New Coherence and RIP Analysis for Weak Orthogonal Matching Pursuit

In this paper we define a new coherence index, named the global 2-coherence, of a given dictionary and study its relationship with the traditional mutual coherence and the restricted isometry constant. By exploring this relationship, we obtain more general results on sparse signal reconstruction using greedy algorithms in the compressive sensing (CS) framework. In particular, we obtain an improved bound over the best known results on the restricted isometry constant for successful recovery of sparse signals using orthogonal matching pursuit (OMP).Comment: arXiv admin note: substantial text overlap with arXiv:1307.194

High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels

The solution of the Volterra integral equation, $$( * )\qquad x(t) = g_1 (t) + \sqrt {t}g_2 (t) + \int _0^t \frac {K(t,s,x(s))} {\sqrt {t - s} } ds, \quad 0 \leqq t \leqq T,$$ where $g_1 (t)$, $g_2 (t)$ and $K(t,s,x)$ are smooth functions, can be represented as $x(t) = u(t) + \sqrt {t}v(t)$,$0 \leqq t \leqq T$, where $u(t)$, $v(t)$ are, smooth and satisfy a system of Volterra integral equations. In this paper, numerical schemes for the solution of (*) are suggested which calculate $x(t)$ via $u(t)$, $v(t)$ in a neighborhood of the origin and use (*) on the rest of the interval $0 \leqq t \leqq T$. In this way, methods of arbitrarily high order can be derived. As an example, schemes based on the product integration analogue of Simpson's rule are treated in detail. The schemes are shown to be convergent of order $h^{{7 / 2}}$. Asymptotic error estimates are derived in order to examine the numerical stability of the methods

Interconversion of Prony series for relaxation and creep

Various algorithms have been proposed to solve the interconversion equation of linear viscoelasticity when Prony series are used for the relaxation and creep moduli, G(t) and J(t). With respect to a Prony series for G(t), the key step in recovering the corresponding Prony series for J(t) is the determination of the coefficients {jk} of terms in J(t). Here, the need to solve a poorly conditioned matrix equation for the {jk} is circumvented by deriving elementary and easily evaluated analytic formulae for the {jk} in terms of the derivative dG(s)/ds of the Laplace transform G(s) of G(t)

Titanium and water-rich metamorphic olivine in high-pressure serpentinites from the Voltri Massif (Ligurian Alps, Italy): evidence for deep subduction of high-field strength and fluid-mobile elements

Titanium- and water-rich metamorphic olivine (Fo 86-88) is reported from partially dehydrated serpentinites from the Voltri complex, Ligurian Alps. The rocks are composed of mostly antigorite and olivine in addition to magnetite, chlorite, clinopyroxene and Ti-clinohumite. In situ secondary ion mass spectrometry (SIMS) data show that metamorphic olivine has very high and strongly correlated H2O (up to 0.7 wt%) and TiO2 contents (up to 0.85 wt%). Ti-rich olivine shows colourless to yellow pleochroism. Olivine associated with Ti-clinohumite contains low Ti, suggesting that Ti-rich olivine is not the breakdown product of Ti-clinohumite. Fourier transform infrared spectroscopy (FTIR) absorption spectra show peaks of serpentine, Ti-clinohumite and OH-related Si vacancies. Combining FTIR and SIMS data, we suggest the presence of clustered planar defects or nanoscale exsolutions of Ti-clinohumite in olivine. These defects or exsolutions contain more H2O (x similar to 0.1 in the formula 4Mg(2)SiO(4)center dot(1-x)Mg(OH, F)(2)center dot xTiO(2)) than Ti-clinohumite in the sample matrix (x = 0.34-0.46). In addition to TiO2 and H2O, secondary olivine contains significant Li (2-60 ppm), B (10-20 ppm), F (10-130 ppm) and Zr (0.9-2.1 ppm). It is enriched in B-11 (delta B-11 = +17 to +23 parts per thousand). Our data indicate that secondary olivine may play a significant role in transporting water, high-field strength and fluid-mobile elements into the deeper mantle as well as introduce significant B isotope anomalies. Release of hydrogen from H2O-rich olivine subducted into the deep mantle may result in strongly reduced mantle domains.OAIID:oai:osos.snu.ac.kr:snu2014-01/102/0000043439/1SEQ:1PERF_CD:SNU2014-01EVAL_ITEM_CD:102USER_ID:0000043439ADJUST_YN:YEMP_ID:A076886DEPT_CD:3345CITE_RATE:3.476FILENAME:de hoog et al-14-cmp-titanium- and water-ric.pdfDEPT_NM:지구환경과학부SCOPUS_YN:NCONFIRM:

Late Holocene climate and environmental changes in Kamchatka inferred from subfossil chironomid record.

This study presents a reconstruction of the Late Holocene climate in Kamchatka based on chironomid remains from a 332 cm long composite sediment core recovered from Dvuyurtochnoe Lake (Two-Yurts Lake, TYL) in central Kamchatka. The oldest recovered sediments date to about 4500 cal years BP. Chironomid head capsules from TYL reflect a rich and diverse fauna. An unknown morphotype of Tanytarsini, Tanytarsus type klein, was found in the lake sediments. Our analysis reveals four chironomid assemblage zones reflecting four different climatic periods in the Late Holocene. Between 4500 and 4000 cal years BP, the chironomid composition indicates a high lake level, well-oxygenated lake water conditions and close to modern temperatures (w13 �C). From 4000 to 1000 cal years BP, two consecutive warm intervals were recorded, with the highest reconstructed temperature reaching 16.8 �C between 3700 and 2800 cal years BP. Cooling trend, started around 1100 cal years BP led to low temperatures during the last stage of the Holocene. Comparison with other regional studies has shown that termination of cooling at the beginning of late Holocene is relatively synchronous in central Kamchatka, South Kurile, Bering and Japanese Islands and take place around 3700 cal years BP. From ca 3700 cal years BP to the last millennium, a newly strengthened climate continentality accompanied by general warming trend with minor cool excursions led to apparent spatial heterogeneity of climatic patterns in the region. Some timing differences in climatic changes reconstructed from chironomid record of TYL sediments and late Holocene events reconstructed from other sites and other proxies might be linked to differences in local forcing mechanisms or caused by the different degree of dating precision, the different temporal resolution, and the different sensitive responses of climate proxies to the climate variations. Further high-resolution stratigraphic studies in this region are needed to understand the spatially complex pattern of climate change in Holocene in Kamchatka and the surrounding region.

On the noise-resolution duality, Heisenberg uncertainty and Shannon's information

Several variations of the Heisenberg uncertainty inequality are derived on the basis of "noise-resolution duality" recently proposed by the authors. The same approach leads to a related inequality that provides an upper limit for the information capacity of imaging systems in terms of the number of imaging quanta (particles) used in the experiment. These results can be useful in the context of biomedical imaging constrained by the radiation dose delivered to the sample, or in imaging (e.g. astronomical) problems under "low light" conditions

The Stability of One-Step Schemes for First-Order Two-Point Boundary Value Problems

The stability of a finite difference scheme is related explicitly to the stability of the continuous problem being solved. At times, this gives materially better estimates for the stability constant than those obtained by the standard process of appealing to the stability of the numerical scheme for the associated initial value problem