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On the Limits of Depth Reduction . . . Finite Fields
"... In a surprising recent result, Gupta et al. [GKKS13b] have proved that over Q any nO(1)variate and ndegree polynomial in VP can also be computed by a depth three ΣΠΣ circuit of size 2O( n log3/2 n) 1. Over fixedsize finite fields, Grigoriev and Karpinski proved that any ΣΠΣ circuit that compute ..."
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In a surprising recent result, Gupta et al. [GKKS13b] have proved that over Q any nO(1)variate and ndegree polynomial in VP can also be computed by a depth three ΣΠΣ circuit of size 2O( n log3/2 n) 1. Over fixedsize finite fields, Grigoriev and Karpinski proved that any ΣΠΣ circuit
D:Int Agrophysics1 WlodarczykWlodarczyk.vp
, 2012
"... A b s t r a c t. The effect of intensive irrigation with wastewater on the zinc (Zn) and cadmium (Cd) concentration in soil solution was investigated. The experiment was parallel conducted on two soil profiles. The soil microcosms were watered with purified wastewater and purified wastewater with a ..."
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of their disposal In the soil zinc is found as ions bound by soil minerals and organic matter, in plants it regulates the metabolism of carbohydrate and protein compounds and occurs in enzymes. Excessive concentration of zinc inhibits the activity of proteins bonding calcium and affects the copper and iron economy
Ramprasad SaptharishiARITHMETIC CIRCUITS AND IDENTITY TESTING
"... We study the problem of polynomial identity testing (PIT) in arithmetic circuits. This is a fundamental problem in computational algebra and has been very well studied in the past few decades. Despite many efforts, a deterministic polynomial time algorithm is known only for restricted circuits of de ..."
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of depth 3. A recent result of Agrawal and Vinay show that PIT for depth 4 circuit is almost as hard as the general case, and hence explains why there is no progress beyond depth 3. The main contribution of this thesis is a new approach to designing a polynomial time algorithm for depth 3 circuits. We
RICE UNIVERSITY Regime Change: Sampling Rate vs. BitDepth in Compressive Sensing
, 2011
"... The compressive sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by exploiting inherent structure in natural and manmade signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of t ..."
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of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sampling rates is quantization, i.e., higher bitdepths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs
E.: Substitutionpermutation networks, pseudorandom functions, and natural proofs
 CRYPTO. Volume 7417 of Lecture Notes in Computer Science
, 2012
"... This paper takes a new step towards closing the troubling gap between pseudorandom functions (PRF) and their popular, boundedinputlength counterparts. This gap is both quantitative, because these counterparts are more efficient than PRF in various ways, and methodological, because these counterpar ..."
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Cited by 4 (1 self)
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between the “Natural Proofs barrier ” [Razborov & Rudich; JCSS ’97] and existing lower bounds, in three models: unboundeddepth circuits, TC 0 circuits, and Turing machines. In particular, the efficiency of the circuits computing F3 is related to a result by Allender and Koucky [JACM ’10] who show
Faulttolerant logical gates in quantum errorcorrecting codes∗
, 2014
"... Recently, Bravyi and König have shown that there is a tradeoff between faulttolerantly implementable logical gates and geometric locality of stabilizer codes. They consider localitypreserving operations which are implemented by a constantdepth geometricallylocal circuit and are thus faulttol ..."
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Cited by 1 (0 self)
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Recently, Bravyi and König have shown that there is a tradeoff between faulttolerantly implementable logical gates and geometric locality of stabilizer codes. They consider localitypreserving operations which are implemented by a constantdepth geometricallylocal circuit and are thus fault
Physics
, 2011
"... Ultracold atoms in optical lattices provide a highly controllable environment for the clean experimental realization of various model Hamiltonians from condensed matter and statistical physics. For example, the twocomponent BoseHubbard model, which reduces to an anisotropic spin1/2 Heisenberg m ..."
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Ultracold atoms in optical lattices provide a highly controllable environment for the clean experimental realization of various model Hamiltonians from condensed matter and statistical physics. For example, the twocomponent BoseHubbard model, which reduces to an anisotropic spin1/2 Heisenberg model in a certain limit and thus allows for the study of quantum magnetism, can be implemented by using bosons with two different internal states that couple differently to an optical lattice potential. In this thesis, I present our first experiments with twocomponent hyperfinestate mixtures of ultracold 87Rb atoms in a statedependent optical lattice, both in the strongly correlated regime and in the context of nonlinear atom optics. For the production of 87Rb BoseEinstein condensates we have developed a movingcoil transporter apparatus featuring a magnetic TOP trap which serves as a “phasespace funnel ” to load a
i i
"... , and we can say the Campbell bandwidth is the minimum average bandwidth for encoding the process across all possible distortion levels. IX. CONCLUSION We have presented two new derivations of the coefficient rate introduced by Campbell. One derivation solidifies its interpretation as a coefficien ..."
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, and we can say the Campbell bandwidth is the minimum average bandwidth for encoding the process across all possible distortion levels. IX. CONCLUSION We have presented two new derivations of the coefficient rate introduced by Campbell. One derivation solidifies its interpretation as a coefficient rate, and shows that the spectral entropy of a random process is proportional to the logarithm of the equivalent bandwidth of the smallest frequency band that contains most of the energy. The second derivation implies that the number of samples of a particular component should be proportional to the variance of that component. We discussed the implications of the latter result for realizationadaptive source coding and provided a connection with the familiar reverse waterfilling result from rate distortion theory. From the coefficient rate, we defined a quantity called the Campbell bandwidth of a random process, and we contrasted Fourier bandwidth, Shannon bandwidth, and Campbell bandwidth. ACKNOWLEDGMENT The authors are indebted to the referees for their constructive comments and insights.
c © World Scientic Publishing Company NOISE REDUCTION IN TERAHERTZ THIN FILM MEASUREMENTS USING A DOUBLE MODULATED DIFFERENTIAL TECHNIQUE
, 2002
"... Differential terahertz (THz) timedomain spectroscopy (TDS) is a technique for decreasing noise levels in THz thin film characterization experiments. Characterizing thin films in the GHz to THz range is critical for the development of fast integrated circuits and photonic systems, and is potentiall ..."
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Differential terahertz (THz) timedomain spectroscopy (TDS) is a technique for decreasing noise levels in THz thin film characterization experiments. Characterizing thin films in the GHz to THz range is critical for the development of fast integrated circuits and photonic systems
Results 1  10
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38