Sublinear Algorithms for Approximating String Compressibility

We raise the question of approximating the compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE) and a variant of Lempel-Ziv (LZ77), and present sublinear algorithms for approximating compressibility with respect to both schemes. We also give several lower bounds that show that our algorithms for both schemes cannot be improved significantly. Our investigation of LZ77 yields results whose interest goes beyond the initial questions we set out to study. In particular, we prove combinatorial structural lemmas that relate the compressibility of a string with respect to LZ77 to the number of distinct short substrings contained in it (its ?th subword complexity , for small ?). In addition, we show that approximating the compressibility with respect to LZ77 is related to approximating the support size of a distribution.     

Relationship between bronchial reactivity, airway caliber, and severity of asthma

Electrocardiographic tests were applied to slaughter pigs and showed continuous rise of the heart rate from anaesthetisation to the debleeding prick at which point its maximum was 86% beyond the original value. The duration of the intraventricular electric systoles was 0.290 s prior to the debleeding prick and 0.281 s thereafter. The intraventricular electric diastoles were 0.241 s prior to debleeding and 0.303 s after it. No significant modification in diastolic time was observed prior to the debleeding prick. ST duration dropped from an original level of 0.222 s to a minimum of 0.173 at the point of pricking.     

Learning Fallible Deterministic Finite Automata

We consider the problem of learning from a fallible expert that answers all queries about a concept, but often gives incorrect answers. The expert can also be thought of as a truth table describing the concept which has been partially corrupted. In order to learn the underlying concept with arbitrarily high precision, we would like to use its structure in order to correct most of the incorrect answers. We assume that the expert's errors are uniformly and independently distributed, occur with any fixed probability strictly smaller than 1/2, and are persistent. In particular, we present a polynomial time algorithm using membership queries for correcting and learning fallible Deterministic Finite Automata under the uniform distribution.     

Straight-chain alkylbenzenes: Structure and performance property relations III. Light-duty dishwashing formulations

A relationship between mixtures of straightchain alkylbenzene sulfonates and their performances in light-duty dishwashing formulations has been established through studies of many pure isomers and isomer mixtures in both liquid and powder systems. The foam performance characteristics are shown to be directly related to carbon chain length, phenyl position, and water hardness in a readily calculable manner. Solubility studies on pure isomers are also reported. Presented at the AOCS Meeting, Houston, April 1965.     

On the time and space complexity of computation using write-once memory or is pen really much worse than pencil?

We introduce a model of computation based on the use of write-once memory. Write-once memory has the property that bits may be set but not reset. Our model consists of a RAM with a small amount of regular memory (such as logarithmic orn ^α for α<1, wheren is the size of the problem) and a polynomial amount of write-once memory. Bounds are given on the time required to simulate on write-once memory algorithms which originally run on a RAM with a polynomial amount of regular memory. We attempt to characterize algorithms that can be simulated on our write-once memory model with very little slow-down. A persistent computation is one in which, at all times, the memory state of the computation at any previous point in time can be reconstructed. We show that any data structure or computation implemented on this write-once memory model can be made persistent without sacrificing much in the way of running time or space. The space requirements of algorithms running on the write-once model are studied. We show that general simulations of algorithms originally running on a RAM with regular memory by algorithms running on our write-once memory model require space proportional to the number of steps simulated. In order to study the space complexity further, we define an analogue of the pebbling game, called the pebble-sticker game. A sticker is different from a pebble in that it cannot be removed once placed on a node of the computation graph. As placing pebbles correspond to writes to regular memory, placing stickers correspond to writes to the write-once memory. Bounds are shown on pebble-sticker tradeoffs required to evaluate trees and planar graphs. Finally, we define the complexity class WO-PSPACE as the class of problems which can be solved with a polynomial amount of write-once memory, and show that it is equal toP. The research of S. Irani was supported by NSF Grant No. DCF-85-13926, and a Tandem Corporation Fellowship. R. Rubinfeld's research was supported by NSF Grant No. CCR 88-13632 and an IBM Graduate Fellowship.     

Designing checkers for programs that run in parallel

Program correctness for parallel programs is an even more problematic issue than for serial programs. We extend the theory of program result checking to parallel programs, and find general techniques for designing such result checkers that work for many basic problems in parallel computation. These result checkers are simple to program and are more efficient than the actual computation of the result. For example, sorting, multiplication, parity, the all-pairs shortest-path problem and majority all have constant depth result checkers, and the result checkers for all but the last problem use a linear number of processors. We show that there are P-complete problems (evaluating straight-line programs, linear programming) that have very fast, even constant depth, result checkers.This research was done while at the Computer Science Division, University of California, Berkeley, and the International Computer Science Institute, Berkeley, California. Supported in part by an IBM Graduate Fellowship and NSF Grant No. CCR 88-13632.     

Deletion of an amino-terminal sequence beta-catenin in vivo and promotes hyperphosporylation of the adenomatous polyposis coli tumor suppressor protein

Regulation of cell adhesion and cell signaling by beta-catenin occurs through a mechanism likely involving the targeted degradation of the protein. Deletional analysis was used to generate a beta-catenin refractory to rapid turnover and to examine its effects on complexes containing either cadherin or the adenomatous polyposis coli (APC) protein. The results show that amino-terminal deletion of beta-catenin results in a protein with increased stability that acts in a dominant fashion with respect to wild-type beta-catenin. Constitutive expression in AtT20 cells of a beta-catenin lacking 89 N-terminal amino acids (deltaN89beta-catenin) resulted in severely reduced levels of the more labile wild-type beta-catenin. The mutant beta-catenin was expressed at endogenous levels but displaced the vast majority of wild-type beta-catenin associated with N-cadherin. The deltaN89beta-catenin accumulated on the APC protein to a level 10-fold over that of wild-type beta-catenin and recruited a kinase into the APC complex. The kinase was highly active toward APC in vitro and promoted a sodium dodecyl sulfate gel band shift that was also evident for endogenous APC from cells expressing the mutant beta-catenin. Unlike wild-type beta-catenin, which partitions solely as part of a high-molecular-weight complex, the deltaN89 mutant protein also fractionated as a stable monomer, indicating that it had escaped the requirement to associate with other proteins. That similar N-terminal mutants of beta-catenin have been implicated in cellular transformation suggests that their abnormal association with APC may, in part, be responsible for this phenotype.     

A Self-Tester for Linear Functions over the Integers with an Elementary Proof of Correctness

We present simple, self-contained proofs of correctness for algorithms for linearity testing and program checking of linear functions on finite subsets of integers represented as n-bit numbers. In addition we explore a generalization of self-testing to homomorphisms on a multidimensional vector space. We show that our self-testing algorithm for the univariate case can be directly generalized to vector space domains. The number of queries made by our algorithms is independent of domain size.