International Business Machines Corporation

Geoffrey Grinstein

Neil Adam Gershenfeld

Yuhai Tu

Glenn Allen Held

Techniques for analyzing gene expression levels are provided. In one aspect of the invention, the technique provides a method for determining a concentration level of a target nucleic acid, the target nucleic acid comprising at least one target oligonucleotide. The method determines (i) a measure of affinity value of the target oligonucleotide with a probe oligonucleotide; and (ii) a hybridization intensity value for the target oligonucleotide and the probe oligonucleotide at a probe spot. The measure of affinity value and the hybridization intensity value are used to determine the concentration level of the target nucleic acid.

Method and apparatus for determining gene expression levels

A communication and/or measurement system includes in a a transmitter an analog feedback system that modulates a pseudo-random noise signal with a message signal to produce a wideband signal for transmission. A receiver, which demodulates the wideband signal to recover the message signal, includes an associated analog feedback system that reproduces the noise signal based on the received signal. The analog feedback systems (AFS) are continuous-time generalizations of a linear feedback shift register ('LFSR'). The AFS are characterized by a function that agrees with the function that characterizes the LFSR, at the points at which that function is defined. Further, the AFS characterizing function has stable periodic orbits at these values, and the stable periodic orbits are attractors. The AFS thus produces a signal that relaxes on to a nearest periodic orbit that generalizes to continuous time the maximal sequence produced by the corresponding LFSR. The AFS in the transmitter, which operates in accordance with a harmonic oscillator, is characterized by the following differential equation: ##EQU1## where the .alpha..sub.i 's are the coefficients of the maximum length polynomial used to produce the maximal sequence. The AFS in the receiver is characterized by the following differential equation: ##EQU2##

System employing continuous-time dissipative pseudorandom dynamics for

A communication and/or measurement system includes a transmitter that modulates a pseudo-random noise signal with a message signal to produce a wideband signal for transmission. A receiver, which demodulates the wideband signal to recover the message signal, includes an 'analog' feedback shift register that reproduces the noise signal based on samples of the received signal. The AFSR is characterized by a function that agrees with the function that characterizes the LFSR, at the points at which that function is defined. Further, the AFSR characterizing function has stable fixed points at these values, i.e., it has a slope of less than one in these regions. Specifically, the AFSR's function has stable fixed points at integer values and unstable fixed points at half-integer values and, the stable fixed points act as attractors. The AFSR thus produces a sequence that relaxes to the nearest integer-valued sequence. In one embodiment in which signal values that represent binary values are -1 and +1, the coupling circuitry compares the quantity .vertline.(.vertline.S.sub.n .vertline.-1).vertline. with a predetermined maximum value. If the quantity exceeds the maximum value, which indicates that the received signal sample provides a poor estimate of the transmitter LFSR state, the coupling circuitry uses the feedback signal y.sub.n to update the register. Otherwise, the coupling circuitry uses as an update signal y'.sub.n =(1-.epsilon.)y.sub.n +.epsilon.sgnS.sub.n, where sgnS.sub.n represents the sign of the received signal sample.

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Yorktown Heights, NY, United States of America

Geoffrey Grinstein