front shovels and transported in trucks to the processing area. The machines are manned or robotic. Ilmenite and agglutinates occur mixed with silicate minerals which are not hydrogen-reducible at 700.degree.-1,200.degree. C. and consequently are separated and concentrated before feeding to the oxygen generation process. Solids rejected from the separation step and reduced solids from the oxygen process are returned to the mine area. The plant is powered by nuclear or solar power generators. Vapor-phase water electrolysis, a staged, countercurrent, fluidized bed reduction reactor and a radio-frequency-driven ceramic gas heater are used to improve thermal efficiency

Overcoming Memory Limitations in Rule Learning

Adults, infants, and other species are able to learn and generalize abstract patterns from sequentially presented stimuli. Rule learning of this type may be involved in children's acquisition of linguistic structure, but the nature of the mechanisms underlying these abilities is unknown. While inferences regarding the capabilities of these mechanisms are commonly made based on the pattern of successes and failures in simple artificial-language rule-learning tasks, failures may be driven by memory limitations rather than intrinsic limitations on the kinds of computations that learners can perform. Here we show that alleviating memory constraints on adult learners through concurrent visual presentation of stimuli allowed them to succeed in learning regularities in three difficult artificial rule-learning experiments where participants had previously failed to learn via sequential auditory presentation. These results suggest that memory constraints, rather than intrinsic limitations on learning, may be a parsimonious explanation for many previously reported failures. We argue that future work should attempt to characterize the role of memory constraints in natural and artificial language learning.National Science Foundation (U.S.) (NSF DDRIG #0746251)United States. Department of Education (Jacob K. Javits Graduate Fellowship

Connections Between Adaptive Control and Optimization in Machine Learning

This paper demonstrates many immediate connections between adaptive control and optimization methods commonly employed in machine learning. Starting from common output error formulations, similarities in update law modifications are examined. Concepts in stability, performance, and learning, common to both fields are then discussed. Building on the similarities in update laws and common concepts, new intersections and opportunities for improved algorithm analysis are provided. In particular, a specific problem related to higher order learning is solved through insights obtained from these intersections.Comment: 18 page

AAT/WFI observations of the Extragalactic H I Cloud HIPASS J1712-64

AAT/WFI optical images of a candidate extragalactic HI cloud, HIPASS J1712-64, are presented. The g and r-band CCD mosaic camera frames were processed using a new data pipeline recently installed at the AAO. The resultant stacked images reach significantly deeper levels than those of previous published optical imaging of this candidate, providing a detection limit M_g -7 at a distance of 3Mpc, the inferred distance to HIPASS J1712-64. However, detailed analysis of the images fails to uncover any stellar population associated with the HI emission. If this system is a member of the Local Group then it is pathologically different to other members. Hence, our observations reinforce earlier suggestions that this HI cloud is most likely Galactic in origin and not a Local Volume dwarf galaxy.Comment: 8 pages, accepted for publication in PASA (Figures reduced in resolution, please contact gfl if you wish the higher resolution versions