Spl Rarr Research Articles

Noise stability of functions with low influences: Invariance and optimality

In this paper, we study functions with low influences on product probability spaces. The analysis of Boolean functions f {-1, 1}/sup n/ /spl rarr/ {-1, 1} with low influences has become a central problem in discrete Fourier analysis. is motivated by fundamental questions arising from the construction of probabilistically checkable proofs in theoretical computer science and from problems in the theory of social choice in economics. We prove an invariance principle for multilinear polynomials with low influences and bounded degree; it shows that under mild conditions the distribution of such polynomials is essentially invariant for all product spaces. Ours is one of the very few known non-linear invariance principles. has the advantage that its proof is simple and that the error bounds are explicit. We also show that the assumption of bounded degree can be eliminated if the polynomials are slightly smoothed; this extension is essential for our applications to noise stability -type problems. In particular; as applications of the invariance principle we prove two conjectures: the Majority Is Stablest conjecture [29] from theoretical computer science, which was the original motivation for this work, and the It Ain't Till It's Over conjecture [27] from social choice theory. The Majority Is Stablest conjecture and its generalizations proven here, in conjunction with the Unique Games Conjecture and its variants, imply a number of (optimal) inapproximability results for graph problems.

High-speed automatic microscopy for real time tracks reconstruction in nuclear emulsion

The Oscillation Project with Emulsion-tRacking Apparatus (OPERA) experiment will use a massive nuclear emulsion detector to search for /spl nu//sub /spl mu///spl rarr//spl nu//sub /spl tau// oscillation by identifying /spl tau/ leptons through the direct detection of their decay topology. The feasibility of experiments using a large mass emulsion detector is linked to the impressive progress under way in the development of automatic emulsion analysis. A new generation of scanning systems requires the development of fast automatic microscopes for emulsion scanning and image analysis to reconstruct tracks of elementary particles. The paper presents the European Scanning System (ESS) developed in the framework of OPERA collaboration.

Bounds on expansion in LZ'77-like coding

We investigate the maximum increase in number of phrases that results from changing k consecutive symbols in a string x having length n parsed using an LZ'77-like algorithm. We consider a class of compression algorithms that partition a sequence into a collection y of nonoverlapping, variable-length phrases and encode them. Each phrase either is a singleton or matches a substring that starts to its left. We show that changing a single symbol of x in position i can yield an expansion that is of order O(n-i)/sup 2/3/ as (n-i)/spl rarr//spl infin/. Our lower bound requires an alphabet size of O(n-i)/sup 1/3/. We also show that changing k consecutive symbols starting from position i can yield an expansion having a similar but somewhat more involved form. The paper contains both analytically derived upper and lower bounds, and algorithms for numerically computing tighter bounds. While deriving the bounds, we provide a detailed analysis of how expansion can arise when changing consecutive symbols. This problem is motivated by management policies for computer systems, such as the IBM Memory eXpansion Technology (MXT) or the IBM iSeries compressed disks, that use LZ'77-like coding on small compression units, such as 1-4 kbyte, and store the compressed data in memory or on disk tracks. Here, when a change of a portion of the compression unit occurs, for example, an L2 cache line, or a 512-byte disk sector, the data is recompressed and potentially stored in a different location. Knowing the maximum expansion, rather than the average expansion, is an important factor for designing policies for allocation and management of memory or disk space.

How to fool an unbounded adversary with a short key

The symmetric encryption problem which manifests itself when two parties must securely transmit a message m with a short shared secret key is considered in conjunction with a computationally unbounded adversary. As the adversary is unbounded, any encryption scheme must leak information about m; in particular, the mutual information between m and its ciphertext cannot be zero. Despite this, a family of encryption schemes is presented that guarantee that for any message space in {0,1}/sup n/ with minimum entropy n-/spl lscr/ and for any Boolean function h:{0,1}/sup n/ /spl rarr/ {0,1}, no adversary can predict h(m) from the ciphertext of m with more than 1/n/sup /spl omega/(1)/ advantage; this is achieved with keys of length /spl lscr/+/spl omega/(logn). In general, keys of length /spl lscr/+s yield a bound of 2/sup -/spl Theta/(s)/ on the advantage. These encryption schemes rely on no unproven assumptions and can be implemented efficiently. Applications of this to cryptosystems based on complexity-theoretic assumptions are discussed and, in addition, a simplified proof of a fundamental "elision lemma" of Goldwasser and Micali is provided.

Monomial bent functions

In this correspondence, we focus on bent functions of the form F(2/sup n/) /spl rarr/ F(2) where x /spl rarr/ Tr(/spl alpha/x/sup d/). The main contribution of this correspondence is, that we prove that for n=4r, r odd, the exponent d=(2/sup r/+1)/sup 2/ allows the construction of bent functions. This open question has been posed by Canteaut based on computer experiments. As a consequence for each of the well understood families of bent functions, we now know an exponent d that yields to bent functions of the given type.

The Influence of Pump Wavelength on Er:YAG Green-Emitting Laser Characteristics

Mathematical modeling is used to study the influence of pump wavelength on the emission of an Er(0.5 at.%):YAG laser on the transition /sup 4/S/sub 3/2//spl rarr//sup 4/I/sub 15/2/ (561 nm). Three pump wavelengths (direct pumping: 488 nm, upconversion pumping: 800 and 810 nm) are investigated and the corresponding laser emission regimes are discussed. For upconversion pumping, we find an optimum pump wavelength and optimum resonator losses for lowering of the continuous-wave emission threshold.

Simultaneous measurement of strain (to 2000 /spl mu//spl epsiv/) and temperature (to 600/spl deg/C) using a combined Sb-Er-Ge-codoped fiber-fluorescence and grating-based technique

An optical fiber-based sensing scheme for the simultaneous measurement of strain and temperature over a wider range has been demonstrated by writing a grating with very high reflectivity in a 10-cm-long specially fabricated antimony-erbium-germanium (Sb-Er-Ge)-doped silica fiber. The scheme exploits the grating sensitivity to both strain and temperature in association with the temperature-dependent peak power ratio of the two fluorescence peaks around 1535 and 1552 nm of the amplified spontaneous emission due to /sup 4/I/sub 13/2//spl rarr//sup 4/I/sub 15/2/ transition arising from the presence of erbium ions in the fiber core, using a 980-nm laser diode as a pumping source. The sensor created using this fiber can be used for the simultaneous measurement of strain and temperature over the wide ranges of 0-2000 /spl mu//spl epsiv/ and 20/spl deg/C-600/spl deg/C, with root-mean-square errors of 36 /spl mu//spl epsiv/ and 2.8/spl deg/C, respectively.

Optically active erbium-doped waveguides fabricated using a single-sol-gel-deposition technique

We present the results of optical-characterization experiments conducted on optically active erbium-doped waveguides. Using selected characterization results presented in this paper and a simple analysis, the device operation is evaluated. Each of the core and the cladding layers were individually fabricated using a single sol-gel deposition. These are, to the best of our knowledge, the first optically active waveguides to be fabricated in such a way. Characterization results include gain, fluorescence-lifetime, waveguide-loss, polarization-dependent-loss (PDL), and erbium-absorption measurements. Relative gains of over 1 dB/spl middot/cm/sup -1/ were measured. Fluorescence lifetimes of the /sup 4/I/sub 13/2/ /spl rarr/ /sup 4/I/sub 15/2/ transition as high as 5.6 ms were observed. Waveguide losses as low as 0.13 dB/spl middot/cm/sup -1/ were measured.

On the optical behavior of the electromagnetic field excited by a semi-infinite electric traveling-wave current

A closed-form solution for the spatial distribution of the electromagnetic field excited by an electric traveling-wave current source is presented. Incomplete Hankel and modified Bessel functions are employed to represent progressive and evanescent wave fields, respectively. It is shown that these fields are expressed in terms of spherical and cylindrical waves exhibiting optical character. Using the properties of the incomplete Hankel and modified Bessel functions, the spatial regions where the fields exist in optical sense are determined. It is shown that different shadow boundaries (SBs), featuring complex shapes, identify discontinuity surfaces for the geometrical optics (GO) field. Three surfaces, one being the well-know Keller's cone, are found to describe in the general case the SBs for both the progressive and the evanescent wave fields. It is demonstrated that these surfaces collapse to the Keller's cone surface in the limit of /spl beta//spl rarr//spl infin/.

The Empirical Distribution of Rate-Constrained Source Codes

Let X = (X/sub 1/,...) be a stationary ergodic finite-alphabet source, X/sup n/ denote its first n symbols, and Y/sup n/ be the codeword assigned to X/sup n/ by a lossy source code. The empirical kth-order joint distribution Q/spl circ//sup k/[X/sup n/,Y/sup n//spl rceil/(x/sup k/,y/sup k/) is defined as the frequency of appearances of pairs of k-strings (x/sup k/,y/sup k/) along the pair (X/sup n/,Y/sup n/). Our main interest is in the sample behavior of this (random) distribution. Letting I(Q/sup k/) denote the mutual information I(X/sup k/;Y/sup k/) when (X/sup k/,Y/sup k/)/spl sim/Q/sup k/ we show that for any (sequence of) lossy source code(s) of rate /spl les/R lim sup/sub n/spl rarr//spl infin//(1/k)I(Q/spl circ//sup k/[X/sup n/,Y/sup n//spl rfloor/) /spl les/R+(1/k)H (X/sub 1//sup k/)-H~(X) a.s. where H~(X) denotes the entropy rate of X. This is shown to imply, for a large class of sources including all independent and identically distributed (i.i.d.). sources and all sources satisfying the Shannon lower bound with equality, that for any sequence of codes which is good in the sense of asymptotically attaining a point on the rate distortion curve Q/spl circ//sup k/[X/sup n/,Y/sup n//spl rfloor//spl rArr//sup d/P(X/sup k/,Y~/sup k/) a.s. whenever P(/sub X//sup k//sub ,Y//sup k/) is the unique distribution attaining the minimum in the definition of the kth-order rate distortion function. Consequences of these results include a new proof of Kieffer's sample converse to lossy source coding, as well as performance bounds for compression-based denoisers.

High-Performance InGaP/GaAs HBTs With Compositionally Graded Bases Grown by Solid-Source MBE

N-p-n InGaP/GaAs heterojunction bipolar transistors (HBTs) with compositionally graded In/sub x/Ga/sub 1-x/As (Be doped) bases have been successfully grown by solid-source molecular beam Epitaxy (SSMBE) using a gallium phosphide (GaP) decomposition source. In this paper, the dc and RF characteristics of HBTs with different indium mole fractions in the graded In/sub x/Ga/sub 1-x/As base (x:0 /spl rarr/ ;0.1 and x:0 /spl rarr/ 0.05) are measured to investigate optimum-grading profiles. The measured average current gains, /spl beta/s of a control sample, a 10% graded-base sample and a 5% graded-base sample, are 162, 397 and 362, respectively. To our knowledge, these current gains are the highest values ever reported in compositionally graded-base InGaP/GaAs HBTs with a base sheet resistance R/sub sh/ of /spl sim/200 /spl Omega//sq establishing a new benchmark for InGaP/GaAs HBTs. Furthermore, these compositionally graded-base HBTs show higher unity current/gain cutoff frequency, f/sub T/ and maximum oscillation frequency, f/sub max/. Compared to the control sample with the same base thickness, the base transit time /spl tau//sub B/ of the graded sample is reduced by /spl sim/15% to /spl sim/20% by the induced built-in potential, resulting in an increase of f/sub max/ from 16 to 18.5 GHz in a device with an emitter size of 10/spl times/10 /spl mu/m/sup 2/. Additionally, for the 5% graded-base sample, with a 5/spl times/5 /spl mu/m/sup 2/ emitter region, f/sub T/ and f/sub max/ are 16.3 and 33.8 GHz, respectively, under low-level collector current. These results demonstrate that InGaP/GaAs HBTs with In/sub x/Ga/sub 1-x/As graded-base layers (x:0 /spl rarr/ 0.05) have the potential for high-speed analogue to digital converters.

Improved determination of coastal water constituent concentrations from MERIS data

The algorithm to derive the concentrations of coastal (case 2) water constituents from the Medium Resolution Imaging Spectrometer (European Space Agency satellite ENVISAT) is based on neural network (NN) technology. The NN not only transforms water leaving radiance reflectances with high efficiency into concentrations but also checks if its input is in the domain of reflectance spectra which were simulated for the training of the NN. Two NNs are trained with simulated reflectances: (1) invNN to emulate the inverse model (reflectances, geometry) /spl rarr/ concentrations and (2) forwNN to emulate the forward model (concentrations, geometry) /spl rarr/ reflectances. The invNN is used to obtain an estimate of the concentrations. These concentrations are fed into the forwNN, and the derived reflectances are compared with the measured reflectances. Deviations above a threshold are flagged. The paper describes a further improvement: the result obtained by invNN is used as a first guess to start a minimization procedure, which uses the forwNN iteratively to minimize the difference between the calculated reflectances and the measured ones. The procedure is very fast as it takes advantage of the Jacobian which is a byproduct of the NN calculation.

High-power continuous-wave intracavity frequency-doubled Nd:GdVO/sub 4/-LBO laser under diode pumping into the emitting level

The continuous-wave high power laser emission of Nd:GdVO/sub 4/ at the fundamental wavelength of 1.06 /spl mu/m and its 531-nm second harmonic obtained by intracavity frequency doubling with an LBO nonlinear crystal is investigated under pumping by diode laser at 808 nm (on the /sup 4/I/sub 9/2//spl rarr//sup 4/F/sub 5/2/ transition) and 879 nm (on the /sup 4/I/sub 9/2//spl rarr//sup 4/F/sub 3/2/ transition). It is shown that, in spite of a lower absorption at 879 nm, the infrared emission is comparable under these two wavelengths of pump. The green emission performances were, however, improved by the 879 nm pump: 5.1 W at 531 nm with M/sup 2/=1.46 and 0.31 overall optical-to-optical efficiency was obtained from a 3-mm-thick 1-at.% Nd:GdVO/sub 4/ laser medium and a 10-mm-long LBO nonlinear crystal in a Z-type cavity for 16.5 W pump power. In similar conditions, the maximum green power for the 808 nm pump was 4.4 W, with 0.26 overall optical-to-optical efficiency and M/sup 2/=3.40 beam quality; at this pump wavelength the green emission shows evident saturation for pump power in excess of 9.9 W. This behavior is connected with the enhanced heat generation under 809-nm pumping, as evidenced by the increased thermal lensing of the fundamental emission. A careful alignment of the laser enables emission almost free of chaotic intensity fluctuations.

Asymptotic Properties on Codeword Lengths of an Optimal FV Code for General Sources

This correspondence is concerned with asymptotic properties on the codeword length of a fixed-to-variable length code (FV code) for a general source {X/sup n/}/sub n=1//sup /spl infin// with a finite or countably infinite alphabet. Suppose that for each n /spl ges/ 1 X/sup n/ is encoded to a binary codeword /spl phi//sub n/(X/sup n/) of length l(/spl phi//sub n/(X/sup n/)). Letting /spl epsiv//sub n/ denote the decoding error probability, we consider the following two criteria on FV codes: i) /spl epsiv//sub n/ = 0 for all n /spl ges/ 1 and ii) lim sup/sub n/spl rarr//spl infin///spl epsiv//sub n/ /spl les/ /spl epsiv/ for an arbitrarily given /spl epsiv/ /spl isin/ [0,1). Under criterion i), we show that, if X/sup n/ is encoded by an arbitrary prefix-free FV code asymptotically achieving the entropy, 1/nl(/spl phi//sub n/(X/sup n/)) - 1/nlog/sub 2/ 1/PX/sup n/(X/sup n/) /spl rarr/ 0 in probability as n /spl rarr/ /spl infin/ under a certain condition, where P/sub X//sup n/ denotes the probability distribution of X/sup n/. Under criterion ii), we first determine the minimum rate achieved by FV codes. Next, we show that 1/nl(/spl phi//sub n/(X/sup n/)) of an arbitrary FV code achieving the minimum rate in a certain sense has a property similar to the lossless case.

Single-User Tracing and Disjointly Superimposed Codes

The zero-error capacity region of r-out-of-T user multiple-access OR channel is investigated. A family F of subsets of [n] = {1, ..., n} is an r-single-user-tracing superimposed code (r-SUT) if there exists such a single-user-tracing function /spl phi/:2/sup [n]/ /spl rarr/ F that for all F' /spl sube/ F with 1 /spl les/ |F'| /spl les/ r, /spl phi/(/spl cup//sub A/spl isin/F/'A) /spl isin/ F'. In this correspondence, we introduce the concept of these codes and give bounds on their rate. We also consider disjointly r-superimposed codes.

Granular Mappings

We are concerned with the granular representation of mappings (or experimental data) coming in the form R:R/spl rarr/[0,1] (for one-dimensional cases) and R:R/sup n//spl rarr/[0,1] (for multivariable cases) with R being a set of real numbers. As the name implies, a granular mapping is defined over information granules and maps them into a collection of granules expressed in some output space. The design of the granular mapping is discussed in the case of set and fuzzy set-based granulation. The proposed development is regarded as a two-phase process that comprises: 1) a definition of an interaction between information granules and experimental evidence or existing numeric mapping and 2) the use of these measures of interaction in building an explicit expression for the granular mapping. We show how to develop information granules in case of multidimensional numeric data by resorting to fuzzy clustering (fuzzy C-means). Experimental results serve as an illustration of the proposed approach.

On the Throughput of Multicasting With Incremental Forward Error Correction

In this paper, we consider a multicasting model that uses incremental forward error correction (FEC). In this model, there is one sender and r/sup n/ receivers. The sender uses an ideal (n,n(1-p),np) FEC code to code a group of n(1-p) data packets with additional np redundant packets so that any set of n(1-p) packets received by a receiver can be used to recover the original n(1-p) data packets. Packets to the receivers are lost independently with probability q. For this model, we prove several strong laws of large numbers for the asymptotic throughput as n /spl rarr/ /spl infin/. The asymptotic throughput is characterized by the unique solution of an equation in terms of p, q, and r. These strong laws not only provide theoretical justification for several important observations made in the literature, but also provide insights that might have impact on future design of multicasting protocols.

Piecewise fractional Brownian motion

Starting from fractional Brownian motion (fBm) of unique parameter H, a piecewise fractional Brownian motion (pfBm) of parameters H/sub o/, H/sub i/, and /spl gamma/ is defined. This new process has two spectral regimes: It behaves like an fBm of parameter H/sub o/ for low frequencies |/spl omega/|</spl gamma/ and like an fBm of parameter H/sub i/ for high frequencies |/spl omega/|/spl ges//spl gamma/. When H/sub o/=H/sub i/, or for limit cases /spl gamma//spl rarr/0 and /spl gamma//spl rarr//spl infin/, pfBm becomes classical fBm. It is shown that pfBm is a continuous, Gaussian, and nonstationary process having continuous, Gaussian, and stationary increments, namely, piecewise fractional Gaussian noises. The asymptotic self-similarity of pfBm is shown according to the considered regime: At large scale, the process is self-similar with parameter H/sub o/ and with parameter H/sub i/ at low scale.

Switching behavior of indium selenide-based phase-change memory cell

A cross-point-type phase-change random access memory (PRAM) cell without an access transistor is successfully fabricated with the In/sub 2/Se/sub 3/ resistor, which has much higher electrical resistivity than conventionally used Ge/sub 2/Sb/sub 2/Te/sub 5/ and of which electrical resistivity can be varied by the factor of 10/sup 5/ related with the degree of crystallization. Thus, the switching power can be delivered more effectively due to its higher electrical resistivity and device failure related to phase decomposition can be avoided since In/sub 2/Se/sub 3/ is single phase binary compound. The static-mode switching (dc test) is tested for the 5 /spl mu/m In/sub 2/Se/sub 3/ PRAM device. In the first sweep, the as-grown amorphous In/sub 2/Se/sub 3/ resistor showed the high resistance state at low voltage region. However, when it reached the threshold voltage, the electrical resistance of the device was drastically reduced through the formation of an electrically conducting path. The pulsed-mode switching of the 5 /spl mu/m In/sub 2/Se/sub 3/ PRAM device shows that the reset (crystalline /spl rarr/ amorphous) of the device was done with a 70 ns 3.1 V pulse and the set (amorphous /spl rarr/ crystalline) of the device was done with a 10 /spl mu/s 1.2 V pulse. Reading was accomplished by measuring the device resistance at 0.2 V and as high as 100 of switching dynamic range (ratio of R/sub high/ to R/sub low/) was observed.

Evidence of enhanced hypersensitive transition in erbium-doped fibers with different Al/sub 2/O/sub 3/ content

Precise spectroscopic absorption measurements of erbium-doped aluminosilicate fibers with different Al/sub 2/O/sub 3/ content were performed with the Judd-Ofelt analysis. From the Judd-Ofelt analysis, the /spl Omega//sub 2/ parameters of Er/sup 3+/ ions in these fibers were found to be about three times as large as those in aluminosilicate bulk glasses. The enhancement of the /spl Omega//sub 2/ parameters led to much stronger line strength of hypersensitive transitions in a fiber form than in a bulk glass form. This indicates that the distortion of the ligand field around the Er/sup 3+/ ions are more enhanced in a fiber form than in a bulk glass form. Furthermore, the /spl Omega//sub 6/ and the /spl Omega//sub 2/ parameters increased with an increase of q content up to 20 000 ppm. This Al/sub 2/O/sub 3/-content dependence of the /spl Omega//sub 6/ parameter was consistent with that of the line strength and the spontaneous emission probabilities of the transition corresponding to the /sup 4/I/sub 13/2//spl rarr//sup 4/I/sub 15/2/.