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2afb2f6069a5cc7be7b2cf4be6e37f18c73eb383 | subsection | 7 | 9 | Discussion and Conclusions | The method outlined here for correcting near-surface effects can be applied
to model frequencies before they are compared with observations. As in the
case of the Sun, we expect that the correction is independent of degree at
a given frequency, for low-degree acoustic modes, and thus the correction
determined from radi... | {
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6d234a48ea6c01898713602df167deee8424c7f4 | subsection | 8 | 9 | Discussion and Conclusions | This work was supported financially by the Danish Natural
Science Research Council and the Australian Research Council.lcrrlcl
6
0pc
Details of theoretical models
Model ID Star Mass Radius
Luminosity Age (Gyr) Reference
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053e49d596c3864ba9bde76cc61bc9836d830ff4 | abstract | 0 | 11 | Abstract | Non-gaussianity in the initial conditions of the universe is one of the most
powerful mechanisms to discriminate among the competing theories of the early
universe. Measurements using bispectrum of cosmic microwave background
anisotropies are limited by the cosmic variance, i.e. available number of
modes. Recent work h... | {
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8b1937ce4cd1fb24afe041b1aa5c594f622e9ea2 | subsection | 1 | 11 | Introduction | One of the major unsolved mysteries in cosmology is the creation of structure in
the universe. There are many competing theories that differ in their predictions, some of which are
accessible to cosmological observations today.
Inflation , , , , the oldest and most successful of these theories, predicts that correlatio... | {
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23dfefcf2104584b38a1a95a5b2a6da9553573e3 | subsection | 2 | 11 | Introduction | For example, the limits
should be improved significantly with the higher angular resolution Planck satellite, where
95% interval on f_{nl} of 30 is expected , but this will be limited by astrophysical uncertainties such as the
secondary anisotropies in CMB. Because the primordial CMB is damped on small scales it seems ... | {
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264dccbc1ada6369907e89a5185776fe84f3678d | subsection | 3 | 11 | Introduction | For a given multipole moment l the
k-space projection window is broad and the effect of f_{nl} extends to fairly high l, but it does not have a very characteristic
scale dependence that would allow one to separate it from the other parameters.Above discussion suggests, firstly, that
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104a01bb97570f8f586158c2de19555532112803 | subsection | 4 | 11 | Error Analysis | Let's assume we measure two tracers of matter density field, \delta _1 and \delta _2. They are both biased tracers of the underlying
matter density field \delta , \delta _i=b_i\delta , where b_1, b_2 is the large scale bias of two tracers. We can introduce relative bias \alpha =b_1/b_2 and the corresponding covariance ... | {
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f36a6b4309c3e2bd3c8bb4f08ba4020ba0de21cd | subsection | 5 | 11 | Error Analysis | Hence the relative error from a single mode is limited from below to 2^{1/2}
and this irreducible error is called the cosmic variance.We can also apply the above expressions to compute the diagonal component of the Fisher matrix for relative amplitude \alpha ,F_{\alpha \alpha }={\alpha ^2 X_2(1 +2X_2)+r^2X_1(1+X_2)+\al... | {
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3fc1b889cd3b2cf906ba623bdf1055257e8e9309 | subsection | 6 | 11 | Error Analysis | From the power spectrum estimator for a single mode we find
F_{f_{nl}f_{nl}}(P_2)=F_{P_2P_2}(2\Delta b(k)/bP_2)^2, which in the sampling variance limit gives\sigma _{f_{nl}}(P_2)={b \over 2^{1/2}\Delta b(k)}.Here we have assumed the non-gaussian correction is small to simplify the expressions. We have also assumed that... | {
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5441f67569d8ea3ab715d638248c653f5ae55762 | subsection | 7 | 11 | Error Analysis | We find{\sigma _{f_{nl}}^2(\alpha ) \over \sigma _{f_{nl}}^2(P_2)}=2(X_2+X_1/\alpha ^2)\left[{\Delta b /b \over \Delta b_1/b_1-\Delta b_2/b_2}\right]^2.If we assume we have two tracers, one unbiased, b_2=1, which contains no information on f_{nl}, and one biased with b_1=b
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981e360ba023a77878b6437122e651f9b4fd5f7e | subsection | 8 | 11 | Discussion | Let us apply the above derived relations to some examples of interest.
SDSS-III plans to do a spectroscopic survey of about 1.5\times 10^6 luminous red galaxies (LRGs) out to z \sim 0.7 over a quarter of
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db48332072101655b6e72b95210483aa20094cf5 | subsection | 9 | 11 | Discussion | Indeed, currently the strongest constraints come from the power spectrum method using
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c4be7640780df9a5de92e0cb874dace22d266f69 | subsection | 10 | 11 | Discussion | Still, the results suggest that the cross-correlation coefficient is indeed small on very large scales, with
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1a69f04368eda51afadb76b3ef7b25f880024c1a | abstract | 0 | 14 | Abstract | This report summarizes the most recent progress in measuring the angle gamma
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8c3fbd74263bb2380d5e3696964ff3c40497e497 | subsection | 1 | 14 | Introduction | Measurements of the Unitarity Triangle parameters allow to search for
New Physics effects at low energies. Most of such measurements are
currently performed at B factories — the e^+e^- machines operated
with the center-of-mass energy around 10 GeV at 焇(4S) resonance,
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f5ff1b409a95f19c3eb244d8fadc5a8da2b29769 | subsection | 2 | 14 | GLW analyses | The technique of measuring \phi _3 proposed by Gronau, London and Wyler
(and called GLW) makes use of D^0 decays to CP eigenstates,
such as K^+K^-, \pi ^+\pi ^- (CP-even) or K^0_S\pi ^0, K^0_S\phi
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f0c18bc7cebd23f862413c47370d0d042a359cf9 | subsection | 3 | 14 | GLW analyses | Here we assume that mixing and CP violation in the neutral D meson
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[Figure: Feynman diagrams for B^{-} \rightarrow D^{0}K^{-} andB^{-}\rightarrow \bar{D}^{0}K^{-}.]Instead of four observables \mathcal {R}_{1,2} and \mathcal {A}_{1,2}, only three
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0793bd96eb290e6738cacf04027f7bf6e2e4f595 | subsection | 4 | 14 | ADS analyses | The difficulties in the application of the GLW methods arise primarily
due to the small magnitude of the CP asymmetry of the
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f481f909bfd57167c8aedb885ad15b5a70aa0f8f | subsection | 5 | 14 | ADS analyses | Somewhat tighter constraint
can be obtained by using the \phi _3 and \delta _B measurements from the
Dalitz analyses (see Section ), and the recent CLEO-c measurement
of the strong phase
\delta _D=(22^{+11}_{-12}{}^{+9}_{-11})^{\circ } . | {
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] | [
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01f9e2de0f6e81fb1255cf23411f9788cac0ea09 | subsection | 6 | 14 | Dalitz plot analyses | A Dalitz plot analysis of a three-body final state of the D meson
allows one to obtain all the information required for determination
of \phi _3 in a single decay mode. The use of a Dalitz plot analysis
for the extraction of \phi _3 was first discussed
by D. Atwood, I. Dunietz and A. Soni, in the context of the ADS
met... | {
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7d35597dccd19552491f6b41ae881b020fc61c34 | subsection | 7 | 14 | Dalitz plot analyses | The preliminary
result obtained by Belle uses the data sample of 657M
B\overline{B} pairs and two modes, B^{\pm }\rightarrow DK^{\pm } and B^{\pm }\rightarrow D^{*}K^{\pm } with D^{*}\rightarrow D\pi ^0.
The neutral D meson is reconstructed in K^0_S\pi ^+\pi ^- final state
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4ab863c7ad3a2f5661f7461a3000de48c73381d1 | subsection | 8 | 14 | Dalitz plot analyses | Errors are statistical only.]The selection of B^{\pm }\rightarrow D^{(*)}K^{\pm } decays is based on the CM energy difference
\Delta E = \sum E_i - E_{\rm beam} and the beam-constrained B meson mass
M_{\rm bc} = \sqrt{E_{\rm beam}^2 - (\sum \vec{p}_i)^2}, where E_{\rm beam}
is the CM beam
energy, and E_i and \vec{p}_i ... | {
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} | 0807.1772 | Measurements of gamma/phi_3 at B factories | [
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] | [
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2ebcc3b67ed9c8b49f419982d9030d9b91c91040 | subsection | 9 | 14 | Dalitz plot analyses | The statistical confidence level of CP violation for the combined result
is (1-5.5\times 10^{-4}), or 3.5 standard deviations.
[Table: Results of the combination of B^{+}\rightarrow DK^{+} and B^{+}\rightarrow D^{*}K^{+} modes.]In contrast to Belle analysis, BaBar uses a smaller
data sample of 383M B\overline{B} pairs... | {
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66fb137572b3c2c1439502bcaf99887c5931cabc | subsection | 10 | 14 | Dalitz plot analyses | The values of the amplitude ratios are r_B=0.086\pm 0.035\pm 0.010\pm 0.011
for B^{\pm }\rightarrow DK^{\pm }, r^*_B=0.135\pm 0.051\pm 0.011\pm 0.005 for B^{\pm }\rightarrow D^{*}K^{\pm }, and
\kappa r_s=0.163^{+0.088}_{-0.105}\pm 0.037\pm 0.021
for B^{\pm }\rightarrow DK^{*\pm } (here \kappa accounts for possible nonr... | {
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} | 0807.1772 | Measurements of gamma/phi_3 at B factories | [
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236dcdf895f6d1373521cd289fa2ab883e3ebc9a | subsection | 11 | 14 | Other techniques | Several other decays involving neutral B mesons have been tried by
BaBar collaboration for \gamma measurement. One of them is the decay
B^0\rightarrow DK^*(892)^0, where the similar Dalitz analysis of the
three-body decay \overline{D}{}^0\rightarrow K^0_S\pi ^+\pi ^- is performed. Similarly to B^{\pm }\rightarrow DK^{\... | {
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] | [
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958e725ea2f8dc2460ac09c6185ea0db5cf79d96 | subsection | 12 | 14 | World average results | The world average \phi _3 results that include the latest measurements
presented in 2008, are available from UTfit group .
The probability density functions for \gamma and amplitude ratios r_B
are shown in Fig. REF . The world average values for these
parameters are \phi _3/\gamma =(81\pm 13)^{\circ }, r_B(DK)=0.098\pm... | {
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867ca4caf97a31cb492884d6bf476c33191ca896 | subsection | 13 | 14 | Conclusion | In the past year, many new measurements related to determination of
\phi _3/\gamma have appeared. As a result, strong evidence of a
direct CP violation in B^{\pm }\rightarrow DK^{\pm } decays is obtained for the first time
in a combination of B-factories results. Essential is that the amplitude
ratio r_B, which determi... | {
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} | 0807.1772 | Measurements of gamma/phi_3 at B factories | [
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2f3a9ebec94a82474c11db9c99495137e5e0af3c | abstract | 0 | 46 | Abstract | Interference between nodes is a critical impairment in mobile ad hoc networks
(MANETs). This paper studies the role of multiple antennas in mitigating such
interference. Specifically, a network is studied in which receivers apply
zero-forcing beamforming to cancel the strongest interferers. Assuming a
network with Pois... | {
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} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
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0820cf8e8ca29183eeb73092f873f18439d620f6 | subsection | 1 | 46 | Introduction | In a mobile ad hoc network (MANET), the mutual interference between nodes poses a fundamental limit on the throughput of peer-to-peer
communication. This paper studies mitigating the effect of interference by provisioning nodes with multiple
antennas. Specifically, each receiver uses zero-forcing beamforming to cancel ... | {
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b3ab9c993ea9432ab4cc76c6cbb001eb71463ea1 | subsection | 2 | 46 | Prior Work and Motivation | For Poisson distributed transmitters, TC was introduced in for single-antenna MANETs assuming fixed transmission power and an ALOHA-like medium access control (MAC) layer. TC has also been used to study opportunistic transmissions
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22e5a3798cd70557905df5b573ec8a6b93a449ce | subsection | 3 | 46 | Contributions and Organization | Our main contributions are summarized as follows.Assuming Poisson distributed transmitters and spatially independently and identically distributed (i.i.d.) Rayleigh fading channels, bounds on the probability of signal-to-interference ratio (SIR) outage are derived with either perfect or imperfect CSI. These bounds are ... | {
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ba39d6444cda1d3ee90b725197fe4893f262a8a9 | subsection | 4 | 46 | Network Model | The locations of potential transmitting nodes in a MANET are modeled as a 2-D Poisson point process with density \lambda _o following the common approach in the literature (see e.g., ). Time is slotted and in each time-slot potential transmitting
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069d53b7ee4223984f44f77da01541c7fe91ec1c | subsection | 5 | 46 | Channel Model | Let every node be equipped with N antennas, so that the link between each transmitter and receiver can be modeled as an N\times N multiple-input-multiple-output (MIMO) channel. We assume narrowband channels with frequency-flat block fading. Moreover, each
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7c1ef5e08fd97ecd960552170804bbde2b7b3b7b | subsection | 6 | 46 | Transmission Capacity | Correct decoding of received data packets requires the SIR to exceed a threshold \theta , which is identical for all receivers. In other words, the information rate for each link is equal to \log _2(1+\theta ) assuming Gaussian signaling. Note that, with everything else the same, the outage probability increases with t... | {
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b4c090ea36caaf74b52444fb480c69ca8f8198f7 | subsection | 7 | 46 | Zero-Forcing Beamforming | From the perspective of R_0, the interference channel from an interferer T is in effect a channel vector {\mathbf {h}}_T = r_T^{-\alpha /2}{\mathbf {G}}_T{\mathbf {f}}_T. For convenience, we refer to the channel norm J_T =\Vert {\mathbf {h}}_T\Vert ^2 as the pre-cancellation interference power for T. The receiver R_0 e... | {
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24ac8fa53c5ca7a6a557ebd370d678784740c66e | subsection | 8 | 46 | The Effective SIR Model: Perfect CSI | We first characterize the SIR at R_0 assuming perfect CSI and hence perfect cancellation of the L strongest interferers.
Since {\mathbf {G}}_0 is isotropic, {\mathbf {G}}_0{\mathbf {f}}_0 is an i.i.d. \mathcal {CN}(0,1) vector.
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"raw": "N. Jindal, J. G. Andrews, and S. Weber, “Multi-antenna communication in ad hoc networks: achieving MIMO gains with SIMO transmission,” submitted to IEEE Trans. on Communications.",
"source_ref... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
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1b431ae663cc8a1d71934fe67e3dcb6160500761 | subsection | 9 | 46 | The Effective SIR Model: Imperfect CSI | Without the assumption of perfect and readily available CSI,
receivers estimate the signal strength of their interferers and then identify the strongest ones by using the random training signature sequences inserted into transmitted signals . Subsequently, each receiver requests their strongest interferers to transmit ... | {
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"doi": "... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
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eaaab53047e1e8aff36f593698f770fa2b69b388 | subsection | 10 | 46 | The Effective SIR Model: Imperfect CSI | Using (REF ) and under the zero-forcing constraint: {\mathbf {v}}_0^\dagger \hat{{\mathbf {h}}}_T=0, \forall \ T\in \mathcal {T}, the residual interference at R_0 after beamforming, denoted as I_{R}, can be written asI_{R} &=& \sum _{T\in \mathcal {T}} {\mathbf {v}}_0^\dagger {\mathbf {h}}_Tx_T \\
&=& - \frac{1}{\sqrt{... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
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360eb07668f8720a3bd9d36dc8fb225f32d9118e | subsection | 11 | 46 | Transmission Capacity with Perfect CSI | This section focuses on the analysis of the outage probability and TC assuming prefect CSI. In particular, we derive the TC scaling with respect to the number of canceled interferers per node and the outage probability. | {
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} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
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d3247203849e895780aeb319ffcb093a0c45438b | subsection | 12 | 46 | Point Processes and Auxiliary Results | Since the L strongest interferers are canceled, we refer to
the (L+1)-st strongest interferer (in terms of pre-cancellation power) as
the primary interferer and denote it as T_P, whose pre-cancellation
interference power is J_P = \Vert {\mathbf {h}}_{T_P}\Vert ^2.
The interferers with smaller pre-cancellation interfere... | {
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"... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
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c9ef7c4b00fe2880e2f3d01cafa249277de1d5a1 | subsection | 13 | 46 | Point Processes and Auxiliary Results | From (REF ), \mu ^*(\mathcal {G}) can be obtained as\mu ^*(\mathcal {G})&=& \lambda \int _{t\in {R}^2}\int _g^\infty p(t, du) dt\\
&=& 2\pi \lambda \int _{0}^{\infty }\int _g^\infty r p(r, du) dr\\
&=& 2\pi \lambda \int _{0}^{\infty }r\Pr (J_T> g \mid |T| = r)drwhere (REF ) follows from the homogeneity of \Phi , and ()... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
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4c68fe5b86089a19ef5273cd746ae9429685d0d6 | subsection | 14 | 46 | Point Processes and Auxiliary Results | Then I_T and J_T are related by I_T = J_T\delta _T. The distributions of the random variables \lbrace \delta _T\rbrace are specified in the following lemma.Lemma 3
The set of random variables \lbrace \delta _T\mid T \in \Phi \backslash \mathcal {T}\rbrace follow i.i.d. beta(1, N-1) distributions as specified by the fo... | {
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... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
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ec2287ee88b65ec83a1780aa9950589143aca2dc | subsection | 15 | 46 | Bounds on Outage Probability | From (REF ), the outage probability P_{\mathsf {out}} can be written asP_{\mathsf {out}}=\Pr (I_S+ I_P> W\theta ^{-1}).It follows that P_{\mathsf {out}} can be lower bounded asP_{\mathsf {out}}\ge \Pr (I_P> W\theta ^{-1})by considering only the primary interferer, which is tight if the primary interfererence is dominan... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
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"Randall A. Berry"
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3546548a58f2dbf6c79d523ce6a64a0ec45d83da | subsection | 16 | 46 | Bounds on Outage Probability | Define the subsets \mathcal {D}_1 and \mathcal {D}_2 of the product space {R}^+\times {R}^+ as
\mathcal {D}_1 &=& \left\lbrace (w, g) \mid w\theta ^{-1} - \mathbb {E}[I_S\mid J_P = g]\le g \le w\theta ^{-1} \right\rbrace \\
\mathcal {D}_2 &=& \left\lbrace (w, g) \mid g < w \theta ^{-1} - \mathbb {E}[I_S\mid J_P = g] \... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
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6f41d546ac1c4e6376b4caf30dfae197b957619c | subsection | 17 | 46 | Bounds on Outage Probability | In particular, for M=11, CSI inaccuracy increases outage probability by less than two-fold.
[Figure: Compare outage probability for perfect and imperfect CSI given different transmitting node densities. The training-sequence length is M=\lbrace 3, 5, 11\rbrace and the number of canceled interferers per node is L=3.] | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
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"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
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b30ce11331cfc2b7d783806e8fb0b615dd9fc5ea | subsection | 18 | 46 | Asymptotic Transmission Capacity | Using the upper and lower bounds described in Lemma REF , the TC
scaling is analyzed for a large number of canceled interferers per node (L\rightarrow \infty ) or varnishing outage probability (\epsilon \rightarrow 0) as follows.Increasing the number of antennas at each receiver allows more interferers to be canceled, ... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
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926ba8652290344737de6c626d3a1a0aeca6ff25 | subsection | 19 | 46 | Asymptotic Transmission Capacity | If L+1> \alpha , for sufficiently small \lambda ,
\kappa _1\le \frac{\epsilon }{\lambda ^{L+1}} \quad \textrm {and}\quad \frac{\epsilon }{\lambda ^{\alpha }}\le \kappa _3
where
\kappa _3 = \frac{8\theta ^2\nu ^\alpha \Gamma (L-\alpha +2)\mathbb {E}[W^{-2}]}{N(N+1)(\alpha -1)\Gamma (L+1)}.Proof:
See Appendix REF .
... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
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d6d55dde162d8943c2c70213550b52b7e1f1e3e2 | subsection | 20 | 46 | Asymptotic Transmission Capacity | Reducing the outage probability by two orders of magnitude decreases the TC by 10, 3.2, and 1.8-fold in the case of 1, 3 and 7 canceled interferers per node, respectively.
Last, from simulation results in Section , the TC scaling in Theorem REF is observed to also hold for outage probabilities of practical interest (\e... | {
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"raw": "P. Gupta and P. R. Kumar, “The capacity of wireless networks,” IEEE Trans. on Inform. Theory, vol. 46, pp. 388–404, Mar. 2000.",
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... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
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b18c20da972f795805c3d8f7ce507fc5769e6fdd | subsection | 21 | 46 | Transmission Capacity with Imperfect CSI | This section addresses the effect of imperfect CSI. First, consider the scenario where the network remains unchanged except that the CSI is imperfect and
the users have to relax their quality-of-service (QoS) requirements, namely to tolerate higher outage probability represented by \tilde{P}_{\mathsf {out}} and to lowe... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
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23bcc0c6cf68cdc06a0fc4b9b59a161f11a71d9b | subsection | 22 | 46 | Transmission Capacity with Imperfect CSI | Also, the upper-bound in (REF ) suggests that the normalized capacity loss is more sensitive to the variation of \vartheta _p if \epsilon is large and \vartheta _b if \log _2(1+\theta ) is small.Next, for small outage probability, the required training sequence length is derived for achieving the same TC scaling as for... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
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4ae6832b4d24ac491d70a57c5803501be57aabbe | subsection | 23 | 46 | Simulation and Discussion | In this section, the bounds on outage probability and TC are evaluated using Monte Carlo simulation. The procedure for simulating a MANET follows that in . The simulated ad hoc network lies on a two-dimensional disk and contains a number of transmitter-receiver pairs, which is a Poisson random variable with the mean eq... | {
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Networks | [
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e8222eae417e750c7e1ec17ddda27e5909dc2362 | subsection | 24 | 46 | Scaling of Transmission Capacity | In Fig. REF , asymptotic bounds on TC in Theorem REF are compared with the exact values obtained by simulation for perfect CSI and the range of target outage probability \epsilon \in [10^{-5}, 10^{-1}]. The corresponding curves are identified using the legends “asymptotic upper bound", “asymptotic lower bound", and “si... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
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2de63101a534e1204754c798dc1a8ceb7592c7a2 | subsection | 25 | 46 | Transmission Capacity vs. Size of Antenna Array | In Fig. REF , the transmission capacity is plotted for an increasing number of canceled interferers per node assuming perfect CSI. Furthermore, different target outage probabilities, namely \epsilon = \lbrace 10^{-1}, 10^{-2}, 10^{-3}\rbrace , are considered.
As observed from Fig. REF , the cancellation of a few interf... | {
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} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
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0cd23e5c0d950910cd10bfea3195c4b442dbe5a7 | subsection | 26 | 46 | Proof for Lemma | Consider two disjoint measurable subsets \mathcal {B} and \mathcal {C} of \mathbb {R}^2\times [0, g). Let \Xi be the counting function such that \Xi (\mathcal {B}) gives the number of elements in \mathcal {B}. We first show that \Xi (\Pi (g)\cap \mathcal {B}) conditioned on J_P =g is a Poisson random variable as follow... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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4db18f53d68b089b8a1d5a6885098ce25f6eaf97 | subsection | 27 | 46 | Proof for Lemma | \end{aligned}Following a similar argument as for getting (REF ), we can obtain from (REF ) that\Pr (\Xi (\Pi (g)\cap \mathcal {B}) = m, \Xi (\Pi (g)\cap \mathcal {C})=n\mid J_P=g) &=& \Pr (\Xi (\Phi \cap \mathcal {B}) = m, \Xi (\Phi \cap \mathcal {C})=n)\\
&=& \Pr (\Xi (\Phi \cap \mathcal {B}) = m)\Pr (\Xi (\Phi \cap \... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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0.... | |
e5386295a57d8888bb5f0dde267c4e7cd918d149 | subsection | 28 | 46 | Proof for Lemma | It follows that\Pr (J_T> g \mid r_T = r) = \int _{r^\alpha g}^\infty \frac{u^{N-1}}{\Gamma (N)}e^{-u}du.Substituting (REF ) into () gives\mu ^*(\mathcal {G})
&=& 2\pi \lambda \int _{0}^{\infty }\int _{r^\alpha g}^\infty \frac{ru^{N-1}}{\Gamma (N)}e^{-u}du dr\\
&=& 2\pi \lambda \int _{0}^{\infty }\int _0^{\left(\frac{u}... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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-... | |
7c1db96bae6e0d94981603821239c974bf66772b | subsection | 29 | 46 | Proof for Lemma | We can write the effective channel vector as {\mathbf {h}}_T = J_T\tilde{{\mathbf {h}}}_T. The isotropicity of {\mathbf {h}}_T has two consequences: J_T and \tilde{{\mathbf {h}}}_T are independent and \tilde{{\mathbf {h}}}_T is also isotropic. Recall that J_T is the criterion for selecting interferers to cancel. Thus, ... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1204,
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"raw": "C. K. Au-Yeung and D. J. Love, “On the performance of random vector quantization limited feedback beamforming in a MISO system,” IEEE Trans. on Wireless Communications, vol. 6, pp. 458–462, Feb. 20... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
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] | 2,008 | en | Computer Science | [
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-0.... | |
93ef775de960d907058f095f357c756663658bb2 | subsection | 30 | 46 | Proof for Lemma | Given \mathcal {D}_1\cup \mathcal {D}_2 = \lbrace (w, g)\mid g < w\theta ^{-1}\rbrace , the second term of the P_{\mathsf {out}} upper bound in () can be expanded and then upper bounded as\Pr (I_S> W\theta ^{-1} - &J_P\mid J_P\le W\theta ^{-1})
\Pr (J_P\le W\theta ^{-1})\\
\le & \Pr ((W, J_P)\in \mathcal {D}_1) +
\Pr (... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
-0.03018447570502758,
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0.010872820392251015,
-0.029482511803507805,
-0.008... | |
a521f8ba703d1f24dea030054b11a404feebcd2b | subsection | 31 | 46 | Proof of Lemma | Define the sum pre-cancellation secondary interference power as J_S:= \sum _{T\in \Phi \backslash (\mathcal {T}\cup \lbrace T_P\rbrace )}J_T.
Using Lemma REF , the application of Campbell's Theorem gives that \mathbb {E}[J_S\,|\, J_P=g] &=& \lambda \int _{{R}^2} \int _0^g u p(|x|, du ) du dx\\
&=& 2\pi \lambda \int _0^... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 831,
"openalex_id": "",
"raw": "D. Stoyan, W. S. Kendall, and J. Mecke, Stochastic Gemoetry and its Applications. Wiley, 2nd ed., 1995.",
"source_ref_id": "2ee13d13c0e531c0c30fc8036cf680fefd78f887",
"start": 142
}
... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
-0.0317394845187664,
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0.05865700915455818,
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0.03750752657651901,
-0.009773625060915947,
-0.... | |
a4eb29d51f617a6cb2b1a7bcd923d0d62f212163 | subsection | 32 | 46 | Proof of Lemma | Substituting (REF ) into () gives the desired result in (REF ).Like (REF ), the conditional variance of J_S is obtained by applying Campbell's Theorem as follows\mathsf {var}(J_S\,|\, J_P=g) &=& 2\pi \lambda \int _0^\infty \int _{\left(\frac{\rho }{g}\right)^{\frac{1}{\alpha }}}^\infty r\left(r^{-\alpha }\rho \right)^2... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 764,
"openalex_id": "",
"raw": "J. F. C. Kingman, Poisson processes. Oxford University Press, 1993.",
"source_ref_id": "716e68d6357cc5e56eb9b9557bffaae6f6cb90f2",
"start": 553
},
{
"arxiv_id": "",
"... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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0.02230929583311081,
0.011246204376220703,
0.017334720119833946,
-0.01883014477789402,
0.0240... | |
07a4dc642c5c67a2078baeb37a5471433fcdd5bd | subsection | 33 | 46 | Proof of Lemma | This completes the proof.For \lambda \rightarrow 0, we can obtain from (REF ) thatP_{\mathsf {out}}^\ell (\lambda ) &=& \sum _{k=L+1}^\infty \frac{\left(\nu \lambda \theta ^{\frac{2}{\alpha }}\right)^k}{\Gamma (k+1)}\mathbb {E}\left[\left(\frac{W}{\delta _P}\right)^{-\frac{2k}{\alpha }}e^{-\nu \lambda \theta ^{\frac{2}... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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0.02461613528430462,
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0.029041850939393044,
-0.03186515346169472,
0.01957... | |
6112efac7acce679407d3c2c4690fa9c68338040 | subsection | 34 | 46 | Proof of Lemma | To derive the asymptotic expression for \Lambda _3 in (), it is split into two terms as \Lambda _3 = \Lambda _{3,1} + \Lambda _{3,2} where\Lambda _{3,i} = \iint \limits _{(w,g)\in \mathcal {D}_{2,i}}\min \left\lbrace \frac{\mathsf {var}(I \,|\, J_P=g)}{\left\lbrace w\theta ^{-1} - g -\mathbb {E}\left[I \,|\, J_P=g\righ... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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0.014377656392753124,
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0.024926356971263885,
-0.01661248691380024,
... | |
0a9cbb2065477be050e082dfb5681605166d3032 | subsection | 35 | 46 | Proof of Lemma | To simplify notation, define
\eta = \frac{8\theta ^2 }{N(N+1)(\alpha -1)\Gamma (L+1)}. | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
-0.027638649567961693,
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0.03302597254514694,
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... | |
08528fdf82745cfeafbdca2f000799a4760309bf | subsection | 36 | 46 | Proof of Lemma | Substituting the distribution functions in (REF ) and () into (REF ) gives\Lambda _{3,2} &\le & \frac{2}{\alpha }\eta (\nu \lambda )^{L+2} \int _0^\infty w^{-2}\int _0^{\frac{w \theta ^{-1} }{2} + O(\lambda )}g^{-\frac{2}{\alpha }(L+2)+1}e^{-\nu \lambda g^{-\frac{2}{\alpha }}} dgf_W(w)dw\\
&=& \eta (\nu \lambda )^\alph... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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0... | |
76998b19f735e70b0997411f7eb9a6a591aeb9d8 | subsection | 37 | 46 | Proof of Lemma | The second inequality in (REF ) follows.
For L-\alpha +1 \ge 0, \Gamma (L-\alpha +2) is finite and hence we obtain from (REF ) that\Lambda _{3,2} \le \kappa _3 \lambda ^\alpha + O(\lambda ^{\alpha + 1})where \kappa _3 is defined in the lemma statement.
Substituting (REF ), (), (REF ) and (REF ) into (REF ) gives the se... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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0.... | |
036b810acee9e2d2f3de461d1581f81e67ee7ab9 | subsection | 38 | 46 | Proof of Theorem | Given the distribution of J_P in (REF ),
and applying Campbell's Theorem, we obtain that\mathbb {E}[I_P] &=& \mathbb {E}[J_P]\mathbb {E}[\delta _P]\\
&=& \frac{2 (\nu \lambda )^{L+1}}{N \alpha \Gamma (L+1)} \int _0^\infty g^{-\frac{2(L+1)}{\alpha }} e^{-\nu \lambda g^{-\frac{2}{\alpha }}} dg\\
&=& \frac{\Gamma \left(L+... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1603,
"openalex_id": "",
"raw": "N. Jindal, J. G. Andrews, and S. Weber, “Multi-antenna communication in ad hoc networks: achieving MIMO gains with SIMO transmission,” submitted to IEEE Trans. on Communications.",
"source_re... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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-... | |
7915ac34a0ddfb810fc32e48ed70a5f072f0b1a7 | subsection | 39 | 46 | Proof of Theorem | Thus, the weakest interferer in \mathcal {U} corresponds to \acute{J} = \min _{T\in \mathcal {U}} J_T. Using above definitions,1-P_{\mathsf {out}}&\le & \Pr \left(\frac{W}{\sum _{T\in \mathcal {U}}J_T\delta _T}\ge \theta \right)\\
&\le & \Pr \left(\frac{W}{\acute{J}_T\sum _{T\in \mathcal {U}}\delta _T}\ge \theta \right... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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0.010088259354233742,
-0.... | |
67c676a9ac31806242f34aa84c56c4aaa9978c35 | subsection | 40 | 46 | Proof of Theorem | Thus, similar to (REF ), it can be obtained that\mathbb {E}[\acute{J}^{-1}] = \frac{\Gamma (2L+1+\frac{\alpha }{2})}{\Gamma (2L+1)(\nu \lambda )^{\frac{\alpha }{2}}}.Substituting the above equation into (REF ) gives\lambda \le \frac{1}{\nu }\left\lbrace \frac{\mathbb {E}[W]}{\theta (1-\epsilon )}\times \frac{\Gamma (2L... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 723,
"openalex_id": "",
"raw": "D. Kershaw, “Some extensions of W. Gautschi's inequalities for the Gamma function,” Math. of Computation, vol. 41, pp. 607–611, Oct. 1983.",
"source_ref_id": "3e9a9b385cdbb66f5be109c48a3b86ba7... | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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... | |
35f21849459dbc0483cd7b43624f5c6b20052973 | subsection | 41 | 46 | Proof of Theorem | Using Kershaw's inequality, for L > \left\lceil \frac{\alpha }{2}\right\rceil\left(L - \left\lceil \frac{\alpha }{2}\right\rceil +1 + \frac{\Delta \alpha }{2} \right)^{1-\Delta \alpha }< \frac{\Gamma \left(L - \lceil \frac{\alpha }{2}\rceil + 2\right)}{\Gamma \left(L+1 - \lceil \frac{\alpha }{2}\rceil + \Delta \alpha \... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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0.... | |
69a3a0258a8ddd50993a6cc6be802e58a1cff5a3 | subsection | 42 | 46 | Proof of Theorem | Since (N-L) is fixed,\lim _{L\rightarrow \infty }\mathbb {E}\left[\frac{1}{\sum _{T\in \mathcal {U}}\delta _T}\right] =1.Substituting (REF ) and (REF ) into (REF ) gives\limsup _{L\rightarrow \infty } \frac{\lambda }{L^{1-\frac{2}{\alpha }}} \le \frac{2}{\pi }\left\lbrace \frac{\mathbb {E}[W]}{\theta (1-\epsilon )}\rig... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
] | [
"cs.IT",
"math.IT"
] | 2,008 | en | Computer Science | [
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0.02... | |
f429f35fd8638714bdbe6c8402aa971a64d49062 | subsection | 43 | 46 | Proof of Theorem | \mathcal {CN}(0,1) elements, we obtain from (REF ) that conditioned on \Phi and \lbrace {\mathbf {h}}_T\rbrace ,\sigma _{R}^2 &\sim & \frac{1}{M} \sum _{T^{\prime }\in \Phi \backslash \mathcal {T}} I_{T^{\prime }} \sum _{T\in \mathcal {T}}z_{T}\\
&\sim & \frac{\zeta }{M}I_{\Sigma }where \lbrace z_T \rbrace are i.i.d. e... | {
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ab6594ec4871481af5bebc216c7f465e12c65bfe | subsection | 44 | 46 | Proof of Theorem | Moreover, given \theta = \left(1+\frac{Z}{M}\right)\tilde{\theta }, the rate loss is bounded as\Delta B &=& \log _2(1+\theta ) - \log _2\left(1+\frac{\theta }{1+\frac{Z}{M}}\right)\\
&\le & \log _2(1+\theta ) - \log _2\left(\frac{1+\theta }{1+\frac{Z}{M}}\right)\\
&=& \log _2\left(1+\frac{Z}{M}\right).From () and (REF ... | {
"cite_spans": []
} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
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8b643d5658d0537a75298709700dbc9096979625 | subsection | 45 | 46 | Proof of Theorem | Thus, it follows from (REF ) that for sufficiently small \epsilon ,\kappa _2^{-\frac{1}{L+1}}\le \frac{\tilde{C}(\epsilon )}{\log (1+\tilde{\theta })\epsilon ^{\frac{1}{L+1}}} \le \kappa _1^{-\frac{1}{L+1}}.As in Appendix REF , we set \theta = \left(1+\frac{Z}{M}\right)\tilde{\theta } with Z > 0 and thus () holds. Furt... | {
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} | 0807.1773 | Spatial Interference Cancellation for Multi-Antenna Mobile Ad Hoc
Networks | [
"Kaibin Huang",
"Jeffrey G. Andrews",
"Dongning Guo",
"Robert W. Heath,",
"Randall A. Berry"
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bdbd1d2d9b6a95269cf2355e166fea4429a14081 | abstract | 0 | 10 | Abstract | We have performed three dimensional nonlinear fluid simulations of electron
fluid turbulence at nanoscales in an unmagnetized warm dense plasma in which
mode coupling between wave function and electrostatic potential associated with
underlying electron plasma oscillations (EPOs) lead to nonlinear cascades in
inertial r... | {
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} | 10.1088/1367-2630/10/8/083007 | 0807.1774 | 3D Electron Fluid Turbulence at Nanoscales in Dense Plasmas | [
"Dastgeer Shaikh",
"P. K. Shukla"
] | [
"physics.plasm-ph",
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5aca0e1d0473feb0b5afed9a96b4019c8efbb49c | subsection | 1 | 10 | introduction | Studies of collective phenomena at nanoscales in dense matters are of
great importance in diverse areas of physics, including the fields of
plasmonics , , , , , semiconductors ,
nano-electromechanical systems , quantum-diodes ,
nanotubes and nanowires , quantum free electron lasers
, as well as astrophysical bodies , a... | {
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"raw": "W. L. Barnes, A. Dereux, and T. W. Ebbesen, Surface plasmon subwavelength optics. Nature (London) 424, 824 (2003).",
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"start":... | 10.1088/1367-2630/10/8/083007 | 0807.1774 | 3D Electron Fluid Turbulence at Nanoscales in Dense Plasmas | [
"Dastgeer Shaikh",
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ecaf4b2dc63720fdbd5bbe25b6c00d461e868f4b | subsection | 2 | 10 | Model equations | In dense quantum plasmas, the Wigner-Poisson (WP) model has been used
to derive a set of quantum hydrodynamic (QHD) equations in
the mean field approximation. The QHD equations include the continuity,
momentum and Poisson equations. The quantum nature appears in the electron
momentum equation through the pressure term,... | {
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{
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"doi": "",
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"raw": "G. Manfredi, How to model quantum plasmas. Fields Inst. Commun. 46, 263 (2005).",
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813cba9ccf910c1f6083f89674748ea29dad7585 | subsection | 3 | 10 | Model equations | We have introduced the notations \lambda _D=
(\epsilon _0 k_B T_F/n_0 e^2)^{1/2} \equiv V_F/\Omega _{pe} and \sqrt{H} =
\hbar \omega _{pe}/\sqrt{2} k_B T_F, where \epsilon _0 is the
electric permittivity, k_B is the Boltzmann constant and the Fermi electron temperature
k_B T_F = (\hbar ^2/2m_e)(3\pi ^2)^{1/3} n_0^{2/3}... | {
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"raw": "S. H. Glenzer, O. L. Landen, P. Neumayer, R. W. Lee, K. Widmann, S. W. Pollaine, R. J. Wallace, G. Gregori, A. Höll, T. Bornath, R. Thiele, V. Schwarz, W.-D. Kraeft, and R. Redmer, Observation of p... | 10.1088/1367-2630/10/8/083007 | 0807.1774 | 3D Electron Fluid Turbulence at Nanoscales in Dense Plasmas | [
"Dastgeer Shaikh",
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6d6878f597b1b71ed7f0630491b567aa1056ad62 | subsection | 4 | 10 | nonlinear 3D simulations of quantum plasmas | We have developed 3D fluid code to investigate nonlinear interactions
between multi-scales EPOs described by (1) and (2). Our 3D fluid code
is based on Fourier expansion of the bases using a fully de-aliased
pseudospectral numerical scheme . The nonlinear
de-convolution of Fourier modes is performed by computing the
no... | {
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"Dastgeer Shaikh",
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f45067d08e0467158f8dec64c96fcd6b2530c120 | subsection | 5 | 10 | nonlinear 3D simulations of quantum plasmas | Figures (c) and (d) depict the electron number density and the electrostaticpotential for H=0.01.]The localized initial turbulent spectral distribution, concentrated
at the lower wavenumbers, evolves in time following 3D nonlinear
electron plasma wave interactions. Since the initial energy is
localized in the large sca... | {
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"raw": "G. Murtaza and P. K. Shukla, Nonlinear generation of electromagnetic waves in a magnetoplasma. J. Plasma Phys. 31, 423 (1984).",
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78a3d5318306e2ae7dc33de09a9e5f8edfd047ef | subsection | 6 | 10 | nonlinear 3D simulations of quantum plasmas | On the other hand, 3D MHD
turbulence exhibits forward cascades of energy and an inverse cascade
of magnetic helicity. In these processes, the energy cascades towards
smaller length-scales, while the magnetic helicity in MHD transfers
spectral power towards larger length-scales. By contrast, the fluid
vorticity in 3D hy... | {
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ef112c3c60e8cbde057280fa2f9dc2562cb8c584 | subsection | 7 | 10 | nonlinear 3D simulations of quantum plasmas | Interestingly, smaller values of H corresponds to aneffective low diffusion coefficient. The latter characterizesthe presence of small scale turbulent eddies which results insuppression of the electron transport.] | {
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} | 10.1088/1367-2630/10/8/083007 | 0807.1774 | 3D Electron Fluid Turbulence at Nanoscales in Dense Plasmas | [
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9fcc97bcd2da6668bcbe6d1db00c6782e5299d9d | subsection | 8 | 10 | Electron transport caused by turbulent fields | We finally study the electron diffusion coefficient in the presence of
small and large scale turbulent EPOs. The effective electron diffusion
coefficient produced by the momentum transfer can be calculated from
D_{eff} = \int _0^\infty \langle {\bf P}({\bf r}, t) \cdot {\bf P}
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fcdacb9269967aabfd4a86f5ef1f2d000880b700 | subsection | 9 | 10 | Summary | In conclusion, we have presented results from 3D
nonlinear fluid simulations of the electron fluid turbulence at nanoscales
in an unmagnetized warm dense plasma. The mode couplings between the
electron wave function and the electrostatic potential associated with
the underlying electron plasma oscillations (EPOs) lead ... | {
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} | 10.1088/1367-2630/10/8/083007 | 0807.1774 | 3D Electron Fluid Turbulence at Nanoscales in Dense Plasmas | [
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bc4e04e083871877e5302cb073702b199760123d | abstract | 0 | 58 | Abstract | At Crypto'07, Goyal introduced the concept of Accountable Authority
Identity-Based Encryption as a convenient tool to reduce the amount of trust in
authorities in Identity-Based Encryption. In this model, if the Private Key
Generator (PKG) maliciously re-distributes users' decryption keys, it runs the
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} | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
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f80b4b9c454cbd17d7d8b73d5d30d5191770ca50 | subsection | 1 | 58 | Introduction | Identity-based cryptography, first proposed by Shamir ,
alleviates the need for digital certificates used in traditional
public-key infrastructures. In such systems, users' public keys are
public identifiers (e.g. email addresses) and the matching
private keys are derived by a trusted party called Private Key
Generator... | {
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ece492035e13571f1d72ed4996c380b65c8e70e6 | subsection | 2 | 58 | Introduction | For the usually required security level, ciphertexts contain more than 160 group
elements and decryption calculates
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aa649217b68d4bf3ce14a0b05544d921fb098668 | subsection | 3 | 58 | Introduction | In these regards, the key
generation protocol of {Goyal}-{2} makes use of
oblivious transfers (OT) in sub-protocols. It thus supports
concurrency whenever the underlying OT protocol does. As already
mentioned however, our
scheme features a much better efficiency than {Goyal}-{2}.
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-0.06743746250867844,
-0.01585238054394722,
-0.013479864224791527,
0.... | |
d810256da1fe318778d4a7579c7bf29dfbbcb266 | subsection | 4 | 58 | Background and Definitions | Syntactic definition and security model. We
recall the definition of A-IBE schemes and their security
properties as defined in .
An Accountable Authority Identity-Based Encryption scheme
(A-IBE) is a tuple
(\mathbf {Setup},\mathbf {Keygen},\mathbf {Encrypt},\mathbf {Decrypt},\mathbf {Trace})
of efficient algorithms or... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 128,
"openalex_id": "",
"raw": "V. Goyal. Reducing Trust in the PKG in Identity-Based Cryptosystems. In Crypto'07, LNCS 4622, pp. 430–447, 2007.",
"source_ref_id": "b84dc7b5bd5079ccf2f8967d900222c20b4f87ec",
"start": 4... | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
0.030557502061128616,
-0.014775055460631847,
-0.017217213287949562,
-0.020590445026755333,
0.008784136734902859,
-0.028893781825900078,
0.05955812707543373,
0.028466403484344482,
-0.027275850996375084,
0.02645162306725979,
-0.032541755586862564,
0.005124715622514486,
-0.0036384337581694126,
... | |
481d3d033d4f35cdd1993316a95c9f8bc184e49b | subsection | 5 | 58 | Background and Definitions | The
output of \mathbf {Trace} is either “PKG” or “User” depending
on which party is found guilty for having crafted \mathbb {D}.Goyal
formalized three security properties for A-IBE schemes. The first
one is the standard notion of privacy for IBE systems. As
for the
other ones, the FindKey game captures the
intractabili... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 255,
"openalex_id": "",
"raw": "D. Boneh, M. Franklin. Identity-Based Encryption from the Weil Pairing. In SIAM Journal of Computing 32(3), pp. 586–615, 2003, earlier version in Crypto'01, LNCS 2139, pp. 213–229, 2001.",
"so... | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
0.0021510119549930096,
0.015255404636263847,
-0.05260063707828522,
-0.006037326529622078,
0.004466019570827484,
-0.01414175983518362,
0.050495389848947525,
0.002059479709714651,
-0.01801663264632225,
0.024042516946792603,
-0.018748892471194267,
0.002377936150878668,
-0.026452871039509773,
... | |
428ced05be33c553c30d8d8463237469b2fda28d | subsection | 6 | 58 | Background and Definitions | We call this enhanced notion FindKey-CCA
(as opposed to the weaker one which we call FindKey-CPA).Finally, in the black-box model, instead of outputting a new
key d_{\mathsf {ID}}^{(2)}, the dishonest PKG comes up with a decryption
box \mathbb {D} that correctly decrypts ciphertexts intended for
\mathsf {ID} with non-n... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1864,
"openalex_id": "",
"raw": "R. Canetti, S. Halevi, J. Katz. A Forward-Secure Public-Key Encryption Scheme. In Eurocrypt'03, LNCS 2656, pp. 254–271, 2003.",
"source_ref_id": "95f2c72c0be82a1408cec85d584396ade465f367",
... | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.020551996305584908,
0.015852654352784157,
-0.038571231067180634,
0.007270249538123608,
0.001523853512480855,
-0.017378414049744606,
0.058589208871126175,
0.03677083179354668,
0.010253111831843853,
0.0343296155333519,
-0.029523469507694244,
-0.010008989833295345,
-0.047634247690439224,
0... | |
c6c06c7dd8512a60bafa7804917c1a1657a1a857 | subsection | 7 | 58 | Background and Definitions | We
use prime order groups (\mathbb {G},\mathbb {G}_T)
endowed with an efficiently computable map e: \mathbb {G}\times \mathbb {G}\rightarrow \mathbb {G}_T such that:e(g^a,h^b)=e(g,h)^{ab} for any (g,h)\in \mathbb {G}\times \mathbb {G} and a,b\in \mathbb {Z};
e(g,h)\ne 1_{\mathbb {G}_T} whenever g,h\ne 1_{\mathbb {G}}.... | {
"cite_spans": []
} | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.00325567414984107,
-0.021529026329517365,
-0.038694269955158234,
-0.022932762280106544,
-0.01531139574944973,
-0.03848065808415413,
0.03603937849402428,
-0.01814175210893154,
0.015204589813947678,
0.045651912689208984,
-0.05614941194653511,
-0.008681797422468662,
-0.01763824000954628,
0... | |
54625a0c2d624eaab49c27ded02eedbac19db80f | subsection | 8 | 58 | The Basic Scheme | The scheme mixes ideas from the “commutative-blinding”
and “exponent-inversion” frameworks. Private keys have
the same shape as in commutative-blinding-based schemes
, , , . At the same time, their first element is
a product of two terms, the first one of which is inspired from
Gentry's IBE .According to a technique a... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 93,
"openalex_id": "",
"raw": "D. Boneh, X. Boyen. Efficient Selective-ID Secure Identity-Based Encryption Without Random Oracles. In Eurocrypt'04, LNCS 3027, pp. 223–238, 2004.",
"source_ref_id": "4dd7000228b5adaa9b28ee2aec... | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.05548371374607086,
0.019135473296046257,
-0.021638037636876106,
0.0055582900531589985,
0.0035669193603098392,
-0.033906713128089905,
0.07709123194217682,
0.023988008499145508,
-0.004223079886287451,
0.030946362763643265,
-0.03067169152200222,
-0.00898024346679449,
-0.020234160125255585,
... | |
22feb6955076a7c86afae612037a1b61cfdbe69d | subsection | 9 | 58 | Description | Setup:
given \lambda \in \mathbb {N}, the PKG selects bilinear groups
(\mathbb {G},\mathbb {G}_T) of prime order p>2^\lambda with a random generator
g \stackrel{\begin{} _{\$}
\end{}}{\leftarrow } \mathbb {G}. It chooses h,Y,Z \stackrel{\begin{} _{\$}
\end{}}{\leftarrow } \mathbb {G} and x \stackrel{\begin{} _{\$}
\end... | {
"cite_spans": []
} | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.029034167528152466,
0.005389553029090166,
-0.05358276143670082,
-0.025998013094067574,
-0.005816750228404999,
0.018110118806362152,
0.03884445130825043,
-0.03982090204954147,
0.016309786587953568,
0.03441990539431572,
-0.026272641494870186,
0.026318412274122238,
-0.03652537986636162,
-0... | |
eff6e4d896b282cb2f9c8ec1f6cce0915bdf1d2c | subsection | 10 | 58 | Description | \mathsf {U} picks r^{\prime \prime } \stackrel{\begin{} _{\$}
\end{}}{\leftarrow } \mathbb {Z}_p^* and computes
d_{\mathsf {ID}}=({d_1^{\prime }}/g^{\theta } \cdot (g^{\mathsf {ID}} \cdot Z)^{r^{\prime \prime }},~d_2^{\prime } \cdot X^{r^{\prime \prime }} ,~{d_3^{\prime }}+t_0)
which should equal
d_{\mathsf {ID}}=({d... | {
"cite_spans": []
} | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
0.015974704176187515,
0.029721800237894058,
-0.04284333437681198,
-0.0279214046895504,
-0.014784611761569977,
0.022718563675880432,
0.051631711423397064,
-0.027204297482967377,
0.009108785539865494,
0.036770809441804886,
-0.015944190323352814,
-0.009352907538414001,
-0.028653768822550774,
... | |
577dd83d5ec49bd3bac54023c939ea47730ebf42 | subsection | 11 | 58 | Description | By raising both members of
(REF ) to the power s\in \mathbb {Z}_p^*, we see that the
quotient of pairings
in (REF ) actually equals e(g,Y)^s.The scheme features about the same efficiency as classical
IBE schemes derived from the commutative-blinding
framework . Encryption demands no pairing calculation
since e(g,h) and... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 261,
"openalex_id": "",
"raw": "D. Boneh, X. Boyen. Efficient Selective-ID Secure Identity-Based Encryption Without Random Oracles. In Eurocrypt'04, LNCS 3027, pp. 223–238, 2004.",
"source_ref_id": "4dd7000228b5adaa9b28ee2ae... | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.009118791669607162,
0.0018437891267240047,
-0.018878569826483727,
-0.0008379559149034321,
0.01645197905600071,
-0.03729929402470589,
0.040382131934165955,
0.029897427186369896,
0.013155478984117508,
0.008042850531637669,
-0.0543312132358551,
-0.010332087054848671,
-0.03757400065660477,
... | |
69332e17a21e5ccb3628e78b7a3819512cc33285 | subsection | 12 | 58 | Security | Selective-ID Security. We first
prove the IND-sID-CPA security under the modified DBDH
assumption (mDBDH).
The scheme is IND-sID-CPA under the mDBDH assumption.
We show how a simulator \mathcal {B} can interact with a selective-ID
adversary \mathcal {A} to solve a mDBDH instance (T_a=g^a,T_b=g^b,T_c=g^c,T
\stackrel... | {
"cite_spans": []
} | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.008360750041902065,
0.015005105175077915,
-0.025219561532139778,
0.016767270863056183,
-0.05001193284988403,
-0.009146477095782757,
0.053276896476745605,
0.005187326576560736,
0.024349922314286232,
0.030345860868692398,
-0.016935095191001892,
-0.01710292138159275,
-0.018460780382156372,
... | |
24e21ac5b6d4d29b30296c74b3f093fb5aa036aa | subsection | 13 | 58 | Security | If we set
\tilde{r}^{\prime }=r^{\prime }-\frac{w}{ c (\mathsf {ID}-\mathsf {ID}^\star )}, where w=\log _g(W),
we observe
that (d_1^{\prime },d_2^{\prime }) has the correct distribution since
W^{1/c} \cdot (g^\mathsf {ID}\cdot Z)^{\tilde{r}^{\prime }} & = & W^{1/c} \cdot (g^{\mathsf {ID}-\mathsf {ID}^\star } \cdot X^\... | {
"cite_spans": []
} | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.02280336432158947,
0.05009413883090019,
-0.028756050392985344,
-0.024986015632748604,
-0.0336403027176857,
0.005418470129370689,
0.060076333582401276,
0.004762148484587669,
0.025291280820965767,
0.05216994509100914,
-0.005685577634721994,
-0.024894434958696365,
-0.023001786321401596,
0.... | |
1f4fd4991a3c3e423c0d519ac682acdcf9c1fa9d | subsection | 14 | 58 | Security | It flips a fair
coin d^\star \stackrel{\begin{} _{\$}
\end{}}{\leftarrow } \lbrace 0,1\rbrace and encrypts m_{d^\star } as
C_1^\star =T_a=g^a \qquad C_2^\star =T_a^{\alpha } \qquad C_3^\star =T
\qquad C_4^\star =m_{d^\star } \cdot \frac{e(C_1^\star ,d_1)}{e(C_2^\star ,d_2) \cdot {C_3^\star }^{d_3}}.
We see that (d_1,... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 1400,
"openalex_id": "",
"raw": "R. Cramer, V. Shoup. A Practical Public-Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack. In Crypto'98, LNCS 1462, pp. 13–25, 1998.",
"source_ref_id": "2a7bc504db64b... | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.011933823116123676,
0.04071539640426636,
-0.04941396415233612,
-0.01117079146206379,
0.0014449922600761056,
0.014779933728277683,
0.025988876819610596,
0.020418740808963776,
0.02533266879618168,
0.021670114248991013,
-0.032810382544994354,
-0.0036320332437753677,
-0.034977395087480545,
... | |
0488d47da93cb0ac99ef782fbd3e42a86bcd8862 | subsection | 15 | 58 | Security | Since the
commitment R=h^{t_0} \cdot X^{\theta } and the proof of knowledge
of (t_0,\theta ) perfectly hide t_0 to the PKG, all elements of
\mathbb {Z}_p^* are equally likely values of d_3=t_0+t_1 as for the last
part of the user's eventual private key.
The original version of the paper describes a hybrid
variant of t... | {
"cite_spans": [
{
"arxiv_id": "",
"doi": "",
"end": 502,
"openalex_id": "",
"raw": "B. Libert, D. Vergnaud. Towards Black-Box Accountable Authority IBE with Short Ciphertexts and Private Keys. In PKC'09, LNCS 5443, pp. 235–255, 2009.",
"source_ref_id": "7cecdf170dc89c935e7b0d... | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.036093566566705704,
0.015529691241681576,
-0.05134866386651993,
0.0014721170300617814,
0.010464997962117195,
-0.009282727725803852,
0.05134866386651993,
0.023508107289671898,
0.028298208490014076,
0.020457088947296143,
-0.043812643736600876,
0.0006421443540602922,
-0.030571218580007553,
... | |
19c54cfbf0fe7a002066577bbeeecc2b3b95fcde | subsection | 16 | 58 | Security | Next,
\mathcal {B} computes t_1=t_1^{\prime }-t_0
picks r \stackrel{\begin{} _{\$}
\end{}}{\leftarrow } \mathbb {Z}_p^* and returns
(d_1^{\prime },d_2^{\prime },d_3^{\prime } )=\big ( g^{\gamma + \theta } \cdot (g^{\mathsf {ID}^\star }
\cdot Z)^{ r}, ~X^{r},~ t_1 \big ).
To see that
the above tuple has the appropria... | {
"cite_spans": []
} | 0807.1775 | Towards Black-Box Accountable Authority IBE with Short Ciphertexts and
Private Keys | [
"Benoît Libert",
"Damien Vergnaud"
] | [
"cs.CR"
] | 2,008 | en | Computer Science | [
-0.018843168392777443,
0.05001449957489967,
-0.021482737734913826,
-0.0190262608230114,
-0.0119467219337821,
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0.05285241827368736,
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0.017881939187645912,
-0.04742070287466049,
-0.001968233846127987,
-0.02128439024090767,
0.... |
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