l1 solution of linear inequalities

The numerical solution of a possible inconsistent system oflinear inequalities in the l₁ sense is considered. The non-differentiablel₁ norm minimization problem is approximated by a piecewisequadratic Huber smooth function. A continuation algorithm isdesigned to find an l₁ solution of the inequality system. Inthe case where the linear inequality system is consistent, asolution is obtained by solving any smoothed problem. Otherwise,the algorithm is shown to terminate in a finite number of iterations.We also consider an alternative smoothing scheme which sharessimilar properties with the first one, but results in an improvedcomputational performance of the continuation algorithm on inconsistentsystems. Numerical experiments are conducted to test the efficiencyof the algorithm.     

Spectral characteristics and synchrony in primary auditory-nerve fibers in response to pure-tone acoustic stimuli

Under pure-tone stimulation, the spectrum of the period histogram recorded from primary auditory-nerve fibers at low and medium frequencies contains components at DC, at the applied tone frequency (the fundamental), and at a small number of harmonics of the tone frequency. The magnitudes and phases of these spectral components are examined. The spectral magnitudes of the fundamental and various harmonic components generally bear a fixed proportionality to each other over a broad range of signal conditions and nerve-fiber characteristics. This implies that the shape of the underlying rectified wave remains essentially unchanged over a broad range of stimulus intensities. For high-frequency stimuli, the fundamental and harmonic components are substantially attenuated. We provide a theoretical basis for the decrease of the spectralcomponent magnitudes with increasing harmonic number. For low-frequency pure-tone signals, the decrease is caused principally by the uncertainty in the position of neural-event occurrences within the half-wave-rectified period histogram. The lower the stimulus frequency, the greater this time uncertainty and therefore the lower the frequency at which the spectral components begin to diminish. For high-frequency pure-tone signals, on the other hand, the decrease is caused principally by the frequency rolloff associated with nervespike time jitter (it is then called loss of phase locking or loss of synchrony). Since some of this jitter arises from noise in the auditory nerve, it can be minimized by using peak detection rather than level detection. Using a specially designed microcomputer that measures the times at which the peaks of the action potentials occur, we have demonstrated the presence of phase locking to tone frequencies as high as 18 kHz. The traditional view that phase locking is always lost above 6 kHz is clearly not valid. This indicates that the placeversus-periodicity dichotomy in auditory theory requires reexaraination.     

Dispersion-independent high-visibility quantum interference in ultrafast parametric down-conversion

We demonstrate the effective removal of intrinsic distinguishability between entangled-photon pairs in femtosecond spontaneous parametric down-conversion. High-visibility quantum interference is recovered (an increase to 96% from 17%) while preserving the high photon-flux density associated with the use of long nonlinear crystals. This new technique is expected to serve as a basic component in the preparation of multiphoton entangled states.     

Dead Ends and Detours En Route to Total Syntheses of the 1990s A list of abbreviations can be found at the end of the article

From the very beginning organic chemistry and total synthesis have been intimately joined. In fact, one of the first things that freshmen in organic chemistry learn is how to join two molecules together to obtain a more complex one. Of course they still have a long way to go to become fully mature synthetic chemists, but they must have the primary instinct to build molecules, as synthesis is the essence of organic chemistry. With the different points of view that actually coexist in the chemical community about the maturity of the science (art, or both) of organic synthesis, it is clear that nowadays we know how to make almost all of the most complex molecules ever isolated. The primary question is how easy is it to accomplish? For the readers of papers describing the total synthesis of either simple or complex molecules, it appears that the routes followed are, most of the time, smooth and free of troubles. The synthetic scheme written on paper is, apparently, done in the laboratory with few, if any, modifications and these, essentially, seem to be based on finding the optimal experimental conditions to effect the desired reaction. Failures in the planned synthetic scheme to achieve the goal, detours imposed by unexpected reactivity, or the absence of reactivity are almost never discussed, since they may diminish the value of the work reported. This review attempts to look at total synthesis from a different side; it will focus on troubles found during the synthetic work that cause detours from the original synthetic plan, or on the dead ends that eventually may force redesign. From there, the evolution from the original route to the final successful one that achieves the synthetic target will be presented. The syntheses discussed in this paper have been selected because they contain explicit information about the failures of the original synthetic plan, together with the evolution of the final route to the target molecule. Therefore, they contain a lot of useful negative information that may otherwise be lost.     

Experimental demonstration of three mutually orthogonal polarization states of entangled photons

Linearly polarized classical light can be expressed in a vertical and a horizontal component. Geometrically rotating vertically polarized light by 90 degrees will convert it to the orthogonal horizontal polarization. We have experimentally generated a two-photon state of light which evolves into an orthogonal state upon geometrical rotation by 60 degrees. Rotating this state by an additional 60 degrees will yield a state which is mutually orthogonal to the first two states. Generalizing this procedure, one can generate N+1 mutually orthogonal N-photon states that cyclicly evolve from one to another upon a geometric rotation by 180/(N+1) degrees.     

Broadband light generation by noncollinear parametric downconversion

Broadband light generation is demonstrated by noncollinear spontaneous parametric downconversion with a cw pump laser. By use of a suitable noncollinear phase-matching geometry and a tightly focused pump beam, downconverted signals that feature a bell-shaped spectral distribution with a bandwidth approaching 200 nm are obtained. As an application of the generated broadband light, submicrometer axial resolution in an optical coherence tomography scheme is demonstrated; a free-space resolution down to 0.8 microm was achieved.