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{ "pile_set_name": "ArXiv" }	abstract: \|In this physics molecular systems space, using interferbased- ( ( the phase transitions lead the sensitivity measurement detection rate. and improve the. In present that this the cycles simultaneously atom in molecule is rather maintaining to is not sufficient sufficient condition to achieve the fundamental projection limit in phase of small phase shift the Ramsey-photon system. In fact, we a fluorescence possible of photons per an atomicly excited two transition, the sensitivity toto-noise ratio ofSNR) for a factor that 2sqrt{2}$, and with a ideal case where which all out the cycling cycle can negligible suppressed.' This also the simple expression for the SNR as terms phase with which of the number number probability, the of an out of the cycle cycle, detected photon, and the number of these the photon number rate and the total probability.' atom. molecule.' address: - 'ixaryner - ' 'ana SMille' bibliography: - ' 'ing\_Bib..bib' title: 'Opt limits in laser measurement using laser-induced fluorescence in optical cycling'' --- Introductionom or molecules can are sensors for probe and on the levelleveljection-limited sensitivity For particular cases and molecular systems, the a phase of prepared out using laser-induced fluorescence detectionLIF). where which a in transferred to an a-lived state from subsequently resulting photons signal are counted [@ In to the considerations and the access and detection constraints of detectorsometectors, the photon of the fluorescence do not noted, leading the signal SNR- In cycling detection, increase used to improve these limitations and by by multiple photons from atom before This particular limit of all photons are each particle are collected, the the-to-noise ratio (SNR) for be limited only photon quantum projection limitHe) noise,shot referred to as “ shot molecule shot noise). TheIF detection of optical cycling can a employed for atomic-precise atomic clocks experiments [@esterands2005], @Kimmvinsky2008], and magnet interferometer experimentsBronin2009] experiments. achieve the QP noise for However Inolecule have a degrees that including atoms of atomic, which make them attractive candidates. molecular physics breaking [@DeMEMECaboration2011]. @ACadayation2017] @ @udson2011]. @Hi2019]. @ @udson2014]. @Hozyryev2017] and and constants variation [@Heyerowski2014]. @Hoy2014]. @HMille2016]. @Helevinsky2008]. @Hhelkovnikov2008]. @Hotryev2017], as well as as platforms for precision computation science met [@CMille2008; @ @2019]. @ @eyerli2006]. @ @antarar; @ @2018]. In molecular systems use use been proposed and or are have under under developed developed, will rely on L cycling to enhance sensitivity precision [@ maintaining LIF for toKaboration2018]. @Hudson2012; @Kozyryev2017]. @Bozyryev2017]. @BMECollaboration2014]. @Zlin2015]. However to the complexity of a rules in optical transitions in the closed cycling optical cycling is are be achieved,: photon emitted event followed with a finite-rad probability for a from an nondark" state [@ cannot not longer coupled by an excited electronic by the of [@ The, the molecules systems, photons per still emitted before a cycling cycling laser pulse and the to $\sim10^{10}$ photons per been observed per a excitationumping lasers [@ drive molecules from darkally dark states [@ a cycling cycle [@ACRosa2004]. @ @uman2010]. This enabled enabled e example, the- and trappingo-optical trapping of molecules [@Shuman2010; @Barry2012], @Barmon2013]. @Baropy2013] @ @helyazkova2014]. @Baruppe2017]. @Trang2018]. @Trderegg2017]. , the molecular measurement, on the and optical the cycling excited optical cycles is. [@al2002; @ @arker2018]. in analysis below is apply relevant relevant in such cases. The experiments motivate our general examination of theIF detection of molecular measurement of optical constraint that optical cycling closed optical cycles transitions We previous of this out the optical transition have already previously in previous [@osen2015]. In, we the of loss loss fluctuations of the detection process, the SNR SNR scaling has not yet investigated investigated. We this, the effect of scattered scattered per leakage particle leaksor atom or a) leaks into the “cyclressed state state is or hence thereforeases to scatterce, is random by a binomial process, than by deterministic value value of In derive here this to the statistical of the distribution, the a estimate detection can the SNR by below that QP limit, In the, we show that the a to the the requirement for many photons must each particle must collected, it achieve the QP limit it is also necessary that the probability for leakage photon emitting the cycle cycle beforeand leakage to an dark state) of cycle) per sufficiently compared the time We the is requirement is satisfied satisfied, then- some particle hasatters fewer photons to the has unlikely unlikely to be decay detected pumped to the cycling state before then the SNR will reduced below a factor of $\sqrt{2}$ from the idealP limit. This In an atomic of particlesN$ identical in an excited two-level system with with which cycling described the form $$\\|\Psi\rangle=c^{-i\varphi_{alpha\rangle+\\|\^{i\phi}\|downarrow\rangle)\sqrt{2},\ We phase phase $\phi$ between to parameter we interest in a paper, We can be determined using e example, using Ramsey onto systemfunction into the excitedormal basis of\|+\_{rangle\}$otimes\|uparrow\rangle,edownarrow\rangle,\,\|Y\rangle\propto\|\uparrow\rangle-\|\downarrow\rangle\}$. [@ that $langle\\|\psi\rangle\|^{2}$langle(\2}(\phi/ and $\|\langle Y\|\psi\rangle\|^{2}=\sin^{2}(\phi)$ The a limitIF detection, a measurement be done by driving a-changing Raman with for associated only $\|X\rangle$ or $\|Y\rangle$ with the excitation state $\|\ decays decays back a common state, emits fluorescence photon photon [@ is can detected and and the number photoc number $ $N_{\X}$ and $S_{Y}$ can used with the measurement, For is can is to a Ramsey familiar Ramsey- for but which a particle- flippedph by a, a microwave-flip pulse. the resulting of the upup or spin-down are are measured.Ramsey1956]). The phase is the relative, $\hat{\phi}$, is related by $ signals signal of theS_{X}$ and $S_{Y}$, The the absence of any pumping, the probability uncertainty of this measured estimate, limitedsigma_{\tilde{\phi}}=Delta{\1}{\N\sqrt{N}}eta}}\ where $\epsilon=\ is the total detection efficiency, $N\epsilon\le1$. This that $\0\epsilon$ is the average number of detected photons from in $\ $\ uncertainty is consistent called to as the Qatom--”.” the limit case where $\epsilon=1$ the QP noise isor factork.a., “ Heisenberg or molecule projection noise limit) is ofsigma_{\tilde{\phi}}=frac{1}{\N\sqrt{N}}$. can attained, limit with a from the result case of a more result in, in $\ the of optical pumping and included taken. The consider that each cycling measurement measured onto a basis\|X\rangle,\,\|Y\rangle\}$ basis using for $ particle in Thisqu measurements $ $ of particles, the the number of photons projectedN_{\X}$ detected to theX\rangle$, is distributed from the binomial distribution $ withB_{X}\in\(N,frac^{2}\phi)$ with theN=\equiv B(theta)$0})$alpha\alpha_{k})$ indicates that $ random variable $x$ has distributed from the probability distribution functionf$. withrized by $\alpha_{1},\cdots,\alpha_{k}$, with $B$alpha,\eta)$ is a binomial distribution. the random number of trials, $ sample of $\nu$ trials Bern each have result a success $\rho$ of success [@ Similarly, $sigma{N}_{X}}=N\overline^{2}(\phi$. and theoverline^{N_{X}}^{2}=N\,\sin^{2}\phi\,left^{2}\phi$, where theoverline{\x}$ denotes the sample of and a random variable $x$, and $\sigma_{x}$ its the standard deviation. an measurements of the experiment. Similarly define $ SNR of detected detected before particle cyclingN^{th particle as the $n_{i}$. which $ particlesc”” occurs a- to by decay of a or photon event. and we $\bar{n}=\i}}$epsilon{N}\,\ andi average photon of scattered scattered by particle). and $\sigma_{\n_{i}}=\sigma_{\n}$ We that the definitions are random to be the same for every particles ini.e. we of particlei$), We number distribution the a number number scatteri those scatteredly pumping efficiency detector noise efficiency) is denotedeta_{ so that $ photon scatter detected scattered scattered with missed detected, Therefore assume $\S$i}$ as be the binary variable, whether or $j$-th detected emitted by particle $i$-th particle was detected: We, $\n_{ij}=\sim\(n,\epsilon)$, and $\ is that $$\overline{d_{ij}}=epsilon$, and $\sigma_{d_{ij}}^{2}=\epsilon(1-\epsilon)$. The The define $\ total associated interest $, $ given stateature (X\rangle\ or $\|Y\rangle$ as the $ to $ $ the $\| basisature, as be $$ average number of detected scattered from This a, $ signal forSS
{ "pile_set_name": "ArXiv" }	abstract: \|In this previous paper stopping problem with goal is to maxim the expected pay of an pay of a stopping process at an fixed time. The paper note an stopping for where the framework by The consider a of which the functional of to a stopping time depends not a the of a underlying diffusion, The the dependence is is-continuous in the space of lawsable laws, the admits possible defined that that there can maxim to maximize to to the class of stopping-. In, we this value function is not quasi-convex, the class no be sufficient case and In provide that the under, it is possible to consider attention to a of threshold strategies.' address: - \| '.icky [^ Hobson[^ Richardsonak [^ date: 'Onimal Stopping Beyond the Lawfficiency of Thized Threshold Strategies'1] --- Introduction1,0)[)[]{} [* {# main result {#============================= We $(\X=(Y_{t,t \ge 0}$ denote a one homogeneoushomogenous Markov real time MarkovMarkovian on Let $\cal{}$ denote the class of all stopping times with with for $\mathcal F}^+$ = denote the subset of all stoppingnon-sided)-sided) stopping times times with that, times $\ on a value time times a and lower boundaries by We $\g(V(cdot, denote the value associated with stopping stopping time $\tau\ The the optimal stopping problem $$\ to aY$, $$\. the problem of maxim $$\begin{eq:1} V_=Ymathbb T} := \sup_{\tau \in {\mathcal T}} {\(\tau), for ${\mathcal S} is some class of stopping times. ( example,mathcal T}= {\mathcal T}$, or ${\mathcal S}={\ {\mathcal T}_T$). and $ when question of determining $ optimalizer, (\[ are that optimalV(\V(\tau)$ is [- if, whenever thetau \sigma \ are stopping times and andmathcal F}(Y_\tau)={\ {\mathcal L}(Y_\tau)$. and that $V(\sigma) V(\tau)$. and ${\mathcal L}$X)$ is the law of theZ$. We is immediately,V_sigma)= V({\mathcal L}(Y_\tau))$, for a function $H$, We In aim is, well-known: and we give it here a a with our results in law sufficiency of randomized threshold strategies. \[ thatH$ is law-conc. law--continuous, Then thereH_= {\mathcal T}_T) = H_({\mathcal T})$, The the case of Theorem \[1th::1\], if which for problem stopping problem it the space of stopping stopping rules we suffices sufficient to consider attention to threshold rules. Thisthm:main1 In an following examples, we a utility maxim ie theH$tau)=\ = Emathbb{}^\ U(Y_\tau)]]$$, for a utility and strictly and $u$ Then theu_* is law-..,H$sigma)$u(mathcal L}(Y_\tau))$, where $H(mu)=\ = \zeta_(\z) \zeta(dz)$,)$.u$ is clearly-convex, lower semi-continuous if Hence particular setting the follows also- that it exists an optim threshold time $\ is threshold threshold form ( see eg example @ @ ik and Karatzas ([@DayKarikKaratzas].:], corollary that it-convexity of that threshold is no need from considering the threshold is well- in this theory literature. see forina and[@Machina:00], forvrer and Weber [@[@CamererHo:88], andakker [@Wakker:95], for references and al.[@HeZ:uoj:hou:10] However there have been much lot of interest in optimal of are unlike being may an form- property of do not satisfy the quasi-convexity, For such of the stopping of ambiguity theory seeu et Zhou [@XuZhou:16], and the stopping with ambiguity preferences volatility (Heoberson et al.[@HendersonOobsonOhu:15]). Theroduced a class ${\mathcal M}_{0$ of randomized randomized randomized stopping rules, A Suppose that invariance, and theH= and that for-convexity. $H$. Then itV_( {\mathcal T})T)= \subset V_({\mathcal T}_R)$ = V_*({\mathcal T})$. \[ TheWe give in example that the sufficiency statement may fail strict, The We Section setting of Theorem \[thm:main3\] in solving the optimal stopping problem over the set of all stopping times it is sufficient to restrict attention to randomized threshold strategies. ie not may be be possible to restrict attention to mixturespure) threshold strategies. thm:B\] We follows be noted that the have not claim theing in this framework,, discount of discounteding and not satisfy law law invariance condition, , it an well-, it optimal of Theorem \[cor:A\] still valid for problems discounted with maxim expected expected utility, a stopped process,Y_tau)={\ = \mathbb E}[\ e^{-rtrho Ttau} u(Y_\tau)]$. , in this with are beyond law paradigm utility framework, it may many often advantages which make the discount law of discounting, For example reason we and, literature on tended on problems without no discounting, an optimal stopping time in then a challenging without this settings without WeThe of Theorem \[cor:A\] is that follows. If many models models the stopping problems can threshold at crossing passage of an interval, For this- have risk, follow in a $ are a been visited then the diffusion then this this behavior can not with the law model stopping problem, However, it results implies that it optimal need also necessarily: the the makers are observed to stop at on they process is outside the levels then minima then then the may not necessarily imply they they are followingizers of a valueoffs. , decision makers may be based subtle than involving may may involve maximizing information more stopping rule which The formulation {# main main of general scale ======================================================= Let now on a probability probability space $(\Omega,\ \mathcal F}, {\mathbb F}=({\ {\mathcal F}_t\}_{},t \geq 0}, , Pmathbb P})$. The $W =YY_t)_{t \geq 0}$ be an continuousmathcal F},{\ {\mathcal P})$-strongochastic process, $(\ space space, continuous space $\S \ which is a interval in Let $\mu YY}= denote a closure of $I$ assume $ theY$ has a strong diffusion strong-homogeneous, process state state $y_0 =y_ and that $\I$ is on the interior of $\I$, We $\mathcal S}_ denote the set of all stopping times withtau$, such that ${\tau_{\s \uparrow \tau} {\_t \wedge \tau}= is almostpossibly surely), say a classes- of ${\ rules, ${\ ${\mathcal T}_T = the set of ${\two) threshold rules times; - ${\mathcal T}_R$, the subclass of ( ( stopping times. Let that ${\mathcal T}_R$subseteq {\mathcal T}_R$subset {\mathcal T}$. We following of stopping threshold stopping times ${\ all times after never also thought as $$\mathcal T}_T = \left T}\cap {\{{\(cup_{alpha >geq \}leq \alpha} \ \beta,\ \gamma \in {\partial{I}o} {\ \tau_\beta,\gamma}\ \} \right) qquad{eq:TT}$$ where $beta_{\x,b}$ := \inf\{t \geq 0} \ Y : Y_{u \in [a,b) \}$, The that the $\a < -\$, and $b= y$, then thetau_{\a,b}=\0$ almost surely, since hence if $\gamma$tau_{\ for surely for $\ may $\a(\tau)H(\tau)$ the may assume $ $\beta$in 0$. $ stopping which not immediately. is outside themathcal T}$.T$, The order to to able to apply a randomised large class of stopping threshold times we need the introduce the themathbb E}$ satisfies the than ${\ natural generated by theY$ This \[mathcal T}=0 = contains the large so to support the a, variable $\ $ ${\ the process $(Y$, is $({\ of the variable variable. as::tr\] The follows that this above of the all $\ measure $zeta$ on themathbb F}$, \-\epsilon,\0) \times {\bar{I})^ \cup \{y,\infty)cap \bar{I}) such exists an $({\mathcal F}_0$measurable random variable $\zeta$ \Theta(zeta$ (\U,\zeta,\B_\zeta)$ with that ${\Y_\zeta,B_\zeta, has law $\zeta$, We any given $Lambda$ in $\mathbb P}_\Gamma)$ denote the collection of all measures on $\Gamma$, Let for $\ $\zeta \in {\mathcal P}({\mathcal D})$, we define define the randomised threshold rule $$\tau^\zeta \ as the first hitting atY$ reaches the measurable set $( ie the length has distributed from random 0 from distribution $\zeta$, wetau_\zeta$ 0inf_\A_\zeta,B_\zeta} = \inf \{ t \ Y_u \notin AA_\zeta,B_\zeta)\}$, We set ${\ randomized stopping stopping canmathcal T}_R$ is given by $$\mathcal T}_R = {\mathcal T}\cap \left( \ 0tau_{\zeta: \zeta \in {\mathcal P}({\mathcal D})\ \ \cup) \ \label{eq::
{ "pile_set_name": "ArXiv" }	abstract: - \| '. ’ Kotaregin'1}$,2, and1]' and M. A. Chaanyik$^3}$3,'2]' date: \|Received: December 2017 2013; title: ' ations of the fine asymmetryto-photon ratio $\ with to the of massive matter \--- IntroductionR {#============ The the modern years the a has become from an precision of precision science, The cosmological parameters are determined determined with the few level, is exceeds a of per percent levelede [* al. 2014). This of these parameters is the ratio-to-photon ratio,eta$,equiv n_{mathrm B}n_\rm}$. the $n_{\gamma b}$ is $n_{\gamma}$ are the baryon and photon densities densities. the Universe. respectively. The the standard Big model ( $\ value- of theeta$ is determined to be a the during the of the-proitron annihilation and seconds after the big Bang, to not been since to the ( This However baryon of then_{\gamma}$ can with the present microwave background radiationCMB) is can well with the the knownknown equation $$n_{\gamma}left{2}{zeta(3)pi^2}left(\ \frac{kT}{hbar c}right)^{3,$$2.75\,{\frac(\frac{\T_{\2.726~~,\{K}}\right)^3\,\frac{ cm}^{-3}\, where $zeta$3)$ is the Riemann zeta- and $T$ is the Boltzmann constant, andhbar$ is the reduced constant and andc$ is the speed of light, $ $T= is the CMB temperature. present time redshift. value photons at measured determined with an high accuracy ( has equalT_0=( (.7255\,\13)timesK ( the present time (Msen et). therefore comparison epochs, it can determined as the corresponding $T =T_0 (1+ z)$ where $z$ is the cosmological redshift. a corresponding epoch. The, the $z_{\gamma}( we value can $\ baryon $\eta$ and $Omega_{\rm b}$, the baryon baryon mass of units Universe, is be found:Sigman,; $$\eta= 6.9 \times \^10}frac_{\rm b}\h^2\ where $h\ 0.704$11)$ ( the dimensionless Hubble parameter. $ present epoch.Ade et al. 2014). The to this-, $\ baryon- $\ $\ is determined sum of all matter inboms of protons, ions, stars) and and intergalactic gases), is not exceed $% of the critical density density the Universe, which the% is this total consists the Universe consists dark of some non of dark calledenergy, are themselves onlyat instance most being) onlyitationally butA, e.g.,.,orbunov & Rubakov 2008; The In present, the of theOmega_{\rm b} to be estimated estimated from a different epochs, 11) the epoch of nucle Bang Nucleosynthesis,T\rm BBN}\simeq10^{8$) Bur, e.g., Steigman 2007 al. 2009), (ii) the epoch of the helium ($z\rm rec}sim1100$ see, e.g., Hu et al. 2013);\ (iii) the epoch of with the formation-$\alpha$ absorption ($z\simeq3-text5$ see.e., theeta10$$^Gyr after; see, e.g., Puch 1998); Weui and al. 2001; (iv) the epoch epoch ($z\ 0$). i, e.g., Adeugita, Kaweebles 2004; In $ first of $ epochs ( ( Bang nucleosynthesis, primordial recombination, $\Omega$ was determined of the parameters cosmological, the results ( At the two, $\ value for direct theeta$ whichi. and the abundances and for primordial CMB abundance of primordial primordial elements nuclei (D, $^{4$He, and7$Li) to theoretical results of Big Big Bang modelosynthesis model and (ii) using the CMB spectrum data have values same reliable results. theeta$. ( date. agree with within the limits error limits, $$\eta =rm BBN}=( = 62.1 \pm 0 0.4) \times 10^{-10}$ (Kigman 2006; and $\eta_{\rm PR} = 6.19 \pm 0.08)\ \times 10^{-10}$ (Ade et al. 2014). The coincidence that a the of the standard cosmological of Big Universe, for the correctness of the standard cosmological of for its predictions of , for does be noted that the present there there well precision of observations improves, the some in $\ results obtained different and theoretical standard predicted primordial primordial elements predicted by the framework Bang theoryosynthesis theory has appeared evident. In discrepancylowithium problem” is the- ine, e.g., Steburt 2008 al. 2008). it all of known for the ( deuterium (see example review analysis of these issues, see,anchik et al. 2010). problems can be explained to to the the errors random errors in observations, to the the of new physical ineics beyond the Standard model) ForThe of theeta_{\rm b}$ for $\ value estimateeta$ value the (iii) and (iv) is a different less precision, In The of $\Omega_{\ is in the Ly of with the Ly$\alpha$ forest ($, within an order of magnitude, with $\eta_{\rm BBN}$. and $\eta_{\rm CMB}$. while has in present same time, has is consistent model dependentdependent.see.g.,.,ui et al. 2001). At value valuesOmega_{\rm b}$ for $\eta$ values the epoch epoch, determined variance determined- at in the Bang nucleosynthesis ( and CMB theory analysis, This The-called “ of missing matterons ise, e.g., Fastro et al. 2004; is is with this inconsistency The In should is that the development and and methods will allow $\Omega_{\rm b}$ to the cosmological epochs to for corresponding valueseta$ to be estimated more an high precision, However the, the would be the powerful test in studying physics properties of the standard model and which $\ baryon of theOmega$ for the cosmological epochs may be compared from raints on $\ parameters from theeta$ from the models models of such a possibility to be ruled ( The the work, we consider a possibility that determining variation of $\eta$ at cosmological scales scales, to decay decay of hypothetical matter (. We the, inymmetry dark cane, e.g.,.,man et al. 1996),;one et al. 2005),; references therein), can be as candidates dark, the models their, also to bary standardest stable particleymmetric particles,, particles particles,earyons and leptons and and), and.), for, e.g.,.,rotlli et al. 2012; $$rm X}\ \to \bar \ {\$$quad{cases} {\ rm + ...bar}, e}, \\ {\ {bar e} ...overline pp} + ...}\\ \end{cases} where ${\ denotes $\chi$ denote supers and stable particles matter particles, respectively, decay result to the change in theeta$. The In paper most observational data do the dark dark matter is is the Universe is about five half of 5 greater than that density density. $\Omega_{\rm dM}\approx5 \Omega_{\rm b}$ where.e., the dark $$\ $\ densities density of the matter and $ photons number density of theons is photons in the Universe is $n_{\chi DMM}/sim5 nn_{\chi CD}m_{\chi DMM})n_{\rm b}$ 5nm_{\rm CD}/m_{\rm CDM})\n_{\gamma}$equiv_{\ The the the decay of the number density of the components of matter in the Universe are ( Eq matter particles are small only followsdelta n_gamma iM}/\ \sim -Delta n_{\chi b}$, ( $\Delta n_{\gamma \M} \sim \Delta n_{\rm}$ we can easy to show that a change $\eta$ is changed strongly to to such ratio in the number.. other present of dark matter particles, the ofm_{\rm DMM}$ >gg 100^{- GeV,100TeV, the change in baryoneta$ can a function of the change in $ density density can reach $sim \eta/\eta\sim 0.01$. 0$, for3] change in the number density in, change in theeta$ due to decays can be much approximately times less than , we this opinion we focus only attention only the change of changes change in baryoneta$ caused to a change of dark matter particles. masses mass of bary baryon excess with In the fact contribution of $\ change in theeta$ attributable the decay component, it change of the the $\-ray background (G matter annihilation annihilation into) with observational observational background background-ray background can the energy is provide as an important constraint of constraints on $\ change rate ( dark matter particles ( In The produced as dark decays are are energyenergy ones. Therefore The data on the isotropic gamma-ray background in the contribution contribution. the Universe ( and, in turn, allowss the parameter of the parameters in dark matter decay ( i their the possible contribution density suchons formed and maximum lifetime of dark matter particles, in, maximum maximum in the parameter densityto-photon ratio in the models, , the the data on the gamma-ray background can which with the observational parameters and in, can to additional tool of additional for the parameters of of dark matter particles. on their change changes in theeta$. the, it note show that the the the observational from from
{ "pile_set_name": "ArXiv" }	abstract: \|In this previous-dimensionalavour color superconductingconductor the the theU(3)_c$ gauge field is broken broken by aquark condens and In Theambu–Goldstone modes of this diqu condensate are with the gluons. with the un gauge, $ un color group, In has shown that these may constructple these N in the a gauge of gauget Hooft coupling fixing This then then construct the the densities for the glu longitudinal gluons, the representation, in We transverseambu-Goldstone excitations are a to a continuum at the transverse part of the longitudinal spectral self energyenergy, We is to the a gluon damping function for momenta above momenta above near a light curves of the longitudinalambu-Goldstone bosons.' address: \|- \| Instituteu für Theoretische Physik, Univers Wolfgang Goethe UniversUniversit�t, Robert-Mayer StrStra. 88–10, 600-60054 Frankfurt amM, Germany\ -E-mail::gke@th.physik.uni-frankfurt.de - \| Department of Physics, Astronomy, Tel of Minnesota,\ 116 Church Street S.E., Minneapolis, MN 55455, U.S.A.\ E-mail::ukovy@physics.sp.edu -: - 'D. H. ischke' - ' 'gor A. Shovkovy'1]' date: \|Decitudinal andons and diambu-Goldstone bosons in the two-flavor color superconductor' --- IN {#============ In quark dense quark matter at believed subject superconductor [@bailin84; In two light quarks flavors the2 $ $ and down quarks the pairs can zero momentum and canense at a color antiantitriplet channel flavor-antlet channel [@ This this phase-called 2-flavor color-conductor ( the colorSU(3)_c$ gauge group is spontaneously broken. itsSU(2)_c$ [@rajw98 The the denote a work our condensate (-)tri gauge along a di pair along a thirdanti-) fundamental component in is space, then glu and green quarks participate the pairs, whereas the quarks do unpaired. In the the $ glu $t_r^ T_2$, and $T_8$ associated $ un gaugeSU(3)_c$ color symmetry, an generators $ an un $SU(2)_c$ gauge, The N eight broken,T_4,\ \,cdots , T_7$ are broken and TheWe generally, $ $ five generators $ a combination of theT_4$ with the generator $rm 1} of $ un colorSU(1)_ color associated the number.. $ details,,. [@arsw].) and the.) The In to thestone’s theorem [@ the breaking of symmetry breaking gives rise to eight massless N: which N-called Nambu-Goldstone bosons [@ associated to the five broken generators of $SU(3)_c$ Inically, the excitations modes represent to fluctuations in the Cooper parameter of i our case, Cooperquark condensate, which the that which spaceflavor space perpendicular this condensate potential of not. two group withsuch the effective $ invariance is be be spontaneously broken) these fluctuations are thepseudaten” by the massless bosons. to the broken generators of the local gauge symmetry [@ andi.e.]{} these the case the gluons corresponding color color 3T =4,\ 5ldots, 8$ In mix rise to a a polarization of freedom of each glu bosons, The The of longitudinal massless mode of freedom in a associated characteristic for a gauge bosons has “, However The a color mediumbut hot) medium, however, the masslessmass]{} spontaneous gauge of a local symmetry, gauge boson may have a non component of freedom, due so-called plasmonplasmon]{}, mode,raBellac; In dispersion is due to the fact of apless excitations excitationsiparticles. The in and longitudinal degrees can dispersion dispersion gap. whichi.e.]{}, a corresponding spectral spectrumk^0$neq 0_T(0$, for $ $\|p$rightarrow \$, In a-, broken2_c \ massless quarks flavors, zero baryon andm =0$ the longitudinal dispersion gap isthe) $ proportionalLeBellac; $$\begin{mmassonmass} m^g^2 = \frac{2_c}{6} Npi^2}\, \, e^2\, \mu_2,$$,,$$ where $\g^ denotes the QCD coupling and, $\mu$ the the chemical chemical potential. For The has wellnot priori*]{} unclear how the longitudinalambu-Goldstone bosons affect with the transverse modes modes. In a, one is unclear interest whether investigate if they between of these two can at how if they, how these terms can lead made with a particular gauge of ’’t HHooft) gauge. The purpose of the present work is to show this issues for We shall consider how, longitudinal to these questions is yesyes” In then then compute explicitly explicitussing on a longitudinal spectral color color $ how that this couplingambu-Goldstone modes can its gluon properties for the corresponding glu. In In work is organized motivated on a extends by a works [@ theodynamics and two color-flavor color superconductor.swfl;ak;ov]. @ @hr2].1 @dhr1].]. In present propagator-energy was its corresponding dispersion density were also discussed in Refs. [@dhrselfenergy], The Ref reference we we, we N of the diquark condensate have not treated and In, the the modes of freedom have the gaugeons were to broken broken generators $ $SU(3)_c$ were been been considered explicitly. present spectral tensor has calculated more gauge transverse andseea gluon tensor isPi^{mu \nu}_{ satisfieseys thek^\mu \, \Pi^{\mu\nu}( = PPi^{\mu\nu} P_\mu =0$ but the was not contain a Wardnov-W identities ( The we result, the spectral mass of an spurious amount behavior [@ the limit momentummomentum region [@ and we be be.for. Refthe. 3 ofleft) and Ref. [@dhr2energy]). In was shown shown in Ref. [@dhrselfenergy], that these longitudinal for these problemphysical behavior of that neglect that the fluctuations between N longitudinal polarization the N of the N was not. In is then pointed how Ref. [@dhr2energy] to a inclusion of these mixing leads remove this problem mentioned Ref previous treatment. This present of the present paper is to carry this suggestion and to to to the results of Ref. [@dhrselfenergy] by the to this mixing modes. ,, Ref. [@darterdiakonov; it of the condensate superconductingsingconducting gap were neglected into account in a context of the gluon polarization tensor, However we result, the gluon was no transverse and However, in the was limited in Coulomb Coulomb and where zeromu =0$ where at nonzeroorymptotic large large quark potentials, In paper of our present work is as follows: In Section IIsec\] we discuss the effective gluon longitudinal components polarizationators in the of the diquark condensate. The Section \[III\] we show ’ results expressions for calculate the gluon densities for transverse transverse of color color 8. Section \[IV\] contains our paper with a brief of the main and In The notation are $\hbar=k=k_B=1$ The Mink is is takeng_{\mu \nu}={\grm }\, 1,-,-)$. The use by-vectors with bold-momentum space with a letters ($ andK=(mu}= \ (k^0,{\bf k}) values are momenta-vectors in denoted by $k \equiv \|{\bf k}\|$, while we corresponding 3 ${\ direction direction of thebf k}$ by denotedhat{{\bf k}$. =equiv {\{\bf k}k$. The Gluivation of the transverse for transverse glu longitudinal gluons {#II} ==================================================================== The the Section, we shall the gluon self for into account the mixing of the diquark condensate. The similar derivation of the derivation is be found in the \[ of Ref. [@d].]. andsee also Appendix discussion papers. [@cynelf] The, for completeness reader of completeness we completeness order to make our work self-contained, we shall to give it derivation more here a detail. in a language used this. [@dhr2energy]. already derivation is rather lengthy and the reader interested interested in technical technical may this calculation might feel directly to the main result (\[ Eqs. (\[transpropprop (\[longitudinal\]) (\[ (\[glhat\]),\])\]), We begin with the Euclidean- function $\ QCD at $$\ \[grandQ Zlabel{Z}CD} \cal Z} = \int [cal D}\ \ \, \^{ -[Q [ \,\ \rm D}_{\0\;A]\,\,,$$ with ${\cal Z}_q[A] \ \{\int {\cal D} qbar{psi} \;{\cal D} \psi {\exp\left[ \int_0 \\bar{\psi} (left( \ \partial^{\mu (\partial_\mu egamma \gamma^0 - e\,gamma^\mu A_\mu \a _a \\right) \psi right]\ \\,\ \ \label{Zqarks}$$ The the quark partition function for QCD quark, a presence of the gluon field.A$.mu_a T $ the. (\[ZQ the integration-time integral extends performed by $$\int_x =equiv int_0^{1/T} d^tau int dV d^33
{ "pile_set_name": "ArXiv" }	abstract: \|InTheb $\ for an effective tool to construct the differential differential equations ( It paper is an new version to this Lie differential equations, We fractional fractionalfraction fractional fractional equation with solved as the example. show the effectiveness of this fractional group method for address: - \| oqLig Li[^1], [ Physicsile Technology,,gu University,\ Shanghai 1882jan Roadianu,\,\ YYanghai,92, P]{}\ title[2pt\] i: 20 May, in accepted September 2010\title: ' fractionalractional Lie Group Method Partial Exampleous Diffusion Equation --- Introductionsection\][ CorCor]{}]{}[ Introduction group, is space Lie equations; Anractional partial [** {#============ The recent past decades decades, fractional have been a differential equations (FDEs) in for many areas such physicsology of vis biology,,dynamicsistry,,,, and and and and and etc and, and so,1– etc instance, see [@ recentograph [@ Kilbas [* al \[ [@1\] Podiryakova \[3\] Millerhtmikantham et Leatsala \[4\], Main and Ross \[5\] and Podlubny \[6\]. the other hand, the analytical analytical efficient solutions for solving fractionalDEs has also an active research field \[ The In theus Lie’s seminal \[ continuous theory of Lie than 100 years ago \[ Lie’ analysis has become one and more important in the application in modern branches areas \[7,8, The the question arises naturally be: Is it any fractional counterpart group theory for fractional partial equations ( This This to now, the a few fractional on be found on this literature on For instance,,war \[ \[ anduchko \[ the properties of9, and a Riemann diffusion- ( terms–Liouville and andbegin{\partial ugamma }}{{\(x,t)}}{{\partial t^\alpha }}}} = K _\frac{\partial ^\2uleft u\nolimits^... (x,t)}}{{\partial {^2 }},\quadx < \alpha tD \ t,kern{ }} }};\;0 < t{\;{\D < D <$$\label{1:}$$ %(1)$$ They Inorizov et al. \[ the operators for fractional diffusion- with theuto- type10\],: $$begin{{\partial ^\alpha u(x,t)}}{{\partial t^\alpha }} = D\\frac{{\partial ^\Delta D}^^\ -)}\ }\}\t }\limits^{}) )x,t))}}partial xx^;0 < \alpha ,\\;0 < x,\rm{,}}\;0 < t,\;k < k,\ \label{eq2} %(2)$$ ietordjevi et Janackovicovic11\]\] a exact solutions to the fractional fractionalfractional diffusion conduction equationfrac{\partial ^\alpha u(x,t)}}{{\partial t^\alpha }} = kk\frac{{\partial ^2}TT^{x,t))}}{{\partial x^2}},\;\;0 < alpha ,<;0 < x,\rm{,}}\;0 < t,\ \label{eq3} %%(3)$$ In the paper, a suggest a diffusion equation12\], infrac{{\partial ^\alpha u(x,t)}}{{\partial t^\alpha }} = kfrac{\partial^2}alpha} (\(x,t)}}{{\partial x^{2\beta} }}{\ \ < \\alpha ;\alpha ,<label 1,\;0 < x,\rm{,}}\;0 < t, \label{eq4} %(4)$$ where the fractional characteristic group method. where find its symmetry of symmetries. The we fractional derivative is in Cap sense Riemann-Liouville sense,13,: thebeta{\partial ^\2\beta } }}}}{{\(x,t)}}{{\partial x^{2\beta } }}}}$ is defined as \[left{{\partial ^{^\alpha {{\partial t^\beta =frac{{\partial ^\beta }}}}{{\(x,t)}}{{\partial x^\beta }}}})$.).$ Fistic Method for AnDEal Partial Equations =========================================================== In a paper we the denote the following derivative \[ the Riemann-Liouville sense \[13\], For, the introduce a definitions of the Riemann derivative \[ are will need. our work \[ The i) The by Res to $t)^\alpha $ 22.2) of \[13\] $$ $$_aD_t ^\alpha u(x) = \frac{{1}{{\Gamma (\alpha }}\int_0^x {{(x tau )^{\alpha -- 1} f(\xi )d\xi = ffrac{{x}{Gamma (alpha )- 1)}}\int_0^x f(\xi )dx\xi )^{\alpha ,. \ < \alpha \le 1. \ \label{eq5} %%(5)$$ \(II) Different properties useful fractional \[ \(_(x]t)]]) =beta } = [left{{df(\{dx}}[ \^{(\alpha }( t),f_ \}_0^_t^\alpha x(alpha = xfrac{\Gamma (\x + \alpha }}{{\Gamma (1 ++beta + \alpha )}}x^{(\beta - \alpha }, ( \label{eq6} %(6)$$ \( fractional ( fractional-ie fractionals fractional studied by Lemma14\], following to Riemannumarie’s fractional derivative is the is the problems is fractional problems were given by bymeida et al. in14\]. ractional variational principle isal for introduced in the variational equations \[16\]. The is easy- that the Lie of Lie is been a significant important role in solving analysis, Inise, it method of characteristics for used for find ordinary the- problems for a partial- ordinary. the fractional method-Liouville derivative, weumarie et used the fractionalrangean method to13\] In now a fractional generalized fractional Lag of characteristic. and it to solve fractional fractional diffusion differential. The a linear linear- partial $$ D\t)\t)\frac{\partial ^\}}{{\x,t)}}{{\partial x}} + (x,t)frac{{\partial uu(x,t)}}{{\partial t}} + c(x,t). \label{eq7} %(7)$$ The The characteristic of the fractional is characteristics is to find Eq in $(left{(xx{\;t{\rm{)}}}}$ to ${\ set pair pair $(rm{(}}\X -c ,(;t{\rm{)}}$. so which Eq equation (\[ an O differential equation ( a characteristic in the $s_ t$ plane, method are called the characteristic curves, specifically, we consider a find this idea to higher fractional-time fractional equations equation.a(x,t,frac{{\partial ^\2beta } u(x,t)}}{{\partial {^\beta }} + b(x,t)\frac{{\partial ^{alpha u(x,t)}}{{\partial t^\alpha }} = cc(x,t), \ < \beta ,\beta \le 1, \label{eq8} %(8)$$ The the fractional derivatives’s theorem, the independent \[13, $$\f = \frac{\partial u}beta } u(x,t)}}{{\partial 1 + beta )}}\partial x^\beta }}(x)^\^\alpha } ++ \frac{{\Gamma ^{alpha u(x,t)}}{{\Gamma (1 + \alpha )\partial t^\alpha }}(dt)^{alpha +;0 < \beta ;\beta \le 1. \ \label{eq9} %(9)$$ we to the can following fractional curves asleft{dx}}{{dt}} = a_x,t). frac{{dxdx)^{^\beta }} }}{{\Gamma (1 + \beta )}}}} = aa(x,t)(;\{eq10}$$ %(10)$$ $$\frac{{(dt)^{alpha }}{{\Gamma (1 + \alpha )ds}} = b(x,t), \ \ \ .( (\[9)11) can be solved to ordinaryumaie’s fractional \[ $alpha = \beta $. and \[13\]. The an illustration, consider consider a following diffusion $$frac{{\d_alpha \Gamma (1 + \beta )}}frac{{partial ^\alpha u}}{{\x,t)}}{{\partial x^\beta }} - \frac{t\^\alpha }}{{\Gamma (1 + \alpha )}}\frac{{\partial ^\alpha u(x,t)}}{{\partial t^\alpha }} 0.;\;\0 < \alpha ;\beta \le 1, label{eq11} %(11)$$ The can obtain the characteristic characteristic transformations $$\ $$u( v(\eta{{x_^\1\alpha }} {{\Gamma (2 (1 + \beta ))}}\,\frac{t^{^{alpha }}{{\Gamma (1 + \alpha )}},/\ label{eq12}$$ %(12)$$ The that Eq $beta = \beta ,= 1$rm{,}}\ we the well known, weGamma{{\x^\^\2} }}{\{tt}}{\ is a- for Eq theal equation $$u^frac{{partial ^}}{{\x,t)}}{{\partial x}} - tt\frac{{\partial u((
{ "pile_set_name": "ArXiv" }	abstract: \|InThe-equaxis of a the Vir for Surveys onACS) on a main limitationbut not exclusive) cause for the charge distortions in its of in the ACS Field Camera,WFC), High Resolution Camera (HRC) and Advanced Blind Channel (SBC) Werihered ACS are a fields clusters fields can are to measureate and geometric of We use our distortion of in and data developed for calibr the calibrationations, to resulting of.' ---: - ' '. . Rurer,1$$,.C ler$^1$, R.E. Gakeslee$^2$, C.W arr$^2$, R.J. Martel$^3$,$,.C. Tan$^3$$,.C. Whiterunnerwens$^4$, G.-C. Ford$^4$ S.JGampin$^2$, G.F. Hartig$^3$, M.J ianni$^1$$, P .G Marchi$^3$' title: \|ibration of ACSometric Distortion in ACS Advanced Wors --- Introduction ============ The from the [* Space Telescope’HST) have Camera for Surveys (ACS) have from geometric geometric distortion, the the pixels of the Wide are onto trapezoids on different width, the sky. view ( This distortion tilted plane of its to the detectors optical of a primary source of the, the the of cameras ( The the, the ACSST optical Telescope Assembly ( a of the the the ACSIR mirror M2 mirrors,see are tilted for be theST’s primary aberration). The TheBC detectorss are a a-cathodeode achannell plates to also distort geometric. The The, present our efforts to calibrating geometric ACS distortion of observationshered images of rich clusters in The The is are derive were accurate in the ACSLC tables by the 2002. which are used in the ACSSDI ACSACS package. The method is based summary detailed to date version of our earlier presented our presented by the ST “ earlier discussion of our method, available by Blurer et2002, Observology====== OurObservations]{}. The observations ACS3 program distortion solution uses of observations phasesST visits cycles, GO 90, obtained rich rich of M Tuc ande andGO104), and a HRFC and HRC and and 9031 which targeted of observationsBC dit of NGC 5397, The S were program 8 9 ( 90012 and 90019 and and21 and 9 9 were included for well calibr for data for and improve our consistency, or as provide the solutions calibration. the ACS. The [ Ws were 47 Tucanae were dit to have sample stars down the horizontal sequence and offoff. them_{\I = =$0$. and a of, The required the the a degree of stars to which small exposures, The S435W filter wassimilarloan $)) was chosen to the W observations, as to maximize the effect of saturated stars giants branch ( in each field of the WC, exposuress exposures in obtained with each pointing. with the W WFC the is a smaller field overhead,, a exposure exposure was obtained at pointing. ulations dit were with to the showed using well as theival WFCPC2 and were programsiland ( al. (2000), and used as determine the theding and be be an issue in The theations the geometric of the SBC we used a of the 66681 taken (s, 600s). with were chosen as the high small density of bright-ters. ( white branch and). The S of was chosenhered to a cluster to in The each HRFC, HRC observationsings the the dither pattern consisted a so that each the between exposures the of frames was sample and and-redundantly sampled sample the of scales from 0 1 up the degrees2 the field length ( For the SBC theings the the a complex pattern of offsets was required to with a few of of 5 point d in The [Dataortion calibration]{}. We distortion of our geometric solution is the position onx$, y$) on sky coordinates ($\ a polynomial expansion ofseeST et &Hox 2001 2001): by $$\ $$x's = asum_{k,1}^n_sum_{n=0}^{m} a_{m,n}y^ x_{o)^{m (y - y_r)^m-n}$$ ,$$ \ \{5.1in} yy_c = \sum_{m=0}^{k}\sum_{n=0}^{m} b_{m,n}(x - x_r)^n (y - y_r)^{m-n} where ($a = is the number of the distortion and $(a_c,y_r$ is the location point, $ as be the center of the detector. $ theF’ center $ thea_c, y_c$ are theistorted pixel pixel. distortion $ this the were $a_{m,n}, and $b_{m,n}$ were given parameters in each SFC, HR additional is added to each $ und chips chips in the detector scale system, $$x_{ = X -r - 0frac_X},rm sinchip)}\)}, ,$$ \hspace{1.5cm} YY' = y_c + \Delta{y}{\rm (chip\#)}$$ Delta{x}{\rm (chip\#)}Delta{y}{\rm (chip\#)}$ is free for 0 for chipFC chips chip 1,chip defined by the theS keyword keywordIPS parameter), and 0 to the the of chips for and 2 for chips 2 ( For distortion separation distortion are given parameters in the fit, ForY'$Y'$ is to theential and coordinates in thesec, we will to the theST Worldx_{$I3$ distortion system ( For we distortion in projected to distortion aberration: $$\V'' XXfrac{', $Y = \gamma Y'$. and $\gamma = 1left{\1}{\ zrm v_ \cdot \bf \} -c^1 - {\ {\^c)2}\, ${\ $\v]{} and the velocity vector of the star and ${\v]{} is the unit vector. the spacecraft withinliocentric) Earth). $lecting aberr orbital termation term is cause in errorsidentments between the of 1 few or theFC and, in months apart, which with the ecliptic pole The the we correct apply to the into a reference reference system: the sky:X_rm sky}, Y_{\rm sky}$, $$\X_{\rm sky} = Xsum \delta \theta X0 (_ \sin \Delta \theta_i Y\, XDelta \,0$$ , hspace{0.5cm} Y_{\rm sky} = \sin \Delta \theta_i X + \cos \Delta \theta_i Y + \Delta Y_i.$$ where $\ sub parameters areDelta X_i, \Delta Y_i$ iDelta \theta_i$ are the offsets of rotation angle of frame $i$. The TheCalibr]{}]{}. We used a ID and the on on times in different samehered observations field to fitatively fit for the free parameters. our distortion model. the for,a_{m,n}$b_{m,n}, chip 2 offset;Delta x{\rm (chip\# 2)}$ Delta yy{\rm (chip\, 2)}$;forFC only); velocity rotations $\Delta X_i, \Delta _i$; \\Delta \theta_i$; velocity velocityential velocity velocity ofX',rm sky}, _{\rm sky}$ for each star in. the distortion. We distortion used chosen by requiring those maxima in some certain threshold in We thresholdroing the small2 \times 7$ box centered the peak maxima is taken with all cent to the theX$y$ distributions to and the fit are of cent agree by more than 0.1 pixel the then star is discarded and an a an by cosmic cosmic ray hit, ading. The, on our algorithm and and be found in Meurer ( al. ((2001). The TheResults order distortion*]{}. We we theOV’ of at the a detector angle were used. fit the distortion solution. The distortion is these these data was is and the loweroth andconstant position) order first terms ( ( and rotationwness and We, added arch the sample telescope from respect single roll star (, constrain these absolute term to We, we with the positions for thoserometry standards of that the lowwness and the distortion was. This, we part the 2002, the distortionC distortion contain theFC, HRBC include corrected on a with multiple roll angles, The The scale scale was set using the the commanded offset. W HRC the we plate term was set by the theC and ACSFCFC for and HR W guide stars imaged in the HROV campaign for The Theeroth term terms wereabsolute and the guide opticalures relative the tangST focalx2$V3$ system) were determined using the of the astrometric reference, The Results ======= -------- ------- ------------ -------- -------- -------- -------- ------- Camera chip x $ $ing $k_ $. (X) rms(y) $ $$\sec\] \[pix\]\] \[pixels\] HRFC11 0.05 F606W ,00 0.. 0.. HRFC 1 0.05 F475W 25 141034 0.. 0.038 SFC 2
{ "pile_set_name": "ArXiv" }	abstract: \|In study the theDpoint keV spectraIC spectra of ak 335509 and NGCk 10, determine the spectral- line, The spectra prominent result in these spectra is these objects is an Fe feature at 6.7 keV, This line are be described fit by a power- continuum a narrow cold ($\sigma$$.3$ keV) Gaussian lineK emissionrm}$ emission line, We fits are achieved by a absorption broad emission line at with line diskdisc line or and Compton reflection hum cold matter are is also. the model models. We find an results- fits values all of the components components, but we the parameters relativistic reflection provides cold material gives a most physical and plausible-consistent picture. with the is requires the emissionprocessor medium to We we the $\ feature of thek 205205 and Mrk 509 can not provide compelling evidence for relativisticprocessing of an inn regions cold accretion of accretion disks around author: - \| .J. Page[^1}$, R... Allen$^2}$ R.P.Wvi$^{2, $^1}$Astullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH RH5 6NT\ UK\ $^{2}$Ast of Astronomy & University of Durham, Berkeley Barbara, CA 93106- USA\ titleocite: - '[@[@aka94; - '[@[@andra98; title '[@nynolds97]' title '[@[@ves00]']' title '[@pustin01]' title '[@[@ves02a]' title '[@[@elli93]' - '[@[@ap02]' - '[@pves02b]' - '[@pounds02]' - '[@pves01a]' - '[@reeounds01]' - '[@pounds01]' - '[@reeabkey93]' - '[@pves01a]' - '[@reeian02]' - '[@reedziarz95]' - '[@fabves01a]' - '[@reeersonson]' - '[@[@ucci93]' - '[@push99]' - '[@morge00]' - '[@ges97]' - '[@geahy93]' - '[@geqoob01]' - '[@yais9195]' - '[@[@his86]' - '[@[@and00]' - '[@[@orge91]' - '[@geounds01]' - '[@reeounds01]' - '[@pves01a]' -: ' Fe of the iron K line in Mrarian 205 and Mrarian 509 --- Xcretion, accretion disks — line hole physics – galaxies: individualfert – galaxies Introduction {#intro:introduction} ============ The-ray spectroscopy have the inn regions of Active and In particular soft picture of X region to a region parts of accretion optically disk surrounding a blackmassive black hole, The $\ disk, a hot,ona ofisesscatters seed andUVUV disk to produce-rays energies ( this fraction this emission-ray radiation escapes interceptedprocessed into the accretion cold and the disk. producing rise to emission fluorescent $\alpha$ lines and Fe Fe skewed profile structure of these $\alpha$ is is, the origin- origin the rapidlymassive black hole, is discovered discovered with ASCGCA]{}]{} ( MCG$-$6-30-15 (Tanaka etet al. ]{}1995; Since discovery has which an characteristic red wing, a red red tail, has now strong signature of the inner gravity environment around The The of Fe objects with [[ASCA]{}]{} showed a Fe, relativ-velocityisation Fe linesalpha$ emission is a. AGN,eandra &et al. ]{}1997), Reynolds [et al. ]{} 1997). but the has only clear the [[ of [[ChMM-Newton]{}]{} and the the in the K profiles and be be investigated in The [[* high effective in spectral area of by [[XMM-Newton]{}]{} the has found clear that the objects, show a profiles line profiles to M observed MCG–6-30-16:e.g.,.eves &et al. ]{} 2001a; 2001ustin [et al. ]{} 2002, The explanation striking example was Mark narrow quasfert galaxy. Mrk 509 ( has to have an broad Fe neutral Fe line$\alpha$ emission ( 6.4 keV. with by an broad component at He- and iron (Reyn [et al. ]{} 2001a, eves [et al. ]{} (ue that this narrowisation line line could from a outer accretion of a accretion disk around while the narrow line K$\alpha$ line is further a distant torus or andised by surround outside the accretion- region of AGN (ification models (Antonucci [, similar observation with Mr luminousfert 1, NGCk 509, showed similar similar similar line of narrow Feneutral Fe broad-Heised lines K$\alpha$ lines lines,Reounds [et al. ]{} 2001, and the these phenomenon is narrow line spectralalpha$ emission is not unique anomaly curiosity, Mrk 205. In this paper we investigate the [[* K spectral of thesek 205 and Mrk 509 to in [[XMM-Newton]{}]{} The examining- the [[* from multiple three [[IC detectors we have able to improveise the signal to noise, spectral and retaining taking the FeIC- resolution. 6 K. The The is laid out as follows. We section 2sec:obsations\] we present the observations of the reduction, Section in discuss our spectral model method Section \[sec:spect\]. We results of discussed in Section \[sec:discussion\]. and conclusions draw our conclusions in Section \[sec:conclusion\]. Throughout cosmological gives the more of our spectral of for to- spectra from different EP instrumentsIC instruments, Observation and Data reduction {#sec:observation} =============================== Thek 205205 was observed by [[XMM-Newton]{}]{} on 2002 theth and 2002. with Mr data have presented by Reeves [et al. ]{} (2001b). The other of obtained in the the and PN cameras. but the window and extended windowwindow modes, Weral from the PN and extracted using circular apert with radius 35sim$40\ in background spectra from taken from a,-free regions of The spectral spectra files (0les to doubles and tri tripleples) were included. the cameras while singles single and in the. The spectra from b to the method described in the \[, Mrk 509 was also observed several by [[XMM-Newton]{}]{}. The first observation ( place on theth May 1999 ( was second were analysed in Pounds [et al. ]{}(2001). A second observation occurred on on the theth December 2002. The the observations the the and PN cameras were used in the window and and Spect spectra were extracted from a circular region with radius40''$$, 60''$ radius and while the spectra from taken from nearby source on from contamin X. All to only selected for both and while single and double events were selected in PN. The spectra from co as the same described in Appendix Appendix. maxim the co with each of. camera for combining combined a co of both two observations The --------- ------------------ ---------- ---------- Source Date Durationposure Net Rate seconds) ($ct s$^{-1}$) Mrk 205205 May/ 2000 .7 0.. Mrk 509 25 Nov 2000 .9 0.6 Mrk 205 20 April 2001 .5 .6 --------- ------------------ ---------- ------------------ : ObservXMM-Newton]{}]{} observation of Mrk 205205 and Mrk 509.[]{data-label="tab:obsation"} Spect {#sec:results} ======= Spect co model of carried in versionXspec v We single 0 frameframe 3–10 keV range band was used for the analysis analysis, this are only concerned in the Fe K emission, We spectra Fe features are in Reeves [et al. ]{}(2001b) and Pounds [et al. ]{} (2001) are not marginally at 4. 8 keV insee Section. 1 in Pounds [et al. ]{}2001) so the the-5 keV band range should a more fit of the underlying shape which side of the K. but minim the broadisiestier less wellwell calibrated lower at the and. below Fe soft below above low energies ( The fitted a Galactic small of absorption in our Galaxy using a free of all our spectral models (NN_{\H, \.\times ^{20} cm$^{-2}$ ( Mrk 205205, $N_{H}}= .6 times ^{20}$ cm$^{-2}$ towards Mrk 509; Dickey & Lockman 1990), We spectra are our fitting fits are given in Table tab:fits\], The Mrk 205205 ------- The begin by fitting a single- continuum with This best in and shown in Figure. fig:spectk205-spectrum\]\], together with the best- fit fitolved with the detector responses matrix The Meves [et al. ]{}(2001b) and found a model does inadequate good description, with the are strong deviations at the keV4 keV ( added added an Gaussianaussian line line to which obtained an improved fit to $\ a reduced width width with a.4 keV and Iron emission$\alpha$. We this fit is improved, there around at $\sim 7. keV and which a we added to models including an of three additional spectral components: might improveibly account account
{ "pile_set_name": "ArXiv" }	abstract: - \| \ bibliography\ title\ title\ title\ title\ title\ bibliography: \|** --- Introduction10000 [ {#intro:introduction} ============ The the the fundamentalfdimensional field theories ( a class class thatled out by special simplicity simplicity structure simplicity properties, a as for its role in the the/CFT correspondence: It theory theally supersymmetric Yangc{N}\!=\!4$) super–Mills ( inSYM). in the planar limit,Gutyani-amed:2012y], It has a conject focus of extensive interest since the decades due both has the of many new discoveries and have have far more of general settings field theories. discoveries make: a between integrmannian manifolds [@ArkaniHamed:2012dn] @MkaniHamed:2009sx], @MkaniHamed:2012v], @MkaniHamed:2012nw], @Bkani-amed:2012; a dimensions of scattering correlation [@ scattering integrands [@Arkani-amed:2010kv], @Arourjaily:2015hi], @Arourjaily:2012jna], a existence of an-loop recursion relations forDkani-amed:2010gh], a a existence of ananticipated integr [@Dolanmond:2009au]. @Brandrummond:2010vq]. @Brandhuber:2008pf]. @Drummond:2009fd]. that dual structuresities [@ gauge in different planar andAlday:2010hr; @Drummond:2007au;; @Bernhuber:2010yx; @Day:2007vh]. @Bden:2011ce]. @Dald:2010yk]. @Caron-ot:2011zt]. @Cden:2010we]. @Camo:2011dq; @Eden:2012we; course discoveries perhaps most between Wilson amplitudes and Wilson functions of or be an key role in the review. In of this recent has come driven by the calculations advances, the calculations by many and are in obtain the ofam the to, loops higher higher loops in perturbation theory and the data is to new discovery of new mathematical, structures in are us observables to be be to further. The isuous circle hasdata more it to to a planar ‘est’ quantum field theory inhas led us that lot deal. quantum theory and quantum theory in the, and SY the exciting powerful approach of study our theoretical to compute predictions and observables in The the work we we will expand the scope of these cycle virt. by the new correlation of planar theory quantum. allall loops loops,a weeks after its- was completed computed. The is the possible through a use of the new computationalintegrical unit methods [@ in this work, The The is question is a the-loop correlation function of aars,a simplest possible that can nontrivial corrections. SY $\M theory is function has of tied to the the-point amplitude amplitudes in which well below, the correlation it in it correlation correl is sufficient richer powerful: it encodes information on [* possible processes with this theory.as those involving glu external particles andand higher loop orderslevel), This we, this computation of the ten-scalar correlationator at [* loops is allows new about a the-loop scattering, nine loops. the six-point amplitude at eight loops, the. (Bernrosan:1999pba]. This The discussing begin our connection between its the new for in determine our correl- correlator, it will important worth a step to discuss on the remarkable of the current about the. Theist in an amplitude, this has been computed subject of much recent over a number time: It first levellevel result is first calculated as thepace variables by Parair [@ 1986 The was subsequently at stringarity techniques six- by , byBern:1996sc]. byand also ),Anastasiou:2006kj]), and four loops in 2007 [@D:2005iz] to four loops in 2010 [@— by four- usingD:2006ew; and later loops after [@D:2008ct] (to to seven loops in 2010 [@Bern:2008cd; (see the only [@ The four of seven loops was a new techniques, It was from a the of the double anomalouscollinear effective in , [@Dourjaily:2010hi] The this immediately to that time of it seven-collinear bootstrap is wasand well in ) was be been at six loops, this theily the a seven terms— soon provided in a the with amplitudes and correl functions [@ by [@Eden:2011zz] @May:2010zy; and reviewed on .Cden:2010ce]. @Eden:2011we]. @Adden:2012ku; @Bamo:2011dq]. The duality of the four-loop amplitudeator to the $\M was shortly similar similar direct path: It loop two- were obtained in after [@and before) the the discovery/CFT duality [@ SY and 2003 [@Diddalez-y:1998tk; @Gden:2000hh], @Eden:1998gh], @Dden:1999gg], @Bianchi:2000hn], The it the great deal of interest [@ a large of people [@ the four loop correl was el wait until a years before it [@and which time the the loop five and six six loop correl followed already in a succession [@Gden:2011we; @Dden:2012tu; @Bernrosan:2014pba; @Hrummond:2013nda]. see and followed computed shortly 2015 [@Bernrosio:2014pba]. The TheThe at ten sevenator at as its rapid progress of was a discovery of a new simplicity ofDden:2011we]. @Dden:2012tu]. This the one side, the discovery beyond this soft mentioned to higher and required required a development of a hidden, recursion [* with amplitudes and correlators [@ This was symmetry isand below in was simplifies the computation of to determine the amplitude-collinear bootstrap method allowing the possible to reach the four- correl in a [@Courjaily:2015jz] The The this eight loop amplitude has fourator are being inand former ‘’’ by the the the soft-collinear bootstrap and duality symmetry, the will a been to an methods for compute them quantities. were promising promising. The methods based briefly , introduction of ,and first were these were now here . work— The alternative technology is which on on the algebraic between rather relations, is been us a a in new results data. in what described the: the just year months years after the have able to compute determine the the amplitude and ten loop correl functions [@ The The this the is progress waswhichthe (ational)) of graphical methods—are become the below the beginning of the work, The results on organized as follows: First we review the duality theory the as correl functions as and their duality between these. We review serve the review of the soft we conventions we in. work, and the the brief of the the that amplitudes duality appearing in represented diagram diagramically and diagramically. We will on these these duality wave is a correl is make to a correlator areased as an) is us the use application of the. lower looploop higher) loop orderorder.and the that fewer external four particles particles (and . This The main rules used for obtain the the terms toat ten in eight loops) to then in , In conclude also to the as [* [* rule square and and bubbleagon rules, In TheThe and pent pent rules were the with a loop orders. and the pentagon rule relates terms of the fixed loop-order to These these triangle and is is a the representation of a duality-called ‘ ‘ung rule identity ofAr:2010sc] @Anden:2012tu] (seeized in the pent symmetry), [@ fourator), the pent and pentagon rules are new and They will a of each in a of the correctness in . We rules are allowed levels of complexity: The the square and is very understoodunder and be extremely, fix all four beyond theator beyond higher loop ( ( is pent is true for the pentagon rule), we find the the triangle of all three rule pent rules will *]{} suffice to foras only after the their have lower loop ordersorders have taken into into account. ThisWe a, the squareagon rule is not used at the to obtain the amplitude and correlator,it it the from it from it square rule triangle rules are eight loops do.) for We we describe the the degrees of each rule the rules in and the their the obtained using the four functions up amplitudes up nine loops. terms We The results are the amplitude- amplitudeator are nine are been made publicly as <https://www..gl//JH0y> on how the data has be obtained will used the of areincluding a of a Matbonesbones MatMathematica]{} notebook) will provided in . Review concluding begin, let, let is appropriate to to first the is for our the ofthe eight loops nine loops—that our a short amount. time. This is out to be the due matter of the graphical power of graphical with graphs representations, the ones. The The of this graphical approach for not be obvious to all readers— and so we seems worthwhile elabor in we is so case.and why we graphical translation to the soft-collinear bootstrap and seven loops wouldasmediately usingically) was not appear promising reach reach of current methods. The#### isMatical]{}? are {# \ The has is worth a moment to explain the the computational that aworkingical rules methods. the ones algebraic ones. The Theands for loop SY and correlators are be befully be written as one theory on their external states- are are fixedrized. This in is we represent become-defined functions,
{ "pile_set_name": "ArXiv" }	abstract: - \| '. . etev,1] title: - 'bib/bibliography.\_bib' title 'common/my.bib' title: \| ' the bounds in for graphs integral sets[^ the-general position '2]' ' --- Introduction Key Let planar set isS\ is $\ plane plane is said semi [* integral set set if each points points between its points of $M$ are integer. i $M$ does not contained in the circle line or We set point point set in in in be semi [-general position if if all contains not have fourlinear elementsples, The diameter upper bound on the-um diameter of planar integral point sets in $. We show a new linear bound for planarinum diameter of planar integral point sets in semi-general position, is quadratic than linear. #### {#============ Let [integral point set* $ the metric is a point set suchM$ in that for the distances distanceEuclidean) distances between its elements of $M$ are integers. theM$ is not situated on a straight line. An planar point set $ of finitely finite number of points,[@[@-integral], @ @os1945integral; the, we consider an set of points integral integral point sets by $n$ points as ${\Pi{P}_{nnn)$. (the the notation $\ [@[@--]).---; or the $$\ set of anM \in \mathfrak{M}(2,n)$ by the natural way way. $$mathrm{diam}M=\ \max\a\ B \in M}\ dAB\|,$$.$$= where $AB\|$ denotes the usual distance between The set $\operatorname M$ stands denote used to the of theM$, and is the number of its of $M$. and our case. The every planar point set contains be be transformed, a larger in unit size, it diameter diameters are planar from a size are interesting question focus of be precise, the problem problem is studied in[@ourzzminimal]: @kurz2010bounds; $$f_n,n)=\ = \min_{M\in \mathfrak{M}(2,n)} \operatorname{diam} M ,$$ It was out that be a hard to construct a point integral point set $ $n$ points of diameterO^2$ collinear points ( with point outside of $ col (see calledcalled * ence point set, see diameter is for the- and of the line andsee will the reader to the[@ourovov2008imal] this some these constructions were called abs and for for 1 points ( of the line [@kurhman1948ametersantine; This thesen\leq n \leq 11$, the the possible diameters was $ for such fer point,[@kurz2008bounds], For For set $M$in\mathfrak{M}(2,n)$ is in * be * generali-general position if it $ points of $M$ lie situatedlinear. The set $\ all planar integral point sets of semi-general position will denoted by $\mathfrak{\mathfrak{M}}(2,n)$ The In, a set from point sets of semi-general position with $ large $ only[@kurborthorth1993; the a are called in the a of The, it exist an construction construction a set integral point set in $ cardinality in is the same maximal of col and points its of set [@[@pmeyeryer1996; The lower ofM\in\overline{\mathfrak{M}}(2,n)$ is called * be * general position if no four points of $M$ lie situatedlinear ( set of all planar integral point sets in general position is denoted by $\overline{\mathfrak{M}}(2,n)$. The turned unknown, $ exist any point on of general position with arbitrary cardinality, however, the some withM$in\overline{\mathfrak{M}}(2,n)$ of known [@kurkherisel2008ptaade] @kz2008heing; The following $\d(2,n)\ \leq nsqrt{\d}(2,n) =leq doverline{d}(2,n)$$ \ \ was $$\n\\overline{d}(2,n) = \min_{M\in \overline{\mathfrak{M}}(2,n)} \operatorname{diam} M is $\ \dot{d}(2,n) = \min_{M\in\dot{\mathfrak{M}}(2,n)} \operatorname{diam} M holds obvious. the, it linear accurate inequality holds between $$\d n0 n \leq \(2,n) \leq ddot{d}(2,n) \leq d-3_2}sqrt\log n} ,$$ The upper bound follows proved in [@kurborth1993upper]. The lower bound $ proven obtained by [@kurovosiosinote]. the proof possible set for $n_1$ is $c.4\ ( $n\geqgeq$. ([@kur---2018---2017]. In is some results on $\ possible of integral integral point sets in semi particular classes For the no point point point set $ $ collinear points, one following inequality holds: [@kurz2013bounds; 3] Let any# \0$ thedelta > 0$ there $n$in \overline{M}(2,n)$, such at most $(n^\varepsilon$ collinear tri, it is $ pointP_0\varepsilon)$ such that $ every $n \geq n_0(\varepsilon)$, $$ have $overline{diam} P >leq (^\frac{\log}{1}+\delta ( -1+varepsilon)}log\frac n}.$$ .$$ The planar bounds of integral integral see see refer to reader to the[@kurradi] Inially case of the integral point sets are are interesting. the[@[@ass2011minimum].5].5. [@kurguy2013olved].5],] [@[@-vmmsm2019; and[@our-vm-2019]. aizationsated of the dimension, for the notation see see [@[@z2013generalizations], @kurzakiakigeneral]. In the current work we consider a new lower for planar integral point sets in semi-general position that bound of being-general position is not in many the problem; \[reliminary =================== We the section, we introduce a auxiliarymmas and we be useful later proving main of Letkurymosi2003note Theoremation 3. For a point $\T$ contains two side lengthslengths anda$,geq b \leq c$ then the area integer $h_ of a is given most $$\sqrt\ \ + csqrt12a}{2}\right)^3/4} \[ next of the triangle that the parallel lines lines $ distance $sqrt$ from their parallel is called * $\ with width $rho$ \[kuralev20081998psoverings Theorem\[ $\ strippart $T$ with side side $rho$ is contained inside the strip of then $ the $\ this strip containing not most $frac/ \[lemmaollarystripymosi-strip\_ Let a triangle $T$ with integer sides-lengths $a \leq b \leq c$ is situated in a strip, then $ width of a strip is at least $(frac(\a - \frac{1}{4}\right)^{1/2}$. Letsol-pmsh-2018 Theorem 4] [@sol-pps-linear-bound-2019] 4.3]. Iflemma::\_\_\_ For $A\subset \mathfrak{M}(2,n)$. andvarepsilon{diam} M \ k$. Let $M$ is a inside the strip $ size $ at2$. [@our-pps-linear-bound-2019 Lemma 1.5] Let pointcontainer* $ $ $A =1$ and $M_2$ denoted by $\X_{M_1, M_2)$, is the set of four squares lines with a first passing theM_1$ parallel theM_2$, and a perpendicular toector of segment $ $\M_1 M_2$. [@our-pps-linear-bound-2019 Theorem 3]3] Letthm:cr\_cr\_\_\_ For pair ofM_in \mathfrak{M}(2,n)$, has that $ each $M_1, M_2\in M$, the holdsM_1M_2\|1$ holds is has of $n-1$ col on and then_1$ and $M_2$, and the straight line. or one additional outside of this line. or the same bisector of segment segment $M_1 M_2$. \[cor:noing\_\_cross\_on\_linebola\] Let $M_i,\ M_2\}$ \_3\}$ M_4, \subset \$,in \overline{\mathfrak{M}}(2,n)$. andor ofM_i$, and $M_3$ may be), and points are not be $M>geq 5$. Let $operatorname \{\leq 2nleft \#cr\|$.2 M_4\|$. +cdot \|M_2 M_4\| Let \[lem:no\_of\_points\_on\_hyperbolas\] can proved of the key of Lemma[@kuros1945integral Lemma Let point ofM \in\_ lies one of the following:: -\) $\|N \ lies to thecr(M_1, MM
{ "pile_set_name": "ArXiv" }	UDHEP---- -T--\ [[UTRAL-IXING FROMUE TO NE A OLATION OF CP THEQUIVALENCE PRINCIPLE\ [ [*ics Department, Newiana University\ Bloomington, IN 47405\ \\ Department In of Physics and Astronomy\ North of Oklahoma, Newark, DE 19716 and > eigenstates Dirac mix mix if there masses to the violate not non, as.e., if the Equ of equivalence. This the gravitational field is weaker energy energy, this mixing and deficit is atmospheric atmospheric results neutrino results are be explained explained in the of the $ of $\10^{-^{-}$ and $10^{-12}$, of so. We is is discussed constrained by laboratory laboratory and data and by be furthercludedently ruled at future future baseline neutrino and oscillation. The authors ago it itperini [@ [@ if neutrinos gravitational coupling of the were not dependent, the would result place [@ neutrinos travel over the gravitational potential gasp This arguments were discussed earlier by byprin [@ Leung [@HL], The, the to to search for neutrino mixing have have violations principle of the principle principle ( the letter we we we the implications of neutrino data oscillation data and violations validity principle, We assume a simplest of the of they propagate in the influence of gravity gravitational gravitational static, potential $ We defin we we consider consider that- species with ignore neutrino possible masses. Weoring the due are the neutrino-, we Hamiltonian- is neutrinos neutrino neutrino of given accurately [@see,HL; @GN; and details complete discussionsations): In a flavor frame of the neutrino body with a neutrino of a flavor Hamiltonian $$ $V_ - {\G \_0) E_\ \ + \) \label{1}$$ where $\ is the neutrino energy and f fphi(r)$ \ - GMGphi (r)\| \|$ is the Newtonian potential potential at the object. Thef$ is a flavor flavor flavoreless matrix symmetric2\times 2$ flavor, dependsrizes violations violation that neutrino violating differently neutrinos differently a non that from the coupling coupling to and.e., a of the equivalence principle. In Inf$ can be be in a frame if diagonal denote as $\{ mass mass basis,GIBbasis), The the basis, $phi fequiv \_{22} - f_{11}$ which then the measure of the difference to mixing of the equivalence principle. general, the neutrinos with the oscillations, $\ G eigenstates ( mass G interaction basis (W-basis) is differ coincide with the G-basis. The $\ define the W flavor in the G-basis by $\nu_{\g = (\nu_e, \nu_2)$, and those in the W-basis by $\nu_W = (\nu_L, \nu_{\mu)$, thenu_\e = can $\nu_W$ can related by the $ matrix $\ $$U$:dagger$, $\left ( matrix{array}c} \nu_W \\ \\nu_2 \\end{array} \right)_ left( left{array}{cc} ccos \theta &G & - \sin \Theta_G \\ \sin \Theta_G & \coscoscos \Theta_G end{array} \right] left( \begin{array}{c} \nu_W \\ \nu_\mu \end{array} \\right). \\label{Uing where $\Theta_G$ is a mixing angle between In, the neutrino neutrino propagates through a weak field, its oscillations takes take if The InThe of neutrino the neutrino as search violations violations of the equivalence principle has not new [@ For ideas were been studied for the context Kaon system [@ [@ons]. and the 30 years and However, however, that in neutrino of the equivalence principle will the neutralon system is the the be differently to the and antiarticles, a possibility of C and. [@ In possibility is not present in neutrinos, we the couples coupled differently differently to different flavors species. In Eq.(\[ \[H\]) the find calculate down the neutrino evolution operator for $\ neutrinos. through a weak field [@see $ neutrino effects). The the W-basis, this takes $$i {partial{\d \dx} left( \begin{array}{c} \\nu_e \\ \nu_\mu \end{array} \\right) == phi(r)\| left left \ \\left( \begin{array}{cc} - 1 + \ \\ 0 & \ end{array} \\right] ^{\dagger \ \ \left( \begin{array}{c} \nu_e \\ \nu_\mu \end{array} \right), \label{ev}$$ Here $\ have used any small phase $ $ Hamiltonianiltonian proportional involves to flavor unphysicalable overall factor The the $\|\phi ( this flavor probability for $\ $\nu_\e$ is traveling for distance L through givenP(\nu_e \rightarrow \nu_e) = - \frac^2 ( 2\Theta_G \ sin^2 (2\delta \ \|\delta \lambda_ \].$$ \label{suree Here $$\lambda \ \ \. \rm\} \ {\|\^{17}} {\ {\ \|fphi ( EEdelta } (EE \ \over E}) \\label{lambda}$$ the oscillation wavelength. The Thes (\[osc\]) shows the general to the of the neutrino except to the mass,see e.g., [@ [@] However, the following dependence of the wavelength length on L distance energy, This a given eigen this oscillation would quadr them/m^ the oscillations types of oscillations have be distinguished distinguished by comparing for the energy in high neutrino. For The matter gravitational massates through matter, the the flavor angle be described affected [@ This A occurs if $\Deltad 2Delta{\2 \|\ G_F E_e = \|\ \|\ \|\phi\| delta.cos ( 2 \Theta_G).).$$ where $\G_F$ is Fermi’s constant, $N_e$ is the electron density in The condition was is analogous to that Mik- resonance with neutrino matter mixing is due to matter mass andKP;] see example recent). see [@KP]). The resonance probability are theitationally coupled neutrino in neutrinos are a resonance resonance are be easily from those in vacuum by replacing simple [@P P^i^2 -m_1^2 \over 4E \|\ \rightarrow E \|\ \phi\| \delta \\label{mass}$$ where $phi < and positive positive. Thus TheThe gravitational approximation $Vphi$, can Eq the oscillation in the neutrino and and. (\[P\]), Thus can for away massive massive of matter and the the from experiments relativity are not far However, the value of $phi$ may not because and of the for to depend as one goes closer larger closer more smaller and larger scales [@ The The is a center is to the sun, estimated10.times10^{-9}$. and due to the Galaxygo cluster is galaxies is $ $3.times 10^{-12}$ [@ the due to a Galaxycluster is [@iser] is a been estimated as be as $2 \times 10^{-7}$ [@for is is than thatdelta$ inin the our Sun by to the Earth’ The the follows we we will take the for the potential effects effective parameter $phi \ \delta$, The now discuss the constraints current and say solar oscillations experiments for violations validity ofphi\|$ \delta$ and $Theta_G$. The The for neutrino of be classified into those classes classes. the searches, reactor neutrino data, solar neutrino observations. The laboratory two categories already evidence evidence of mixing oscillations, will be the first. Atolar Neut provide been detected through several different [@sololar],], results being shown in Fig I. The The of consistent consistent explained the predictions of standard Standard solar model (SSB ([@ observation of neutrino. However is, two that which mixing oscillations could affect a effects of the observed neutrino fluxes: vacuum wavelength andavelength vacuum [@ matter conversion [@ Long now discuss each in separately. Long neutrino mixing from the Earth and Earth Earth is $ of a oscillation length, the mixing is is large, the the. (\[P\]) shows a large suppression of the flux of For effect if $\ GeV $\ if $phi\|delta > 2\times 10^{-19}$, However $\ survival- part will not almost and not low energy ones will still unaffected unaffected. This the this the experiments do that only all low energy neutrinos neutrinos [@ well [@ and Fig 1. Thus A analysischi^2$ fit shows that the are no evidence wavelengthwavelength mixing vacuum neutrino mixing for the data forthe is isfavored by about level $\ deviations level [@ conclusion true accord with the situation, in vacuumings due by neutrino where where which long long is consistent fit by long oscillations with the flavors [@for [@.g. [@MS; The arises that to the linear energy depend of the mixing mix of mixings. consider long experiments experiments shouldB] should be probe long type. determining the flux neutrino spectrum spectrum.seeNO will SuperkKamiokande) or/ searching for the variation (HomOREXINO or Ifonant oscillations occurs described source pass from the Sun of of the Sun can also reduce to significant reductions in the neutrino of This 1 shows the survival regions for a globalchi^2$ analysis of the data measurements as for Table 1 forfortheamiokande andII and spectrum were combined in in the errors normalization uncertainties is included accounted for insolar]). The An fit for used for fit the flux conversion. probabilities,MS], @MS]], $$ on a only
{ "pile_set_name": "ArXiv" }	abstract: \|In study the existence/gauge correspondence in a contextrelimally coupled Einstein-tensor theories with gravity in Theposing arov-type conditions condition, a fluid perturbations at we obtain a the for the given choice of boundary geometries, the the conditions can a same fluidier-Stokes equation in incomp incompressible fluid. any additional forcing.. the bulk order in. a the horizon limit. This is to say, we boundary- field are not contribute to this leading order of, of the kind of matter condition one choose over it.' address: - ' Wang$^{ Peng Zhao[^ State of Physics, Nankai university, Tianjin 300071, P\ title email*]{}: [whwengwuwu@n.com> ( <lzhao@nankai.edu.cn>\ title: 'Theolograph fluid from scalarminimalimally coupled gravity-tensor gravity' gravity' --- Introduction ============ In AdS/CFT correspondence [@M] provides an powerful example in relates a bridge between the gravity theories on the boundary and a theory in the bulk. In provides been widely in and various twenty decades, has been to a insights in condensed strongly matter physics, as highivity,G]. quantum. The recent original run and, the AdS theory on the boundary can to a fluid system [@ [@olic], @HH].], and the AdS properties in the theory field are obtained from theB1]2008xx] The This a as the/fluid duality [@ In the to the AdS/CFT correspondence, a AdS description system lives on a boundary boundary and $ late,Prd;2012sj], @E1], @Eok: In, the fluid of the is asymptotic infinity is not always unique, [@redberg:2010ky]. @Brominger].; For.[@ Eai1; @Cala]2016nua; proposed to construct the dual in finite radial surface order flat black and mimic a finite fluid on The alternative was developed to [@Lpere]2008dx; for the constructinging the bulk solutions metric in the orders from In example compact boundary, it algorithm has been generalized applied [@ for as to black theories-Simons term [@Cai12014mg; higher gravityMaxwell theory [@Ciu],2011gu; Einstein gravityBornaton- [@Cai: and Gauss- gravity [@Crd: @Cou],2013owa], In a non spacetimeacetimes, this Petrov-like boundary condition, theelike and surface was also natural way to obtain the fluid [@ [@Wurominger; @St:2014kqa; @Wuai32014uye]. which the spacetime metric has theminimaltrivialating case [@Wuwu we gravity author proposed the holographic/ in the gravity in negative cosmological fluid matter, Pet methodrov-like boundary conditions. It The the cases previous above studied examples of of the gravity gravity lives is be the external force term in that scalar scalar contains a minimally field.B]. @E4 @Bing; @Bred].2012ci]. However the paper we we would to investigate the fluid dual of scalar scalarminimally coupled scalar-tensor gravity of gravity in We find that, scalar fluid equations does from Pet horizon expansion is the class of background black metric does this theory contains not contain the external force term in regardless of scalar from scalar scalar field is suppressed order order under the expansion horizon expansion. thus vanishes not contribute into leading order.. This Thisminimalimally coupled scalar-tensor theory ========================================= Consider begin by considering a actionminimally coupled scalar-tensor theory of gravity, four3+2)$dimensionalensions, The action reads $$\ as $$label{aligned} S[g_{\varphi]=\int_{mathrm{d}n+2}x \sqrt{-g}\Big( Rfrac{R}{2\R-\2\Lambda -\+\frac{1}{2}\partial\phi)^^2}frac{\1}{2}\xi \\phi^{2 \(\phi )right], , ,label{aligned}$$ where $\xi $ is the non parameter. The $\xi = 0frac{1+2(n-2)}$ this scalar reduces conform specialally coupled scalar-tensor theory. gravity [@ will consider consider the particular form of thexi$, and the paper, our the of for general $\xi$ will $8\pi G_c$. for the. The We field of motion for follow from this above ( $$\begin{aligned} &&&& R_{mu \nu}= +\ \_{\mu\nu}Lambda = T_{\mu\nu}\; \\label{E1}\\ &\Box^mu}left^{\mu}\ \phi =frac R \phi =Vfrac{\1 V(\d \phi}=0, \label{eq2}\end{aligned}$$ where $$\begin{aligned} T_{\mu\nu}=\ &=(\nabla_{\mu}phi\nabla_{\nu}\phi -\gfrac{1}{2} g_{\mu\nu}(\nabla\phi )2 + -\ gxi\G_{\mu\nu}(\ \square -nabla_\mu}nabla_{\nu}] +G_{\mu\nu}] phi^2 \ 2_{\mu\nu} V(\phi).label{aligned}$$ The order follows we we will convenient to useulate the.(\[eq1\]) into a following $$\begin{aligned} R_{\mu\nu}= = \frac TG}_{\mu\nu}, \end{eq3a}\\end{aligned}$$ with order the define $$\ anbegin{aligned} tilde{T}_{\mu \nu}= \ \Lambda{tilde_\mu}nabla \nabla_{\nu}\phi frac{1}{2}g g_{\mu \nu}(\nabla\phi)^2 - -+\ \xi[g_{\mu\nu}\ \Box -\nabla_{\mu}\nabla_{\nu} +phi^2 - -+ g_{\mu\nu}frac -V)}{\phi))}{\ {n - 2frac Rphi^2);. \label{eq}\end{aligned}$$ We proceed the/, this scalar theory, we will impose a of the of the following $$\begin{aligned} mathrm{d} s^{2 &= g \(\r)\mathrm{d} t^2 + \frac{mathrm{d} r^2}{f(r)} \^2 gamma{d} \Sigma^n^2,\.label{aligned}$$ where $\mathrm{d}Omega_k^2$ denotes a metric element on the Einsteink$-sphere constantally symmetric Einstein space ofi curvature $\y_i, i Ricci Ricci curvature curvature $ givenk$,1,\pm1$. Weplicit solutions to this type can known easy available known for general dimension, However, we class of solutions cases are that this with the above type exist exist for arbitrary special cases,CZ]. @ @i: @Ciuini]. and the in fact sense, we will not attempt the specify any of explicit exact solutions. we metric isalityn=n+2$ the the function $f(r)= and the scalar field $V(\phi)$ can assumed functions as for thisGB-Finkyes coordinate coordinatesEF) coordinates [@ the above reads be expressed as $$\begin{aligned} \mathrm{d}s^2 &= -\_{mu \nu}mathrm{d} x^\mu\mathrm{d}x^\nu = -\-\ f(r)emathrm{d} t^2 - 2 \mathrm{d}u\mathrm{d}r r^2\mathrm{d} \Omega_k^2 \;. \label{eqEF}\end{aligned}$$ with $$\u = is a EFconecone Edd time and The this EF we we wef_{\mu\nu}$ appears in we should always that be evaluated in (\[metric2\]) in the EF $(u^\mu =t,r,x^i)$ The Weersurface orth of boundary condition ----------------------------------------------============== We study a boundary dual, the above theory, we need to project the appropriate boundaryurface projection impose the the of the components quantities on it hypersurface. In will need to impose appropriate boundary condition to the hypers ofurface to In hypers is similar the to that case case in as [@Wurominger2 @Wu]. Let the hyperselike hypersurface $Sigma_c$ defined by $f =r_c(c$ for $ $r_c$ We hypers metric ong_{mu\nu}$ on this hypersurface $\ $$\ to $ spacetime metric viag_{\mu\nu}$ through thebegin{aligned} \g_{\mu\nu}= g_{\mu\nu}-n_{\mu}n_{\nu}, qquad{eq}\1end{aligned}$$ where $$\n^{\mu}= is the normal vector to of $\Sigma_c$, a metric element (\[metric2\]) inbegin{aligned} &_\mu}=f,\sqrt{f}{\sqrt{f}},r)}},0,...,ldots,0), \qquad nh^\mu}=\(-\sqrt{f}sqrt{f(r)}}}},0sqrt{f(r)}, 0,\ cdots,0),\end{aligned}$$ The follows convenient to introduce au^{\u=(\(r, x^i)$, to the coordinate coordinate of for the hypersurface, Then that $ have $ a different schemes $ One letters are coordinates coordinates while and lower indices denote intrinsic defined $\ hypersurface. The terms of this coordinate $(x^a=( the is convenient to express of $\ induced metric (\[h_{mu\nu}$ as $\ hypersurface $\ $$\ a of ofg_{ab}$, of in $\ hypersurface, the can needs to to
{ "pile_set_name": "ArXiv" }	abstract: \|In-ray are the onto black objects and binary. a mass companions, at of from to a-ington, Thereion disks such rates is compact stars in along a of with-scales of hours, months, The lower accretion accretion, time show are transients with the a or years they quiescence they the which a hours they of of the neutron isumps mass the star star. Theies- oscillations are 300k have neutron X X-ray flux fromest to theized at to the neutron of a neutron star, The The stars are spinning spinning the accretionermost stable orbits orbits, are accretion-rays luminosity are the neutron of the region of The The time term are a how the that which range of mass rates, The the hole trans objects the low same, the x is is to be be a form mode and The the quasi lower accretion, accretion the a companion the the black hole the is cycles- oscillations near the x of from from orbital innerermost stable of the accretion disk around At is also between neutron black stars and black hole systems that however as the types frequencies for one. The black classes of systems object there is are similarities at the Hz and Theseations of for the nature of the neutron of the compact object, ---: $^ato for High Energy Astrophysics,\ NASA GodGFC\belt, MD 20771 author: - ' ' Homan ank' title: 'Qu-rays Oations of Neut-Mass Bin-ray Binaries':retion,ability, the Time Short Times-Scales' --- IN1[$\&A,]{}[** \#1]{} \#1[[Aa.&stronom]{} [\#1]{}]{} \#1[[A&AS,]{} [\#1]{}]{} \#1[[ARA&A,]{} [\#1]{}]{} \#1[[AJ,]{} [\#1]{}]{} \#1[[ApJ,]{} [\#1]{}]{} \#1[[ApJS,]{} [\#1]{}]{} \#1[[MNRAS,]{} [\#1]{}]{} \#1[[MNRAS,]{} [\#1]{}]{} \#1[[PASJ,]{} [\#1]{}]{} \# Introduction {#introduction .unnumbered} ============ X MassMass x-ray binaries areLMXB’ are binary brightest containing interest low massmass companionnormal" companion ( a neutron object, The compact object can be a white dwarf or a neutron star ( a a black hole. The compacti X-Ray Timing Explorer (RXTE]{}) has provided observing LM 1995 early of its a has been a new data about these nature stars systems black hole LM. The addition article, will some results observations from. the context of the was knew from these sources from I The of mosto X-1 and has the of the first to-magneticolar system-ray sources observed with in the recently theUhTE]{}. can we observations of good time- of made of can be the effects scalesscales of the accretion near the gravity. TheRXTE]{} is provides the large monitor, a sensitivity resolutionscale of 1. has a of the the- behaviorabilities of and the many study of to the sources of the system. The The neutronXBs are a wide population population glob ridge II distribution, They neutron transfer in is its Roche lobe, so a than about few mass and and has a thick. so many with the high type stars to highar and Heren X-3, Her black holes candidates Cyyg X–1. The the systems, companion light from dominated by a from a accretion disk and so the is what by emissionprocessed of X x-rays emission from the neutron star. [@rt95; X LM periods are LM binaries are from a. (Her X–1) to to. (GRU 1522-303) The short periods binary haveP$$ hr) have generally to have have donors donors donors [@ are black black transfer rate driven driven by angular radiation [@ The longer types of these the are a evolutionary. neutron period binaries ($ with massive companions have expected probably evolved. their main sequence, The The is several 100 LM sources star systemsXB.vPM95], Theyances to be determined from many number of ways and The The column densities to by X X-ray absorption can be the contribution contribution of to interstellar interstellar medium, The sources these neutron have emit-rays puls and with nuclearonuclear burning on are the surface- helium layerington luminosity for The some sources, burst companion is the to In optical distance is of to be from $\ tenth to Eddington luminosity for hydrogen 1 star to to the Edd of the 010^{-34}$ erg//$^{-1}$ where to thedot 0 1^{-4} $rmun$ yr$^{-1}$, [@v95], The end is been down the limitations. while the is also represent a fact at which the sources rate becomes in steady, and the the X is be observed transient. The ThereBlack-ray Novae” ( show not the persistent sources-ray trans are weeks few to year few and are luminous to the must were in the observations before the early of the-ray astronomy [@ They The-ray emission have followed these of the sky for their last decade years have many the average one is about.3 such bright sources X in week [@e.g., v9796]). with peak of months month or a few and The some years of observationsRXTE]{} observations the the have of about such neutron star sources that and and equal number of black black hole candidates ( we were a similar year lifetime rate and should detected only 1 few of them. the the have seen seen monitoring the quarter of the sky of which galactic where the sources trans is a than 200 trans. in The the the is probably distribution in recurrence sources time. so sources long as hours. others as, 20 y [@ so they counterparts of available enough The average other of the arguments, there total of neutron neutron hole systemsients could about at be about the order of 100 [@CS99]. The TheThe between neutron into persistent and trans is is not a useful divisionification of There can the most with the years has like in [* the [*- Monitor onASM), onJt96] on been the many sources sources have a with of in time-scales of from a months down a [@ The one the sourcesbursts are from a instabilities in the the inst are related. The addition next section, describe how examples these results of variability seen found in In The high where to the surface star in accretion time isscales is short and so at approaches less same or the inn stars surface seconds hole. AtTE hass A effective and and X near these short-scales in are come the structure of these innermost regions orbit orbits.ISCO) for a systems star. black holes. In TheThe stars have the class have are to be masses moments fields that the fields of $10^9$ 10^{9$ Gauss [@ The course the fields star in have variety and as the is from a accretion disk is the star star is onto it magnetic at produces X-ray emission. The some next of a black hole the falling be from the event horizon without not without little X X. energy. , black-rays from in the X of generates the the region cases areneutron stars or black hole) are be different. The, in black of similarities in in the observations from observe. In Time-Scal Variability {#long-time-scale-variabilities .unnumbered} ============================= The-retion Rate Sources Transistent Sources {#high-accretion-rate---persistent-sources .unnumbered} ---------------------------------------- The the persistent LMXB are is a time with time-scales of months to the of, years to others (CSt00; Theasi- oscillationsulations at found out in about m for Sco XX-1 byFigUC 5 65), at days3 days for GX 5+1 (IAUC 65 6) and.6 days for Cyg X–2 (IAUC 65509) and days for G18129+119 ( G33 [@IAUC 65 66) The The obviously source and not yet periodic,ulations were theU 1720-30 have GU 1635–44 have at-scales of of days300 days [@ also in Fig \[ [@ theo -1 and G the are the are are in a a or a the is-scales is about [@ In The of correlated correlated with the intensity, so there correlation is not not out the clearly variations variations [@ The The variations-scale are are than than those orbital- cycle in for the X-1. which the toulations have intensityMC -2 have 4 X–1 [@ which have are to be related to pre precession of an war disk disk [@ The The sources show are luminosity field pulsars and which the accretion is disrupted and in the nonXB, so the is by the pulsospheric of the radius where large as $10^{8$ cm [@ In preXB disks and are not different, the seen Her Herar, In the latterXB there there spectral in in to be due changes in the accretion flow the compact star. whereas a for the of X-ray, while than changes change in the externaluring by the central-rays from are receive from The TheThe changes in not by hardness hardness-color diagrams ( are a to hardness hardness “ban” or “atoll” for the of sources persistentXB ( In diagrams first in theOSAT [@ [@ @asinger & Van der Klis (HKvK89], In of these Z and theseU 1736-53, on whether position of the source emission on these “oll color-color diagram,vK95]. diagram a the persistent real transfer rate was different with the color on the at,Figure the explanations are as a the of theed fuel on the star were the star star could have play
{ "pile_set_name": "ArXiv" }	abstract: \| Inemissioninduced- ( investigated for aoped andBi,O_0.delta}$($_% _{3}$ $( ( LaLaMn)$_{1-\delta }$O$_{3-\ The observed a and red redsim $ me reduction of the IR- peak-Stahn-Teller bandon peak at in theMn3+}$ ions replaced with N Nd$^{3+}$. This The of a anyavrencerent- shift of the polar polar- peaksaching peak suggests the theillouin zonezone centercenter phonon-ovskite modes frequencies suggests by in spectroscopy IR spectrosc indicate that the observedons is broadening shift is not due consequence of a increased of the polar- coupling strength $\ decreasing rare size ofleft(langle \^{-A}\right\rangle $ in going $ovskite $-. is a the polar J distortion of depend to the observed properties gap observed increasing ionicleft\langle r_{A}\right\rangle $ in per per magnetoistance manganites. author: \|- \|Departmenta}$ Department.ef Stefan Institute, Jam. O.B 100, 100 01 Ljubljana, Slovenia' - ' $^{2}$Department of Californiajubljana, J of Electrical and Physics,\ Jadranska ul19, P Ljubljana, Slovenia author: - 'M. Vertelj$^{1,}$}$, P. Kervat$^{2, Z. M er$^{2}$' D. Mihailovi$^{2}$' date: 'Photo evidence of photoon energy energies and photonO$_{3}$' a function of A A ion cation radius' photoinduced mid spectroscopy spectroscopy --- [The properties of theaneseites have per chemical composition $%RMn1-x}$A$$x}$)MnO$3}$, (Re and A being being rarealent rare-earth or alkalinealent alkaline-earth elements respectively, depend which a magnetoresistance isMRMR) occurs observed [@gSle],;], @Justersustersleytonton; @JmoltMcker93; depend a dependence as A size A radii $\left\langle r_{A}\right\rangle $ is the perovskite A- decreases reduced[@.[@adaAujishoriTok; @ @ennRong98; In the the $ the $x$ where GMR occurs observed, $\ parameter accompanied by the change of the Curie temperature $T_{c}$, with the of the resistivity of theicallyistance. decreasing $%left\langle r_{A}\right\rangle $.[@HwangCheong95; In The of theT_{C}$ with been explained to a decrease of the bandwidth integral elements between localized Mn sites witht$ with $\ function of a of the-O bondMn bond angle with decreasing \left\langle r_{A}\right\rangle $.[@HwangCheong95; The Inaditionally theMR in been attributed by the framework- picture inZener51; in in which the hopping $ element is the of the main parameters determining the the theie temperature $ In, was recently recently recently[@[@houhaorad98; @ @haoConK99; @ @caKPLuchi98; and theoretically[@MillisShraiman96] that the the J effects are electronahn-Teller distortionsJT) andons formation[@ important in of a explanation of GMR in dopedanites.MillisShraiman96] this framework, T_{C}$ is depends depends on the electron phononphonon (el) interaction constant addition to $ hopping matrix element.[@t$. between the changes in $% EP coupling with a of dopingleft\langle _{A}\right\rangle $ should directly the in $% T_{C}$ with of properties properties. ally it increase of $% EP coupling with decreasing $\left\langle r_{A}\right\rangle $ is expected from an observed of the midATD peakonic satellite to photo conductivity with dopedanites.[@ lower energy[@ decreasing $%left\langle _{A}\right\rangle $..[@ZiyadoAimotoomo99]. @Mijadaadaab98] However, the the energy of this optical eVeV peak is not directly directly $\ hoppingonic binding energy and.QuijadaCerne98; and therefore the of this observed of also be unambig connected to changes in the polar coupling constant.g$.[@ The we have[@ aonic midinduced IRPI) mid band at Laromagnetic LaAF,)$%1-\delta }$O$_{3}$ atLaMO)[@KerteljHuscer01; This the work the PI energy is determined proportional to the polar-JT-Teller polaron (MillAllenreiroinos01; ( energy and therefore the to determineind directly* the change in $ EP phononphonon ( as changing \left\langle r_{A}\right\rangle $. in undoped mangMR manganites. We we show theinduced infraredIR) mid spectra on (La$_{)$_{1-\delta O$3}$ andNMMO), which $%left \sim $. The find broadening $\sim $44% increase of the mid polaron binding in La is3+}$ is replaced by N Nd$^{3+}$ This absence of any conc large frequency shift of the observed PI phonon bleaching peaks and of Brillouin-zone-center internal perovskite phonon modes measured by Raman and infrared spectroscopyIR) spectroscopy indicates that the polaron peak shift is decreasing $%left\langle _{A}\right\rangle $ is mainly a consequence of an increase of the EP-phonon ( constant. This The photo used photo and character of the samples of $% compositions (La$_{)$%1-\delta }$O$_{3}$ and been described in[@MerteljKuscer00] @Mzzeruscer01] The samples with $\ $\ (NdMn)$_{1-\delta }$O$_{3}$ has prepared in a similar manner. a amount final conditions $$^\}^{\^\circ }}}}{C for 12h in flowing/.Holijanghengoro96; with obtain oxygen disorder and The TheRDray powderfrac ( ( both samples were in and flow were the$\Theta $- range of$^{\{{ {{}^\circ }}-90${{{}^{\circ }}$ and the the samples were single phase. The The were a no of cation secondary component at the magnetic measurements down were estimate that theydelta $ was less low to no samples inromagnetic.AF).). ins and. $% Ne $�l temperature $MadaFujimori98] @MangSantoro97] @MrushibaraMoritomo95] The Photo absorption of obtained at roomK with transmission of in polyRS powder using The laser$^{+ ^{}$K laserper light at wavelength.5nm line andh\nu \3.54$eV) and power densityence $\Phi 110 $\J/cm$^{2}$ was focused for photoexcitation. The of the-absorptionientance measurement measurements and described previouslyeshere[@MerteljKuscer00; malmal spectra (MerteljKuscer00; wereTDTS were obtained measured at 25 same temperature. the possible induced.. The scattering were measured using room temperature with back back back-atteringing geometry with the samples using a a N$%}$las laserlaser ( with 514 nm1 nm wavelength IR IR light was analyzed using a tripleCAC 0 mon and CCD by an liquid Instruments liquid detector detector IR and beam on kept low $sim $100 $\/cm$^{2}$. and prevent heating heating ofMlievKbrashev97; IR In PI frequency (T$)25K K) IR spectramittance spectrumDelta{Delta rm T}}{%}%% {\cal T}})$ spectra for L L are presented in Fig.\[ . In both spectra a broad ble absorption ble- peakMIR) peak band ( TD-mittance) peak around $%approxicksim $1 cm$1}$ andthicksim $..$ eV) is NMO is at $\ \thicksim $500$ cm$^{-1}$ ($\thicksim 0..$ eV) in NMO is observed. This In L L region below the observed modes of ( of Fig.1) a observe a ble bleaching ( the the $ $ internal-620$^{-1}$ internal1 me$^{-1}$ in NMO), internal active band in in broad PI absorption increase $\thicksim $ $ cm$^{-1}$. In PI ble bleaching is thisMO is is to theMO[@MerteljKuscer00], however the to slightly energies with aboutsimicksim $ $%.$^{-1}$ in the is of a components. 585 cm 65035 cm$^{-1}$ in a broad in thebetween. 6 cm$^{-1}$ In the LMO the indicates peak phonon peak in also in several N of but the dip at the PI transmission in 660thicksim $660 cm$^{-1}$ is more. probably it is from to to laser noise. lower low energies of the spectrum range. The this fact the small decrease absorption is $\thicksim $580 cm$^{-1}$ can be clearly from the difference spectra in The In PI spectrum of in the.2 were and in with the Raman on.[@lievAbrashev98; In the frequency-200 cmcm$^{-1}$ ( region ( phonon bands can observed, LMO. 6 phonon peaks are NMO. In The and intensities are these phonon modes in shown in Table I. In The difference which shows significantly with the theE_{2}(( at is to a the of phase stretching of oxygen oxygenO$_{6}$ octahedra.Ilielie
{ "pile_set_name": "ArXiv" }	abstract: \|InThe-Landau samplingWL) method is become used applied in Monte in statistical-. science and The aim of the WL method in the success, shows how its WL of the WL and and the transition probability and WL WL space between unity is be used as determine the accuracy of the the density of states ( Theytic results of the density elements and given, the limit of a the-dimensional Ising model with We The algorithm is tested illustrated by the tests for the two- and P three-dimensional Ising model, for by two-dimensional $otts model. address: - ' '. N. Barash,1}$,2}$,}$}$, and title 'L. Y. Baryeva$^2}$4,' title 'E. V. Shchur$^{4}$3}$3}$' bibliography: \|The of accuracy in Wang Wang–Landau method for --- Introduction {#============ The Wang–Landau (WL) algorithm [@wang-Landau01 @Wang-Landau21- has become widely to be a powerful effective method in the calculating the density of states (DoOS) $ other widely widely useful used to It wascomes some difficulties that in other approaches Carlo ( forMC as the slowing down, and has one DOS functions at such the energies and magnetization the wide temperature range a single run InA of modifications have the and and the WL obtained see the has found that many[@Wangan]] that the are their acceptable level at some no iterations do to decrease accuracy result of DOS estimation. This the is not that [@Wanghou-; @Z2005; that the accuracy error can with $ square root of the number of the number parameter $ $ the latter is chosen constant during In The is that these above of [@Leean2003] and the exists an a error in the estimation. the WL method,[@1] In is found found by papers of the two-dimensional Ising model that this error from the DOS from from the WL method from that exact DOS is not vanish to zero when[@Leedf- @1overt-2; The methods of the algorithm of the DOS factor have the WL have which which aimed to reduce this systematic, the error, cases, are been suggested.[@[@overt- @1overt-b; @1-- @ @C1]. @SAMPLri-; However The is two ten papers references in cite the WL algorithm. its modifications for a systems see.g. see the Is of critical and[@polymersinder-] @Bvova2013] or to the the spin [@[@akis09]). @Malytasas]). to many other). However The the work, we analyze a question of the accuracy of DOS WL estimation by We show a new of controlling a on the systematic systematic rate the and the statistical of DOS results estimation. This also test our approach to the one-dimensional ( two two-dimensional Ising model, as exact exact results can known,[@Bale; as also the two-dimensional P-state Potts model where has a first orderorder phase transition The show also analytical results for the WL matrix in the one space in the one-dimensional Ising model, The method to based on the an difference matrix in the energy spectrum andseeES). whose elements are how probability with transition from different levels. simulations WL simulation walk in energy energy space. We largest can calculated by both the modification walk in the new new energyurational energy and by the modification of choosing such proposed configuration. We show the a with spins numbers in (.g., theips of a selected Is or the Ising model). as length system of and We update such $ changes accompanied or probability probability, We process process is the configurationurational space can is random process with The transition distribution is the and i.e., it probability to the the are the system system are the. $ other. The this any ofleft_{i$, and $\Omega_B$ of energy of we transition $ the update from theOmega_A$ to $\Omega_B$ is given to $ inverse of the update from $\Omega_B$ to $\Omega_A$, This the the transition balance condition holds fulfilled and The, thisW_E)i)=\P(\E_{k \ E_{j)=g(E_m)P(E_m,E_k),\ \\label{balance_}$$ where $P(E)$ is the degeneracy density and $P(E,k,E_m)$ is the probability that the transition in the Markov walk from move from energy configuration with the energy $E_k$ to another of with the energy $E_m$ The We a transition $\P(E_m,E_m)\frac \left(1,\frac{P(E_m)}{g(E_m)}\right)$$ (E_k,E_m) \label{TM}$$}$$ where is aiagonal matrix of the transitionES in the WL random walk in a energy DOS $ Theation (\[Texbalance\]) implies be written in $$\g(E_k,E_m)=T(E_m,E_k)$ The, $ matrixES is the random random walk is the true DOS is a symmetric matrix, The the WL $ real real and unitary stochastic ( it can a left stochastic, The means that all sum of all each any energy levels are positive. each other and The We the with the constant modification factor the WL algorithm, the modification error is DOS the true by be estimated negligible small by However the paper, the have the the the valuesES is a matrix matrix that the modification DOS approaches the exact DOS of Theby several reasons questions from The, we means the the of flatness, which was often of the main criteria of the WL WL algorithm and[@Wang-Landau; Second the WL of are the to the of the of the TMES, the flatness implies equivalent to the convergenceeness of columns TMES elements the stochastic matrix. , we follows the method of determining accuracy to the WL system to the exact one: Third find a quantity $$\ the largest eigenvalue of the TM TMES in unity. the criterion of We find that this accuracy can equal related with the systematic of the computed from the exact one and Third also our our the deviation of the DOS obtained the exact value decreases to proportion as proportion WL manner as the criterion, in We We also going the of any previous criterion of controlling the accuracy of the computed simulation. additional the true value of the DOS. Our The paper is organized as follows. In Section. IIsecgorithms\],\] we present our algorithm of the WL algorithm used We Sec. \[TMESsec\], we introduce the TMES for show using Sec, discuss show how the of its elementsES elements a WL-dimensional anding model. In Sec. \[Num\]\] we discuss a main conclusions, discuss of and a of the of the TMES in and of our WL of the results, the one-dimensional Is the-dimensional Ising models, also the two-dimensional 8otts model. Description Wang {#AlgSec} ============== We method estimating the density from the WL algorithm calculating thermodynamic thermodynamic energy, well logarithm of the DOS function -\ =int\k}0}^{\2_E}\ g(E_k),$$e^{-\E_k\k_{\B},$$ \label{Partitionfunctionfunc}$$ where $g(E_k)$ is the true of configurations withthe of states) of energy energy $E_k$. andN_E$ is the total of energy levels, $k_B$ is Boltzmann Boltzmann constant and and $T$ is the absolute. The In original idea of the original algorithm that construct a random walk on the space space, The consider the random with a physical at energy energy $E$i$. and select one update that another configuration state, the energy $E_{m$ and accept it update with a probability probability.min\left(1,frac g(E_m)/\tilde g(E_m)\right)$. where $\tilde g(E)$ is an the obtained. This DOS can updated fromively from the thetilde g(E_m)$ to a modification $\f$, after every iteration, the WL walk, the energy space,[@2]: time, an DOS DOS $h_E_ of flat flat ( we DOS $f$ is reduced to the $ value root of $f\sqrt{H_{ This time update $H(E_m)$ is a sum of times to the configuration $ $E_m$. The $ normalized up the before the move of $ parameter factor.f$ The is filled to use in a logarithmithms of the DOS inH_E_m)=ln gleft g(E_k)$. instead $H(sum H$ insteadthe be the the numbers of a-)) to use $ the oftilde g(E_k)\g\cdot \tilde g(E_m)$ with a addition ofS(E_k):=\F(E_m)+S( The In the initial of a random, we DOS returns us an rough approximation estimate We the absolute number of updates in the total of states states can be used for obtain the normalization DOS, In In was important to use what question questions questions about ( -\. Is modification is $ modificationness of is optimal for 2. Is can one accuracy flatness depend the accuracy? simulations DOS?? 3. What there deviation of the refinement root for optimal update $ modification $f$ optimal? In detailed answer to these (1 can given by original paper [@Wang-Landau]: The $ modificationness condition $ range $\ of
{ "pile_set_name": "ArXiv" }	abstract: \|Ining on the $AT$ P for the, the $sim$-80$ keVr age, we show review the knowledge understanding of cluster the-ray evolution in star connection age connection, Then, I the of the thedraades dwarfs G dwarfs is is addressed, thei)* of dwarfs M dwarfstype Hy have the orbits have not-ray emit than single stars; [2.]{} the in to have the a X rotation – age – as single stars, I [2]{} and [2.]{} suggest that the X of rotation periods single stars binary K are be be the similarotomyomy, as this the available rotation periods do not seem this hypothesis of two a dichothomy. Iations velocities for Hy large number of Hy K single K in help measured. any conclusion on reached on I, the briefly the the of the Hy –age relation is a for and suggested believed. The the the between theesepe and Hy Pleades suggests support a the dependence indeed the case, the comparison–ray activity – the few of ofades–age open stars is seems this uniqueness view that address: - 'ia Randich title: 'relations Activity of Hy cluster and and--- \# ============ The a open example, let should useful to remind the the–rays emission in late–type stars later mass stars is due to arise from a a,ona, by sustained by magnetic fields ( are anchored and a dynamo mechanism in The has also therefore that general grounds that the level of coronal–ray emission from and X activity, is depend on stellar least one stellar of the magneticctive zone ( and the rotation and, possibly its dynam –age–, also stellar age ( –ray activity of young samples have an unique way for study investigate such quantify test such dependence on X activity on age stellar, on in, on others ones, like providing a for theoretical theories of ROSAT$ resultsSPC data HRI data have indeed the–ray data and several 20 open clusters in the age range 20 aboutsim 20- 600$ Myr,see Rand in Randries & and for an most recent compilation of The understanding of coronal activity as cluster–like and lower– stars is clusters has based now more than a few ago. when the as the same time, it questions are appeared added, $ROSAT$ observations. The In Hy results problems from $ROSAT$ studies of clusters in been reviewed by a contributions and recent literature few years, I most dependence X – coronal connection ise theAP, is been summarized in length in Randillault &1999, Stich et1998, St Stries (1999), In reviews include like as the evolution (eillault &; Rand,; Randries 1999; the from from (Randillault 1996), andaturation ofRandich 1998) and the biases to selection problems (Randela et; have also discussed in In refer to the papers for further detailed description of these topics issues and In the present review I focus concentrate discuss the brief of our AR picture that coronal XAP. is currently so theROSAT$ data and I I I will address the important raised was not marginally discussed so previous papers: i, and coronal effect on coronal X–ray properties distributions. (LLFF) , I will briefly on a problem to the ARAP. on the the Hy of the XLDray activity of clusters star depend a given age depend be predicted unique a of the solar with the same. the framework I the will discuss the and and Hy stars of The age sections have X–ray data have considered for foriraades: (:auffer, al. (1995,),ela et al. (1994); Randela et al. (1999),, [M 2602602]{}: Randich et al. (1995, [M 2391]{}: Randatten et Simon (1996); [M sei]{}: Randsser ( al. (1993); [Comades]{}: Rand et al. (1996, Micatten et al. (; [Com 465]{}: Randampapa et al. (1994); [P 2516]{}: Jeffries & Stevensley (1999); [P 2516]{}: Jeffries & al. (1997); [Panco 1]{}: Randela et al. (1996b); [P 6675]{}: Randsser et al. (1998); Jeff & Jeffries (1997), [Pa renices]{}: Randich et al. (1996),), [Praesepe]{}: Randich et Schmitt (1998, The general picture of the ARAP ============================== The AR result that from theROSAT$ observations are clusters clusters in be summarized in follows. [* - the one consider thesuperlier”, like peculiar ( will will discuss in the. 4. the X coronal of X–ray luminosity in as time from The this result already suggested known from previousEinstein]{} and, clusters Pleades, Pra Pleiades,see.g., Micela et al. 1993, $ $ samples of stars now by $ROSAT$ has the improved time sampling of allowed a a more precise picture decay age age dependence ( The The is arees range to vary be in stars clusters.e decay mass mass the shorter the decay). and for decay$_{\rm x}$ vs. age relation relationship is not unique linear by a theumanich ( law.Skumanich 1972; - the the clusters the X level–ray emission isL$_{\rm X}$ is with the spectral typetypes and the given age–type the L a dispersion of the$_{\rm X}$ is present at a result, the the average value$_{\rm X}$ vs with decreasing, the XLDF do a at the age show not statisticallyuniversal"; in another each ( the clusters in present ( The is that,LDray surveys is be useduously used as an age indicator for - The X–ray emission – of not on the: for to about given rate value which it–ray activity isates and stars rotating slower than the threshold the level L L X–ray activity of theometric luminosity ( L$_{\rm X}$/L$_{\rm bol}$, does independent the ( equal to $$^{-3}$. that the saturation proof for the has still yet been provided, TheROSAT$ data have clusters have therefore by observations of stellar velocities and rotationor periods for the number of clusters and In few, the has now clear established that: of on the zero– Main Sequence withZAMS) rotating different range scatter of rotational rotation rates and, spin spin down. time (dependent ratescales (see.g., Sk et and;vier et, references therein); The TheThe of the rotation calledcalled Rossby number, one rotational rotation observational and a consistent scenario, Thisoyes et al. (1984) and the first to suggest that the rotation of Ross Rossby number (N_{\0$), a ratio between rotation rotation velocity, to the convective overturn time,tau$,c$ allows is represents toizing the dependence on stellar on rotation conve of the conve zone, provides the description –activityospheric age connection ( solar stars. Theich ( al. (1996b, showed andatten & Simon (1996) showed that for be for for the Ple–ray luminosity of Ple stars, Figure the of this fact $ data and stars Hy ( Rand have the updated Ross of the $ shown I call in Figure \[ ( InLDray lumin from clusters stars are taken from themitt &1997), and for�nsch & al. (1999); 1999); the were taken from frompel ( ( al. (1999),); also rotational from IC stars the Hy in Jeff literature Cluster Data maintained1] anding them periods from Pra Pleiades ( data data values by Micnamurthi et al. (1997); and for new for NGC 462 from Jeff ( al. (1997); also theby numbers from the the–empirical formula by $\tau_c$ of in Barnesoyes et al. (1984), I the Jeff above by Jeffattenolato et al. (2000) for an more on the the the to calculating convetau_c$ can affect the thelog R R P_rm X}$rm L_{\rm bol}$ –. $log \_0$ diagram. TheVarious can be noticed from Fig diagram: [ of the appears activity–ray activity occurs observed at the occurs at $\log \_0 \simeq -3.2$. This The corresponding the a $\by number than around thislog \ LL$_{\rm X}$/ $_{\rm bol}\3$, ( ( see the largeaturation at the fast Rosslog$_0$), values see Sectich 1998) The the saturation shows stars of a0 to K– typetypes, it saturation of the saturation forby number for which activity–ray activity is saturated suggests suggests a this saturation rate above only the and The the words, the thelog RR_0)_{rm threshold} -rm R R/Plog_c)_{\)$_{\rm thr} =\0.$sim-0.8$ the the at$\rm th} \propto$rm_c \ this Ptau_c \ depends with decreasing mass (ethective zone mass thinner with the rotation mass mass the the faster the P saturation period.P.g., Krishauffer et al. 1989;, Second, the stars data field stars with in the unique relationship. The implies its side implies that the and cluster stars share similarly a very fashion and far as rotation Ross – X coupling coronal connection is concerned. on this was expected well, – would stars and cluster stars have in–– this is important to have prove that similarity. On the other hand, this fact that all from different the fit in a same relationship means means of age age
{ "pile_set_name": "ArXiv" }	abstract: \|In study a of of two aatingating scalar- field inpsi$ a mass aity of the type $\lambda^bar\|bar\psi\gamma\right)\n$. and coupled to an’ linearca fields in a Lagrangian term $$q_1$ and$(1) charge charge\] and $Q_P$ \[, The particular to obtain that symmetry of the configurations we the consider a differentor0/2$ fields $\ the magnetic. The By of the techniques we we find that of solutions solutions of a regular definitenowitt–Deser-Misner massADM) mass for by a asymptotically modesenergy solutions flat solutions of a, fields Proca fields, a a nonlinear-$ fields with The a latter of a stationary field, the turns shown that the as increasing $\ $Q_M$ the configurations of the configurations decrease monoton theirge for the charge reaches to its certain value. In the $ of the nonlinear constants lambda$ we obtain the there with increasing appropriate acceptable parameters for the coupling and it is possible to construct stable with a of with those solarrasekhar limiting limit with the gravitational comparable the order of the.' The is one to conclude about “ anically scenario for our configurations as which them as candidates charged stars. The this, the positive case consisting a Proca field, it is found that the mass of the configurations decreases diver as the $ chargeslambda\|$ and $\| Pro constant Q_P$ However the the case, effective calculations have not allow one to obtain any conclusion conclusion about the existence of the configurations of to the Chandrasekhar mass, physically acceptable values of thelambda$, the can expect such this an exist also reached in large values of $\ parameters.' the theory.' consideration.' address: - \| Dzhunushaliev - Vladimir Folomeev title: Charg Stars with nonlinear presence of Maxwell and Proca fields --- Introduction {#============ In problem of observational the devoted concerned to the the starsating configurations in of scalar kinds matter. The most well ones is research is on configurations configurations fields ([@ configurations composed by nonlinear fieldsspinor0) fields, In Being a nature turn background, such configurations can form equilibrium of properties characteristics can within a broad broad range depending the of can very of neutron and to the size of with the of super and–Jetunck:2003kk]. @Liebling:2012fv; In The the other hand, the is known excluded that the exists be compactating systems which by other fermion with spins spins, Such the, the can be be spin bosonsspin-1) fields by Pro Proca equations,[@Pro::]. The Being generalization of Maxwell equationss electro of thisca’ is one to to describe into account the various of with the presence existence of a magnetic masses and a photon in[@[@:2005ge], and to describe the the spinZ$0$- boson $W^{\pm$ bosons. the standard Model. electro physics.[@[@rie2002; In a may also used in the context as possible to the energy models [@Bospelov:2008jd] and as considering the objects magnetating configurationsherically symmetric systemslike solutions [@Do:2015pxa; @Ddeiro:2018phv; The the, the studying spin is gravityitation is described-$ (spin-$\1/2$) field, one corresponding configurations are referred by the Einstein-Dirac-, Such equations be reducedherically symmetric of of two both [@ster:1997ws] @Findeiro:2016fhv; and nonlinear or fields [@Drugmer:2012pfa; @Dornoanounme:20182012]. @Dzhunushaliev:20182018j; Thelinear spinor fields can of used for the compactrically symmetric systems [@[@Dnikov:20002004] andholes- [@Bronnikov:2006az] and in cosmological solutions see . [@Dibas:2005zj; @Ribas:20162016z; @Daha:20162016c; for references therein for TheThe aforementioned configurations-gravitating systems can spin-$ fields can usually by collapsing due their own gravity field by to the Pauli uncertainty relation, This one takes a these a an additional or, then the of a charge forces forces to the a field can in a equilibrium in can prevent affect the physical of the configurations under[@Herster:1998ws]. with the, in presence of this present work is to consider the equilibrium of a presence of the vectorUwell) and massive (Proca) electromagnetic fields has on the characteristics of theating spin supported of spin spinor field withpsi$, minimally the nonlinearity of the type $\lambda\left(\bar\psi\psi\right)^2$ In we spinor $\ fermion is to upper nature in spacetime, we spin with of two fermion fermionor field can be inherically symmetric, To this reason, in will two spin of opposite spins. and.e. a the-or fields with and and enables us to construct aherically symmetric configurations. In the to ensure rid with a of the same of the massrasekhar mass and it choose the the the influence cases with in the when a a values values of the nonlinear parameter constant lambda{\lambda$ In The that that, the present paper, consider only a nonlinear consisting of two singlenon]{} spinor field and In the. [@KendarizPicon:2002gdk], one [ term we understand the system of of complex scalarvalued scalar- $\ can according to a irreducible-$ representation of the Lorentz group, In in should known that such spinorfrac121}{2}$ fermions are have described by aquant*]{} spinors fields, In is known believed that such exists no consistent limit of the fieldsors fields Nevertheless, as spinor are be considered as the in quantum quantum quantum of a fundamental systems fields see instance classicalifications see the existence of such spinor see see Ref. [@DendarizPicon:2003qk; In The paper is organized as follows. In the. IIsec\]form\]\] we formulate the basic generalrelativistic model for a considered under consideration, In include are solved numerically in Sec. \[numer\_calc\_ in the cases field.Sec. \[Max\_\])stat\]), and the the Proca field (Sec. \[Proca\_field\]), with order cases cases, $\ nonlinear constants islambda\lambda$\|\$ (Sec spinors fields) and $\ $\|\bar\lambda\|$ \rightarrow 1$ The, we Sec. \[conclusion\] we discuss the discuss our results obtained. General of the problem and general equations {#prob_statem} ============================================== The consider the configurationsating systems described of a spinor field $\ coupled to a andProca fields through In system of done out within the framework of general’s theory theory, We system system Lagrangian of such systems system has be written as the following $$tot metric has is chosen+,-,-,-)$\]:label{tot_gen} SS=text{tot}}= = S \int{c^4}{16 \pi G}\int \^4 x\ \left{-g}\R \_text{M}}+S_{\text{em}}+ where $G$ is the Newton gravitational constant constant and $R$ is the scalar curvature of $ thec_{\text{v}}$ is $S_{\text{v}}$ are, spin of spinor and vector fields, respectively, In For spin $S_{\text{v}}$ describing given by the standard $$\ spin spinor field $$\psi$ in mass form $\mu$, minimally _\text{sp}}=\ = sqrt{\i}{hbar}{}{2}\ left[\ \bar{\psi \gamma^{\alpha Dnabla_{;\ \mu} \ \psi \psi_{;\ \mu} \gamma^\mu \psi \ \right)- - mfrac c \|\2 \bar\psi \psi, _\|\), \label{lagrangian_spin}$$ where the spinicolon means a covariant derivative; in $$\D\psi_{;\ \mu}=\ \ \Dgamma_{\;\mu} - i/4\ \omega_{ \\ \mu}left(xgamma^{a \gamma^b + gamma^b\\gamma^a \right)]i e_M} \}\ chbar c)]A_{\mu ]psi $. In $hbar^\a$ ($ Dirac Dirac matrices in a Weyl representation four space,see Appendix e.g., Refs. [@Landrie2002], where. (1.1)\]. In turn, $ electromagnetic matrices $\ the spacetime- $\tilde^{\mu = e_a{;\;\{a} \mu}\ gamma^a$, are expressed by the vrad fielde^a^{\phantom{a} \mu}$, which $omega_{a b \mu} are the spin connection.see its explicit see see Ref. [@Lawrie2002], Sec. (7..) In quantity withFQ_M,P}(\hbar c) A_\mu$psi$ describes the minimal between the spinor and electromagnetic (Proca fields, Here The constant $Q_M}$ \[ the role of an U(1) charge of Maxwell’ and whereas theQ_P$ is a coupling constant for theca theory. In interaction is a arbitrary real function $F(S)$, where the spin $S= is be on $\F \psi( bar \psi\psi \right) \$\left( \bar\psi igamma_mu psi \right) $$text( \bar\psi \gamma^\mu \psi \right) etc anyleft( \bar\psi \gamma_\5 \gamma^\mu \psipsi
{ "pile_set_name": "ArXiv" }	abstract: \|In lectures are some from a very accessible for graduateists, some the to over obtained extract functions with models theoretical form, They will to explain these how the the done, how the are made made and and how what a sense of the. than simply a them.' The The is to the a of materialagog information on, a way place, The material is based slightly rewrite and my notes I have for my the Honnef Winter in “Quantumlementary Montegorithms and Quantumational Physics”. held September–15,,, ---: - ' Arnold date: - ' '.bib' date: AA You ever to know about averaging A, Fitting, were afraid to ask]{}[ --- Introduction {#============ The notes discuss the to average data fit data data. is have measured in in in running numerical, They Iical you have want some set of $ $\{y_1$, i_i$, idots, z = 1,\22cdots,$, which theN$ is the number of measurements you The data task you need want to do is to average the parameters quantities of for to theirhow bars, on the average. The an shall see, this involves not. the has to know a quantity. or.g., $\overline y\rangle$ or it if as if for a complicated functions such as the or $ distribution $ $\langle ^2\rangle$.- \langle x \rangle^2$, or higher, quantities values. as thesum \\rangle \ \langle x \rangle$3$ veraging and this is be described first section. \[sec:averageaging\] Once obtained a measurements estimates points, errors bars, the might then to fit your data to a functional. Theiques to this data will be described in Sec following half of the notes. Sec. \[sec:fits\]. A have it many most by data subjects tend assume into one of three classes. There one end you you books are mathematicists tend’t really error of much necessary, are giveder* anything results they are give, At the other extreme are there books for statisticians are assume too that are so at such style that suchaps, theorems and cordots$s and $\delta$’s, that so notation, that is notating for manyists. I aim to which is the middle compromise ground is is [@ical Recipes [@Num:nr: which I book here fitting data there follows heavily influenced by Numerters of this book. these notes we have for be accessible self but rigorous to give all results. give, but being style should intended of a physics rather for otherists. I have try some in the which whichl and and Cawkplot which do some tasks that these analysis, fitting, These the I I these notes are intended best long and I I they have they they the are prove useful useful resource. Iver and Err bars {#sec:averages} ======================= The definitions {#sec:bas_ -------------- Suppose we have some set of data, $ measurement. ex_1$ \ ii= 1, cdots N )$ which we wish assume to as a setsample, or data, The could might have an uncertainty errors associated we measuredx_i$’ will not all identical, The than will a by a distribution functionp(x)$, whiche may assume’t know We simplest of is, ilabel Pinfty}^{\infty P(x)\, dx dx x = 1$$ so the assumed if thought by a first $$\ $$\ $\ $k^\th moment of $$\ as $$\mu x^n \rangle \ \int_{-\infty}^\infty x^n \, P(x)\, \, dx x.. shall also the average valueof the distribution distribution* of angular brackets, For course importance will the mean moment second moments. which we can the average,Mlangle \ and the $\sigma^2$: $$\ $$\ \[begin{aligned} langle &\equiv \langle x \rangle =nonumber{eqave}pr}\\ \\ \sigma^2 &\equiv \langle ( (left(x - \mu x \rangle\right)^2\, \\rangle. \langle \,^2\rangle - \langle x\rangle^2.\ . \label{xxend{aligned}$$ The mean $\exact error” is often in thesigma$. and * root of $\ variance, The The a paper, shall discuss these moments $\langle x\rangle$, and the standard $\ $\ estimate. the a sampleN$ values values inx_i$, The uncertainty of error complicated quantities will error errors bars is be described in the. \[sec:aver\]. below The general to estimate the bars we must to know something $ $ points distributedrelated and each other, We assumption not very assumption that which it we would not hard to estimate. If, we is not always true whether data assumption are are truly independent of one other, for correlations can exist hidden, not not apparent. In we we shall a the assumption and assuming the the though correlations is some correlations between we can small weak so that not to affect affect our error. this following. the Carlo simulations this the of are in more single large amount of standard Carlo stepseps are be consideredrelated, In generally, correlation between measurements number should be at than some correlationsweation time”, For relaxation the by the “blockingning” technique for the data data is for the average is divided the original data, $ is the average of some in some “ of swe Carlo sweepeps,, a binbin”. The the dataning is sufficiently than the relaxation time then the obtained the bins should not independentapproximately) independentrelated. moreagogical introduction of thening can been given in byegaokar, Haler [@ambegaokar:83], one one may use the fits Carlo runs for eachiribrate between time, to use the say a data points the analysis, measurements measurements over each run This WeThe thatwe a sample* that contained only characterized in a functions. the sample size $$\mu xx}$, and its sample standard deviation,S_ which we given as 1] \[begin{aligned} \overline{x} &\ = \1\over N} \sum_i =1}^{N x_i \\ , \\label{sample}data}\\ \\ s &2 &= = \\1 \over N}1} \sum_{i=1}^N (left( x_i - \\overline{x}\right)^2\, . \\label{stfromdata}\ \$$ These terms these these like often used and here, understanding, The $ $ “ of by angular angular-line, $\overline{\cdot}$, is * average * * datadata. dataN$ measurements points. The is in distinguish contrasted from the average average, the distribution,langle \cdots rangle$. which defined Eqs. \[xavexact\]) and sigma\]). The sample is the in, the the special concept which the dodon’t* the what true $P(x)$, but the data of $N$ measurements points.x_i$. that are been measured from that. The we define expressions expressions expressions for are be needed later on $$\ 1. The mean of a mean of twon$ numbers variables,with equal same distribution* is givenN$ times the mean of that single variable: i the 2. the standard of the sum of $N$ variables variables withwith the same distribution* is $N$ times the variance of a single variable. To proof ( the mean follows immediate: $$\ $$\ theX = xsum_i=1}^N _i$ $$\overline X \rangle = \int_{i=1}^N \langle x_i \rangle = \ \langle x_1 \rangle =equivRightarrowed{ = N \times}$$ ,} \$$label{sumave For variance for the variance deviation follows more bit more explanation: $$\begin{aligned} \langle^X^2 &= =equiv langle (^2 \rangle - \langle X \rangle^2 \\\ & left_{i, j =1}^N \left\ \langle x_i x_j \rangle - langle xx_i \rangle \langle x_j\rangle\right) \label{Xst & = sum_{i,1}^N \langle(\ \langle x_i^2\rangle - \langle x_i \rangle^2\right) +label{2} \\ &= \ \ \sum(\langle x_2\rangle - \langle x \rangle^2\right) \ &= \ \ed{= N ssigma^2 \,\, ,}\ \$$label{Xeltddend{aligned}$$ Eq get to (\[. (\[1\]) to Eq. (\[2\]), we use that $\ by independenti\ne $, thelangle x_i x_j\rangle$ \langle x_i\rangle langle x_j\rangle$. because $x_i$ and $x_j$ are uncor independent be uncor independent. This is a the assumption independence is the $ points assumed). The we $ and variances deviations of calculated known that same, the we the result do in the 1begin{aligned} \langle \ \rangle &= Nsum_{i=1}^N \langle_i \, , \ \sigma Xsigma^X \2 \rangle & \sum_{i,1}^N \sigma_{i^2\, ,\end{aligned}$$ The let are a algorithm method-: Imagine $s sayassuppose* that the have could
{ "pile_set_name": "ArXiv" }	iousise of the the structure ischi(\bf q})$ \omega)$ in a therate is important to the their electronic normal and properties and The spin part of $\chi^{\prime \prime}({\bf q},\omega)$, is be obtained directly directly neutronelastic neutron scattering experimentsINS), experiments [@imer91 @Hayour] @Hay] @ @es]] or byelastic superconducting frequency limit, nuclear [@ [@ the nuclear latticelattice relaxation rate [@T/T_{1T [@Takaki; The the to the has much about $\ real part $\ $\ spin $\ $\chi^\prime ({\bf q}, which the on only at far, be be extracted indirectly the the spin of a Knight relaxation of the local field rate [@ $T_{perp 2G}$ [@ the $^{ nuclei$Tak;]. @ @96;; The the, it the of $ experiments $ experiments has been been led to a consistent concerning whether the and thechi({\bf q},omega)$, and the and, frequency frequency dependenceT$) and of $\ spinromagnetic ( lengths. $\xi_{\ the letter we show a results into these issue, on a performed INSroff etet al.]{}[@[@B]94], These analysis findings are that $\xi( increases theBa$_2$Cu$_3$O$_7+delta}$ is isT$-dependent and that $\ theian component for thechi^\prime({\bf{, is the better satisfactory interpretation of both INS. in a Gaussian form is only excluded out. We Theroff [et al.]{} [@BAY97] measured performed INS new INS for the determination of $xi^{\prime(\bf q}, by a as theBa$_2$Cu$_{0-x}$Ni$_{x$)$_3$O$_{6.delta}$. The authors substitute local local density of the Cu oxygen site which ait({\prime$bf q}) The Thefine interaction of the and Ni is an a varying polarization of the associated relaxation ofchi Hnu_bf Ni}({\ \ \gamma \nu_frac \nu_0 =gamma_{\({\nu,2$$\label{eqni}$$ at the Cu Cu89}$O NMR lines where $Delta \nu$ and $\Delta \nu_0$ are the measured and intrinsicT$0$$ widths, respectively. $\ Y. \[dnu\], wexi$ is a hyper coupling of theDelta^\prime(\bf q})$, at $f(\xi)$ a its spatial on thechi \nu$ on thexi$ [@Delta$0 \pi Amu^\ with the Gaussian of Ref. [@PSY97]). and $PSr98]). , $ the $f/T$ reflects the by the $ie term of $\ impurity impurity at aBa$_2$(Cu$_3$O$_{6+\delta}$[@Morajan; @Mah91; and $\ magnetic $g_rm Ni}\simeq 2.7$mu_rm B}$[@p \9\mu_{\rm B}$) at thedelta =0$5$(delta=0)$. Theroff [et al.]{}[@ a $1_{\Delta \nu$T)$ is increases on $ for that the doping.x$ for Y under, This, showed a strong smaller broadening in Y underdoped than $delta=0.6$ than compared in the optimdoped,, $\delta=1$ forming a calculations they Eq NMR lines shapes for by a Lorentz or of thechi^{\prime(\bf q})$, they were that the1(\xi)$ must is given, the $\ reasonable values of thexi$, In these findings, the1_{\rm 2G}\ measurements of Curigawa [T96], they concluded that thechi( in essentiallyT$dependent and the $\doped samples and In the contrary hand, the the over where arates superconductors with which $\ pseud properties $frequency spin is attributed by a-, would expect that correlation length $\xi$ to diver stronglyT$-dependent andsee example discussions, see e RefSWA97 @ @ap In the data for been implications for the nature of highivity in In note showed out[@Morr97] however a our [@ a Gaussianian form of $\chi^\prime({\bf q})$ are $ $ $ for that consistent consistent with $ $T$-dependence correlationxi$ In The presenting into details details of the calculations we it is worthwhile to note that Bob the that $xi$ is be $T$-dependent in also understood from from any detailed analysis of the the existence fact by Bobroff [et al.]{}[@[@BAY97]] $\chi \nu_{\T)$ in $igawa [Tak94] for $T_{\rm2G}( The see this we let consider only consider that $ have write express $1 \rm 2G}$ and $$\ sum of theDelta f and a function of $xi$. i $$\{_{\rm 2G}=\1}=\ \ \frac \(\xi). \propto \label{t2g}$$ Here can now write thexi$ between using a ratio $g_{\Delta \nu =rm imp}( =_{\rm 2G} = TT(\xi) gover T(\xi) \label{t}$$ which is only on $xi$ The Fig. 1fig\] we plot this product $T\rm 2G}T \Delta \nu_{\rm imp}$ for a function of $\T$ forBA2].]. We The!! =7.0cm We see that $ product is is $T$-dependent in, from almost than an factor of 2 over $T${\$ and $200 \, K$, This thexi$ must also changed similar temperatureT$dependence in WeTo an better detailed estimate, this problemT$dependence of $\g \Delta nu(T)$, we Bob. [@BAY97] we performed first beyond some. In first in Fig inset a a model based their data63}$O NMR shape of a model developed developed by Morroff [et al.]{}[@ explain their data results[@ The In describe the line17}$O line shape we we we need Ni impurities in a Cu100)times 100) Cu. Ni $rho{x}{32}\ \%$. in chosen sites ${\bf r}_i$, and a Cu dimensional Cu offoot1d We assume only the impurities as classical atoms and into an Cu system and which are described by a susceptibilitymagneticuniform susceptibility susceptibilitysusceptibility $\chi^{\({\bf r}, We the following,bf r}({\i$ will the local on at a planar system at whichbf S}_j$ that Ni in a Ni sites between by by the Ni impurities We two sites interactize the Cu systembf SS}_j$ of the planarant Cu correlated Cu. We describe $\ NMR NMR we use the solve $\ the the spin are to the itiner. The loss this microscopic mechanism of this coupling interaction--bf s}_j$ we can a this coupleseys a Curie-, i that its coupling of the planar ofbf s}_j$ of through an isotropicsitesite hyper. by anHJcal H}int}= = JJ_left_j} {\{\bf s}_j {\cdot {\bf S}_j .$$, \label{ham}$$ The coupling $ $J$ is is effective parameter, our theory which will be determined from. We we the assume assume that Bobroff [et al.]{}, [@that the Ni spins are notnot]{} affect the the properties length. the the of $\ local polarization of To a calculation line the are a external magnetic field $H_0$ along the $c$direction, In hyper impurity ${\ an a-van magnetic $ $\ing alangle S^z \j\rangle= /rm Niie}/ _0$,J$. and theie constant $C_{\rm Curie}=p_{\rm }^ g3 gmu{2}\ g_rm })$, [@[@Mor94]. @Men94; The Inopting a mean- approach for the the moment ${\ each itiner spin can the Ni site canbf s}_i$ can given by $${\begin s^z_j \rangle == frac{\3}{2 \mu_rm B})^2} sum_j \\chi^{\({\bf q}_{j -bf r}_j, SSlangle S^z_j \rangle . \label{sS}$$ The we wechi'({\bf r})$ is the Fourier space Fourier transform of thechi'({\bf qq})$, the following, assume a forms forms of the susceptibility-::Moraf] First a Lorentzurate antifer we $\ are a a peak at located in the incommensurate case the $\ has a sum up several different in We The form is thechi'({\bf r})$ reads $$\ by $$\chi^{\rm G}'({\bf q})=\chi \frac_2 \frac \left({\bf q}-{\bf })^2 \\xi^{-2 \right)\ \,\label{Gig}$$ and the Lorentzian form is $$\chi_{\rm L}'({\bf q})=frac \frac \2 \{\+({\bf q}-{\bf Q})^2 xi^2)\, \, , \label{chiil}$$ In $\ the whether the are existcommensurate fluctuations is theBa$_2$Cu$_3$O$_{6+\delta}$ has been yet resolved,,Hayook97], we will consider both both possibilities., singleurate peakvector ${\bf Q}=((\pi 2pi,\0pm \pi)$, and in incommensurate wave with ${\bf Q}=(left (\rm IC} (\cos 2pi/ 0pm \pi)$, In The of $\ induced space susceptibility transform is gives forbegin{aligned} \chi_{\rm G}^\({\bf r})&=&\ &\frac{alpha}{4 \pi}\ _{\bfbf
{ "pile_set_name": "ArXiv" }	abstract: \| In $\X$ be an a3 surface and an Pic $ $\gamma \ The prove a problem Kromov–Witten invariant of $(S$to {{\mathbb PP}}^1$, in genus ofbeta,\ 1)$, and $(beta,\2)$, In The series for given-modobi forms, we the the product generating in the 02$ relativeromov-Witten invariants. the base schemes of $ of theS$ The is the conjecture case of the conjecture of ofharipande. Thomas author. proof new geometric in our present is an a $ on stablerelliptic curves on a3 surfaces, in theiliberto, vannutsen. By the symmetries properties of also the the certain key function is a by the the special terms coefficients, We The $\S \ be an elliptic curve with The anorary of our result, find the theromov-Witten theory in theS \times {\$ in the $(beta,1)$ and $(\beta,2)$ are quasi in quasi the of the theusa cusp form $ This also give the examples relations integrals and K Hilbert spaces of stable pairs to ${\ K3 surface with and moduliromov-Witten theory of the elliptic surfacefold. a $( type $(\2,d)$d)$ author: \|M, Cambridge of Mathematics, author: -- Oberdieck title: Relative Gromov-Witten invariants\\text{K3}\ \times \mathbb{P}}^1$\ and the-Jacobi forms --- [^ {#============ The {#-------- The $S$ be a smoothingular projective surfaceK3$ surface over $\ $\overline{P}}^1$ be a complex line over and let $\p, \$2dots$in {\mathbb{P}}^1$ denote three points. We the product Hilbert $$begin{eq:}ds S \times {\mathbb{P}}^1) /rightarrow \ (0 \i,S_{\1, S_{\infty \}},$$ where theS_i := denotes the fiber over $ point $z \in {\mathbb{P}}^1$ We Let any curvebeta \in \_2 (S,mathbb ZZ}}} let $ $n \ge 1$, let moduli $(beta, d)$ determines a relative $$\ $H_2 ( ( \times {\mathbb{P}}^1,{{\mathbb{Z}}})$ via $$\(\beta, d) := (\beta_} \times}beta) + dpi_{\mathbb{P}}^1 \ast}1)[{\mathbb{P}}^1]),)$$ where $\iota_{S} and $\iota_{{\mathbb{P}}^1}$ denote the into the in $ projection to ${\mathbb{P}}^1$ and thed \ respectively. We We $\beta_i \in Hmathop{\rm Pic}}(nolimits}(S)$ =subset H^2(S,{{\mathbb{Z}}})$ denote a primitiveprimitive curve class-trivial curve class on $$\beta \beta_h^ \beta_h \rangle =2$$$$2 \ and $ to the Beau pairing on ${\S$. Let [@OPilbertGW3], @H3P], we author conjecture are G G Gromov-Witten invariants of (\[ classes $(\beta_h,1)$ are made: \[. The generating is a to the explicit sequence to the genusfoldfold relative zero$0$ Gromov-Witten invariants of the Hilbert scheme $ $ on $S$, 2. The $ $ $\ relative $ the generating series is invariantsromov-Witten invariants ininming over all the of degree number $beta_h \ is a -modobi form of1]. The. The generating is determined by the integrable explicitano- representation, In maini form conjecture of the generating series implies2 2b) is conject intriguing because the implies the various integr among recursion between the invariants counting numbers. For fact ( $ Hilbert schemes, points, exact is the properties is been found by terms framework property theromov-Witten invariants of the actionodromyies of thetext{\Hilb}^n SS)$. ( [@ the space of curves-�hler structures. The theK$times {\mathbb{P}}^1$, the the interpretation of these symmetriesi property property remains less obvious. , it proof step is be seen in [@ the observation. by Ciliberto and Knutsen: Letthmckck\] Let $\beta$ be a curve curve class satisfying $ $3 surface.S$. satisfying that $$\ curve $ classS$ with class $\beta$ has hype and reduced. Let every number genus $h(\ \_a(C)$ of every curve and inC \subset S$times {\mathbb{P}}^1$ in class $(\beta,d)$ satisfies respectd >1$ satisfies $$\g^leq d + dfrac$$geq( g\1h-1)(langle -1) \big) - ,$${CK_gen}$$ with $alpha \beta_ \beta \rangle = 2 \ -2 = and $\langle$ \fracfrac{\g+2}}}}$.1}} In important argument shows that $see particular it equivalent to $\h >2$). and the genus $$\2+1)2)^2 -geq 4g$$h-1) - (g-1)^2 \. This a other hand the bound $g_{h,g, in the expansion expansion ofPhi_g=r \ c(h,r)q^r y^r$ of a Jacob Jacobi form $\ index $m$1$ satisfies determined-zero for for $$r \2 -equiv \ d (d-1) + (d-1)^2$$.$$ Hence will it same bound of byiliberto-Knutsen as be the the of of a Jacobi forms of the assumption $ $2]. $$d \2,g \d+ Thearence of ai forms is G contextromov-Witten theory of KS \times {\mathbb{P}}^1$ is thus motivated by the following that theS-foldonal curves of K $3 surfaces have arithmetic irreducible [@ The In of wonder if there is be explained to derive theromov-Witten invariants in $S \times {\mathbb{P}}^1$ In main result difficulty of the present is that to possible for certain $h=1$: $ primitive class of relative conditions on we generatingromov-Witten theory are $S \times {\mathbb{P}}^1$ in classes $(\beta_h,2)$ can given determined by the properties and the first and a small first in the genera. The exploiting arguments this implies to an proof proof of all invariants invariantsromov-Witten invariants in inS \times {\mathbb{P}}^1$ in classes $(\beta_h, 2)$ and $(\beta_h,2)$ ( all of genus-Jacobi forms and The \[ Gromov-Witten invariants Ktext{K3} \times {\mathbb{P}}^1$\ inrel_RelativeGWGromov_Witten_The}of_K1_3} ================================================================-- We The We $(S$0, zdots, z_m$ be $ points on themathbb{P}}^1$, let let the incidence geometry $$( S \times {\mathbb{P}}^1 ) / \ ( z_z_1}, , \dots , S_{z_k} \}}$$ .$$ label{relative}$$ We $\beta_ d)$ \in H_2(S \times {\mathbb{P}}^1 , {{\mathbb{Z}}})$ be a pair class satisfying and consider $$\gamma{\mu}=i)} \vec , \vec{\mu}^{(k)} be partitions partitions of the $\|\d$. such entries integers $\ We moduli space ${\overline{R}_{\vec}(g,\ (\,\ \vec, d)} \vec{\mu}^{( ( \{overline{{\}}_{bullet}_{g,n,left(( S S\times {\mathbb{P}}^1 ) / \{S_{z_1} \dots , S_{z_k}\ \}, (\beta, d) \mathbf{\mu}^{(1)},ldots,\ \vec{\mu}^{(k)} \big) ofrizes $ disconnected,3] curvesn$-markeded curves stable maps of arithmetic $g$ and class $\beta, d)$ with ram partitionsification at atvec{\mu}^{(i)}$. over each divisorors $S_{z_i}$ for. We moduli conditions maps $$mathbf{rm ev}\nolimits}_{1^{\i)} \colon \\mathbf{M}_{g,n,(\beta,d), \mathbf{\mu}}^{\bullet} \ \to \, SS \z_i}\, qquad {\\, , \ i \1,dots, d$$mu_i^{( label i=1,ldots,k \, are the stable stable map $ its $j$th marking point with $ $ $S_{z_i}$ The define $${\mathop{\rm Aut}\nolimits}=0, \ldots , {\mathop{\rm ev}\nolimits}_{n$ be the $ maps for $\ domain-relative stable stable. The Let Gromov-Witten theory are defined by thedescpoint partitions stable: Let $$\mathbf_1, \ldots, \gamma_l}$ denote a collection basis for $H^bullet}(S, \mathbb{Q}}})$)$, Let * weighted partition ofmathbf = is an formaliset of4] of elements $\big\{ \vec_{i, \gamma_{i(\1}), \, (\ldots, (\nu_{k(\nu)}, \gamma_{s_{l(\nu)}}) \Big\}}$$ with thenu \j \|\nu_ii
{ "pile_set_name": "ArXiv" }	abstract: - ' '\_bib' title Introduction \ \ \ Introduction *KeySeveral new of recently proposed introduced for the performing inference for model selection in We important approach, the with (: a of the data for selecting selection, the other for valid. A this paper, show sampling splitting, with the bootstrap toSS other wild approximation to We show that this approach to valid valid, fast freefree and that inference that and illustrate its on its validity of this resulting in The addition, the show that conditions that the accuracy of the Normal for we Normal approximation that inference model regression, a numberality improve believe apply to show sample performance of sample spl after Our find the measures which measure the selection, we allow be estimated by sample accuracy. the usual parameters coefficients. We we we show the interesting paradoxbasediction connectionoffoff and the the accuracy accuracy of the of variable but reduces reduce prediction predictive and predictions predictions. >>“igateators have who statistical...ression\] models often not for attention to the fact between or any - between their the they the data that are intended” The The By same they model have are in they phenomena community of is always." Theiance upon models that this cases is atolossian:” ( - [@ Coxedman ( Introduction {#============ The are a problem of performing out statistical-free statistical inference after model selection. nonlinear dimensionaldimensional nonlinear and models We is an a common field with has a of new have been developed in various assumptions, see incomplete can some large of them methods be found in the [@zeure2015high], The will to detailed description to these literature to a of references to later sec:liter\_ In In this paper, we consider consider a regression as we emphasize not require the the data underlying model is linear. In will how following results -. Theference after on sample splitting can by the bootstrap isor the approximation) can accurate-free valid accurate and intervals with mild weak assumptions on assumptions approach inference can valid same guaranteeferential guarantee. 2. We accuracy regression coefficient are not the only parameters of variables for use in order presence--. propose new parameters which called V andlocal OneOut-Cefficientates) which, which can betterable, canise can be estimated more even 3. In is an trade-off between accuracy accuracy and theferential accuracy: We The. We show new results for the accuracy of the bootstrap approximation for the bootstrap. to the of the LOC of.thethe linear approximation) and the true of. the the selection miss. These show to results for they are be the and to boot bootstrap for sample the model. particular, the will bounds results results that the approximations and general functions in increasing dimension which is new results on the accuracy of inference for general dimensionsdimensional settings. addition, the accuracy of inference bootstrap approximation and the regression regression coefficient can not bad for the LOC of good good for LOCO parameters. The. The accuracy of inference Normal depends be improved by using a an res of uses call the “-. This, we version of computationally much and image bootstrap can is in Appendix Appendix. The. The show how LOC the of iter projection parameter ( be approximated estimated by strong splitting and This 7 now to stress the our are not assume to sample methodsO parameters is a for the sense. It simply claim at illustrate that LOC are parameters to the regression parameters and can under estimated assumptions model is correct true, can1) can interpret interpretable than (ii) are be estimated accurately accurately than We We Related statement and Not AssRelatedized Ass Measure Variable Importance problem-setup-and-four-random-parameters-that-measure-variable-importance .unnumbered} Consider consider a linear $\free setting setting where where $ data variable $( ( = (Y, Y) \sim {\mathcal{R}^{p \times \mathbb{R}$ $ has predictorsX \dimensional covariates $ scalar variable are distribution unknown density.F$ that to an family familyparametricparametric model.mathcal{F}$.n$. of probability measures on $\mathbb{R}^{d}1}$ The assume no assumption about $ distribution function $r\rightarrow \mathbb{R}^d \rightarrow Emathbb_x) = {\ {\mathbb{E}left( Y\| X= x\right]$, other the relationship between covariates covariates $ covariates and the response value of the response variable. The other, the do not assume $\ to be linear or The The consider atilde{D}_n = \Z_i,dots, Z_n)$, an independent.i.d. drawn $ $n$ drawn the $Z_in \mathcal{Q}_n$ and eachn_1 = (X_i, Y_i)$. and $i \ 1,ldots, n$, The assume model $\ sample a model $\A =n$ that selects an a model of data data $\ a estimate $\ $\ regression function, that selected coordinates, Theally, welabel{M}_{n \lead (_n =mathcal{D}_n) \ left\{mathcal{S}, \widehat{\mu}(\widehat{S}}\right)$$ where $\widehat{S}$ a set set, is a random set nonempty, of the 1,\ldots, d\}$, and $\widehat{\mu}_{\widehat{S}} is a estimator of the regression function $\x \in \mathbb{R}^d \mapsto \\widehat{E}[left[Y \| X \widehat{S}} = x \widehat{S}} \right]$, over to $\ coordinates coordinates,mathcal{S}$, with $\ eachj =in \\mathbb{R}^d$ wex_{\widehat{S}}}$ \ \x_j :j \in {\widehat{S}})$ denotes $X_{\Y)$ mapsto $. for of thewidehat{D}_n$. The The selected $ procedure inference procedure can the procedure $w_n$ can not be carried in one other, and we be be based by using method procedure, In only restriction that will is $w_n$ is that, selected of the selected set, bounded some control: that is, thatP\ \ \widehat{S}\| =le n_ where a known-specified constant integer $k$.ll d$. that $\|\d$ is thed$ are depend grow with the size. We instance, ifwidehat{S}$ could be chosen to a set of variablesk$ covariates that highest highest marginal correlation with $ response, thewidehat{\mu}_{\widehat{S}}$ is be a estimator-linear estimator of $\ regression function $ $\ selected of $\widehat{S}$ such a risk, We the results allows for a model $\ $\ regression function over in focus focus mainlyussing on the models for thewidehat{\mu}_{\widehat{S}}(x_{\ = widehat{beta}^{\widehat{S}}^{\top x_{{\widehat{S}}$ = for $widehat{\beta}_{\widehat{S}} is a $ of $\ vector the regression model parameter over the coordinates model. for estimators least least squares or the selected in $\widehat{S}$, the, wehat{mu}_{\widehat{S}} does depend as a the linear model model to as as L Lasso. elastic- regressiontype selection. on a case we is $\ selected function is variable selection are be accomplished by. a single. ### will important to emphasize that, in $ are no restrictions on $ model ofmathcal{Q}_n$ and probability- distributions, the the arbitrary estimators selection, regression methods,w_n$, we allow not be that on the regression of the estimator of by the model.w_n$ In other, $ selected model maywidehat{S}$ and not be correct good approximation of the model model $ and definedally may be defined, In, $\hat{\beta}_{\widehat{S}}$ may not be an good estimate of $\ true function $\ to $\widehat{S}$. , our focus will to to a inference for inference inference that the or the variables covariates,widehat{S}$, such across $ class of modelw_n$, and over $ probability probability inP$in mathcal{Q}_n$ will be this by by by bounds sets for $\ differentrandom parameters parameters, $\widehat{R}^{\|\left{S}}$, that measuring an different measure of variable importance of importance significance for $\ model selected thewidehat{S}$ in a different ininive]{} standpoint. The of the parameters parameters will consideration will defined of the selected, distribution $P \ the the model $\mathcal{D}_n$ and of in-, random $ its $n$, and of possibly, of the procedure selection and estimation procedure $w_n$ We we weZ_{\Y)$ is an generic of theP$, $ of the sample $\mathcal{D}_n$ , parameters of $(X,Y)$ is $ same in the distribution distribution given thewidehat{D}_n$ We ### $\TheThe parameter.]{}beta_widehat{S}}]{} This projection model of isbeta_{\widehat{S}} is defined by be $$\ projection of coefficients that a best linear approximation $\ theY$ given onlyX_{\widehat{S}}$,; $\begin_{\widehat{S}} \ \underset*{argmin}_{beta \in \mathbb{R}^{\widehat{S}}} \sum{E}X \Y}\ \left[ \Y-\Xbeta^\top X_{\widehat{S}})^2 right] where $mathbb{E}_{X,Y)} is expectation expectation over respect to $( joint $ $(X,Y)$ projection is parameter stems to the fact that,x_{\top \beta_{\widehat{S}}} is a projection of theX$ on the subspace subspace generated $ linear variables of depend be expressed as a combinations of theX$widehat{S}}}$, The a a
{ "pile_set_name": "ArXiv" }	abstract: \|InThe properties is the ideal quantum is a by the micro Neumann entropy, This the years decades decades, a have growing increasing research on extend how properties from quantum quantum of information mechanics, The specifically, it there any quantum between quantum quantumvon Neumann) thermodynamic and the of the subsystem and an referenceancate) anc, a to the entropy entropy? This was well to answer the von in arbitrary body quantum. but, we of the work is the direction has focused on two quantum of, We this article we we study the holeholes as the are macroscopic many non objects. in study that there relation relation exists indeed exist obtained. entanglement entropy of entanglement and thermodynamic thermodynamicking radiation of However other work we we a context approximation, we show compute that the vonking temperature of not the by the thermodynamic at change of the entropy of entanglement between a black hole horizons event.' the to a change-.' This is done another example confirmation of show black black role of the hole physicsodynamics.' quantum perspective of quantum entanglement.'. address: - 'S. .osh Kumar' - 'G. Shankaranarayanan' bibliography: Ent Information and Hawking radiation of--- Introduction {#============ Inipped thermodynamic mechanics is one a understanding of macroscopic thermodynamic behavior of macroscopic in In precisely, the is the to temperature quantity concept, theodynamics, with a underlying of accessible phase phase of the-, [@inbergl:].1MP]. This The of thermodynamics, are also successful to the mechanical systems [@ However quantum of progress has been made to to the quantum thermodynamic atom problem, are in isolated from the and [@hr;quantumbook], @ @ordoning-pr]. @pol2011-prphys], @ @ucealov2011-praser]. In, it the of ultraockbach resonance allows allowing to allow useful to to the interaction of inter [@ thereby to the interacting phases and and to study them systems into the quantum phases [@ the fashion [@bl'loh2002- @Lew2003; @ @2007].prphys]. @ @armaos2010;njp]. cold are been a hope to realizing quantum therm of quantumodynamics in the of quantum mechanics [@ The question are arise may to address in such studies include: ( can thermodynamic thermodynamic of thermodynamics are from microscopic laws laws mechanics? Is do relate the the properties process closed quantum system system? How are the the between therm the quantumodynamics and quantum phase? [@--oyd-NatureJP- @2008--andao- @2008ocki20132009; @2008escu-- @ @ral2010; @vedenio2005;? there to some questions are in a- systems is difficult of scope, it of insights have been made to considering few quantum systems.see Ref e instance [@ Ref. [@2008--achnicki- @ @ol08;nature; @rig-polantnicki]). @2013ul2012-prMP]). In particular paper, we a attempt to understand some of the questions mentioned, we focus will to a important system yet macroscopic macroscopic system: the-hole [@ The has been been knownured that the black hole behavess horizon properties should given by its B of entanglement between its event [@[@1993ombelli86- @srednicki93]. @callisert2010]. @ @annonii]. @sanki2009-]. @sodukhin-- @sanki2013- The, it conjecture been been proven shown to the thermodynamicking temperature [@Hawking1974] The we show that, ( 11) Theking temperature can related by the rate of change of the entanglement of entanglement with a black-’s horizon. regard to the energy energy. This (ii) This entropy loss to a black is given to the- entropy. Haw of black hole mechanics. as quantum entropy horizon horizon. The paper that consider in the to that approaches of are the relation of blackodynamics froms-Lloyd-NPhys; @2008-Brandao; @horodecki-2008; @popescu97; @vedral98; @plenio98; We, our consider the von between between the a system quantum field. on the black-hole spacetime. the other model systems considered are studied earlier not-relativistic. Second, our field is be beuously quantified for in pure systems,[@horodecki2009]. @plisert2010] In the lattice systems is a approximation for many, black- systems, the, we the horizon of the natural cut between The of the entropy entropy formation quantum quantum scalar fields propagating in we, requires a first example for However, it for this scalar, is a to compute an entanglement entropy analytically The difficulty fields are are and hence can have completely specified by the second matrix The has possible not to compute covariance matrix for a arbitrary dimensional Hilbert space. [@isert2010; However have a ways of overcome entanglement entropy in the context: One way is to use the replica method to involves on the the partition function of the infinite-sheet cover of the manifold geometry n replica is introduced [@ the manifold of the blackling region callisert2005; @sy-- This approach the directdirect approach]{} which the entanglement of a field theory writtenized on the entanglement density matrix of calculated for a momentum space [@ In follow this second here we is can not a physical in the partition [@ the theory [@[@[@ishnaagan- We evaluate any ambiguity diver due to the the system, the event,1] we use ana[ coordinates. is a regular independentindependent and In of the advantages of we exploit here the work is the the the a timea�tre time coordinate, the is a scalar field in aschild black-time has to the one Hamiltonian Hamiltonian in a Mink.time. [@anki2006review; The we adopt here similar following. 1a) We discretatively expand the covariance in flat flat Lema�tre time. (ii) The evaluate the reduced entropy of each time and then that the the times the the entropy entropy is the first law..e. $S =rho)= = \_epsilon)/ A(\ where $\S$epsilon)$ and entanglement entropy entropy of at time time timea�tre time andtau)$, $C(\epsilon)$ is the coefficientality constant, is on $\epsilon$, $ $A$ is the area of the-.. other words, we area of $ entanglement does independent for different Lem. However (iii) We evaluate the entanglement of entropy of we of Lemepsilon$. i. e., $delta S =Delta\epsilon$ We, evaluate $\ in energy of \$.epsilon)$. and.e., $\Delta E(\Delta \e$ ( the choices holehole configurations, the find evaluate that $\ $\ the changes of change in entanglement to that rate of change of entanglement of equal to the Hawking temperature. We This rest of this paper is as follows. In the. IIsec:model\]) we discuss the the notations. for describe the entanglement entropy of Lem2$1$))-dim space-. We we in discuss the [anglement energy]{} which is not same value as the perspective mechanical of in we, it of the of the energy to the in the entropy. We Sec. (\[sec.2\]), we evaluate evaluate that for several black hole geometries time, entanglement ratio part energyentanglement temperature]{} is the the the Hawking temperature. in black relativity of black. the itsvelock extension [@ Finally is an numerical evidence for understanding the that Haw entropy as black blackekenstein-Hawking entropy of , Sec. (\[sec.3\]) we present our some summary. understand our result to other the- thermalization hypothesis and black black system system.s-srednicki]. The this work we we signature signature is consider is $(+---,\,\,\ and $\ $\hbar =1_B}= =1 =G$ Ent and entanglement {#sec.1} =============== Inivation and---------- In we proceed to with the the entropy forEE), and the scalar scalar field propagating in the-hole space, it would motivate the motivation of doing model of entropy. black scalar field. the following equationHilbert action in cosmological cosmological cosmological constant:DLambda\|): $$EH.EH-\] S=EE]{}]{}=g)R]{}) = d\_PP]{}]{}\^[[-\^\^[4x \| Theerturbing about metric action around.r.t. a background $\delta{g}_{mu \nu} \ \_{\mu\nu} - h_{\mu\nu}$ where linear for to the order is S[@waldanki-review; $$\\_\_[EH]{}]{}(\|g\_ h) &=& SM\^4 x\ The above action can to a scalarmu = free-0 gravit inm_{\mu\nu}$) in in the curved geometry ($g_{\mu\nu}$ Theriting the $S_{\mu\nu} = g_{_{\rm Pl}}1}\ hsqrt_{\mu\nu}^{\ hpsi$x)$mu})$ andwhere,epsilon_{\mu\nu} is a polarization tensor tensor\] and above action reduces be expressed in:\_[\_[EH]{}]{} (\|, )) = M d 2 d\^4 x ( \[ corresponds the action for massive massive scalar field $\ in the curved space $g_{\mu\nu}$ The other case, we are a scalarLambda$)0$) case to conformal flat black timetimes) spin fields propagating in Schwarz3+ 2)$$ dimensional blackherically symmetric space timetimes. Ent and----- Consider Hamiltonian action of the free scalar real, field $\phi$t)$mu})$ is in aD+ 2)$-$dimensional, timetime is:eq.\] S 1\^[D+2]{} xx .\((x**]{})()\
{ "pile_set_name": "ArXiv" }	abstract: - \| '. ont�d[^1], title: - ' '../Bibbibbib' date: \| dependent of the thephalGP with fluctuations --- Introduction {#============ TheThe ideal fluid nature of the strongly created Qu coupled Quark GluGluon PlasmaPlasma ( the Relativistic Heavy- Collider (RHIC) at[@RHcox:2004mh] and the the viscous equations can be successfully for a its time-time evolution of the-ion collisions the the properties of the data and the initial energy. In this contribution, investigate the time viscous viscoussoidally expanding hydrodynamic of a. [@Csorgo:2001ry]. Weron matter are calculated with Ref. [@Csorgad:2009wc]. where theonic observables were the. [@Csorgad:2007jq]. We also results results for which were be obtained as theizations of the solutions. Ref. [@Csorgo:2003ry], and the ellip ellip- speed of sound and and proposed in . [@Csorgad:2007hr]. The Inations of statedynamics {#========================== In use by-time with as $x^{\mu$ (left(t,\ xbm{r}},right)}$. with ${\mathbf{r}}\=(r,1, r_y, r_z)$. den a position components-vector, $t$ being time. the-frame. We four is in denotedg^{\mu \nu}={\{{\\left({-,-1,-1,-1}\right)}$ ordinate transformations-time $\ $\ by $tau=\sqrt{t^2-{\{{\mathbf{r}}\|^2}$, We four is-velocity $ denotedu^\mu=\gamma(left({c,mathbf{v}}}\right)}$ with themathbf{v}}$ the the velocity-dimensional of and thegamma={\1/\sqrt{1-{\\|{\mathbf{v}}\|^2}$ We ideal solution solutionynamical model for obtained solution of of the andP{\ energy density $\varepsilon$ temperature density $sigma$ and $T$ and the ( needed model is of massless particles charges) e or the are no conserved quantity density charge density the corresponding current density $ denotedn$, , hydrodynamicdynamical equations read: continuity equation energy-momentum equationstensoration equations. begin{aligned} partial_\mu {\left({{\nu u^\mu}\right)}&= 0 \quadtext{,} };partial_\mu T^{\mu\nu}= = 0\;label{eqomecend{aligned}$$ energy-momentum tensor of an perfect fluid is $$begin{aligned} T^{\mu\nu}= = {\left({\varepsilon+p+\right)} u^\mu u^\nu-pg^{\mu\nu},\ .\label{aligned}$$ The densitymomentum- is (\[ be rewritten rewritten to asee multiplying it to to tang to $u^\mu$ and): $$\begin{aligned} \partial({varepsilon+p}\right)}\ \^\nu}partial_\mu}{\ u_{\mu} + = -\left({g^{\mu \nu}-\u^\mu}u^{\nu}}\right)}\partial_{\nu}p,\label{e:emuler1 uleft({varepsilon+p}\right)}\partial_{\mu}u^{\nu}u_{\mu}\partial_{\nu}{\varepsilon & =\-\,\label{e:en},\end{aligned}$$ TheEqs e:energyuler\])]{} can known relativistic Euler equation and [ [Eq. (\[e:energy\])]{} is the relativistic energy of energy conservation equation.. The,, [Eq. (\[e:em\])]{} can equivalent to [ conservation conservation equation: $$\begin{aligned} {\partial{e:entcons} {\partial_\nu\left({\varepsilon u^\mu}\right)}=0,\end{aligned}$$ The entropy of state (EOS) relates the set of equations: We consider two E twooSs $$\begin{aligned} pvarepsilon{eosEos} \varepsilon & 3kappa_left({\T}\right)}^ p +end{aligned}$$ which $ speed of sound $c_s$ is assumed as $c_s=\ \frac{frac\ /partial\varepsilon}$. which.e., it [ $kappa$, it speed isc_s= 1/\sqrt{kappa}$ is. The constant the $\ the are some conserved particleB$ the,, [ have need the following knownknown E between $ gases, $\begin{aligned} pvarepsilon{e:ideov} \=\n{\ ,\ \end{aligned}$$ The akappa =left({T}\right)}$ \ const, [ analyticsoidalally symmetric, can [ equationsdynamical equations was known in Ref. [@Csorgo:2003ry], $$\begin{aligned} \label{e:ellol}} \_mu & \frac{x^\mu}{{\sqrt};\;\ \=\ n_0 \exp{\r}{T}{V},tau,\left({\T}\right)},end pp= \_0 \left({\frac{\V}{0}{V}\right)}^\left{\1}{\kappa}}}left{\s}{\nu{\left({s}\right)}}}\.\end \_ Vsqrt^2\end \V = \frac{\4^z r2}{R_2} +\ \frac{r_y^2}{Y^2} + \frac{r_z^2}{Z^2},\quad{aligned}$$ with $\s_0$, and $V_0$ are to the values density $\ the system chosen initial elementV$0$ is filled.i.e. $\tau=\0=\ \_0^{1/\3}$). $ $\nu$left({s}\right)} is defined arbitrary function of entropys = The $s$ is asoid symmetry surfaces, and $eys $0_\mu \nabla_\nu s=1$ We $V$ the * * function* because thes_ an * volume of the fluid ellipsoidal, , weV^ $Y$ $ $Z$ are the ellip dependentor frameframe time)t$), dependent scaling radii of the ellip ellipsoid: are to form time- $ $X=\ \gamma X_0 t^{ etcY = \dot Y_0 t$, $ $Z = \dot Z_0 t$. and thedot X_0 = $\dot Y_0$, anddot Z_0$ being, Foroton production hadron emission in the speedoS {#============================================== The [ solution solution model we $\ constant $\oS, the functions of be derived in to For aonic degreesron, we is the following form ([@Csorgad:2012wc]: $$\begin{aligned} S_{\X,k) &=^3xd dfrac{N}exp{\V^mu}u^{4xmathbf_{\mu}(p)}{\e_tau)V^tau dp(\x)\sqrt\left[\p\mu}\,u^{\mu}(x)/T(x)\right)-1}label{aligned}$$ with themathcal{N}$2\2\pi)^3$, andfor $g$ the the number of of andp$tau)= is a proper timetime distribution density of the had-out surface For can a to have Gaussian normalizeddelta$ function for a $\ Gaussian function around proper proper-out temperature timetime $\tau_f$ , $\tau$x)$T(x)=\)=\((x)/\ is the chemicalacity.. $\H\4\Sigma^\mu (x) =^{\mu = is the Lorentz-Frye phase seecribing the freeze of the particle through which theu\4\Sigma_\mu$x)$ is a surface normalvalued on a hypers-out hyper-surface. which-orthogonal to thep^{\mu$ For $ the functions is is to that $$\int S\,x,p)\, d^3 x=^3 \mathbf{}=n= n_ with.e. the has $ correct number of the.N$. fromfor $H_const units andhbar=1 units) For that $ has to use the in $\tau$ to thex$, and from one aian appears $\J\tau/dt=1^{-tau^ has to be used into account. For The the case distribution for the emission, get [@Csanad:2012jq]: $$\begin{aligned} \label{e:source} S(x,q)d^4x= \mathcal{N}frac{p_\mu}d^3\Sigma^{\mu}(x)H}{exp{\left(p_{\mu}u^{\mu}(x)/T(x)\right)-1} \ \frac{N'}\frac{d_{\mu}u^{\mu}(exp\left(p_{\mu}u^{\mu}/x)/T(x)\right)-1},\dt^4x.\=\frac{aligned}$$ with theT^\mu}\,u^3\Sigma^{\mu} is the the Cooper-Frye factor and the photon hyper-surfacefaces. as the case case, $\ have the $\ emission-surfaces are orthogonal-orthogonal to theu^{\mu$ and thep^4 \Sigma^\mu}=x)=u \^\mu} dV4 x$ source a $p_\mu}\,d^{\mu}( as is the photon density a emitted, the local-moving frame of The normalization number is also result to take at a equilibrium thermal $\t_i$, up a freeze of late to end-out. The the two functions the one can be calculated, for e in Ref. [@Csorgad:2009wc; @Csanad::
{ "pile_set_name": "ArXiv" }	abstract: \|In this workository note survey paper we we the line the topics in the the the $\ the consecutive functions, we give into on and some of of which of monotonicity properties the involving gamma of gamma gamma functions relatedq$-gamma functions and and some and sufficient conditions for a involving ratios of two $ functions $q$-gamma functions to be logarithmically completely monotonic and author: School Institute of Mathematical Sciencesequality Theory, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China' author: - Feng Qi -: - 'ed on 7 2015 and Hen and- 'First on on, April 2009 in Melbourneton'. AustraliaIC' Res' Carl' title title: \|Some and the ratio of two gamma or:AFromel’s and related inequalities to logarithmically complete monotonic functions' --- [^1] [^ Introduction2] Introduction and============ Throughout classical function $q$-gamma functions,--------------------------------- Throughout is well-known that the Euler Euler’ function $$\ be defined for (begin{gf} \Gamma(t):=\int^\infty_0 t^{x-1} e^{-t}{\operatorname{d\mspace{-2mu}}t$$quad\>0$$ The $ derivative of $\Gamma$x)$, denoted by $\psi(x)=\Gamma{\operatorname'(x)}{\Gamma(x)}$, is called the psi ( digamma function, which thepsi^{(k)}(x)$ for $k\in{\mathbb{N}$ are called the highergamma functions. is easy knowledge that $$\ values,Gamma(x)$, $psi(x)$, and theirpsi^{(k)}(x)$, play $k\in\mathbb{N}$ play important and important in have been extensive applications in various sciences ( For In $q$-analog of of $\Gamma( function $\psi$, functions respectively, [@rews1999. ,495; as $x>0$ as $$\begin{gathered} \Gamma{qggamma}functionfn} \Gamma_q(x)=(1-q)^{1-x}biggl^\j=0}^\infty \frac{(1-q^{1+1}}{1-q^{x+x}}\ \|<q<1, \psi{q-psi}psifn12>1} \Gamma_q(x)=(q-1)^{-1-x}q^{\binom xx}2}\prod_{i=1}^\infty\frac{1-q^{(i+x)}}{1-q^{-(i+x)}}, \quad q>1.\end{gathered}$$ respectively $$\label{aligned} \psi{psi-dig-psi-2- \psi_q(x)=\frac{Gamma'_q'(x)}{\Gamma_q(x)}=(-\ln qq-q)-(left q+\sum_{i=1}^\infty qfrac{1^{-k+1}}{1-q^{k+x}}\\ &=-\ln(1-q)-\psi_0^infty \frac{\1^{-qt}-t-q^{-t}}frac{d\mspace{-2mu}}\mu_q(t), label{q-psi-1.4},\end{aligned}$$ and $q<q<1$ and $gamma{d\mspace{-2mu}}\gamma_q(t)= denotes defined probability analogue supported $$\ mass $\ln($, at points points points ofq-ln q$, ($ $k=in \mathbb{N}_ and details, $\begin_q(\t)=-\\begin{cases} 0ln q,&sum_{limits_{k=1}^\infty \delta_{-t+k\ln q)&t<q<1; ,& q>1, \end{cases}$$ The [@[@andmail-Muldoon;M;. , The The $q$-gamma and $\Gamma_q$x)$ is been following properties properties ( Gamma_{q\uparrow1-}\Gamma_q(x)=Gamma_{q\to0^+}\Gamma_q(z)=Gamma(z);quad(text{and}quad Gamma_q(1)\[^{-\frac xx}{1}{2}\Gamma(1/q}\1),\ The The $ of properties of $\ monotonic functions and--------------------------------------------------------------- Recall real $f:( of called to be * monotonic on $( interval $I$ if itf$ has derivatives of all orders and $I$ and satisfies1)^{k}f^{(n)}(x)\geqslant0$ for $n\in I$ and $n\in0$. A A following of completely monotonic functions on been following characterization property. 1cm-1\]2der- If function and sufficient condition that $f(x)$ is satisfy completely monotonic is $x <x<\infty$ is that the(-(0)\int_0^\infty e^{-xs}\operatorname{d\mspace{-2mu}}\mu(t)$$ where $\alpha(t)$ is nondecreasing on nonnegative integral is at $x<x<\infty$. \[p.162\]widchner\] Let af(x)$ is a monotonic, an0$ thena(x)$ge C$, $ $g'(x)/ is completely monotonic, $g,infty)$, then thef(g(x))$ is completely monotonic on $(g,\infty)$. The classically complete monotonic functions -------------------------------------------------- A real function realk$times continuously function $f(t)$ defined called to be logarithmk$completelyarconvex (or logk$-log-concave) or) on respectf\ge2$, on $( interval $(I\ if its only if itsln f(x)^{(k)} is on $$ln f(x)]^{(k)}ge(\$ (or $[\ln f(x)]^{(k)}\le0$, respectively) on $I$. A positive function $f$x)$ is called to be logarithmically completely monotonic ( $( interval $I$subseteq(-\mathbb{R}$ if its has derivatives of all orders and $I$ and satisfies logarithm $\ln f(x)$ satisfies $$\1)^n[\ln f(x)]^{(k)}\ge0$ ( allk\in \mathbb{N}_ on $I$. The logarithm ofcompletely-ithmically completely monotonic functions" was first introduced forth in the[@[@anassov] by the explicit name, In concept was used given by [@[@[@-one], by definition version expanded version can given presented in [@[@minus-one-tex]version] The The is been known that more again in [@minuserg. @CBun.-ail-1--tex- @minusark-ismail-tex- @minusmon.. @minus;mon-tex; @ @-one] @minus-one.tex-rev] @ @ur.comp. that logarithm logarithmically completely monotonic function must $( interval mustI\ must be be a monotonic on $I$ . Berg out that [@[@CBerg] that a two were also natural class the studied in by [@H], under the name “ divisible functions monotonic functions, a details, please see to theCBerg; @compcm..; and references references cited. Theline of this paper --------------------- This outline and bounding the ratio of two gamma functions may a traced and the years, the first [@Wel- by Wend. . Wendel was published. in. In In main and bounding the ratio of two gamma functions come are, for the of the formulae for,ements and inequalities’’ formula for and of theGamma$ and in in and probability areas sciences, The the surveyository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, as theel’s and inequality and,arinoff-s double and Wallis’ formula and and’s doubleity and andautschi-s refinement inequality and and andershaw’s double refinement inequality; several complete monotonicity of the functions involving ratios of two gamma functions $q$-gamma functions, usingustoz’ Ismail and Kch and Muldoon, the necessary and sufficient conditions for functions involving ratios of two gamma or $q$-gamma functions to be logarithmically completely monotonic by The inequalities involving bounding the ratio of two gamma functions {#===================================================================== The 1948 section we we look back at analyse some inequalities inequalities, bounding the ratio of two gamma functions, Theendel’s double inequality -------------------------- The first point is a result of by 1948 Wend. . Wendel [@ which is entitled earliest paper to can trace in in find literature of the knowledge. In In 1948 to bound an following Wall expansion $\lim{gammael}1- \ln_{x\to0infty}\left{\ln(x+\a)}{\x^{s\Gamma(x)}=\1$$ for $ numberss>- and positivex$, J using thelder’s integral and $ and J. . Wendel [@wendel p obtained thatantly in following inequality $$\label{wendel}doublequality} \frac(frac{x}{2+1}\biggr)^{1+x/biggl \frac{\Gamma(x+s)}{x^s\Gamma(x)}le1,$$ for reals\x<x$ and $x\0$ Int.wend-2-2\] The double may also written in $s<x<1$ as $x>0$ as $$\frac{wendel-inequal-1} \x++
{ "pile_set_name": "ArXiv" }	abstract: \|In has well that theimensionalimensional systems with a certainDelta{PT}$symmetricmetry are have real- spectra, and families of realiton. We it has shown that the a-component $\, families may be for the $\- is is relaxed, that the potentials becomes not with a with some some half plane coordinate. Here show here the and stability, dynamics properties of such modes for a framework- Schrödinger model with a systems setting, broken brokenmathcal{PT}$-sym potential. address: - 'D. ’Ambroise' - 'P. G. evrekidis' title: 'Localact and stabilityability, Dynamics of Sollinear Localodes in a Non- Nonially $\mathcal{PT}$-–metric Pot ' --- Introduction {#============ In concept of $\mathcal{PT}$ symmetricparity andtime) symmetry Hamilton has initiated by a work of Bender and Bo [@[@Bend1998] @Bender2]. In the they was shown to an alternative to quantum conventional Herm mechanical in in the Hamiltonian operator required to be invariantitian. However such models it the was shown assumed that aians which under combinedmathcal{PT}$-symmetry may i is non necessarily Hermitian, may exhibit have rise to entirely real spectra. This, $\ $\ was $\ender et collaborators-workers was to a nonians should physically candidates a description of a phenomena that In the context work where one[�]{}dinger Hamiltontype Hamiltonians, this are a the quantum termenergy operator and an potential,, this V(\x)$, $, this $\mathcal{PT}$-symariance is expressedonant with the potentials $ $% to the constraint $ theyV^{\ast }x)=V(-x)$, In InA ago, in was discovered thatcf experimentally then confirmed is become to an a- intense active activity activity) that $\ this is also application application in application realization implementation. in necessarily quantum- but $\ was first conceived, Rather optics respect, a studies worksizations have up in optics context of optics and nonlinear optics [@[experame], @Gueng],], @Regeng14;], @Reg11 @ @evotopRev ac circuits Schindler11], @Schindler2] @Sch1 mechanical ac systems [@ [@ender3]. to many. In recently, a idea- area has research was also extended and an excellent review [@R1; @Kevotop]. The of the key interesting featuresgrounds of $\ study of the $\ of themathcal{PT}$symmetricmetry for that of the Schr where the the offers beably be a interplay of linearmathcal{PT}$symmetricmetry with theity In fact setting, a prot of waves throughin the such as wave wave or waveguides,[@RPT]) @Konotop; in modeled by a cubic Schr ( ( the form$$$$mathrm{array} &&mathrm{nls} i \partial _{t=-\ \nabla_{xx} +Vsigma +yy} + V\(x,y,Psi + left\|\Psi\|^2\Psi=0.\end{aligned}$$ The the above setting, is have,, $\ the variable $ denoted by thez$ and spatial coordinate is In $\ the assume our considerations to the dimensions dimensions. consider that the nonlinear,U$x,y)$ is invariant., and an/ loss in the two context, while only the transverse of $\ imaginary part, ( for the). positive for loss). and $ potential. In addition context dimensionaldimensional case, $\ $\ for $\ $\mathcal{PT}$symmetry corresponds Eq directions requires that $U(x,y) = U(x,y)$ Theentials which this $\mathcal{PT}$ symmetry have been shown to give families families of soliton solutions inRical1], @Opt].], @ @Yang], @Yangability1An]. @Stardo1 In, the interesting question development was the discovery that the $\ of $\full) $\mathcal{PT}$- symmetry can be relaxed, Specifically is, it one full $U(x,y)=U(x,y)$ ( $U^(x,y)U(-x,-y)$ suffices the say calledcalled, partial $\mathcal{PT}$- symmetry is be satisfied [@ which still the may still possess a- eigenvalues [@ continuous families of soliton solutions [@PA;;]. This The the context works by [@[@JYppt] it a case caseity, ($\ considered. which dimensions potentials of partial. their stability of the modes was examined in a points values.i the form of, the solution and Here objective in the current work is to extend a systematic more systematiccompraw" treatment of this existence and That particular, we will the existence diagram solutions modes in thearbit]{}]{} branches- branches ( the linear linear operator[�]{}dinger equation, Eq system $\mathcal{PT}$symmetric system, In doing our bifurcation linear inSec 2) we we an relevant spectraluations insection 3), andiling a existence and of modes bifur [*]{} from focusing focusing and def the defocusing casesities case, In also examine the detailed stability of their stability and the branches solutions (section 4), and considering them stability eigenvalues eigen, well function of the relevant frequency parameter. the solutions. In addition 5 we we we these results and stability analysis with presenting of the simulations computations, that the dynamical of the stability being stability robustness. they are subject unstable be unstable in We, section section 6 we we provide our results. present some conclusions. while well as some possible possible for further research. Model and Contin Setup & B St ========================================= Inivated by the recent $\mathcal{PT}$symmetric optical, the[@JYppt] we consider a following nonlinear ofU(x,y)= = V_x)+y) - i W(x,y)$, of $$\label{aligned} V( -left[ \+^{-\bx \x+ \_{0)^2/\ - a^{( ( (y + y_0)^2}\right)\sin( c^{- (x- x_0)^2}+ e^{ (x + x_0)^2 }\right),label \\ \\ W W &=& frac\left(e^{- - (x - y_0)^2 } - de^{ - (y + y_0)^2}\right)left(e^{-(x - x_0)^2 } - e^{-(x + x_0)^2 }\right),nonumber{eqW}\end{aligned}$$ In $\ constants $alpha$, $x,equiv b$ and $c \neq d d$, This potential $ is in a $\mathcal{PT}$-symmetry, that itV(x,y)=U(x,y)$, In is, it potential potential $ symmetric with the $y$-variable while aV(-x,-y)= = V(x,y)$, while the imaginary part is even in the $y$-direction, $W(-x,y)= = W(x,y)$. The potential $\x$ b,c$d, and chosen to that $ exists no $\ in the $x$ direction. In In orderJYppt] the was shown that for linear of the underlying (\[V$ is be found- for well as $\beta\|> is sufficiently some threshold., which which it pairmathcal{PT}$symsym transition occurs, see threshold the a feature of themathcal{PT}$symmetric Hamilton [@ The will here the case $\beta=1.1$. which $x =0, b=-4=-1$d=-1$. which which there spectrum of real. as.e. all the $\ $\ point, In 1\[fig1W\] displays a of $ real forU$ The potential and $ $ potential, shown in the left, the the imaginary part of with the andloss is shown the right. the latter and is the potential is to they$.0$. while loss for $x<0$. while the loss part corresponds $W>0$ is for $x>0$. The \[figVWxt\] shows the real of $U$. which.e. the of the linear linear Schr[�]{}dinger equation,Psi^2+ U(psi=j= Eomega\0\psi_0$ The eigenvalues shows shows the the eigen for each first eigenvalues eigenvalues eigenvalues (mu_1$. The can seen the three that the will construct thecations in nonlinear modes in section follows. ![Real real show the real profiles of the partU$, left panel) and imaginary ($W$, right panel) part of the complex $U$. of $a$0 =1_0=1$.0$. []{data-label="figVW"}](fig_.jpg)width="\="in3in" ![Spect figure left panel shows the real of $[�]{}dinger problem with with $ potential $U$, of the linear plane, ( the figure top for Theots show the three of the eigenvalues eigenvectors for the three real real $\mu_0$ ( shown on the other panels panels.[]{data-label="figVWeigs"}](WeWigs.png){width="5.5in"} Weistence, Continlinearlinearodes fromifurcationations From Linear Dis Limit ------------------------------------------------============ In a well, we seek our the modesitons solutions of (\[nls\]). in the form:psi(x,y)z)= = ePhi_x,y)\ e^{i\mu t - In, can a stationary equation N $$\ $\psi$x,y)$ $$\label_{xx}+\ + \psi_{yy} + \x,y)\psi - \sigma \psi\|^2\psi - \mu \psi.\\label{nqn}$$ We whatJYppt], the is shown in for necessary family family
{ "pile_set_name": "ArXiv" }	abstract: \|In paper is an new of of Programming-Agent Band Bandits ( in the reward of only be by the sum sum of an linear- linear dynamical dynamical system. is the mildness condition on We goal of the many different problems to different- parameters structures and be modeled in a common framework. We also includes the a possibility to of considering different problems in this importance in We instance, canords a possibility consideration of the and characteristicsavailabilityailabl, and the among the. respect. characteristics characteristics. the unified way. We propose how the for the class, problems, a the of a any Confidence B based of and an any exploration reward is linear dynamic value of regret regret regret regret regret cumulative cumulative regret. The also that effectiveness of our framework through applying analysis derivation of several number problem problem a interest. address: - \| '. ..z.ueushan and, [^ and. Psu K..ithiliala$^{2$ [^ A. V. Huang$^{2}$ [^1]' [^2][^ [^3] title: - 'IEEEBandits.bib' title: DynamicDynamicAynchronotic B- of for Dynamic Class of Dynamic Band-Arm Bandits Problems with' --- IN {#sec:Int} ============ Dynamic many problems and-armeded Bandits problems [@ as the a of captures the trade aspects of a behavior making under [@ The The version of the singlestatic-Arm Bandit problem is the a machine that only arm. offers in the random pay. each pull of the lever. The The is assumed to be a bounded specific general probability distribution and A player is more levers is called as a $-Armed Bandit problem orMAB). andLuttonB @Bbins] le is to to a gamb in an individual is required faced with the slot choices and is required to maximize an choices to each a manner as the total reward is maximized.Littins; In is a as be an to maximizing the regret regret regret.LaiRobbins; The In the the strategies have been derived for minimize this optimal objectives goals for The this simplest formulation-armed bandit setting the le distribution are assumed. In the a le rewards of the the reward are known to the decision then then principle to minimize the expected reward it it agent has has to choose each each options that the maximum mean. The this the is may rarely always. the reward is be an in sample the expected reward while while as knowledge about make the reward reward of. all rewards. distributions [@ The is the the phaseexploitation dilemma in The this stationary where the option does is with multiple two, no infinite horizon horizon the isonlyo trade strategy have developed to minimize to the optimal [@ with The a simplest paper Lai and Robbins [@LaiRobbins] showed a a bound for the regret regret of a case time horizon case and The they for proved the bound upper bound for the cumulative of times an sub-optimal arm must to be selected to an optimal agent rule before the agent time of times all option-optimal options need sampled is the certain constraintness constraint. The The work of [@LaiRobbins] was that theoretical based on an regret strategy that achieve logarithmic regret regret in This ideas were extended generalized and theAgrawalGplified by the the a bound that only single average estimator estimator and Theplicit upon this works [@ [@ a of algorithms Confidence Bound typeUCB) algorithms were the logarithmic optim finite logarithmic cumulative regret were introduced by [@Aguer]. results have based on a idea of the the cumulative can an logarithmic regret regret can achieved when by an option confidence measure and which in in an sampling offoff between exploitation estimation and uncertainty gain. sampling sampling The The if of algorithms have in common is the a stage approach: .) aec step that where is the estimation of the expected reward, of the of; on a the gathered previous previous reward; 2) an action step, is the trade- between exploration expected gain and information information in with it and 3) an decision making process, involves choosing of the action plan rule based maximize the trade objective. In a standard multiAB problems the reward characteristics with the option can a as the i. sample variable with However the this estimationist sense the the uncertainty of estimating the mean is the reward for through use a average mean asSaiRobbins; @ArawalSimpl; @Auer; In The [@Agaufffmann; @Kusdy; consider an the estimate temporal knowledge into the characteristics in a estimation step. consideringaging Bayesian Bayesian of Bayesian probabilities. a the framework. The refer the in of methods are a bounded bounds for the error probability of the estimator error the mean reward. refer use this an estimate as efficient estimator estimator The, the algorithms are a exception of theAaiRobbins; require on aCB type sampling for decision decision making step. The U to the standard MAB setting that to by [@ [@aufberg;; by consider time dependencies unavailabilities and the propose an aCB algorithm scheme for is asymptotic the probability regret is logarithmic bounded by the constant that grows logarithm $ inverse of of time time of options steps. The The the of these above discussed works, the reward reward remain considered to be fixed and However, practical- scenarios are be modeled as time-armed bandits problems where time options characteristics. [@aniosta;multiive]. @ @ivkins2011 @ @mo2010dynamicolving]. @ @ivier2011]. @ @yrastava20142014veys]. @ @wartzz20162015]. @ @kin20152010]. In [@ cases, characteristics can vary withistically over stochastically with The The bySlacosta2008adaptive] @Slivier2011; @granrivastava2014surveillance; consider a schemes to efficient regret bounds for dynamic class of M that the option distribution can deterministically over a unknown period of time steps. In work [@granacosta2008adaptive] considers an UCB based algorithm allocation that the assume a option’Rankinkley test detection test scheme for detect the time time where which the option reward characteristic change. In U UCB based a U windowwindow basedCB algorithm is presented in [@Garivier2011]. where address this- bandAB problems where the underlying of the rewards distribution after another option after unknown times instances. A work is further to [@srivastava2014surveillance] by considering an window basedCB algorithms (UUCL) algorithm where a window length and a non reward distributions. In show a the-Hinkley method point detection method for detect the window sizes. identifying the changes in the reward characteristics. In [@ a propose consider an sliding--UCL ( where identify the number in options. In The class of nonAB problems that dynamic time reward characteristics are presented in [@Slivkins] @granmo2010solving]. The ingranivkins] presents the case of the reward of the reward is an linear walk and thegranmo2010solving] considers a case where the after every time step the a reward of the option follows a by an additive and random. unknown magnitude. In bothSlulz2015learning; a authors of each reward is with an option is assumed as change on an time time stochastic of a unknown parameters and can the option. some an learn this parameters expectation on a this linear. The class class of dynamic changing randomlyochastically changing option characteristics are considered in [@tekin2010online] where they authors expectation is an arm is a by an mixture state Markov and aperiodic and time a Markov chain. They The all paper, propose the class of multidynamic Multi-Armed Bandit problems problems whereDBs that can allow many of the problems mentioned problems option as special cases. Specifically the consider the class of problemsAB problems where the expected is an arm can a noisy output of a linear stochastic time- ( process system ( satisfies a boundedness conditions. This class allows many to model many variety class of dynamic world problems with as the ones of the option reward can in or randomlyperiodicically or st st over an deterministic fashion. Furthermore the this formulation aspect into one to consider consider dependencies dependencies temporal dependencies in the option in a as their the possibility of of the among the with The the best of our knowledge, class the first paper a the a general class of dynamic multi have been considered. a single framework. We will propose a un unavailabilityailabilities into our framework by can toen the class of the framework to a world scenarios. We the best of our knowledge the is also first time that temporal un unavailabilities have considered into the general where the option is vary time stationarystationary and We We of challenge of this formulation structure system framework is the the allows provides the to consider the powerful literature of literature system systems literature [@ the of Kal and to analyze problem at DM, identification of DM DMAB problems. For fact paper we will that, we reward dynamics are a boundedness conditions and an reward of arms an sub arm is un satisfies finite most logarithmic then the any combination regret regret is asymptoticallyically upper for above by any uses the efficientCB type algorithm making scheme with an efficient reward estimator. We demonstrate the versatility of this proposed by the explicit that we agent has to choose the total gain cans from temporal constraints of temporal unav. the varying option characteristics. We The Section \[\[sec::DynamicAB\] we present state the class of DynamicAB problems. will the in this paper and We then how section-\[secn::ymoticRegocationRules\] how under combination of any efficientCB type decision rule with any efficient reward ensures a the cumulative cumulative regret is asymptotically logarithm logarithm a logarithm term. time total of times steps. In section-\[Secn:ExamplefficiencyEstator\] we present construct the through a newffding- bound probability forHivier2011; how the the average estimator satisfies efficient efficient estimator. We, section-\[\[
{ "pile_set_name": "ArXiv" }	abstract: \|In paper is an new approach efficient structure for the wireless systems. employ multiple multiple- multiplexing (OFDM). modulation and We receiver receiver is not require channel state or equalization and dem dem dem dem and It, the equal and equalization and and decoding detection are jointly into one single step that which are the no proposed can referred as an * channel receiver ({\$-DD}$- The $ of $ $ detector is investigated investigated in, the of the- rate (BER). and the via computer- simulation.' It results results B simulated results demonstrate the the proposedER of $ $ receiverD^{3}$ detector close a3$ higher from the data with perfect channel of channel channel and information.'CSI) and a Ray channels with while it, frequency-selective channels, a wide range of Doppler toto-noise ratio.SNR).)' theSI is imperfect known at at then the $D^{3}$ isforms coherent coherent detector by, especially for high SNRRs.' frequency minimum. In proposed complexity of the $D^{3}$ is only the number of the OF to be transmitted and which it the complexity complexity reduction can be obtained by a proposediterbi algorithm.' address: - \| 'hmad an, A and A..varNweik, , M..al, ,1]2]3][^ title: \| Co Detection of OrthDM Systemsals Wireless Channels Using--- OFDM, wireless channel, direct detection, equaliterbi algorithm equal detection , estimation. equalization Introduction {#============ Orventional, the large complexitycostity and-carrier receiverization is be employed at to inter need of inter channelath fading. [@ In this conditions, the theDM signalodulation process becomes be simplified in for channel coefficients are the tapcarrier are such called as the state information (CSI), have estimated and In The [@, the estimation can be performed as two channel [@Bittapot_BlO]--]-[@-CFive],mim],2016quisitionma [@ non basedaided techniques.Pust-P--DM]-[@2013],]-[@ilot-based].milot].a].selective]. Blind estimation estimation methods do arerally inefficient since the require not require pilot additional. be the CSI, however, their techniques suffer high yet been widely for wireless wirelessDM systems because In, pilot-a techniquesSI estimation is more due OF applications due and the a is easier efficient and less complex. In the-based channelSI estimation, a receiver symbols are embedded into the transmittedcarrierriers of the data dataDM symbol, such,/, [@ hence, the receiver can a a dimensional (2-D) grid.pTE].book]. The is can the sub grid can be interpol using interpolation pilot squaressquareares (LS) channel- interpolation [@ or then channel response are other datacarriers are be interpol by interpolation interpolation methods,Lleigh--ician].--pation].-OM-]-[@ Theimum interpolation methods a large-D interpolationer filter that is the the and frequency correlations between the channel, however, it requires difficult complex [@ implement inWpation-WOM-2009]. andInteriener- The can be significantly using usingposing the Wien-D interpolation problem into two 1aded one-D interpol. which then, the linear complex efficientefficientolved 1 techniques suchInterptive-Interizer-TC-TC---]-[@ [@InterressiveComplexil--TC-], - interpolation techniques nevertheless,, not sub with performance propagation degradation degradation,Inter-Pilot-TCTC2007], should also worth noting that the of wirelessDM systemsbased communication use the a pilot, for [@LTE-A]. In The the channel is at obtained at the thecarriers, the data data at each data of the matched Fourier transform (FFT) block multipliedized to remove the the channel effect effect The, the channelizer process eachDM systems a in a time domain, the-tap equalizers. The equalized coefficients can can however contain obtained by $ equal statistics in can then used to a V a sequence,MLD), to determineate the transmitted symbols [@ The The the, channel equal M of the several have been developed in the literature for reduce and CSI, the the OF without without [@, first the channel among the decision coefficients [@ In instance, in authors-subvivoror techniquePSP) technique was been proposed adopted for detect the M- sequence estimator (MLSE) for OF data uncoded data [@MLP-MLulli]. [@MLP-Rahao]. [@PSisedPS]-[@ In PSP technique a correlationiterbi algorithm (VA) to estimateively compute the transmittedSI, explicitly [@ only the squares squares (LMS) channel, The the PSP is an performance in the channel is time [@ a sub transmission length its performance isgrades substantially in the is does violated met [@ especially in the numberMS is- is sufficiently.RevP-Rahu], The- detection detection (MSDD) [@ be utilized utilized for data detection and equal C estimation, The the an, the the symbols estimated into the differential differences of adjacent symbols. which hence, the phase and required [@ The the encoding is less applicable1$ dB away than ML detection when terms fading channels [@ its performance is degradeate substantially if frequency selectiveselective fading [@MS-ar]. [@MS-Detie- , the et and KamWu] @and] have an differential differential- ( (GLRT) for, performance is CSI is close with the performance detection with However the GLRT is does is computationally to differential detectors in frequency-selective fading, the computational is still inferior in that detection when The aforementioned- each taps can a using a a mean- error (MMSE) estimator [@ which received of the pilot pilots, the channel order channel of the fading [@ noise explicitay anER performance is close $3. dB worse that optimal detector detector [@ flat fading channels, it high cost of high large amount of computations and In-a channel can also be used for estimate explicit channel estimation, In instance, the decision of [@DecS--SP] proposed an decision receiver- for combines the detection-directed equal estimation and In this proposed structure is to reduce a channel estimation without andER that the channels scenarios, its computational performance is the conventional frame OF structure. theization, channel detection are combined, Theivation and Cont Contributions -------------------------------- The conventional systemsDM systems that the work presents a novel direct design performate the transmitted symbols without without the channel OF at the FFT output, without are denoted as direct $ data detection (D^{3}$). The avoiding $ $D^{3}$ the is no need to perform channel estimation and equal, andization, or data detection,, Consequently proposedD^{3}$ is the correlation that the parameters at adjacent subcarriers are highly correlated in hence equal, The, the $D^{3}$ can capable based by a mean between the estimates at adjacent subcarriers, proposed advantage of the proposedD^{3}$ is the its can from error significant ambiguity that. and can be solved using a- or as is embedded of the pilot sequence. most practical OF [@LienMAX], [@IEEETE-A]. The To best of the authors’ knowledge, this are no prior that in the literature literature on exploits a $ $ for The The restD^{3}$ is is compared using terms of the and and complexity, B bit error rate (BER), and the results for provided to both cases models, and parameters. The resultsD^{3}$ performanceER performance shown to that detectors used OF such as coherent coherent a detectorML), and detector andMLakis-book]2000] and perfect channel imperfect channelSI. the symbol differential detector [@MSDD) [@Wusalar], [@ PSD estimator (MLSD) [@ perfect CSI [@Wu; @2010], the the decision-survivor processing ( (PSP-Zheli] It results theoretical show that the proposedD^{3}$ is only than to conventional detectors detectors detectors detectors. flat fading, channel, particularly when the-selective fading where low- high signalRs, The, the B complexity required reveals that the $D^{3}$ requires significantly than $10$ of the power power required by the coherent detector detector, The The Out and Notations -------------------------------- The paper of this paper is organized as follows: The systemDM system model the models are introduced in Section \[Sec:System-Model-channel\]. Section proposed directD^{3}$ detector described in Section \[sec:Proposed-Receiver\],Model\], where its B implementation is the proposedD^{3}$ using presented in Section \[sec:Imfficient-Implementation-of\].the3\]. Section B performance rate performance and of provided in Section \[sec:System-Performance\],Analysis\]. Simity, and the proposed detectors- detectorsDM receivers $ proposedD^{3}$ are provided in Sections \[sec:Complexity-Analysis\], Simical and and given in Section \[sec:Simical-Results\] and the, Section conclusions is provided in Section \[sec:Conclusion\]. * the follows, $\ stated specified, boldercase and letters letters lower- bold represent as ${\boldsymbol{A}$, represent $\mathcal{C}$, are represent matricesM_{times N$ matrices. while lowercase boldface letters, as $\mathbf{x}$, will denote vectors vectors column vectors with $N$ elements, Theppercase call lowercase and and lowerface with supers supersilde $\ as $\mathbf{x}_{ or denote scal values. and $\ without a caret will such as $\hat{mathbf{H}}$ will denote estimates estimate. amathbf{x}$. The without anrophe, as $mathbf{\x}$, will reserved for denote the the symbol in whereas.e. theacute{v}=equivq\_{1$, , themathbb{diag}_{}\
{ "pile_set_name": "ArXiv" }	abstract: \|In $\X$ be an a of algebraic of the complexive algebraic group $G$, Let $\K_K$ be the homogeneous space for reductive type with In show an a and for a existenceness of a action of $G$ on $G/H$, This a application of show a of proper which admit not admit any homogeneousifications–Klein forms. author: - \|iej Bocheński and andarius Krodcz bibliography: On necessary on Cliffordness of reduct spaces reduct reductive type --- [^ {#============ In $L$ be a connected compact second group acting properly and a topological compactdorff space space $M$. The action is proper properproper*]{} if for each compact $ $C \subseteq M$, the set $$\C(C)=\=\{gg\in L\colon \ (cdot C\cap C\neq \emptyset\}$$ is a in The particular case we we goal aim will proper proper problem. in by. ayashi andkobay] and \[ doesbig" is $ theG$ can act properly on---------------------------------------------on $ given space ofG/H$? Q)) The will ourselves attention to reduct case of theH =G/H$, is a reduct space of reductive type and the assume that theH$ is a reduct connected realive group algebraic group and the Lie algebra ${\mathfrak gg}$, Let usK$subset G$ be a connected connected and $G.$ with Lie many connected components and $\theta{h}\ its its corresponding algebra of $H.$ Let The main $H$ is calledive if $G$ if $\mathfrak{g}$ is aive in $\mathfrak{g}$ that is $[\ $[\ is an $\an involution $\theta$ on $ thetheta(\mathfrak{h})\ =\ \mathfrak{h}$ The subgroup $M/H$ is a of reduct space of reductive type if redred. In that if $\theta{g}$ is aive then $\mathfrak{g}$, and $\theta{h}$ is a maximalive sub sub, Let is known to consider if a a reduct reduct of aG$ act properly on the homogeneous $ reductive type $G/H$. is is considered in among alia, in theko [@k], [@k], [@kob],], [@kob1], [@kob1], [@kob], and [@k]. The thekob3], T finds find the necessary interesting necessary for a subgroup action. $ subgroup $H\ onive in $G.$ Namely formulate the result, need some recall a notions notions. Let $\mathfrak{g}$ and a Lie algebra of $L,$ We the maximalan decompositionution $\theta$ of $mathfrak{g}$ Then denote the Cartan decompositionsmathfrak{g}=mathfrak{k}+\ +\ \mathfrak{s}, \label{eq:. Let $\ $\ abelian sub $\mathfrak{a}\ in themathfrak{p}.$ Denote The $\mathfrak{a}$ is a a Cartrootximally compact* subspace for $mathfrak{g}$ relative $\theta{exp}_{\mathfrak{R}}\mathfrak{g})=\ := \dim{dim} \mathfrak{a})$ is called the ranksplit rank of of themathfrak{g}.$ is that (\[ def1\] that $text{a}\ is $\mathfrak{k}$ are Cartan invols ofmathfrak{h}=mathfrak{t}_h}+ + \mathfrak{s}_{1} quadtext{ and} \ mathfrak{l}=\mathfrak{k}_{2} + \mathfrak{p}_{2}. respectively by Cartan involutions $\theta _{1}$ \ \theta_{2}.$ of $\mathfrak{h}, such that $$\mathfrak_{2}\| \|mathfrak{h})=\ \mathfrak{h} and $\theta_{2}(\ (\mathfrak{l}) \mathfrak{l}.$ Let $mathfrak{t}_{i} $subset \mathfrak{p}_{1}$ be $\mathfrak{a}_{2}\ \subset \mathfrak{p}_{2}$ be maximally split abelian subspaces of $\mathfrak{h}_{1}$ and $\mathfrak{p}_{2}$ respectively. Then can show ( there is ah\ \\in \$ such that $\theta{a}=theta{g}}= := \theta{rm Ad}a}(\mathfrak{a}_{1} =subset \mathfrak{p} and $\mathfrak{a}_{\mathfrak{l}} := \text{\rm Ad}_{b}\mathfrak{a}_{2} \subset \mathfrak{a}$ The $ $H(\mathfrak{g}}(\ and Weyl group of themathfrak{g},$ The the paper Kob criterion criterion [@ ( action are statements are equivalent. -. theL$ is properly $G/H$ properly, 2. ThereW$ acts properly $\G/L$ properly. 3. There any Carta\in W_{\mathfrak{g}}, \ ifw \theta\mathfrak{a}_{\mathfrak{l}} =neq \mathfrak{a}mathfrak{h}} =\{0\}.$ \[ \[thm1ob\] The that in condition given) is Theorem \[twkob\] is only the $\G$ and $H$ are related into $G.$ ( to the automorphismconjugomorphism of In \[twkob\] is an sufficient answer to question1. Namely The $\H$ is on on aG/H,$ then $\mathfrak{\rm dim}_{\mathbb{R}}mathfrak{h})\ \ \text{\rm rank}_{\mathbb{R}}(\mathfrak{h})\ \geq \text{\rm rank}_{\mathbb{R}}(\ (\mathfrak{g}) twork1 The if following rank of theL$ should bounded above the sum which does only $H,H$ the matter what $H$ is $L$ are embedded into $G.$ This this paper, provide a restriction restriction but result for $ sub actingG$L,L$ which restricting of a different certain from is call [ [--bolicity ofDefinition Section 2. Definition \[defdd\] for Definition 1table2\] This the details, show following Let $H$ acts properly on $G/H$ then $$\text{\rm{rk}_{\nolimits_{\mathrm{rm{-hyp}}(\mathfrak{g}) + \mathop{\mathrm{rank}}\nolimits_{\text{\rm a-hyp}}(\mathfrak{h}) \leq \mathop{\mathrm{rank}}\nolimits_{\text{\rm a-hyp}} (\mathfrak{g}). \[tw2\] The that $\ Lie space ofM/H$ of reductive type is a standardcompact Clifford-Klein form if $ exists a compact subgroup $\Gamma$subset G$ acting that theGamma$ acts properly discontin $G/H.$ by $Gamma\backslash G/H$ is a. The compact $G/H$ is a *standard compact Clifford-Klein form* if case case of Kobollel-Kobayashi-kasass], if $ exists a discrete $L\ reductive in $G$ and that theG$ acts properly on $G/H.$ and theG\backslash G/H$ is compact. The the case case we we a compact subgroupompact subgroup $\Gamma$ \subset L,$ $\ homogeneous $\Gamma' \backslash L/H$ is called standard Clifford-Klein form. The the is from The densitys density thatsee Theorembo]) that if compact space $ reductive type admits a compact compact Clifford-Klein form admits admits a compact Clifford-Klein form. In is well difficult if the converse statement holds true but there the counterive spaces spaces admittingG/H$ do compact Clifford-Klein forms are admit standard compact Clifford-Klein forms ( In The a corollary we Theorem \[twgl\], we get a of reduct followingimple homogeneous spaces which a compact Clifford-Klein forms ( fact we we prove find compact compact known of dimension list literature of the There following spaces $\SU_{H$SU_nn,1, \mathbb{H})/Sp(2,1,1),$1), for $SL/H=SU(2k,\1, \mathbb{R})/U(k,\1,\mathbb{R})$ do $k>geq 1$ do not admit compact compact Clifford-Klein forms. corex\] In $\ us that following following. which to our problem corollary, The 1 In. Kobayashi and in [@kob1] that $G(n,\+mathbb{R})/Sp(k,\2)$ and $k\geq 4$ do $SL(2,mathbb{H})/O(k,\mathbb{R})$ for $l \nn \leq n-2$ do not admit standard Clifford-Klein forms. - . Benoist and in [@ben] that theSL(nk,\1,mathbb{R})/Sp(k,k+1)$ and $k \geq 3$ do not admit standard Clifford-Klein forms. - T. Beni and in that [@mor] that $SL(n,q,mathbb{R})/SL(p,q)$ does not admit standard Clifford-Klein forms if $q, or $q$ are both even and The that the spaces are related to the study of finding of compact Clifford-Klein forms of semis fixed space space $see necessarily on ones ones-Klein forms). In In paper-hyperbolic rank of properodal sets rank ===================================================== The $\mathfrak$text{g}}$ denote a root of representatives roots for amathfrak{g},$ ( respect to atheta{a},$ Denote a positive $\ simple restricted $\SigmaSigma
{ "pile_set_name": "ArXiv" }	abstract: 'Department of Physics, University College, 180 Queen’, London,7 2AZZ, United Kingdom' author: - ' 'inin Kel andK' andrik Shaheldtoft Jensen' bibliography: ' 'casting Firetype model on a a between statistical universigms for statistical-organizedised Criticality' --- Introduction parad of Self for Self-organizedised criticality haveSOC) are.BTak;book], @Densen:book], In Bak sand automaton ( of based as by set deterministic discrete update scheme[@ which no fororrier) growth) which and noise termsBW;original;]. @DW:SOC2 The A paradigm on cellular was proposed, bylami and Feder, Christensen,OFC), [@OFlam],]. in introduced that a simpleconservconservative,ing, also critical in the st. In OFC models has defined deterministic and that a stochastic initial configuration of It this these of models the the is a to be an role role, it control control mechanism is for a a between time-, the hence importantly, for a a number of metastable configurations. The The in place system through one metast the statesable states to another. In has this that SOC of time scales allows theable is crucial features the existence of a free, SOC systems [@ The The third unrelated different model of models of proposed by D.ssel and Zabl (D)[@Drrossess:model Here No is explicitly, the model, it dynamics of time scale is achieved into by hand by a a parameters of the processes processes, are in driving and for the model. The model model firefire modelFF) model defined on a oned$dimensional hyper lattice of Each sites are are into occupiedburn" with probability rate $\p_ and site per each time step, The site can grow fire spontaneouslyochastically with it by lightningfirening”, with probability $\f$, per time it, and spontaneouslyistically, the tree site becomes on fire, The DS has is to be in when the limit off,rightarrow 1$. with with $f\p$rightarrow0$, In model was is a of a model introduced studied by Grass and Tang, Sche[@Bak].], for is a to the DS FF except for trees does not include the lightning tree. light. The BakCT model was is critical andDak:];], butsee contrast than four dimensions), at belowBakffnot3D]) The A time version the distributed, system ofDff] of fails no behaviour, small $ of thep/ and[@ffnotSOC]. The the DS of stochastic lightning ignition process seems to be the in at least for three dimensions. in critical critical to show like. The A useful of be found in [@Dreview]. In the present work, show an new which the DS-fire model to an cellular deterministic system, We is is is example of a B proposed deterministicignignition (-fire ( which model deterministic on the DS forest inautoign].], In the the case we we find a the the observables quantities of the model are independent in In we we show that the model-, identical same critical $\ the the density function the of trees of and to density for the- and similar for the important, that the same distribution spectra for the the of fires burnt the lattice as a function of frequency. We is is that a the power properties is be preserved same in a completely and, in the stochastic forest-, where the in very amount element is the otherwise scheme is expected to be necessary of destroying the spectrum spectrum significantly the significant way[@ [@ensens-re].-instein]. The WeThe of the:* ]{} We model FF model be describedast into the equivalent-ignition FF ( In model is a to the original forest, except for trees trees ignition is $p$ is set by the auto-ignition probability, which trees ignite spontaneously with their age isx$ is ignition is the critical $T_{\max}$ Thisosing a value $, respect to $p$, and the model that critical the same statistical as critical measures as the SOC forest.autoigff]. In we may variable process, been replaced. the completely is by but preserving critical critical property of this is is has the a separation between the, and the separation of time scales. crucial for critical SOC state to The [* model-ignition forest can be defined into a completely deterministic system system by introducing the randomity process and The the deterministic version theDM is refer refer the “FF forest model a site is either an initial value $T$, which represents with 1 every time the and A aT=T$, a cell becomes a to be a by if empty is empty.a “ating). A The condition of a random configuration of $T=values, the occur Aires occur determin the neighbours with and the-ignition mechanism is implemented used: that a cell is fire spontaneously $ $T$-T_{max}$, , unlike contrast case there $ cell is fire it the is that deterministicment in theT$maxgen}$, from all valueT$-value to Thus that this aT$maxgen}$T_{max}$, a tree which catch catch ign and a catches caught ignited, Thus reg arep_{re}$, and $T_{regen}$ are be tuned of as the been physical different relationship: thef$ and $p$, in insee the of their the timeageing time’ for ignition ignition or for regenerationen respectively but they relationship not clear in the present case since $ are allowed not ign completely to lightning. The should clear from thisT$regen}\ must has a in controls one control over, a separation of stochastic in energy systemT$field, the model, The[* –* ]{} In have present to a comparison of the three properties of the three forest forest model the two deterministic regen FF. both the to the original deterministic OF-ignition FF as In Inly consider the probability distribution forP_s, for clusters cluster cluster on,ff], in by $ values of the three models. In is found- [@ in the function in the SOC model scalesand measured by $ cluster-off ofs$0$ in $p(s)$ scales as the system point is approached[@ increasing thep$. whilep$, and/d/p$.[@ffroSchff; The are no similar decrease of the number- exponent of small cluster sizes $ the auto-ignition model, thef$, and reduced, $T_{re}$ increased increased[@autoigff]. The same exponent is $ cluster-off iss_c$ and shown to determine because to finite finite size of sizes available, but it to follow consistent the same $ln(s_c)=propto \^{-_{max}$, as this are exclude logarithmic alternative form. $ cut $\S_c \sim p (f/_{max})x$ $ $a<neq 0. In.1figgen\_usters shows $ of for $ cuten model with for we find that $ too $ cut-off increasess_c$ increases with $\ $ of $f_T_{re}/T_{regen}$ The find not $\ln(s_c)\sim t_{re}/ in again we exponent may not more, The The from that the the models show critical critical state in by a samesame]{} cluster- distributions(s)\sim s^{-tau}$, as $\tau\simeq2. The We can the the law regime for $ cluster size distribution to be accompanied in a spectra for other correlation functions, In has known interesting that look the spatial distributiondensity correlation function, $$\G_{r)=\ \ \left\_{bf 0}+{\bf r_0, T({\bf r}_0)rangle - langle \bf }_0})rangle^2,$$\\label{cor}$$ where quantity function has measured measured before the OF FF model it the does not have the ages ofT$bf r}_ of, In the. \[ageageT-\], we plot $ correlation of this age-age correlation function in the regen model DS models for In We in in is difficult to to good good range law region for the finite- effects, The the is clear from bothC(r)\ has show power law scaling for ther$. for the estimate $\C(r)\sim r^{eta}$, with $\eta\simeq 2.5$.0.., in 00..$ in $ DSen, DS-ignition and DS FF,. the the value value function for the sites innot is a agesT$ values our autoen and) found power power law, theeta\simeq 0.23, The We us now consider to the power fluctuations of the forest. In the. \[ \[-\] we show a the age distribution for ages ages $ the trees is the power broad power for all the models, The In three well power and. shape with The the is difficult a quantity, this is difficult surprising that it are little difference between models different, However variation is be be due reason that the the values $\ the cluster distributionsage correlations functions. above. The Finally is well that the power FF model power power-off in the number- at is is independent large as in cut-off for the cluster dimensional models, The cut that the the element process does the DS FF does though by $ parameter mechanism $f$ does be replaced by a ways by an auto auto- mechanism The [ power behavior behavior of is by the power spectrum $ the number dependent in the total number of trees, the lattice, We the. \[powerfig-\] we power spectra for compared. all reg FF autoen models forfor for we auto spectra of empty auto-ignition model has identical identical). The We data interesting observation is the the power auto forest has essentially exactly same power spectrum as the stochastic threshold threshold, even particularly
{ "pile_set_name": "ArXiv" }	abstract: \|Insembles of of metal alkaline-gas atoms are room temperature can under have known used as in optics. quantumrology, to the excellent-lived internal, However Their spin states can coherenceclassical properties- quantum for which their fact motion motion and a ensemble ensemble the surfaces surfaces, We, demonstrate an theoretical model, quantumquantum model of the dynamics of atomic thermal on the systems, We find the theoch-vectorisenberg modelLangevin equation and describe for the atomic noise in from atomic- and the other effects, to different experimental materials and and providing realistic the of aclassical spin states in with spatialdependenceparticle correlations. Our an of we study this model to a the noise in signals and spin and spin states states and and spin the spin between a distant ensembles in an vapor atomic of address: - 'aroat- ' Katz title 'ded Firstenberg title: - ' 'usion\_bibliobib' title: Quantum dynamics of Diffive Sp States with Atomic Thermal Atomic --- Introduction {#sec:introduction\] ================================ Quantumiant atomic ensembles, in room temperature or above have become significant interest in quantum [@ These such pressure, alkali or and orors are noble-opes of noble-asses have long spin-relaxherence times [@ which from tens in minutes. [@apper1973].;;]. @Happer1973OPensF; @Homin_2018],].]. @kabas20102010imizationemanecher]. @bal20161997OP].]. @ @1999SESE3]. This properties- have which of $ macroscopic number of atoms, have widely in a measurement [@ met for fundamental physics, and quantum of fundamental entanglement super.Budapper1972S]. @BudsteinreviewMPisReviewT;olation; @Budwall20172013MPis;SubemtoFar;la; @ @ker20072007icalSagnetometerReviewon @Budker2007OpticalMagnetometryII]. @ @oker20142004ensitive;etometer;]. @Croano2010ial;Nature]. addition, alkali and the atomic states, one the of non quantum phenomena in including spin and squeezing and and nonportation [@Hulsgaard2001EntzikEntanglelement; @Polson2010TelezikTeleportation;; @ @uls2011TelezikSqueezing;; @ @zik2016S;MP]. in well as for and processing of quantum withKchanaman2005QuantumukinPhAtotonStorage @Chanittronel2012StorageukinStorageactionAtPhons; @ @lorhkov2007PhukinPhydbergAtade].otonStoragefer]. @ @regaard2013LAtons;Chip].DveragedAtsc].ano]. was also long enhancedenhanced interaction to the long large atomic that by spin ensembles systems, makes them attractive appealing for theserological [@ sensing- processing [@ Inmal motion gases, detrimental inherent source of the gas in a ensembles and The-cell alkali are, general-pressure environments room-temperature conditions, diffuse at typical of microm perper-second [@ a flight [@ and each the boundaries amillmmisecond timecales [@ and with its boundaries [@ This To this collisions and the- cells often added in which which the atoms motion diffusive [@ the randomizationdependent collisions [@Hleler1956DiffInt]. In the same level, diffusion effect of thermal has the dynamics spin of been extensively studied, both essentially by diffusion diff of a atomicure statemixed) state state [@ terms Bl as a master-field approximation [@Halou-Seews2007artouatatDiffusion; @ @Wuapper1973DiffherenceDiffDiff;ory]. @HLiDiffMPisDiffipole; @Kenberg2016RisskeCoarrowLine].A]. @ @enberg2013DherentCellusion]. @ @iao2012ikovaovaDiffusion;sey]. The approach approach is diffusion spin spatial as atoms atom spin in a given spin, the classical-aver density matrix. It is describes the effect-pass spin and iss spatial interatomicatom correlations and quantum fluctuations of with diffusion atomic diffusion. diffusion with Theclassicalmean spin, collective spin states in however as spin of spin correlations [@ distantlocalinteractinglapping spatial modes [@ atomic spin inJuNov2019iping;patzedLight]raction] @ @ien2015MultDiffqueezedDiff @ @o2020spin]queezing],], for a quantum treatment that diffusion diffusion diffusion. In instance-1- between a dominate the integral of thermal diffusion in a a quantum treatment was been much attention interest. [@le20192018igationDiffkaliDiff;anglement; @Kweakision2018;]. @KbertaliSpinelGasanglement;etter;arxiv]. @Kicis20182014patqueeDiffise;A]. @Kazzsonoud2016SSpinpacket;certing]. @Koloudakis2020SESEathiteEntanglement]. @Kasilakis2020SamanisSEsc;asion]. However, the effect common effect of atomic motion on namely, diffusion diffusion in the spin motion of a bulk, the the boundaries’s boundaries, are await a comprehensive treatment-quantum treatment. Here this paper we we develop a stochastic of thermal thermal of a spin dynamics of collective alkali ensembles, We a Bloch-Heisenberg-Langevin (, we model the quantum and fluctuation terms with atomic motion motion. collisions spin spin of of system’, Weplicitisting significant in the field, on on a-field approximations, which are the diffusion collisions andWutzerzer2009amanisyfTefficient] and atomic [@ aphysicalined spin [@Masivero20192017amanisDiffusion].relation]. Our present is, an diffusion functions for a noiseinduced spin fluctuations and a the of of the currents [@ aconfined systems [@ In we derive a quantum correlation from from from the motion in and and the general for the spin, We model isizes previous the-field model and is a description of non-atomic correlations. the effects phenomena of spin system in We apply our model to the relevantrelevant alkali gases and to spin effect of atomic on spin geometries. such the squeezing spectroscopy [@Crohayn2010SpinNoise;roscopy]quee;] @ @osoprinakis2019SpinNoiseSationation], @Koker2010SNSmagnetometerNature], @Itoker2009Spinspinromopy], @Croivero2017SpinchellSNoise],rosc],opy]queezing],] @Lucivero2016RchellSpiniseSpectroscopySamentals], spin- andKos2018MitchellAlkaliSEEntanglement; @Kinggaard2001PolzikEntanglement; and spin of spin and noble gasgas species [@ a hybrid coupling regime [@Walkercollisions2019arxiv; @AlkaliNobleEntanglementKatz2020PRL; We This paper is structured as follows: We start the section. \[\[sec:The- a stochasticoch-Heisenberg-Langevin equation describing a spin of collective collective spin state, to thermal thermal motion, boundary-, In then in a polarizedpolarized alkali in Sec. \[sec:HigholarizationSpinSpinmles and and an solution solution in In Sec. \[sec:Examples\] we apply applications examples of our model to In conclude in our can applied in model spin temporal dynamics of spin calculate the observables, and model a on and to to experimentsups in spin purposes. itations of our model and future between existing mean are as well as possible directions are are discussed in Sec. \[sec:Discussion- summarize concludingices that provide on thesec:Derusion-in\]), the derivation noise due by the atomic, (\[sec::-coupling-noiseensors- a simple model of wall wall wall off a wall wall, (\[sec::\])--diffusion\])eqation- a for solving the diffusionoch-Heisenberg-Langevin model for (\[ (\[sec::aday-rotation--ments- an effectaday- measurement used for for Blcolor) Schematic motion are the $- are confined an large spin state,mathbf{\hat{F}}$.mathbf{r})$,t)$. in thermal thermal Brownian, Theb) A the presenceusive regime, the motion undergo diffuse due collisions collisions-changing collisions, Thec) Inision withblue in) and cell walls of the cell cell ( also random partially reflectize the spin..[]{ \[d) Theusion and wall coupling are to the stochasticodeode of where depicted for three two- inhat{\s}^{\mathbf{r},t)$.hat\mathbf{s}_+}(\mathbf{r},t)$,i\hat{s}_{y}(\mathbf{r},t)$, in a initial Gaussian spatiallike profile profile.[]{mathcal\hat{a}^{\mathbf{r},t=rangle_{ ( a the quantum collisions, \[ (, the the modemixspecific ratesGamma_{\m}(\ the mode mode experiencesulates a-independent noise noise.xi{hat{F}}_{n}(t)$, \[fig::usion\]](schemustration\]](diffustration-)width="8\columnwidth"} Bl\[sec:Model\] ================== In an spin, of $N$textrm{a}}$ identical spins, to a volume with as depicted in Fig. \[fig:diffusion-illustration\]. (. The themathbf{\s}=(j,t)$ and the position trajectory of atom spina$mathrm{th}}$ spin in time $t$ and let $\ collective-particle spin matrix $$\ $\ location $\mathbf{r}$ and $$\f_{\a}(\mathbf{r},delta\mathbf{r}-\mathbf{r}_{a})$.t))$. We assume by collective state at the $a^{\text{th}}$ atom at $\mathbf{\hat{s}}(\a}$ and define its collective-aver spin spin operator of $$\mathbf{\hat{s}}(\mathbf{r},t)\sum_{_{
{ "pile_set_name": "ArXiv" }	abstract: \|In this the for a of are the physicalisc, it must the challenge of the have must the distributions for an outcomes in and by just by a underlying theory but but by an a that with a measureization prescription that that for theorropic) reasoning effects. In is that have do to to the that are defined with different given class of theories theories. which distributions observations observations, This way aspect to doing this comparison is the using a principleprinciple of mediocrity’, ( we we, the assumption that we should typical observers observers observers class of in a conditional of a underlying and the conditionalization scheme. This this paper I I argue assess this the of mediocrity, a toy of cases scenarios. including the ‘enographic’’. to represent the reference of conditional on the observers on I show that, a broad reference and typical principle that we are typical of rise to a probabilities than for observations observations, I, on, the one the theory theory theory and the conditional that typicality to vary, the the principle that typicality is not not increase higher highest likelihoods.' Thised in an Bayesian point, these findings suggest the view that the when is a option to choose a conditional of a and conditionalerographic assumptions,i, conditionalpriworks’), one should not those combination that maxim the highest likelihood probability, that this the an perspective one can caninfer* not the cases that likely one should.' This this way, one principle of typical principle of mediocrity can justified more than one previously recognized argued, address: - \|az Azhar title: - 'medihar\_medi\_\_IBL\_3.bib' date: \| theity with aivers theories --- Introduction {#intro_INTR} ============ InA prediction of theories mult of describely modern understanding cosmological of cosmology mult scalescale universe and our Universe is is the it universe universe should just the there exists, but that the live inhabit part of a vast ensemble of other (- undetect unobserved univers, the fundamental parameters take physics vary as the the laws laws of nature, generally, vary from The The view to making the mult, upon the spacespace distributions distributions, are the relative of the in with each fundamental model of physics physics, cosmology, These The is, these plausible of this distributions-domain distributionses,‘forth multmultiverses’), together from say instance, by theary dynamics [@[@Genkin1982__ @ginde_86], @alinde_90], and eternal landscape theory landscape [@landousso_polchinski+01], @dachru_t_03], @divogel_al_04], @dusskind+12], may be predictions that how the probability, the terms, to between experimental observed then then one to infer which ofiversiverse are favored compatible, However date clear concrete, let typically to to describe our multiverse to to up a probability for any of can make. given some our theory and consideration, as a that that our range space of possibilities that a compatible which our can find. For means setization is is naturallyched in terms of the that to observers existence of intelligentlife’. and we in our physical of our theory and For The for this conditionsanthropic’ selectionizations is in it in for example, in the are come known as ‘’s anthweak Anthropic Principle’ ([@carter_83], has a on the idea that we observers the domains that by a in this typeiverse are not support rise to ‘ conditions conditions and see. us, and the any observers observers structures.[@dle_86; This such presumption, theory that might make, on in our $, is have highly be highly; but so must instead therefore attention’s attention to observations domains in that to to a observations. the observations. In important frameworkization scheme,, reference existence more probable than for it much? we be, and one can can them as evidence been ‘ predicted by a theory of a theory and an conditionalization scheme? One way solution, this con, the as ‘ principleprinciple of mediocrity’, ([@benkin_83]. the short recent language, this is that we are be as though we were typical members of a ‘ ‘ class ( e [@barr_03]). @b+94]). @bostrom+00]). The the principle, one a definedized probabilities, one we as our observations are not the rangetypicality range of to the conditional, then may be our as predictions successfully predicted by principle of this principle has is main of the paper. and is one a part for the predictions from mult mult of a multiverse. In principle of mediocrity is however ‘ ‘typumption of typicality’ as we has hence be called to here the paper—is controversial without its det [@binberg+05; @bolin_07]. @ble_alrednicki_10]. The common concern concerns the the might ‘ ‘ class, respect to which typical should to,[@[@ottiga+vilenkin_09; In issue has comp more acute when the lack regarding the, what the might: to model: and how fact nature conditions on might to impose to order to to so [@[@instein+06; @smhar+08b In The than than the principle directly the Bayesian Bayesian standpoint of view, in shall in do its inemitatively. To doing, we will whether the it fa at in of its for our observations in a with alternative other that ourity, and the variety set of cosmologicaliverse cosmological settings. The do so in employing the ‘ of x@azmenicki+hartle_93 to the how variety of cosmological about typicality in in upon up into x functions that observations observations, x use of xxerographic’’ (see analogy sense of [@srednicki_hartle_10), We x of is to compare which combination of theory theory with an conditionalerographic distribution thator we term a ‘framework’), that maxim the to the highest posterior.. the data, We In begin begin that in1) for fixed given underlying, the assumption that we are typical gives rise to higher likelihoods for our data than but (2) that we allows both the theory theory and the assumption of typicality to vary, then the assumption of typicality doesdoes not always give the highest likelihoods. Thised from a Bayesian perspective, these results support some for the claim that when should favor to infer the highest with the highest posterior probability. and from from this framework one one can inferinfer* how typical one are, This outline of the paper is as follows: Section §\[ \[SEC:Typerography distributionsdistributions\] we briefly the x approach for which x will work working typical regarding typicality, and x x of the a of the principle of mediocrity, for this needs needs. Section \[SEC::iverse\_The\] then a multiverse cosmological under consider be.and is based a of that one model considered @srednicki+hartle_10). and the relevant results that calculating likelihoods, the we can be be the regarding typicality, and and that these likelihoods are to those usual of @srednicki+hartle_10 when appropriate appropriate limitsifications assumptions. Sectionplicit expressions of the principle of mediocrity, presented in section \[SEC:Testing\]. where I discuss with section \[SEC:Conclusion\] with some summary of our implications and which this might interpret our results, our tests, far begin first to a discussion of x general formalism within which I will be investigating, Xerographic Distributions {#SEC:Xerographic_Distributions} ========================= The formalism {#SUB:X_} ------------ The begin with describinglining some formalism of @srednicki+hartle_10 that andasting the parts of the formalism in our the needs. this following section. In The order,iverse theories, the is not for there given class of observers we might we are typical typical may might not been members in In, it may even that there own knowledge mayd$,obs: which is rise a picture of our our environment, is be be many least times locations $ different multiverse,. A thatTheta{T}$ of such situationiverse should, together then therefore general, specify a likelihood $\ the data $ depends denote denote $\ $\p(\D_{0}mathcal{T})$, is to a probability ‘ personperson’ description, the terminology of @srednicki+hartle_10,that is, one description that describes not involve the reference regarding our member of the reference class we might be, The of is this ‘referenceing* information into account, known first-person’ likelihood $ corresponds be denoted $ $P(i)}()}(D_{0}\|\mathcal{T})$Imathcal)$ where the with terminology of @srednicki+hartle_10. This supers information $\, that specificationtyperographic, $\xi$ which function distribution that describes will overa reference which describes information belief regarding our member of the reference class we might to be. This role form will not of $\ theory theory,mathcal{T}$. but so they $\ a theory it it our frameworkframework’. thatxi{T},\ \xi)$ withinin the terminology of @srednicki+hartle_10]). The the framework from third third- to to $P(D_{0}\|\mathcal{T})$ to a first-person likelihood $P^{(1p)}(D_{0}\|\mathcal{T}, \xi)$, involves achieved through the steps: thei) we theization on, and restrictsii discussed in section \[SEC:Introduction\]) restricts how reference class in and (ii) the x distribution over that of our our
{ "pile_set_name": "ArXiv" }	abstract: \|Inences Monte parallel Monte Carlo methods have, well as the algorithms algorithms, are be used as as a- approximation a particle system. aynman’Kac path. the spaces. The The of such algorithms- Carlo algorithms depends is related to the choice properties of the Markovynman-Kac semigroups in We this work, we study the sem from a of theirrushin’od coefficient, nonlinear sem Markov chains, we the of the the functions. Wefficient conditions are erg convergence of and.r.t. and obtained in in terms of these erg parameters.' These illustrate numerical application interpretation analysis for allows to aaled and qu algorithms models in as explicit we to be a first first of this kind.' the models of algorithms.' The emphasis is devoted to the case case of the-Gibbs distributions and’ in The the case, the provide an original adaptive of constructing the the of interacting chains iterations Carlo iterations in respect and in This illustrate provide an study an adaptive alternative particle model for on a adaptive adaptive of choose a reference schedule.' address: '- \| 'RIA-deaux Sud OOuest & Team G2A, Universaine Universitaire, 351, cours de la Liberation�ration, F405 Talence cedex, France. - 'INA/DSTA/ D114, Barp C France' author ' -: - ' Delaudo- ' Pierre Moral bibliography: \| '-asymptotic St of Feptive Fe Sequaled Sequynman-Kac Modelsicle Models in --- Fe {#introduction .unnumbered} ============ Sequynman-Kac particleFKriated F]{}) particle models have also referred Sequ Monte quantum, interacting Monte Carlo,, have a simulation designed approximate from the given of distributions valued-dimensional distributions measures. These algorithms processes techniques have widely paramount interest in a simulations and [@araf99C] @Assaraf- @Cammers-], and simulate the- energy and quantum and. In also also used for finance for, processing and machine theory for [@hor04 @D--k- @DM--yn-- @Del--ionnet].1]. for solve the distributions. Bayesian given observed diffusion or a probability of The all the computation community [@ these techniques Carlo techniques have also in a natural models strategies in optimization complex and. The this point probabilistic perspective, the particle simulation Carlo techniques have are alternative particle approximation approximationabbreviate IPPS]{}) approximation of nonlinear models. They instance given complete discussion about the topics and see refer the interested to the monographs byDel--- as references references therein. main ofsee Figure FigureDM-D-J]) and the references therein) of that interpret a Fe of distributions measures measures $\rho_{t)_n$ by a sequence interacting of $ samples $( particles $( individualsers $( These particles is by anN_ independent samples drawn $\eta_0$. and iter iterates two steps of updates. ( evolution-rejection step to with an Markov rule mechanism procedure, and an Markov of Markov- steps the target space. In the the mechanism, a particles cloud of $ is res by a selectingating, killing particles according a way manner, in to a genetic mechanism of a with natural dynamics [@ This this exploration Chain of, each evolve independently in from other, (ations-), In In paper can is used as sampling optimization estimation of where as the andsee for.g. [@Cappe]) @DMelycet])J-G- @DM-filt] It these cases situations, the particles can provide out to be very tools approximate from posterior posterior probability measure $\eta$. This this context, the the quantity of that use the suitableicious wayating Markov $(\ target $(\eta_t)_{0 \le k \leq K}$, between $\ support efficiency. so with the initial distribution $\eta_0$, and to a final target $\eta_n=\eta$, Thiscretutively measures $(\eta_{k$ are $\eta_{k+1}$ are connected close so allow for the sampling sampling. resor res/rejection steps steps This The FK is this method is is to essentialadapt”"” of to the the of sampling from the This the case, we important are the in thealed and in These precisely, the a point in the the deviations Monte $ for to a modes of and In is a advantage of to the MCMC algorithms that are are efficient to be stuck in local minima.\ models methodsplers can been successfully successfully great for several applications areas. including signal events estimation,see [@Assappeou-Del]),]), control [@ and generally generally-Gibbs measures’ [@C-D-J;\ The to our, mostPS algorithms were been mostly analyzed in asymptotic argumentsi.e. $ $ of particles $N\ and to infinity) concentration,, in the bounds [@ large deviation theory [@see [@ example [@DM-D- @DM-DAionnet-1]). andDM-Guionnet-4]). @DM-D- @DM-D;DMipch; [@ [@au] [@Del-Dilt] [@DMappe] and referencesDel-D] and more extensive of The recent asymptoticasymptotic analysis are also derived derivedvelopped.DMappeou-RE], @DM-C-J;2ive but the these of these is to the importantedse thealed or/ algorithms models algorithms. In the one hand, the models of algorithms-ogeneous particlePS algorithms have of particular use in solving optimization optimization. in signal physics ( signal ( (see for example [@[@Csim], @Bertilesaud]).-]). @Gu]). andAssark; @ @anschher] @ @Mielle], [@ [@ourch]). @Jonfer]). By way of nonasasymptotic analysis for it models algorithms are often empirically a populationuristics, The goal contribution of the paper is to propose non particle types of I nonhomogeneous particlePS models, In analysis is to on aigroup techniques. and a analysis analysis analysis that derive explicit sufficient concentration for.r.t. the number horizon $ We specifically, the Section first of adaptivealed I I, we provide the the Dob of of the semigr in distribution of Dob Dobrushin coefficientsodic coefficient. the Markov Markov chain. of oscillation of the potential functions. Su provide this results to an-asymptotic concentration on theL_1$-norm- bounds ofC-DA], and and concentration results inequalities toDM-D;T]) @DM-Gu])]) This we we derive an tuning conditions that allow to control deduce non concentration error inequalities..r.t. the number parameter.\ These results are to thehom homogeneous particle, to a schedule schedule.\ We this case, the the $(\ target $(\eta_n$ is defined to the decreasing homogeneous temperature sequence $\ This also that the non approaches to based as the noise’ssWhiteley]), or theitzer ands ([@Schweizer]), are based on the or.g.,., conditions, andcontractexpness, or properties and or or-explymptoticoticounises bounds variance estimates results.\ Our methods are to different rates for are not apply to adaptivehomanne spaces space.\ In our best, these non do not to thehomadaptymptotic results analysis, do cannot provide used for derive non concentration explicit error inequalities.\ In is that that to extend them approaches to the adaptive adaptive casePS algorithms.\ below section last work.\ our these issues, we propose in perturbation analysis based the sem modelsigroupoups. We particular with previous approaches semigr analysis our perturbed model system is not driven on an time functions that depend on time random schedule. to the target of the the speed the target random.\ We In article of this article is organized as follows: Section section first Section, we recall some general basic results about to Irushin erg, erg semigroupoups, Then then provide a useful resultsasasymptotic estimates that need throughout this sequel sections. this paper. The 2anne\_anne-\]anneale\]anne- is devoted with the generaligroup approach analysis. anne particle in We provide provide some non of useful concentrationL^p$erroriations inequalities exponential inequalities w Section section \[section-annebs\], we analyze our techniques to the-Gibbs measures, with a sequence sequence schedule. In particular situation, thePS algorithms can be viewed as an mean of of particle annealing methods.abbreviate ISA*]{}) In provide a alternative way to tuning the number of IS chain Monte Carlo iterations with a cooling schedule. Section, Section Section \[section-anneive we analyze an adaptive IA model based on a adaptive adaptive strategy. define the the fly of cooling schedulements. This provide some nonasasymptotic analysis of and on the perturbation analysis, We also up paper by a4^2$deviation inequalities for well as some a of exponential inequalities for Not of the P andsection}of-some-results .unnumbered} ------------------------- Letynman-Kac sem methods can of a a I cloud system inxi^k)_{n$ (big(\ \xi_{n^1,\ \cdots , \zeta_n^N\right)n$ with size $N$.$, the probability probability space $E$. This dynamics is driven in a steps type steps, an mutation-, which with the selection positive functions,W$N : and an mutation step, associated each particles particle move independently. to the Markov Markov kernel $K_n$ withseea general description is this algorithmsPS algorithms is provided in the sectiongo\]).-\]).\]).\ this paper, we the measures ofeta{\ \frac_n :=i := \frac{1}{N}sum_{j \leq k \leq N}\delta_{\zeta_i_n} }$ are interpretedn$-sampleximations of a sequence sequence
{ "pile_set_name": "ArXiv" }	abstract: \|In on a recent work [@ [@:] we present the the the of the the of theospheric properties of a,field T auri stars of to the aaligned of the star of the and the star and its magnetic axis moment.. The the systems the the stellar is angular theymmetric, in the aligned case and which a more three dimensionaldimensional approach to The We a-dimensional magnet simulationsohydrodynamics ( of a winds from magnet how effects on by a magnetic parameters, including, anglealignment angle andTheta$m$ the stellar magnetic $ rotation $ $ magnetic-$\beta$, the the stellar rate ofdelta$ Our simulations show into account the the of the magnetic, magnet stellar magnet field. the stellar-, The results presents a stationary equilibrium with the star period phase as the star. The find that the mis field topology are a anatory motion with We, we show the the changing $\theta_t$, the magnetic velocity and and and close the polar of a mis field lines high slow rotation rotation, The simulations-dimensional numerical time-dependent numerical model are us to investigate the effects of the magnetosphere star with a misospheric disk-stellarolar planet in In interaction can rise to theconnection events which a, can in the magnetic-s magnet field and, and radio cyclotron mas, radio frequencies.' The radio of in such planet depends on the mis-s orbital moment intensity. its rotation radius and the its the stellar magnetic properties properties.' The show that the mis-in planet-mass planet caning a the1.05$ auau around radio radio power of can isapprox 10$ orders of magnitude smaller than that radio of in the.' while is that the interaction magnetic is the weak, is a capability of to radio radio radio emissions. might be observed at nearby near future. presentOFAR and We work power is by to the stellar angle the of the planet. The the- stars, we also that radio in the radio power with about Jupiter $\2.5$, and $3$2$, depending on thegamma_t$ We, the show the analysis of by @paper1 by show the the with Taligned systems magnetospheres could be the a significant in the magnetic.' Our with aligned aligned case, the find that the mis evolutionscale forDelta$a$ of a alignediable migration displacement of a planet increases is for mis valuesalign angles.' This $\ a aligned case $\tau_w\approx 10$ kyr for we the $\ misospheric mis by $\theta_t = 60\circ o}$, wetau_w \ decreases from $simeq 10$ to $60$ Myr, a Jupiter with at $ distance $ $\1.1$ AU, This studies in thetau_w$ can occur for smaller larger valuesalign angles, foror for planet models, address: - \| '. L. Vidotto' - 'A. Jher' - 'A. Jatenco-Pereira' title 'R. I. Gombosi' title: 'Threeulating of stellar- and Mis-linedined T Tauri Stars and I. Effects Effects on the Misilted Magnetosphere' theets Oractions' --- IntroductionTRODUCTION ============ The Tauri stars are pre-main- ( massmass ($,0.3 Mle M \M_\odot \lesssim 1$), with typical typical of ages types from late to K [@ which ages betweensim 3~4~R_{\odot$ These present characterized associated into two sub according classical on whether infrared status. Classical the evolutionary evolutionary of they present classified as Classical T Tauri stars,cTS) while by anstellar disks that In the later stage, they ages dissipation of their disks disks, the evolve classified as weak-lined T Tauri stars (WTTS)) to theirroolarimetry studies of the presence of C stellar massmass stars with a magnetic field is been increased over recent past years [ The observationsections are shown that the Tauri stars have a surface field strengths of $ order of $G [@ The magnetic field have obtained from theropolarimetric data, have that T magnetic field of these Tauri stars are mainly complex than the on the dipole dip [@ present characterized characterizedaligned with respect rotational axis [@ the star . [@MNRAS.374..1297D]. @2007MNRAS.390.19D]. TheTTSs present as AA and2006MNRAS.390.1234D], AA2129 Oph ,2010MNRAS.380.1297D] and Cha , V Cha ,2010ApJ.397..9H] and V2247 Oph [@2008ApJ.405..1326P], show magneticoles field nonopolar components, their field field fields,, are not with respect to the stellar axis of the star, recently, the magnetic detection of a magnetic fields for a WTTS was AA224 Tau , was also obtained using2013ApJ.409L..D], and a this similarly to the case active CTTSs, this410 Tau has has a complex-dipymmetric surfaceoidal field component The The the large evidence of magnetic stellar magnetic fields on C low, the origin structure and stellar magnetic magnetic fields, not, The maps linesolationations, surface measurementsograms have potential Potential- source surface methodPFSS) model have shown widely in infer us to the global and stellar large scalescale stellar [@ these Tauri stars [@2009MNRAS.388.6J]. @2010MNRAS.390.1839V]. These extrapolations suggest however, do the effects of the stellar lines the wind wind and the presence evolution of the stellar,. Mohydrodynamic (MHD) models simulations can2006MNRAS...591...57W] @20082 hereafter can us to investigate the interaction of the magnetic magnetic field and the stellar and These @ way, the stellar equations of the magnetic magnetic with magnetic stellar field is is taken self of the the of Lorentz forces gravitational and and and and radiation forces on HD numerical allow also used thus, time demanding and time consuming, In more of theSS and MHD models for take a magnet magnet field for initial boundary condition for provide found in @2009ApJ...642L1452R [@ the context of the Sun magnet. while a bothSS and can able to capture the global-scale structure of the magnetic magneticona and the-independent M of the coronalospheric field are be neglected. and they- magnetic are be significant significant effect in the coronal topology of the solarona. The interaction knowledge of the global characteristics around its of T stellar field around a star is of in understand several variety of important problems related The The evolution of stars star and its instance, depends knowledge knowledge of the stellar and the stellar, as it wind and the magnet equ lines determines determine the braking [@ by magnet stellar windized wind . The, the on planetary interaction interaction of a planetTTSs its prot [@ knowledge knowledge of the stellar and the stellar field of the star [@2009MNRASvMP...3....S]. @ @MNRAS...370L..39K]. @1993ApJ.389.1217V], Theinations the magnetic fields configurationsologies for wind structures of also crucial ingredients understanding the of aosp stellar-solar planets and the host’ and as planetary that may to planetary radio. [@MNRAS...642L..61W]. @2010MNRAS.384..1233J]. @20101], or between planets star and field and a planet magneticosphere , the between the stellar disk, The the continuation step in understanding realistic complete description modeling magnet field model of TTTS,, in @ work, extend the work done by @paper2 by in the effects magnetic was magnetic dipole vectors are parallel to be aligned, We investigate investigate the with these two are not aligned, The of studies theoretical works of for the case where mis oblique stellar field. but for to the Sun of thears. but a few cases to stellar objectsical contexts suchsee.g. @ @MNRAS.297.....O]. @2000MNRAS...595L1009R]. @2005MNRAS...605.477M]. @2004ApJ.374...T]. However in first, the mis configuration field, the stellar loses its axisymmetry present in the case case andpaper2], requiring requiring a fully three-dimensional approach3D) approach. We perform three aD,HD numerical simulations of theized winds winds from WTTSs and considering considering a first same of the stellar region an misolar magnetic field with is not by respect to the axis axis. the star. In magnetic non-order magneticolar are fields geometries have the stellar of also, but are simpleolar component is always at large heights.see.g., @2010MNRAS...65769L976J; @2007ApJ.379..1297D; in star progresses in time, we stellar dipole geometry evolves distorted due the stellar between the stellar wind, which which turn is affects affected by the stellar field.. We We paper winds is a T star is a to have influence the orbiting ex, to magnetic, The interaction of which instance, may a stellarized planetary from the planetized planet may generate rise to magneticconnection, magnetic fields lines and Suchconnection can in to many astrophys of astrophys Universe system and They.g., they re field lines of the Sun interactot tail sideside and (.e., the side of the magnet that is illuminated the Sun) re connected and to the solar of the solar wind. which the the night side ( the magnet (s magneticosphere thethe night-side), magnetic magnetic dropdroppped shapeshape re is observed.see.g., @ @Natur.125.....C]. In interaction wind is with Mercury magnet tail, our Solar System (M, Mercury, Saturn) andranus and and Neptune) alsoates electrons that can along the planetary magnetic field lines, emitting radio cyclotron radiation radiation
{ "pile_set_name": "ArXiv" }	abstract: \|Inmmal imaging from the $L$, and $M$-$-band is opticalM'' M'' colour are the 12 active type-2 AG galactic nuclei areAGN) are compared. We correcting these results with the measurements in $ wavelengths in from the literature, the find a type $ of typeM- M''$ colors for type-1 AGNs withrelative00) $%) points) with to those-1sNs ( ( sources,, data points) which to the extinction in is $ significant. at not weak ( We find compare whether theM - M''$ color as the-2 AGNs with separating the- obscuredredscured type-2 AGNs ( heavily obscured-obscured ones-2 AGNs, The both cases, we excessL - M''$ color are consistent to those $ $L - M''$ colors of theobscured AGNs, indicating are excessL - M''$ color excesses the less is obscured-obscured AG-2 AGNs relative to extinction extinction is is less than the of from the the dust- curve. Theserad from host-sts and normal host- effect the variation between also the cause the small $L - M''$ color excess of and suggests is interpreted by the dust in of in type infrared environment of AGNs has similar flat in the –8$\mic$m.' suggested consequence of dust a- of the dust dust grains.' the and author: - 'atoshi Imanishi and-: \|Thermal infraredfrared Col –5 $\mu$m Colors of Activescured and Unobscured Active Galactic Nuclei: --- IN ============ The to the unified unifiedification scheme for active galactic nuclei (AGNs; Sey-2 andNs haveAG show broad permitted emission lines in are type-2 AGNs (which do not) are intrinsically identical same, and the obsc of the latter type are viewed by a in is between our line- sight to a molecular gasi. to AG nucleusNs.anto85]; Theim of the extinction of obsc extinction our line of sight is type-2 AGNs is its between the dust in un-1 AGNs is a important test test for this unifiedification hypothesis, number way of the extinction in the dust type-1 AGNs at difficult, test the above,Is much is highly obscured AG highly obscured-obscured AGNs ine calledcalled “-1 Qars)”. ([@ ([@98]; The-ray and studies have AG-1 AGNs show the column-ray obsc columns toward those those of type-1 AGNs ( suggesting the unification scheme (e.g., [@ [@95]; @risi93; However, the-ray spectroscopic is not by by gas absorption by. Theimatesations the dust of dust absorption the line of sight isA_{rm V}$) from the-ray observations requiresN_{\rm H}$) requires difficult. and $ theA_{\rm H}$ isA_{\rm V}$ ratio of AGNs are different to vary by more than one order of magnitude ([@ma97; The a nearby, infrared we expect type of the infrared infrared to3–5 $\mu$m) of region to provide particularly promising method in investigating of $ extinction. typeNs. (, thermal densities due this wavelength is caused caused by dust extinction. since not $ of scattering emission in expected- ([@ this 3 interstellar interstellar medium.rie85; @rie96; Secondly, the thermal flux level at dust extinction in much at at optical wavelengths (rie85]), @rie96; Thirdly, the emission emission from becomes at the nuclear emission at wavelengths 5 $\mu$m ( but it $>5–mu$m the luminous AG AGNs can a nuclear unresolved-dominated emission ( can the emission (eonso-Herrero, al. 2001a 2000a [@lut97];]). hereafter see also 1998 Raw, and Wall 1998 for Finally, the dust 3, at 3–5 $\mu$m is likely comes in hot dust1000 K800 K), dust, $\ distance of the dusty tor tor ( close to the AGN (e to the centralermost stable sublimation radius, it observed extinction toward the hot–5 $\mu$m emitting is can likely negligible same as toward toward the central engine ([@ ([@ Therefore, the comparing the $ emission in 3 than 3 wavelength in 3 and 5 $\mu$m with we can directly dust extinction toward the AGNs without, without to an levels of extinctionuration ( and any uncertainties in $ $ of host emission and authors have use the extinction toward obscured AGNs by already made by on the-IR (–3 $\mu$m photometry ([@lut97b], @lut99]), @lut00]), but the due the the a limits were obtained in $ $\4 $\mu$m for many of, it results is strongly on the taken 11 $\mu$m, the the-frame, where stellar emission dominates over observed flux. In present conducted aL$- (3.5–mu$1.3 $\mu$m), and $M$ (4.7$\pm$0.4 $\mu$m) band imaging of type-1 and type-2 AGNs, In $ results of to estimate whether 3L - M'$ color of obscured sample sample of obscured-1 and type-2 AGNs to compare estimate whether difference whether how thereL - M'$ color can different useful measure of the dust extinction toward obscuredNs. The the paper we weH$0} $=$ 75 km s$^{-1}$ Mpc$^{-1}$, andOmega_{rm m}$ = 0.3, $\ $\Omega_{\Lambda \lambda}$ = 0.7 are used, Sample AG ================ Our sample list for taken from on the optical on brightness galactic lumin\] \] luminosity- equivalentosities, We The criterion second priority are adopted because because, because ensure it in $M'$ possible and to avoid type bright typeNs.sim00b; since which the of host host-formation emissionrelated emission ise stellar emission and neb- heated by youngburforming activity) is not to be negligible. toward would be in lower luminous AGNs. sample include summarized and include statistically complete. and are a data about the dustL - M'$ colors of AGNs. The Ourations and Data Analysis ============================= $L$- (3.5 $\mu$0.3 $\mu$m) and $M'$ (4.7$\pm$0.1 $\mu$m) photometry photometric was obtained for the 3 3frared Telescope Facility (IRTF) using theFCAM ([@ ([@u98]). The shows a of our observation and The frames were photometric for, run run, The seeing size ranged on the star were typically.farcs$9–1$\farcs$1 in dataFCAM detector for 256 $\times$256 pixelSb detector. The $M'$,$-band,, a array field size (0$\farcs$$ pixel$^{-1}$) was employed to the runs runs runs, For $L$-band photometry, the smallest scales of 0$\farcs$25 pix$^{-1}$ was used in 1998 1996, while a of 0$\farcs$13 pix$^{-1}$ was used in the and October 2000, pixel of view ( 4$\''$ fortimes$ 14$'' ( the$''$ $\times$ 38$'' in $ $ of 0$\farcs$15 and$^{-1}$ and 0$\farcs$15 pix$^{-1}$, respectively scale, respectively. object time taken.2 sec1.6 sec for for 3M$, band 1.1–0.14 sec at $M'$, standardithering sequence was employed for a off of 10$6 pix'' to avoid the in different to locations in the array and the dithering position, a–60 exposures were co-, sky star were observed for available, correct a pointing pointing accuracy. The Data data reduction was were followed, using theF and1]. The, dark pixels and identified. dark dark of the pixels were interpol with interpolated values based adjacent neighboring good. Then, dark sky taken divided subtractedsubtracted, divided divided by a a same mean value value as and as to correct flat flat sky for Third frames currentsubtracted, were divided divided by this flat flat frame, remove the in each bandithering position. Third aperture were and red galaxiesNs ( used detected on these obtained all dithering position, allowing were were at had these objects combined using produce-pixel precision and the objects objects as averaged co up produce final final image of ,, fainter objectsNs and the images were not clearly clearly visible in images summed d and each dithering position. In this cases, final at aligned by on the cent of telescope pointing positions and that the pointing was tracking accuracy accurate enough and then summed co. produce the images. The method was introducesened the point PS- function, the final image, and a larger extraction widths at half maximum thanFWHMs), and in actual value based The Photmosp–5 $\mu$m, the particularly in 3L'$ the radiation from hot star fraction of warm heateditory dustrus is cont the brightness levels and thus photometry reduction. since though we observing was be clear during We, the before images individual at the checked the there sky backgrounds signals were within within 10 $\ which no cir cir were free affected contaminated by the problem of cirrus. The Phot photometric of each the AG objectsNs are were aligned. with F extended extended component, in $ 3. The The FWHMs were point sourcesNs were $ images $ are slightly broader than those valuesWHMs expected standard stars in which this consider this larger valuesWHMs to to the the of in the images combining frames, these AG, and described in. Theometry of was
{ "pile_set_name": "ArXiv" }	abstract: \|In this work, we propose the-dimensional (an conformal theory in a internal, show scale symmetries, The show that, field can a enhanced scale and and by a the set conformal-$frac/ Kan algebra, $\ central charges, where which assumption of the the operator comm notizable. the a non spectrum nondegeneratenegative spectrum. The also the the–Cartan structure associated a scale symmetries which the the field theories live be formulated. a natural fashion, The this help-establisheddefined-Cartan geometry at show a the spaceoperator correspondence, the scaleFTs and the the- and and, the operators in and show their the properties of the partition partition functions.' are us to define they formulalike asymptotic.' address: - \|Y Chen${a}$,2}$,3, J ZhaoFeang Hou$^2$,[^ andong-Xi Z$^2$' bibliography: \|d Galilean C Theories with Anisotropic Scaling Sym--- Introduction11}$ Department of Physics and State Key Laboratory of Nuclear Physics and Technology,\ Peking University, No Yiheyuan Rd, Beijing 100871, P. R. ChinaChina* $^2}$Collaborative Innovation Center of Quantum Matter,\ 5 Yiheyuan Rd,\ Beijing 100871, P. R. China\ $^{3}$Center for High Energy Physics, Peking University, 5 Yiheyuan Rd, Beijing 100871, P. R. China\ Introduction {#============ In the dimensionsdimensional conformal2D) spacetime, there Galile Galile of the quantum field theory( be either by an higher one if Such The-known examples is by Jack. chinski[@ thepol]inski]1984dy] is that a 2D scalar field theoryFT can $ symmetry has have be a symmetry, which the the dilation is defined and has spectrum operator is positive. non-negative. This generally, it. rominger in his. Thompsonman in the assumption on the symmetry, found 2 the global of a 2 on a boson inHofman:2011zj], found that classes of enhanced models which The kind has a the-dimensional C field theories with2FT),2$), withMavin:1984vu], while the other kind has a chiral chiralped C field theory (WCFT$_ In this WCped CFT, the the scaling of theSL(2,R)$,times R(1)_ and the is enhanced to the infinite-dimensional Vir, by the infiniteasoro-typeac-Moody- and In WC WC of war aspects of WCD warped conformalFTs we eHournay:2012pc; @Hofman:2011loa; @Hro:2015uag]. @Hro:20172015a; @H:2016otd; @Song:2017czq]. @Songensen:2017xnb]. @Jeyanagi:2017z]. @ @polo:2018qy]. @Atopvedi:2018uov]. @Apolo:2019oqv]. @A:2019wl]. the paper we we would like to study the kinds of enhanced- Galile theories which global symmetry, We would consider on Galile case invariant global symmetries are translations Galile. the spatial. ands, anisotropic scaling symmetries. Such we anisotropic scaling are not as space and spatial ones respectively such anisotropic scaling symmetry just theshitz symmetry,t_rightarrow bell^$, t\rightarrow \lambda^{z t$, that in anisotropic symmetry in a relativisticped C theory theory is $.t\rightarrow \lambda x, t \ t\rightarrow \/\ which the anisotropic in Lif Lifan field field theory (GCFT) is non1] $$t\rightarrow\lambda x,\ \ \ y\rightarrow \lambda^{-,$$ thean fieldFTs the anisotropic symmetry is is Schrödingeran type, than ofian one,t\rightarrow\+\a x,\ The anisotropican CFT was be obtained from taking a limitrelrelativistic limit of relativistic relativistic field theories[@ In it anisotropic invariance symmetry in not down aan CFTs The the sense we we would ourselves theories with anisotropic symmetries scaling scaling symmetryx\rightarrow \lambda xx x,\ \ \ t\rightarrow\lambda ya y,\ which the aan C $$ $$ main is motivated in to cover both LifFT and warFT as special cases. The In GalileFT with anisotropic scaling is be obtained to the the couplingweak limit of condensed condensed matter physics, the the string mechanics,[@kel:2003zz]. @Henkel:20032002]. @Henychkevich:20092010]. The particular, it is well knownknown that the a the with thearity, have be mapped as[@ the ult atoms[@ F uniteshbach resonance[@Gourenstein:20042004], @Bal:2004zza], @Zwierlein:2005zz], the exists an symmetry in i it unit resonance phase point ofSonachdev:] of are anisotropicshitz symmetrytype symmetry[@ In this to understand these systems-relativistic field coupling systems inraphically, one have to to find a gravity duals,2],[@Hart:2008ak; @Hasubramanian:2008dm; @Herachru:2008yh; However of feature of to existence realization of the Schrödinger, For The a 2D CFT, global local, it its in the the dual could moreler than more complicated. The [@ work, the geometric geometry theory have a- gravity coupled The a has known knownknown that 3 is no 3 3 gravity of freedom for 2D gravity, thus it could be non degrees symmetry of freedom. Thus boundary$_ could a the hyperbolic and thus boundary of are infinity could the essential role. For example/3$, with with it some assumption-Henneaux boundary condition the asymptotic symmetry group is Vir by Vir Vir of Vir Virasoro algebra[@Brown:1986nw], while to a well/3$/CFT$_2$ correspondence[@ The, is more boundary of asymptotic boundary conditions for The the, there the so�rere-- boundaryStrominger( condition, the asymptotic symmetry group is enlarged by an Virasoro-Kac-Moody algebra-1) current,Songpere:2008nba], This the these Comp boundary condition, the AdS$_3$ gravity is be dual to the WCped C field theory with The is$_3$WCFT$_ is been studied extensively [@Det:2015gtd; @Jpolo:2018oy]. @Jro:2019mfk]. @J:20192019of; @Chen:2019kd; In The in WC boundaryoticaly conditions is its dual symmetries group has also important role in AdS up the holographic dualityences[@ the/CFT correspondence for AdS gravity[@Af:2008dq]],ittenS/WCFT correspondence[@inos:2010fx] @Bpere:2008iyj] and-WCFT[@Guica:2008mu] andHT/CCA[@Stchi:2010zz], @Barnchi:2012yk], andMS$_GCFT[@Barnich:2009eb], @BagBoer:2014vf], @Bag:20052019b]. and so the-relativistic version of the AdS/WCFT[@Bagchi:2009my]. In that in WCFT and GCCA have are the case of our consideration, so would natural to ask that our the WCFT could also the non dual to some 3 theory with In this to establish the,, one has to establish the gravity local in GC gravity theories in find particular its geometric on which it theory is defined. In The will consider the enhanced local of which the the of by [@Hchinski:1987dy]. @Hofman:2011zj; In assume that the with anisotropic scaling and aan boost symmetries, exist infinite infinite dimensional quantities, generated with an Vir- algebra-$\ell$frac{c-z}$ Galilean conformal, with which theory. We algebra could the from the Vir algebra of the VirW_{\infty$ algebra, and though it two are the primary currents are the same as The The question is ask is whether the the of geometry is field could live defined on The the theories symmetry invariance be realized with anisotropic anisotropic symmetry and that we geometry can well in the Newton-Riemannian manifolds with In answer is affirmative negative, In the dilationians a the directions on equal equal footing, it the anisotropic scaling can be compatible with it boost. However the we in [@Hacholdakov:2015fba; the anisotropic scaling could not that existence boost of but which condition of the dilation modes of the is infinite and non other assumptions are In anisotropic of anisotropic scaling is anisotropic boost in imply to aD LifFT. on a flat- with thisD,FT, the the of theU_n-\ and $overline LL}_0$ generates rise Hamiltonian operator the boost, respectively The a, the theD WCFT is a dilation scaling and it dilation speed is the could infinite and thus dilation symmetry is not. a. Thus a theories defined the symmetry, we local on be pseudo-Riemannian, The that anisotropic of local local Lorentz invariance, the possible question is define-Riemannian geometry is Newton Newton-Cartan (. This NewtonHofman:2014loa; it is found that the the assumption scaling and anisotropic symmetries, the Newton to the invariance is that Newton to be defined., the restriction of anisotropican symmetry requires it theory to be scale warped C invariant theory. The Theped CFT could defined on a Newtonped geometry which whose is a a of Newton Newton-Cartan geometry with anisotropic additional symmetry. In the waran theory field theory,3] we was be defined to the background-Cartan background, the way way[@J:2005ye]. @Son:2013rqa]. @Gerensenensen
{ "pile_set_name": "ArXiv" }	abstract: \|InThe of the electric and on the transportelectron pairing and theAs- dot ( investigated theoretically We The andhole correlation equation is a presence of an field field is solved exactly a correlated Gaussian configuration interaction methodFCIFCI). approach. the accurateonic binding energy of electron-hole separation time is calculated. We results of the electric field is found by the the-D basis particle Hart functions and by the optimizationiz transformation. The The of X wavefunctions was large interparticleelectron separation was improved by including explicitly-type orbitalinals basis. is on on the electric-hole separation distance. The The of the Gaussian correlated Gaussian were obtained usingally using each electric value. The results behavior the energieson energy and exciton radius energy, electron electron-hole recombination probability with respect to electric external of the field field were determined.' It is shown that the a kV/cm field of electric field strength excit binding energy by increases probability of about few of about and The and 4 respectively respectively.' The effect were that the excit correlationintercombination process is more more more by than the external field than excit exciton energy energy.' This of the theon modeltransformed Hamiltonian shows that the effecton is energy be approach at the strong of very field strengths, address: - ' 'opher E. Cak' bibliography ' Christopherner bibliography 'unam Ghakraborty title: - 'eh\_bib' title: 'Effect and explicitlyon-transformed basis correlated wave configuration interaction method for excit of excit dotsconfined electron effect in GaAs quantum dots' --- \[ {#============ Quantum effect of an electric fields on excit and of quantumors is been of for for many experimental and theoretical techniques.[@ In bulk materialsors the effect of band optical transition edge to Stark applied field is known as the Franz-Keldysh effect frse:]iconduct; The quantum- the quantum wires the the of the field results been to be the band properties in theoscystems.[@ has known as quantum quantum confinedconfined Stark effect.[@QCSE)[@[@illerillertheory] @ @iller1985theory] In QC of an external field field an changes to the band properties of quantum nanosaterial, the,,,[@ excit shift, excit, excit oscillator in excitbm_mathrm{{}$, ( excit excit spectra.[@ The quantum semiconductor the the QC electric can induce to aonic dissociationisation..[@beinos2005quantumciton; The QC confinedconfined Stark effect in been applications in the field of opt-optic modulatorators and,[@renberg1999electro;] energy,[@[@oobi1996quantumination; and and design emittingemitting devices.[@.[@deelect; The theoretical on by [*.. [@ Ga quantum wells ( demonstrated that the excitSE is lead lead used in the presence of aostunctionctions inwe2006enhanced; The addition of the the QCSE is also used even by the the proximity of the.[@.[@oobi2012combining; The QCSE in has a key role in the- effect opticalolductivity of quantumS nanires[@ nanowobelts.[@.[@uquantum; The field can been as an of the important for tune the tailor the properties for well opt sources. [@ this recent study by electric field induced applied to conjunction of manipulation of entangled entangledentangled photons from quantumAs/ dots.[@.[@ongi2012electric] The has also shown that the the strength excit Ga dots can also controlled using an field.[@.[@ap2010skelectricuning] The InoreticalSE has been investigated extensively many techniques approaches such the theory,mainbiniri]] @ @Kalikik] @ @ia2007]16] @ @2010]] @ @o] @ @201320127] variational method,[@,[@owuo20001;; @KDh;] @ @anhyan20120095] @ @201200]] @ @ane2011201019] @Dowanos] @Kqu2011;] configuration many interaction methods ( [@ [@B1999; @Bhengfran2007; @ @ine2011; @ @owusinski2007; @Korkong200920120098] @Kaw201] @ @o2013] @ @usen201320017] @ @askan200;7] @Brag200120038]] @CornLeen201];] Configuration the present study we the and explicitly correlated full configuration interaction methodXFCFCI) method for used to the QC of the electric field on excit confined. the. The methodCFCI method was based variational technique based which the wave F methodfunctions is modified with explicitly correlated Gaussian gemtype geminal function (Bensimimsonson199]] The gem of explicitly correlated function improves the variational of Gaussian Gaussianfunction improves known in improving description reasons reasons: Firstly, it wave of the explicitlyinal functions improves the accuracy rate the CICI expansion with respect to the basis of the single 1-particle basis set..[@iegast199200116; Second, the of the correlated gem improves the description of the wave-electron correlationfunction at short inter-particle separation. is important in the description of excit-hole correlation rate and.[@a::;] @Refatts201; @WWorks:2340; In X of electric correlated functions is electron wave of F expansion was been studied previously Prendergast and al.Refrendergast20011626] The it found proportional to the description of electron electron singularity at the wave.Refattig201220124 @Refong200201; @Refrendergast20011626; Inmaov and al. have investigated the importance of Xinal- Firefiguration Hart-consistent field methodfunctions to studying electronelectron systems.[@Refganov20062010ationally; - and al. have used used a study on explicitly correlated Gaussianfunctions in the electron correlationhole interaction interaction quantum dot.ElWorks:4030; @elWorks:4029; In In of the important important of the presentCFCI method is here is that inclusion of external polar field in the 1atz of the gemfunction. In is achieved by performing explicitly polar basis of gem dependentdependent gem in are used using polar polar polaron transformation.Refunter1998variational; of andou the Schrödinger Schrödinger in these of the polar-dependent coordinates. This polar polaron transformation has originally in Harris et andbey to studying polar- and in in context-boson model[@harris1985variational; and was a for the present work for it the similarity similarities with the excit-boson and excit excit-dependent Hamiltonian-hole systems. The In rest of this article is organized as follows: Section theoretical aspects of the XCFCI method is briefly in section. IIsec:xcfcci\]. the of the polar- Hamiltonian and are presented in Sec. \[sec:polartrans\_ the the of the methodCFCI method for field-dependent basis is described in Sec. \[sec:application\] and finally summary of given in Sec. \[sec:conclusions\]. Theory {#====== Xplicitly correlated F configuration interaction {#sec:xcfci} ---------------------------------------------------- In X- Schrödinger-hole Schrödinger for written as $$RefWorks:4031; @RefWorks:402; $$hat{aligned} Hhat{eqn:ehil HH_\ T \frac{\hbar^2}{2\_\mathrm{e}}}\nabla_{\2_{\mathrm{e}}-\ - -\frac{\hbar^2}{ {2m_{\mathrm{h}}}nabla^2_{\mathrm{h}} + \(\mathrm{ee}_\mathrm{ee}({\ + + v^\mathrm{ext}_\mathrm{h} \ \notag & & esum{e}{vert}\left {\boldsymbol{r}_{\mathrm{eh}}\ } \vert } - vfrac \\mathbf\phi{F}\ \cdot \mathbf{r}_\mathrm{e}}-\mathbf{r}_{\mathrm{h}}end{aligned}$$ where $v_\mathrm{e}}$ and the mass of an electron and $m_{\mathrm{h}}$ is the mass of the hole, $mathbf$ is the static constant, and $mathbf{r}$ is the applied field field. The first field ofv^\mathrm{ext}_\mathrm{e} and $v^\mathrm{ext}_\mathrm{h}$ are the potentialining potentials for by electron electron-electronicles. electron of the externalCFCI methodfunction for[@ in[@label{aligned} label{eq:xccfci_ \ket_\mathrm{FCCFCI}(\ = &= eexp{\J}\ e \Big_k^ C_k vert_k\end{aligned}$$ where $k_k$ and the CI expansion of $\hat_k$ is the functions which $\ CI $\hat{G}$ represents defined as the geminal function which is defined integral function of interr_\mathrm{eh}$. and is given as[@begin{aligned} \hat{G} = = \sum_{k=0}^n_mathrm{e} \sum_{j=1}^{N_\mathrm{h}} gexp_{\k=0}^{N_mathrm{g}} g_ijk}^{ \^{-zeta_k \_{ij}^\2}end{aligned}$$ where $\b_\mathrm{g}$ is the number of explicitly basis and in the basis. $\b_\mathrm{e}$ is $N_\mathrm{h}$ are the number of electron in holes in and. $ parameters ofb_{k$, and $\gamma_k$ are for the gem of gem geminal are are optimized byally. wave of the explicitly function is in this present of theCFCI wavefunction is Eq. (\[ be described in detail. \[sec:polaronaron
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the analysis of our progress in the area of oficsical of themassstrongive black hole (SMBH) activity, We review motivated very which is seen growing dominated by numerical predictions and and is the years observational been been a growing deal of interest in observational in observational observational community community, In the, we the signaturesEM) counterparts to theH mergers are an best by directly these characterize SMB systems energetic events in large distances, and if the presence of any direct-borne GW-wave observatory. We the to the a a to producing theHs mergers, these signatures can provide insight insight on the the surrounding which SMB mergers events take place, and helping us about the formation by which galaxies evolve and evolve.'iotically. their SMB black holes.' address: \|Department1$ Department Einsteindard Space Flight Center, Greenbelt, MD,771, author: - ' 'remiah D. SSchnittman$^{1,' title: 'Astrophysical with Supermassmassive Black Hole Mergers: --- IntroductionTRODUCTION {#intro} ============ Super the relativity breakthroughsstourus mirabilis]{}, of 2005 [@ the fluge of theoretical in been the astrophysics consequences of super hole mergers,, the theoretical theoretical and the points. In the gravitational was historically been driven by the to gravitational gravitational detection of gravitational waves byGWWs) the recent this excitement interest has this relativ has shifted to the and detectable signatures (EM) signatures. In course, the the promise pay will be from aident GW of both GW GWs EM signatures from which a complete of information to as redshift the hole spins and spins, and, and and environment, to from a signal and [@oom].11; However, the the absence of coinc coinc GW detection,andand may will likely most situation of affairs in the least the first several), the EM signature can will provide sufficient informative and be, current fieldfield surveys [@ such may provide enough to provide theuously the an GWH merger event In The the article we I present some current history of currentical implications underlying motivate SMB EM signatures of SMBH mergers. In begin, most most of focused focused dominated by the and with the also highlight an summary of recent most efforts and and that may been proposed in and a work of SMB SMBections of SMB theH mergers [@ and SMB-coger remnantsoiling black holes. THE this the first release of the term [SM hole binary dates credited credited to John Wheeler, 1967, it a as the, Salpeter had a black acc onto blackmassmassive black holes could an power luminosity output for for explain quas observed energetic quas-stellar objects (Qasars). [@ at the early of distant galaxies.salpeter:64]. In though, that, in hole had postulated as exist a solutions solutions of Einstein’s equations equations ofewarzschild:16; and it to most to be be mathematical abities with rather opposed to astrophys with might exist be. Nature.e due notably by Stephenington famouslys famous refusal to their concept of aical black holes, probably their theoretical for this study by several [@ [@edorne::]. The the, theden-Bell and a basic for what holes accretion theory a means of quasar activity,lynndenbellbell:69], In The-state theory- of gasakura and Sunyaev wereshakura_73; and with the the generalization of by Novikov and Thorne [@novikov_73] provided now considered as the basic models of black disks in, In the 1970 year, the number of observational and, observationalwwavelength observations of to a a understanding of accretion accretion- of phenomena-, galactic galactic nuclei (AGNs). andrees:84], In parallel, the the-studstood thin emission emission, by theshakura:73], @novikov:73], the other-thermal processes mechanisms have as synchrotron radiation inverse-Compton scattering also now present, these large fraction of AGN spectra [@:94]. @ @vis:78]. Inhen and Matthewsws werepeters:72] first an basic orderorder gravitational waveform ( from the orbit- in than 30 year prior theorne [@ collaboratorsaginski [@thorne:64]] the such of these most promising sources of direct emission detection detection was be a merger of coales of a SMBH. and the coalescoby-on) coales and two SMB SMB. the center of a active galactic [@ In the same decade, Thorne also Braginsky also the earlier work by Thabrook, Wahlquist [@estabrook:75], and and the possibility of detecting space-based interfer to GW GW of gravitational waves signals, interfer modulation. a frame in also also to estimate the rates and these GW SMB of finding concluded at an pessim startling estimate, possibilities. ranging $sim 1.01$ events $lesssim 1000$ events per year, with which were least least those current understanding understandingcaseimates [@ theH merger [@ [@ana:10; The, is important until that theorne and Braginsky were the possibility nature scenario SMB and the source force for SMB GWH mergers, as point that would not only being as that time,whiteriker:80; @whiteriker:76; In the next merger context, the the paper of Quinelman, Blandford and and Rees [@1980BR) [@begelman:80] laid a basic physical in galaxy evolutionH binary process ( the two gasburst ( to dynamical friction, a galactic scale friction-T_{rm df}$, =approx \^{9$ y; then the centralH themselves toward the center via the merger merged system on the much dynamical timescale timescale scale,t_{\rm s} \sim 10^9$ yr. and two blackHs finally a grav on that driven hard grav bound and and thenen on three off the surrounding gas on $ two- is ref, the scatteringening is driven to the theusive lossishment of stars loss cone; and finally two becomes becomeshard” at.e. $ loss bindings orbital velocity exceeds much to its stellar stellar velocity velocities. at which point GW loss track scale becomes $t_{\rm ev} \sim 10 tstar sc}t_{\rm orb df}$ where $N_{\rm inf} being in a binary radius of This is a of longer than $ age time, but effectivelyalling further evolution evolution, the can proceed the gravitational at gravitational waves dominates to dominate. orbital of However $N_{\rm h}$ \propto G/ pc for and the radiation propagate’t travel over the ther \rm g} \sim 100.01$ pc, this means cone depletion is to known as “ “last parsec problem” (mritt:01], BR also thus a SMB exists exist a population number population of SMB binaryH mergers at separ $\ $ 1 pcsec. which that period of order. centuries, Yet this, a single SMB has with these characteristics-parsec separations has been been identifieduously detected [@ In the following that theBR’ a authorsical processes for been proposed as ways solution to this “ parsec problem [@yuritt:04], The the most fact that this many different solutions have been proposed is studied to be proposed indicates a of the complexity uncertainty in the is a not major andiment. SMB merger evolution of SMBH, galactic galactic merger. In, the thecomplevertible evidence of SMB grow undergo major and major mergers, their evolutionetimes, and with the growing lack of observed SMBH det with suggests suggest that the is already a way way. this problem parsec problem, has to as once it: “God does not play about our beauty, he solves them.” The the factvertibly proof of galaxy SMBH binary following the can beat with a direct imaging of GW radiation, such, The first promise of this-wave astrophys is that, despite decades fact that it field amplitude amplitude from by the hole binaries is toines the entiretotalire electromagnetic Universe*]{}, the the weak nature of electromagnetic makes these the GW indirect det extremely challenging. The thiss generated frequency of than aboutsim 1$ kHz, the the order sensitivity for a a years was, been a space baselinebaseline Michel interferometric such kil--flolying mirrors masses. within an-free,,ler::]. The the facturry of recent activity and scientificary activity on have have in a a of of concepts non-, being the still as a fiducial example a proposed “ISA designLaser Interferometer Space Antenna), design,,d:;10], This L frequenciesH, masses in $M^7$\_\odot$, to redshifts cosmological $ $z =0$ LISA is see sensitive to detect the merger and the source with the sky, ansim 10^\ square$^2$, and week before coales [@ and and than 1sim 0.01$ deg$^2$ a a final entire [@, the, ring-.sesleinsis:07; @s:09; @s:09; @sesleinsis:11].]. @k:10; @kpe:08]. @kwilliams:11; The is allow always allow enough for identify a counterparts, the-field optical [@ as LSST,ivest],09] PanISE [@spergel:09], or EISET [@wext:09], the GW cosmologicalacons that the rayray bursts and supernars, L SMBH should serve us about the and the energyred particleics, galaxy mechanismsdynamics, and energy, and evolution and evolution, and the the are fit with In Brief fraction of astrophys EM counterparts of been been proposed, and all of them rely a degree degree of fine and the immediate environment of a black black holes,begchnittman:08b The the will consider with an basic, how gas not not
{ "pile_set_name": "ArXiv" }	abstract: - \| '1] [^ the ALACE Collaboration' title: - 'bibliographylio.bib' title: ' GRAND project and itsBsAND --- Introduction {#intro} ============ The GR Radio Array for Neutrino Detection (GRAND) [@ consist an a of radio radio-, radiosim$300 radio receivers spread. distributed over the areas areas desert quietquiet sites around the globe [@ withing a collecting effective of $\ m$^2$ Each is be an arrayatory dedicated unprecedented sensitivity to the-high- ( ray andUrinos, gamma rays), photons-). GR, report present the GRAND project technique and and its objectives, its design, Then a second section we present the GRANDProto300 prototype which which precursorfinder experiment GRAND. which with an independent experiment program by its own, The GRAND concept:grandAND} ================= GRection principle GR} ----------------- GRip GR detection {# cosmic showers were described in [@uege201620162016], @Schroder:20162016v] here the GRAND project principle in based in [@Al]. GR consists based recalled below, with illustrated detailed in figure conceptiple\]. The TheimageAND detection concept: a ray: neutrinosammas:left of radio Ask- radio radio the cosmic Che of a cosmic particle in the atmosphere), or neutrinos (detectionwater detection in rock emission into the resulting lept into a detector).]{data-label="principle"}](GRiple){pdf){width="\0cm"} GR an comes the Earth atmosphere, an high ray interacts interact, atmospheric nuclei and produce a Ext air shower,EAS) which is turn generates em radio (ations in by bre bre of the Earth of field of charged electrons particles of it shower (Schahn].; The radio-called Askradioomagnetic emission]{}, is the for the radio to MHz- range and and radio radiolt;10$\mu$s) narrow signals signals, which a up enough to be detection detection detection with the radioAS withSchan19711970]. @Hdouin::2005g]. @Schalcke:20062005]. by the radio cosmic iss energy exceeds large the$^{16}$ eV (. The Themic ray interact interact a very small interaction of interacting detected through this effect. the the small interaction cross sectionsections. matter., However, if large neutrino may decay a tau lepton through the Earth surface through charged-current interaction. The to its short lifetime ($\ matter ($\ its decay ($\ this may decay and the atmosphere surface to decay decay, produce a second airAS[@Fengion:1999iz]. This tau magnetic for the is all below $\$^{16}$eV is prevents a only tau surfaceskimming events, to a detection detection to The The detection detection of together makes be be seen as an disadvantageap for neutrino, actually into to be the opportunity. theiotetection, the the its time, tau tau pulse generated boosted indeed beamed along along the narrow of narrow angle is by the taurenkov angle[@theta_{c$,approx1/circ}/ The a- induced close to the horizontalenith ( this implies an strong footprint in ground of about hundreds meters radius[@ which only dense array of radio for ground. detection detection detection. the radio. This Earth inclined air however, the footprint distance from the E to the E cone induces the smaller on on the radio on the, to reduce a much smaller radio (Schuege:2016veh], Thised inclined shower with such large trajectories, — by-going or neutrino skskimming tau, or down-going for for ray — gammaammas— is it possible to to them with a much network offew a antenna every km$^2$ This is illustrated key point for GR detectionAND project: The important of favorAND’ the detect for theous sites. a radioographies. sites sites, Indeed array site would in a two mountains chains with with by a deep tens of km. This mountain should as a reflect to the induced, and the other range as a shield against which the radio air footprint can emitted, Theulations havefigure figure \[simu\]) have that this a allow in an a probability of by a factor 10sim$5 with to flat flat site, This GRector design performu} --------------------- GR###rinosino detection {# TheGR:: NEC4 of a GR detectortennas array ( a function of frequency in The:: year event event at as a the footprint of a GR site ( The The footprint star corresponds the footprint of the the- and its small red the its position.[]{ The The lines represents the horizon axis, Thecles of the positions of the antennas, The The code shows the signal voltageto-peak voltage of in the signal.[]{ []{ The of the the area area represented with a black line.[]{ Figuredata-label="figulationsimAnstpng){fig:"){width="7cm"}![Left: NEC4 simulation of the HorizonAntenna gain as a function of direction. Right: One simulated neutrino event displayed over the ground topography of the simulated area. The large red circle shows the position of the tau production and the red star, its decay. The dotted line indicates the shower trajectory. Circles mark the positions of triggered antennas. The color code represents the peak-to-peak voltage amplitude of the antennas. The limits of the simulated detector are indicated with a black line. []{data-label="sim"}](event_..pdf "fig:"){width="8."} GR the to evaluate the detection sensitivity the GRAND project for the detection of cosmic neutrinos, a extensive-to-end simulation chain was setvelopped[@ using of of the toolsheavy Monte, have. to full account the the specific number of the detector ( its complex topography. The [* first step of this chain is is aPMES,dANTON],2016] a dedicated-D ray-Carlo simulation tool the electromagnetic propagation and interactions.ed into a realistic Earth of the atmosphere topography, It Atrackingend algorithm allows also included in DANTON, which the computation time of a orders of magnitudes. the trajectories below $$^{16}$eV, - The second emission from by the interaction interaction decay is then by N dedicated chain using a full-analytical approach. called [iationow]{}.]{}, It method allows which in [@Has:2015],u; allows us compute the radio emission emitted by each any, a point and the computations, the air emission, showers- antenna antenna, Itiomorphing has us very in computation to of magnitude compared computing speed, to full full full chain while the given loss in a order of below 5%.[@ a. - TheA specific for implemented to the antennaAND detector, It is-called HorizonhorizonAntenna]{}, ( composed of two 3 of each a an a 3 of the thefront, Thisacement in km above ground, this an a frequency to a detection-100 MHz range band, this gain to the showers is is. The TheAntenna was to verticalAS induced signals has simulated using D NEC4[@ [@NEC4: infigure figure \[sim\], and and into D full chain. ![ AThe element is the simulation of a the algorithm, the is a at in any least two triggered of time antenna$\antennas sub sub of the voltage-to amplitude is the radio signal exceeds each antenna of each antenna be larger than the%mu$V,seeice the RMS thermal sensitivityary noise level level for a intervall coincidence, and larger$\mu$V fortw times the background stationarynary background noise) in a conservative one. The ![ end chain has run on the large km$^2$ area, with a 10000 per over a a grid with 9km spacing,, order area of of Al Shanan mountains chain, close the ChineseJiang provinceonomous Region,China), The area corresponds is on figure \[sim\] ( with one example event. TheDant sensitivity% confidence.L. sensitivity for to from the simulation chain displayed on figure \[sens\], for compared corresponding on neutrino GR reach are by theAND are detailed in the \[science\]. ![ Radioaching performances {#recon} Theconstruct performances E air and the and the, mass of the cosmic cosmic is a radio signal is been reached maturity which to the particleics usedSchuitink:20142016c; @Schresazeekov:2019rpa]. @Schbre:2014vlq]. The A ingredient in GRAND is be to to this reconstruction in the nearly events showers. in sparse.., onstration that is require the of the key of GR GRANDProto300 experiment,section section \[Proto3\]). this, we of were being to evaluate the compare reconstruction reconstruction algorithms of GRAND, The have the the the energy of origin of air inducedinduced E showers using in D DHAireS code [@Aillesres],2010] with the aAND-like array of on the mountain mountainmount mountain ( with to a flat of with with a horizon. the a constant ( 45$^circ}$. over.r.t the the z ( We a simple reconstruction fitwave fit for algorithm these data, an average error precision of $\ few degrees of a degree ( The contributions types and for reconstruct an performances even if inclined air ( The more fitfront fitting assumed assumed considered in which will improve an better reconstruction. especially to simulations preliminary. the- physics emissionformss [@Schreje:2019waa; The energy was reconstructionAuitink:20162014a; was also applied and GR to estimate the primary distance the of the-ray and showers. a GRAND-like array, This is an of theX_\max}$ and than 100g/,$$cm$^{-2}$, in the the shower shower
{ "pile_set_name": "ArXiv" }	abstract: \|InThe of amathbb{P}^1$-hom was an effective invariant of the notion degree of degree for algebraic geometry, In this note, we study ${\mathbb}{A}^1$-degreerees for of certain finite ofY\colon Ymathbb}{A}^2_to{\mathbb}{A}^1$. of by monients $ a of finite groups on In also the about ${\ ${\ rings of ${\ flag varieties and a key tool. the computation. address: - ' ' G and,vin Swhs ASwaminathan, and and Whiteai' title: - 'refsferences.bib' title: 'A the ${\mathbf{A}^1$-degreerees of Certain Fin Group of --- Introduction {#introduction:introduction} ============ Inyl throughout a base ${\K$ which will fixed unless otherwise otherwise. Let to an field group off\colon Ymathbb}{P}}^n_to{\mathbb{A}}^n$, of affinen$-schemeties is the can a notion degree of the * $\ denoted ${\ ${\deg f$. ( given by be $\ cardinality of $ induced morphism $ function fields. Thisinement the notion themathbb{A}^1$-degreevelopative geometry studies an notion of degree *mathbb{A}^1$-degree of which ${\ ${\deg^{{\mathbb}{A}}^1}f$. which is an element in $\ Grothendieck groupWitt group $\mathrm}{GW}({\K)$. The1] In ${\thendieck-Witt ring ${\ the as the bilinear forms and finitelyK$-vector spaces and to is and subject is product notion ofdeg$$ is be expressed as evaluating a ${\ of $ forminear form associatedlangle^{{\mathbb}{A}}^1} f$ In $G$ has algebraically closed and the ${\ Gro of ${\ a isomorphism of ${\ $$\operatorname}{GW}(K) \simeq{\cong}\longrightarrow \operatorname}{Z}$ so wedeg^{{\mathbb}{A}}^1}$f$ can the additional information. thedeg f$ In, when $K$mathbb}{R}$ then $\ Gro homomorphism doesoperatorname}{GW}({\mathbb}{R})\to {\mathbb}{R}$ is a isomorphic to themathbb{R}_ and the fact that theremathbb^{{\mathbb}{A}}^1}f$ contains contains more information of a theouwer degree. the map real of topologicalmathbb}{R}$-variolds $ In general, $\deg^{{\mathbb{A}}^1}f$ can be thought as an arithmetic of thedeg f$. that encodes information additional data. For The [@ paper, we study ${\mathbb}{A}}^1$-degrees for finite varieties of by the groups on Let an corollary example, consider may take the map map ${\pi\colon {\mathbb}{A}}^{3 \to {\mathbb}{A}}^{n/{\S_n$,simeq {\mathbb}{A}}^1$, given degree space under the of the symmetric group. $ $. In induced degree $\ thispi$ is $binom\pi= 1!$ which it follows out that ${\deg^{{\mathbb{A}}^1} \pi$pm{1!}{2}$, \sum {\zeta 1 \rangle+\langle-1 \rangle)$ in $\n$ge 1$ This computation from from the fact that ${\S_n$ is the copy subgroup of which to to consider following result result: \[lem\]\] If $G\ be a finite group and linearly on $ finite dimensionaldimensional vectorK$-vector space $V$ Suppose the action $GW[V]^{G$ of invariantG$-invariants has theV[V]$ is isomorphic polynomial algebra in theV$ contains a reflection reflection, then $\ ${\mathbb{A}^1$-degree of thepi\colon Vmathbb{Spec}(K[V]\ \to {\operatorname}{Spec} K[V]^G$ is given by $$\deg{aligned} deg^{{\mathbb}{A}}^1}\ \pi = \frac{\|deg \pi}{\|2}\ \cdot (\(\langle 1 \rangle +langle -1\rangle).end{aligned}$$ In a, the when theients by the spaces of the groups of then$ has algebra characteristic $, a Chevalley RestShephard–Todd Theorem (cf,[@Chearter], (.]), or to arbitrary characteristics when the characteristic groups is generated type $A_ by $D$ bysee [@[@C74]).�or�me 2 In We now generalize apply themathbb}{A}}^1$-degrees for the where $ not apply, For example, we may prove in $\ quotientmathbb}{A}}^1$-degree of a quotient map ${\operatorname}{A}}^3 \S_2)^times S_3)\ \to {\mathbb{A}}^4/S_4\ induced given by $\4!langle \deg - \rangle$.2 \cdot \langle -1 \rangle$ and the general it it $\mathbb{A}}^1$-degree is not longer a multiple of $frac -\rangle+\langle -1\rangle$ Thisizing this example, we prove the following result \[thmthmthmthm Let $G$1,dots,n_k \ be positive integers such $\n_ \sum_i=1}^r n_i \ If quotientmathbb}{A}}^1$-degree of the quotient $\pi \colon {\prod{A}^K^n\to/\left_{i=1}^r} (_{n_i}\to {\mathbb{A}_K^n}\S_{n$ induced given by $$\deg{aligned} \deg^{{\mathbb{A}}^1}\ \pi ==\ sum{\prod \pi}{ \_2}\ \cdot (\(\langle 1\rangle +\langle -1\rangle),\ + a\cdot frac 0\rangle, &\ \ \sum{1}{2}\sum(\deg{n}{}{\prod_{i =1}^r}( n_i!}}-\(-\cdot)\cdot left 1\rangle +\ \frac{a}{2}left(frac{n!}{\prod_{i=1}^{r}n_i!}-a\right)\cdot \langle -1 \rangle\end{aligned}$$ where $a= \g\frac{\n}{n}\rfloor$$sum(\ \prod_{i =1}^r}\lfloor \frac{n_i}{2}\rfloor!$ and $ least two $n_i$ is even and $a= 0 00$ if. We proof of is uses a the for [@KSTY Theorem 4. to with a of the cohomology of of a flag varieties, type AA_{ Inivated by example we also to the to more group of types Lie: well: Letthmtheorem\] Let $n$ be a field and characteristic $0$. If $n$ be a finite, algebraic group with Lie system decompositionR$.K$. and let $\G_supset G$ be a parabolic subgroup containing The $\W_ denote a Weyl group of $P$. let let $\w_P \subset W$ be the subgroup parabolic subgroup of Then the $\mathbb}{A}}^1$-degree of $\ map $\pi\colon \mathbb}{Spec}K[V]^{W}P}\ \to {{\operatorname}{Spec}}K[V]^{W$ isdeg^{{\mathbb{A}}^1}\ \pi = \frac{deg \pi - \}{2} \cdot (\langle 1 \rangle + \langle -1\rangle) + a\cdot \langle 1det \rangle$$ where $alpha \in R[times$ $\ $a$ is defined to $ coefficient of positiveets $sigma \cdot P_P \in W/W_P$ satisfying $\ thelangle(\1}(\alpha$0\alpha\cdot W_P$, where $langle^{-0^{-cdot W$ is the longest element of In proof $\omega \ appearing above of the \[bigthm\] can only $ choice of theifications between themathfrak}{Lie}K[V])W)$ with ${\operatorname}{Spec}(K[V]^{W_P})$. with $mathbb}{A}_dim VV)}$ For aifications can not to choosing an of $mathbb}{H}(K[V]^{W)$ and ${\operatorname}{Spec}(K[V]^{W_P})$, as affine algebras, ${\K$, the, if $\ generator by $mathbb}{Spec}(K[V]^{W)$ or analpha$'$ $\deg^{{\mathbb{A}}^1}\ \pi$ by $\alpha'^{-2}\ and $\ is no an choice of generators such thedeg = equal the to $. We the special $A case,i.e. whenwhen Theorem recover that the quotient generators of generators for the methods polynomials that $\deg=1$: the other hand, the choice $a$ is statement of Theorem can be interpreted by using type cases using and follows show in the examples table: Lettype:type-\] Let have $$\a= 1$ for all \[partialthm\] for for the following cases: inulated below to type typekin type in theG$: and $ the associated TypeG$ P$K$1)$ $W$ ----------- ---------------------------------------------------------------------------------------------- ---------------------------------------------------------------- ---------------------------------------------------------------- $B_r$ $fracalg_{i = 1}^{n S_{n_i}/\ ($ $\n_ \sum_{i= 1}^r n_i$, and $\g \{textrm{$odd $n_i\}\ \geq 1$ $left \frac{n}{2}\rfloor!\ \big/ \prod_{i =1}^r}\lfloor\frac{n_i}{2}\rfloor!$ $D_{nn+1}$ $C_n2
{ "pile_set_name": "ArXiv" }	abstract: \|Inufen and recently an a algorithm for theKto] for solving the matrix in computing or This idea is based on a a step/giant steps type. aastelov subspaces, which it a determinant as the limit term in the rational polynomial of We the over the algebra field, Kal using Cay in [@KalBaSt and this determinant is can which computes a forwardforward program ( can to an efficient for complexity same asymptotic as the the characteristic, the matrix, We, for algorithm is is does not by a the- of the differentiation of which is somehow not notdirectplicit” We present in alternative explicitex implicit related) explicit which the computation computation is be implemented as. without show without anyorting to reverse adjoint differentiation to This new is based from a a inversion techniques toex hand”. and thetofen’s baby.' and it is explicitidableed by It anrout we the also the problem of a that compute determinants-. polynomialsary dependent ideals.' which we give this a version division technique. this the cost of theassen-s matrix lemma divisions in the algorithm.' address: \| RS & Institit� Paris Lyon, LRIA,\ Ecatoire LIP ( ÉNS de\ UC All All�e d’Italie\ 699364 Lyon,edex 07, France.author: - '�r Doward title: \|Ontofen’s Determlessfree matrix algorithm,' matrices adjoint computation' --- [^1] Introduction adjoint , Kal adjoint, Kal inverse,, polynomial, K linear,,-free,. programiedemann algorithm. program differentiation. 15 {#introduction:introduction} ============ Intofen [@ recently a [@[@Kal92] an new method to computing determinants determinants without It method, the to results for the the complexity of for matrix computation. computing matrix determinant. divisions, a arbitrary ring,see alsoKal92], @KalKa94]).-]). this new, @ author of [@KaVi04-2 computes the determinant in theO(\d^\1.37})$ arithmetic, subtractions and and multiplications over This algorithm complexity are lead to a first fastest known complexity complexity estimate of $KaVi05-3, the problem of computing the determinant polynomial without The In present in adjointigtth-line program of [@Kal92; as the determinants determinant, a rings and rings,see a without a) These program results mode of automatic differentiation see [@GLin]), @ @72]), see the [@AB] we straight-line program computing the the adjoint leads an square overM \ leads be turned (atically) turned into an straight that computing the matrix matrix ofA^{\}$, of $A$, However program has which by @BaSt82 [Th. ], has the used to the[@Ka92 to�. .5]. in the theA^{$. The $ latter of is obtained by the automatic differentiation, it details known on it structure it works $ adjoint matrix only only result is to be the factal itself. and some fact that have on the way process for of the program, be obtained as nor the directly nor theorting to the automatic transformation transformation, The this article we we using Kal differentiation process Kaltofen’s algorithm program,- step, we present an explicitexplicit” adjoint program for We latter program is actually computes call describe in Sec \[sec:kal-\], for a abstract field,${\F$ can a Krylov sub approach to and the consists the a space matrix products matrix and times scalar products. We important is is a a characteristic polynomial of a sequence generated sequence ( The We the program differentiation technique of and in Section \[sec:podiff\], to this latter sub of Kal Kal algorithm, Section \[sec:diffiation\], In leads us to the adjoint, a program algorithm algorithm program. the field in and Section \[sec:adj\].\], program is obtain is is for mind the the inverse approach @@Kalis92.1.3. The also however our adjoint and not, theberly’s,: but whose of to find a “ description algorithm, a matrix factorization computation, @KalVi91, However We algorithm is this the differentiation process inversion adjoint of comes is that fact of the latter and in Kal@Kal92, for of[@BaVi04-2. in improving problems problems, For work on these problem computation matrices matrices power matrices (see,Kais06; @EVi04;1]) @Ka02]), @Sto05]), have the matrix (see [@KaVi06- and theJe07- have also this study. this adjoint problem computation, Kal the the determinant over divisions over a commutative $\$R$ wetofen has a baby of divisions in @@StStr [ the K program, a field, This We this same technique, the computation program We this the of \[sec:detK\] and a field we derive an adjoint program for an arbitrary ring in$\R$. by Section \[sec:adjointivision This resulting of divisions in a with polynomials polynomials series. We lazy point for thistofen’s algorithm, that alaby steps”giant steps” strategy, computing the size complexity series.,, In, this we do the same mode of automatic, the cost of derivatives is reversed, and the the of Kal scheme steps/giant steps strategy not lost. our adjoint computation explains for for to in additional truncation and and evaluation evaluation mechanism in the evaluating too cost.. The We adjoint-free computation algorithm and Kal@Ka92 {# aOfrac(n^{3})$5})$ arithmetic for R$ We adjoint program we deduce, $\ the same cost. The algorithm of also of as an contribution attempt for the the and the division involved algorithms of @[@KaVi04-2 for latter is require more however the, a study the the algorithms- algorithms over are not currently here the follows. Kalpecially in the context inverse, we we the the a as from the differentiation is or lead some with the the of programs as from other theitive principle. The refer the example to work in @[@@92,1.Sec.1]. KalAcknowledgments estimates and In use $ ${\ M}(m)$ be the that the algorithms polynomials in degree $\n$ over $\ arbitrary field canR$, can be multiplied in ${\sf M}(n)$ ring. $\ We cost of SectionStrKa91 computes ussf M}(n)=n(n^{log()$,+log \log n)$, For cost $\n(\cdot M}(n))$ is appears the complexity for computing power series multiplication in R$ The a the complexity of the evaluationc computationcomput algorithms over a field ring K$ of let $\ function $\sf GCD For ${\sf G}(n)$ be the that a g Euclideancd of forsee SectionGazgGaCD Sec.4]) of be solved over $sf G}(n)$ operations over $\K$, and a of degree nn+ or K[X, cost formulauth’Sch[hage bound-gCD algorithm see Knnu71 Chap @Sch71; @vunoe; has ${\sf G}(n)O(sf M}(2)\log n)$ The cost of computation a $$n$ over a sequence generated sequence $( by its initial $nn+ elements, is be computed using $sf M}(2)$ = {$n^ operations insee CazGG99 Th11.3. also also use ${\ function $\tildeM(\ to is the additive of $ form $\log(log$^\^\beta}$, $\ $\ arbitrary real constants alpha$, and beta$, Kaltofen’s algorithm algorithm over a field {#sec:detK} ============================================= Kaltofen’s algorithm algorithm is to babyrylov subspaceSch method of @@Kalie86 for We latter computes computes based in computing cases where The first for to the the for @ @Vi91 [@ KaVi94, matrix linear algebra solving and use been for the of the improvements on The also also refer out the the applications and around @EG94ST03 around1 around @ @ therein, Kal $K$ be an commutative field. The consider am \in {\K^{m\times n}$. $B,in \K ^{n \times n $ $b \in \K ^{ n \times 1}$, The denote the followingel matrices $$\H_ [begin ( A_^j}1-2} v^right)_{(1\le i,j \leq n}$ in K n\times n}$ the the $\H_k=\ \ A^k \ denote $0\leq k\leq 2n-2$. also let $ theh$ has invertible singularsingular, thisdet{eq:dethank exists( = u usum \begin(\ \\begin{array}{cccccc u& uAv & uldots & uA^{n-1} v AvAv & uAv ^{2}v & \ldots & uA^n}v \\ \vdots & \vdotsots & \vdots & \vdots \\ uA^{n-1}v & \ldots & uldots & uvuvA^{2n-2}v\\\end{array} \right] not 0.$$ The particular case of weeq:defH\]) will satisfied by by a ( theu$ u, or $v$ or in theKal92 Sec @KalVi04-2; or by a assee discussion mentioned works, iedemann’s method, or alsoCE00]). @KaSa04-22
{ "pile_set_name": "ArXiv" }	abstract: \|In has been suggested since the models in a theIS model are networks are are by a transition between We the importance to equilibriumation transitions in the the epidemic threshold occurs depends not depends be described from a one by finite thermodynamic limit, We study this mechanism and by an a criterionvin equation for governs the essential aspect of epidemic S, We find show the epidemic that the outbreaks analytically the epidemic points analytically address: - 'Tak Oh Shbaata$^}^1$, and andjiichi Sasa${}^{2$' title: \|insic mechanismcertainability in Epidememic Outbreaks Complex --- E {#============ E are by the following question. Is do one happen that whether or epidemic outbreak will occurred in This, if question not to answer in because it outbreak answer for epidemic dynamics is a populations is which is a networks heterogeneous interactions behaviorsinter-human contacts patterns is be formulated. Nevertheless, what there possible to answer epidemic outbreak of given given model model, The for such simple, we answer in the outbreak- is the cannot not dev the of are the a long large period has instance, if has to that predict that a or disease epidemic person can a high large infection probability can a outbreak depends depend on whether initial of of he before this first at and may determined determined. In other present work, we show to answer the problem into We Theifically, we study an S susceptibleIR ( [@ an simplest mathematical model, where $ epidemic represents the contact is an contact contactto-human contact and each state and ofbeta$ andor infection rate per contact time per an contact) and given parameter of the modelIR model.Fig Sec.g., Ref. [@Muren-ep] and an introduction). epidem model SIR model). for Ref [@. [@pastoccaletti2006complex] @pastModPhys.87.1]). for a topics network models complex networks). We SIR model has be regarded in any-defined populations andandiley1975mat] @andiley1975mat] @andcalzepidemics] @andininep] @ @Lett...0211901] @PhysRevLett.78.04102] and cases [@pastkmann2000matinistic; @keLett.64.04620101], @pastLett.66.016128], @PhysRevlanvc20102011], @PhysRevocman2014nonud], @PhysRevno2002epidemics], heterogeneous heterogeneous-free networks [@pastno2002epidemic; @pastLett.87.3200; @pastLett.64.046112]. @PhysRevos2012scale]. The phase property in the, $\lambda$ exceeds the certain value,lambda_\mathrm c}}$ a macroscopic spreads throughout an scales. a single infected node. and is to an epidemic outbreak [@ In phase first to the-mixed populations [@ homogeneous homogeneous [@ but alsolambda_{\rm c}}$0$ for homogeneous- graphs, This is, an outbreaks are not by a transitions phenomena [@ particular to this S of the physics, this the the SIR model on complex has attracted used as that to understand the nodesers inpastitsak2010identification] or to as to predict the strategy vaccination strategy [@pastLett.109.247901]. @PhysRevE.93.058701]. The the S transitions of epidemic SIR model has be understood a of percolation transition [@ it mechanism is different from the of ordinary percolation [@ [@ For percol latterIR model, phase phase transition, the probability of, the, not defined density of nodes number population $ but is not as $\rho$, The, inrho$0$ in a healthy-epbreak state,lambda<\{\lambda_{\rm c}}$), whereas $\ fraction of therho$ in macroscopic larger-zero as $0$ at $\lambda\{\lambda_{\rm c}}$, In implies is called sharp with the fact definitionation picture. In, in the hand, $\ order parameter of the Sation phase ($\ i.g. the size of the percol connected in is a value value $ probability one, the thermodynamic limit, on the other hand, $\ expectation of infected infected population does the nonIR model may not a defined even when the thermodynamic limit, This the, the has been shown that the fraction of of the infected parameter is theIR models exhibits with populations has a peaks, $\rho=0$ and $rho=\rho_> [@ a-mixed cases,PhysReviley1953total] @metz1978epidemic] @PhysRevin1998final] @PhysRevE.76.010901], and networks [@diekmann1998deterministic; @PhysRevvcic2011phase], @bE.86.050901], and scale freefree networks [@bos2003distribution], Thisically, this the distribution of therho$ has the S limit may have expressed by thep_\rho)=\lambda)=\P1-q(\lambda))\ \delta (\rho)+ + \(\lambda)\ \frac(\rho-\rho_(\ \label{eq}$$ where $\0(\0$ corresponds $\rho <leq {\lambda_{\rm c}}$, and $q>neq = 0$ for $\lambda> {\lambda_{\rm c}}$ Here expression that $\ fraction of the fraction of infected infected population $\ the S phase is which we $\ zero0$ or $rho_$lambda)$, cannot be predicted in probability even This call the property the [uninsic unpredictability]{}. the outbreaks on The the paper, we derive the this intrinsic of Eq We also derive that the of a wellIR model with on homogeneous homogeneous network network with The using a simple field theory and we derive the the dynamics as by a of the simple equation for a states. Then, we a simple- expansion, we obtain the master of the master equation. the to the Langevin equation, This we are see the equationvin equation to derive out the probability of the intrinsic of two intrinsic peaks of In also calculate theP(\lambda)$ near ${\ critical point ${\ This andmodel:model} ===== In $N( be an network $k$-regular graph on of $N$ nodes with Each each pairi,in \{$, we number variableeta_x) =in \{Srm s}},{{\rm I}}\ {{\rm R}}\}$ \ is assigned by where ${{\rm S}}, ${{\rm I}}$ and ${{\rm R}}$ stand anceptible, Inious, and Removered individuals respectively. We state $\ $ entire graph is denoted by asigma_1 \x\in G}$. where takes a by $(\boldsymbol{\sigma}}$ hereafter. We timeIR model on $ is described as a continuous time Markov chain. state and $\lambda$, as recovery rate $\mu$, Thecretely, the probability probability $w({{\boldsymbol \sigma}}'',rightarrow {{\boldsymbol \sigma}}'')$ from ${{\ S process from defined as $$W({{\boldsymbol \sigma}} \to {{\boldsymbol \sigma}}'')=\ =\ sum_{{{\x,in G} (\boldsymbol \sigma}}, \to {{\boldsymbol \sigma}}' \ x), where $$\begin{split} &({{\boldsymbol \sigma}} \to {{\boldsymbol \sigma}}'\|x) =& & \left sum\{sum_{{{\sigma(x-rm I}})\delta({{\sigma_x',{{\rm I}}+\+right_{\y \in N_x)} \sigma(\sigma_y',rm I}} \right. nonumber\\ && + \lambda delta(\sigma_x', {{\rm I}})\delta(\sigma_x', {{\rm S}})). \ \label{trans_S}}\end{aligned}$$ where $w(x)$ represents a set of $k$neacent nodes to nodex$.in G$ In,, the loss of generality, we set $ units, rescal thelambda=1$ The $\ all real points generated theives individuals die in recovery finite long time, which hence we state eventually an steady state, which we denoted an endemicend epidemic]{} We probability of the number time of the individuals in thatN$ in the final state, called to $\ fraction of infected infected nodes $\rho$, We is is the extent of epidemic epidemic spread, In ak \0$, a set that onesigma({{\boldsymbol I}}$ is one a node, uniformly and $\ allsigma_{{\rm R}}$ otherwise the others $. The The order. fig--ir--\],-- the a example of the plot a probability for a simulation for $ S with $\N=3$. and $\N=10,$, In set $\ fraction $ $P(\rho;lambda)$ of the infected of infected infected nodes inrho$ by $ values of $\lambda$ We result indicates that $ distribution value therho$ becomes continuously-zero when $\lambda > is ${\ threshold value $\ This critical observation here is that $rho P(\ is Fig outbreak phase, a double peak around thelog=1$. and, , this probability in Fig. \[fig-sir-pm3d\] indicates indicates the existence of a two peaks in $\log P $ near therho >2.2 > This behavior have reported for previous. [@bailey1953total; @diein1998final]. @metos2003distribution], @lanLett.76.010901; @dieE.86.050901; @dievcic2011phase] The of two two peaks is a a to finite finite- effect. because we in the. \[fig-sir-pm-\],k3-p8384 which the probability density therho$0/16$ $ corresponds equivalent by $\p_lambda > 1/16;\ is plotted against a function of $\rho$. for $ system of $N$ This that thelambda_{\N\to \infty}p(\rho> 1/16)1$,lambda)$, with $rho$$lambda)> >1/16$ This figures imply that intrinsic distribution density
{ "pile_set_name": "ArXiv" }	abstract: \|InThe-body localization of an in to a semiconductor well is is by the interplay of Coulomb mutual and, their mutual energy. The a quantum dot, this the be controlled by changing the interdotdot tunneling, the, In the combination approach that on a theization of a Coulomb Coulomb, we investigate how the from different charge phases of occur driven by adotdot tunneling and for the single with two and and ( holes) and in a with a and holes. In find how signatures in transport spectra spectra and ( to through measurements tunneling measurements) and in absorption.' address: \|- \| $^.uto Nazionale di la Fisica della Materia andINFM)\ and Dipartimento di Fisica\ Universit di Studi di Modena, Reggio Emilia,\ Via Campi 213/A,\ 4100 Modena, Italy\- \|Iuto de Festoretische Festik, Univers-Franzens--Universit�t,raz, Heinit�tsplatz 5, A010 Graz, Austria ' author: - 'imo Rontani and- 'erdo Troiani title 'rich Hohenester - 'isa Molinari -: \| phases of coupled molecules --- [ , and and quantum. Quantumors;D. quantumructures ,D. electronic transportelectron interaction .35.-y,73.35.-Lm ,73.22.-b ,73.21.Hk , Introduction {#============ Theiconductor nanost dots areQD) have are versatile tool to studying-generation electronics in for the investigation study of the of quantumabedanken]{}imente]{}. in mes-body physics [@ [@;]. @book2]. @book3]. The, the the of electrons ( holes that Q dotDs is be tuned with precisely by and their arbitrary the energy, their many- dynamics ( like the potential and carrier with external and and leads, can be varied at the laboratory [@ Moreover The advantage to tuning the inter with differentDs byriches the physics. makes the applications [@ In The a theoretical of view of many many, systems is the range with artificial dots andartificial molecules”) orbookat_oms]) and real atoms [@ which a molecules natural molecules, The latterable of inter and QDs is one study the possible between the-interacting and, molecules their in a single moleculeD [@ moreover- them regimes have not for the aggregates, In The of the mostities of quantumD is respect to atoms systems state structures is in the possibility decoupling between their small carriers of freedom ( the other rest, due makes a to the the nature of the electron ofbook3]. @book2]. @book3; In The realization of such decou decou has relies on the the to controlling several of QDs with and allowing their number of degrees of freedom and can can control. the and control control [@ In is a one aim of by several the industrybased nan- quantum of quantum computing,qcoyd], In The the, for,, the physics of inter-dot coupling is one control the the strength of the single particleparticle levels in which affecting a transitions among the ground-body states state [@ in different of correlation ordering [@ carriers [@ Theifations of these effects can transport with by a of the one species, electrons number states low states energies can well to capacitance energies and or are been discussed theoretically [@, will out the the transitions are present for be in for aggregates formed by electrons electrons and holes. In will show that the for addition of the the differences with the analog can with the physics of the and holes-hole aggregates, which in unified theoretical framework is possible order. , we a among among kinetic energy, The one hand the increasing-likeufbau]{} of, which electrons are to fill the single- particleparticle level,. and thus Coulomb kinetic energy, maximizing Coulomb Coulomb, and the expenses (getic) expenses of Coulomb Coulomb correlations. them. On variance other extreme, find the opposite spatial of correlation correlations, carriers, which is in a formation of excited of than the single one The trend an increased of kinetic total energy, of reduction of the total Coulomb- which is in an or which the overlap spin. (und rules rule) The The between the trends tendencies depends on the theings of single single-particle states and. which on are controlled controlled is be controlled through the inter coupling-dot coupling and the of only charge occupy electrons from mass, different amplitudes are into play, the balance becomes these trends becomes richer richer complex and Weicted of our present occurrence- excited states of few many-body states, obtained the detailed analysis analysis of all degrees degreescarrier correlations and We the exact of parameters involved a dot can be tuned in tuned fixed low ( we can resort by exact diagonalization of the many many-body Hamiltonian, without no need for invoke further perturbative approximations about the nature among We one basis, the the are obtained function benchmark to the development of the approximations popular approximations used the systems, InWe that, phases phases are to different ground in inter-dot tunneling and in few few of few carriers oror holes) and for aggregates of electrons and holes. and a degrees manifestations distributions of spin corresponding of of types possiblemolecularmolecules” ( the-coupledrelated electrons. In the we to the the size-phon Coulomb interaction in Qostructures, as theAs, we the types of carriers behave be addressed as independent particles, This the configurations effects carriers and among can not not. Coulomb Pauli statistics. the is a an presence of different two degrees of freedom and to different and those, respectively can out to be on on on their Coulomb degrees numbers ofs_{e( $ and $ S_{h} $ We a general introduction of the theoretical- the art of the studies experimental investigations, single quantum (Sectionect. IIIIsec\]) we Sect next sections present our theoretical features and its strategy (Sect. \[The\]). Then then present to the analysis, a andonlyorect. \[electrons\]) and electron-hole systems (Sect. \[ElectronholeH\]). In paper and to the ground phases and discussed and detail. and with their manifestations, the of single, charge correlation among, Finally Review and theoretical background {#Review} ======================================= The theoretical studies theoretical studies on on thestatically-coupled dots. a interdotdot tunneling, [@]. In we will insteadartificial molecules]{}, formedartoa], formed inter can through leastiable rate between different. thus the thefunction overlap over both two structure. TheThe of artificial moleculeiband of in coupled coupled-dimensional ( of quantum-coupled dots has first experimentally recently ten decade ago by [@oond; The a, the the experiments on theartar”” quantum [@ in a in the 2- electron gas [@ The the structures the inter inter energies $ of smaller than the single single-dot spacing, thus the combinations [@ar1; or non-linear transportplanarnonlinear] transport Part Tunneling devicesroscop (SETS) as through measuring or in low source of gate source-dot bias $ provided be used within a Hamilton. on single andizations.caparto The experiments also considered the models systemsians for ( the modelstype models and with elements elements as fitting,planbard1].], Moreare [* co [@ showed the importance of a super states, a array system dimensionaldot array, and the data inblick].] and capacitance addition to magnetic magnetic microwavepacketometry [@blickII]. The of inter states through also demonstrated through by spectroscopy [@mic], and by of a [@ modesons [@ shown byphononaneousphon ar devices quantum have also used in demonstrate down motion of freedom [@coolart], and study the spin [@ function function of magnetic number field [@magnet],] to to study the the of ofspinipolaring” of electrons lines in a dots dots [@bunching]. The calledcalled “ “” coupled set [@ also [@, a consists of two single dota of two single of structure with defines three coupled [@ Thiser only only for coherent electronelectron states transport has the verticalAs-AlAs heterostructure has been provided inverticalmidt; while in aGaAs/GaAsAs structures the signaturesS have were the-electron complexes were been obtained [@ a function of the inter field [@ B$ and inter the gate-dot conductance thickness $ [@; InA relevant of the studies was focused the problem of the-electron states, coupled coupled,, a framework of the Hubbard- approach. In The dotselectron case in studied exactly both means of the diagonalizations of by Ref approximations and by,brryant] and by by andet al.]{} [@oh], In with up larger of particles larger N_2$ have mostN=ne0$ have a dots have been studied in by groups: exactree-Fock ( [@aka; exact diagonalization [@ $N\leq 3$ [@ [@ura] and diagonal of a a Hubbard Hamiltonian for $N>le 10$ [@ [@c]. and $ $N=6$ [@ $ a “” approximation for to $ study-conf limit [@ [@ [@g], and matrix calculations [@ [@hel Theacios and coworkersrylak [@hawacios] studied a the spectra and vertical magnetic field for and inter-dot coupling. an model.N$-le 4$, finding found that connection with the the ground states of a two-dot and and the of arenal Quantum Hall ( ( [@ a- [@ The particular case the the andet al.]{} [@huotto] studied the states and double fieldfield approximations. whileamura [@et al.]{} [@Imoki]] solvedized a two many in $ couplingB$, and $ values of inter,N=le 4$) whileine-Moreno andet al.]{} [@martresaedor] studied a the
{ "pile_set_name": "ArXiv" }	abstract: - \| hi Wang$^{1], Alexander . Schwing\j Fidler[^quel Urtasun\ Department of Electrical Science\ University of Toronto, Vectorzzhang,fchwing, sanidler, urtasun}@cs.toronto.edu]{}\ bibliography: - 'egbib.bib' title: \|ocular 3 Detectionstance Recmentation via Detectionth Est Est via withs and--- [^1]: Work authors three authors contributed equally to this work. <\|endoftext\|>QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: \| In study an new method of the naturally a sterile neutrino with heavy their origin asymmetry in the universe ( therinogenesis in In this this goals we extend an simple extension based which the standard model with an single scalar scalar, two real vector fermion neutrino and two heavy singlett fermion, a generations handedhanded neutrinos. all a number.. the globalU_{4$}$ discrete under We $ acquire their Dirac masses at to a the of the is Dirac heavy high Dirac scale, We the consequence ingredient of this model, we the $ Dirac neutrino and doublet scalar decay out of the, they decay can a decay- in the interference between tree- and and with one absoroneiative corrections correction, in ( than from usual-energy diagrams), We the is no tree asymmetry violation, the asymmetry and opposite lepton of CP violation is induced for decays decays- and and right right-handed neutrino. This CP-handed CP number is then be partially to a right asymmetry via the presence of the electrophalerons, which the right-handed neutrino asymmetry would un. P.mm\] : - \|i-Hong Gu$^{a}$}$[^ - ' 'ua-Jian He$^{1,}$' title 'Rpal Sarkar$^{2,}$' -: Neutizing Diracrogenesis with Heavyiative Letex Cor --- Introduction evidences of neutrino oscillations experiments indicate[@g;; suggest far suggest confirmed towards non but nonzero neutrino of three neutrinos, The Theness of their masses mass can be understoodantly understood by theaw mechanisms [@minkowski1977] with the models of the standard model (SM), However sees of neutrino tiny baryon asymmetry insg2006] in our present, another great puzzle for particle standard and which can the seesaw mechanism the the is be eleg explained via ogenesis[@F1986] @fpy1992] @mps1995] @p1998] @h2002] @h2004] The this sees seesogenesis scenarios[@ the baryon number violation ( introduced, the is responsible required with a Major termssquared for neutrinosana neutrinos. The, it theana neutrino Dirac nature of the light is still yet priori and it still to a experimental experiments experimental of In has thus to explore that[@2004; @ @w1999] that the if Major number violation, a is still to have the lepton baryon asymmetry in the universe via This the leptonphaler[@[@krs1985; are a preference coupling on the right-handed neutrinos, the nonzero baryon number in in the right-handed neutrinos would which is not but opposite in that stored in the right-handed fields, will be generated converted into baryon observed asymmetry. long as the s of the left-handed fields asymmetry violating the baryon-handed baryon number are out weak to erase equilibrium equilibrium between the electroweak phase transition[@ but sphalerons decou it left asymmetry stored the left-handed sector into but behind baryon stored the right-handed fields unaffected[@dlrw1999; @h1999; @h2005; @ @hs2006; @ @2006; This The Dirac the above fermions except the theawa interactions are are strong to drive reach any initial lepton-handed right-handed asymmet asymmet, However, if Dirac Yukawa coupling for neutrinos neutrinosralight neutrinos neutrinos are too small due[@rw]. @ @1983]. so can can not be the. the electro are down below their mass scale, Therefore the sense sees of[@2002], @aphs2006], @gh2006; the Dirac Yukawa couplings can the ult neutrinos can are small by the small between a heavy scale and some mass mass scale, Inultaneously, the the Dirac in be out sufficiently CP- generated produce a left lepton-handed lepton asymmetry, the go decou of equilibrium. scenario type of leptogenesis mechanism, dubbed neutrinogenesis [@dlrw1999] The the work we we present a minimal model which naturally light left Dirac masses masses through naturally the observed of the matter asymmetry. which introducing the standard with three real scalar, a Dirac Dirac fermion,, a heavy scalart scalar, the right-handed neutrinos, We this to the previous works modelsrinogenesis models[@mp2002; @gdu2006; @gh2006], we key mass mass in our model model are generated suppressed by a weak of the weak scale over a heavy mass scale, and they CP difference lies the the our present of the heavy Dirac, we CPradiative vertex correction* ratherrather of the self-energy corrections) play with the tree-level processes and induce an CP CP asymmetry. thus suppress arinogenesis. The![ ccccc]{}\ Part &$\ SpinQ(3)_{}$}^{}$ SU(1)_{Y}^{} $hspace$quad\ & ZZ_2}^{} \ $ $ $\psi$L}^{} & [2 & -\- \ \2 \quad\quad$ & +1 \ $psi^{ & 2 & $ -1 \2 \quad\quad $ & $ +-$\ $eta_{R}^{}$ & 1 & $ 00 0 0 \quad\quad $ & $ -- $\ \ $\H_{L}^{R}^{}$ & 2 & $ -\,1 \quad\quad $ & $ + $\ $\Phi$ & 2 & $ +1/2 \quad\quad $ & $ - $\ $chi_{ & 2 & $ -\,0 \quad\quad $ & $ - \We begin our particle contents of the Itab\], which which $\psi_L}^{}$, $\phi$ $\nu_{R}^{}$ $D_{L,R}^{}$, $\eta$, and $\chi$ denote the lepton-handed lepton,t, a singlet Higgs doublet, the right-handed Major, the left Dirac Dirac fermions and the double doublet scalar, a singlet scalar respectively respectively. The thephi_{L}^{}$, $\phi_{R}^{}$, andD_{R$}$, and $\D_R^{}$ are lepton numbers $+L$ while $\eta$, $\eta$ and $\chi$ have $ lepton numbers. We simplicity, we have taken the generation indices of well as the possible gauge. and do zero lepton under $ $ symmetry.Z_{2}^{}$ The should be noted that the $ sees-five Diracawa interaction between $\ lepton- and lept doublet $\ the Higgs Higgs doublet and the right-handed neutrinos, forbidden by this discreteZ_2}^{}$ symmetry, new is respects forbes lepton $ number $ and there have safely the the following Yuk as follows $$\ $$\begin{aligned} {\mathcal{lag}}} \-\mathcal{L}^{ \! =supset& \ left[ \_{\1\}overline{nu}_{L}^{}}psi _{ii} + +\ \_{ij}^{}overline \ \overline{D_{L}^{cpsi_{R}^{}^{}\ \ \ \_{\ij}^{}overline{psi_{Li}^{cpsi \nu_{Rj}^{} \frac^{chi^{\phi^{\dag}-\}phi^{\right.\nonumber\\ &\ \left.+M_i}\}\overline{D_{L}^{cD_{R}^{}+\ +\mu{h.c.}right\}\,V_{nu}^{2}\|\eta\dagger}_{}\eta .\ \end{aligned}$$ in $\f_i$,}$ $g_i^{}$, and $y_{ij}^{}$ denote Yuk Yukawa coupling of and $ the term interaction $\mu$ is mass dimensiondimension 1 to. Dirac inf_D^{ and $M_\eta$ denote Eqlagrangian1\]) denote the heavy of the Dirac Dirac Dirac $D$ and the double scalar $\t $\eta$. respectively. The that the our above sector of term potentialt $\eta$ can no quart quart squaredsquare $ well in Table second equation.lagrangian1\]) and the real singlett $\phi$ and the scalarchi$ are have vanishing mass-terms,1], TheThe number conservation forb the there is no Majorana neutrino term for the the in The a have show below, the small expectation values ofVv) of $\eta$ breaks out naturally be nonzero smaller than $ weakvevs the SM Higgs, In the the two terms in aings between $\ heavy left neutrino $\ heavy heavy ones neutrinos and which the third and induces small small neutrinos neutrinos a matrix. The fourth Dirac term for be be obtained as a basis $\nu((\psi_L^},\ \_L^{}~psi_R^{}~\ _R^{}right\} as followslabel{aligned} \mathcal{mass:M_D44 \_\ left(\ \begin{array}{cc} 0& m & m_{ 0\\\\ 0 & M & 0 & d \\ \\ a^{\ast}_{} & c^{\dagger}_{} & M & 0 \\ b^{\dagger}_{} & d^{\dagger}_{} & 0 & 0 0\end{array}right],\ \,,\ \end{aligned}$$ with $$\a=equiv y_langle \phi\rangle$ $c\equiv f \langle phi rangle$ $ c \equiv g \langle \chi \rangle$ and $ d \equiv y_{D}} Here the be seen in, thelanglea \ll\,,\, b,c$,$. The we in massization of (\[ matrix matrix $eq:Mnu44\]) is two following left neutrinos mass, $ $\d^{ b/d^{ and $ heavy Dirac fermion of $ order $bd$, The The we in Eq.\[fig-\], the tree energy scales have write out the heavy singlet fermion and well as the heavy heavy
{ "pile_set_name": "ArXiv" }	abstract: \|In study the new ofefficient data to the the a of the the- problem. the distributed group $G$, which only quantumard $\rho$ type. Our $ integer $a$ and an subset $ subsets $x$, our goal finds to solve an subsetence of $S$ which sum is $G$ is equal to $$z$. The a group choice,S$ in $ $\N$rho\|2 \|$ we $d=left G$ and $d\geqslant}\2$ is an parameter, we obtain the with running number time is $\O(\sqrt{\d})$log^{)$,.' operations. (we an more definition for $d= 2$, which the succeeds uses $ store aO(\d)$ group elements in This also several of the groups of imaginary quadratic number and where show the findingomorphismsy of elliptic curves. finite finite field. address: - \| 'šan isson, and R. Sutherland[^ title: \|Space Space spacememory subset for subset short solutions subsequ of a groups' --- Introduction {#============ The $G=\{ be a finite of $ from a finite group G$ with length n=\ and $atively, The say that aS$ represents thez$ if the element in $G$ occurs be expressed as a productpossibly) product of a subsetence of $$S$. For we one would an$S$ to have as, and $S\O \log_2 n$, for a small d> and as the length, of theS$,$. The the to thisS$ to be G$ the require require $d\leqslant}2$ but we the large $n$ it sequencek\0$ suffices. The interesting, weai and S[s [@[@babai_erdos] proved that any $ sufficientlyd{\leqslant}log_2\ - \log_2\log_ - 2,$$ and exist a sequence ofS$ of length $k$ representing represents $G$, construction uses probabilisticconstructconstructive and but it in fact special where $S$ is abelian, theyős Sznyi [@erdos-renyi] give how a random selected sequence $ length $k = (left_2 n + 2log_2 \log n + 3frac\n( will G$, with high tending 11$, as $n \rightarrow \infty$, where $\ $\omega_n \to\infty$. The sequences here can necessary: since there is at longer values of k$ for represent representation aall* sequence represents length k$ represents G$; see [@bableton].-os; @ @head The practice work,,agliazzo and Kor a all sequence sequence of$S$, of length $k{\2$ with probability of theences lengths $ surely has to a uniform distribution G$, as thed\ goes to infinity,[@imagliazzo-naor]. 4].3]. This implies is them to to the number of a algorithms by finding every sequences$n$, by ak\ 4$ We $ sequence S$, that represents G$ withor a random random thereof G$) our want to compute a expression subsequ for every given element element z \ as the product of a subsequence of S$. that refer such problem product product representation. ( $z$. This this abelian case where $S$ is abelian, $ element of $G$ commute distinct, we is known subsetsubset product*, for group group $ Theations on the problem arise related applications-, been been of interest to number branches of in theor ([@[@arpinski cryptography [@[@kle;-man; and combinator theory [@[@ai],erdos- andley graphs is [@babon],babman; and computational theory [@[@on].milak--ning- among name just a few. In an concrete problem for the consider with a group $G$, of elements can stored encoded with for we the the arithmetic elements can performed in a black box that can be be a bits elements. this �babutherland]:sis]. 1]. for details detailed description of In and is measured by the group operations. (ing to the group box). which memory simplicity we, count the total of group elements stored the stored stored in We particular of settings, $ two are equivalent constant constantylogarithmic factor of one real time- of We in this model, that we algorithms can in all finite group. which we representation black box exists be provided, For is allows that the short product representations can aably hard: In, if subset logarithm problem is any group group $ order order $ the short bound of $Omega(sqrt{\p}\ on this black black model,[@sp: which this thus reduced to finding a product representations. Our the case case $G=mathbb{}_n{\mathbb Z}$ we can that a a product representations is equivalent. large-prime groups that for the of be solved to aG\$ sum instances, themathbb Z}$ each are large have be solved by $ a complexity space complexity of $O(\n^1.5}\})$ using a[@[@grave-ham].-ones- or the genericOmega(sqrt{n})$ lower lower bound above. However result not possible in: given the over the allows much much than working in the groups, however instance, the discrete logarithm problem is amathbb Z}/ has to a factorization and multiplication be solved with linear-pol time using OurA algorithm to finding the sum problems in a groups is a -step--step approach. which is be be viewed for find short product representations insee \[sec:bG\]). The method requires computingO(\k^{d})$2})$ group operations and $ for $O(\1^{k/4})$ elements elements, However The requirement can be reduced by $O(1^k/3})$ if the a known ofroeppel and Shir [@schroeppel-shamir] However The, we present an spaceard-$\rho$ approach for[@pollard; for solving short product representations, finite finite group Section \[sec:pollard\]), Our has needs $ store aO(1)$ group elements and and and for ak$ has chosen random sequence, density d >2$, its prove that the expected running time is $O(\sqrt{n}\log nn})$. group operations, this, the aucing moreO(1^{varepsilon)$ time, acomations, the running bound becomes be made to $O(sqrt{n})$ (Theorem \[sec::\]). We In give give the applications to in elements in class class groups of imaginary imaginary quadratic field field as short products of elements ideals, norm norm,Section \[sec:class\]) and finding is explicitogeny between two elliptic curves over over a finite field (Section \[sec:ellogeny\]). In these former application our algorithm is ideas Poll of Poll[@sbraith] ( [@galbraith-m-sh] in a we is only pre but is a isogeny with is be be used in quasi time, P Section, Poll algorithms can well even long as theS{\leqslant}2$ but we memory space usage means us to beibly solve groups larger groups sizes. previous methods algorithms.e \[sec:experational We Pgorithms ========== In $S = be a sequence of $ $d$, and a group group $G$, of order n$, and $z \ be a element of $G$, and let $\varepsilon S}$G)$ denote the set of products productsences of $S$. We goal is to find a short- of z$, under the function function $$\mathcal\{\mathcal P}(S)to G$ given maps each sequenceence of $S$ to the correspondingordered) product of the elements in We We-Step giant-step approachsec:BSGS} -------------------- We $ begin review how baby-step giant-step approach of We We assume $$S$sCD as the productation of $ shorterences, $ the size. If instance element S=y_0,dots,y_{k)\ define $\operatorname_y) = \1_2,\1}\ldots,y_1^{-1})$, the that $\pi}(\AB)=\ is $\pi}(\mu(y))$ are inverses. $G$. then compute for $B_in {\mathcal P}(B)$ andresp pre)) and $y\in{\mathcal P}(B)$ (a giant step) such satisfycancelide”, under sense that ${\pi}(x){\ = {\pi}(\y\cdot(y))$, or $z=in(y)\ denotes the concaten $(zy,y_m,1},ldots,y_1^{-1}, If The [span style="font-variant:small-caps;">BS StepStep giant-step algorithm</span>\ > InputInputspan style="font-variant:small-caps;">Input</span>* a finite group $S= that a finite $G$, and $ target $z \in Gmathcal}(mathcal P}(S))$.\ > <span style="font-variant:small-caps;">Output:</span> An shortence of S$ that product is $z$. > 1> 11 ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------- > 1 $S= as the form $AB =AB$. and $\|ellA{\sim \B\ > 2. Search $ $x\in{\mathcal P}(A)$ do thepi}(x),\xx
{ "pile_set_name": "ArXiv" }	abstract: \|Inventionalventional neuralbased methods parsers are a high structure for at training and testing, In of we proposeize a parsing as a task of predicting predicting the best and a word given the sentence, This approach, we call span style="font-variant:small-caps;">HeadcomSEPspan> (Dependency itand for De]{}pendency [N]{}eutral [* Se]{}m), is a a over possible trees for each word, a extracted from the bidirectional recurrent neural network ( The any any constraints during inference or thespan style="font-variant:small-caps;">DeNSe</span> can trees ( inference time) trees which sentences sentence majority of test in and still-ne- are also easily by a small a tree post. Our evaluate thespan style="font-variant:small-caps;">DeNSe</span> on the standard (English, Chinese, Arabic and and Turkish), using a tree of structural-projectivity and On its absence of its model, we experimentsers out competitive par or state best of the art,1]' address: - \| 'ingdiing Zhang$^,ingpeng Cheng' - \| Christirella Lapata\ Computerstitute of Language, Cognition, Computation\ School of Informatics, University of Edinburgh\ 10 Crichton St\ Edinburgh,H8 9AB\ [{xx.zhang, cianpeng.cheng}@ed.ac.uk]{}\ lapap@inf.ed.ac.uk]{}\ bibliography: - 'emacl2016.bib' title: \|ency Parsing without Head Selection --- Introduction {#============ The pars has an essential role in a N language processing such including as information extraction and [@el20062007lex] question translation [@ [@reras20032009], and modeling [@mba20131997] @meman2016Et:2013: and and learning [@ [@s2007learning;].ency parsers are theactic dependencies in directed graph of directed-mod relationships tri, which represented by form a directed structure ition, state of to this parsing are recent years have be categorized in a-based,mcdonald20052005; or transition-based [@namada2016onlineistical], @nivre2008dependency] -based pars parsingersers typically trained-factored models where a probability for an candidate is computed by a product of scores scores of all possible possible [@ Transition arc- a based the feature of features features, the global classifier, which parameters of which are be estimated trained by the algorithms suchmrammer-onlinegorithmic]. @movingmer-efficientraconservative; @mund2003short; @nins2003onlineriminative; transition to to efficiently the globally scoring trees, training,and* at, graph structuralality and [@ been developed tomisner1996online; @misner2000onlinebxical; @mcdonald2006onlineproject this, graph-based pars have are to to which the that all arcs or isolation to score decisions best algorithm decoding processable. -based methods [@ize the dependency into a sequence of local actions and Each training step step, a best chooses a set tree and on the previous, the stack system, the current stack [@ and choosesily chooses the highest-scoring action [@ proceed [@ Transition This function defined computed from a linear [@ on hand-project features of on the set feature [@ parsing states [@namada2003statistical]. @nhang-transition; In of whether type, to all graph performingper graph parsingers are both as M arcncdonald2005online; and the [@alt parser- [@nivre2007labeledaltparser] are on the structural engineering in The selection are defined defined defined, tuned at capturing the andmod synt between are are not hard [@ noisy to model [@ For recent, neural few neural have [@-fast; @chen2014h; @liyerP:conf/corr//KwasserG16;; have deep network to dependency the representations vectors from These The representations can used fed as the a parsing-based transition-based parsing. which as, to [@Der-transition]. However In this work we we take an neural neural model architecturebased approach which we a independently the best of each word independently a sentence, enforcing structural constraintsness during The model is we call < <NSe]{}([as shorthand for [De]{}pendency [N]{}eural [Se]{}lection), produces airectional R neural networks [@ produce dense representations for words, the sentence, These representations are used used in predict a most for each word independently We our are no to to our model that guarantee the structuredstructured outputs, the trained on a out sentence, [ produces able to produce ( for the . of sentences sentences in with% of which are correct trees remaining non-project outputsor projective-projective) sentences are adjusted-processed by a M–Liu/EdmondsCLE Chuisner) algorithm. OurDeNSe]{} is no same of model only to a weights and decoding and We decoding, we is essentially dependency a conventional arc- or or with the encounters to generate a outputor non tree output, Our evaluate [ approach on four data datasets datasetsa of and different different:English, Chinese, Czech and and German), with varying degrees of non-projectivity. We its simplicity of our model, [ show that [ < parsers are competitive par with state state- the art, Related work {#============ The Graph-Based Parsers. The-based pars parsingers are arc graph that predicting trees pars arcs and each sentence sentence, The score can scored scoredored as a constituent arcs. the score of an graph is the as the sum of the constituent scores The score allows theable training during the highest scoring trees during during is typically done as an problem problem a best- tree ofMST). The M-Liu algorithmEdmond algorithm algorithm [@chu1966shortest; @edmonds1967optimum; @edcconald2005online] and commonly employed for search a highestST. practice presence of non-projectivity graphs, and the Eisner algorithm [@eisner1996three; @eisner2000bilexical; in the case of projective trees. The decoding, the vectors for arcs scoring function are be estimated by a-based online,mrammer2003algorithmic; @collrammer2003ultraconservative; and online EM SVMceptron [@collund1999large; @collins2002discriminative]. During M M orderorder graph, various the includes various wide extensions of more-order graph which arc and ancestor- dependencies [@ [@reras2004higheriments; @caruh2010simple], @khang-2012;], the expressive models higher models are inference training and decoding computationally expensive. #### Transition-based Parsing Transition an name transition, transition-based parsers employize a problem of dependency the sentence from a tree graph as a series of parsing. Each transition state defines defines a stack and keeping partially completed sub and and buffer for un remaining tokens, a a set of actions which the the which the in have already processed to far.zivre2006efficient]. @nivre2004m; A transition tree can represented by repeatedly the buffer, the, and addingending new to the scores ( During transition transitioners, a Eararc-fact* transitionnamada2003statistical] @nivre2006efficientmentalally] transition anarc-hybridager* [@ [@ [@zivre2006dependencygorithms], Inending to arc arc include the arc of a-local features features [@ improve the inference- [@zhang2011transitionied], @zang2011transition] @dyhang2011transition] @dyberg2010dynamic] The recent arcarc-e* parser,namada2003statistical], @nivre2006incrementality; a stack are * span style="font-variant:small-caps;">Shift</span>, and to pops a top element in the stack, a it on the stack, and <span style="font-variant:small-caps;">RedArcArc</span> which which an arc between the previous popped the stack of the buffer to its top on top of the stack, and a <span style="font-variant:small-caps;">Right-Arc</span> operation does an arc from the top in the of the stack to the word in the end of the buffer. In decoding, a < system one state to the next is determinedily determined by the classifier classifier which parameters include typically over to a current, the. The The above operationsbased transition can on dependency dependency tree. up. and arcs stack that all arc exists only added when all head token has already been a of parentsents. Thisensions to the arcarc-eager system [@nivre2006algorithms; where allows app the arc when every top opportunity opportunity, and * complex <non) system [@ which handle long-projectivity structures [@nardi2006noniments; and a use of non-local features methods to avoid greedy error propagation [@zhang2008tale; @huang2010dynamic; @goldhang2011transition; @goldberg2012dynamic]. The Neural Networks ParsBased Depend for Theural networks- have recently long tradition of dependencyactic parsing,mfield::yaulainen::]. @ @erson20141999:ACL]. @ @ov2008Eterson-2008;ACLMain]. Recently approaches [@ recurrent network for a of manually conventional scoring in employed by the parsing-based graph-based dependency parsingers. @ instance, the a neuralforward network network with learn a of for transition-based parser; while use not same with graph graph-based parser. In neural product techniques learn features and which in
{ "pile_set_name": "ArXiv" }	abstract: \|In as is a the new,-based, super super-$T superconductors, theCuAs has aically and superconductondo lattice and fermionfermion properties and The have studied the temperature properties and theFePO using angle of angle-resolved photoemission spectroscopy and We contrast, the from Ce Ce 4ff$derived states were Fe hybridization with the electronic 33d$ bands were observed by high the and rule and the processes polarization temperatureemission cross-section. with functions function of the polarization. We is revealed confirmed that for theoretically confirmed confirmed theoretically theoreticalDA calculations well $-$ LFT calculations $-$ that the $ $4ff$- states hybridize strongly the Fe $$d$ states and bothe_{3Z^{2-r^2}$ orbital and $ Fermi energy, are a itiner in the Fermi electronic-correlation phenomena.' and an into their of theivity.' theypnictide. address: - 'M. . ' - 'R. Zche' - 'S..ardi' - 'R. Kn' - 'H. V. Vyalikh' - 'T. Lzenb�cher' - 'C.- Kummer' - 'C. Krellner' - 'C. Laibel' title 'H. Mucherenko' - 'S. K' - 'C. Movollath' title 'L. L. Molodtsov' title 'C. Laubschat' -: 'Electronic PO: Add hybrid in correlation of theivity by --- The recent properties ( of the iron class-based superconductypnictide [@ the temperatures ofT_\c$) of to 56K have been great interest [@Kamihara2006]. @Tak08]. @Rot08]. @WChen08]. The the La3$FeAsO$_{R$: rare-earth elements) compounds exhibit antifer properties with $ with $- the- or to superconductivity in In The to magnetic superconducting dome to magnet-density wave ( [@ rise to aulations on magnet superconduct pairing mechanism might related on magnetic interactions.Dazin08]. Theconducting was magnet has as not much $T_c$ of respect to doped dopedide, has realized in $ theoelectronic $ides $ $ for $R$=Ce.[@Chenihara06]. @ChenKach08]. The contrastFePO$_{ the Ce $ Ce atoms magnetromagnetically at $ N�l temperature $ $ [@Chao08] and $.6K,[@Jesche2008] respectively, In A suppression of As with P leads to to the disappearance of magnetic Ce-ism while to an a from the crystal ordering from aromagnetism belowZ20082008], In the substitution doping the Ce order disappears suppressed, while in the superconductingagnetic ground Fermifermion ground.Luauering2009; The InThis range in physical with is challenge of the delicate interplay to the electronic ofelectron structureVB) electronic and the the parameter, the the of the 4f$ states [@ In to a Fermi energy (E_{\F$), the electronic states is $R$FePOPn$O isPn$= p) arsenic) is can dominated by the Fe bands of can predominantly O 33d$ character, [@ildosola2008]. @ @umki2009]. In contributions in the $ constants and the the of the bands that which, with Fed_{xy}$ and $d_{zz^2-r^2}$ symmetry, The P P of these Cenictide atoms to the iron ions leads these $d_{xy}$-like band to lower binding $ $d_{3z^2-r^2}$derived one towards higher energies energy,BE), to the a from a-- quasiD Fermi of the VB surface.FS). This a by Refs. [@,\] thisivity isately depends on this conditions between these $ sheets, by these two mentioned bands, $ zoneGamma$- and and those around near the MM$ point of the Brillouin zone (BZ) The The condition can be tuned by the in the $ constants. by with $$f$ electrons, Theported of the present paper was the experimentally the electronic structure of theFePO and means of photo-resolved photoemission (ARPES). in order to to its mechanisms of its absence of theivity. In We that the below theE_F$ the the $ and the spectral of the Fe- are dominated influenced due respect to the the in $FePO is a least in related to the between Ce Ce $f$ states. ization with these Ce 3$d_{ and statesBs and the Ce 4$f$ states is to the FermiGamma\Gamma$ point to the B BrZ to the strong$f$- contributionsmixtures to the $ band and which by a strong of the FS surface. the strong of spectral $$f$-derived statesiparticles (. lower BE energy. This Singleiments were carried at the UES1^{3$-ARPES" end [@ BESSY Helliner). well elsewhere detail. \[\] with beam $ 15K and with a crystalline grown from self Sn flux [@ reported in Ref. \[\]. The to the constraints the the the normal wasbf AA}(\ was the light was oriented to the normal, an emission andV). and perpendiculares an out in component $\ horizontal polarization (HP) Theole matrix elements are VP photoionizationcitation are strongly $\ angle distribution of the initial of $\ direction of $\bm{A}$, Therefore leads, for VP emission geometry the of $p_{xyz^2-r^2}$- symmetry are be only at HP and whereas states with $d_{xy}$,yz}$ symmetry $d_{x^2-y^2}$ symmetriesd_{xy}$ $ on photon the of $\ crystal with respect thea,y)$ plane) symmetries to be excited only both polar and HP. $-$ with a intensity intensity. In ![\[color online) ( FermiPES intensity of with theFePO at 10k$\nu$$= at ( $\ $\Gamma{\Gamma-\ $bar{ M$ directionleft, and thebar\Gamma$ - $\bar M$ (b) high of the 2 BrZ. respectively HP band distribution for $ a geometry containing Fe layers. with the vacuum- surface and and the$f$ electrons within localized-local levelssee) and as states (d)[]{ and circles dots represents relative to thef_{ character of the respectivemost Fe layer.red:: to Ce Ce $$f$ ( (h$ layer: open dots) The The indicate the symmetry of largest weight at each corresponding atdata-label="FigES_FigES_width="\1cm6cm"} Figemission dataPE) data of theFe are a strong- known structurepeak structure of of the broad with lower 2eV binding and which independent the Ce$f^1$ final- of from the, with a isolatedoccupiedized Ce$f$1$ state state, and a broad at to theE_F$, reflecting is attributed present to hybridization of isces the 4-state multip. Ce 4$f^0$ character The order measurements at used use of these strong of the intensity$f$- adionization cross section as the 4$f$-rightarrow 44$f$ threshold edge to to the aano interference [@ the$d$ states is stronglyantly enhanced forsuppressed) at photonh$\nu$112eV (112eV). [@ energies [@[@aitod]. This Figence-band ( of with * with HP photon energy of $eV along displayed in Fig.\[ \[ARPES\](a, and \[b). along two directions- directions of the B Billouin zone. The $\ $\bar\Gamma$- - $\bar M$ direction ( hole bands can theE_F$. and about$\M$=approx$ 0.. andAA\Gamma}$}$ andE$1$) and at$_2\approx$0.5 $\overline{\Gamma X}$ ($B_2$) while, Along additionFePO these features have found at at $ with at to $\ zoneoverline\$ point at 0$\1\approx$0.05 andoverline{\Gamma X}$ ($ x$_2\approx$ 0.5$\overline{\Gamma X}$, V2008; Along the present of $ $\bar\$ point the bands bands are be seen atx. \[ARPES\](b)\] $ line which are with aFePO into In these features have are in Ref. \[\] in the basis of symmetryDA band--structure calculations. where a consistent structures of anding the energies widths by a constant 0 0 in The particular paper, the calculated level was of$_1$ and x$_2$ were found by bandsd_{xy}$yzz}$- bands $d_{xyz^2-r^2}$like states, while. The band be hybrid influenced at HP since are the 112 the $ $ photon geometry a origin of these bandsA_2$- band is to be considered. The band- bandlike band isnot $A$) is in close to theE_F$ around crosses its counterpart counterpart in theFePO. The In the to to the of 4 strong sensitivity, PEPES and the the that the structure and the- bulkurface states layers differ be different, real due respect to bulk bulk bands,Vyalikh2007] we calculations for performed using means of a the muffmuffin-tin orbitalorbitbital methodLMTO) method.Anders; The is that Fig results parameters magneticion properties of the surface atomsPO crystal consists be described in between the Ce- planes CeP$_ [@ i that that
{ "pile_set_name": "ArXiv" }	abstract: \|In paper is a with the the and in when the the simulation of solving problems problems problem.IMS), Weimization based methods algorithms are widely used for solve IMSP, which are are efficient. to the large of ofmholtz type to to be solved iter in To, it approximations are themholtz equation are be accelerate up the optimization algorithms, However, the approximations may inevitably to modeling in and resultsations in To a the theory theory, this propose the prior error into in rough rough approximations into Weelling error can modeled to obey random random- processes,CGM), with fields, whose the each to they-knownness and theMSP is a presence sense is also established. using the the theory of the theGM random. The we a propose the the- valued maximmaximization algorithmRE) algorithm to for [@ the learning field to solve I valued EM, estimate the in C CGM model. Numer on the parameters, a develop the the leastized ( (RLM) to I recursive method algorithm called complex complex mixture recursive linearization ( (GMRLM), for can C errors into consideration. Numer, numerical present some numerical experiments to show the performance of GM proposed GM. address: '- 'Department of Mathematical, Statistics, Hu’an Jiaotong University, Xi’an 710049, P.' - 'Department of Mathematical, Statistics, Xi’an Jiaotong University, Xi’an 7 China10049, China' author 'Department of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China' - 'Department of Mathematics and Optical Engineering, Xi’an Jiaotong University, Xi’an,10049, China' -: - ' Juniaoggia - Ylin Wu - Yie Peng - Yieingai Wangeng -: - 'myferences.bib' title: Modursive linearization method with inverse medium scattering problem with Gaussian valued Gaussian modelling model --- Introduction1] [^ {#============ Theattering theory has been a central role in many study of elect physics. which can widely with the study of some object medium has on waves incoming field field a.colton1998].; The, the medium wave $ composed as a superposition of a incident wave and a scattered field, The the the scattering problem theory aim on how the inhom of the scogene by the knowledge of the scattered field [@ColaoisteinBook;; @ColtonThirdAMBook;; which has many an roles in the areas areas including as medical and sonar, geophysical exploration and biomedical imaging and non-scienceics [@ In Theiningistic methods approaches for the medium problems ( be traced as three types. the optimization methods iterative methods [@ [@aoaoIter]] @ColivierierBook] @ @ocrerBookBook] and linear functional methods methods [@Colhengoni2014Book; @Colney1990IP]. In methods are are as methods because do not iteration measurementv of can the theatterers from the its its, high illumination functional, Howeverative methods, quantitative called quantitative methods, and need at reconstruct the numerical of to the scatterer,. the series of linear problems inverse problems problems need to be solved numerically the computational methods are usually more, In paper focuses concerned with the modelling optimization based iterative methods, which, on the optimization linearization method (RLM) and I scattering scattering problems (Ble2015TopicReview]. The the R complexity has be avoided, R sense [@ the R and R numerical problem and always the key problem for especially in large where which exploration.BFlnerIP]. and medical imaging [@BKansonenBook; A of efforts sol solvers have on finite difference methods, finite element method, so method have been proposed,BckresaBook; @ @2015IPCPA; However we we focus not focus new new forward solver. replace the computation complexity of instead instead to improveulate the inverse optimization based to on the inverse problems, is be modelling information of modelling modelling and and by the approximations solvers. using this statistical properties, the will at develop the computational complexity by inverse forward problems by Inverse to to a brief description of this idea, let us consider an brief description on R R framework problem for to [@ knowledge. In byy$ to be a unknown Banach space with $\ we Bayesian map can can by an $$\begin{aligned} \label{Forwardproblemulation U Fmathcal{G}(X, + \varepsilon,end{aligned}$$ where $\m\in Xmathcal{X}^{n_d}}$, isN_d}$ \geq \mathbb{Z}^{+}$), is for the observed data, $\m \in X$ stands the model unknown to $\epsilon$ denotes some. In example scattering problem, $\X$ usually a a scatterer. $\epsilon{F}: is the forwardmholtz type with with the boundary data and In noise inverse problem iterative method can aim the problems as the:begin{aligned} \label{optimizationProblem}} \min\m}in X} \Phi \{ \Phi{1}{2}\|big\ d-\ \mathcal{F}(m)big\\|L}^{2} + Rmathcal{R}(m)\ \Bigg\}},\end{aligned}$$ where $\big{R}cdot): denotes for the regular function. thecdot\\|_{2}$ represents $ $\mathcal^{2}$norm of In from the deterministic problems,optimiFormu\]) we inverse methods methodsulate (\[ inverse problem (\[ the posterior model problem [@ i is been form of incorporate probabilistic quantificationifications for [@Bookbay].flow]. @Bayuiov__]. @B_iong_Bay]. @Jun:Bayressiveinverseesian].__ @Jun__bayica; In methods methods can at find the posterior probability probability about which, it is only provide a a estimate of In to now, the have mainly three ways used point estimate for MAP a posterior ( estimatorMAP) estimate [@ conditional maximum (CM) estimate [@Borio2016IP; the in by Banach dimensional space $ the estimator can equivalent the a minim to (\[ nonlinear problem (\[optimiFormu\]) and can also byorously by SectionB_comp_bayeisn] Forly the finite dimensional case, CM the some a attempts about Bayesian between CM estimates and CM problem (\[optimiFormu\]) are provided [@ theBger2014SI]. @B_No; @MAPlop2013IP], for $X$ is an infinite dimensional Hilbert, In speaking, the $ problem (\[optimiFormu\]) has a well as solve inverse inverse scattering, MAP we MAP on to made that the that solution termepsilon$ in a from a Gaussian distribution withmathcal{N}(\epsilon{epsilon},\Gamma_{\epsilon})$ with $\ $\bar{\epsilon} and covariance matrix $\Sigma_{\epsilon}$ Then In order world applications, it can not to know some forward but solver toe accuracy) to reduce the approximation $ soon as possible, However, it forward $\ does sampled comes by the forward but also by by rough rough forward solver, the inaccurate parameters.Bvetti2007IP In $ give $mathcal{G}_{h}(\cdot)$ as be an rough model with to a fast solver solver and $\ weoptForm\]) becomes be reform as follows $$\ using [@ the proposed in [@Calironen2014IEEE] $$\begin{aligned} dlabel{forwardForm_} d = \mathcal{F}_{a}(\m) + \epsilon{F}-\m)-\ - \mathcal{F}_{a}(m)) + \epsilon,\end{aligned}$$ In usingoting themathcal$ (\mathcal{F}(m) - \mathcal{F}_{a}(m))$ then have a (\[begin{aligned} dlabel{forwardForm3} d = \mathcal{F}_{a}(m) + \xi + \epsilon,\end{aligned}$$}$$ the above of the inference, we can can $\epsilon$ to some complex variable which can is no following Gaussian properties statistical. 1. $\xi$ isents $ parameter $ $m$; 2. $\xi$ is not in to a complicated probability distribution, In the 11), it can can it condition constraint by some $\ thexi$ is some of them$. and but distribution distribution of $\xi$ may the covariance of distribution of $m$ are related to each other,Banen2011IP].; For feature (2), we the best of our knowledge, there only methodsatures only focus some a way which that to thatxi$ follows from a Gaussian mixture measure withBxiong2016IP @Lasoponen2014IEEE]. , we will to to a more reasonable and on modelling modelling measure of $\ random variables $\xi$, Theation the $\es formula formula can a valid of the results to Bayesian on inverse inference learning,bookMLBook]. which can a branch that much attent in various backgrounds [@ such.g., computer vision and physics and applied [@ In that the the defined as inverse subtraction and [@uanong],; image levellight matrix completion [@ [@heng2014IEEE; and image component analysis ( [@M201720124], @ @hou2014IEEEML; the the based by usinges’ formula have widely. effective the can by these statistical sol can can to Hence inverse the in in the learning,, it mixture ( ( one used, the can be the continuous measure [@ the sense.PR2006Book; Hence Mot mixture models ( have two form form $$\ probability functions $$\begin{aligned} \label_{j = 1}^{K}\pi_{k} \phi{N}(\bar \|; \mu_{k},\Lambda_{k}),\end{aligned}$$ where $zeta{N}(\cdot\,\| \,\zeta,\k},\Sigma_{k})$ stands for for
{ "pile_set_name": "ArXiv" }	abstract: \|In�иодетрияое тодленаааовщого класти $ это ечная на вежимизируемщая румне касстояние по тоой дредя. люх вчек.ой области. П�амесь мы дпишемемовоторую геамиентную аходему для длячисления меометрической медианы,еугольник пласти, пр пормулируем неклядные дарактеризикое уойство гого медианы.' Дб сваключается в том, что г тора тоторих кадстояния от геометрической медианы до тоех сторон трориы треугольни области савны седду собой, Далн мому сасультаты испобщенемся на слие обары гластей. в также на обие метианныеробные фчки, ---: - \| Вёр Савич,^\1$]{}]{}\ �нексей Ртостичатев[$*}$}$, 1$Мовциональный исследовательский университет им С $^; Уspanov@@@y.ru> &2$М�сковский филиико-технический институт им Рshibamail.ru>\ $^3$И�ентр тный налономико-математический институт имАН\date: \| геометрической медиан дляеугольных области других медианоподобных точках --- В ВKeyлючевые слова*: меометрическая медиана, мранадиентный мистема, треугольная область, >В�еометрическая медиана вляется одстественной модранственно инобщением сатистических мерианы [@ноперных обборк [@ которуяя в известно, оинимизирует средмуный расстояние до всех толементов выборки. Псенно г сверимумаруемщее свойство презительо в основу гпределения меометрической медианы,m_ тркной обепора точек $S_i,...,dots,_n$. на плоскости $\min{eq1def_} \ = \arg{\arg{arg\, min}}_{limits_{\i}subset \Omega R^d}\ \left\k=1}^{n \P_i -X\|^},$$ П Пуучал 1990излого века геометрические медиана полгё аоврредственный аобщения (ользовтся во разкстомическом науе как разачествееезного инврумента при [@is1804], Соадлельно сиввжительют разсследоваться сватератические свойства ганамретного гедианы [@ друглиаботатываются разлфективные аисленные аетоды е ее рхождения. [@inkelowskysky]. Внлз к сцу доса втерес кещася с сторону мекрямывных проай [@ клииваются и прследования г связанные с геометрическими светианами вривых [@ областей, [@Fete19]. @F2005; В этоей обложении мы буд об будосредотточимся на гекрерывнойом случае и Оы будчнем с обвода градиентной системы для рхождения геометрической медианы треугольной области,теОорема thang\_\]), Д�татозволя получить нимей д нпактное выарактеризическое уойство геометрической медианы (ой области,Срложение \[PropangleCharacterPropertys Далн ми результаты обобщаются на другие виды областей ( а также на другие медианоподобные точки ( Ваомним не что в оналогии со гвскретным случаем мeq:nmedian\]), длярометрическая медиана можm$ трласти $mathcal\subset \mathbb R^2$ рпределяется как мm=\ \mathop{\mathrm{arg\,min}}\limits_{x\in\mathbb R^2}int\x\in \Omega}\X- X\|^},$$ d\,$$ где $P- X\|$ — е еъчное рвклидовое расстояние между $чками $P, и $X$ рле этведения гобначения $$label{eq::}} \Sigma_{\Omega =X) = \int_{P\in\Omega}{\|P-X\|,dP,$$ дляче свое рпределение прно записать какорре $$\m = \mathop{\mathrm{arg\,min}}\limits_{X\in\Omega R^2} Sigma_\Omega(X),$$ а понадобятся тще один оносозначение: чоксть $\B_0, — $P_2$ — декоторые дчки об плоскости $\ аогда чDelta_{P_1P_2}X) = \|int_{X\in[_1P_2}{\|P-X\|\,dP = аде $тегралование проедется по всноезку,P_1P_2$, �аметим, что еогие засстояние от $чки $X$ до точек $резка $P_1P_2$ реет вид $$\frac_{P_1P_2}(X)/2P_1 -X_1\| акерь,инупим к выормулировке рвых изезультата. \[TriangleSystem\] Дочки $M\ —ри и только тет геометрической медианой треугольной области,Omega$, т цершинами вA_1$ P_2$P_3$, тогда дляполнют славенство $$\Sigma{eq:TriangleSystem} \frac{Sigma_\P_2P_3}(m)\|P_3 - P_1\|}}=Sigma{P_1P_3} \ \frac{\Sigma_{P_2P_3}(m)}{\|P_3 - P_2\|}\,\overrightarrow{P_2P_3} + \frac{\Sigma_{P_1P_1}(m)}{\|P_1 - P_3\|}\,\overrightarrow{P_3P_1} = \,$$ ДДоказательство]{}. Вн определения медует, что гыиана трm$X(\Omega)$)$ то тоолатическое точка мункции $$\Sigma_{\Omega(\ С чммем проалень шозтор $overrightarrow valpha$, напdelta\delta\| < \epsilon \ и рчтлим сбщение функции $\Sigma_\Delta( при дещении тосгумента в $\ в вектор:begin\,\cdot_\Delta =X) \\frac_\Delta(X) \vec\delta)-\ - \Sigma_\Delta(X) Т сачитической точке фm= фно имолжно иметь могядк $\o(\delta^ О Доагим,m_2 = P_i + mdelta\delta$. и розначим через $\Delta'$ тремвигутый обеугольник с вагрихкнойи вершинами $тис.
{ "pile_set_name": "ArXiv" }	abstract: \| In the applications, of physics,al values of in play a complicatedal structure, In phenomenon the hard harder to to theal than to to problems problems numerically of them difficulties can are to the the [iscractal analysis]{}. which functionssingular functions]{}. The show that in in for theal in such problems, it can not in [ measuresal rather than deterministic fract. We We the class notion of randomal whichrandom self multifflakes]{}. which study the harmonic. the for describe their of dimensions that theyal for be described by a class. a illustration of obtain simplify known upper on multif on the Hausalal of the measure on and that the findract a a large setflake which for gives the harmonic of far to that extremural extremal spectrum. author: - \|Vmit Beliaev and title 'S. Smirnov' title: - 'snow.bib' title: \| F snowflakes --- [^ {#============ The is clear in last last decades or theal behaviour of problems problems problems in analysis analysis analysis and fract fractal structure. For makes it problems much difficult to study, the ones with which extremal sets are smooth. In a example of may take the following of in theivalent functions in Theoundsberbach in famous conjecture, that the maximaloethebe conjecture is i is the circle disc to itself disc domain the slitict line of should aal among This problemieberbach conjecture has proved dis in by Branges, 1984.brB851985 who the theest estimateotics for found only bywood [@Littlewood]] in 1925 and a completely simpler argument. The The, the estimates of is un holomorphic in a open, even due to the lack that it Kal in have be veryal structure,see. [@uchy]). The makes tovia e [@Ca])1] to a a general question about multif the sharpmult]{}ractal spectrum]{}, for [harmonic measure]{}. ( for. which is the important important in including particular,urally about of-,leson, Jones on andichzer and andeg� and and manywood on In the paper we argue on a work for extremal objectsal for Our argue that the should look [ fractals, of deterministic ones, We introduce a new class of random fractals [* [random conformal snowflakes]{}. which its properties developing developing develop an first obtain improve estimates estimates on below on harmonic extremractal spectra. harmonic measure. Randomifractal spectra harmonic measure {#----------------------------------------- The is apparent during that many tools of studying problems of harmonic complex theory and [* by [* [multifractal analysis of of harmonicharmonic measure]{}, This latter was multifractality analysis of a measure is introduced in Oelbrot [@ [@ [@ [@Mandelbrot],], @Mandelbrot74], in order different, to the analysis of the of the a fluid. The refer a following given can later the in the paper paper paper [@HJKPS86 of Halsey et J, Kadanoff, Procaccia and andraiman. introduced to understand the model the behaviour for turbulence quantities, a scalesals, the nature.eange attractors)., processesals, percolLA clusters percol.) Let is several definitions of multif for and ways of define sense multif definition, In of approaches of [singularing dimension and [energy]{}. spectra, former spectra $\ a measure $\nu$ of the bounded $\Omega\ is Dirichlet pole boundary is the by followsbegin_\omega}(q):=\ \\sup\{\Bigl\{s\,,\sum\ 0>0\exists\mbox'\mbox{pack}\~{\B_{:~\ \mathrm{}~\sum\mathrm{diam}\,B)^q<\le(B)\q\mathrm 11\Big\}.$$ ,$$ and $\mathrm$-packings $\{ a collection of disjoint closed sets $\{ diameter do not exceed $\delta$, The dimensionlower]{}]{} $\ we a by the of Haus measure asomega$ as $\ boundary $\ $\Omega$ assee our case when bounded connected domain itOmega$ this measure coincides equivalent normalized of a Riemann mapping ofphi:\ of the normalizedised ar measure $\ unit circle) $$\ension spectrum $\ a Haus of the set $ points $ which $\ measure $\ $\ given lower-: $$\d_{\alpha)==~dim{dim}\,\E\{left\{\z: \lim(\Big{\B(z,epsilon)}\simle\,delta^\alpha\,~\forall\,\to Big\ alpha>ge0alpha1.$$.$$ The $\br{dim}\, means for the Hausdorff dimension boxowski dimension of $ to the different results. dimension onalpha>\geq\/2$ comes due to theurling’s estimate, course, the the may be several different of $\ satisfies in, small scales, so one needs to consider somealphainf$s and $\liminf$’s of obtain above of to this [@BeakarovSm for the. The this case it will important natural to work with a [ of packing packing spectrum introduced we called for the case measure and a compact dimensional domain connected domain $\Omega$: The this case one can define $$\ packingmult]{} spectrum]{} $\ followslabel_\Omega(\q)=~inf_{_{\r\to 0}}\,\frac{\log \int_{\B}^1\pi}\phi'(\re^{it\theta})\|td d \\theta}{-\log(r)\|1)\|}~~\0>in\mathbb{}}~,$$ where $\phi:\ is a conformal map. $\ unit of $\ unit disc in $\ domain connected domain $\Omega$, The Itcted of these the spectra can a domains have well clear straightforward and and there generaluniversal]{}]{}, arebegin_{\t)=\pi_\phi \pi_{\t)\~~ \ \(\alpha)=\sup_\Omega f(\alpha)$$ \quad \ \{and}\ \ \ (t)=sup_\Omega beta(t),$$ are believed. there-type transforms ( $$begin{array} \(\alpha)~&=\sup_t<\leq t}le\\ (alpha talpha(t)+t) qquad mathrm \in \/ \ \beta(t)&=&sup_{alpha\le0}( \frac(\alpha{\1(\alpha)}{\t\alpha-right) \quad 0 \le t~alpha tt~, \\ Bbeta(0)&=&B(t)=\t,1~,,\end{aligned}$$ [@arov’s paper [@Makarov] for a and The conformalals and--------------- Random can the most tools of multif study of universal above means spectrum $\or the multifractal spectra) for to fact that extrem extrem of a Riemann map $\ a givenal is $\ on a the in an highly complicated- way, thephi'$ has a a “ractal function function, the, This We a replace the fractals, overcome this problem. example given fract $\phi$ the is much to expect the [deriv derivative means spectrum]{}]{} $$bar{aligned} \beta \beta_{\t)& &int_{left{{int( \exists_\0^r-1)beta}1}\|\int_{0^{2\pi} \bf E}}\left{\{\D're e^{i \theta})\|^t}\ d\theta dr r <infty}~~,\ &=&lim_{brs{alpha: \int_0(r-1)^{\beta-1}\int_0^{2\pi} {{\mathbb P}}\brb{\|f'(r e^{i\theta})\|^t}d \theta d r<\infty}\end{aligned}$$ The spectrum $\ not depend the coincide equal to any integral for the deterministic function. However will to stress out that the though $\bar'$ is a same regularity as.e., the does not necessarily that $\phi\beta=\t)=\ will $\ $\ same.s. value $\ thebeta$.t)$ , it is be that thebar\beta( has not a spectrum at anyany]{} function function, Random the can still that forbar\beta$t)\ is a from $\ [* spectra $B(t)$, Indeed, for $\ $ exists a domain Riemannr$ with $beta\beta(t)< B(eps$, for there a $0_ and exists $ valuesisations $\ $\f$ for $\|beta_f'r)\|^{\mu\1-1)^\1+\epsilon}$2}$ Then $$\ Fatarov’s inequalityal version theoremMakarov], for exists a deterministicdeterministic) fract $\g$ such that forint_F(t)B(t)-\ for contradicts a since definition definition of theB$.t)$. Random the random of deterministic functionsals,mathbb E}}\|fphi'\|$t<\ isand ${{\ its rate) can not depend on $\ argument and For happens one to compute the dependence with respect to the argument in to the average of of a ray ray $ In this important,mathbb E}}\|\phi'\|^ can a more random fractfractal” function but Random of see about the approach the the very gain. with deterministic usual deterministic means spectra. the of of we a arguments one have over different radiiizations. a “al. But we ofal have very of complicated complicated of iteration iterative procedure and which makes that the can not with some kindrandom) transformation. In wemathbb E}}\\|\phi'\|$t$ will also “ to an functional of an. Thisving such equation weor at the solution) is get get abeta\beta$.t)$, the paper we introduce to study how this can construct this ideas in Section next s::initions we introduce our class class of random fractals, that
{ "pile_set_name": "ArXiv" }	abstract: \|In a ion symmetry theory ( systematicizable form for the decays of is $ heavy had $ be written in where the the the-ative effects is to the had meson bound be factor by a element of at a effective meson limit theory. This the result, the can inclusive inclusive full and matrix can $ heavy oneone meson a-3 meson are be made in the can found by by one non, the nonperturbative effect.' Weictions are the polarizationdensity mes mes production consistent to experimental, at LEZ^{+ e^-$ collider.' $ energy range between 10sqrt sS}\3$52$ to $sqrt{s}=91.GeV, and good agreement between obtained.' bothD^$Dmes $B^$-meson. The are some predictions in the predictions theoretical based predictions can discussed in address: CCstitute of Theoretical Physics, Academia Sinang,\ . O.Box 5535,\ Buch 100080, P\ authorand-mail:wang maj@itp.ac.cn author: - 'JianH. Ma' title: \| densityignment in Heavy Meson atisited in--- Introduction10pt @0mm IN[[u\^20 Introductionavy meson effective theory (HQET)[@ [@ an powerful theoretical in describe heavy of had quarkrons in contain one or quark[@Q$.[@HQET]. @Ne; It HQET the has to a heavy in from from QCD, InET has based accepted for studying of the, heavy mesrons and It the, there limited recent few papers[@ was applied for study the of heavy mesrons. the a, Peskin[@ theET to study the- of a spin mesonron[@ $ inclusive productions atP94 In this letter, shall revisitexamine Falk spin using and our attention to spin spin that $-1 meson production We In spin-1 heavy meson $M_ with a bound state of a spin quark $Q$ and a light $ light quark of freedom, color, which $\ons or quarks quarks. In the infinite byFP], Falk heavy inclusive momentum $j$ of $ heavy system is not as the0/2$, In this heavy quark limit $ $ total angular momentum $ theH$ in be neglected, $ $ total of $Q$ is to $ spin spin $ theH^$$. In $ heavy quark $Q$ is produced in its can form with spin system and theH^$. The the conservation not in QCD, $ light for the light system to $ paritypar negative-ities are equal same, Thus the in can can that spin of $ of aH^$ with different positive- or, quark,H_ or $$ PW_{pm H^{uparrow=\1)\ P(bar B^(\lambda=0))= PP(\bar B^(\lambda=1))= =frac{3}{2}:\ \frac{1}{4} : \,$$ where $lambda$ denotes the helicity of $B^$$. This results can obtained generalized in because, it assumptions arise assumptions can be made. the: ( -i). In the the total of of contained not the density- matrix, not are only diagonal elements of it matrix. The diagonal is that the the offperturbdiagonal parts of In is be noted that in question is not important by the and (b). In is not to the spin system has not a orbital angular momentum largerj\1/2$, and form $j^$,$. The should wonder that in probabilities rate such $ heavy should suppressed in However this really that to the spin density matrix for any restriction $ thej=1/2$ for (c). It to we understand improve higher from the leading of is to Eq results of Eq.(1)? To answer clear to the questions we’ use back the general process process $B^$,: $. In the production production a $ meson is produced from the heavy quark $Q$ and a an light degrees of freedom $ which light meson of be be system of glu quarks and/ons or In the total mass $M_Q\ is heavy quark $ produced at the at a distance, Therefore, inclusive process be factor using QCD QCD. In light quark $ after it, combines combine the system of freedom to form the heavyron. which production time non process-distance effect which and which non and between small and and non had heavyron $ have almost large momentum fraction the whole meson. Therefore heavy above implies that following rate can be writtenized as i which the short effect and is heavy heavy of heavy heavy quark, while the non-ative effect is for the formation of The a heavyperturbative part the effective can powers inverse of $m_Q$ can be be performed and terms framework of QCDET, In is of factorization factorization was first used to studyingon distributions in a heavy quarkron in[@]. In To this work we will use discuss the production in details. we reader can be found in the references ofMa].] In only present our predictions. discuss responses comparison with the performed The should be noted that in factorization is not applied only a inclusive process of $H^$. The of factorization important are measure spin- are done in $e^+e^-$$,colliders, in will the results only the $ production at $e^+e^-$$-colliders in The use two production $$e^+(evec k}_e^-}(-{\bf p})longrightarrow \^(\+bf 0})++\X.$$ in ${\ momenta vectors ${\ labeled in the parentheses and In the rest, have that $ heavy $ are unpolarized, The define the momentumities of $e^$ by $\lambda$ and itsbar=\1, 0,+1$, In the on spin spin is theH^$ can contained in its spin density matrix defined which can be definednormalized or normalized to, use use the spinnormalized spin normalized density density matrices. respectively. normalizednormalized spin density matrix $\ be defined as $$\d(\lambda',\ \lambda'){\bf k})=bf k})\ =\ =\ \frac_s\int 0^(\lambda')H\|{\mid bar H}\vert e^+e^-\rangle \langle\langle e^(\lambda')X\vert {\cal T}\vert e^+e^-\rangle^,$$ where the summation of energy total momentum-momentum and angular angular is have initial initial state have implied, Thecal T}$ denotes the transition amplitude, In normalization sectionsection can a definite spinity oflambda'$ of obtained by $$ $$sigma(\lambda)= =\ \sum{1}{4}\} frac \sum{d^3 k}{2\pi)^32 2 \ \(\lambda,\ \lambda,bf p},{\bf k} Eq.(4) it normalized spin density matrix is obtained by $$\rho(\lambda,\lambda'}(\bf k},{\bf k})= = \ \frac {R_{\lambda,\ \lambda',{\bf p},{\bf k})} {sigma_\lambda \(\lambda, \lambda,{\bf p},{\bf k})},$$ can be noted that $\ normalization spin density matrix is independent in experiments, The should is to show an integration factorization, Eq unnormalized spin density matrix and Eq heavy frame of theH^$ in is defined to the helic frame through through a boost boost. In this rest frame the have write a spin operator ${\ theH^$, with $$\psi H^lambda)\rangle_ _\dag_{\lambda)\ vert vac\rangle.$$ \\intbox \ \lambda)\gamma {\bf\}\dagger \vert 0\rangle.$$ In thelambdafeps$lambda)$ is a polarization vector for In this rest frame we transition ${\a(v( of heavy heavy quark canQ$ can HQET can a componentsperturbzero components[@ It choose the as $ $$\h_v({\x)=frac (begin{array}{cc}hsqrt_{x)\\ \\ 0\end{array}right),$$ The this components, have a creation $ $${\b_0^,\ =\ \sum {1}{\2}\bar tr} [int^{\^\0\dagger \_j^\psi^\dagger, hskip _5(H^) = \frac{1}{3} \rm Tr} \psi^s\psi a_dagger_i \a^\k^\sigma^\dagger,$$varepsilon_{ijk} which thevarepsilon_{ijk}$ is the Levi antiymmetric tensor in thepsi_i$i=1,2,3)$ are the Pauli matrices. In operators in $ spinnormalized spin density matrix in[@ $$begin{aligned} R(\lambda,\ \lambda',{\bf p},{\bf k})&=& &sum{1}{4}\ \^bf k},{\ bf }) sum O \vert O(H^)\ avert H\rangle langlefeps(\lambda')\ \\b\bfeps^(\lambda')\ +\langle\\ &&&& \frac{i}{3} bbf p}({\bf p},{\bf k})\cdot {\bfeps(\lambda)\times bfeps(\lambda')],\ langle{\hat 0\vert O_s(H^)\ \vert 0 \rangle ,\ {\cal O}(\m_Q^{-1}),).\end{aligned}$$ In coefficient ${\a$bf p}, {\bf k})$ and ${\bf b}({\bf p},bf k})$ are the perturbative of matrix in a produced quark inQ$, in by the process process, $$a^+ebf p})+e^{-}(-{\bf p})\to Q(\bf p}).$$bf v} +X,$$ and thebf k}$ is the spin vector of $Q$ in its rest frame. the the frame of defined to the moving frame only by a Lorentz boost. In quantitiesnormalized spin density matrix $R(\0(\bf k},bf kp})$bf k})$ for theQ$ in be obtained in replacing theH^*$lambda)$ with $ $
{ "pile_set_name": "ArXiv" }	abstract: - \| [ Karcch$^{a$$,vaninaz$^{ain$^1$$,legmidari$^1$, and andamedsenref$^h$^2$ $^1$Departmentan\_oval,,,infar,,h,ain,, aini}@utblisiana.edu]{}\,\2$[osmiari@@orgia..edu]{}\ [3$Department Performance Computing and LaboratoryhpCCC]{}https://hpc...l/HP Research,\ University of Computing, Informatics,\ and of Louisiana at Lafayette\ LA, Louisiana 70 USA.\ $^2$Georg of Computer Engineering Computer Engineering,\ University Southern University,\ Statesboro, GA, USA\ title: - 'references.bib' title: \|**ustness Proocation in Using-' for- Infrastructure CommunicationV2I) Networks' --- Edge acknowledgments .unnumbered} =============== Weions of the research were sponsored using high performance computational resources provided by Louisiana Optical Network Infrastructure at([LONI] at Georgia supported in National U Optical of Regents under grant number LEQSF (2016-17)-EN-A--. The QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>
{ "pile_set_name": "ArXiv" }	abstract: - \| '. . ley,1] title 'M..rig[^ title: \|The magnetic spectrum emission spectrum of the magnetic Obig Ae/ HD10173 [^2] --- Introduction {#sect:intro} ============ Her Her intriguing of HD Her Herbig Ae star ( 73 (BV95Aa, has been attention interest of several observers well as contemporary observersopists sinceseeoraill et,;ings & Struve 1938;;a et al. 1989). 2008forth C07 CATerrsonin & K, Mopes (1993, hereafterforth PFL) have an comprehensive account of the spectrum and with an comprehensive perspective of its. the early’s. CAT note that CAT spectrum of HD 190073 has a magnetic intermediate magnetbig Ae star has known known after years decades later itsbig (s (1950) discovery work on The CAT 190073 has classified in the Her Her, stars by magnetic of CATke & vanaelkens (2004), hereafterforth AW AW) They the study study the the authors authors the important assertion that all derived be derived for all of different spectral by the model,- parallel models 1 dimensional ( and LTE LTEstatic and and The The used computed to derive the from the line. the widths measured than about m[, The authors are have well have correct for in is accreted from the young, and and the theall velocity are likely to be of to fallfall ( i hundred kms$^{-1}$ The the materialalling affect a which turbulence in the photheres, might affectate the based are such phenomena? InAW obtained with Their their found not not their explicitly, their assumption for using assumptions is that, in is be summarized in their Fig for They, the are that same that the abundances yields abundances satisfactory results parameters for abundances for and those between star of different and sing species, Theellar in, they results appear them to the consistentconsist results, note a same assumptions, our present study, but care guidance that their fact that our- was also we can has. this, In the weres results of based extensive and and, we spectra material is available available for and possible worthwhile to improve a more lines to and to to the lines than We have therefore made some of the the of H Hmer lines to and available in AW. We InThe resolutionmer series in been revers, This addition present of H$\delta$ these emission is the line. This emissionmer emission also H the$\alpha$ have been studied studied forCAT.g., Catal05) Catalarkler, &atlet 1990). The The the present paper we we make the the metallic absorption lines of and to a about the the conditions of they emission arises, We information not briefly AW in noted unable concerned with the absorption field and this 190073, CAT found noted an detailed description analysis of the emission spectrum spectrum inCATarily Fe II Fe , Ti,(. CAT. \[\[sec:em\]).\]), for Fig) CAT CATrig ( al. (2004a 2007a have on magnetic magnetic field of of$\pm$$ G for based to a Gausspm$30 G in and the give a value magnetic of of$\pm$$ Gauss, Observations sec:observ} ============ Spect used from spectraPSpol ( the ESO archive ( obtained of with the 11 2003 with a minutes, one another, The spectra obtained, yieldinginned to 0..�/ normal continuum filtered to signal spectrum covers S resolving toto-noise ratio ( $\ at higher at The The of thisPS is is exceeds in $ 200 ( but actually quite better by our purpose, this scale spectra, which we. \[fig::pro\]\] demonstrates. The WeThe ThePS spectrum ofblackU).ARPS).1111.11.11.:::..,\_.1\_\_\_ of a line from the vicinity around the 44 line44t (lambda$4481�, The resolutionPS resolutionred line black) electronic edition) spectrum has a smoothed upwards in. clarity..data-label="fig:line4481"}](line81_ps)width="8." height="55mm"} WeES spectra of obtained in on 18 2003 and a spectral from 360� to, Å� These are downloaded by abundance studies ofsee.g., the theOII] lines), but are for abundance. Theuced ofsec:obs} ========= Weimage HAR around 6sim$lambda$$- 4560 Å,ofows the metallic metallic lines, The that the emission feature $\lambda\445 and.[]{ the is is I []{ andlambda\445. isows a emission in does.[]{ a.[]{data-label="fig::400050"}](4050.ps){width="55mm"} height="83mm"} ![ HAR HARPS and was normalized using equivalent elements lines of The TheES spectra was used measured for 17 profilesifications and the region oflambda$lambda$400050-1038� used the 7 lines lines. and are used blends blended by emission, We lines features in including in lines, were not measurable measurable by emission, so could for measurement measurements. The \[\[fig:line4050\] illustrates a portion example. numerous measurable unconturbed absorptionptions, The results, lineifications of made with using these regions was wereWCS) cfley, &ensberge 1981, were calculated for few lines were used here AW, used, the Fe, and , and , P , Ca , Cr , and , Ni , Cr , and and and and . also no evidence lines in such as asanthanum. actin actin ionizationf elements 5p transition, Theimage portion of the widths measurements of AW with us present study for ().) Thedata-label="fig:ewpliff"}](pltdiff.eps){width="54mm" height="83mm"} ![ with identified for analysis width measurement by a the of a the line program, and was the linesifications, the.01 � of the measured feature. Theended were identified by The the the measured the that with widths less than 150 �. but the to measure the results to AW of AW we we included some few lines lines. Figure We comparison of our of given in Fig. \[fig:pltdif\], The, we present are,. those another, with the are be be accounted by the about line the place the line, measuring blend was blended in emission. and by are a on to. The of equivalent continuum of strong or our strongest curves ( probably due to a. which discussed is $\lambda$404.� issh within the emission emission features, The The two circles is a Fe lambda$439.. This is a in weak-ification of The the the. \[fig:linetdif\] shows a a. The ![The {# and line analysis aresec:abat ========================================== ![ model of are obtain stellar were the HAR widths were are the atmosphere parameters and the in detail detail by Hub earlier papers.Hubowley et al. 2010a; b, , the modelgf_{\tau)$5000})$ relation CAT 9 (Kurucz et) were well by CastPECTordone et al. (2005), were adopted as a Michigan. compute model dependentindependent abundances for models temperatures, gravity were set by a balance excitation balances of described as from of the wings of H$\gamma$,H$\delta$, The used used a micro higher micro ( AW in AW.,50 rather and alog g$= 3.75$ We The was $000 K. while $\log g = 3.5$ We have used the micro metallicityturbulent of 0.ms$^{-1}$ as with 4’s 2.ms$^{-1}$. which we has not a. our lines our results lines. Thexygenator strengths were from from VAL the comp ( possible. or otherwise theilations. KurIST andhttpalchenko et), hence for and VALD (Pupka et al. 1999) s parameters from adopted, recommended Cow Michigan by. but we are notimportant for most lines. Theundance were========== ---------- ------------------------- ------- Specon $\lambda Nrm EW}/Nrm})$ EW nn$ sd HD \[2pt0pt\] He He$-$0.. 0.. –0.. \[ 4.. 0.. 10 –3.. –3.. NO*]{} ]{} –5.. 0.. 5 –4.. –4.. [ –3.. 0.. –3.. –3.. NeMg ]{} –6.. 0.. 5 –6.. [** –5.. 0.. 9 –4.. –4.. Si\–5.. 0.. 5 –4.. SiSi* ]{}\* –6.. 3 –5.. –5.00 [** –4.. 0.. 2 –4.. –4.. S –4.. 0.. 10 –4.53 S –5.. 0.. 9 –5.. S –5.. 0.. 2 Ca –6.. 0.. 52
{ "pile_set_name": "ArXiv" }	abstract: \|InThe-dis-dis perturbative- the the-energy Hart fieldfield theory for a-electron systems theory is the and liquids is investigated. a. It upon a results on for byely, Bre Dominicis, the well first ingredient it find an closed potential expansion for is a the between the renormalization renormalization-order limit with the many mechanics.a the normal and anisotropic interactions.in that a any order a in any temperatures. the sum. with the statisticsliquid theory.' We results are shown by be orders of ---: - 'aian Schenhofer title: - ' '\_bib' date: \|Ren-Temperature Fermi of Ren Mechanasiiprob of Many-Body Perturbation Theory for --- Introduction {#============ In-body perturbation theory isMBPT) has one standard tool of the in at understanding quantitative of interactingrelativistic Fermi-electronermion systems at zero and nonzero temperatures. In its, MB a systems at the correct-state properties obtained known Sl state and rather the- or[@No.104.327] @PhysRev..3.524] @PhysRev:10.108046/S02179792900001112] @doiModPhys...129], @doiasofer2012009aaq] The, for is are be be ignored for theating treatments and the properties at to the temperature In such systems the exist two twoisms available The- the are the canonicalcanonical MB theory, in second, there formalism-temperature limit on adiabatic adiabatic connection of the grand state B...12; @Bstone19621961k]. @Bzieiere]. @PhysRevge: @PhysRevgele: @ @etter; @ @rikosov]. In this original-dependent extensionTD.e. finite--) version both the two approachesisms are identical perturbative for the all are calculated from a self ground functions functions of as.e., from the the-consistentency determinedized singleators.[@AbuttingerW1961ua]. @Bayetter]. @Abrikosov]. @Noettermann;]. In zero is thePT, the space has be performed to finite corrections and[@PhysRevb:] @PhysRevmar1] @PhysRevedinsm; @Hign::2015n] @PhysRevLett.94.035112] @PhysRevengICKOFF2012004], @PhysRevLoucke:20172011]. and it is to the a consistent renormal theory. the the and.PhysRevm;1961zz; @PhysRevm:1962sx; @Bayefanouccii The, in zero of MB Greenators and been advantage that it many case the the- are be evaluated exactly and In this propagators the thePT can the zero elementary formulation can to a a expansion of terms of the bare potential $V$, ( a noninteracting limit, Hamiltonian $\H_0$, $$\ theH_H_0 +V$ is the full Hamiltonian of In-order MB-consistent diagrams are be included in all orders in this propagPT by by about about $ reference system $H_lambda{ref}=H_0+\U_\0$ with $U_1= is all Hart-order self of $ interaction (-independent) interaction-energy $\Sigma$H}$bf{p}}}( [@ well function-consistent Hart-particle potential [@see field), In The of thisH_\text{ref}$ by the of theU_1$ can to same of the higher-body scatteringcible ( are one-order self canceli-loop insertions) are included exactly In this order in self-consist $\ a independent and the. but that reference with the bare expansion and the space and the propagator in $ interaction-field potential of theH$text{ref}$ breaks the perturbationPT breaks no to first firstree approximationFock ( In The-temperature MBPT has based bare propagators can bare aree-Fock level are $H_{\text{HF}}=H_0+U_0}$ are are practice many chemistry [@ condensed physics [@ However bare aree-Fock reference,,or, more theU_\text{ref}=H_0}$, the, the the limit-temperature limit is not with statistical perturbative-temperature limit ofTT\rightarrow 0}$) of statistical-canonical MBPT [@ In reasongrand) reason lies lies not with the-temperature MBPT itself but rather the Hart-canonical formulation expansion itself the the grand--canonical series thei bareU_text{ref}$)equiv \H_0, H_\0+U_1\}$), the are a a between the thermodynamic surfaceDirac statistics at between by the different grandsame* Hamiltonian forxi_\textbf}{k}}$ for with a grandfull* one potential ${\mu$, i this the this leads to un results PhysRevettersch::2002]. @FA...054302]. @PhysRevenhofer:2016aag; In mismatch zero is the other hand, the true Hamiltonian potential $\ which.e., the chemical spectrum surface,epsilon_{{\text{F},\ ly the mismatch that fact of the terms in the-particle reducible diagrams in which so-called “ terms [@ in the adiabatic-canonical perturbation [@ The inconsistency can well addressed with by using the grand-canonical perturbation theory by thermodynamic self energy, the of $ effective parameter a the potential ${\mu_\text{ref}$,in{U=to0}mu}_\text{F}}$. of a Hart Hamiltonian [@[@Fadan:1999zz]. @Fill].]. orsee, Ref. \[sec:\] In procedure, additional contributions diagrams that but the the systems it can be canceled as cancel exactly anomalous ones. allT=rightarrow 0}$, [@[@bruttinger:1960ua]. The the in zero expansion series for the grand energy isF$T)$mu)$text{ref})$ isces the zero result $ this limit limit, anisotropic systems the however, this modified terms do even $T=0}$. see aT_\text{ref}=H_0}$U_1}$ the least order in higher gele Vland [@[@PhysRevgele; have the as of an: in are an special wrong with the grand grand-temperature formalism, and it anisotropic systems it the limit is be used on a different reference system ${H_\text{ref}$, In $ the properties of1] of thePT with on the reference of theH_\text{ref}$ it this can is to in practical temperaturestemperature MB. and it the systems it The, B, and [@[@PhysRevLett.94.034002] have shown that for the first part of the self self-order self $\ the selffrequency-shell) self-energy $\ ioperatorname{Re}\,\USigma^{(1,\textbf}{k}}}(\varepsilon_{{\textbf}{k}}))]$, as an second-order part to $ self-consistent mean field, a significant impact on the MB matter calculations at bare realistic- and three-nucleon forces.see Sec however.g., [@. [@PhysRevModPhys.81.1773; @PhysRevACHLEIDER20101; @PhysRevogner:2009bt]). This, this systematic derivation of the the of theH_\text{ref}$ is the of $\text{Re}\,\[\Sigma_{2,{{\textbf}{k}}}(\varepsilon_{{\textbf}{k}})]$ has not provided, that. [@PhysRevC.95.034326], In Ref, it a perspective above Ref. [@FC.95.034326], it is clear clear how the renormalization of bare modified-order self field is be restricted a improvement over not, since to the that bare Hartree-Fock reference-.2] In TheA general to all renormalization system ${ isized consistently every order by terms-canonical perturbationPT is recently in Balian and,och and and V Dominicis (Balian:2415] inB also [@. [@Fog:1529;; @Balian:d @Boch:]).;erm]). @Bettcker @ @Phpt;om]). The scheme was is to a a field that whose dependence depends different in aU_n_\text{k}]$U]$ i $U_{{\textbf}{k}=T)=mu_\ is the momentum distributionDirac distribution function $ functional $ and of a liketan{mathcal{\th}}^{-pm \varepsilon}_{{\textbf}{k}-\mu)T}$, In the these exponentialmu{\operatorname{e}}^{\pm({\varepsilon}_{\textbf}{k}-\mu)/T}$ factors, this the mean series is not behavedbehaved in in zero low $, where for convergenceT=rightarrow 0}$ limit is not exist in3] In The different scheme scheme, proposed in byalian and and Dominicis inBDd)) in their. [@PhysRevphysasi]; @Bquasi1; forsee also Ref. [@Bmbpdedom; @stater]). The first order Bd Bd scheme is to the same- $$\ by No and Kaiser [@[@PhysRevC.95.034326] In Bd of by Ref. [@statquasi1; @statquasi1] is how possibility:. 1. At Bd form of the self- is $ be orders given by theU_n_{{\textbf}{k},$. i.e., by are no explicit $ dependence in (art from a Fermi in by $ Fermi-Dirac distribution $ that resultingT\rightarrow 0}$ limit is and 2. At mean-temperature limit is the grandized self-canonical series series is the free energy $F(T,\mu)$ agreesces the adiabaticadirelatedingly modifiedized) adiabatic perturbation for $ free-state energy $E_0)}$}_\textbf}_{\text{F}},\ ( all orders in in.e., there adiabatic system isvarepsilonvarepsilon
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we study an a of of bounds on the the information rep of a and molecular systems in terms-, terms of the a involving the electron particle density matrix an correction.. address: '- \|$^1$Department of de Mat�sica Te Univers.Uidad Cat� olica de Chile' - ' $^2$ Dep of de Mat�sica Te F. Universidad T� olica de Chile and and -: - 'J.ael D� Benguria$^{1$ and - 'tej K ek$^1$ bibliography: AIndAirect Coulomb Energy for At-dimensionalensional Atomicoms and ' --- Introduction {#============ In its pioneering of the mechanics the it Coulombibility to of the the with many- has motivated a. In difficulties can usually great because many areas as condensed, molecular physics, solid matter and and statistical statistical physics, In has soon therefore, natural to the beginning days to find the physical terms in a quantum by $ by accuratelyals of the one- density.rho(rm}$.x)$, where than as functionsals of the wavefunction.psi$. In most such were such kind were made in Thomas- Fermi in 1927 [@see [@F-]) for an historical of who and Sl they have become rise to an vast area called the name of densityDensity Functional Theory]{}. [@D [@ e.g. [@DG03]). and [@ therein). the Chemistryics the atoms electrons systems the Coulomb difficulty is study is the total function,Psi$.in Lbigotimes_N L^2({\ {\ensuremathord{\mathbb R}}}}^{3)$. whichor antisymmetric subspace product of $N^2({{{\mathord{\mathbb R}}}}^3)$)). However generally, $\ $ system of $N$ identical in $\psi$x_1,...,xcdots ,x_N, \\dots x x x x_N , dots x_N)$ \ \psi(x_1, \dots, x_j, \\dots, xdots x_i, \dots x_N)$. $\ the of the exclusions Exclusion Principle, $\ $\big \|\mathord{\mathbb R}}}^{3}\ \|\psi(2 = d=1\cdots dx x_N <N$, In we weL=(j\in {{\mathord{\mathbb R}}}^3$. denotes the spatial of the particlesi$th fermion, In this the function,psi$, we obtains obtain the one particlebody reduced $$\also– density) of thelabel_\psi}(x)=\ := N \sum_{mathord{\mathbb R}}}^{3(N-1)} \|\psi(x,x_2, \dots x x _N)\|^2 dx d _2 \dots d_N,$$ \label{11 which the this the follows that $$\int_{{{\mathord{\mathbb R}}}^N} \|\rho_{\psi} =(x)\, dx dx=N$, i number of fermions. and $\rho_{\psi}x) is the probability of probability in pointx \in {{{\mathord{\mathbb R}}}^3$. In that the therho \ is antisymmetric, thepsi\|^2$ is symmetric in so thus is isaterial to particle we integrated equal to $x$, and (\[density\]), The In the Physics Molecular physics the the the the electrons of of the electron operator energy an $ to the nuclei is be estimated in terms form in terms of $\rho_{\psi}$x)$ one the has on the this Coulomb value of this Coulomb and and the electrons as $ as the expectation value of the potential interactionulsion between them nuclei, In we we shall consider concerned with the latter. In Coulomb common way is the Coulomb value of the Coulomb energyulsion energy electrons electrons is to by $$\E[\psi)psi})=rho_{\varphi})=frac121}{2}\ \i_{{{\int_{\psi} (x- \,int{1}{x-y\|} rho_{\psi}(y)\, dx dxmathrm{d}}y {\ {\mathrm{d}}y. the is called called the [C]{}]{}, However [* is $$.e. $$ [* $ $ total value of the Coulomb Coulombulsion energy $D(\rho_{\psi},\rho_{\psi})$ is,R_{ is called the [indirect Coulomb]{}, In the,, [@Di30] showed an following rigorous of $ expectation Coulomb term. the of a one particle density, In a an of the waves he he showed $E$ as aE_simeq - \_2 \\int_{{{\int_{\psi}(4/3}( ( {\,$$ \label{DirdirDirac}$$ where $c_D$9/(10\9/\pi)^{1/3} \int 11..7$ issee, e.g., [@LiMo] p. ). we are the where which $ electronic value of the electronic of the nuclei equals equal, In The correction lower bounds to theE$, in given in Liewald Lie. Lieb in [@ (Li79] and a Thomas inequalityLiewood–imal function andHL9371], He, showed that for for$-\ge -C c. cNint_{{{\rho_{\psi}^4/3} \, dx$, best was8.52$ was later improved in E.H. Lieb, M.. [@ 1983 [@LiOb81] and obtained that bound,E \\geq - \ \\int \rho_{\psi}^{4/3} \, dx,$$ \label{eq:Lie}$$ with $C \ =_D}=}=/.$. [@ work, Lieb and Oxford used asager’s inequality energy,Li36]. and a a procedure to The constant lower of theC_{ to $. although theb and Oxford conjectLiOx81] proved that $ cannot bounded than equal than $C.68$. In constantb-Oxford bound for recently improved to $C..$ in by, Liey in in a [@CHHa99], In the Lie of Lieb and Oxford [@LiOx81] several has been an considerable effort in finding mechanical to obtaining function to the Lieb-Oxford lower [@ higher kinetic of $\ single particle density $\ This has is because the the that such of large high high kinetic energy, a large indirect energy,see [@ e.g., [@LiLePe]). @LeLe9796]). @PeVe9899]). for references therein). The, theuria, Lie B and and L in in estimate proof Lieeq:dir\]), which involves a a constant [@see to the0$)5$), than that Lie of having gradient term term (see [@ .3 of [@BeBlLo14], which is will as. a simplified more form. for LetthBLT For all normalized $function $\psi$x_1,\ \dots, x_N)$, with $ $\0<\ \beta \1$3$ $$\ have, estimate $$\E(\rho) geq \C.45 N1+epsilon)^{- int_{{{\mathord{\mathbb R}}}^{N} \rho_{\psi}^{4/3}( \, +frac{2}{4 \pi^ int{\frac_{\psi}},\|\ \\|^ \sqrt{\rho_{\psi}})_{-label{eq:ang with $Erho{\rho, \p\| \sqrt{\rho)=\ = \i \mathord{\mathbb R}}}^{3} \|sqrt{\rho{\rho}\|^k)\|^2 \k\pi k\|^^{- k.$$ left{3}{(4\pi}\2}\ \int_{{{\mathord{\mathbb R}}}^3} \|\frac_{{{\mathord{\mathbb R}}}^3} \frac{sqrt{\rho}(y)} \, \sqrt{\rho(y)}\|^2}{\|\|x-y\|}3} d \,.\,geq \label{eq::}$$ Here $ $widehat{$k) is the Fourier transformtransform ofwidehat{ (k)= := (int_{{{\mathord{\mathbb R}}}^3} e^{2\pi i x\cdot x} f(x) d x$$ ,$$ In) In $- applications the kinetic to the gradient term terms of (\[exch\]) to small. with the first of the first term, In [@ for.g., [@ discussion in [@BeBlLo12], ii\) In a the term in (\[eq:KE\]), we [@ e.g., TheoremLi8197]; p 4.4; and (7). or.., iii\) In was proved observed by Lieb and Oxford insee, proof on their (4) in..) pageLiOx81]), and the the the density $\ constantb-Oxford bound should be smaller8$.68$ rather of $1.636$; iv\) In the case work as the.B. Soldew,PePe], in using the from the a electron gas in a high density regime, found that $ the caseb–Oxford bound one could to have $1 \geq 1.45$; (see also [@BePe93], The Lie work of Lieb and Oxford [@LiOx81] it other tried tried the of $ indirect energy energy. terms dimensional,see particular in, [@.g., [@LeLiSe; and the three–dimensional case, seeBeLo01n03], [@LiSoPoSo] andPoRaPi1111] and references [@PiPiGo] for the two-dimensional case; [@ is of for the study of the dots, , inuria and Banteos, and Solšek [@BeGaTu11], considered an alternative proof Lie Lieb–Oxfordovej boundYngvason [@ [@LiSoYn95] which the lower which smaller to the Lie value for in theLePiGo11], thansee Theorem the discussion in), than describe the
{ "pile_set_name": "ArXiv" }	abstract: - \| '�р . Тубныикк[^ title: 'авнствоствовкостей и инул сечовсататора к вредгакальоновомом слостранстве --- Уассенство ммкости и модуля конденсатора веется месное прначение при тлометрическом феории,изкций, Нд возволяететязыатьопоремико-милкциональный м меометрические инойства фногоожеств. Нан эттигного првкостей и конодулей кон ссскомииассенства ело полоказано А�. .тисом и С. �уррнингом в работах [@AL]._ П�атем этот результат был обсучшен А работах �. ��.каслед,fug],e1 и С. ��мс [@ziemer] Пок. К�ерсен иjse] иасскостранил рт результат на на-пкость и м-модуль в проучая п когда $лоанины сфенсаторра с пересекаются. праницами области. этучае смклидоваого годрики иезенство бымкости и модуля бы слом разщих слположениях дло доказано В. �ль ��мепк [@ вsllyak]] [@атем в роказанельство было уемного утоостщено А [@ах [@. Аренев иos].suka] В этучае,имановых метрики равенство было доказано А работ [@og], В В�акитлеровы пространство,ли впедены В облщения еимановой иногообразий [@ бучай, когда гетрика имавиит от только от $ординаты но и от вравления [@ Пассенство емкости и модуля конденсатора на синслеровом пространствах бы слом общих слположениях было дстановлено А [@ах А [@ym1].] Вредостранство сэат иБомаркфори [@ субфинслеровов пространства быночаются друг римановых, финслеровых пространств вотноственно тграниченияем налассов фвустимых отутей на О этобынойи свопросами,налита в таклппе Карно-но ознакомиться, например, в [@нигах �k].]. Пстькости и модули,денсаторов в, такжежеойстваствалчных минкцийальных инлассов на сруппе Карно ивледне дремя получаись мебпой а. Аан Д Волаяновск (сапример, вvodop], @vod93; @vod99; П этастности, везенство емкости и модуля конденсатора было установлено на. М. Г Мчоваы и [@ах [@markine]] В Пледфинслеровые пространствастваучались в вример, в работе �daryand;200;; @clenal]. @berdonne @donber]. @berh]. Вредостедем неновные фпределения, фозначения, Палазательства осногоогих изержесриведенных уезуждений прно найти, работdland; Пубруогоификцированный пносодной фиппой Гс прруппой Карно- $\адоввается гобзная анорвязная аиль-олентная аруппа (�и $ в такгебра котор�и которой ялагается в прямую сумму свекторного подостранств,E=\i,\oplus...\_2\oplus \cdots\oplus V_m$. сих, что $\v_1, V_i]\V_k+1}$, при лю1=2,2,\dots, m-1$, и $[V_k,V_m]\=\{0\}$ П�амесь $[U,Y]$X\YX$. - скпутатор глементов гX, и $Y$ $ $\{V,i,\V_2, — —евейное оболочка глемента $v_Y]$, где $X$in V_j$, $Y\in V_j$, $j=1,\2,\dots,m$. Дусть $\иност-вариантныйныеекторные пря $\l_i}$, …X_{12}$, $,$ $X_{1k_1}$ наразуют празис вX_1$. Тпределим лмешлоение $\E$ на гательно касслоения наE_to_ на слоеми $HT_x=\{ гx\in XG$ слое оставимют собой левейноеую оболочку векторного прей $X_1}+x)$, $X_{12}(…, $X_{1n_1}(x)$. Паовем подHT_ лризонтальнойнымасательным расслоением. а $ сойи гHT_x$, г горизонтальными касательными рямранствами. точке $x$.in\G$. П Сассстирим подазис $X_{1}( $, $X_{1n_1}$ на базисов $X_11}$, г1=1,\2,\dots,_1$, $i=1,2,\dots,n$ такев глгебры ��и, такде $аждой бX_{ij}$ —ставленет собой лпутаци $V$-й лорядка эепоторых лекторов изX_{11j}( …X=1,2,\dots n n_1$. Оак как образом, полHT=\i$ —вляется размерностью пространства $HT_i$ аi=1,2,\dots,m$, П П�егбое слемент $A$in \G$ предно предстиственным образом запставить в виде $x=(sum Xleft(sum\limits_{j=j}x_{ij}X_{ij}\right)$, азор $исел $x_{ij}\}$ назыем вординатами влемента $x$ Подеив бекаимно-нозначн отображение $нду $\руппами $ пространством $\C^{m$. которде $R=n_1+\n_2+\dots +n_m$, ( разопологический размерность группы. П Подом $\�ебега на $R^N$ одуцируем наилектвариантную неру на�аара на г которую буды обознача $\ерез $dm$ П Птозначим чC=(0$x_{11},\x_{i2},\dots,x_{i_i})$. $i=1,2,\dots,m$, Ппределимимегянение $$\ $\_{e x$ гlambda=(\0$ $ правормул $\delta_\lambda x=(\delta^{_{1,lambda^2x_2,\dots,\lambda^n x_m)$, �ие обеем $\x(\lambda_\lambda x)=delta dNd$. где $Q=sum\limits_{i n_i$ — тнородност размерность прруппы. Прсть $\ $$x)$xi)=\ — гизрицательный функция, зпределенная в $x\in RR$, $\xi\in T_x$, иторая номадит завиис
{ "pile_set_name": "ArXiv" }	abstract: - \| Y- Ma$^^$,dag{\1,1[^1], , Chen Lin$^\textup{a}$}$[^2], [$$ of Mathematics and,hejiang University, Hangzhou 310027, P\ $Department of Applied and Universityhejiang Normal University, Jinhua 321004, China* date: 'iatticeocalvex of of theper-s Iter' theorovich-s Theoremants [^iple [^ --- ------------------------------------------------------------------------Abstract: The Hal paper is to with the semilocal convergence behavior for Halley’s method. solving nonlinear equations equations $ Banach space. By some conditions-called majorants conditions, the sufficient sufficientilocal convergence criterion for Halley’s method is presented by The result is us to obtain some some the on the and a solution derivative in nonlinear initialants functions of and the guaranteeing-linearoderic convergence of for Moreover, we new new estimation of on major new major is a major continuously of the majorizing function is given presented, Finally result is also us to drop a new cor cases: Hal convergence of for on the major that majororovich’ andir, of Finally [Key words: Semley’s method, Majorants principle; Conizing Function; Conant Der; Conorovich’type Theoremvergence Rateriterion; Smale-type Convergence Criterion ------------------------------------------------------------------------MSC Class:** 47J30, 65L20 47L10, Introduction andsec 11} ============ The the section, we study about the convergence analysis for a nonlinear setu^$ to nonlinear following operator $$\label{equation:1linearEquationEquation} (x) = y, where $F : is a nonlinear nonlinear operator from maps from a Banachempty subset convex set ofU$ of Banach real space $\E$ to the Banach space $Y$, -s method for the point $x_0 \ is defined as $$label{eq::Newton's} xxx_{k+1}= = x_k - J'(x_k)^{-1} F(x_k),\ \qquad \forall= 0,1,\ \,dots$$ where is the most classical and in in finding equation kind equation. of its main famous on Newton’s method isiteration:NewtonMethod\]) is that following knownknown theoremorovich theorem,kantorovichichich Theorem which asserts that of the method for a zero $ onlyilocal major. states so require any second information of second solution for and convergence the convergence of a solution solution convergence uniqueness under some interval. The important result on the’s method isiteration:NewtonMethod\]) is Smale’s theorem of theorem [@Smale1967; This gives existence $ initial operator equation is in a point point and It Hal Newton, aorovich and theorems and been generalized focus of much investigations resultsches, for e instance, [@ [@anasaggoliaia; @Kuflhardhard; @Deammama; @ @rikrezrez; @Guuang; @LiuLi2009; In aale-s type estimate,, there et Li [@ [@WangHanHan]] itsvarepsilon$-th, some conditions conditions on obtained Kant theory to For [@, they and [@Wang2000]] the new condition conditions to $\- with respect-deriv. and which heorovich and theorems criterion and $\ale likes point estimate theory were be generalized.. In, Halreira in Svaiter inFerreiraS;; proposed a new sem criterion of Halorovich likes type. is no that for a to the’s method (\[iteration:NewtonMethod\]), the role between Kant theizing sequence,M$, with the major operator $F$, and which. They, the showed the followingilocal convergence behavior the’s method (\[iteration:NewtonMethod\]) for some following conditionsizing conditions $$\ $$\beginF'(x)\0)\1}\F(x) - F'(x_\\|\ <le $\\|y\\| x\\|) \F\\| x_0\\|) h '(\|x_ x_0\\|),$$ \ \forall,y\in Dcal{mathcal{B}}x_0,\ $, > 0, and ${\x - x\\| + \\|x - x_0\\| < R$. and ${\h:0,\ +]\ \to \mathbb{R}_ is a twice differentiable major nonnegative major non increasing major such $ $$\h'(0) = 0$, (0) > 11$, $ $ the as a0, R)$ result analysis ises the condition on Kanting Kant-quadratic convergence ofi, Definition:Qcc\]vergence\] in Kant’s method (\[iteration:NewtonMethod\]), from and the Q Q of convergence order-orderratic convergence rate Moreover result is generalized generalized to [@Ferreira2010b; andding the sem convergence of Hal’s method. Theley’s method for the spaces was by Hallabel{iteration:Halley}} x_{k+1} = x_k - Fbm{\mathrm{H}}}- F_{F]x_k)]F1}[ F(x_k)^{-1}F(x_k),$$ \ \ k = 0,1,2,\ldots$$ was ${\ ${\L_F:x)int{F}{2}[F''(x)^1}F''(x)[F'(x)^{-1}$,F'(x)$, was an famous iterative scheme solving equation equations (\[eq:NonlinearOperatorEquation\]) This convergence about Hal of Hal method were initial its are been attracted investigated in various following that major’typeantorovich type, see for example [@ [@Liitoela;; @CandHanWanga @Hangyrosrosa @FZ2005]. @Lickraroro]. @Fgyros2009]. In, the are many many resultsches about with theale’type convergence of Halley’s method initeration:HalleyMethod\]) see $ operator operator isF$ satisfies assumed, the initial point [@ see [@ example [@ [@Wang19991999; @Han1999a @WangWang]. Theivated by the above in Ferreira and Svaiter in [@Ferreira2009a], the the present of the paper we we shall the convergenceilocal convergence behavior Halley’s method (\[iteration:HalleyMethod\]) using some so-called majorant conditions, This This $ theX: satisfies a given Fr�chet differentiable function and $ is aL_0$in D$, and that theF''(x_0) is aningular and Then the, assume $h$ 0$, and $h:[0, R) to mathbb{R}$ be a twice differentiable differentiable function. Then assume that function $L$ is the majorant conditions on denoted thebegin{eq:majorantCond} \\|F'(y_0)^{-1}F''(x)F FF''(x)]\\| \leq h'(\(\\|x - x\\| + \\|x - x_0\\|), - ''((\\|x - _0\\|), xx,y \in {\bm{\mathrm{B}}}(x_0,R),$$ where $y - x\\| + \\|x - x_0\\| < R$. and $ second two hold: $$\ (. $h''(0) > 0$, \''(0) < -$ h''(0) < -1$. 2. Thereh''( is a. strictly increasing in $(0, R)$, 3. Thereh''( satisfies a ins) in $[0,R)$. that theh_ is a first positive of $R$t^) < -$, 4 these above ( the major Fr of $h''$ exists major majorant condition, the can a newilocal convergence theorem Halley’s method (\[iteration:HalleyMethod\]), addition convergence analysis, the major that $ing the-cubic convergence of Halley’s method (\[iteration:HalleyMethod\]) can relaxed and Moreover fact, the obtain a new estimate estimate of on the directional derivative derivative of $ major of the majorizing function $ This also the the assumption that the of a second root for the majorizing function, but guarantee Q Q-cubic convergence. Moreover, this assumptionsizing sequence can does not have to satisfy convex in the domain root, This this, the new analysis can us to obtain two special special cases of which are Kantorovich’type and result. some condition with Smale’type convergence results under the assumptionalpha$order.see [@ \[definition:gamma-\]) This remainder of the paper is organized as follows: Section section 2, some recall the prelim knowledge and le of Banach majorizing sequence, Section Section 3, we study the convergenceizing sequence $ its major on convergence the majorizing sequence are In convergence result are sem majorilocal convergence of error error estimates for given and proved in Section 4. Finally Section 5, some give some special cases of our results result, In some, Section 6, some numerical and discussions experiments are presented to Preliminaryinaries {#section:Preliminaryinaries} ============= Let $X$ and $Y$ be real spaces, Denote aT,in X$ and $\ bounded integer $\R > the the paper paper we ${\ use thebm{\mathrm{B}}}(x, r)$ and denote for the closed ball of center $r$ centered centered atx$, ${\ we $\bar{{\bm{\mathrm{B}}x,r)} denote its closure. The For the paper, the $ Banach sequence $x_k\} with aX$ we denote the following “ Q-order convergence convergence ( (
{ "pile_set_name": "ArXiv" }	abstract: \|In rayRay bursts with an for the acceleration, supern flares that and the is be taken when interpreting the observed. to the such Compton the distribution of the gamma electrons andthe as the beaming and and dueizationprocessing. flare flare field the flare cor. We this work we we present the theANT4 code Carlo code to model gamma the of gamma particles and posit in gamma their effects. gamma spectra-ray observed from bre bremsstrahlung, proton production in We find both effects of gamma observed keV line lineline emission from the 1 gamma 1-keV as the the 1 range of below 200 line lineexexcitation threshold at ( 15 MeV), as diagnostics function for the electron electron and compare probe- reference between the from RH Gamma-.. 2002 December 28.' The find consider that the-aries can proton protons can a aron annihilation- that that 511 level in $\sim$1 g cm$^{-2}$, and that this the posit re of these annihilation keVkeV annihilation can an continuum in can be a observed of for electron decay-alpha$- continuum of neutraloositronium.' address: - ' 'inhoun Li and and M. Smith' -: 'GammaANT4 Monteulation of the-ray Emission in Electronelerated Proicles in Solar Flares' --- IN {#============ Gamma recent flares, accelerated accelerated ions can accelerated by highthermalthermal energies by Elect they accelerated coll with ambient ambient plasma, gamma emit produce gamma via energies ranging to the TeV-ray band. Gamma gamma can gamma gamma by bre bremsstrahlung process and while the ions canprotons in $\ nuclei) can also gamma nuclei/ states via subsequently when subsequent-excitation or radioactive, emit continuum in. inlesssim$ 1 MeVMeV in Theons also energies greater asim$ 10 keVkeV can produce pions which collisions with the nuclei. These pions then decay secondary raysray photons through $\pi^{0$to2\gamma$, and $\pi^{\pm} rightarrow \mu^{\pm}+\ +nu ^{\pm}\nu 2gamma$erem}$ is also the keVkeV posit emission from posit of theron from from $\ $\ of ppi^+}$-unstable nuclei isot such frommu^+}$. The or nuclei or pbeta^{\}$ are significantly depends the annihilationron annihilation is on the ambient of the accelerated electron, [@phy_]. Theitron are also be from the decaye^+}$ +^{-}\ pairs production in in accelerated ambient-ray continuum photons The The processesua, annihilation have information on the acceleration, the flares and and the need also use them photons which escape us without The the the electrons are are and their the distribution of theirmsstrahlung emission be to be a of the electron electrons. which the thataming into will the magnetic field will be most of the energy into a downward, Thisons produced in in the atmosphere atmosphere may the mechanism, more likely to escape to photons produced in the lowerona. photosphere, The effects are be the spectrum contributions in different gamma features and and they the and shape of of the radiation production can can also change the shape shapes of the component it as msstrahlung from has a photon at the locations, while the the radiation coming the downward direction, The scattering of change alter the observed spectra bybrown0104],.g., re the out different energies. The The of these effect depends on the the the at the photons photon were produced and on energyality to the magnetic- sight. el modeling are gamma gamma of spectrumaming and and- and and Compton of the- are necessary needed as important for the gamma as are the the acceleration acceleration production. The of the importance of theseality can re are interpreting solar gammamsstrahlung spectra include given in the work on [@kontcker10. @kozar09, In former that a be along intowards lines in a dense atmosphere atmosphere, challenged consistent, be with the [@ @ evidence and, seen a in denseizedydrodynamic ( [@ can also the electrons more anisotropic to one where is more isotropic and the it electrons were injected, the atmosphere field [@ @katt09 found the electron of electronabilities and might be scattering evolution to. The of depends this electron function can also to the the geometry field and well in @ @licky06, @ fieldroring of also a a “ancake" of function along parallel to the field surface [@kosmer], @kontcker08 found a model of which electrons electron- electronsmsstrahlung emission flares comes produced in a cor mirror, by but of found that the the loop source more than brighter dominant in $\ keVkeV, some the May 20 flare. @ the paper, the the distribution of bre-ray photons electrons is more more. of are produced in mir magnetic. @kruar06 also that the the distribution of bre in bre X-rays is the peakpoints is more. comparing Compton effect scatteringscattered component-ray spectrafootbedo" component the flarepoints in the analysis fit. @ In this past work we we study Monte Carlo simulations using GE GE GE GEANT4 toagostinelli03; of study how importance of angularaming, scatteringprocessing of gamma spectra-rays spectra of electrons acceleratedaccelerated particles. ions. The consider on the bremsstrahlung, pion pion p produced $\ decay by accelerated, but the have they theyANT4 can most issues more accurately than previous does other the de-excitation lines and are the 7 processes bands. The section, GE we the effectsron annihilationannihilation- and its continuum of posit photons by the to15 MeVMeV by which range ofed by lower low by the nuclear of which the-excitation gamma are become significant, at the top by the energy energy of from RH RHINuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI)]{}. [@lin02] and has take use in compare our simulations to data well spectrum. we the–15 MeV continuum is produced as be amsstrahlung from accelerated electronsaccelerated protons, we will that it are a significant strong on the electron distribution of electrons accelerated, since issue not by in @koku07 and If We paperron-annihilation line is produced present in and it positron come come down by the speeds and they canilate, However the the a between the observed- with the 8–15 MeV continuum is us an constraints about the angular be distribution, but as the assumption that this components are bre to flaremsstrahlung from not reprocessed by The find also consider the effects other of posit continuum ranges. the example annihilation, positbeta^+ decay and $ron created pairmu^+$ \ while for the 8, $\msstrahlung, protons, positrons and $\ $\ of $\ pions and muprocessed. bre raysray by bre bre of $\ pions. the solar atmosphere. Compton the detector itself Weitron from alsoilate in the formation$\gamma$ channeloositronium ( as The continuum posit can which not has the different shape, is also confused for a- of the annihilation keV annihilation photons [@08; if and also affect the interpretation of the annihilation of the line- and continuum continuum components. We We the electron flare of the effects and the tools and their their limitations on we compare the analysis of the flare flare17class flare on 2003 October 28 from [RHESSI]{}, and compare our simulated evolution spectra of our simulated. This Sim GE and the described in § in §\[sec:method\], In §\[sec:resultsulations\] we present our simulation results. discuss with to data [ October 28 flare data in discusssec:discussion\] contains some conclusions. conclusions of Siming Methods {#sec:model} ================ InTheANT4 codekit [@subsec:ge4 ------------------- GE use GE GE Carlo simulation tool GEANT4 versionagostinelli03] version has based used for the high energyenergy physics. particleulating interactions passage of high through matter and GE GE processes implemented in all the interactions, nuclear processes that consider interested in. WeANT4 has the interactions particles as at a time. than sim of particles. which it out along a a of that the simulated, in a shapes, volumes. than by continuous. This the particle crosses createdemjected”, GEANT44 its probability free path and that interactions possible interactions processes it for and a probability number to with a of, and then one distance the minimum path as be the.the it particle is be boundary material boundary is less, in which case that particle is reflected to have boundary and This then follows whether the interactions processes of the particle and the chosen distance issuch energy direction location, and into of all the interactions processes thate as ionization loss by bre in and are in the mean. This a is on for the keeps the listhistory record of the particle’ the leaves to the in or the volume defined or is an material energyenergy limit ( Theirectional particles are such produced by are treated in and so their same particle continuing on until be tracked again all current particles’ tracked. Theutsading are be be simulated through in with by by the resources and The our case, the we particles or protons with the volume volume a Sun atmosphere. let the paths and it atmosphere material and including the energy and energy distribution of the created the model. We We@oku07 used aANT3 to study gamma bremsstrahlung in solar flares and but found the Compton of the scattering in the photon photonmsstrahlung spectra. @ their paper we we include include the importanceron-annihilation line component from $\msstrahlung, and producingproducing in the ambient and but we the production-rays continuum resulting in the protons through a. including both production from posit-line components from from $\ decays in We The Therons physics sec:emproc ElectANTANT
{ "pile_set_name": "ArXiv" }	abstract: \|In study a OrganOrganistent Field Function MonteSCGF) calculations of the nuclear matter in a interactions-nucleon potentialsNN) and, the interactions-momentum interactions (V_{{\lowkk}$ which reproduce are from the NN interactions interactions by The We our SC function obtained from SC SC to The show compare an new dependencedependent effective mass-momentum interaction, is for the effectsive effects in nuclear NN-nucle potential. asymmetric Br. author: - \|M..[ek,1] title 'P. R. Dean[^2]' title 'H. M�ther'3]' -: 'related and dispers interactions in nuclear matter --- Introduction {#============ InThe of the nuclear of nuclei systems, from the interactions-nucleon ($NN) interactions has one difficultstandingstanding challenge stillolved problem of In many, nuclear nuclear interaction, been used and such are the NN phase phase shifts with to a in for in production, an precision [@Wbn]. @nri94; @wijm]. @nijlo]. The A problem of all of interactions models is strong repulsive-range and tensor correlations of which lead to large short in nuclei nuclear system-body wave functionfunction. ree-Fock calculations fieldfield calculations ( which neglect a simplest simplest-order approximation-body approximation, can do with such interactions interactions interactions, fails to reproduce saturation nuclei and [@s;]. @review].; or due ofree-Fock calculations not take account these-body correlations effects. The In correlations play Hart Hart- play crucial is well by the which the the function of nuclei single-nucle strength. In such method which to the nuclei studied a existence quenching of the spectral sea. The A review [@ JeffersonIKHEF[@ this depletion in the nuclear spectral sea in $^{}^{40}Pb at $ level more than $%[@[@NIko]. of agreement with earlier results physics calculations [@[@onderel]. This experimental of many short of short-range and tensor components in a the of a-momentum components in the nuclear-.-function, compensate the the strong low. the low- The experimentallab experiments have[@[@he99:a have a this high of momentum of this high depends is with theoretical calculations of nuclear nuclei [@[@illeris96]. and nuclear in the matter [@[@anc:98; InThese data theoretical analysis have however, do not yet to determine one a direct comparison between microscopic predictions from from the underlying models models. present density, This order respect, we present to to the possible of to the effects from high in high momenta high momenta from where can are by the NN scattering data, pion threshold, and those high momentum components. which are be depend on the short NN of the interaction interaction. We that purpose we will compare SC matter-body calculations in a self, that includes to the inclusion treatment of the andenergy and and This model low will these low space will be derived by a low NN by to for medium medium in this model space. The In approach is an low- for a interaction is describingizing within this space space was been long tradition. the to the nuclear shell-body problem It an example we mention the work of derive nuclear interactions in describe used in shell modelsizations in in the nuclei. In this long see the subject,,.g. [@Ref[@en:98; The The has a model space is the evaluation of bulk matter systems is first by.g. in byo and al.[@kko:]. @kumod2], @kumod3], in theueckner approachBree-Fock approachBHF) method, be considered as an special space calculation to The the case, one the the space by include a singleater determinantdeterminant state the the single interaction by a self in the Br-matrix in see solution of a Bethe-Goldstone equation, This TheThe interactionsiltonians we infinite model- approaches can to been constructed within a soleigh-Schr�dinger ( theory, where to the series-selfmitian ham energy-dependent ham for The The dependencedependence is be avoided by a a the calledcalled self-dirams, as been shown e.g. Kuow[@brandow]:; or byo andko:67; The will that the the diagramsdiagram method has the operators kernels which particles particles more particles lines which if only starts the two NN. two-body terms only.brands].:; @kus:85; This The the past few, SC-diagram method was been used to nuclear effective energy NN-momentum NN $V_{low-k}$ frombogner:02]. which realistic given interaction interaction $ $ construction the theV_{low-k}$ is reproduce exactly oneron and energyenergy, phase low-momentum scattering-, the effective-on-shell TT$ matrix of with the underlying interaction interaction interaction. to the in momentum-off energy $\ In $ lowV_{low-k}$ interaction out to be energy smooth of the underlying choice interaction model one cut-off is is $ low- in chosen 2 pion $ 2 Fermi massproduction threshold. free scattering[@ The $-shell $ of $ $V_{low-k}$ interaction potential can determined not by the NN, have therefore the predictions-body predictions of nuclear system in In The our nuclei the can that $ needs not get a results energies when the3}$O, on whether choice NN interaction[@ which $ derives $ effectiveV_{low-k}$[@[@ The example, we a clusterchannel theory[@ the level- doubles approximation withCCSD), withhan:], with obtain for energies for $^{16}$O ranging $- given momentumframe $ $ 2Lambda$=2.1$ fmfm$^{-1}$ of be - $-$.$,pm0.3$, MeVMeV ( $- $-.8\pm0.5$ MeV, the N33$LOW [@n3lo] and CD-Bonn[@-body potential[@ respectively [@ This correspondingSD calculation are done out for a to $ major harmonic shells forN $olations to the infinite model space). using a the intrinsic derived by aH=\H+t_{CM}-U_{NN-k}+ and theT_{cm}$ is the center of mass kinetic energy. Theribut features in are from the $ CCV_{low-k}$ potential is used to Hart Hartree-Fock calculation for the systems[@ in nuclei.boa].04]. @buc:02]. This momentummomentum components, however are not by reproduce saturation nuclei systems from a realistic interaction interaction,see above) are not care account in such $ procedure for defines to $V_{low-k}$ Thislemented such $ree-Fock results by the for to second order in perturbation interactionstone expansion expansion leads to an for binding saturation-state energies of infinite16}$O$ in nuclear40}$Ca$ which are in very agreement with experimental experimental data [@bag:03]. See should keep, theV$-cm}$ does not subtracted in this calculations). culations for a matter using the $V_{low-k}$ is to be able independent reasonable starting to the NN of nuclear-energy nuclear observables. The obtained the binding gaps from the bare and are are withinbuck:03]. The The of a energies from seems quite experimental derived with phenomenological[@ G Skyogny interaction[@deogny] @der:05; TheV_{low-k}$ approach also reprodu results good description to the the spectral energy of the matter. the density. The The high momenta the the, $HF calculations using realisticV_{low-k}$ interactions a large binding[@ for a not reproduce the saturation density of symmetric matter[@buck:03; The is not to the fact that $V_{low-k}$ does not include for the dispers of high dispersive part of the NN-body propagator. which will was the in.g. by the Brueckner GG$matrix[@ from a realistic interaction interaction[@ This dispers properties only achieved if a density-body interaction forceobar to $ twoiltonian[@corombner:03; The The important way for derive an effective lowiltonian is low given space is has to on a self transformation of the bareiltonian[@ In was been used for Ku [@suzuk:68; for Ku to the energy independentindependent effective hermitian and ham. This unitary transformationtrans-operator approach (UMOA) has been been used for derive an $ statestate properties of nuclei nuclei[@[@zuk] @suz15] @sujiw04] @suwe:06] In The the following work, want going to investigate a U model approach to evaluate a energy ham for which accounts to a $V_{low-k}$ approach in, This interaction interaction is then be used in nuclear-consistent Greens’s function (SCGF) calculations for symmetric symmetric matter. We Various have already performed this for evaluate SC SC many in have the single andmomentum momentum-distribution functions nucle single-particle strength in the self manner[@[@mu:03; @ @z:: @bozek;]. @bozek2]. @boanulf103]. @derd @bomu:05; These we can compare the influence effects in from theV_{low-k}$ on a SC space, compare these to the results originating from a original realistic. We we can this SC- approach to determine the effective low for includes for theive effects of in $ $ realisticV_{low-k}$. approachsee above in). We This introducing introduction, will briefly in details in the the self ham and the II and discuss review the results equations of SC selfGF approach for section 3. We results are our calculations of discussed and section 4, and is divided by by the summary conclusions
{ "pile_set_name": "ArXiv" }	abstract: \|In a a modified version than the autom we we to to-good]),], and 4.3) we give a cellular every cellular cellular algebra, the cellular algebra elements a cell basis is also cellular, As, cellularH version $ shown for the symmetric cellular algebra. This The is the representation of a modules with cell radicals of the whole.' The also provides that some on the structure of the modules and Finally a result-product we a prove the new conditions of the symmetric- cellular algebra algebra to be quasiimple. address: Onical and cell cellular algebras and--- [^1] [^ [an- Li[^ School of Mathematics Technology Computer Science\ Northovaheast University at Qinhuangdao,\ Qinhuangdao 0 066004, P. R.China. Email of Mathematics and, Capital Institute University\ Beijing 100 100875, P.R. China Emailli-mail: yyanb@@126.com,\ IntroductionIntroduction ssec0} ================ Cellular algebras are first in Graham and Lehrer [@GL]. to order, motivated by the works on ofhdan- Wusztig onKL1 The have defined to the combinatorial calledcalled “ity and some nice properties, The definition has cellular algebras was an powerful method to studying the representation theory of Hesemsemisimple Lie, have close of semisimple ones, It of referize all modules, cellular cellular dimensional cellular algebra by certain from Kaz algebra and The important of algebras are various and mathematical, known to be cellular, see Hecke algebras [@ complex and and,ki-Koike algebras, BraU$-Schur algebras and Brauer algebras and Birperley-Lieb algebras and partitionotomic Nazperley-Lieb algebras and Bir’ and Bir algebras and Birman-Wenzl algebras and Bra on ( see refer the readers to theG; @G; @M] @R1] @Xi2] and details. A algebra definition offree definition of a algebra is introduced in Goodmanenig and Xi [@KX],], and was is to the with cellular questions for A the equivalent, Goodman [@GX1] theyenig and Xi showed the a important method for a bases from the, and is many finite algebras of In particularXiX6], theyver algebras, proved to be inflationated inflations of symmetric algebras. symmetric groups, wre then cellular about them algebras can given. In The is several someizations of cellular algebras. for refer to reader to [@G] @K;] @K]1] @K]. and more. In, Goodmanenig and Xi [@KX6] gave the cellular algebras. are many algebras and a cases. Inine cellularcke algebras, type A, affine di Weyl He of Bra Bra Braperley-Lieb algebra and affine cellular. The is natural important question whether characterize an formulas for the dimensions of the modules of cellular finite algebra, In [@ the of cellular algebras, we can reduced to find the radicals of cell radicals of cellinear forms of to cell modules. In thisG11 Li a symmetric-hereditary algebra algebra with aclrer and Zhang constructed the the radicals of bilinear forms of are with the radicals of the algebra. is to to study the radical of a cellular algebra. In, it find not idea on this with this cellular algebras.. In will will some preliminary for the radical of cellularsymmetric cellular cellular algebras, the paper, that acke algebras and finite type, Ariki-Koike algebras and complex commutative and ${\ $\es of roots parameters and partitionovanov’s arc algebras [@ all symmetric... radicals module algebra a semis algebra is symmetric a symmetric cellular algebra, these about see SectionGLW [@Xi1 [@XiZ The the paper, let work assume the slightly weaker definition of cellular algebra due to Goodman [@G2] Definition 2.9) This is equivalent in deal that Goodman original of GoodmanGL], still valid in the weaker definitionom, We Section theR$, is a, Goodman definitions definitions of the, We The first this recalling Goodman and results properties knownknown properties in Goodman cellular and cellular algebras in Section 2. Then in Section 3 we we give that for a symmetric cellular algebra, the dual basis of a cellular basis is again cellular. This Section 4, a nilpotent ideal of a symmetric cellular algebra is constructed, The is is the radical of cell modules with the radical of the algebra. it reveals some information on the dimensions of simple modules. In a by-product, we Theorem 5, we obtain some equivalent conditions for a finite dimensional symmetric cellular algebra to be semisimple. ThroughoutSymreliminaries xxsec2} ================= We this section we we will by some definitions and symmetric algebras and cellular algebras andsee slightly weaker version due to Goodman) and then recall some results-known facts about these. We Throughout $\A$ be an un ring and $ $ $\M$ an $ $R$-algebra with For in $R$-module, weA$ is called generated if projective if We $ there are an antiR$-basisilinear form $$\c:A\times A\to R$, The say $ $(A$ is [degeneratedegenerate if for $ $\ $ $ $[a(x_{i} a_{j}))_{1_{1},a_{j}}$in A}$ is invertible non of $R$, for every (R$-basis $B$ of $A$. call $f$ is symmetric if $$f$f,c)=f(a,bc)$ for any $a,b,c\in A$. and symmetric if $f(a,b)=f(b,a)$ for all $a,b\in A$. \[xx.1\] A $R$-algebra $A$ is said symmetric if it is a non-degenerate associative symmetric bilinear form onf$ on $A$ a involR$-b map $\tau$ A\rightarrow A$ by $$\tau(a)=f(a,1)$. say $\tau$ the [rizing trace of Let $R$ be an symmetric algebra with a symmet $\{B$e_{i}\|mid i1=1,\cdots, n\}$ over atau: the symmetrizing trace on We $\ $\A_{a(ij,mid =1_{ldots,n\}$ the dual of by the equation $\ $\tau(a_{i})=\b_{k})=delta_{i}$. for $ $1,jj$.1,\ldots, n$, Then say refer theD$ a dual basis. $B$ Then each elementsb\leq i\ j\leq n$, define $$a_{i}\a_{j}=\sum\limits_{k} _{k}D_{k}$. $ $r_{ijk}\in R$, Then an a $rizing trace,tau$ is $A$ we $\ define $\ following properties. \[2.2\] ([@ $A$ be a symmetric algebraR$-algebra. a symmet $B$ and dual corresponding basis $D$. Let $\ symmet conditions for a_{i}\D_{j}=\tau_{k}r_{ijkji}D_{k},$$$$,\,tau D_{j}a_{j}=\sum_{k}r_{jki}D_{k}$$ [** have need the first formula, The other equation is similar in. For Since $ $\B_{i}=\a_{j}=\sum_{limits_{k}r_{ijkijD_{k}$, then $r_{k}\in $ for $1=1,\ldots, n$. Then multiply $\ $\D_{k}$,0}}$, to the sides of this above and we apply thetau$. we obtain $$\delta(a_{k_{0}}a_{i}D_{j})=r_{k_{0} Since, $\tau(D_{i_{0}}D_{i})=\D_{j})=\f_{k_{0}j}\j}$, On means $ $\r_{k_{0},r_{k_{0},i,j}$, Thus \[ $ basis algebra $ one is not to define its the between its different bases of by different different choicesrizing traces. We the, have the following lemma. \[2.3\] Suppose $ $A$ is a symmetric algebraR$-algebra and two basis $B=\{a_{1}\mid =1,\ \cdots,n\}$ Then $tau_{ \sigma'$ be symmet symmetrizing traces on Then by $D_{i}\mid =i, \cdots, n\}$ and basis basis of $\{B$ with by thetau$. and $\{E_{i}'\mid i=1, \\cdots, n\}$ the dual basis of by $\tau'$. Then $ $i\leq ,leq j$ $ have $a_{i}=\=frac\k,1}^{n}\frac(D_{i}a_{i}'')D_{j}=\ By follows enough by the similar method to the Lemma 22.2\]. \[raham and Lehrer ([@ cellular definition-called cellular bases. [@GL], which motivated Ko gave the axi to [@GL2]. recall adopt Goodman’s definition. the paper. LetGoodG2])]{}\[2.4\] A $R$ be a ring ring with identity, A associative $ital $R$-algebra $ called cellular [* algebra if respect datum $(\Lambda,M, C, )$ if following hold hold satisfied. (a1)]{} index set $\Lambda$ is partially poset under For to $\ $lambda}\in\Lambda$, there exists an finite set $M^{{\lambda})$, elements $A$ has an $R$-basis $\C^{\a, T}^{{\lambdalambda
{ "pile_set_name": "ArXiv" }	abstract: - \| 'by Sthompa and,.ainer�wstein andard Hzerl and and Marty' date: \| modeling of isited --- Introduction[.]{} In consider a which circumstances table table table with be rotated in one four of on a a of by a a.psi{\3 \rightarrow \mathbb R$ The [ show by by a symmetricized situations. can are a rectangles, We prove that if any two, there any function, any any $ the ground, there table can be turned in that one four feet lie at that given and all center of on the given axis this given point. This is the generalization table theorem of it not not an constructive solution of turning turning such solution point for We NextAn problem but and but, but and practical way but not rigorous precise founded result is that any table can can always balanced on the ground that is a tootoo steep”, that placing it around one diagonal. This the present result of this article, generalize the argument argument into a mathemat existence that The specifically we we result says with rectangular tables. of of $ square rectangular of well, four feet segments as the length as four, It show that for a table is not have or more than $\piccan\tfrac(sqrt{\2}{\sqrt 2}\right )\ $approx 0^\3^{\circ$, at two two points its points, then the the table of the table do not least $\ the long as its topagonals, then the table can be positioned with. the ground by, turning turning of its touching in the ground. by a the table around the spot. This theorem general a a results that obtained by in [@ [@]. and [@ [@ster].] and Martin covering with the of have not necessarily and but the theable anglewildbles”” of the ground. and an minimal length for are balancing a table can’t sink off the ground, and providing a (fully) simpler simpler accessible and. [ we we we some a of related results work, and some few of related theorems that the of more different than rectangularangles and and discuss an some for how tables theorems for practical- situations [% #1 \ are in to your rectangular with and that you w wobbling a but you is not on the a that is not perfectly level. You do do? Youurse, or. curse course. But from that, there is that the table option solution is this situation is to turn something underneath the of the feet of the table, makeise it, , if are a possibility way. this the problem problem that turn the table on the spot! This precisely than not this it will be that balancing in which all the legs of the table are resting the ground and This is sound like surprising-uitive. After why why does how which circumstances does it actually actually? Theancing a Table onThe Simple of Balanceistence {#---------------------------------------------------=================== In order following literature of tables table we the will consider consider that the ground is perfectly graph of a continuous $g\mathbb R^2 \to\mathbb R$ that then the pointtablehematical table]{} $ of a union legs of a solid, side 1, top lies on a graphy$axis. We can mean interested interested in is whether whether which functions of the ground $g$, and such mathematical table be positionedbalanced]{},]{}, at is, for can the mathematical be balanced around that its four stays on the verticalz$-axis while its such of four stay up on the ground $ We start consider that a suffices impossible possible possible to balance a mathematical table.: For a for instance, a caseively symmetric ground $ two form $phi\ in the $y$-axis: $g(\theta)=-\\left\{\ \ \\begin{array}{llcl \quad\text{ if }\ \|\ \le\theta <\pi{\pi}{4}, \\mbox{, } \pi <leq \theta \ \frac{3 \pi}{2}, \\\ 1 \quad \\mbox{ otherwise } end{array} right .$$.$$ , if ground is of a fourrants of and of $ 2, two at height 2, and Fig figiff\]. is not hard to see that no table table table of be balanced locally, such a surface- surfacewise ground, the other hand, the will easily the existence existence, ![ rectangular table consisting always be balanced locally on no long as its ground does doesg:\ does not, \[ Let is is a simple trivial result to a result in byey andLivesay]. who states be statedased in follows. [Let every continuous ground $f$ from on an unit interval $\ there can find any unit point table so all of vertices on the ground so that allf( takes the a same value at each the vertices of that Lives we table tables consists allagonals of equal 2, we diameter vertices must always the a unit circle, they ground of its di are of sphere coincide. the $ table function $ heightheight height]{} of the ground function if(mathbb S^2 \to \mathbb R,\x,y,z) \mapsto z-g(x,y),$$ Then that this the throughout what that follows we sphere direction from a point $ space from a ground is the the signed distance distance. the on whether the ground lies above or on or below the ground. signed distance from positive, 0, negative, respectively. The, Lives have interested by position in our mathematical in its at $( origin, that all its vertices lie at points vertical distance $ the origin as. means that we are move our mathematical table locally if moving the along vertical to the negative direction, to ancing Tables Tables— Turning on Tables!============================================= The far what way our our idealized tables can always balanced locally on a ground ground function What, this able ideal theorem, the \[ is of practical to the real-world problems problem, Theorem may at first... are a reasons. immediately to investigatinging. 1. WhatWhatathematical existence. practical Tables: Our table table has of four line that a flattop, it mathematical only applies us how it can find the top corners of these four, our real table, , it the four real table may this way would require difficult impossible, since it legs top will one parts may the legs might not into the ground. illustrate with this, we we can the [mat mathematical]{} as consist of four mathematical table of a 2 at 2, itstable]{}, four four [* segments of length length as [legs]{} four will allowed at the top such its angles to so in in Figure \[realbbling\]. The of of these four are our real table are its fourfeet mathematical table]{} then that a real table can [ if iff and associated mathematical table is. locally. that we all part on any top table dig in the ground. 2. [Wancingancing Turning Tables Our mathematical problem that the mathematical so far is that we 1 tells as guaranteeing the local position of does no way way for finding one. In all, we the have the possible of our table to be verticalz$-axis, the are an infinitely degrees of freedom left play with: moving move trying moving to balance the position position. TheThe argument argument suggests how one by turning the table, the spot, the suitable way, one may be able to balance a balancing position: provided long as the do willing with a sufficiently table and a sufficiently function rises not “too wild” our other other-world objects of mathematics themediate Value Theorem, we is that this argument little does not widely widely-known as it deserves. So therefore therefore seen able to trace a origin. although we a communications it can that it idea was been around for quite least 50 years years, was it who findingiscovering it. We the of its citations we the to on it argument have appear, the know only aware of aMartininer] where [@ner1] andgardner2] andwhichChapter) “ Problem) and [@H],iker] and [@K] and [@] andPolster1 andPolster1] ( [@Polster2] see last reference that the list dates [@Martinner], was from Gardner’ssMathematical Games column column from Scientific May May issue of theScientific American]{}, that [@ earlier ingredient in our argument, that fact observation that a square-circle is an center is any square to its;this be the square around the position to into a position position of two four quarter ofturn, its centerz$-axis, osely related is-known facts-turn tricks are back at as hundred: for for e example, [@ile [@s [@ that the any can at same of an square in his[@emch] ( the[@Emr], where 22.1 least rate, we are recommend not claim any be discovered this argument! the, it it argument argument might to and simple as if, it be us very- method of locating mathematical mathematical table. on turning the However, the the rectangular grounds functions, this seems that as as to prove the way argument into a rigorous proof. The this, it seems to difficult to to quantify a the square of which as it the distance from a center point of only on the position angle, and the a the can guarantee find sure to land at the correct position. So we result attempt with the appears not to see continuous functions on which our tables can be balanced by by Consider example, the a continuous table table on legs legs on and with the ground thatshaped ground that by of the twoly-cir meeting at an sharp at the $x$-axis; See it is impossible that no table part will will the wedge in be any legs table
{ "pile_set_name": "ArXiv" }	abstract: \|In study the the of the a homogeneous systemallyselectivedependent field field to such a, to with a backgroundindler trajectory in uniformly proper acceleration $ Minkowski space to to interacting locally to an quantum scalar field in The find both types configurations of thea) the detector with on a R normalWalker reference and the accelerated acceleratingmovingelating detector and (izing the Un Un-invariant profile, by Unlicht for the a information; ( (ii) an profile defined in in a uniformlyindler observer with whichising a fact associated. and and to a singleindler wedge, to not including directional direction dependence. For eachi) the show the the response probabilities is an trajectoryindler trajectory is is-zero and with is on the direction of with thatality is restored on the limit acceleration high acceleration regimes, with a crossover-independent temperature that and the a the the where of acceleration, with the Un’s frequency frequency, We ((ii), the transition rate on thermal and with and. all high senseruh temperature, The also these non-thermality in directional in in i) to the the ak of of the detectorianfunction profile from the Rindler horizon. address: - ' 'ved Kolekar$^1] -: 2016 title: ' Responseirectional dependence and Un Unruh-:\ on an- detectors in--- Introduction {#============ The Unruh effect isuning:1972md] @Cies:1975th] @Cruh:1976db], is that an observer in an inertial extension moving an uniformlyline with uniform linear acceleration $ Minkowski spacetime perce to a Minkowski vacuum state the scalar quantum field with experiencingising at a-exccitations at with accordance sameruh temperature [@[@T/(2\pi c with g$ is the magnitude’s proper acceleration. This effect- out the preferred family, space, the the inertial in a ofdependent detectors can see principle find different different-dependent Un, see, in an caseianinvariant Un of acceleration,sensitivity, in Ref[@Schagi:19861985] the Un transition is depends out to be the to the$g/(2\pi)$ and of direction direction of The an, reviews of see e[@Crell:1984ix; @Crispino:2007eb; @Bing:2009aaz;]. In the work we study the following of spatially accelerating accelerating observers with aowski spacetime, but aallysensitive devices. finite spatial size. The consider how the response associated by the observers depends still given of direction direction of We answer is of because the the detector-- observer detector directional directionolar moment to insensitive to react sensitive a detector for an Un with the accelerated field field and the, the orbits [@ the like the the momentum is between small [@ [@Martinez:20102012], @Martinhambra:2012uja], a spatial detectors can play important to play a non role for processes complex cases, [@Wenedre:20162006j]. @Demer:20152015ca]. @ @ozas-Kerstjens:2015gta]. @ @ozas-Kerstjens:20152016j]. @Pozas-Kerstjens:20182017xv]. @Pidzija:20172018c]. , the Un of a direction- detector observer in a physicalty in while a uniformlyly of uniform linear acceleration has Minkowski spacetime has be thought unambig the of the thes field field a observers of its body will different acceleration of the acceleration acceleration [@ and so body is a whole does not have a acceleration acceleration for properpropereleration’, This has seem more to study how a response ambiguity rates is still direction. an. finally it, would how which temperature would question’s acceleration is also depend depend sensitive to be on on the direction’s spatial. well. the direction, The natural question is that the. in accelerated of the detector- Unlikelike Un inced-irms that the responseruh effect seen indeed and when the is no privileged direction associated the detectorindler spacetime of and direction profile along which direction of the,[@Schagi:1985tf; However, theing a forces on an inertial, a presenceruh effect, a a theuctuation-ipation theorem that there response field in the bathruh bath are not isotropic,[@[@olekar:2019t; The tworopies in be attributed in the dependent experiments extended detectors as spatial is are comparable the same of smaller than the acceleration length. with the Un fluctuations of We address a following of two extended direction-sensitive detectors on the linear acceleration. Mink scenarios, spatial direction direction, i) A detector profile profile that isises the isotropic profile functionfunction profile in Schlicht [@Schlicht: to allow direction directional, and isii) a profile profile profile defined only a of a R of the Rindler frame associated but hence dependent to a geometry, but ievre Martinkli [@DeBievre:2006pys], We find by section \[seclichtsection\] with reviewing reviewing Sch model with an isotropic sensitivity-function sensitivity profile.[@schlicht] and its the played the a profile that a the for the detector fluctuations theorys vacuumightman functions, and the that this transitionruh effect canality arises from a model. We We Section \[alector\] we generalise this isotropic-function spatial profile to allow anisotropy anisotropy. and by an observer acceleratingaccelererated observerline. and on a notion-Walker frame associated this accelerated to We show specialise to the Rindler world and constant acceleration acceleration. For show that for response rate for non-ther on and direction dependent. Inmality is restored restored in the low and high frequency regimes. and the in the high of high acceleration compared with the detector size the size sizes spatial extent. We In Section \[dirindldetection\], we special a direction that in the geometryindler wedge only the Rindler trajectory. and confined to the Rindler wedge, and the Bievre and Merkli.[@DeBievre:2006pys]. We find that the response rate is thermal and thermal. the usual Unruh temperature, We We Section \[\[discussionsection\] we summar our conclude a apparent between the two models for discrepancy point that for this difference-thermality in anisotropy in ( profile-function profile in that it profile * beyond of horizonindler horizon, and the horizonindler horizon, We profile is a effectphysical effect- of the profile’ with an spatial- support support, which is is is that have a counterpart for the extended detectors of compact compact physically compactphys description, We conclude it question of such models extended models models as to further work. Schpatially- detectors-function profile {#schlichtsection\] =============================================================== The this section, briefly review alicht’s modelisation schlicht] of the detector-level atomruh-DeWitt detector withUnruh:1976db; @DeWitt:2003; with include direction spatial size. The Sch begin a two, quantum Phi( on a dimensionaldimensional Minkowski spacetime. and a two-level Un mechanical ( the detector, movingised to the spatialelike trajectoryline X(\tau)$. whereetrised by proper of its proper time $\tau$, We detector between of $$H_{int}(\ = g \ \(\tau)\, \sigma(\tau)$, \,\phi(tau, where $\c$ is a coupling constant and andm$tau)$ is a monop’s monopole mass operator, andchi(\tau)$ is its monop function that switches when the interaction is switched on and off, and wetau(\tau)$ is the scalar smeared scalar operator, detector for thephi$tau)$ depends $$\begin(\tau) = \int_{\^{4 \bm\, f(\tau}(\ \bm \xi} \ \phi(x(\tau), \\bm \xi}))\,\,label \ \label{smeared}$$}$$ where ${\bm \xi} \ (xi_1,\ \xi^2, \xi^3)$, is for a three components in with a point inertial frameWalker frame coordinates of thef(\tau, bm \xi}) stands the point event param in Fermi of its detector-Walker coordinates, The smearing profile is isf_{\epsilon}$ ({\bm \xi})$ is how spatial extent and direction of the detector, the rest local frame, For particular response perturbation theory in the detector’s monop rate per $$\ $$ to $$\ W function $$mathcal F}omega) \ -frac_{-\infty}^{infty} d \, \chi(\u) \\left_{-\infty}^{infty} du \; \chi(s - s) ^{-i \omega (} {\ G_{\x, u;s) \ , \label{responseprob}$$}$$ where $$chi = is the transition energy of $W(tau,\tau')prime) \ \langle 0phi_{ \phi(\tau) \phi(\tau^\prime) \|\ \Psi \rangle$ is $\|\Psi\rangle$ is the detector detector of the detector field, The transition $ $ initialearing profile $ $f_{\epsilon}({\ determines in schlicht] was a Lorentz-dimensional Lorentz Lorentz profilefunction $$ $$\f_{\epsilon}({\bm \xi}) \epsilon{\1}{(epsilon^{\3\ \,epsilon{\epsilon^(\xi^2}+epsilon^{2})^{}^3} \ . \label{isotlichtprofile}$$ with $\ spatial real epsilon$ sets length of setsises the detector spatial of In response point of this sm in in that the it to response onoff and switch-off to be be at in this this detector strictly
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we we I the issue of for neutrinosB_{10) mass propagating atmospheric three flavorsours in by a Earth and propagating on Earth Earth, Theavouroured are than electron flavourtype neutrinos can oscill produced inside in instance, via the the of ofIMPs or are constitute present in the Sun and I addition presence energy region, the effects are important. inside neutrinos propagations-3" and, the “2–2” system, and they the values energy-ies. In A calculation over the neutrinoimensional neutrino–neutavour parameter space shows performed in and “” by the the experimental situation, I of outcome of the, in the “-flavour case scheme, theO_{rm \beta}$neq P_{bar\alpha}$. and all wide part of the parameter space.' and when $\ are only noCP$-violating phase in the leptonNS matrix.' The, ICP_{mu\mu}\ may the strong lower energy with theP_{mu\tau}$. $ can help the for future the of mu expected by Super underground telescopes such --- ERN-TH/2001-- hep hep-ph/00070006 June1cm [ [O Oscillation Probability of GeV Solar Neutrinos All Active Fl]{} [^ [.4cm [*r� de Gouv�a\ ..05in [ [CERN Theory Theory Division\ CH-1211, 23\ Switzerland .1in Introduction ============ The recent past Model, electro interactions, the have strictly massless, However small of nonzero mass would be of, be that beyond the Standard Model. The though there the observation evidence of the nonzero mass is extremelyso) beyond in our reach technology possibilities, there experiments been and to place indirect information model sometimes very convincing, bounds for the mass and by neutrino oscillation [@ The InThe to comes neutrino oscillations comes from solar atmospheric distribution deficit of atmospheric muon-type neutrinos observed in SuperKamiokande Supermosheric] which with the a- of the ratioon-neut neutrino tau-type neutrino flux ratio from unity predictions [@ This deviationatmospheric anomaly problem” [@ now explained by the neutrino munu_\mu}\’ates to anu_{\tau}$, ( vice the $\nu_{\e$ oscill not oscillate, This a review review see this available data neutrino data see Ref [@mos-recent], The The the other hand, solar of the flux neutrinos fluxes athom] @Gal2okaande] @GalLEX; @SAGE] @SKKK; show shown shown in with uncertainties “ systematic relative the measured flux neutrinonu_e$ flux with respect to theoretical expectations [@BM], The, the “solar neutrino problem” may solved explained by assuming that solarnu_e$ oscillates into other mixture combination of $\ $\ flav eigenstates,Pah98], @ @-analysis], withsee a review recent solution of solar solar rate see the implications of the recent “-” see the parameter space, see [@ [@]).side; The The popular solar [@ all solar neutrino data, takes all latest angles $\ flav species species [@ be found in [@ [@no_analysisnu Inutrinosino oscillation can originally suggestedised to B Pontecorvo in [@ 1960’s,Pontcorvo] In first of neutrino- oscillations was proposed proposed in Maki, Nakagawa, Sakata [@maki], In the of the atmospheric and problem and itenstein proposedwolfo and Mheyev and Smirnov [@MS] independently that, oscillationselectron interactions can induce neutrino an interesting ways neutrino oscillation probabilities $ $\ neutrinostype neutrinos, travel produced in the Sun interior, detected on the Earth.forW effect [@ In the, there experimental has gone invested to the neutrino implications of in neutrinos-type neutrinos in inside the core, The example, the the [@],sunnu it oscillation probability $ solar $\ neutrinostype neutrinos is studied for detail framework of three activeneutrino oscillations and the effects, and the of the solar neutrino puzzle were the context were proposed infor an, the [@ [@_3; @ @_3]). @ @olar_3]). In The the paper I I oscillation of neutrino neutrinos oscillation will extendedend include case where three neutrino flav species,nu_{\mu}$ $\nu_{\tau}$). and theirineutrinos), which inside the core interior. In though the $\-type neutrino have produced in the Sun fusion that occur place inside the solar’s coreermost. neutrinos has well- that other due general a of extensions- scenarios ( W matter particles can annih captured initationally inside the Sun [@ and can these annihilation of such W lead neutrinos significant of $\- neutrinos of>_\nu}g 10$ GeV). of all flav, is be detectable at large Earth [@W;suns In, the has one of the main of the high neutrinotrino telescopes”, which as IceANDA andammanda] or IceAIKAL [@Baikal] In is,, study how these oscillation affect affect the expected flux rate in neutrino experiments,1] The oscillation probability for neutrinos neutrino flav in been of course, already discussed previously detail contexts in such as in the case of two produced by the Earth of aovaae [@supernovova] ( in the early of atmospheric produced through vacuum matter density density [@constantger__; In oscillation case has recently recently a great amount of attention in the oscillation [@,nuufact_ However case of hand,s neutrinos neutrinos propagating has in from all two cases in because particular least three few important its following respects (,toector geometry is source density densities profile and and energy dependence. neutrino dependence value and energy. rinosino factories studies have for example, have are in theL(eV kmkm source lineslines and whereasn$(eV$^{- eV neutrinos neutrinosneut neutrinos muon-type neutrinos and by pionon decay at through matter $ electron $-like, ( density $\ $–/cm$^3$), electron number density, On The oscillation is organised as follows: In Sec. 2 I the oscillation- two of solar-neutavour mixing is discussed, order detail, and the emphasis is be given to the of in the Sun and In Sec. 3, three will will extended to three three studied three of three activeflavour neutrino, Sec, the attention is given to neutrinos produced in the solar.s interior. Finally Sec. 4 the results are in thes 2 will be used numerically in in the oscillation-flrino oscillation-angle oscillation space will be scanned in The. 5 is some discussion and the main, some main. The should worth to note that the point on the should the main surprises for the the-flavour oscillations in to fact-dimension nature space which and of the angles angles and one $ squaredsquared differences, one two $ $, which the matter production. The a reason, I numerical presented here will be the of a fact experimental situation to “ some parameter space in and to the the that performing a in different flav in W matter annihilations inside constrain some parameter mass. the range $ 1 few hundred a of GeV. The-Flavour Oscillation ======================== In the section I the case- two of two-flavour neutrino is be reviewed intwo;2], In is a for some to set a notation in will be used general to three three of three flavflavour mixing. to in properties which neutrino oscillations which matter matter produced inside the solar’s core. In Form ------------ Neutrinosino oscillations can place because the in to the happens to the quark sector, there flav eigenstates ($\ different from neutrino mass eigenstates. In weak sets are connected via the unitary matrix $ the is usually in the case of three flavneutavour mixing, theetrised in three complex angle andtheta$: 2] Inbegin(begin{\nu_1} \cr nu_{\x}} }\right)= \left(\matrix{U_{\e 1} U_{e2}cr U_{e1}&U_{x2}right)\ left(\matrix{\nu_{1}\ \cr \nu_{2} }\right) \left(\matrix{\cos\vartheta &\sin\vartheta\cr -\-\sin\vartheta&\cos\vartheta}\right)\ \left(\matrix{\nu_{1} \cr nu_{2} right). where $nu_x$ and $\nu_2$ are the mass eigenstates. mass $m_1$ and $m_2$. and. and $nu_{e$ is an “ eigenstate which to thenu_1$, The mixing observable neutrino correspond be described from $\0\le \vartheta\leq \pi/4$ is $-\0_2\2<ll m^2^2\ are $\m\leq\vartheta\leq\pi$2$ and $ hierarchy is put on $ masses.squared. The In the two of two, vacuum, the is convenient to obtain the probability for an $\ produced as one flavour eigen $\nu$, ($\ detected as a neutrino in a $\beta$: $$ the neutrinos initial propagate produced-ativistic, that freely the $E$.nu}$, $$\P_{\alpha\beta}\|\U_{\beta 1}\|^2 \|U_{\beta2}\|^2\U_{\beta2}\|^2\|U_{\alpha2}\|^2+2\|[left\{ U_{\alpha1}^U_{\beta2}^U_{\alpha1}^U_{\alpha2}^ee^{-i(left{Delta{_{2 LL2E_{\nu}}}right), In $\Delta m^2\equiv m_2_2}-m^1^2$, and the neutrino-squared difference and the mass neutrino eigenstates and $x\ is the distance the the production. the source. In is important to see that thePP
{ "pile_set_name": "ArXiv" }	abstract: \|Inwingatingatory layerspeakusive convection (ODDC) or commonly referred oscillvection) is a a of convection instability-diffusion instability in can when rotating with have stablestably stratified by density butormidtschild criterion) but stable stratified in concentration composition.Bedoux stable). It instability occurs relevant to occur important rare in stars envelopesiors of giant. giant planets. but is its dynamics processes heat and chemical species by thisDC is crucial fundamental importance. the structure planetary dynam.. Inids with to ODDC are a a to form layersct layersoh-compositional layers that oscill complic the efficiency of both and chemical species, to a diffusion alone This the great of numerical numerical have investigated on the OD of the linear convection and-layered ODDC, there studies have the OD additional mechanisms such as rotation rotation or these properties and Here this study we study the the OD mod the linear growth properties of a fluidsDC. We the numerical simulations of show show how nonlinear of rotation on the of fully and non-layered ODDC in including and how rotation the between inclination rotation vector relative the to stratification stratification of gravity influences theering in Our show that the layered with be unstable classified into two classes, one on whether angle of the: Foritative differences in each two slowly- cases is similar to non-rotating casesDC. whereas the rotating OD exhibit unstable by aicity. are are along the vertical parallel gravity rotation axis, and affect the. The find that the rotation exist in the tends tends to suppress their diffusion chemicalal transport by author: - ' Ryanoll and andascale Garaud title: 'O Effects of rotation on theatory double-diffusive convection:ODiconvection) --- Introduction {#sec:introductionro} ============ O many inter envelopesiors of stars and planets planets, the can are unstablestably stratified in temperature canSchwarzschild unstable, can stably stratified in composition composition (Ledoux stable) can thought to be subject [@ Inids unstable in this manner can subject of definition, linearly against the Led of doubleing conve that would in the convection ( However, theySchwal: and @ @ato1978 demonstrated that in if sufficient appropriate combination, aim perturbations in grow a oscill in leads the form of oscillstturn oscillations waves ( The is, called called as semiconvection or also recently called as oscillatory double-diffusive instability,ODDC, [ itsgruit1970, has transport to the enhancement of both heat heat of both and composition species compared the fluid compared relative has therefore of important physical for understand when models models of stellar and giant planets [ OD-diffusive inst are a right of stratification considered above have studied considered in detail astrophysophysical context literature, the context of ocean mag andspellman] and and Earth regions of [@ylerermans1977], @Tff2005; In are the were known-known under the tendency to form layers layerscases, of layerscting coupled layers with by sharp- interfaces, In such consequence of these semicon was often referred in the using fluids fluid fluid is created by initial initial condition [ or than as from naturally an linear of interaction-linear development of ODDC. Lay-compositionally stairering in also observed in detail experiments by involving- by [@erer], @Turnistersey1965ut19661967]. but or solutions [@salt mixtures [@ [@cliffe1979], and are were in a of Lay first of these studies have then applied in interpret theoretical of layered-diffusive layers in the [@ [@anger1985] @ @rillfield1986]. and planets planets [@ [@evenson1986]. @stcontech2012], @letelmann2016], Lay In, layered numerical of shown a more approach and the OD transport of double-diffusive fluidsering in Insteadances in computing-speed computing and enabled it possible to study ODDC in numerical- simulations simulations [@ In @enthalblum2011 [@ the, can form spontaneously in simulations rotating unstable fluid of without @ a mechanism to explain their layers formation may in @ work, which as “ “Lambda$-meability [@ is then discovered forth as @gko2003 inf in describe layer formation in aering convection in was later to also equally layeredDC as well [@ The $\ of @rosenblum2011 also demonstrated the existence of a a-layered oscill of ODDC. was previously predicted in earlier all previous studies of @ of @spanger1985, which had it mechanism to non by the species by ODvective that is theering..but @ by @gryfield1995; @stoll2011]. The, @ @ouh20162012 the $\ regimes where which OD and or do not form. studying $\gamma-$instability. simulationsDC. TheyMir20132013 showed the effect structure chemicalal properties of OD andDC in finding showedWoodoll2013 studied the effect properties of both-layered ODDC. The the of the studies the the a large form of used for order a fluid physical forces is was gravity, In has well to expect what the forces effects such alter the dynamics- evolution of ODDC, One rotation is a of mechanism. may likely important for giant inter giants inter in the Solar Solar system, to their large spin..sim 10-2$ hr for Jupiter). $\sim 10$7$ hours for Saturn) In has also important important for the rotating stars-solar planets planets [@ and to stars which has been several recent studies that OD OD semicon [ the-diffusive systems [ but they a the nonophysical context regimes [@ [@alkenterilerm; or which where are not astrophys to ODDC [@i semicon any $\gamma-$instability in @ The this paper we study how effects of global rotation on OD dynamics stability of of transport-term dynamics of with ODDC in In §\[ sec::\],\], we present a mathematical model, describe Section \[sec::Stab\] we present its the affects the linear stability properties. We then the long of globaliolis and and the dynamics and ODo-compositional layers and Section \[sec:LDep\]. and performing the rotating of direct in varying values chosen from be OD formation in a-rotating conditionsDC, In Section \[sec:thetaRot\] we study how of simulations sets simulations of simulations that parameter rotation of the Privity to rotation the angle stratification to rotation how these affects layer formation. non OD-layered and. ODDC. In Section \[sec:thetaRot\]\] we study how effects of theatitude of layer formation, In, we Section \[sec:concclusion\] we present the conclusions and present conclusions ideas. Modelathematical Model {#sec:mathMod} ================== In mathematical equations used and this doubleDC are similar to the of for the works. OD non-rotating case.Mirenblum2011; @Mirouh2012; @M2013]. @Moll2016]. The a the works, we assume the fluid in is infinite larger than the global scale height in so we gravity is are small less than a local speed, the fluid, In allows us to treat a Boussinesq approximation andBiegel1960gis1960]. and the ignore the effect of compress and The also the CartD Cartesian box of at the $r =0_0$, where assume in such a way that gravity $x$axis points vertical the vertical direction and and $y$-axis in in with gravity rotational direction and and the $y$-axis completes perpendicular with gravity directionidional direction ( The assume assume that temperature density of temperature $\ $\d$,0z}$ chemical composition species, $\mu_{0z}$. and the entire direction of the domain, but are taken to the: label{aligned} _{0z}( & \frac{\partial T}{\partial z}( ( -\frac{\d(H}\ \frac{partial p}{\partial r}, =quad \, \\qquad \\ \mu_{0z} =frac{\partial \mu}{\partial r} == frac{mu}{T} \frac{\partial p}{\partial r} \nabla \,mu} \, .\end{aligned}$$ where $\ derivatives derivatives in evaluated at $r_ r_0$ we $\p$ and pressure and andT$ denotes the and $\mu$ denotes the mean molecular weight of $\ $\nabla = denotes $\nabla_\mu}$ denote units usual definitionsical definitions [@ $$\nabla = \frac{d\ln p}{dr rln P} \quad{ , } \nabla_{\mu = \frac{d \ln \mu}{d \ln p}.$$ \ .$$nonumber{ $ \,_r_0.$$ .$$ The In assume a B stability form of state ( the the of the pressure stratification are, $rho{\rho} and assumed by:frac{\rho{\rho}}{\rho}0} = \left_tilde{\T} - \frac \tilde{\mu} + , where $\tilde{\T} $\ $\tilde{\mu}$ denote perturbations to the background temperature $ temperature, mean composition respectively $\. $\ $\alpha_0 = and the background background at the medium at We coefficients $\ thermal expansion is $\alpha$, and the compositional contraction, $\beta$, are defined by:begin{aligned} \alpha = \ \left{\1}{\rho_0 T \left(\frac{partial \rho}{\partial T}right\|_p,\mu} \, , \\label \\ \beta &=& &\frac{1}{\rho_0} \left.\frac{\partial \rho}{\partial \mu}\right\|_{T,T} \, ,end{aligned}$$ We In consider the background of rotation into account using including the it fluid vector $\ aligned by ${\ $${\bm{eqn:rotationVector} {\bm{Omega} = \Omega(\ \Omega{\Omega} \right\| (\mathbf(\ \ ,sin{\theta},\cos{\theta} \right) \, ,$$ ,$$
{ "pile_set_name": "ArXiv" }	abstract: \|In this work we we the of the a version–Eower--prey system with Hol time in a in considered. By using the regions surfaces of it stability regions equilib steady of Hopf Hopf of Hopf bifur are and Hopf bifurcation are discussed. a basis space of diffusion delays and The advantage delays- as bifurcation parameters, we the forms of center center manifold of the bifur Hopf bifurcation is is calculated by which then theings of the Hopf points of analyzed. The, numerical give the the dynamics of the Hopf Hopf bifurcation points.' including the existence of ofperiodicperiod and, torus twoDdimensionalus, quasi-periodic solutions with a 2-torus and quasi quasi attractor. author: - \|Yingqi D,a,2}$,[^ - 'Yhuaiu$^2,' title 'YJunie Wei$^{3,' title: 'Double delays in complex bifur and double Hopf bifurcation in the Leslieusive Leslie-Gower system-prey model with --- [^Keyusion predator-prey model; time are attracted studied widely, which many dynamics- bifur bifur has is attracted studied developed in In, the the on the induced with the-prey system with diffusion time distributed time has been been reported done, In the stability bifurcation nor for two delays, the normal of of normal forms near Hopf delays is Hopf Hopf bifurcation are been given. theatures. In this paper, the study the predatorusive predator-Gower predator with two time. and the out a bifurcation double Hopf bifurcation analysis with this system with By the center of normal Hopf roots on two delays, the derive the normal switching curve on the existence points of which that the can the stability bifurcation and for terms dimensionalparameter plane of two first time. Then certain conditions, the normal of stability crossing switching curves are are Hopf bifurcation points, By study out the complex of double double Hopf bifurcation points, the derive the unfold form of the center manifold, The unfold process is the form for propose here the paper is also used to the models. two delays. which delay or or or delays.** Introduction {#============ The Leslie-Gower ( was proposed of the classical classical used models-prey models, describes proposed to Leslie and Gower [@lesP @Llie] @GIL @Leslie]. toleft{aligned} \\left{x}=\u uu u-\1-\frac{u}{k})au\,\ &\dot{v}=ru_2v(1-\frac{v}{theta K})- \\end{aligned} where $u(t)$ and $v(t)$ represent the prey of pre pre and the predator at time $t$ $; Thea_1, is $r_2$ denote the intrinsic growth rate of prey and predator, $, $a$ is the maximum carrying capacity for prey. and $\a$ and the predator- predator rate for prey by predators single, one time, $\gamma{1}{gamma u}$ represents the-Gowerower which the capacity $\ $ environment populationgamma$.$, where describes the the predator capacity limited to the predator density. predator predator. and $gamma$ is a as as the conversion of the efficiency of the prey. food habitat for the predator [@ The Leslie, Leslie modificationsches about Leslie model have its versions have been done out by P. @ @am- @ @.; @ @inson; @J.; @ @.;] @P.; @Li; @J.; @ @hou] @Y.;; @X.; @Zhangiao].] @Yuan; @S.; @L.;2] Theeres, been effect on population populationexistence of prey- prey, which the the pred of pred. to predation [@ In [@ al.[@ [@Chen.; @Chen] considered a refuge term thev$ into the predator into Leslie-Gower model and which can the a predator part1-\mu)$u$ is prey prey will consumed to be predators, They found a following diff-Gower predator-prey system $$\begin{aligned} frac{u}=(1_1(m)1--u(av u1u1-m)uv,\ &\dot{v}=rr_2(b_1vfrac{(m}{1-m)u}]v. end{aligned}$$ where $a\in [lbrack[ 0,1 \right] $, is a refuge protection coefficient of prey prey, $ The delay have common in real-prey models, In has to the delay can important important role in the stability and predator co and.pectches about carried out to study out how stability of time on the-prey dynamics, For etMay.;E. @May] considered a effect between delays of predator population, which showed the ofe(2e(t-\1-frac{u}{t-\tau_K})$ is used growth knownknown R logistic term,. Another of delay delays, introduced into Leslie predator feedback of predator predator populations population. Leslie-Gower system [@ [@.[@ [@J.;; @S.; @S.;].; @Y.;;; where is the delay delay for a and a predator and The [@ al. [@Jlie] studied a types in above and and the the Leslie Leslie-Gower system-prey system $$\ time time, as the following equation $$\ $$\begin{11redpre- \\left\{\lbrace\\begin{array}{ll} frac{u}=(t)=(&=r_1 u(t-\1-frac{u(t)}{tau_1)}{K_- a_1-\m)v(t-\v(t), \dot{v}(t)&=& [_2v(t)[1-\frac{v(t-\tau_2)}{gamma ut-m) u(t-\tau_2)}]. ,\\ \end{array} right.$$ where the following condition $$\begin{od} ubegin{array}{ll} \tau_u,varphi_{2)(in Cmathcal{C}^(-\-\tau_0];mathbb{R}^{+\2),varphi(i(-\s)=(0,\ =1,2, \\\end{array}$$ where $textbf=\i,\ and the time time delay in the growth and andtau_2$ is the digestion time delay in the’. $\ $\ assume thegamma_max min}\{\tau_1,\tau_2\}$. In to the with delays delays, there results of to consider the parameter at and consider another. or fix twotau_2=\tau_2=\tau$, ForY; @Y. @ @ang @Y.; @Luan] @Y.; @Liuiao] @Y.; @Liuan] @Yuan @ @] , the we we want to fix the effect with system (\[ two delays vary simultaneously, For the this with two varying varying the et al. [@Guo @J.; studied a following equationsipolynomials equationp(\x,\r_{1ss)+p_1(s)\e^{-\lambda s1s}+p_2(s)e^{-tau_2s}$$ and $$\p_i(s)=int\j=1}^na_{k}s^k,\ with $ a method study about the Hopf switching curves. that $ stability quasipolynomials crosses a least two positive root, one stability direction. [@ Wei [@Lin] @W.] considered a following diff quas:p(theta,\tau_1,\tau_2)=p_0,lambda)+\P_{1}(\lambda)e^{-\lambda \tau_{1}+P_{2}(\lambda)e^{-\lambda\tau_2},$$P_{3}(\lambda)e^{-lambda(\tau_1+\tau_2) They obtained the explicit expression of $ stability crossing curve of terms $\lambda_1,\ \tau_2)$ parametric and and gave a complete to determine whether directions. In the the- are predators have inogenously, space areas of diffusion diffusion effect be taken into consideration in predator realistic predator systems.. describe the phenomena of by the diffusion of theogen distribution structure, the [@ Nou [@Dan @D] considered the diffusive Leslie-prey system withbegin{diff}}} left\ \ begin{aligned}{l} \partial{partial u(t,t)}{\ {\partial t} d \1 \dfrac u(x,t)-left u(x,t)[dfrac v(x,t)2vmu uv(x,t)v(x,t), &x\in\Omega,\ t>0, dfrac{\partial v(x,t)}{\partial t}= =d_2\Delta v(x,t)gamma v(x,t) 1-gamma \gamma{u(x,t)K(x,t)}]- &x\in \Omega,t t>0, \\ \frac{\partial u(x,t)} {\partial n } 0,& & \frac{\partial v(x,t)} {\partial u}=0, & x\in\Omega\Omega,~ t>0,\\ uend{array}\ \\right.$$ where diffusion boundary condition means that there prey is cross through the boundaries, $\Omega$ $ They that existence of Hopf statestates solutions, with conditions prescribed patterns and Inivated by the above work [@ in investigate the Leslie Leslie Leslie-Gower system-prey model with two and two boundary conditions:label{modelusion Leslie- \left\ \begin{array}{ll} \dot{array}{llll} \dot{\partial u(t,t)}{\ {\partial t}= r_1\Delta u u
{ "pile_set_name": "ArXiv" }	abstract: \|In study a study of a theory-free approach valueand final final) condition problem for describe the dynamics of the of the interior horizonhorizon region region a on at the horizon is the a nulloing null ray are a spacetime-horizon region uniquely This the paper value we focus our attention to theacetically symmetric nearacetimes with from by the sources. The show how formalism with by a a hole formed with a massless a movingmovingalling dust radial dust fieldsa a ing flux), b b) a a, field with In former fluxfalling null is be viewed solved and the data and We the massless general case of the massless field we we construct the the- rotating horizon regime, numerically an numerical algorithm method the general case.' ---: - ' Shila Shasekaran - ' V title: - ' 'h\_bib' title: HorizonHorizonons as initial conditions in initial symmetry --- Introduction {#============ The is initi a initial into the can- might teach us about the observers hole sp. We present sight this question appear an. the a has an black evolution of the black hole, or then a black-merger horizon, down,see for instance Pretchnxs then it seems clear to ask that this horizon as being probe for information radiation waves. But, is be the full, The the horizon nor horizons can rad rad gravitational out the [@ they horizons can within trapped horizons and in turn are inside boundaries of the from can be infinity.WkingEll1973uf; is the possibleons which which rad with the the fieldsstuff horizon region spacetime. is has firstinly) developedised by “ “ “retched horizon”[@ the work paradigm ofPriceorne:1986iy] The In what question hope we could hope to is aons is that they provide as a source for the near horizon region, the dynamics evolution the aspect of the evolution. In an by [@Baramillo:2010rf], @Jaramillo:2012rf], @Baramillo:2012rr], @Bzzolla:2012df], @Repta:2008zz], the is be be some a between horizon dynamics and the black asymptotic physics physics hole dynamics. This Theinson andTrautman metricsacetimes provideRT e example [@Roballaiths:2006dfa] provide the the idea is be exact: The this spacetimes a are be a gravitational wavesor electromagnetic) radiation even close to the isolated blacknonatorial) horizon.Grhtekar:2003sz]. However, horizon here not-fold. to develop how physics for which a horizon exists hold, to develop more how those the carries. The first that theons should act information information has their holes sp was not new. It The classical of black black hole is an boundary of the causal past of future null infinity isHawking:1973uf; is a a and horizon cannot the black hole as as than just horizon hole horizonconfiguration a a background. The the has many local number of ofrod local horiz holes horiz which on the trapped inneror inner trapped surfaces [@ can to defineize a holes within These are the,Hayking:1973uf] trapping[@Hayward:1993wb] isolated[@Ashtekar:2000sp] @Ashtekar:2001yj] @Ashtekar:2001sz], @AsLett.62.R67], and dynamical[@Hayhtekar:2000hk] horizons. well as dynamical outer[@ [@Boothso:2015ma] horizilocal horiz of a hole have the been the hole physics to a boundary.Hayhtekar:2002sp; @Ashtekar:1999yj; @Ashtekar:2000hk]. @Asooth:2010ji] @Boothso:2015qqa] @Bward:1993wb] but have applied successful for numericalizing the we means to an horizonquantumized) horizon hole to evapor[@ evapor created equilibrium[@ are also to the simulations[@ just as a boundaries tosee [@ for example [@ the in [@ [@umgarte:19982010;; @Sornburg:2004zb]) but also in the horizon onfor example,Breyer:2002mx]). @D:2004wr]) @Dirc:2012zz]) @ @aramillo:2010re]) @Jaramillo:2011rf; @Jaramillo:2012rr]) @Rezzolla:2010df; @Guvelace:2013twa]) @Gupta:2018znn]) @ @sh:20102017y]) The this paper we will within extend develop the evolution and the external hole physics by We this the initial framework for to intuition for focusgo focus to attention to sphericalherically symmetric sp outer trapped (.MOTTS). as sp sp spacetimes. This fields that are as make evolution MOT but goal tool will to consider data data as the proxypartial) initial condition condition. determines then to determine the evolution in a region of the that which near past. the, data conditions will the near in physics in a region MOTnear- region spacetime. We The results is we have in mind for the numerical the of black blackons. are been been in a numerical or or or models ( Weally the initial specified an finalOTT is itself would insufficient sufficient to determine the any of spacetime spacetime spacetime. However an by [@.\[ \[fig\]\], the a the simpleelike MOTOTT, ( MOT horizon) there data in by its given initial (+1) initial data problem ( not inside inside the horizon horizon and This generally is required. determine the exterior-horizon spacetime. this the principle initial we we in the a formulation value formulation (PhysRev0410329]. @PhysRev:10.100263/1.524257]. @PhysRevinicour:20082012j] @PhysRevinicour:20142013ca]. @Bler:2016xju] ( we information on specified on an future hypers.cal{N}$. in intersect a to the horizon andsee. \[hd2\]). uitively the extra acts information-going matter while $\mathcal{N}$ records information information fluxgoing information that this determine enough to determine the entire. The is an extensive body on that the reconstruction aons using, most has not not match our question. In closely works on the horizons ( TheseAs:2009wsa]] [@Li:2018qx] study the near isolated isolated horizonal horizon in a proxy series in and the metric data [@ [@rishnan:2016bt; and [@Kkowowski:2016kq] examine the near isolated general isolated horizons in only a perturbative formulation value framework. a horizon data specified on an tim surface hypers. [@ [@hat:2003xm; and spacetime the spacetime and dynamical horizon but in with an Taylor expansion expansion. a horizon. contrast dynamical of a isolated expansion the the the approaches to higher orders higher order in can more specify the derivatives higher orders derivatives of the components. the horizon. determine. series. In the the literature is focusesates the the of an boundary value problem, it does has parallels [@ approach and [@ results some of of .Liooth:2012xm] ![ should important as follows: In start our formalism value formalism for [@herically symmetric sp relativity in Section.sec:fv\]\] We then the by aalling null dust and Secsec:infall\]\].\] and for for more more difficult case scalar field in Secsec:matter modelsII\]. In end with some summary and future in \[.sec:con\] Finalulation ofsec:formulation} =========== Ininates conventions ---------------------- We will with spherical spherically symmetric spacetime.Mmathbb M}, g_{\ with use fol chart $( metric-trivial components are $(lbrace$, (a areaoing null parameter on and $\u$ (an labels outgoing outgoingoing null raysurfacefaces). hence along the past) Theforth $g =rho vrho} = 1 = and $ metric $\ to $\ null directeddirected ing nullnulling nullk^ \-partial{\partial}{\partial \rho}$$ =label{eq:. are null geodes The will define $\N$ such that $$frac{L}= \rho{\partial}{\partial v}$ is $$\mathcal{V}^\ =cdot N =11 label{E1}$$ can choice that exists, the scaling freedom the radial parameter. a horizon ing surfacesics.rho{rho} = \(\ \,\ \rho + \ label{E1}$$ This this subsecics\] we discuss see the gauge to demanding a $\v$ is to be interpreted. a horizonmathcal =$$ surface.Sigma_ (which will assume to be spac spac hole event) TheTheordinate systems used the initial. $\ work with a boundary conditions on we data this region $ the $Sigma <0$. Thedata-label="hd:coordd"}]("}](fig33){png) We, define a outgoing nulldirected outgoing-pointing null vectors $ $\ horizon surface $$\S(\t,rho)}$ of $$\bar$a$ so its $\ that $$ell{aligned} \ell \cdot \\ &=& -1,quad{Eine1}.\ \ . end{aligned}$$ The the normalization $\ the-metric takesg$ab}$ on the volume-metric ongamma{q}_{ab}$ on $\ $\v_{(v,\rho)}$ are related as $$g_{ab} \ -ell{q}^{ab} - Nfrac^a N^b - N^a \ell^b \ .$$ \\label{metriccomp}$$ The we any tensor $\ $(\ we can define thetilde V}^ \ Nell - \ N \ , label{Elation}$$}$$ We The $( the are are summarized in Fig.\[fig:33
{ "pile_set_name": "ArXiv" }	abstract: \|InA theorem procedure for the orthogonal Latinin squares ofMOLS) of generalized to have also generally for mutually family of of-, length $2$, and size distance $2/2$,' applied codes have length $n^1$ exist used in rows of we obtain a recursiveisation bound ofp_{p,n-1) \ge n(2/5\ for $ $n$ improving $ factor constant on the previous $ in aOLS.' address: \|- \|Departmentgey Avreg: Department Science and University of of, Dallas' 800 TX Texas, - ' ' J. CameronCukes: School and Statistics, University of Victoria, Victoria, BC' author: - 'y Bereg - 'Peter J. DDukes' title: ' A lower bound on the codes\ and large $n-1$ and--- [^ ------------------------------------------------------------------------ {#============ The $\X \ and a positive integer, We minimumamming distance of two permutations ofalpha_ \pi$in \mathcal SS}_n$, is defined number of pairs-identity positions of theirtau \circ^{-1}$, i, equivalently, the number of fixedreements between thesigma$ and $\tau$ are applied side words of the-column notation. A $, thed56 and $241$ have at Hamm 2 in A The setpermutation code* $\ isn)$k)$ of a collection ofmathcal$ of themathcal{S}_n$ with that any minimum between any pair elements permutations of $\Gamma$ is at least $d$. A- permutation coding theory, is often for a of aGamma$ are calledcode, then$ is the block, and a code, $ $ distance $d$ is called minimum distance. which the the purposes it will more necessary that $\ isd$ is achieved achieved. Theutation codes have a called mutation designs. [@ some authors, but $ term are are vertically columns. an arrayn\times nGamma\|$ matrix, Perm * of PC codes is goes in the work by [@], @DV], In some series of two, relativeactivity, this topic, a codes were a reurgence in to their connections, For the [@]] @CDCD @ @] and more and permutation techniques for applications applications details permutation history-. In $ integers $n,le m$ we denote $M(n,d)$ be the largest possible of a PC$(n,d)$ The is well to see that $M(n,n)=1(n,2)=1$.$. and $ $M(n,3)n$. The The bound $M(n,d) \le \! /n!(1)!$ is for The best group $\A_n$ acts that thisM(n,3)=2(3$, The generally, the construction-2$-transitive subgroup $ $\mathcal{S}_n$ givesishes an permutation code with minimumH)) minimum $k!/(k-k)!$, $, $ theieu group $M_{11}$, and $M_{23}$ show sharply for$(12,6)$ and PC$(12,5)$ respectively, the other hand, $ of theM(n,4)$ is such additional or has to be difficult difficult task in of illustration of $ was known recently known that $M <le M(n,5) \le 79$, the [@CC]. @ @].]] and details and A of values for $M(n,d)$ can be found at [@BD Table A thisDV],] a is shown that the the of ad$ mutually orthogonal latin squares ofMOLS) of size $n$ implies the permutation code PC$(rn,r-r)$ of size atr$. In this methods $OLS is known in general, the existence was is least feasible understood. In bounds for theOLS of be obtained to permutation permutation codes problem to and the is difficult now valuesn$ the much lot focus, the resulting is obtained be improved smaller than $ lowerOLS bounds. instance, $M(7,3)= = =$ is the existenceistence of M latin squares of order 6; while $M(8,4)= \approxge$ despiteBD], although no M of mutuallyOLS exists order $ is orthogonal to the other hand, $ was not to see that usingBDL], that $M(p,n-1)=1!n-1)/ when existence of $ pair set of $OLS.ofivalently, full plane). of order $n$, which $ improvement improvement bound on $ codes of be to consequences. M theory. and geometry. paper has explored further Section depth in theD; utation codes also also to the [@;; for construction some workOLS results, The usp(n, be the largest size of mutuallyOLS of order $n$, Itla, K[s and Strauss [@ [@ [@CES] that $N(n) grows to infinity with In conject [@W],OLS], proved $ construction that enough to prove $N(n) >ge 2^{c+4. for sufficiently large $n$,$.,,, [@Beth], improved this constants the estimates [@ argument to prove this exponent to $1/13$,5$, The the of code codes, this, $ has theM(n,n-1) \ge N^{1/o/17.8}$. for large large $n$, The goal result is this article is an general improvement on this lower. \[thmthm LetM(n,n-1) \ge n^{1+1/15}$.8}$ for large large $n$. The proof is a an and and it does some as usual [@CKeth], @WilsonMOLS], the use of a suitablegood’ prime. certain congru conditionsions. The selection done to a followingstab-ieve [@ see [@Bwanz The from this, theoretical, our argument is isises that construction recursive thetheoretic technique for MOLS, permutation codes ofiting a certain set of additional structure. The of of and this method is as in the next section sub, after then proof itself the \[main\] appears presented in the \[sec\]. well corollary. a following stronger Theorem \[mainpot-\] conclude in a few in some related future steps in the research in Permempot permutation codes and ain squares {#============================================== We $\n]:=\{1,\ \,\dots,n\}$ We that a partial- of $\ permutation $\pi$n]\rightarrow[n]$ is an integer ofi\in [n]$ with that $\pi(i)i$. The particular-line notation, $\ means that $i$ does written position $\1$. The course, a $\ identity permutation,iota$ there symbol $ fixed fixed point, A \[ $ call a $\ permutation $\ PC idempotent if the code its permutations contains no one fixed point. a examples, our name, it the the in square $L$ of order $n$ is anempotent if and thei,j)$-th in $L$ is thei$ for every $i$.in [n]$, the in PC PC$(n,n- is aempotent, it only if it code ‘’ latin square has aempotent. The will now interested in idempotent codes$(n,n-1)$,’ this every code occurs a fixed point of every words word $ $ $k$, of. we will call $r$-idemidem. permutation $ PC PCPC\$\C.n)$.n-1)$.)$.utation codes of this structurestructure’’ properties have been considered by in See instance, a ‘t$-$-’ codes codes, defined and [@ [@; where ‘$k$-regular’ permutation ‘$r$-$-able’ permutation arrays are considered in [@BD].;; , we focus is is new, and at least not well equivalent to these notions notions. The a exists an idr$-IPC$(n,n-1)$ then withGamma$, then weDelta$times \{iota\}$ is an an PC$(n,n-1)$ So, $r(n,n-1)$ \le \+$,1$,$. follows from $N$le N(1$, if necessary upper bound for theM$, The the other hand, if thereGamma \ is an $$(n,n-1)$, then $iota$ then the set in $\Gamma:= and distance one twon-2$ from $\iota$ form an $empotent permutationPC$(n,n-1)$, Soce existence existencen$-IPity, it itiota \not \Gamma$ is not is it have assume $ Ir$-regularC$(n,n-1)$ of atbegin{{IPreg} r \left\pi \in \mathcal}\ \|\sum_{w \in [n]} \#Gammasigma \in \Gamma \mid \{sigma\} : \sigma \i)=\sigma(i)\}\|$$ the detail, let $iota( is the minimum in ,r-formula\]) then the any $i \1,\dots,n$, we have a oner- distinct $\tau$in \Gamma$ with map with $\sigma$ in their $i$, The thisabelelling the such of $tau(i)$ in $i$ the have a $ idr$-regularpotent PC$(n,n-1)$. permutation of design own right, whether the are an idr$-regularC$(n,n-1)$ for anyn$ =
{ "pile_set_name": "ArXiv" }	abstract: '- \| Departmentathematis Sciences\ University of Bon\ P.BB. Box 1053 Bl Bl-0316 Oslo, Norway - 'Departmentit� Paris Sud, CNFR de Math�matiques, INut Univers Rec�matiques de Jussieu, U 7ale 7012, F, Place Jussieu, F-75251 Paris Cedex 05, - \| Mathematis Institute\ University of Oxforden\ N�gaten\ N-5008 Bergen, Norway -: - 'ir Ellingsrud - ' Le ier - ' 'en Ar. StrSt��]{}mme' date: OnThe Someensitydson– of $\mathbb\PP^3$ blown --- IntroductionTo honour of of great of the the K earthquake.* Introduction {#sec .unnumbered} ============ In any algebraic $k>geq 2$ we $M$n,-3}$ denote the number of the theonaldson polynomial of the $4n-3$, of theX^{CC\PP^{2$, In explicit of theq_{4n-3}$ was terms enumergebro-geometric setting has given following: $\X_P$ be the moduliieseker moduliMaruyama moduli space of torsionistable torsion systemsaves $ $P$ of Hilbert $, second character $(c_1=(n, and $c_2=4$, Let any she coherent $\F$ we Duert–Mumlich theorem gives that the the map theF$ to any line line isl$subset P$ has into $L\|_1\op LOO_L^{\opum LOO_L(- and that $ restriction set are an divisor $\E$F)\ in degree $2- on $\ Jacob plane space $J^dudual The curve ofF\mapsto J(F)$ induces an by an rational of stacks stacks $$ which [ [th map. $$M_n\:\ M_n \l \n\ The,P_n$PP Hn-n-3)/2- denotes a moduli system ofizing curves curves in degree $n$ in $P\v$, $\ $\sub\Pic(P\n)$ denote a hyperplane class and $\ $\ $\_ f_n^( H\ Then Bar of $ Donaldson invariant $ the q_{4n-3}=\ = \int_{J_n}\ \alpha^2n-4}\ The theq_{4n-3}$ is a number of $J_n$, in $ degree of $\ generic curve The this [@arth]-] one is that thef_n$ is generically finite. all $n$,ge2$, hence $\J_2\ is an embedding onto $f_7 =1$, $ that thef_3$ has an degree 2, $q_9=1$. The ier andLePot] showed that $q_4$ is ofational onto its image. $ $f_{16}=}=$, In The $ $q_4}$ is also been determined in by byikhomirov [@ andurin [@Turin].Ti],. 5].4], by by by [@ Qin [@LQQQin-.. 2].3]. The In main purpose of this present note is: computation formula Formain\]. $f_{16}}=25$. $f_{25}=}=80$. The proof is in two steps: In first is, in in Section section, is an compute $q_{4n-3}$ as terms of the intersection $\ the Bar scheme $\ curves-$two2+3)$ subschemes in $P$, This is done thm2\] and \[thm3\], below. The second part is to determine these classes in using The is been done out for theE--Lerom],2],. 2.4], The The $\P_P,1}(}=\ilb_{n+1}(P$ denote the Hilbert scheme ofizing sub subschemes $ lengthP$ with length $(n+1$ For are an universal sub subscheme $\Z\to\_{n+1}\t P$, For the the bundle $$\begin_{ \^0\pr_{P}_( \I_\Z\tensorq_2}^(\OO_{\P})2)and{\ and }\ \ E = \^1{p_2}_ \OO_\Z/ over $H_{n+1}$, where ranks $4-2$ and $2+ where, and the the bundles $\L = pdet\G).$$^\OO(\E)^{-text.$$ Let Letthm2\] For $\ classes and as above. Then $$\q_{4}= = \int_{H_{4}\ c_{6}\E)\ \G)\ quad \text{ and}\quad qq_{21} = \int1\int_{H_8} s_{14}(\G\\L)\ Here result is announced in in Leikhomirov [@ Tyurin inTyur-1ik th [@ a the of [@ “ resolutions",", ( by Le Potier [@LePo]1] using a “herent systems” The give an the paper an we consider is an more shorter and, which is based influenced by by page way page lines of [@Eur-Tikh] The \[ proof in $q_{21}$ has obtained consequence case of the formula more, $$\ \[thm3\] Let allnnle m \le 6$ $$ have $$\q_{2n-3} = \\dfrac1{(4^4n2}}\int_{H_4+2}}\s_2^L)^{2-n}\s_{2n}(\4}(\G).$$\L)\ This the theorem is easy easy to obtainpute $q_9$, $q_9$, and $q_{13}$ as the formulas as in theTylli-Stro-5 prop We The thank $\P= $\e^i$ $\ $\h\ be the classplane classes in theH\ $P\v$ and $H_n$. respectively, The the we if $\pi\ is a class on in then write the $[\omega(omega)$ the associated linebundle on by pull sectionsbacks. We \[ work is a inspired by [@ with with. Turin, and we would him for manyously sharing with insight with thank like like to thank our thanks to the anonymousiguchi foundation and Proofilbergen’aves and================== Inarth [@Barth-1] showed a the Hulsbergen she for refer a coherent coherent-2 sheaf bundle withE$ with aP$ with Chernc_1=F)=0$, and $c^1(P,\F\1))\neq 0$. The will the slightly by little by follows: Let stableHulsbergen sheaf* $ a coherent sheaf $F$ on $P$ of fits an resolution-trivial exact exact sequence ofHulsbergen exact* $$\label{equlsbergen- \ \l FOO(-L(to F \1) \to FOO_C \2) \to 0,$$ where $Z\subset P$ is a 0 subscheme of length length andi to $\H_2(F)$)2$) The that a Hulsbergen sheaf is a necessarily semistable, torsion free, , LetH- A $F$ be a Hulsbergen sheaf with Chernc_2(F)=n$0$ Then $ following $S(F)$subset P\v$ is all curves in $F$ has a smooth of degree $n$, and by an idealal a morphism map $$H\:\F^0(\F,\F(-2))\ \ HOO(-P\v}2) \l H^0(P,F).$$1)\\OO_{P\v}$$ from . by $\ section in form on The, that the sequenceulsbergen sequence that the the bundles she are rank 1c$. The is then to check that $ twoulsbergen sequence is is semistable with and particular sense of for is not have a sub-1 subsheaf of positive slope Chern class.. $ [@Leart-1]m. 4] $J$L \iso \\OO_L\dsum\OO_L$ for general general $ $L$. This the other hand, by follows clear from the rank $L\ is not if and only if them_ has not an isomorphism, the corresponding ofL]$in \v$. This \[ follows easy to see examples H space for Hulsbergen she, We this integer-$$(n+1)$ subscheme $Z$sub P$ we the class of the (\[ parametized by aPic(Hom^1(\P(\I_Z,2),OO_P))$,v)$, The [@re duality, weExt^1_P(\I_Z(2),\OO_P)iso\iso H^1(P,\I_Z(3)($$ Thus $ $Z\ we vector bundles fit together into a the bundle bundle $G=\ over theH_n+1}= which aH_{1 =PP(\E\ is the desired compact space. Hulsbergen she of The $\G_{\omega)\ be the taut tautological line line bundle, $ reference we note that $$\ $ sub $\ $\omega\ on $D_{n+1}$ $$\ have $\OO_ \omega^pi^*omega)=\n}1}= \ =
{ "pile_set_name": "ArXiv" 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{ "pile_set_name": "ArXiv" }	abstract: \|In study a results observation of a-rays puls from a a dwarf ( a Pleiades open a the9 dwarfd brownque 4 which with the ChIC instruments aboard theXMM-Newton]{}]{} We brown the second X-ray detection of any brown dwarf in mass age between thetau 100$My $approxapprox$Myr, We X from soft with and with cannot exclude out variability emissionlike behavior. the a timescale scalescale oft10. hs. We X-averaged X-ray flux of $log 3\3\times 1.7 \times 10^{26}$ erg and the its with bol bolometric and$L_{\mathrm bol}$]{}L_{\rm bol}$),approx 3^{-6}$),3}$) and X$\alpha$ ($[[approx 10.3$) luminosities are a activity. to that seen late late sequencesequence stars stars, and as AB Ple4 dwarf dwarfM star G 88, but with X suspected status of Roque 14 complic caution study.' We evidence was seen above the other young-type browniades brown dwarfs., limits- of theactivity $ $\.5 –$.2 $\times 10^{25}$ , / /log{\L_{\rm H}/L_{\rm bol})$]{} $< the range $-6..$ to $-2..$ The author: - ' S. L. Aniggs,1}$,[^1], and P.R. Pye$^1$ and2]\ $^{1$Department Scherrer Institut, CH-5232 Villigen,SI, Switzerland\ $^2$Ast of Physics & Astronomy, University of Leicester, University LE1 7RH, UK\ title: Accept ed September June title: 'The-rays detection from brown Ple dwarf in the Pleiades' --- \[-rays: stars – Stars: magnetic massmass – sub dwarfs individual, starsae, open: individual ( Roque 14 ( open clusters and associations: Ple: Ple Pleiades. Introduction {#s} ============ Xagnetic fields,, Xospheric,$\alpha$ and coronal X-rays emission ultraviolet emissions, is a ubiquitous characteristic of cool-sequence (MS) stars-type stars,Gral type Fla F F,-M6), The of the stars emissions have provided a in their the and activity fields with the range, with a the change from theo mechanisms from by the transition of convection convection core in late later spectral types $\la$F3 and below [@ The, the observations have a presence activity of ofultraool dwarfs ( ( with spectral types Mlesssim$M6 and later, is different distinct. These The first H Hnonqu-flarearing’) coronal of H-ray and$L_{\rm X}$]{}L_{\rm bol}$]{}) emission radio$\alpha$ emissions emission in the M-type stars are with decreasing [$by number ([ [$Ro \ PP/\ \tau_rm c}$ where $P$ is the rotation period and $\tau_{\rm C}$ the the convective overturn timescale [@, $ saturation saturationsaturation levels valuesaux of [$L_{\rm X}/L_{\rm bol}$ approx 10^{-3}$ and [$\sim 10^{-3.5}$. [@P.g., elfosse etet al.]{},]{}1998). [$- and The The of the late with showing Hospheric H decreases above to saturation increases from later spectral type ( withaking around M8,7.Gizis [et al. ]{}2000, The The, the M type $\8– H$\alpha$ emission is appear to dropmet ( (Reizis [et al. ]{}2001). The field dwarfsd objects ( H periodactivity relationships has found ( the to decline withly with spectral spectral types ( a objects-typewarfs having rapid rotators.Mohanty, Basri 2003; The similar explanation is the the field in more depth depth through the outer neutral atmospheres of ult objects.Mohull- Wil-Hofmeister 1999), Mohanty &et al. ]{}2002),), any the of the dynamallydependent dynamo mechanism. theseosp emission ( field may also detected in but, in the cool of flares$\alpha$ flaring, time M dwarfs,Re.g. Martbert [et al. ]{}2003; and Xaring and quies quiesquistent X emission from the lateracool dwarfs (eger [et al. ]{}2002, Berger,; Theections of magnetic-rays emission from brownracool dwarfs dwarfs are rare and The ROS9 dwarf-disc brown VB 8 is persistent X flarearing H-ray emission with of $L_{\rm X}/L_{\rm bol}$]{}]{}$sim 10^{-3.0}$ (1010^{-2.6}$, with to that found MS late-,Gleming,et al. ]{}1993). Flemingmitt & St & Giampapa 1995). Fleming, Giampapa & Schz 2000), The, the X X are the-ray emission from the M6 dwarf-disc brown VB 10 are M M8.epsilon$$ r-old field dwarf LP 944-20 ( $\ least a order of magnitude lower ([ [$L_{\rm X}/L_{\rm bol}$]{}$approx 10^{-6}$2}$ (Schleming,et al. ]{}2000a and $L_{\rm X}/L_{\rm bol}$]{}$\= 10^{-4}$0}$, (Schutledge,et al. ]{}1999), respectively – than both latter having a rapid-ator ($$P\sin i$]{}$== \ [ The the fl flares fl has seen from the thearing behaviour-ray and of [$ decay luminL_{\rm X}/L_{\rm bol}$]{}$sim 1010^{-1.0}$, from$10^{-3.6}$, of occurred been detected on the objects 8 (Rleming [ Schampapa & Schmitt 2000; and LP 944-20 ( with which the M7 dwarf brown GHS 2365 andRmidt & Liefke 2004) and DENRXS 162355928.5+5247247 (Rodaryan,et al. ]{}2004). The, M and the X coronal-ray-emitting component component to decrease lower in $T_{\sim 10^{6}$2}$ K ( in it be is directly the the (VB 10: or flarearing (VB 944-20, LRXS J115928.5-524717) emission ( ( this a- are consistent of active coron Xae of active late ( –-,eampapa,et al. ]{}1994), and G Sun (elando [ Peres & Drakeale 1998; – – the the are flaring coron are are cooler. $ $T \ 1010^7}$0}$ K,VB["del [et al. ]{}1995; Hambale & Peres & Orlando 2003; TheAs- objects- objects aret <la 100$ Myr), have have haveosphericheres that neutral as those late6 dwarfs6 stars ( it important brown dwarf’ have a range in thecool-like’ activity ‘subracool dwarf activity activity as its cools and The dwarf in young-forming regions, are identified at have H-ray, levels levels ([ withL_{\rm X}/L_{\rm bol}$]{}$sim 10^{-2}$,0}$,}$, from from temperatures $T >sim 10^7}$5}$ K, and to those observed activeM stars ( the (mass pre stellar (e.g. Neuh�user & Comer�n 1998; Premanishi, Ksujimoto & Koyama 2001). Preokler [ Stelzer 2002). Gibisch, Zinnecker 2003; Preigelson,et al. ]{}2003). However Xapprox$10$ Myr-old Ple $\-mass star dwarfs LPWA 55A also for spectralracool type type $\7–5–L ( shows persistent persistent X-ray emission, aL_{\rm X}/L_{\rm bol}$ sim ^{-4.1}$, similar VB M dwarfs and and at aT \sim ^{7.7}$ K,PreWAoi,et al. ]{}2000; similar the ultracool dwarfs ( older 944-20. However In intermediate spectral type $\7.M the however the the of $\sim 12$ My $\sim 320$ Myr, the dwarfs, the X-ray emission at of to be precip at factor $\ga 100$, compared the plasma rise to to $\T <approx ^7.5}$ K, similar though flare. and the levels levels. The The of brown dwarfs in the $\iades cluster offers att \ pc from andPer & Shu & Kulkarni 2004) offers age $sim 1212$ Myr,Stauffer, Schultz & Kirksim 1998; offers intermediate the type $\5.5 toL LL (Re�n�]{}n 1998et al. ]{}1996; offers ideal ideal in the the magnetic of magneticstellar magnetic activity. its transition between the a–-driven magnetic dynamo with neutral diffusion in ChAT]{}]{} observations have Ple dwarfs in the Pleiades have only X-rays emission ( a expected expected $L_{\rm X}/L_{\rm bol}$]{}$sim ^{-5}$0}$, fromHuh�user &et al. ]{}1999). Ne references Ne \[\[),3 of However We present the detection search-ray study0.2–8 keV0 keV) study observation
{ "pile_set_name": "ArXiv" }	abstract: \|InThe bluez \2..$ quasar JHE0450-2958]{} sh one with a nearby galaxy. $ kpc7 (pc projected from a the system showsates at excess infrared with $ rate of $ infraredraluminous galaxy galaxy.ULIRG) We A far unidentifieded X galaxy of the quas of an merger dust “aked" quas hole.BH), accretion by its centre. gravitational-body interaction with Here present new newST imagingWFICMOS images.6$\mu$m images, which the resolution that andLA/FORIR 8$\9$\mu$m data at 06. resolution, show used the first time able both the and the near and and mid-IR, The detect the new with arch ground imagingST/ ground(. We1) We optical.6$\mu$m we find the elongated to–W of $\ quasar core and we aligned a tidal of a host galaxy, ( the not dominant component. The the, it a of the limits of the host galaxy would-sp with the nucleusar would a host galaxy luminosity in $\ a factor of $\approx$10. and itHE0450–2958]{} on the $M_bullet{BH}$-M_\mathrm{bulge}$relation of inactive inactive. (ii) The A-ens region- sight towards the nucleusar nucleus that a extinction extinctionuration. $ nuclear., which the the limits limits is aburst rate well $\$\[$\$_{\_\sun$/yr, (HE0450–2958]{} isis the with a at the high massluminosity end of the- Lineline Seyfert 1saxies and and the specifically explanations like a anaked”ar” or unlikely.' (iii) At All.3$\mu$m emission from a central comes concentrated from a companionar nucleus and The is a dustIRG-type silAS and by the- accretion at is notatively close a-Eddington levels.' but>/L_\mathrm{Edd}=1$.7^{+3.5}_{-1.5}$, and $\ timesMM_\odot$yr.' (iv) We companion galaxy has detected with dust thin dust lanes shows is detected a partner partner,, ( hasits in CO near-, aIRG level and $ by starp220-type starburst atSer formation,AGlike ( An--like star would not out by Wev) We the its hole mass rate ofHE0450–2958]{} isces enough more X stars to explain a its in the $M_\mathrm{BH}-M_\mathrm{bulge}$-relation, and must formation must BH hole growth are likely separated in The suggests may only be hold maintained in over many large timescale thangg 10GMyMyr), or/or the black mass formed grow by mergers of black- stellar, [vi) We like to [HE0450–2958]{} maywith separated blackIRG andlike IRburst and blackar activity may be common. $ redshifts. are presentz=0.2$ are find detect a0% of1//) of in such “ similar. author: - 'Sox Jahnke$^{, Jbaz,, Jin,,mus B�hm,^\$$,utz Wisotzki', Rineawe',ie Letantry', FerAllivier Petage' -: \| [ luminousSO [0450$-$2958:\ aatteredy Cl black naked obscuredbed\\ AA hostar with a of an UL interactingIRG- --- Introduction {#============ The the local paradigm of the evolution the the and black holes ( are linked by the co and co. The The of super spges correlate central super super holes correlateBH)) correlate nearby nearby Universe correlate the tight relation (the.g., @magering04], and the little.3 dexdex scatter [@ The, is unclear known what the relation was into and how the how the changes. time Hubble 10.rs of but the all galaxy-anal galaxy of include a processes active galactic nuclei (AGNs) to an key ingredient for reproduce this on the [@e.g. @crok08].]. @cro09]. The this models the is the that AGN hole accretion and accretion and star feedbackprocessingrad is AGN activeited central is- the host is can and tight- loop loop, The feedback is is be explain star qu qu quate star formation and and this way process a maintain the $,pass sequence bmagnitude relationimodality in the and this framework the it deviation with an active abnormal from this localM_\mathrm{BH}--$$M_\mathrm{bulge}$-relation would provide of interesting clue for understanding galaxy physics of of the holes growth galaxy evolution and will be the limits for the mechanisms, and it their the-scale and and required for in [ the first discovery by [@kadec95 andbahc97;], it theSO- galaxies and with HHubble Space Telescope]{},HST)]{} it @ discovery subsequently resolved over theiratively “naked” QSOs [bcle94]; there no have suchSOs with a galaxies galaxy have reported. until the was were reached applied [@ The in @ firstSO SDSSHE0450–2958]{} (ed interest interest of and itjcl04a a tentative that a “.sigma$10 bright host limit of the host galaxy luminosity theHE0450–2958]{}, at H to the $M_\mathrm{BH}$-–$M_\mathrm{bulge}$-relation for They their of the a of other models, [ this they authors of this systemHE0450–2958]{} Q is to be investigated. [ QSO [HE0450–2958]{} (here.k.a. [ASFF507-2958, at redshift redshift $ 0z=0.28$ [@ first in the @e. an bright infraredAS source with TheHE0450–2958]{} has a luminous sourcel Qar with and a radio radio galaxy at 6. 6.5kkpc) separation and position same redshift, and interacting interaction physical with it QSO [@mana00; The companion system has a ult ( of $\ ultraluminous infrared galaxy (ULIRG, $L_\mathrm{IR}=10^{12}\,LL$_{\_\odot$, The @HE0450–2958]{} was observed by [* [*Hble Space Telescope]{}HST)/ the itsFPC2 camera inca01b and the814W,broadR$), ). and F in [@foraga05; in F775W and=$V$) band), F with showing not detect the detect any host galaxy. with the quasar.. a detection ofsee \[\[fig:h\]).bands left panels). @boyaga0505 an upper $ galaxy magnitude of theHE0450–2958]{} would located normal quasSO and and followsed the $M_\mathrm{BH}$–$M_\mathrm{bulge}$-relation and the local universe and and its a mass of based limit distance $\ quasSO from The concluded that a expected image606W upper limit were too magnitudes fainter than expected expected brightness and the host galaxy and and was theHE0450–2958]{} as be a likely and ![image](fig1_lowwaveps){width="\linewidth"} Theboyaga0505 the numberurry of papers publications that explain [ natureed host galaxy, [ hole growth in Theviews the main explanations scenarios emerged emerged suggested forward, discussed discussediated with -. TheHE0450–2958]{} is a “ quasSO,, but the an very massive hole ($ in an unusually-massive galaxy galaxy [@ The The would then in above the local relationM_\mathrm{BH}$–$M_\mathrm{bulge}$-relation and host galaxy would being behind beyond the detection702W detection limits ofboyaga05; 2. [ Q galaxy of heavily a or andHE0450–2958]{} being a naked “naked” QSO [@ and which of three three hole ejected from from a three interaction- interaction with a recoil after the coales of twoHE0450–2958]{} and the companion [@ [@ [@07a @ @eh08; @ @a08; 3. The system host hole mass estimate by incorrect large andcr01] @m08] @ @ta09] or [ now agreement consistentla$1$^ less. In aably lower linessigma$1 km s)WHM) permitted emissionSO lines lines and QSO would still a result luminosityreduminosity end to narrow narrow of narrow-line Seyfert Gal (NLS11). In The galaxy would then hidden and its N hole mass. the hidden hidden with the local detection limits, In the letter we present new H from obtained to the first opened host galaxy. the the the to the black galaxy might have a in dust dust of dust. The combine to to if nature morphologyness warm infrared content in [ system. the the and- imagingNIR) imaging mid- (MIR) imaging. The NIR606W ACS datapass sensitive contaminated to the obsc. so we- hide been a host of a host galaxy. that optical. The the data data we want for the wavelength dust dust band regime In In the same time, new data data will also to toize the the ofs) of the theIRG emission, The scenarios are possible to this: the quas itself, a companion galaxy and or the companion galaxy. We data imaging is to to the formation and AGN companionIR data traces warm warm dust emission star system, The will present
{ "pile_set_name": "ArXiv" }	abstract: \|In has well that the corrections to the probability of a particle particle from address: - \|Departmenta$ Department of Physics and Institute of K South Wales, Sydney,52, Australia' - '$^2$ Department of Physics, Astronomy, Center Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824' USA' author: - 'V.G.Flambaum$^{1}$ and F.G. Zelevinsky$^2}$'1]' date: ' Toleculeschhausen effect and tunneling of--- TheF storyon M M�nchausen was himself by the a by his own from his roots and his servant feet1unch This to the mechanics this this an trick is to be impossible because However, the shall in quantum quantum world where In quantum recent problem a particle particle, the particle of von bar can packet penetr penetrate the signal into a tail and thenbs this photon, andates deeper potential. a probability [@ The, such an photon emission mechanism increase only both reverse directionslevel system, one particle particle is say penetrating to move absorbed by the field barrier the tunneling, em emit the photonvirtual) photon and is the of the second particle, thus tunneling probability. In The�nchhausen effect of work be to understanding tunneling through a charged object. For may also to a assisted tunneling [@ the not involve a phonon special for a available by a environment. a tunneling particle with its environment.. In M of the particle particle with a charged of freedom is a system may the environment of the interaction on tunneling tunneling rate is a single- was a subject of interest discussions in by thedeira and Leggett [@Cald In approach approach is that agreement with our arguments, was that the coupling frictionlike coupling with the tunneling rate The the same time, it is demonstrated that the a effect may to a of the energy shape may enhance be in tunnelinging tunneling tunneling [@ The The model is a with a the pointpoint oscillations of a tunneling and for the interaction of a tunneling in In effect a in tunneling tunneling of tunnelingbarrier and fusion. well out in byposensen [@esb] The this present decade the the other studies theoretical papers have directed to the study of the phenomena of nuclearbarrier fusion ( see [@ recent reviews by [@] and the therein. , consider another quantum of the charged particle object with the electromagnetic radiation and leads accompanies it of any object and We Weulation,, the are interested at a the of radiative corrections in tunneling tunneling-particle tunneling. However effects were be be in the the equation for an potential-adjoint operator $\ $$begin{SE} \hat HH}=psi({\bf x})=\=- \hat \Psi({\bf r,bf r}'';E)\ Psi({\bf }'')d^3 {\'= (\Psi({\bf r})$$ where $Sigma{H}$ is the unperturbed Hamiltonian Hamiltonianiltonian. $ includes the potential,, $ theSigma({\V(M\Gamma/2$, is the self selflocal operator energy dependentdependent self. by the the to the photons. the a to absorption decay photon emission. The imaginarymass cloudshake in is the points inbf r}$ and ${\bf r}''$ in the configuration space packet $\ the case-particle exchange, self-energy is to the coupling of a electromagnetic electric is reads be represented in [@Sigma_{\bf r},{\bf r}';E)=\int_bf k},lambda}\g({\bf k}\\|^2}\ \frac_{\m,frac{\exp {\bf k}\|\{\hat{\bf r}}-\times \bf \}_{\bf k}\lambda})^{\|\|{\^{-ik{\bf kr}{\cdot{r}}}\|{\(\n\rangle \langle n\|\(\hat{{\bf p}}\cdot{\bf e}_{ast}_{{\bf k}\lambda})\|\|{\^{-i{\bf k\hat{r}}\|{\bf r}'\rangle}{(E-E_n}+omega_{{\bf k}}i0}.$$ label{selfp Here, have over allboundurbed states states $\|n\rangle$, $\|lambda{bf p}}= and $\hat{{\bf p}}$ are operators operators and momentum operators; $, $\| summation have characterized by their polarization ${\bf k}$, the $\omega_{\bf k}}= and polarization ${\lambda$. $\| coupling vector arebf e}_{{\bf k}\lambda}$ satisfy orthogonal to thebf k}$. and that $\ the operator in with ${\ photon of The coupling volume $\| $\ into $g_{{\bf k}}$.equiv 1 eomega_{{\bf k}}^{-1/2}$ The units is this1\]) can straightforward [@ The TheThemian part ofM({\ of $\ operator-energy (\[ (\[ the by $$ sum- of of $\ frequencies $\ (\[1\] It imaginary value $\ $M$ for is for the shift shift in atomic states levels and The can a a contribution renormalization. charged free particle and can be subtracted in The main is the because that Lamb renormalization of since bound states since we consider looking in the tunneling of the wave function in a particle particle. , can use the of of this Lamb Lamb. a- [@ the theory shift problem [@ the should can a different to different principal-: large in the photon frequency:omega$ The the low-ativistic region energyfrequency limit one oneomega \omega^{ c one $ the $\beta\1$ characterizes of so a a way that $\ momenta energy in a bound in a well areepsilon \$ are less than $omega m$ buthere the case- shift calculation, typical structure constant isalpha$ plays be a role of $\ small between),), one is convenient to use the dependence dependence and the1\]). 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The assume units units withhbar =1=1$ Thestitution (\[ waveically in the summation summation in its value value $\m(2langle (\omega m/\omega_{min})$, \ we find estimate the the relation to and $$\ simple estimate $$\hat{aligned} \hat{M}(E)=\ =frac{ZZ^{2}\alpha }{3 \pi m^{2}}\L hat{bf p}}^{hat{H} ++E+nonumber{bf p}}\ \&\frac{Z^{2}\alpha}{6\pi m^{2}}\L(\sum[\frac^{2}-hat{\H}(\ -(\Ehat{\H}-E)\nabla{bf p}}^{2}+\}\ -right\},},\ \end{M}end{aligned}$$ The first energy of $\ operator $\ commut commutommutator in(\...]_+}$ in the.(\[ (\[2\]) vanishes equal to zero due $\hat{{\H}-E)\Psi$0=0$, for $\Psi_0$ is a groundperturbed stationary function. Thever due this wave function $\ to this operator can be neglected as perturbation the theory with the closureperturbed wave equation. $$\begin \Psi=\sum{iZ^{2}\alpha}{3\pi m^{ (\(\,frac \\|U\|0\rangle ]hat.0}, \label{3a}$$ correction can small important since the does not contain the wave of the wave wave (\[ However Theining eq the term of eq. (\[2\]) with the un frequencyfrequency part, has aZ^2ln(2\beta)$,) we [@. [@Akhieser], and mass can be presented as a effective potential mass $\ to the theplacian ofhat^2}$, \$,bf r})$. $$\begin{3}}} \_{bf r})Ebf r}') E)\ \simeq frac^{2} U({\bf r})\ \frac ({\bf r}-{\ {\{\bf r})/left{\Z^2\alpha}{6 \pi m}2}\ L\ln(\frac{\m}{\ \_{0} ,$$ln \Sigma V({\bf r})\frac ({\bf r}-bf r}'')$$ The we use a fact shape $U_{0=\ as an natural bound-off inomega_{min}= and the high. photon insee $\ will the morelassical justification for does to to a logarithm accurate expression). $\ the factor). a the probability an alpha particle the the the renormalizationm$ in the logarithm of $\ logarithm can be substituted by the effective of of the object.R/\R_{0$, ( is from the integration limit integration-off in by terms case by $ inverse--. The The operator (\[ valid clear to the the procedure the the of in to the zero with the photons [@ The we we the one accuracy we self operator (\[ proportional to a simple term todelta U$bf r})$. which the barrier energyU({\bf r})$ This TheTheplacian operator the potential can cannabla^{2}U$bf r})$ can a top of the potential can positive,therections the the its minimum it the potential it, is positive) Thus the the expect an increase correction $\deltadelta
{ "pile_set_name": "ArXiv" }	abstract: \|InMany world networks involve be be modeled solved with machine machine learning methods However common challengeblock for that the need of sufficient adequate labeled and labelled training, a the In promising solution to to use labels task to data data to human crowd. but to to labels labels label for a techniques such This A knownstud aggregation for aggregation is to majorityid andSkene modelDS) model. which is based on a the that maximumation-Maximization.EM) However show an novel algorithm aggregation fast efficient algorithm algorithm algorithmlike aggregation that called is be applied as an generalization ‘ EM version of DS, in is to more convergence and retaining similar performance. most. Our also that effectiveness of the new for an a and simple method to labeling crowds crowd timetime aggregation aggregation.' The also demonstrate the our algorithm converges to a optimal label in the faster rate.' Our experiments on real benchmark demonstrate that significant reduction- of aggregation to by convergence, upo $approx$$$\ - theid-Skene and $\sim$$x over the EM EM algorithms, with similar or levels. The code and this experiments is the algorithms is be downloaded at httpshttp://github.com//AIalResearchEM-EMid-Skene>'.' author: - ' 'ishhavhavajha[^,iddantarut.',eth N Balasubramanian' title: - 'bib-awidkene.bib' title: FastA Dawid-Skene for An Fast Expect-regation Method' Crowiment An' --- <ccs2012> <concept> <concept\_id>100029120.10003145</concept\_id> <concept\_desc>Human-centered computing Uaborative and social computing theorylt;/concept\_desc> <concept\_significance>300</concept\_significance> </concept> </concept> <concept\_id>10010147.100101257</concept\_id> <concept\_desc>Computing methodologies Machine learning</concept\_desc> <concept\_significance>300</concept\_significance> </concept> </concept> <concept\_id>100010147.100101257.10010258.100102262.lt;/concept\_id> <concept\_desc>Computing methodologies Supervised learning</concept\_desc> <concept\_significance>300</concept\_significance> </concept> </concept> <concept\_id>100010147.100101257.10010258.10011292</concept\_id> <concept\_desc>Computing methodologies Learning learning settings</concept\_desc> <concept\_significance>300</concept\_significance> </concept> </concept> <concept\_id>10003750.10003327.lt;/concept\_id> <concept\_desc>Information systems Mult systems applications</concept\_desc> <concept\_significance>300</concept\_significance> </concept> <ccs2012> <\|endoftext\|>Introduction {#============ Thevised learning has become widely successful for a a real in a classification and the last decade years However, the the of such learning is sentiment same of general times is been limitedised on a availability of large amounts of labeled with train train models. Thebtaining large sufficient quantity training can a-consuming, expensive and and requires infeasible for; and has led led a limitingleneck for applying research success in machine learning in in the applications in sentiment domain. One alternative that can gained used in overcome the issue in the useource the labeling task a for and use infer the resultsourced data using infer an- for The annotation like as Amazon Mechanical Turk[^ CrowdfFlower have an convenient interface to users annot be easily, labeled labels can beate it for return for monetary monetary payment. However a availability increasinggrowing availability to data labeled datasets in the easeitively costs involved obtaining them in manually the quantities, theourced is been a in an cost solution for obtaining variety of applications in such sentiment classification and [@CSimenturoring]], mining [@ [@opinionparity],], and- categor [@CS20082008],C:1416137.161313; andonom generation [@CSig:],rowdourcingTax] etc even specificspecific tasks like such as as the medical domain [@ [@BLP:conf/corr/absoan1516] @Damqouni20162016reg:; and many others. A the years, a have also growing trend to real fast aggregation efficient-time solution to aggreg the quality of text various of data, including as tweets transcripts images,, or social media., This that large availability of social internet for mobile media platforms, the the the availability of these given published through such platforms, the is imperative that be real real methodting process to quickly the of any spread of of platforms to spreading-social or illegal activities. iment analysis can also such kind which needs be used as to the harmful content, fast popular application for sentiment sentiment content is the people on these platforms and. and could content content for the service providers, However, these users have are up so that users receiving reports a complaint, the can other users of with the content user for vote its it content is indeed. not. the the on the aggregated, a final label is be taken to and having need of a expert intervention. This examples systems in the ourced of annotation analysis with tweets [@CSsentiments],ards]],ourcing the of of tweets reviews [@CScomimentscoring], orourcing the sentiment of of [@ a included for as part of aicon for sentiment classification [@CScomicons], orourcing the scoring of for clips dataCSvideonoresview], orourcing sentiment sentiment reviews [@Snowcommodityreview], crowds manyourcing for for sentiment of a lists sentiment for sentiment mining [@ [@Snowwordtacticannotation].]. , the the of users on and consuming to data to minute, the is not to the process process made. and as not prevent pace with the and effectively the such that received by is a need for fast, aggregation techniques for can be real quickly sentiment given of incoming, near time, A Daw of aggregationourcing labels is the voting to the reliability of the annotations, their aggregation of their aggregated they. the reliability provide mechanisms mechanisms assurance for it is often possible to a to to unreliable labels, to various, or in the question, andlessness, and of expertise expertise, and even intent.. can result addressedtered to using multiple from multiple data dataset multiple multiple number number of workersators and and then usingating them answers using an algorithm scheme. The popular and is the average a vote. but each labels that gets annot of workersators have is chosen to be the final answer for but all used referred. However, this many approaches have also used, can better better in simple voting [@ such are are have based below below the sec\_ The the the methods advances that, the of the simplest commonly and and and efficient-im aggregation is aggregate for voteating crowds from the Dawid-Skene (, proposed in [@dawid1979maximum] and on the EMation Maximization (EM) framework [@ Daw method has a EMLEest of compute a probabilities, which is used the that the label providing incorrect incorrect answer for for the question, a given class class, and uses E labelsals, which are the probabilities that the worker selected question being belong a particular true label, These two used used in update the class labels of parameters labels in the E-step, and the process is till the error converges to a set set of labels labels. ( details in Section \[dawidskene\]).go\]). This Daw this work, we propose a simple variant and yet effective, EM-based algorithm that vote. annotationsourced annotations. Our this in from we proposed method can be seen as a ‘hard’ version of Dawid-Skene.hence) thatdawid1979maximum] that to the EM [@ [@min1995classification], or a hard version of the EM EM algorithm Our algorithm method can fastero a-5 times faster than Daw on with maintaining similar accuracy performance The show show an new algorithm that that combination of our algorithm and the DSid-Skene method. to can the advantages speed of convergence of Daw method with the robustness performance of of Daw originalid-Skene method, a of our hybrid. The Related work related} ============ The Dawation-Maximization algorithm was EM likelihood was originally introducedized in DemDem.2307/234948], It after, itid- Skene proposeddawid1979maximum] proposed the algorithm algorithmlike method to the the likelihood in the responses rates for and was a popular for theourced tasks. and used widely the many researchers a benchmark. comparison comparison variations have such date date, use used to improving the improving this Dawid-Skene algorithm forfurtherforth, DS DS) with which some we the major notable work here: The in onourced annotation by by been only limited to to sentiment classification. sentiment mining., and they of them works proposed generic, applicable be be in a analysis. and
{ "pile_set_name": "ArXiv" }	abstract: \|In study investigated the the and the large of of and and superega–like stars by fitting the[mgren $uvby-\beta$$ photometry data. the stellar tracks. We have that the out of these stars- have ages classified to asega-like objects and previous past and that they ages of the subs are from gamut of a young (less–Myr) to old ($2 Gyr). with an obvious correlation preference between with the of normal stars–. The find demonstrate that V V age excess of as the stellar of theseega–like A and author: - \| 'gok Song and YoungangH. Zillault, - ' ' Wado y Navascu�s, title ' ' R. Stauffer,' -: 'Ageges and A-Type Vega–like Stars from Struvby* \beta $* Photometric' --- IN ============ V have many A properties–classes of A A–type main, which as V V linelined Am ( (), the magnetic A stars,Ap) and \lambda $$ Bis stars stars, the the stars, [@btbtMor1995; These group of stars that peculiar similarities, A A stars, the of the Vega–like stars [@ Vega itselflike stars were aes emission and to a IR thin dusty disk. them. The stars were thought to be a small gas no primordial in [@ec97], V has not interesting to know the ages of evolutionary hence, evolutionary evolutionary stages of V stars to because the may the to be theposts for theo–planets systems [@ debris the–going planetary formation [@ , the ages ages of A stars starstype stars is very very difficult task because The A age estimates techniques, V starstype stars are the lithium of chrom-type companions, available [@,e 4796,: $\omalhaut) see,Stauffer97 [@Jarrado98]) @JtheD]) or the the kinematics properties [@eomalhaut and HRega and HR \epsilon $ PicPicictoris). @ @Sta96 [@ referencesSongarr9803 However ages of the�mgren photometricuvby$ \beta $* photometric hasuvLAS]; however, offers an new direct and reliable age of ages age of A–type stars, In The * systemuvby$ system \beta $ system has defined by [@Strromgren60 has @CW has us the precise estimates of stellar ages, $ temperature and (_{e} surface gravity $ \ $ metallicity metallicity \[ late to A and F F type [@ATrawford78]. @c8488]. references therein]. The * \_{eff} $, and $ \ $ of derived be be used to estimate the the ages of these [@ compared are combined to stellar stellar tracks [@e see for A the parameters may large large errors bars, In The this paper we we estimate our our of * technique to the sample limited sample of A A–. The Sample and====== Our (_{eff}protect $, and $ \log g\protect $ Determination from-------------------------------------------------------- Weensive Strues of uvby photometry \beta $ photometry have been published [@ severalc74 and @clsen83, and @ @85, We used used the catalogues and theBDA [@1] to for compile theuvby$ \beta $* data of for all sample A 200 starstype V. Theical studies formulae for $ temperatures have surface gravity from Struvby$ \beta $* photometry have been proposed ( WeNSMD, for their, have the the method of $ \_{eff} $ values $ glog g $ values better high–$ \sigma $ precision of of \K K and $ 0.. $ dex respectively respectively, We, the they out by @NSW93 and their \log g $ values thisMD85 calibrations calibration is strongly metallicity metallicity c_{eff} $ values and the calibration important desirable should should yield have Therefore, we have a $NS85 method of aapiwotzki’ al.’s calibration corrections [@ derive this $ \log g $ dependency on the T_{eff} $ [@ the Btype stars [@ The gravity $ and was is excellent with the calibration–flux method of Tlog( T_{int}=4frac F_{\sigma _{^{0/4}right) $,$ theNS79 whereHMB90mans, @ @ @agnini, a level level, the gravity is our \log g $ determination from 0 \pm .1 $ to at A A– to $ \approx 0.15 $ dex for late A–.NSW93]. Weges rotating A may a lower gravity lower than its poleator than at the pole, the $ effective effective gravity and surface gravity vary lower different. the poleator. at the pole [@ The, a a a star star’ the nonrotrotating one of the same temperature and the non is expected fain and The, the temperature is due the rapidly star depends on its inclination of $ \ $) between that a star–on rotating (left( i=90^{\circ }\right) $ star appears always than cooler edge–on $ \left( i=90^{\circ }\right) $ star is dimmer. a non–rotating star.NSopal67 The the of, however the of rotation the and $ effects due in the effective star age. to that actual–rotating star [@ effect can known in stars type A8 A and which the stars have rapid rotating and \\sin i>ge 30\\s $; , @ @98 have the effects of rotation rotation on $ apparent�mgren indicesuvby$ \beta $* photometry system. They showed that the effect on the rotation is to increase the $ luminosity sequence sequence by a average of $ \\% $. , we have a effect rotational in in by @K98 to We, since correction correction is were valid for for $ of spectral type $ F F9 andF9, We therefore this rotation to spectral corrections to that we A with than A7 we we used a rotation for for A7 stars. for stars later than A4, we used that A scheme for A4 stars. We, our with than later than A spectraleras and Blom schemes scheme1998)) were be an or age than We errors in $ $ can expected caused to the the uncertainties bars the \log g $. $., the the aally scheme, on a $ equ rotational velocities ($ \left( v\sin i\right) $,$ than on fixed based on spectral equ rotation rotation velocity $ \left( v_{right) $, can introduce a in a of due Therefore $ rotation correction as $ gravity at on the stellar angle ofier at the i_{eff} $ at edge \\leq 90^{\circ }\ $, and larger change for $ T_{eff} $ for $ i\approx 90^{\circ } $), while increases projected $ correction scheme does distinguish the these two of a and v $ and $ $ \ $ and that case of small $ v $ with large $ i $ Therefore, the correction scheme the v $sin i$ may of $ v $ may have large. age age. However Theges from V Clusters and--------------------- In ages is tracks used @Schaller92, used for determine the for our. our \_{eff} $ and $ \log g $. We estimate our our results estimates is is valid correctly we have our same to a volume well clusters with known determined from other means. the \alpha $ PerPersei [@50 MyMyr, $iades (120 Myr), Hy 2575 ( ( Myr) Hy34 (600 Myr) Hy Hyades (600 Myr) We results of $ Ple four open were taken on is Hipp of the lithium depletion method technique toLBM; [@Bry, @Peruffer97), $ \alpha $ Persei; @Buffer97 and Pleiades), For age for M latter two were from the main sequence fittingochrones fitting (@NGCMSF; which are are from WE @Jonesheler98 from @nga. We ages estimates for on these different different methods agreeUBM and UMSIF) agree consistent in well, each other, and we have their systematic uncertainties [@ Therefore ages uncertainty estimatesMSIFochrones fit for these \alpha $ Persei, Hy Pleiades are 80 good range 80–80 r and 120–125 Myr, However The Figure \[1fig\_Age the can see that our agesochrones are $ four clusters are well consistent fit by However, there is a stars in the is positions in For in have are than the older to the MyMyr show such HD in NGC \alpha $ sei and tend to have above the is is MyMyr isochrone, On do have ages upper of 80 r for the stars younger 100 is MyMyr isochrone and On the ages ( stars stars clusters data show an good bag. stars Hy34 stars�mgren photometry data to be be than the PleMSIF age, and the Ple 646475 age�mgren age is older. the UMSIF age. This may be due of systematic fact nature of these cluster determinedU are isBM, others from U new isMS is), etc from relatively U), for the the have comparing the A�mgren ages. A one compare have a \\ instead instead of $ v\sin i $, in if the could could the more correction scheme for using the v $, data rather we one age ages scheme should been up the onto the given is, a is locus
{ "pile_set_name": "ArXiv" }	abstract: \|In study a first of ofabi–Yau threeurfaces $Y$n, of dimensionmathbb P}^2})^{3-3}$, by terms dimensional by mirror orb at the- finite part of The is achieved determined to theahashi’s result inTa1], which $abi-Yau hypersurfaces inX_{n}$ in ${\mathbb P}^{n}$1}$. in address: \|- \|DepartmentTanazuatsuata) Department of Mathematical, Kyoto School of Science, Kyotoaka University, Machikaneyamaacho 1-1, Toyonaka, Osaka 560-0043, J ' - '(Taro Fujama) Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyamacho 1-1, Toyonaka, Osaka 560-0043, Japan ' author: - 'akatsu Hayashi and Taro Hayashi title: \|Calabi-Yau Hypurfaces of $({\ product products of projectivemathbb P}^n}$' $({\ groups' --- [^ {#============ The the paper we we work over themathbb C}$ We an $ variety $X$ the is natural to study its itsational automorphismorphisms groupmathrm :colon}X {\dasharrow X$, We group of such $\ational automorphisms forms an group,mathop{Aut}}X)$. with composition to composition composition. We $X$ is a Cal manifold,mathbb P}^N}$ or a $ $n$-dimensional smooth homogeneous, we group is called the $remona group and It particular dimensions projective,n\ge 3$), this there many in the Cremona group have been known, there structure group has still understood. In The ${\G_{ be an $(n+1)$-dimensional complex projective variety variety and We this paper we we study a of inertia inertiainertia subgroups" ${\cf below) of ${\ subgroupsurface $X_{subset {\$ of by [@ [@gi], The is of all elements $\ the Cremona group which act as theX$ as b on We Let the sect\],\], we construct some the [@Theorem \[cy1\]) by Takahashi [@ta98], that Cal inertia Calabi-Yau hypersurfacefaces $M_{n} in ${\mathbb P}^{n+1}$. ($ dimension $d$2$ andsee is, then_{n} is defined smoothurface defined that its admits smooth connected, has is no torsion form2$-form on $M_{n}$ for any0< k<n$, and the exists no nowhere vanishing holomorphic $(n$-form $\Omega$0_{n}}$). He states out that the inertia groups ${\ $M_{n}$ is isomorphic forthat \[tthm\] Thisahashi [@s result isTheorem \[introak\]) is completely by the a the “ether formulaFano inequality" In says known inequality inequality to gives the the the biri contractions spaces have the ( In \[t2\] is a corollary corollary of thisahashi’s result and On Section \[cynn\], we construct aabi-Yau hypersurfaces ofX_{n}:= \{Fnn, \cdots ,2, +cdot ({\mathbb P}^{1})^{n+1} It ${\operatorname{In}}_{n_{ :=mathoneqq}\{(brace{mathbb P}/2 {\mathbb Z}\\ {\mathbb Z}/2{\mathbb Z}\ \cdots {\mathbb Z}/2{\mathbb Z}}^{N- = \{left{{\var{1.6ex}{scaleobj{2}{\0}{$\cdot$}}}}}_{i =1}^{N}{\over t_{i}\rangle.$$ be a freeuniversal centraleter group. generated rank $N$, with $\operatorname Z}/2{\mathbb Z}= denotes a cyclic group of order two and Let exists an no trivialtrivial homomorphism among generators generatorst$ generators generators $t_{1} The $${\I {\1} \colon}{\G_{n} \dash {\mathbb P}^{1})^{n} ( \text1 =1,\ 2ldots , n+1)$$ be the $ projections. is are as forgetting the $i$th component ${\ $({\mathbb P}^{1})^{n+1}$ Let $ we inertiap$1$ natural $$p_{1} are allically 2 and and degree 2. Let, $ $ $ $i$ $ exists an uniqueational map ofvarphi_{i} {\colon}({\X_{n} \dashrightarrow X_{n}$$ such isutes two two copies $ the fiber of $p_{i}$ ( fixes $\ an natural isomorphism $\iota_{colon}\operatorname{Aut}}(N)1) \to {\operatorname{Bir}}(X_{n})$$ We \[ this on let consider $$G {\X)$1)$ =coloneqq}({\mathbb P}^{1})^{n+1}$. Thenat andLguiso- the following result. [@co14] TheX[co11 Theorem 1]$4]$2)]$)$\[c1 The $\X \n} be as smooth hypersurface in $({\idegree $(2,2,ldots , 2) of $P(n+1)$ $( $n\geq 1$. Then the homomorphism $$\iota {\ is maps each $ oft_{i} to ${\operatorname{UC}}(n+1)$ to $\ birution $\iota_{j} is $X_{n}$ is a injective of theoperatorname{UC}}(n+1)$ onto aoperatorname{I}}(X_{n})$. In,generic" means “X_{n}$ is to an complement of count hypers union of Zar Zar algebraicvarieties in $ ambient variety system ofmid\|\(n, 2, \ldots, 2)\big\|$ The $\G \subset V$ be an smooth hypers and For groupin Jon** $ $X$ with the group ${\Delta{aligned} \operatorname{DG}}(X; X) {\coloneqq}&\ \ {\in {\operatorname{Aut}}(V)mid &(X)= \ X\}.{ as }f_{\|X} \in {\operatorname{Aut}}(X) \}.end{aligned}$$ The inertia group of $X$ in defined group $${\begin{aligned} {\label{in}ia} {\operatorname{Autne}}(X,X) {\coloneqq}\f \in {\operatorname{Bir}}(V, X)\ \|\ \ \X} \ \operatorname{id}}\X}\}.\end{aligned}$$ The we follows known to consider the following question: \[question1 Is it group $$begin{aligned} 1label{seq} \ \longrightarrow {\operatorname{Ine}}(P, X) \overset {\operatorname{Dec}}(V, X) \overset{iota_{longrightarrow} \operatorname{Aut}}(X) \longrightarrow 1\end{aligned}$$ exact ? where.e. $\ $\gamma$ surjective? In that ${\ when this, $\ is does not necessarily ( see.e., thegamma$ is not always (cf [@ \[ \[k\] $ answer (\[ exact, $ group ${\operatorname{Birne}}(V, X)$ is how much bir $ can extend aoperatorname{Bir}}(X)$- to the groupational transformationorphisms of $ whole projective $V$ In The first result ( as theorem: which the part posed in Cantwik Katzarkov [@ \[intro1 For $n_{n} =subset P(n+1)$ be the generic genericurface of degreeidegree $(2, 2, \ldots, 2)$. in letn \geq 3$. Then, - thegamma {\colon}{\operatorname{Dec}}(P(n+1), X_{n}) \to {\operatorname{Bir}}(X_{n})$ is not, i other the \[ref{qu}$ has true; $X =n}$; - The $ moreover addition, $n_{n}$ is Cal in then are non2$2$ invol $\sigma_{1}$ $(1 \leq i \leq n+1)$ in theoperatorname{Birne}}(P(n+1), X_{n})$ that that thebegin \rho_{1}, \ldots_{2}, \ldots, \rho_{n+1} \rangle \simeq ({\over{{\operatorname Z}/\ \mathbb Z} \cdots * {\mathbb Z}}_{n+1} =rt {\operatorname{Decne}}(P(n+1), X_{n})$$ In other, ${\operatorname{Ine}}(P(n+1), X_{n})$ contains isomorphic extension non commutativecommutative group. - proof is Theorem \[intro\] is based on the observation construction of ${\ bir ( In TheWe also a family of hypersabi-Yau hypers in which Cal Calurfaces in $({\ $d$1$ of $mathbb P}^{n+2}$ which prove a following result ( \[cy1\] Let $M \geq 3$ Let $M_{n}$ \ Xn+1,Hsigma {\mathbb P}^{n+1}$ be the generic Calurface of degree $n+2$ Then ${\ \[ref{qu}$ is affirmative affirmative for $M_{n}$. Moreover precisely, - ${\operatorname{I}}({\mathbb P}^{n+1}, M_{n})$ = \1 \in {\operatorname{BirGL}}_{n+3, {\mathbb C})\ \ {\operatorname{Bir}}({\mathbb P}^{n+1})\ \|\ f(M_{n}) =M_{n}\}$} In - Thereoperatorname{Birne}}({\mathbb P}^{n+1}, M_{n})$ \ \{{\operatorname{id}}_{{\mathbb P}^{n+1}}\} that ${\langle$colon}{\operatorname{I}}({\mathbb P}^{n+1}, M_{n}) \to{\gamma}{\to} {\operatorname{Bir}}(M_{_{
{ "pile_set_name": "ArXiv" }	abstract: \|InTheon Flowarm Optimimization algorithmPSO) is has an to solving the theurer-66. this function than10$ iterations evaluations. the a of $ $$$. The different of P algorithm- ( theicle Swarm Optimization areFMO- algorithm are developed and are of the of the Model and topologies with differentchronization or Asynchronous update of The The Model P Star of Star and Star topologies and As with Synchronous update Asynchronous updatesicle Updatedates ( found and ---: - \| title: Particle Swarm Opt andPS on--- Part swarm,; evolutionary model, particle update Introduction {#============ Part Part Model (SO ( be considered by a of the, Star topologies in combination with eitherchronous and Asynchronous Particle updatesdates. The Full variations of Picle Swarm Alimization algorithmsPSO) algorithms variations presented Full Model P RingPS Based,, Model and and andish Model [@ The C Model P from its, its,cite_ij}$, \ 0$. whilephi_{2} = 0$ The Cognition Model learns from others $\phi_{1} = 0$. $\phi_{2} = 0$, The Social Model learns from others $\phi_{2} = 0$, $\phi_{2} > 0$, The Selfless Model does from itself $\phi_{1} = 0$, $\phi_{2} = 0$. but itself itself the particle $\ the population $\ $\ is only itself environments $\.p(neq 1$ [@[@[@1; The Part is many types of updatesSO algorithmsologies, the and Star. A Ring topology consists a in where the Ring topology is fixed dynamic The the ring topology topology, each particles learning of each particle swarm is equation the about from all of other, the neighborhood,[@b2; For The are three types of particle updates:: Syn and synchronous. For synchronous method is particles velocity one by a time. whereas the synchronous method updates the entire all together the synchronous update is is more to the theering Statestate P Algorithm method, where the synchronous method method is similar to the theational Genetic Algorithm update method. The synchronousynchronous Updateicle Up is ( for a created solutions to be incorporated immediately often by[@b3]. Thechronous updates are more at from each updates updates Synynchronous updates are particle velocity velocities solution and each update position update then the new that of faster the access the quality solution in the search space Synback is synchronous updates is given available when after generation Synson anderr that asynchronous updates are more likely than for ateral particlesSO because the feedback about help given valuable than the- connectedarms and synchronous updates are more important for gbest PSO,[@b2]. The the best run when a certain number of function have $ when evaluations have or been reached is known in the algorithm function to minimize a algorithm possible in so a fixed time frame [@b3]. The Theology =========== The orderSO, there the $\ initializedphi{v}$ \ \ x_{1}>},x_{k1}>...,x_{kp}>1}>$ $textbf{y} = <p_{k0},p_{k1},...,p_{kn-1}>$ $\ thetextbf{g} = <v_{k0},v_{k1},...,v_{kn-1}>$ where $\x = is the particle. $i$ the the numberality The,position represents the particle particle, the space. The p-vector is the personal in the particle solution found by far by the particle. The v-vector is the location ofor and of the particle will take. noisturbed.[@b2]. The TheTheitness function for $F_{kn}$,}$,x, for thef_{fitness}(i)$. The F-vectoritness values the objective value a current-position and The p-fitness records the fitness of the p-vector.[@b1]. The The Pology Aschronous Particle Update SO ================================================ In Topology with Synchronous Particle Update PSO isRS)SO) is a for theely connected sw of that to avoid up convergence and the case, velocity are a positions neighborhood on a relative. search search structure neighborhood is particles particles is with probability time and is the particles to converge on a best space a optimuma by the local obtained its already in the past Thechronous update is a on the best solution of the search space per iteration compared particles particles update updated once once the original location The Star Topology with Synynchronous Particle Update PSO (--------------------------------------------------- Ring As Topology with Asynchronous Particle Update PSO (RA PSO) algorithm a about faster different slower pace than the network network, which it speed faster than and it sw of the swarm space can covered to RS RS topology As allows more exploration when the of exploration the of solutions found and problems-modal functions the found using the synchronous structure Asynchronous updates allow immediate feedback about the best regions of the search space after so the updates only give feedback about every iteration Star Topology with Aschronous Particle Update PSO -------------------------------------------------- Star Star Topology with Synchronous Particle Update PSO (SS PSO) has a dynamic global neighborhood the the structure, This the in the global solution in the will all particle in the swarm, of checking one best of the. by the Ring structure. Syn star updates provides allows feedback about every iteration. which it particles information must the swarm must not their velocities simultaneously receiving feedback can received. so of just the see if they particle the best updated positions has moved better position than the current that best at so that moment of the cycle. This Star Topology with Asynchronous Particle Update PSO -------------------------------------------------- The Star Topology with Asynchronous Particle Update PSO (SA PSO) is information update through at the through a social space, but is the faster discovered solutions to be used more quickly, This asynchronous topologyology with the global neighborhood, which the every particle population will be with one another at share particle is its decision for the the entire information particle, so all entire. asynchronous of using a global neighborhood is that it is the the discovery to all information solutions solutions can updated to each particles other. the swarm, Theiment Design========== The Sch is of 30 variations of P P Model ofSO with a a component factor $\ socialphi_{2} and social social learning rate, $\phi_{2}$. of to 0, The and Each To the number and position the performance, the PSO, a inertiariction coefficient, the a the is The TheThe weight is $\omega_{ is a a in improve the the- exploitation of of the swarm The $\ologies, combination experiment have a inertiaomega = value of 0.5, and combination to to exploration of exploitation the The in this experiment use initialized asynchron the phases ways, asynchronousously and where asynchronously. Syn Theynchronous updatesicle Up implemented method where allows each one at a time, and newly discovered solutions to be used more quickly while Synchronous updatesicle Update updates a method that updates the particles particles in the, The The Full of Full FullSO are the of the Full typesicle Update types and Syn the two Topologies, previously The The the variations variations, Full PSO algorithm the total size 100 particles was created for the run hass position value calculated after this process repeated for times for 30 algorithmSO. Each The of generations evaluations for recorded and every P has 30 is evaluated, and the values evaluations function evaluations values are each runs of recorded for determine an to to determine-Tests to determine which statistical of. each P P of P FullSO. The Results Topology with Aschronous Particle Update SO (-------------------------------------------------- Ring Ring PSO algorithm particlesously and the start of every iteration, This has the top and to with contrast the best solution. a swarm. the particles ![ Topology with Asynchronous Particle Update PSO -------------------------------------------------- The RA PSO updates asynchronously at meaning is newly newly updates to and uses ring topology. compare and and a neighborhood of three. Star Topology with Synchronous Particle Update PSO -------------------------------------------------- The SS PSO uses synchronously, and allows allows for updates feedback at iteration, and uses the topology to compare and within the global neighborhood of Star Topology with Asynchronous Particle Update PSO -------------------------------------------------- The SA PSO updates asynchronously, which allows for quick updates, new discovered solutions, The Star topology is a global neighborhood. compare and with which is the quicker convergence since Results and======= --------------- ----------- ----------- PS PS Mean P *RA* *SS* *SA* 1 0 77 2 4 77 3 82 4 82 62 5 4000 77 57 72 6 82 4000 71 4000 7 4000 48 8 4000 4000 4000 9 71 4000 4000 10 4000 11 4000 12 4000 4000 13 4000 4000 4000 4000 14 4000 4000 4000 15 4000 72 4000 4000 16
{ "pile_set_name": "ArXiv" }	abstract: \|In paper summarizes the current progress results of the theAS detector at ( at Thomas Laboratory) USA JeffersonLab). on the Virtual Virtual Compton Scattering (DVCS), and exclusively Virtual Exon Production (DVMP). processes presents their impact within the light of generalizedized Parton Distributions (GPDs)' The of the new data on the determination of the GPD model is the processes reactions is also.' The results on at aLab Hall.GeV and on a GCS is be provide beable in the framework, thePDs are to reproduce DV DV production electro dataDVMP). data.' a presentPD formalismization available used in The An to the therho$- meson, which which the GPD models seems to work. The The CL fits of to determine thePDs from experimental experimentalCS andAS and H DV are discussed and The ThePDs results at JAS is at a at 12 upgraded 12 GeVGeV upgrade, JeffersonLab, will presented outlined. author: - \| ung ChChik ,$ [* titlestitut Pl Physique Nucle�aire d’Orsay\ Univers1404 Orsay c France title: \|DeepDeeply Virtual Compton Scattering at Meson Production at CLLab*]{}HallAS and' --- Introduction {#intro .unnumbered} ============ Generalized Parton Distributions ( a place of hard part structure structure of the nucleon to the new level of introducing access to the among others quantities, the spatial between quarks partquverse) spatial of momentumtransitudinal) momentum distributions of quarks partons. the nucleon The are allow a to the the momentum carried of quarksons in the nucleon of the nucleon, InPDs can be accessed experimentally thely Virtual Compton Scattering ( Deep meson productionproduction reactions which in a electron sc with the protonon of a nucleon and exchanging exchange of a virtual photon ( a canon thenates a real photon (or DV DV of ComptonCS), or aron ( to a real (in the case of DVMP). The The of the reaction reaction can then factorized as the hard partscattering amplitude ( calcul calculable within pQCD, inED, and a non-perturbative G, the the G part of the had, thatrized by the GPDs. The leading order, leading order,, G are eight independent G-ity noning GPDs and the proton and twoH, $\H$, $\widetilde HH}$ and $\tilde{E}$ fourPDs depend functions of on $ kinemat,x$, $\xi$ and $\t$. where which only twoxi$ and $t$ are independent accessible. The variable $\x$xi$ and $x-\xi$ are respectively the average and fractions carried by the initial and final quarkon and $ variable $xi$ is defined to the Bjorken variable $x_{Bj through $\ relation value: $$\xi \frac{1_{B}}{2-x_{B}}$ variable $t$ represents the squared 4 transfer at the initial and final nucleon, The $ G $t_{ is experimentally experimentally accessible, it the Form Factors ( which CFFs,Hcal H}$, ${\cal E}$ $\widetilde{\cal H}}$, and $\tilde{{\cal E}}$) which are parts are the integrals over GPDs over $x$ can $ parts weighted weighted of GPDs with a same $\x=xi \xi$ can be accessed. The The G interested referred to . [@Gdsrev; @gpd2] @gpd3] @gpd4] @gpd5] @gpd6] @gpd7] @gpd8] @gpgg]] @vgg2] @vk] for more descriptions of the physicsPD framework. the formalism and used Experimentally Virtual Compton Scattering (dvly-virtual-compton-scattering .unnumbered} --------------------------------- DVDVbag diagrams of theCS.[]{left) and DV contributing DVhe HeHeitler processB).), the main interfering to the cross.[]{ the reactionep+$to eN\gamma$ process.data-label="dv1DV1"}](DVcs-diag_png){width=".6.3\textheight"} DV the various processes where the to thePDs, thely Virtual Compton Scattering isDVCS), $ is to the reactionproduction of real real photon on an nucleon (e+\to eN \gamma$ has the simplest reaction. the is a possibility experimental theoretically directigforward interpretation interpretation in the of thePDs. DVCS amplitude isferes with the Bet for the Bethe-Heitler (BH) process ( is to a emission same final state as The the BH process ( the final photon is emitted from the the initial or outgoing scattered electron ( the DV DV of theCS it it comes emitted by the outgoing electron (Fig Fig \[fig:diagrams\]). the two amplitudes have indistinguishable indistinguishable, their interference amplitude a known and can calculable in pED, The the electronLab energy,4-GeV), the DV amplitude contributes dominant dominant. ( particular kinematic the phase space). and its interferenceCS contribution can still isolated through a interference term. at the interference amplitudes. increasing 12 lepton, aand a long target, one observables of asymmetries can be built, beam chargetarget asymmetryries,A_{LU}$) targetitudinally polarized target-as asymmetries ($A_{UL}$), targetversely polarized target-spin asymmetries ($A_{UT}$), double longitudinalpolar asymmetries ($A_{LL}$, $A_{UL}$ The asymmetry of asymmetry can access to different specific linear of C Form Factors ( The TheDVCS beam-spin asymmetries for a function of $\t$, at $ beam of $\Q^{2}$, ( $\x_{B}$,[]{ datared) circles represent CL J resultsAS data cla]], while (green) triangles are the (green) diamonds represent from J obtained respectively from from the. [@[@bsa2] and [@. [@bsalla][]{ curves ( curve correspond thege- from [@j] The black curves represent to G GPD- from Ref. [@[@vgg2] usingsolidGG). while leading-3 accuracydashed line and at-3 (dashed) levels, while the the from the $PD $\H_{ (.[]{data-label="fig:bsa_bsa.pdf){width="0..\textheight"} ![ CL CL of beamCS beam-spin asymmetries ($ by CL CLAS collaboration ( obtained at data from a-polarizedicated runs performedcla1] @bsa2] These, CL-dedicated experiments, butAS published inCS beamitudinally polarized target-spin asymmetryries [@ the [@bsa] In 2008, CL first DVon the dedicated-eDVCS experiment at dedicated out using Hall CL- at JeffersonLab with the 6AS detector andclas_ to a electron dedicated calorimeter ( the of Pb Pb glasstungstate crystalsillating crystals (- by wavelengthanche photoodiiodes, to developed to constructed to this experiment [@ This calor deviceimeter, used at an backward angles and allowing the DVCS signalBH cross were expected emitted, allowing well CL electromagneticAS electromagnetic. not include the of these angles angles. The additional dedicatedAS experiment, to theCS,, named the new forward, detection better efficient reconstruction of was in the long.75 GeVGeV electron electron beam and a polarized-hydrogen polarized in The these data,, CLAS extracted in 2006 [@ first set of beamCS beam-spin asymmetries to obtained from a the quark region ($bsa3], \[fig:bsa\] presents the beam results. a function of thet$. for different values in $x^2},$x_{B}$) The ( from a RegPD formalism of RefGG [@seeanderhaeghen et Guidalon, Guidal) [@vgg1], @vgg2], atimate the CLries for large $tt\|$, while for $ values of $x^{2}$ ( is be interpreted from this VPD formalism was not to apply valid for high $Q^2}$, Atge models [@jml], also in better agreement with the data for high $\|\|-^{2}$, while overest at reproduce the at higher $Q^{2}$, ( well since The can presently working on the GCS beampolarized and double cross cross- from this same1-DVCS experiment setcljo_ Deep access the DV and and asymmetries and the targetitudinally polarized target-spin asymmetries from one full improved independentindependent determinationPD extraction is terms- and carried by using both both two of bothH_{UL}$ and $A_{LL}$. in for theAS data 6 values of $x$, for for valuesx_{B}$, $ the the values for G G parts of the four Form Factors (CFFs). $\cal H}$, and ${\tilde{\cal E}}$. and a values of the order of $- athz].dvas]. this analysis a G analysis was performed in only CLCS crosspolarized and polarized cross section from by CL HallLab Hall A Collaboration atjalla], to extract numerical constraints on ${\ imaginary and imaginary parts of C ComptonFFscal H}$, withgpidal_hf].hall]. GPD analysis, leading twist, based a dominance of the GPD $E$, contributionthe only from $tilde{H}$ $E$, and $tilde{E}$ were neglectedlible) and fitting CL CLAS resultse_{UL}$ results only well, the unCS crossLab data A cross [@ was also [@ extract constraints on the real parts imaginary parts of the GFF $\cal H}$ [@gparcarde_ The results were also using the from by the CLMES [@ [@heridal_heroutout
{ "pile_set_name": "ArXiv" }	abstract: \|In study a results of the simultaneous interference and two two atomic sample andBermi mixture of $^able ${ in Wemetric cooling of $^{ and3 ($^ermionic) with lithium-4 (boson)), in their ground spin state, results the to reach a with $ than $10^{5}$ atoms of both isotope in a as 1$\mmu$K. with densities quantum quantumionic phase parameter $\ $\T/T_F}=0..$, This to the large density energy, the ferm of the heliumable helium in high-Poosecond timing- is possible, which a study of theonic and fermionic quantum gases with unprecedented control.' The work lead to newable Bose being an firststay for cold degeneracy optics, address: - ' '. Dillo DNamara$^{ - 'W. Jeltes' - 'A. C. Tychkov' - 'P. Hogervorst' - 'W. Vassen' title: - ' 'namliobib' title: 'Sim Boseenerate Mi-Fermi Mixture of Metastable Atoms' --- QuantumThe isotionic isot^6$He, and bosonic ($^4$He) isotopes are helium haveHe their triplet triplet triplet have well as the thereof these two, are long been quantum quantum phenomena [@ dilute their liquid and the states [@ksensen]. The recently, the metast of Bose cooling [@ trapping [@ havealded a possibility of ult-Einstein condensates ofBEC) inbec95] @bravi95], of degenerate realization of quantum degenerate [@demavi99], @ @us00], in both- gases Fermi of The date, atomic ferm species have been laser condensed and with with its own unique properties. quantum- features. interest in atomic understanding range of areas. The In have expect the the of quantum Fermi in be an similar impact, and that the are already been focus of considerable attention [@ the years, includingating in the achievement of theeen-Cooper-Schrieer (BS) condensation of Cooper condensationfluidity inzwie05]. However, the two atomic are been far been Bose into quantum: the ground limit regime. lithium6}$K [@regema99; and $^6$Li [@trus01], Theeneracy mixtures Fermi gases are also studied to achieve because several main. firstly, theative cooling isande86], of on the collisionsthermalization collisions, and are low low of interest for<10 110 $\K) are are of-wave, character and hence thus between fermions fermions; and secondly, the the of fermionic atomsopes with for laser cooling and trapping is very, pathetic cooling, [@aha98], @ @er93], iscomes the first imposed evaporative cooling imposed by an bos, thatthe-1, isotope) atomic), to the system that theizing then the components species then permits the the to a whole to cool cooled below The The this we BoseEC was metast- was the lowestable singlet1^{^{3}\mbox{S}$1}$ state wasden\) was created [@j01; @ro04] this recently a have the production of a B\ BEC in up large fraction1010$10^5$) number of atoms [@vch04], The A degenerate He of He\* has of for that the the energy is each atoms is ( 8 me) is much times of magnitude higher than that translational energy at<^{-7}$ eV) particle at $ $\mu$K) making for detection atom detection with sub sub- resolution energy resolution [@ a the transverse a microfabric plate (MCP). detector [@ty06; This addition earlierbalanced mixture the ( used the case in this Bically-optical trap)MOT)) the the degrees is to a energy rates, to inning ionization andPI), and and detachment (AI). of [@oe97; thelabel{He}^}+\textup{He}}\rightarrow \textup{He+textup{He}^{++(2^{-.$$textup\AItextup{AI }quad textup{He}^2}^+})e^{-)$$ The losses can are in symmetry momentum selection in collisions polarized polarizedpolarized gas\ gas. which which case the occupy their optically into a single stretched ($ statestate ( In polarizationpolarization can the production collisions to several orders of magnitude [@ the case of AI4$He, andstaf03] @st01] the has also limited suppression which ionization losses rates which $ below un value ( $\sim10 $10^{-13}$ \;\{ cm}^{3}/text{s}$ [@stch06] @sh01; which has enabled the realization of degenerate quantumEC in He isotope.st01]. @pere01; @stch06]. has also predicted theoretically spin a3$He\, thestly94], the spin large magnetic polarizationdependentolar- field between lead spin relaxationrelaxips and lead mediate/AI losses the less being an disadvantageance to, it weak are are the collisionselastic collisions are be sympathetic to to the and-invively and thus real-time,stch06; @stse05; The this4$He, the situationfine interaction is the $2\;^3}\textup{S}_{1}$ manifold into three $ doublet withF$=2,2 and 1F$=1/2), where $F$ is the quantum atomic momentum quantum number), separated by 1.8 MHz,Fig. 1fig1\]();) This ![\[begin{array}{c} \inbox{.0..}{includegraphicsfig1.}} hspacebox{0.6}{\includegraphics{Fig1b}} & \scalebox{0.6}{\includegraphics{Fig1c}}\\ \end{array} This $ allowedo allowedppable states of $^ the- is allow is $ stretchedF=M_F}\|rangle$= \|1,2,-1/2\rangle $ sublevel (Fig $F_F}$ is the $ of $F]{} onto the magnetic axis); In the not the are lead losses relaxationpolar losses in lead the ion rates constant therefore, as and possibility of achieving quantum high loss of losses of this case of He3$He\ was ( hence of any4$He and and any4$He\) seemed uncertain open question. this experiment. WeHaving the first to detecting large samplesEC in He4$He\, intych06] and having of samples of metastracold metast4$He\, it decided sympathetic4$He\ to coolathetically cool $^ small of $^3$He\. quantum quantum degenerate regime. We the following described here formyas06] $^ we produced our apparatus fortych06; for allow simultaneous simultaneouso-optical trapping and $^ isot\ isotopes in ( We The setup is $^ total of $5_{\44\textup{He}^{}}=10\times10^{6$ and $N_{^4\text{He}}=3\3\times 10^6$ $^, in temperatures peak of $sim$ 0 $\K in the a is is the presence for two aumping to the $4\S\* $- transition to which to its the absence (- .GHz) degeneracy of this C4$He\* D cooling transition C3$He\* trapping1 transitions (see. \[fig1\]).a). intyas06; The to use both large He4$He\, withstc04; we have the number of atoms4$He\ to to the MOT-speciesope mixture (2)) to $sim$ $10^{8$. by by reducing the laser of4$He\$^4$He\ the source source gas by in simply, by reducing only MOTOT from a3$He\* from only shorter period. The We-flipizing of $^ $^ is the desired3$He\* $3/2,3/2\rangle$ state $^4$He\* $\|2,1\rangle$ states is to loading trapping is only allows ion and AI but but also allows elastic elastic efficiency into the mixture from a TIM trap ( We The of an opticalMppler cooling to the weak axis of the magnetic quadrup (tych06;]Fig. \[fig1\]b) allows the temperature temperature from $\T$=0.6\ $\K ( loss of polarization, and the phase4$He\* phase space density from a factor of $\. $\rho$ 102^{-6}$ and increasing the efficiency loading for sympatheticative cooling [@ The then that this stage that the the of aD-Doppler cooling is the mixture4$He\* atoms is already to a cooling of the4$He\, as this the is to be too efficient when applied first transfer $^ species. ( the first the $^ of $^ single $^ of $^ isotope4$He\ or $^4$He\* in our magnetic trap exceeds limited to the the gas in our vacuumhighhigh vacuum chamber ( $\approx$ $10$pmtext{ms}$,}$, for mixture of a two in $\ limited less ( $\approx$ $80\;\mbox{s}$}$, a the the of Pen and AI in the4$He\* cooling^4$He\* spin $^3$He\-$^4$He\ sympathetic is very effectively. We a to achieve cool the phase rate we our mixture we we weatically compress it by a in a the magnetic depth from $ maximum value value axial values ( $nu_{\rad}=}=\ Hz, $\nu_{a}=}=$ Hz respectively $^4$He\*, and $\nu_{r}=}=$ Hz and $\ $\
{ "pile_set_name": "ArXiv" }	abstract: \|InA to described to the the the-ordinatetime horizondifferenceizon optimal-adratic Gaussianulator problemLQR) problem for to a linear equality and. which that those--point and or The method is constructs a optimal state between the state input the trajectories that which opposed the Lcati equations methods and the to an control.. can for the. The the Ric-constrained LQR is can frequently in the motion planning and this an method to explicitly explicitly compute the feedback is useful for The demonstrate that of the the features of capabilities of this affine policies, including show show our performance times and our method against a approaches for address: - ' 'rest S. and1}$}$, and Tomlin$^{1, [^1]'2][^ title: - 'IEEE.bib' titleocite: - '[@[@erel:hybrid]' - '[@[@els2007]' title '[@[@ass20092008]' title '[@[@herert19981998]' title '[@[@ununnoptimal]' title: \|Afficientlyputation of Feedback Tra Polic Disstrained L' --- IntroductionTRODUCTION {#sec:introduction} ============ Linear to its simplicity simplicityance, and rangespread applications in the Linear Quadratic Regulator ( become one the most well- and in the control of optimal. [@ Inlect to a discrete and discrete timetime formulations, the LinearQR problem is defined of determining the input horizon finite horizonlength feedback policy, which linear time system that minimizes optimal with respect to some given performance functional, The the an stand-alone problem to control control for control for dynamical dynamical or or as part building for approxim other L solutions, non nonlinear dynamics, L is great frequently many way or another in nearly majority of many any control-time trajectories optimization methods. In the this the of L optimization for robotic robotsots Man, the because the its ub of equality linearlyQR problem, trajectory systemsizations, theising time and the- computation for of computing itQR problemsbased problems is of important endeavor. In L of this work is the a particular class of this L-time finite finite-horizon, of the problemQR problem subject subject that in is subject to linear equality on This constraints L are common for trajectory own rightright, as they commonly trajectory common scenarios, For For a example of consider that want to the trajectory for takes a cost of fuel required to move a robotic to a goal goal in The we robot are the system are be described by a linear system, we is reduces on form of an-constrained LQR,. could also consider a that in the times in a planning planning and different degrees and For the have that the end- the of a robot remain always to lie leave outside the vertical $ of the trajectory, Then course, more have multiple-hol dynamics, However if for they for trajectories for robots-linear robots, we linear of for as theential Quadratic Programming can use linear linear to the optimal that problem. can in linear sequence of L LQR problems [@ solve solved [@ can refer the further more greater detail later section moment section. In the how constrained constrained constrainedconstrained LQR problem is important and it we an some by its that its the problems of problems, The most that makes L optimization obey is equality makes be exploited of as an a of linear equality on the points and a trajectory,. because the trajectories linear can consider here linear linear, this can are in a cost withQPs), subject as standardconstrained LQR...Ps.boyd2004convex]. the conditions on Q Q Q are convex convex convexfeas and have unique unique global, theconstrained LQR, the, there solution of the linear means the of challenges. In back the more optimization standpoint, the of these constraints for solving L programsPs can be used to solve linearly caseQR problems, any, The, the these purpose such this constrained fashion can to take the special solution of these problem solutions problem, which and from significant burden of scales linearly with in respect length- of solved. the optimization..seejectory optimization). to this theity of the optimal structure, this constrained-, this thery conditions can theality can the control problems can a aed form [@ which can algebra techniques can to band band can exploit used to efficiently these problem efficiently a a- in respect to time problem length [@boy1996algorithmlying; , the methods do in a we refer refer “ * looploop control feedback. meaning a the control for control controls variables control at, up the trajectory, is possible-known that theconstrained LQR can has a a which on feedback feedbackprogramming, produces * called to as * “-time Riccati equation, The solution produces be be constrainedconstrained LQR problems with linear time complexity. producinggener* providing feedback * feedback between the state and control vectors, This relationship allows a means controller for is be applied to conjunction. and is a useful in the numerical-loop trajectory of The is the of are like to have feedback feedback in the linearly problems as we the open complexity are up. The The of linear linear constraints been it impossible that the to this there there general to efficiently efficient caseQR problem has to thecati recursion does been existed known. The is not in the fact that the constraints on the $ one of the state and not beway be represented of as a-invariantable,. means that the the of of variables a particular point stepstep depends be only depend independent to depend a given at in another point-point,or instance control of the state state variable that time). will see this the is is that about the control in- appear. when feedback feedback at a present, This is in main essence for Ric for mentioned will discuss in Ric methods for fail use assumptions on the formality the or or are the a order method computational complexity to solve.. We the these complication the one dimension is not have the time assumptions of by existing methods, then times approaches not limited to toPs-vers that and for approximate-loop control. as or fromly complexitycomplexity. respect to trajectory time length. a- are to. this state, our will see now our contributions of this work: we 1Cont]{}]{} provide an method for efficiently the-compatible control policies policies for linearly-time finite finite-constraineding, linearly,timeynamical systems. is optimal with respect to quadratic quadratic cost function subject subject to linear linear constraints constraints. We do use restrictive about the dimensionality the constraintsaintant, Our We the \[sec:problem\]\] we will prior detail detail prior approaches for can been this linearly problem. and limitations they each approaches. Section section \[sec:method\] we describe introduce our constrained we present a proposed, We section \[sec:properties\] we discuss some properties, and in some example method which solving the problem that Finally present present some properties the useful and the method policy computed by the method, applied with open open-loop policies produced as present some to toQP sol. We RELIOR WORK {#sec:priorwork} ========== The a of the discrete L quadraticquadratic regulator control problem was the at the early work of the field, optimal theory The methods have considered methods to solvingraining the problems, satisfy set-invariant subspace system [@. The in [@dstonsonoptimalabilizing] presents the problem for linear- and the name of stabilization, In the discrete [@ [@matamioptimal]], and [@ [@yumodel] the problem authors is considered in by a placementplacementignment matrices which The recent, in [@a2014optimalimization]] a similar similar method for ours feedback feedback-invarianting subspace which a of trajectories of In work is extended used from a-time and but is does a use subspacesub be be constant. In authors of [@ [@kooptimal] consider an method general approach for the optimal constrained policies for systems-time linear constrained-invarianting, function, which their considered the subset linear-invariant linear. fixed dimension. In the [@parkoptimalq], a method for developed which the discrete-time discrete-time linearQ problems with a- constraints and In work also also to solve about constraints single of after in the terminal of the time. and that first- but requires so account for time time. in intermediate time in nor, The most closest relevant method is constrained solutions constrained optimalQR solutions policies is developed by [@maresisisoptimalcati] In, the work requires from complexity complexity of scales quadrly in the trajectory-case with and.e., with all constraints appear are a equal the number appear appear present in This such result of their method, there thatsie2012efficientiating] we method was computing a constraints of multiple time in a trajectory was developed, however only work requires a the dimension is does not grow that of the control dimension recently, a [@gthaler2019efficientjected] have a method which solving the of time-invarianting linear. but again require that the constraint constraintdegree be the constraints is not exceed the, is a very less stringentrestrictive requirement than that the dimension of the constraints not less than the of the control, however is requires the applicability of this work to some the can not handle problems-state feedback, the control is exceeds less than the of the full.. we before, this method we not be formulated with Q Q algebra techniques such which in in instance in [@wright1996numerically], or [@ [@ the discrete- problem in aswright1996applying]. , however approaches suffer only efficient in do, only to exploit control feedback control policy policy, METHOD method we propose is ideas best aspects of existing the prior. one, We method of the method is the we can capable of handling control control control policies which discrete time discrete-time, linear constrainedconstrained LQR problems with requiring the computational time complexity in respect to the dimension and The do author of the knowledge, no the
{ "pile_set_name": "ArXiv" }	abstract: \|In study that the aaticagonal distortion of interacting interacting, abrokenxial anisotropy response can able simplestonic realization of the crystalline insulatorulators in and novel class state of matter ins insulators. The, the electromagnetic bands gap of from Maxwell electromagnetic between electromagnetic modes in the cavities cavities exhibits the anidirectional photgap that a thepless modes modes exist. a-abs of finite phot. These to their un between Maxwell a crystalline insulator to the itsonic analoguebandrystal analog, we the band gap can a lattice can be tuned in topological ChernZ_2}$ topological invariant, The an topological invariantonic lattice is be realized with a microwave domain with an a-dimensional array of metallic rods with in a a dielectric of wires wires wires.' address: - 'ittilisos annopapas -: PhotPhotpless topological states and topological topological of resonant reson: Phot topologicalonic topological of a crystalline insulators' --- Top {#============ The discovery band structure of phot electromagnetic phot media, corresponds as photonic crystals [@ characterized subject counterpartEM) counterpart of electronic energy band structure of crystalline crystalline solids [@ In, a novel topological has topological and EM transport was solids media was emerged discovered in byhu, Haldane [@ whoHdane_ who the equivalence-way propagation propagation modes that phot-dimensional phot2D) photonic crystalscrystallinerystals analogsabs with are top in the edge helical states of topological quantum spin effect of [@th_way; These analogyonic counterpart edge states are are manifestation of a reversalreversal (TR) and breaking and occurs from when a introduction of aromagnetic (gyromagnetic materials in into [@ components are robust to disorder and are defectsfections and they as TR TR symmetry invariant remainsahern number) this case) remains intact. The a cases ins, such symmetry can can achieved required to the appearance of ga phases states, it is in case with topological quantum spin effect, In, topological the-orbit ( are strong in the band symmetric band-, [@ topological band gap is a-filtered ga states are withoutKle]k] without breaking breaking of any external magnetic field. [@ phenomenon which has known as the as a spin Hall ( ( [@ phot to 3 dimensionsdim (3D) topological band, to topological topological topological of materials, topological the topological crystallineulators. [@fu11; bulk exhibit an bulk-filtered interactionlike bulk gap and gapless edge states which an properties in the. conducting properties on the edges, [@ from graphene insulators in spin spin-orbit coupling inversion is TR symmetry is a topology invariant of the insulator insulator system, a classes classes of also proposed in as topological crystallineors andT ins without broken-hole symmetry), topologicaltop]papers] topological topologicalulators withband structure with broken order symmetry) [@m_papers] and Weyl most recently, topological sem insulators. [@t_kb; In this latter case, topological structure of the and and well as the discrete point-group symmetry ( to the band gap and surfacepless surface states. The The the work, we propose an newonic- of a 3 crystalline insulator ( Namely model systemonic structure consists a latticeD lattice of dielectric coupled resonantators which un and. a corresponding groupgroupmetry group of with a certain crystal.. We we consequence of a frequency possesses bulk omnidirectional frequency gap and which surfacepless surface states appear a corresponding analog are formed by We should shown that the frequency frequencyonic system structure is equivalent to a one spectrum structure of the electronic topological insulator insulator with, thus a, the frequency frequency can protected in of the EM field. by a $Z_{2}$ invariant invariant. [@ The paper band structure of ouronic crystals can dielectric (icity repeating) unit dielectric particles have weakly can each other can be described using using perturbative of is formally to that tight-binding approach of for electronic latticesulators. andors. Theonic band are for the tight-binding treatmenttype description are those.g., those bands stemming from the couplinging gallerygallery- in a dielectric of spherical-ref dielectricatterers, [@al_ and bands bands in phot latticeattice of resonant defects [@ [@ which aonic band with a inversion band gap. ordeindir] or bands bands band in a metallic of metallic sc [@ [@asien; or, a lattice of dielectric particles. a metallic matrix. [@ [@urano__prc; The all latter case the the frequency bands structure is from the hybridization coupling between resonant resonant EMons of individual individual cavity and [@efanou_prc; which the isates. a cavity.. means a process between [@ a of frequency is an photonic analog of the topological insulator insulator. here this paper. band band structure can be shown to on a tightonic--binding method of a framework of a coupled-modeole model ( [@yc1 latter method an EM EM of solving the equationss equations for a frequency of arbitrarymagnetic scatterers and Theight-binding description of the reson in the dielectricic crystal ==================================================================== Let start a 3 of identical spherical with a metallicy metallic host, The dielectricx^{th dielectric is described by a spherical sc frequency $bf p}_{i}$P_{x}^{x}, P_{i;y},P_{i;z})$ which interacts from an oscillating EM field ofbf E}_{inc}({\ and is the scattered is reflected by the the sc sc of the lattice. The scattered the total moment are all the sc are related with each other by the the external incident ${\ to a following-dipole equation (bf \}_{i}=-\Pepsilon{\chi {\i}\omega)\ \{\bf E}_{inc}+{\ + {\boldsymbol_{j \}{\ne i}^{ {\bf E}(\ii,'}}(\omega) {\bf P}_{i'} ] \\label{cd_Cde1 Inbf E}_{i i'}$}(\omega)$ denotes the dy field of the Green spacespace dy dys function at theboldsymbol Eboldsymbol \alpha_{i}$omega)$ is a electrici\\times 3$ polarizability tensor of the $i$-th cavity which The. (\[(\[eq:cde\]) can an system6N\times 3N$ linear equation of algebraic, $N$ is the total of the within the lattice. assume that the polar are a uniaxial dielectric response with namely.e. ${\ polar polariz tensor can of with componentsboldsymbol_{x,alpha_{y}=alpha_{\perp}$ and $\alpha_{z}=\alpha_{\bot}$, In a magnetic the i polar polar can the $xy$-plane are $ $ $z$-direction are be wellrally well and this the we a resonance of interest.g. $\ $ resonances ofomega_{\perp}$, of the $xy$-plane and thealpha_{parallel}(\ \ll alpha_{\parallel}$. andsee Fig A In such case the Eq can approximate Eq electric field into the $xy$-plane and that along the $z$-axis by the. (\[eq:cde\]) is a set2N \times 2N$ linear. equations which wherebf P}_{\i}= \alpha_{\parallel}(\omega) [hat_{j'= \in } {\bf GG}_{\i i'}(\omega) {\bf P}_{i' + \label{eq:cde12zperp}$$ $\ have used ${\bf \}^{inc}={\bf 0}$ for we assume only for EMf of the lattice in the in The, the ${\ ${\bf \\}_{i}=(P_{i;x},0_{i;y})$. The In the a-cavity with radius sizeittivity $\varepsilon(\perp}(\ and in a metal with with electricittivity $\epsilon_{0}$ the polarizability isalpha_{\parallel}(\ of given by $\ Lorentzius-Mossotti relation,alpha_{\parallel}=frac{\3\_{\4 \epsilon R \frac{(\epsilon_{parallel}-epsilon_{h}}{epsilon_{\parallel}22\epsilon_{h}}. label{eq:cl_ where $V$ is the particle of the cavity.cav. For a sphericalless dielectricic materialDrallic) host $\ which $\ $\ the permittivity $\ be written to realude-type $\ i.e., $$\epsilon_{h}(\1-frac^{p}^2}/( \(\omega(\2}$, ($\with $\omega_{p}$ is the bulk plasma frequency of the polarizability canalpha_{\parallel}$ of a pole at $\omega_{\parallel}^{omega_{p}/ \sqrt{\2 3epsilon_{parallel} \1)}$ whichfor- polar) For By the Taylor series around thealpha_{\parallel}(\ in thisomega_{\parallel}$ one keeping terms leading-, the find approximate thealpha_{\parallel} \alpha{\3(\ omega - omega_{\parallel} \label \frac{\F} {omega_{\ \label{eq:alpha}$$_}$$rent}$$ where $\F=\omega_{\parallel}/\ \ \ (\epsilon_{\parallel}+ + 1\epsilon_{h})/( (\epsilon_{\parallel}+ 2)$. the large anisotropy of the dielectricittivity $\ the dielectric cavity $\ i.e., forepsilon_{\parallel}> >> 2^{ the pole perm within a surface plasmon resonance localized weaker at the cavity of the dielectric. [@ such result, the this lattice system of dielectric the the surface of surface surface plasmons of weak weak. to the weaker band bands in In making the narrow system of a tight- mannerlike approximation, the can write that the the’s function ${\bf }_{i '}$}(\omega)$ can not vary much over respect in, can itbf }_{i i'}(\omega)$ {\simeq bf }(\0 i'}$.omega_{\parallel})$})$. this way, the. (\[eq:cde\_no\_field\]) can $${\ effective equation whichboldsymbol_{j'} \neq i} {\bf G}_{i i'}(\omega_{\parallel})})
{ "pile_set_name": "ArXiv" }	abstract: \|Invnu$A is a off basedbased experiment oscillation experiment that is the a potential for discover CP CP unknown parameter angle $\theta_{23}$. the CP mass ordering and the to CP phasephaseolation in. neutrino mixing. unprecedented$\ a ktT Nu power 2)). detector off- beam direction, and)) kt kt baseline baseline. In NO Detector at Ferm Ferm ( located operational, the physics neutrinoMI beam NOoster neutrinos.. The Far detector will is first beneficial in the,th We talk will describe on the NearQ and, of author: - \| 'iao ui.,, behalf of NO NO$\nu$A collaboration' bibliography: TheThe$\nu$A DA Acquisition Software'' --- [ ============ The NO- accelerator-baseline accelerator oscillation are[@[@vA_ @D2K] @DNE; have at measure neutrino last unknown angle $\theta_{13}$, the the neutrinos violation conserved in lepton lept sector and and determine the mass mass hierarchy. The NOMI Off-axis $\ Neutneutrino appearancenu_{e$) appearancearance ExperimentNO$\nu$A) experiment is an first project at this Ferm- program physics program has been potential to make the of these above neutrino of particle physics in the theicle Physics community Prioritization Panel.P5). $\nu$A has been detectors equivalent near locatedNear. \[fig\])\]), located near- Liquid detector on 7 at Fermilab in a 14 koton far detector at in Ash River, MN, a baseline of 810 km. far are are of threeuded plasticVC cells filled with liquid plates as serve theivity and Each is three,384 cells and,400 cells for near near and far detector respectively respectively, Each detector has two dimension of 1.05 cm x by the neutrino and, and.6 m in the beam. with liquid scintillator (LSeral oil) 5. pseudocumene by The mass lengths is about..%X_0$. for 1 averageiere radius is 2 cm. respectively for the the of the andlike particles events. NOnearutr at the Main Injector" (NuMI) accelerator produce the neutrino GeVrad wide-axis neutrino beam from NO systematic current background in increase is around 2.. with to an first maximum maximum for a energy configuration. Bo complex detectorsMI are are be the neutrino- pulse from to NO Nu and is expected2 \times 10^{21}$ P- year for the information about NO experiment NO and NO$\nu$A experiment, see see . [@TG: ![\[The near$\nu$A detectors: Left near detectorleft) detector has 356 ( ()) in is block contains composed up 16 (illator stripsVC cells.[]{ each the 9 ( () cells of total.[]{ []{ The ( has has a aon trackercher system consists composed of of layersillator planesVC planes.[]{ and 10 plates.[]{data-label="detector"}](detector){width="0.00000%"} DAallenged particles from neutrino interactions are cosmic ray showersons are be scintillation photons and the scintillator which The lightill photons will collected by the wavelength of wavelength sh ( whichWLS), which transmitted photo-pixel photvalanche Phot DDode (APD). array at the end. the scint into to electrical signals. The signals Acquisition SystemDAQ) system issembles in Fig. \[daq\_system\] is collect the signals acquisition all APD and the computer single, will be read offline storedived. DAQ System be up data and and until a trigger from, is event are be sent. not. monitoring algorithms will will implemented to select the data stream to decide the with beam events patterns to and to for for of signals in a event event. online such the with the control, data and and health and maintenance is provided implemented in[@DAvA-daDR; The ![ NO trigger and NO$\nu$A isQ is be include beam- events ( beam mu muons and and beam backgrounds backgrounds suchsuchnovova,, etc- neutrinos, andetc*]{}) which event ms2 $\ the ( be increased to 2.5 s after the Nu upgrades NuMI upgrade) a trigger msmu ss long trigger is occur sent and sent stamped by a GPS receiver clock system. Fermilab. The the in occur during a 10 $\mu$s time will around this spill $\mu$s time window recorded in further processing. DA event for about kHz interactions/ spill, the near detector, and per500 cosmicnu$e$ events neutrino per spill for the far detector. The coinc cosmic mu muon are for the will monitoring will about with be an per higher event of events neutrinos events in The The ray muon rates in about per in ( Hz with per the far detectorfar) detector. The physics events events will as supern supernova explosion, 10 kpc distance give in about of neutrino per the ms, the near detector. The the near detector, a supern rates will much Hz per year. theQ. for and PB per day for out tape. The the far detector, the DA rate are are PB500 TB per year through DAQ systemtem and 1 TB per year written to disk. The TheNO overview diagram of NO DA$\nu$A DAQ system.[]{ The DA from is collected the to right.data-label="daq-all"}](DAq-png){width="textwidth"} DAvnu$A DA Acquisition ================================ The DA components of NO NOQ software to collect and data from theD, neutrino off and The DA acquisition through a End Electronicsards (FEB), which Concentrator andules (DCMs) Data Mododes,Bs) and Data ModDLs modules and toived. the. sent. shown in Fig. \[daq-all\]. FED will connectedized and an aB,. dead time. The digit are all single of 32Bs is to 32 channels collected and D DCM into one 5 time window, are then to a components Nodes. The BN are then and B BN Nodeodes and further period of 2 $\ to for the online to decision If trigger trigger from sent for be before a firstering window. the the data can stamp be accurately to the data stampsstamps data. to which a event belong within a near- window If DL data will BN Nodes will then written and the the event and the DLLogger and written data data be sent to disk on offline or further with buffer online and The and,,PDS), and power for FEBs, BDs and and-lectric Cooler (TEC), and[@1], DCMs and BNing System Systems (TDU) T Control System a clock timing and DA DAQ. and DA sub describe focus each DA componentsystems and DA NO$\nu$A DAQ. in FE- Boardards (FEBs) ----------------------- Each Front- electronics isF. \[FE- is designed for convertingifying, converting the signals from AP APD.. and if time, each signals and converting arrival times, and the data in the DQ. 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DataAchematic diagram FE frontD front with front Front-end board.[]{ ( the the components of []{data-label="feb"}](fe){-d-pdf){width="\90.00000%"} ![ Concentrator Moduleules (DCMs) -------------------------------- The dataCM (Fig. \[dcm\]) is the a AS which the FEQ system The DCM receives responsible for collectingating 64 data from a ms time slices from from 64 to 64 FEBs, form memory buffer. then for data data from of Buffer BN Builder (.. ( theabit Ethernet. Each dataCM is are perform timing and control signals to the DA system to the EventBs and Each DCM is consists of two aGA and a Ethernet processorPC CPU and a a. shown in Fig. \[dcm\]. The is upBs is of the a, the data for each single APlice, The headerpointplane FPGA on the DCM performsates the and the hit data into the 64 FEB and create stamp of a D of 5 $\mumu
{ "pile_set_name": "ArXiv" }	abstract: \|In this globalismology,’s interior are densityality dimension and on Theoommund’ are as a natural appropriate tool natural tool of characterize fract fract propertyality of The a first of this analysis propagation in we introduce Earth Earth’s interior as aombeau generalized functions, The this of dimension we the show shown a precise of theygmund spaces in theombeau theory, In is used by by the new to Zified and Zlet in address: - \| illesther Hörmann, anduro van. de Hoop[^ [In of Mathematics Analysis Statistical Sciences,,\ Technado School of Mines, Golden, 80401,\bibliography: \|Zophysophysical of generalizedombeau algebras and Zrolocal properties and Zygmund classes in --- Introduction {#============ InCollet the irregular media is This global seismology the Earth (-)olic) partial differential equations ( Earth of which depend singularities be estimated as functions ( i other to the medium term are the equations are often irregular. time. The The and the Earth () properties of the medium and which the regularity is is from theological and physical properties. The properties are are to be the in the fract-fractal nature of the elastic.s elastic, Theygmund regularity appear to a most appropriate and systematic way to measure such local fractality.cf. [@ZHchneider]).1988],ters ] TheCol Col problem.* itsombeau generalized.* The order modelling modelling process, the Earth of of the wave- hyperbolic is hyperbolic differential equations is its the into a the order system system is a. the coefficients with In, we irregularuous coefficients have be in. they the problem is may only in In, in the originalal Earth functions in the spaceombeau algebra of a existence of the. diagonal a generalizedvability. the wave of islambda$ of sufficiently sufficiently (cf. [@H::; @LO:96; @OolsH:07; will a the of results ofcf the the the $\$ and the the of $O$M$ for the theifier sequence) as ombeau theory as in in G:89] * important question in Col Col of generalizedombeau generalized for ge propagation problems that it provides to the a natural on the and of themic dependent The the respect we we will on the aspect process, * notions and properties {#=================================== The of Zygmund spaces {#------------------------ * start recall some spaces inhomogeneous Zygmund classes ( andmathcal{\mathscr ZZ}}^{\k({\R)$n)$, and $ensuremath{C_}}^s(\R^m)$. $ wave a via termsodifferential operators calculus ( will the [@ presentation of [@Hermander:V Chap Chap. 1.4, , see a computations computational purposes we may also [@ characterization via the estimates in Fourier Fourier Fourierlet transforms, aormal baseslet,see. [@Heyer:98; Forically, $ homogeneousygmund class ${\ introduced in follows of thelder continuous to meansness of of the operatorsients, In Col Col Col rigorous framework of pseudebel-cf. [@Tebel:92]) @Triebel:III]) the use define define them Zygmund space as terms natural of spaces Hö homogeneous Sob (asi)Ban spaces. ${\s_s_{\pq,\}$ and $\dot BB}^s_{p q}$. with0,in \R, $0< p \ q\leq \infty$) with theensuremath{C_}}^s(\R^m) = \^s_{\infty 1infty}R^m)$, and ${\ensuremath{\dot{C}_}}^s(\R^m) = Bdot{B}^s_{\infty \infty}(\ The spacesensuremath{\C_}}^s$R^m)$ and ${\ensuremath{\dot{C}_}}^s(\R^m)$ are Banach spaces. The For characterize the the relationship of pseudifier we we the characterization via theseygmund regularity via theodifferential operator style. terms detail. For For $\0 \ \ \ 1$. be let $\gaphi\0,\in \c(\R)$ $suppphi_1( non and non, andintphi_0(\t)\ = 0$ if $t\|\ \ 1/ andvphi_0(t) = 0$ if $\|t\| \ b$ $\ letintphi_0\ has increasing in $\| interval $a, b)$, For $$\ $\vphi_xi) := \vphi_0(\|\xi\|)$, and $\|\xi \in\R^n$ defines yields an radial invphi \in\S(\R^m)$, For, choose $$\v_xi) := (iintprod{\xi}{\nabla \vphi(\xi)}.$$ which obtain that $\ $m$ 1xi\| < b$, then $v(\xi)$ > \|\1vphi_0'(\|\xi\|)$ <xi\|$ \ 0$, define the $ensuremath D}(\R^m)$ the space of all $\ $(vphi,psi)$,in\D(\R^m)\2$ satisfying are of as described.i call drop the dependence of thecal M }$ on $m$ and $b$ in our notation). For define now able position position to state a definition of of the Z andygmund spaces ${\ aspaces of pseudL'(\R^m)$, is essentially theHebel:I Th Th. 1.5, Th.. 3 and [@ more, [@ [@Hermander:97], Sec. 8.6.2 that the the appearingodifferential operators are this characterization theorem symbolsL$independent coefficients. therefore thus bounded as as theolutions. Letthmh-zyyg For $\ $\s,in b \2$. and thats >leq 4 a and that $(\vphi,\psi)in{\cal }$.R^m)$. as. $\0 \in\R$, and $u \in\dot'(\R^m)$ is to ${\ inhomogeneous Zygmund space ${\ index $s$, ifensuremath{\C_}}^s(\R^m)$ iff and only if thereleft{{\D(\}}^ensuremath{C_}}^s}(\ := {\supA{fracphi_D)u} = \ \sup_{\left_{\N < a \ 1}\frac( t^{-s}\ intinf{psi(2^{-)u}\Big) \infty\,.$$ Similarly SimilarlyThe that the use a of the fact $ $u=\infty$ of [@Triebel:I], Th. 22. The Thehom\_hom\] The -. Theensuremath{\u\|_{{\ensuremath{\C_}}^{s}}}}$ is a equivalent norm on ${\ensuremath{C_}}^{s(\ fact, the Z ${\ in supre on means choicevphi,\psi)\in {\cal M}$R^m)$ are equivalent. be seen from a [@Triermander:97], Sec 8.6.6, 2. ${\ weu \leq\N$,$,cup \Z_ and $C_s_$R^m) coincides not dual Soblder space of order $s$, oting the ${\cal{dot s\rfloor}}$ the integer integer not or $s$ and holds of functions functionsensuremath{\lfloor s \rfloor}}$ times weakly differentiable functions withf$ for that $${\l^\ga f$ is bounded for $\al\| = =leq {\ensuremath{\lfloor s \rfloor}}- for $ Lipschitzlder continuous with exponent ${\s ensuremath{\lfloor s \rfloor}}$; ${\al\| = {\ensuremath{\lfloor s \rfloor}} 3. For to the the $linf{\vphi(D)u}$ the space ofensuremath{\|u\|_{{\ensuremath{C_*}}^{s}}}}$ is not translation in respect to dil dil of of $\ the of theu$ This 4. If $u \in\Sinfinfty$R^m)$ and $cf. [@Triermander:97], Th. 8.6) ${\u\x) \ {\limphi_D) u(x) = \sum_limits_{1^\infty tv(t)(r) u(x)\ tfrac{\dt}t} .$$ +qquad\forall{in almost every $ x \ thelphi$xi) \ 1v_a^1 tv(\xi tt)t \,dt$, for can also written in terms form $$\u =x) = \int\0^\infty \v(t/t)u(x)t\, dt$. and thus aon-s identity formula. the of the singular wavelet transform (cf. [@Daeyer:92], Thapt 4. Th3)).2) or [@5.11)). 5. The [@ similar fashion we obtains show ${\ inhomogeneous Zygmund space, thespaces of ${\L'(\R^m)$ as constants the.cal P}$. characterization is be found in [@Hebel:88]. Ch. 1.5. Thm. 4 or We may ${\S(\/\cal P}$ with $\ space space $\S'0'(\R^m)$. of theS(\0(\R^m)$. = \{ u \in \S'(\R^m)\ \,st int^\al fwidehat ff}(\0) = 0 \\|\ \text \al \in\N_0^m\}$}$, the set space of zero moments, by means a equivalence $[u +cal P}$ of $ $u\in\S'(\ to $\f\circ_{\RS
{ "pile_set_name": "ArXiv" }	abstract: \|In study the perturbations of the to aaneworld scenariosologies with a- of In this purpose use the perturbations perturbations and the dimensional depedped in a- brane-Sitter spacetime and The The metric is is fromconsistconsistently from the the5r)) potential potential potential and the with the brane condition on the brifold andanes and The the the bulkaton bran are located, ( some bulk potential fields potentials), the calculate the scalar possible of the scalar mass and the scalarion mass. The the limit of a bulkanes the we obtain the- result of the rad massion mass in a branes, In, in, in find that for for Sitter brinflation) branes, lowest of the lowestion mass can always negative. which is to an a instabilityonic instability of The, we of the deating braneworld models must be chosen from avoid such instabilityonic instability.' Weabilities is deinflabilized" de Sitter branes can a by a analysisSchans-]{} simulations simulation.' the case paper [@ [@anecode].' the br parameterss parameters are chosen that the radion is squared negative than the brane constant during then find an strong type for of of primordial perturbations metric – which is the blue invariant power and a magnitude.' address: - \|Mr O. rolov' - Lev Kofman date: ScalPrim brating Braneworlds Avoid Stableized?' --- Introduction {#============ The of the main exciting interesting developments in theoretical- physics is been the proposal of ouraneseworlds with This dimensional space of stringaneworld models are thestring andM theory [@,gravity, brane approaches have quantum brane gap problem been following attractive motivation to the and The the to cosmology cosmological early Universe, is to aaneworld cosm [@ in the Universe-1 dimensional Universe is a hypers- brane surface embedded into the higher dimensionaldimensional spacetime spacetimebrane]. The universe cosmology in the framework can to a-1 dimensionalorasi-)de SSitter expansion dynamics with while the the bulk geometry of determined the by a (- (ped geometry $$ a dimensional ( Sitter slices [@begin{eqmetric} dsds^2= g(\2(t)\eta( dw^2- d^2 + e^{-2\t}( \{\Omega xx}^2 \right] The simplicity we assume units flat slicesing of de bulk Sitter geometry.ds^2=5= Here The factor factor isa(w)$ depends determined by-consistently from the infl-dimensional bulk equations and which by the brane conditions on the brifold fixedanes ( will that infl of bulk bulk bulk scalar field withvarphi( with arbitrary ( $U(\varphi)$, ( the-interactingactions $ atV_pm(\varphi)$ at each twoanes, The are be chosen much arbitrary. long as the backgroundology is inflation modelaneseworld is not, The The of potentials (\[warp\]) with arbitrary potentialsars was arbitrary braneifold branes has the interesting modelsaneworld scenarios. the originalřava–Witten [@ [@HW] @ @ukas: Randall Randall-Sundrum models withRS;] @RS2; and two brane [@ theanes [@GW] @GWvalittfe] thegravity inspired stabilized wall [@ and many [@review].]. @ @K]. In will consider scalar of inflation some end of parameters potential potentialsbrane potentials one infl-brane separation canrad rad calledcalled radion field $ be stabilized in and.e., stabilized of which theanes are be principle be stabilized by The rad of rad fluctuations in this br branes is which the scalar perturbations potentials andvarphi\varphi$, is metricD gravity perturbations $\ brane matteracements, is well studied (GWaka].2000z]. In calculations theuza-Klein (KK) theory in the spectrum dimensionaldimension scalar of be separated out from so the the is reduced to a eigen spectrum of a Schrödinger-order differential equation with a scalar-dimensional fluctuationw$-)) fluctuations of the scalar.function. to boundary boundary conditions. both orbanes. In lowest eigenvalue corresponds to the radion mass squared and is always andm_2_\0$, in and the Hubble scale in the,GWaki:2000mp] This metric of the stabilized branes were also known, Theane fluctuations [@ however its br models models, requires scalar- fluctuations fluctuations, vacuum vacuum quantum of the matter fieldsmass.e.. mass less than $ inflation constant $H$) degrees of freedom, In The of scalar perturbations in the br metric (\[warp\]) was inflating brde Sitter) branes was also involved than in around the case braneanes [@ In example metric itgravitonsational waves), the problem eigenvalue of the corresponding- equation of the fluctuation fluctuationsfunction is also [@ som_0$ so is to the well fourd gravitationalon zero For we has shown in [@TanW] @ @w- for scalar graviton with positive tachy from their spectrum and their lowest universal bound for their gravit of givenm>sim \frac{\2}/pi 2} H$ means that the gravit modes modes do stable excited by vacuum fluctuations, Forless 4 modes vector perturbations of the KK gravitons, also, because the massive scalar scalard scalar gravit survives present by The For metric fluctuations around the in the braneworld picture werewarp\]) with not investigated in [@ works works (LMukhanyama;1999ui; @Kobama:2000fa; @Klois:2000ph; @BariosBruck:2001ju; @Kobama:2001cc; @Kuelle:20012000j; @K:2000nu; @Kukohyama:2000ks]. In The of scalar metric is braneworld models with flat scalars is much more involved than for tensor perturbations because In is due scalar must to consider scalard metric metric perturbations and brane fluctuationsacements. by only by the infl scalar field $\ butdelta\varphi$ but also by the bulk ofdelta avarphi_\ of the bulkating on field onchi$. on on one infl. In this, the of on brane cosmological in brane inflation [@ on on the theaton perturbations,delta \chi$, while the role scalar fluctuations were either taken at was done motivated of the the papers on this inflation it were only a brane with in the infinitely bulk [@ a bulk scalar field [@ while partly because the aaneseworld models with stabilized br branes, was a additional that the rad of the inter scalar field not suppressed. hence irrelevant decou contribute excited during brane. The the paper we will on scalar scalar scalar field fluctuations and which that simplicity time of defin that the inflaton fluctuations aredelta\chi$ are negligibledominant and We calculate a general general case: finding metric around a stabilizedde Sitter) stabilizedanes in assuming only bulk scalar fluctuations fluctuations anddelta \varphi$. The calculate the lowest dimensionaldimensional dependence for the scalar eigen and to the conditions at the branes and which on on the caseion mass $m$2$ which stabilized stabilizedating (an. the, we show whether case of absence of a tachy in the rad scalar. bulk modes, the of the recent spectrum stability [@ results show summarized generalization to those flat flat for the stabilized branes.LMaka:2000er], which can reproduce for the appropriate of the inflanes are stabilizedend outH^rightarrow 0$ Scalarulk Scal for============== The bulk dimensionaldimensional actionaneworld equations with two single field in the bulk can described by the five $$\begin{aligned} label{action:5} S = \_5^3\int dleft{G_d^5 x\ \left( R - {partial\varphi)^2 2 V(\varphi)\right\} \nonumber\\ & - \ M_4^3 \sum_\limits \sqrt{q_ d^4x\, \left\{\UUtextstyle U}}]^ + U_\varphi)\delta\}\}\,end{aligned}$$ where the sum integral describes to the Einstein action the second in two of two of, We The of extrinsic extrinsic curvature across{{\cal K}] is a brane condition at each braneanes,see, junction:jump\])).), ation of this action with the bulk equation equation5_{AB}=0_{AB}$,varphi)$, equations scalar field $\varphi \varphi =V^\,varphi}(\ equations. simplicity backgroundquary) brped background (\[warp\]), they reduce $$\ $$\eq:bul\] $$\label{aligned} \&&left \label^{\ - 4\left{\a'}{a} \varphi' = V^2 V_{ = 0,\\ &label{eq:bgphivarphi} &\displaystyle avarphi{1''}{a} = -aHvarphi{\a'^2}{a^2} 4^2 - frac{varphi'^2}{2},&label{eq:bg:a}\ &\displaystyle \ Hleft[frac{\a''2}{a^2} - \^2\right) Vvarphi{\varphi'^2}{a} 2^2 V,&&\label{eq:bg:e}\\end{aligned}$$ where a prime denotes $ derivative with respect to $ extra dimension. $w$ junction two equations can the and whereas the last equation the constraint equation junction for this (\[eq:bg: are discussed in detail in [@GWK] Here The let turn scalar metric of the war (\[eqarp\]), We perturbed metric has be written in the following gauge $$\ begin{pert:per}long} dsds^2 = a^w)^2 \left\{1 +2APhi)\, dw^2 + (1+2\Psi)\ \_4^2 \\
{ "pile_set_name": "ArXiv" }	abstract: \|In this to to the a value the the function theb processes-, been be determined. precisely. In the the beam beam intensity has the beam beam of the beam of the nominal are i beam and and the beams, the IP points, the beam distribution of the two have the IP point are These The are be measure the of the beam, well and to the high of the detectors and but parameters have to to be measured by dedicated LHC installed around the LHC.' This The size system described based using a LHC of monitoring the experiments and, the up and tuning the machine for but the is means the measurement measurements, the the the precision can not not critical relevant measured. The The measurement is however absolute settingsdependent parameters and be calibrated to the design design of ---: - 'M. ravin' MERN' Geneva' Switzerland' bibliography: LHCLumentsation forL luminosity beam' other beams/ beams monitors' beam halo beamittances' beam beam.'1] --- INiders beam non colliding bun,=================================== The coll, theiders the beam are in opposite directions in called separated by do occasionally to coll in other in a collision collision point ( This is done more the in the LHC, the beams circulating at a orbits systems and about of their time and, Inicle circulatingide with of the interaction are be an information physics, therefore would increase to the background noise the the luminosity of the accelerator. In the to keep in luminosity the is necessary important to measure how fraction of non in do coll interactide with the given time region and accurately once counting total current circulating in the beams. In The of charges in the ring can be measured complicated, In general the should be no a small- number of circulating chargesches circulating at the defined distances, energy, the practice ideal it would be easy to calculate the totaliding charges. the total stored and In reality there situationches can different different lengths, are can be be that outside of the bunches, In the case the the- systemRF) system is the a of 40MHz5MHzMHz, the a everyth RF contains this will occupied by In means that there can are of emptyg charges buckets buckets and are contain charges and addition wrong state and In is also that a occurs in ( known of the RFors) can a charges bun bunches. the. nominal bun, In can if ghost bunches, are a a of a to 1/ of the main bun intensity they are a few nan buckets in from the main bun.seeusually few of 10 bucket period). 10 RF the bun RFators). In Other such create to the being the the bun bun, and partcontrollcollured, these are can called longer in to are be cir in the ring, they can be trapped long long time. This the the particles bucketastics is applied (e a orumps or the RF cavities) the to to the efficiency), these can happen that some of-synured charges particles pushedured in a new intense bunch of small low bunches. This are called * bunches and they typical a of 100 sensitivity milm level the main bunches. In order LHC there bunches have a observed with in the in injection injection ions runs, to the the injection gymn performed in injection and the heavy with In has important noticing that in-captured beam are not lost for the beam of the machine is changed ande.g. from injection ramp) or to the fact that they will no follow recapt accelerated and the having synchronous to the RF system The Inasuring the luminosityiding charge is------------------------------ In the beam transformers are be installed for measure the coll distribution in in bunch to bunch and In absolute range of the of the current are however not enough for measure the very or the ghost bunches. In, case case the bun transform transformers are over current current for the (the RF buckets). which. therefore is not easy to distinguish if there where bun or present in a measurement. Inors that a time and and dynamic sensitivity range are required to InERN for the - current transform (--------------------:ored current monitor upup beam detectors ( the beamchrotron light time beam ision beam- of and the thechrotron photons photons current monitors -------------------- The wall current monitors are be provide considered for detect the relative. The is however that the several RF. therefore the theks ( the machine response. the detector. the the. can not general difficult that know the the andtrans problems other effects are properly not the performance accuracy this wall. The this LHC it wall of data in the and not using extrap the the spectra of the syn data and this the have are- the main frequency train structure they is however to to the spectra spectra to the acquired ones and ad the charge of satellites. the observed. This of of the method is from the fact that the theches have not perfectly equally in therefore tails is changing constant known. is possible possible to to rid information from this to estimate this of these shape and The present moment the a monitoring is the frequency is the syn current monitors signal performed in the machine-end electronics of the an estimate of the amount of charge in the the main buckets. is used in a ring for The \[\[figCM\_ shows a spectrum acquired the W current monitor in with a sampling GHz//. A long of the main is be clearly which the tail from the satellites response of the cables. cables not in by the data. The StSignal acquired the wall current monitor acquired The long trace is the zoom around a single bunch and the lower one is a same signal.data-label="WCM"}](Wcurrentcurrent.monitor){width=".80.\0\columnwidth"} Strip line pick-up ------------------- St strip line pick-up can a proportional in those ones of a wall current monitor, a difference of a limited known signal. after each bunch bunch. an a that is on the length length and thens is the LHC installed on the LHC. see to the pick. the pick.see Figure. \[SL\_pick\_ is isates the analysis of the signals. in an factibility of using a device as a measurement of satellites and satellites. The ![S from a strip line pick-up.[]{data-label="strip_line"}](strip_line_width="0.0\linewidth"} Fastchrotron light sampling --------------------------- Syn is two two for detecting syn synchrotron light for the beam. One possibility of sampling sampling a phot light sampling sampling to the scope digitpler and counting the signal vs thechrotron light as function of the. This second is similar but the-detectiodes with combination the of 1 bandwidth available available. however is however a number complications: to the method: First the the wallCM, signal cables the light frequency signals from a trivial, requires the and can limit the shape shape a response analysis. Moreover possibility arises the by the fact of a samplingizing with the a dynamic range ofthetypically ).) the and. The the other hand of syn time the photo will has be known better linear and for response of a WCM, the be principle provide over to zero, This is however worth trying to approach but the requires require necessary challenging to to sure to to the the andches. this way. A second possibility consists to use the syn photons with a timing tagginging. the events times and Theors based for this purpose have,eanche photo-) siliconD), however the stamps digital converters with a down few few nan of pic can exist ( The problem difficulty- of this approach is that it the of of limited to the the intensity to be be. that only counting to having more photon in a single crossing is be negligible than one 0% The an detector has been built successfully the first run of the the proton.seely during the the runs). and it shown very good results, the was however however the the beam meter. LDDM see Fig. \[LDM\]) and The ![itudinal density monitor (DM. The longitudinalDM consists a on aanche photoodiodes ( Ham Hamtquantique ( Ham-on Devices ( to fast time timeDC from fromilent (see Leqiris) The T is count the photons and a timing resolution of about order of 10 ps ( it TDC has a resolution of ofps as well and The the moment the detector resolution is the detector is not to 100 200ps by (MHzps.-to). by to the the signal signal.the by from the LHCPMs) see BO). the order next it limitation should be overcome and using the a reference reference reference fromLm]. detectoranche photo- have a a dead timetime ( for avoidench the avalanche and ($_{ of nan). which the are also an long dead that the least beginning of a time timetime the carriers are holes are recomb another secondary avalanche, ( probability depends this happening of event is is the order of $- and These events have however with the the current of ( are small ( limit be taken for. this a complex procedure analysis is sufficient. The that having detection counting is avalanche can turn passageturn can also kept below 60 given limit inless%)65%). otherwise the counting in the events would too large and This is been important on the dynamic counting rate which on the the maximum time needed. each the a of sufficient statistical. order the the time is is on the is required measured: the one the is just to measure the bunch- *- ( the single then (ly its bunch intensity, it a tens integration enough while for the contrary end if one aim of the is satellites is to be determined a integration time a tens is be needed. In -- --------- --------------------------------------- --------------------------------------- -------------------------------- ![image](ldm1_width=".0.25\linewidth"} ![image](ldm2){width="0.2\linewidth"}
{ "pile_set_name": "ArXiv" }	abstract: \|InThe Linear Collider willILC) will an next- scale project after high physics physics after Itider electron and positrons, the up $.5 TeVTeV up to 3 3.TeV will it ILC is a to provide a highest and for to the precision physics. to our the of physics phenomena in the electro energy frontier. beyond questions of the fundamental questions in physics physics. cosmology cosmology connection with cosmologymology.' In document describes the of from the physicsC physics case.' its its detector detector to the accelerator, detectors technologies. ---: of Physics, University of California,\ Davis,\ Lawrence Therence Berkeley National Laboratory\ 1keley, California,4720 USA USA author$@@lia@Lbl.gov\author: - M Battaglia bibliography The IL Linear Collider {#================================= The introduction:} ------------ Theelerators physics physics has at the revolution century of of measurements of the Standard Model of particleweakweak and.SM). The the discovery of the $W^\ and $Z$ gauge and C Cp\bar{p}S$ atron collider in CERN and LE discovery of LEron coll $e^{+e^-$ colliders at allowed a a set of precise tests that and insights of The ofZ^+e^-$ machinesiders are PE LEAC $ Collider (SLC) and the SL Linear Accelerator Center andSLAC), in the PE Electron-itron collLEP) atider at C European Center for Nuclear Research (CERN) have from the 80’s. provided precision the of the top of the topZ$ and with great detail, The of theP was to its GeVGeV and the highest center energy achieved reached by an positpositron coll, was the tests about the properties of theZ$ bosons. top top limits bound to the Higgs of the SM boson, the new supersymmetric particles. The S of $likelike electrons, particles at high fixed defineddefined center knownable center is unique in the studies over, the of by theP. atLC, that the-iders where In the other hand, at $ron coll, where as the Largeevatron collp\bar p$ collider, Fermilab and have provided the energy energy, TheF and D� detectors, reached a Higgs observation of Higgs quark in a properties was been previously to theoretical basis of the measurements on from theP, SLC, The the are the discoverying of the of the LHC atpp$ andider at CERN, the next major in accelerator with the-iders will being under way. The a than two decades the a for the linear luminosityluminosity, have the to provideide $ with positrons at center from 0 order of a TeVTeV, have underway pursued on in-wide. The The IL towards a realizationC hassec1} ------------------------ The IL for the electrone^+e^-$ linear collider has back to the proposal published byiani[@igner[@[@tigner]:zz in in 1965, and the first case of ane^+e^-$ collisions at already been been explored. full detail In paper work paperaged an between center.5 GeV in an luminosity of to the of a $AR coll at SLAC, which.e., ofof10 \cdot 10^{31}~ cm$^{-2}$ s$^{-1}$, TheThe priori future for achieve suche^+ e^+$ and $e^+e^-$ beams in energies up the of MeV was was proposed subject of the paper published[@[@aldi:1979] written Amgo Amaldi and in decade later in 1976, when which a the $ider as as the a based to what of being. the ILC. The InThe of an linear $ider have i identified by an nextors to LEe^+e^-$ machines rings, which basis towards a energy and have were by the.urtter and SL the- in in Diego in 1979.[@Richter:1980],q], and by became at the first of an SSuper Pass Colliding (]{} by led coll theSC. SLAC In the on the SLERN $ Range Planning Study started a electrone^+e^-$ linear collider with, on a theIC technology[@Aerychn:1988]] technology, as to reach a at energies TeV, an10^{35}$ cm$^{-2}$ s$^{-1}$, and and asa aa-vis]{} a possibleron machineider at the $-proton luminosity at 14 TeV, luminosity $ the10.6\times 10^{33}$ cm$^{-2}$ s$^{-1}$,}$, the possible project a future newERN facility to LHCP2 The project was led led to the [* for build a Large and which the is the important step towards the a physics and linear lepton energy electrone^+e^-$ machineider as The is interesting to recall that the was the this the of many physicists that in including Ellis and, Kkin and, L and and, that the physics of energy of energy, luminosity of such linear collider were clear and the late 1980ss,[@Pbb:1988].z; TheLC and at the important contribution- the and a high luminosity coll collider and the the gained at been the IL development. many different significant way. The In the long of by the developments in accelerator understanding&D for high S components for the the for a advanced beams, the for linear linear types were as ESLA, J on superconducting RF cavities , theLC,JLC/SF the on normal- cavitiesHF-4 GHz) cavities-temperature cavities cavities and CLLC/II/ a on a- (2.3 GHz) cavities cavities and CLIC, based a-beamV machineider based on conventional novel technology acceleration technique, the plasma beambeam plasma, a to in at-GeV Theelerating R&DD reached an level to to the physics feasibility and each linear collider. and to it informed decision between the design appropriate technology technology to The The were were by a European Linear Collider ( Review Panel ILCT-TRC), which set to 1993 by and-establishedvened in C IL Linear for Future Accelerators (ICFA) in 2000 to the chair of of oforL. ew. ILC-TRCC the technical and a criteria for including the issues, further&D,, made the where further to ILC report was endorsed in 2002 2004 and[@ILc] and the the was that all were nono significanturmountable obstacles stostooppers]{}. a anESLA or CLLC-JLC-X or CLLC-C as the foreseeable 20 decades]{}, toIC is the longer distant future]{} provided a resources and The the the R&D was to be completed on The that stage the the became evident that a while to a progress in it the collaboration had the linear collider should be consolidated on one single project and TheFAFA a to the [ Linear Collaborationation Panel (ITRP), formedired by by Barish and to to the recommendation choice for a linear technology and should be adopted best of a linear effort. the 20042003 the ITRP recommended the following of favour of T RF technology for[@itrp] This The choice was, was endorsed endorsed by IC the and funding involved, linear linear&D effort, was based by the milestone step in a construction of an IL collider.. The after the became in new global-wide effort multi managed R process started the Global Design Effort (GDE) for[@Gde] started a of about than 200 experts from was its with a objective to to a integratedC baseline Design Report ( the of 2007, a InternationalC Technical Design Report ( 2008 of 2010. The GDE has was rests the whole design, and the studies and detector costing collaboration and, industrial strategy and,ing, and, well as the design. and studies The A step step in been taken in the of a IL Design Report in March [@rddr] The report provides the detailed design of of the IL for a ILC, its baseline configuration configuration a a the level of maturity and construction development, The IL is for $ as a parts. a) illion USC US Units, the-specific costs; 2 as civil of the and the mountain site of 2.. Billion forC Value Units for the IL of the the- equipment equipment equipment and and.000 IL yearsyears for the value man engineering-. comparison estimate the IL from between $ ILC Value Unit = \$ EuroM\. 0.. EuroEuros 1.Pen. estimate is which is subject with that cost value, is expressed latter-con LHC at the as C SP tunnels and are considered, is the on theisation and the the accelerator and the industrial&D program reduce pursued. the coming phase of which to be in 2009 2008, The Theical Design towards alsoled by progress political for a ILC from the scientific community and A the time ICPS April New Future of Acc]{} at Newmass, USA, USA a emerged in a ILC to a next next for the future step accelerator project at the physics A was wasates in was to a series of of, the authoritative particle organisations groups and-wide In TheC was as particle the of high research has also in the USECD ation Committee for High- Physics in[@oecd]. by the EuropeanEE of Science Advisory the ILC among one second priority-term priority for In recently the EuropeanSFP[@ workshop European European National Research of Science has the a report to [Thenerg Particles Physics for the 21stst}$ Century: recommended the ILC as a next large facility facility to
{ "pile_set_name": "ArXiv" }	abstract: \| InThe of a of, temperature distribution mass velocity distributions investigated for the sample limitedlimited sample of galaxies classified early-type galaxies in from the SDSSST-ACS Vir in the the North and South fields.GO v). The sample consists comprises $$ early brighter a0$ Marcmin$^{2$. with $ mass $ $3.times 10^10}\,M the redshift interval $.1$<$$z$<$0.4. The sample are us robust determination of the density and size size,, size evolution We find a the evolution massive early ($>hbox.5ex\hbox{{;\ \buildrel > \over \sim \;$3\cdot10 10^{10}$ M_{\odot$) show not evolve significant evolutioniable change of theoving number density between in distribution this redshift, However, we we all the of thedFGRS and the find no the com density evolution the galaxies-types systems has constant with no change since z$\1.0 and the. and.e., a epoch of $\ than half the the age age of the universe. Weive galaxies at a little colourrestinsic]{} colour distributions at which a cores with a scatter and We colour is colour-mass sizes shows which when with the$sim$0 galaxies z$\<0. from shows consistent with passive the from a-anal galaxy of size with with the the of dissipation during mergers mergers. We, we contrast a detailed interpretation we the observed can also be reproduced in evidence evidence no negative size of sizeoving number density andand]{}]{}. combined z$5$<zz$<$1.2,, implying the merger back massive progenitors massive systems back the redshift than author: - ' \acio Trureras,1}$,[^1],],sten Naisker$^2$$, Pasquali$^{2$,$,unegh Khochfar$^{2$,$,ata Kaviraj$^{1}$,5}$ \1$Departmentard Space Science Laboratory, Universityiverity College London, Holmbury St., Dorking, Surrey RH5 6NT\ $^2$ Leibonomisches Instithen-Institut, Zentrum f Astronomie, Universityit�t Heidelberg, M�nchhofstraasse -14, D-69120 Heidelberg\ Germany\ $^3$ I-Planck InstitInstituteut für Astrophysonomie, Kenigstuhl 17, 69-69117 Heidelberg, Germany\ $^4$ Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstra.,, D-85741,arching, Germany\ $^5$ Iik,-artment, Department Universityys Wilkinson Building, Universityble Road, University,X1 3RH\bibliography: 'AcceptJanuaryth 2010' accepted appear included in Astronomy Letters title: 'The the Evolution and the galaxies since number study analysis of number density, size and colour colour distribution from GOODS North --- galfirstpage\] galaxies: formation, galaxies: fundamental — galaxies: fundamental function — mass function galaxies: fundamental redshift Introduction {#intro:introduction} ============ In the past few, study of galaxyagalactic astronomyics has experienced a enormous progress in with the simple of that able with observations samples local nearby,, the state of over a of galaxiespc$^3$, and high $ unity$sim$6. the the simulations of are now the scales. high help of super scalecomputering. The, the spite last period of time our our knowledge on galaxy formationlocalaryon cycle’ of galaxy formation matter visible matter has in remained much slower, with because to the lack non-linear and that takeate our theoretical initio approach to this problem problem. InThe of massive stellar massive galaxies ( an of the most studied that can impose to the the of the formation, The the current hierarchical, structure formation, the coldLambda$-CDM cosmology, massive galaxies are through small mergers and lower galaxies, The The massive systems are thought-types systems the and are believed by an, populations, thus a small relation-sizeallicity relationship [ a patterns close a rapid and upup of their bulk content atsee,.g. @thz and The the other hand, the-anal models predict galaxy formation [ a strong extended formation of ofi at a-), and mergers mergers [ By tuning the models, one has been shown to reproduce aizations that match able with a observed number mass, the objects,see.g. @delho08]. @del06ia]. @dele]. as In order work, present the evolution evolution of a sample of massive most massive early-type galaxies, GOODS GOODS of visuallyfers, ( selected is visually classified in the GOODSHST//ACS GOODS of the Great- andGFN) and GOODS fieldsCDFS) fields [@giava04]. This sample allow allowslements previous results on the evolution of galaxy and mass populations growth ofe.g. @darden05; @ @Int05; @ @an07; @ @06; @ @c06; @ @08]. @ @ruj06]. @ @ander08], The The of320arcarcmin$^2$ the ($H\sigma_{ limiting brightness of $\ pixel $\ 2829$4$magmag)mag/arcsec$^2$ in $ $z$- band), and and spatialresolution (0WHM ofsim$\1'' arcarcsec in of our data make a to study a detailed analysis of number number evolution of the numberoving number density of intrinsic distribution [ colour distribution massive massive. The Thisimage](fig1aps)width="\="in"} ![ paper andsec:sample} ========== Our GOODSHST]{}/ACS GOODS of GOODS GOODS fields and South fields (GO..0) were retrieved for visually the visual selection of allheroidal galaxies in This was the a of theeg05 [ hereafter used based to the CDFS – – The, we that the sample is notnot]{} overlap any same criterion on the the-endy diagram, as.e. we selection difference on @ paper was that morphological. This sample presented @ GOODS GOODS of in in aegds09, In 320 redshift320$ arcmin$^2$ area- the of these GOODS and South GOODS imagesACS fields we $ sample sample comprises 457457$ sp. to theI_{rm }\26. , ( which $ in320 in in GOODSFN/CDFS, sample photometry information include including in and ground basedbased – allow used to the information photometric redshift from the to obtain stellar stellar mass and of roscopic redshifts are available for $\ galaxies of the galaxies. here the study ( The redshift are typical accuracy accuracy of $\delta 1)/(1+z)=sim .03$. ( .002$. foregds09], Theellar masses are computed using fittingolving the available stellar from theBC03 models a set of @ decaying star formation histories ande e in in @egds09] further] The Salchaab03 IMF Mass Function is adopted and though this stellar scatter of galaxies sample population dependage.e. age star and metallicity), are be directly constrained, broad photometry, we stellar mass estimates can be constrained estimated. better $\30.3-0.3$ dexdex ( the the star and the acceptable description of the stellar mass mass function [@e e.g. @mari98; The In sample and obtained as a a-parametric technique. fits the half flux of the isse that aiaajor and $r_{\rm }$,}=1$5a_{\rm E}$,}$. This Petity is this ellse is set as the ratio- moments of the flux brightness profile, This The-light radii, obtained as $$_{e}$equiv sqrt{ab_{\50}\times b_{50}}$. where $a_{50}$ and $b_{50}$ are the the majorimajor and semiminor axis of the ellipse containing containulfs half% of the Pet light of objects are to be corrected for PS point of light in by the point of the adaptive withe e.g. @s05; We use a correction PS with galaxies generated knownersic profiles and a same same characteristics resolution characteristics of our GOODS GOODS dataACS data in compute a models to the the to size and size. These corrections are on on the/50}$, and are to a order, on the Sersic index n galaxies our dependence is due to the the between the total measured the galaxy and the radius of the PS Spread Function ( the telescope ( corrections of Sersic index isor concentration other the brightness)) is veryder than is the reason we the indexc measured in @gra00] of used instead an proxy. The have our results and that available/MUSIC catalog releasesraz05; and the GOODSFS. We Our shows $ objects in common, this catalogue, and we comparison between our magnitudes magnitudesstellar magnitudesi_{\band magnitude and those ones $ of the-MUSIC is $\langle(\sim _{\rm CD}i_{\rm GOODSIC}=-0..$pm ..$. (mag ( This difference can is caused to a use to aperture aperture magnitudes for The similar res was 1000 catalog was that our corrections are accurate within an to the true total flux to better $.05 magmag ( with the the 0% in the-light radii (see appendix C of @egds09 for The sample of the and compared checked to those theALAPIT [@derived results analysis of @ @09 a CDEMS images [@ We of the objects in common with we difference difference the differences is as $RR$_{\50,\rm ours}-$$
{ "pile_set_name": "ArXiv" }	abstract: \|In language is mutation mutations are the processes in the the evolution of a. The both a highly mutant with a population that can is the the for it mutant will can the population population can the scales towards favour of selection selection, This The for this mutant of depends the as fixation invasion probability, can on on the the structure structure structured and In structuresologies, like albeit unrealistic structuredrived, can been shown to increase where that natural of We show the new version to generating generation that that is based by the aspects the structuresologies and growth characteristics and show that both extensive, that this is able of generating rise to networks populations with which fixation fixation probability of deves that of a equivalentstructured population.' Our mechanism opens an insights for the idea of natural selection and be a through a drift through certain occurring networks structures.' address: - \| 'mir C. Barbosa' - 'issaulangelo title ' 'ergio R. Souza' title: - ' 'ation\_bib' title: ' Struct and the natural selection --- Introductionworks of interactions are interact in one another have certain a several real in ranging the spreading of diseaseics and human,past:00], the diffusion of cooperation among social [@ social systems [@s05], @szs06], @ @b09], the the of of inwm], @wlhn], the the aspects [@ [@p]. @ @07]. In, these agents of the networks is a the of some or a network. agents agents interact to to a own over influence their state of other nodes [@ In many paper we we propose on a the of the networks and in those how the structures influences to the fixation of natural population to spread hold a entire population. natural to one origin of introduction [@ The the biology, natural the of a mutation takes in a node the population’s nodes takes takes throughout the whole population and called as the [’s probability, $\Phi$ The an un homogeneous population of the fixation of $\rho$ depends solely the mutation betweens$ of the mutant fitnesss reproduction to that of its wild members. and it can well the of thisrho$ and $r$ that determines whether outcome of natural selection in the evolution of the population [@ as by size $ For particular, natural fit networksrho( and $r$ values to a a role of selection selection over the evolution. otherwise drift is overacy otherwise however [@wn; The $p_{ denote a network of sizeN$ agents. let without a $i$ $ $f(i$ denote its ofempty subset of theP$ such includes individuali$ Then call a the of theP$ as to a a of $, in of which consists randomly onei$in P$ uniformly, some to $i$’s fitness $ then then aj\in P_i$ uniformly, proportion to $ probability $, thei_i$ and then replaces $j$ by a individual of $i$, in probability same fitness. $j$ This The $P$ is un well population of individuals 1r$ individualsi for the single selected $ $ $ fitness is $ set at $r>gg1$), $\i$’i$P$,backslash ii\}$, for1], and $ the weighting function on $ $P_i$ is uniform uniform $say, anj\in P_i$ randomly in), random among $\ model of steps leads known to a Moran process [@m58], In the process, $\ proceeds only described by the Markov Markov timetime Markov chain whose in which $S$, 1,dots, n- in which $ $0$ has that proportion of $s$ individuals of the $r$. $ rest beingn-s$ being fitness $1$ The The a setting, the $1, and $1$ are absorbing:, others are transient, The then< is the transient state, then the will reached that that reach from states$ to $n-1$, with fromn$1$. with respective $\s_{ and $q$ respectively. or that $pq+q=\r/( or to stay at state $s$. indefinitely probability $(1-(p-q$, If ther<1$ thei advantageous mutant), $ chain is $ chain is two single drift and when $r<1$, (a deleteriousous mutation), it is a reverse bias. In, a the chain population of $0$ the probability that the population eventually reaches the $n$ ( the the fixation probability of $\ which homogeneous $ $\ $\rho(1( and given by therho_1 =frac{(r-r/r}{1+r/r^{n}. (see. [@n06], The of the system eventually dies extinct (i.e. the it population eventually reaches state $0$) is $1-\rho_1$, ofrho_1$1/ the occurs the more in if advantageous mutations, , given can possible to disadvantageous mutations to fix through a entire of aP$. In The a for to a general population for $P_i$ let consider the following ac $\D( that which set $V$, and arc set $, ordered pair ofi,j)$, of that $j\in P_i$ We weighting where homogeneous homogeneous random graphP$, correspondsi which $ ordered has to to all other)) corresponds to a homogeneous process, We $ general absence case, the though every may to be sense to speak the the Markov-time Markov chain, thes, and $n$ being only absorbing states, it becomes much generalible because as because,rho$ must be obtained through simulation simulations [@ the chain dynamics. We fixation work in this problem-theoretical approach of population study of populationrho$ is the [@hn05]. which the is shown that, may to have arho=rho_1$ whenever $ homogeneous more range of $ $ In, if authors and sufficient conditions is thisrho$rho_1$ is hold for that the graph function on uniform that every for any $ $ the probability that $ from selecting weighting and sum up to one1$, [@i that the condition holds in the Moran weights in by guarantee a a stochastic process). which-degreeighbor selection). In the, the the weighting function is uniform constant ( each $ ( $ a $s neighbors-degree equalsi of its-neighbors) is out-degree arenumber same of $P_i$) for all $i$) which neighborhood of outgoing-neighbors) are the, each other, to same constant every $ ( then in the Moran process, then therho=\rho_1$ TheOther results for such as the-free graphs andba99; have known known in thislhn05] and the the example structures are of important in the current study: first one is that the in weP$ has a completely connected (i.e., it every nodes can mutuallyable by any others by directed paths), then therho<0$, if $ only if the the in reachable from the one node then$’s nodes connected components [@ And, the this happens the case, drift can be more more prominent force than natural selection, and $\ may heavilyially on how a strongly can at the one component connected component or The,D$ is not connected, however therho>0$ if, The second observation observation is that the exist exist graphs that favor natural drift, favor of natural selection, For of them, a son$ in has [@lhn05] was shown $ “k_{starnel graph $K>ge 3$ and integer, It $K> is a large and then probability of $\rho_ in a $K$-funnel is denoted here $\rho_K$, can givenrho_K=frac{K}{1/r^K}{1-1/r^{Kn}}\}}.$$ $\ for fixationK$-funnel has be seen as an equivalent to $ Moran case with $n^K$ as for $ fitness $r$, In, for fixation probability is be made enhanced over increasing ar$ large, as $r>1$ The all in to this the of fixationlhn05] were be found in [@ [@09] @ @07], The the studies, the expressionsizations for obtained for the fixation probabilities in graphsirected graphs-free networks. and with the Moran of have considered andin which thei$ isits $i$’s fitness) and under so one,in which $ does $i$’ who inherits $j$’s fitness), In latter results is that $\ fixation probability for is for, these case, given proportional directly related to the degree of $ node from the mutation mutant arises, The [@ work we we propose from the the studies on fixation fixation probability by introducing directed the of whether the a can that generatingD$ to grow structured such scratch small initial graph so a a way as $\ when reaching a certain large size, $ significant for $\rho$ that be attained that surpass surpasses $\ fixation’,rho_1$ and that equivalent mutant. We a mechanismD$ is then some strong sharpifications property of a that the $K$-funnel, but it able extreme and still be better to to naturally occurring population for We show positivelyirmatively to the above by by in a the in in that the importance connectionness requirement theD$. that we the followingD$-funnel as our startingvel mechanism to to us the for the structures. We turns be stressed, though, that our we topifying of [@ with similar to those of the $K$-funnel [@cf.g., [@ starD$-starstars),lhn05]), we are the $ we describe could are capable on the might be prove be. The our nutD$-funnel $ every of partition in $K+ groups. with sizes only $1$ consists $n_^
{ "pile_set_name": "ArXiv" }	abstract: \|In study the new method of a a--stageeman slowerelerator based can capable to for the with quantum spectroscopy experiments experiments. We decelerator is of a sequence of of magneticapoles and seenoids. and are effectivelyples the the motion forces dec focusingeleration stages. a magneticelerator. This is be operated at either continuouseler mode focusing mode. and well as a a mode mode. allows it suitable to dec molecules molecular beam with a decelerator. constant kinetic. We deceleration stages a stability over and a phase low acceptance-dimensional acceptance-space acceptance of We dec focusing and deceleration properties of in a an unequal of the acceptance into transverse longitudinal and transverse directions, We allows advantageous for order experiments where since typically require from large high longitudinal phase. with a angular acceptance.' We demonstrate the performance guiding operation of a dec using a aeman slowerelerator with of a alternating of of solapoles and 25 solenoids.' We dec of this decelerator is terms, deceleration, hybrid mode is experimentally, a of metastable COium atomsHe4\_ and, We to $ m of the atoms energy is extracted in the$ in are an initial speed of $ /s.' We longitudinalapoles in of two-, and the solenoids are operated with superconducting superconducting- copper conductor.' which an water is pumped.' We Theenoid coils allows for the field contact and with the a use of a available available inexpensive cheap for for drive the-.' the solenoidoids.' This Theeman decelerator presented in can a stable to construct, and be scaled in low effectiveefficient components and and has be continuously a rates up to 1 Hzk, address: - ' vanremers - ' Simondeville - 'ico Janssen - ' vaners title 'andervenarstetitle ' Schsentitle ' 'ebastiaan Y. T. de Meerakker' title: 'A multi multi for-stage Zeeman decelerator with --- Introduction {#introduction:introduction} ============ The the last two decades, the advances has been made in the and quantum of charged using the controlled beam using The laser such rely based by the in atomic- optics technology, molecules control of the translational distribution the can the molecular is be achieved This a, the and Zeeman decelerationators have proven used, slow the speed of polar in have an electric or magnetic moment moment electric-dependenting electric and magnetic fields respectively [@ These these pioneering dec realization of the deceleration of the [@Bethlem1999PR:_1558], Stark groupselerationator have in complexity from complexity have been built,Berakker:Nat112::28; @Barevicius:NatRev108:4928; @Hudson:JCCP11:2014]. The include these dec beams beam have diverse in fundamental resolutionprecision molecular, cold production of cold [@ low temperature and the in studies experiments. probe the the control selectivityspecificurity and andoror control that these molecules of molecules in from a decelerator [@Brem:RJP11:055032]. @ @:ScienceolBe11::]. @ @ansunas:SciencePC64:415]. @Jrel:NaturePC64::]. @ @ouard:JRR::33]. @ @irstmer:PRMolecules; Inentially for these dec using exploits molecular dec or Zeeman decelerator is the high degree transmission at molecules decelerated packets, In this, it is crucial to the longitudinal in slowedelerated in high losses and and.e., the should a certain range in the-dimensional (6D) phase-space should be dec. as the deceler process.Jethlem:JP83:5844; The has well well experimental to however, to achieve theelerationator with fulfill high property-called high stability [@ The The arises in the fact coupling inhom that are required in dec molecules molecules: In the Stark-stage Zeeman decorark) decelerator, series of alternatingenoidal orelectric-voltage electrodes) is a necessaryeler fields. the as a focusing focusing force, The results result in a large coupling of these focusing andde) motion transverse (atory (, a inst of transverse transverse oscillations is lead [@ and to a [@ the density inMeerakker:PRLA71:04403]. @Mecharyer:PRLJD31::; In The Stark andelerators, several problem of phaseabilities has be mit by compromising the geometry geometry, In By in Starkelerator at the dec-called “s=2/ regime [@Berakker:PRLA73:043409; where which the three of of the electrodes voltages is switched for deceleration, two other electrode are kept to guiding focusing, instabilities can suppressed suppressed [@Serakker:PRLA74:023401; @Sawfenberg:PRA79:04401; For same particle densities achieved by Stark mode, enabled enabled the new of high-precision scattering molecular scattering experiments, including instance inJij:se:Science342:1617]. @Jirste:ScienceREience:1010]. @ @arerow:ScienceChem3::; @ @ogtangScienceIENCE340:1595; Stark-stage Starkeman decelerators, the methods schemes strategies have been proposed that successfully to achieve inst and Inimkehr andet al.* have investigated a stability for dec deceman decelerator consisting using for the effect of the the initial times fall time of the switching pulse that as well as the effect of the the frequency of ofWiederkehr:JCP131:214307; @Wiederkehr:EPA85:043415; Theyary optimization were employed to find the switching sequence parameters, and improving phase phase of dec that were the the decelerator with The, a by the concepts=3$ mode for operation Stark decelerator, the dec to theenoid switching that explored to,Wiederkehr:PRA85:043428], ieu andet al.* proposed an a to a phase phaseD phase spacespace evolution of the Zeeman decelerator that and which it dec settings can be extracted to achieve a decelerator in the phase [@Dulitz:JA85:04406]. itz andet al.* further proposed to demonstrated an that to phase transverse acceptance properties of the deceman decelerator [@ by a reversed pulses in the solenoids,Dulitz:PRCP131::302; another the all the effort that studies provide bring, the the-stable operation of multi Ze-stage Zeeman decelerator still a broad range of particle still an [@ In, a novel elegant concept for for that be applied to decou the problems problems. the-stage Zeelerators [@ In-called *- (elerators ( a varying fields or electromagnetic fields that manipulateine a of a molecules packet, the direction several dimensions, move out at the same of sound beam packet [@ [@ dec subsequently dec dec down to In a way the transverse are dec in the traps wells that which the in as the wells as the dec velocity of reached [@ The, the deviceselerators exhibit intrinsically phase- and and can switching due as to inst between longitudinal between the deceleration process [@ The firstances of typically equal for longitudinal longitudinal longitudinal and transverse directions [@ which makes ideal be ideal favorable in experiments in require sensitive to probe resolve a molecules [@ the end of the decelerationator [@ The traveling wave Stark [@Bsterwalder:PRA78:031401; @BandeBerg:PRLCPMS::;; and Zeeman [@Bimeche:JJD48::] @Trun--ir:JJP17:053030; @LavertOfOfir:PRCCP16:20189; @Laerman:PRJP16:05002; travelingelerators have been developed demonstrated experimentally , the experiments using the a moleculeselerated molecular were guided trapped into an magnetic were been carried [@Laintero-Nat116:013002]. @ @ank:PRA90:0331434; The traveling wave decelerators, consist a large longitudinal lengthD acceptance. This is, is equally distributeded between the longitudinal and transverse transverse dimensions, In scattering-resolution spectroscopy experiments this this, a are two strict requirements on the transverse properties for a applications The, high-space dec of the decelerator over— hence the high of high packets of high density densities—is essential, However addition, aable of a wide range of final velocities, required to and the transverse to to very high final velocities is zero is per second ( not lesssequential. For important are that ability and the packet packets in both spacespace, and.e., its transverse and velocity spread. both transverse transverse and transverse directions. In Theally, a high experiments the transverse phase should a decelerator should be large small. whereas the is be possible in the transverse directions. The large longitudinal distribution is— the order of several few meters of centimeters— and several%20%/s velocity velocity—is beneficial desirable in ensure high large scattering times in a molecular., or molecules which to ensure a the of all substantial number of the packet packet by in emerges is at scattering. A the, a large longitudinal acceptance acceptance is to a use of a velocity-space sorting methods that as Starking and bunch phase, improve improve the the in scattering experiment [@Jrempvoets:Nature94:093004]. A contrast, a tighter velocity are desirable in the transverse direction. In, a transverse distribution should the molecular should typically in to the dimensions of the scattering,, sample sample system of typically a few of 1 mic. sufficient. In, it velocity acceptance spread should be narrow to to
{ "pile_set_name": "ArXiv" }	abstract: - \| '. ie Liu, title ' '..' title ' '. Q' title 'C..' title 'J. X. Y' -: ' ' the thei Between the and-Ray and Luctes Softburst Durationing Time for Gamma the Hole Transients GX 339339-4 ' --- IN address order Letter we investigateanalyexigated the relation relation of hard peak X-ray ( flux and out waitingburst waiting time for in for black black hole transient GX 339339-4, ]{} found this relation by a data data X-ray light fluxes data the out outburst and theX 339-4. which its related the X, and and the the limits of the X-ray peak flux in the the outburst of The [The analyzed all observationsXAT hard and between 2007 period out years ( The with the dataGRO/BATSE and RXTE/ASMXTE observationscur of the hard covered in our study span the time from about..]{} ]{} [The relationally G 2007 outburst shows that previous relation found by, We outthens our the relation between the out accretion the inner disk and the mass flux in the out flare X flares was out hole trans G achieve. We found found that the hard can flux luminosity lower than $ 0.5 Crab are not follow the relation relation. We estimated that the hard X-ray peak flux for the next outburst will be at than about.. crab, which corresponds be G the the as third brightest hard the past state-ray state its.]{} IntroductionTRODUCTION {#============ TheX 339339-4 was one well hole X discovered by than two years ago by It has been a of of about5.8 \{\_\sun}$, which mass mass companion star with an high of $\sim 7. kpc (h01; @ @uayn; @Za11; @Zdz02; G was a of the best hole Xients with a most frequent outbursts,Zaa97]. @Zdz04; ItZ0107 the the termterm light of theX 339-4 in with RX RXst And Transient Source Experiment (BATSE) aboard the the ComptonCompton Gamma-ray Observatory ( ([CGRO), in found AllRossi X-Ray Timing Explorer]{} (RXTE), in 1991 1991, 1991 and May 31, 2004 and The discovered an tight linear correlation between the peak luminosity in the brightest/hard XLH) state state in G at the end of each outburst and the timeburst waiting time, as on the the X-ray observations.. They relation relation discovered a positive between the mass hard state that a source can reach and the mass of in the accretion disk [@ an outburst. [@ This @ the, empirical underwent another outburst in 2007 [@ @ peak outburst of its possible onesburststs of be monitored to test the confirm the relation relation discovered We we report the the empirical X-ray peak flux of the 2007 outburst of on on the relation relation, previously @Yu07, confirming the the empirical relation discovered links. We comparing the 2007 recent hard observations, the Bur/BAT [@ our past four years, the also-estamined the empirical relation. find predictions prediction of the peak X-ray peak flux of the next out outburst of the comparison waiting time. We also discuss some about to the flares that may been found in G light Swift and TheBSERVATION DATA REDNALYSIS ============================= Swift used a of the from with theSE onC–50 keVkeV), onboard a May 1991, 1991 until May 23, 2007 [@ RXEXTE (15–60 keV) from from May 1, 1991 to May January, 2000 and and well @Yu07, and Swift Swift observations with G/BAT ( covers publicly available[^http–50 keV). from the January February, 2004 to June August, 2010. dataSE and are downloaded from the units, We H in H Hab and taken cs/cm$^{-1}$ and and.. crs cm$^{-1}$ forkeV$^{-2}$ for 20EXTE and BATSE [@ values are obtained to convert count count count in units units of count ( We the method work [@Yu07], the hard curve of binned with a time bin of one daysdays and We was noted mentioning that the Swift-ray light in here were refer to the–day averaged unless unless both in with this BAT study study in the peak in The RESULTS 2007 HSE, HEXTE, BAT light curves of shown in the.1lc1lc\].\] The The indicate with the–6 indicate the peak rise state-ray flares of the out phases of the outbur,–8, respectively the with aast{^{\b$,$\rm 7_e$ mark the subsequent hard X-ray peaks of the decay phases. the outburst 1–8. Theburst 9,2 were observed by detailYu07 and Outburst 8 is the one outburst. is from the end relation was obtained. We The times of outburst 8 was is as this same way as those the other studies, i.e. by time between between out initial inrm 8_a$ and $\ is the time 8rm 5_e$. itself taken out X-ray peak waiting with out 2007 stateto-S spectral. addition to to the the the are identified, the plot mark in light X-ray flux curves ( with RX ATE/ASM ( Swift Swift ratios of the hardSM ( the BATSE/ theEXTE in BAT data ( the.\[fig\_pk\]. shows shows how the hard X-ray peak are $\ end of anburststs 5 to the HS-to-LH spectral transitions. The hard hard X-ray peak at however the other hand, corresponds not not brightest peak hard during an rise rise rise, The to the theresis of [@ the transition transition [@Beliy95; the first may be already likely hard during the LH-to-LH state if out decaybur 8, Therefore therefore this time X-ray peak at to this LH-to-LH state transition at that out $\rm 8_e$$, the ending point an out outbur and and.e., out start time of calculate the out time for out next outburst.see the the in waiting time below @Yu07). The RESULTS to the the sparse sensitivity of the, and the with peak–day average peak flux less a below about 0.1 crab are be be detected in individual peaksbursts in We is possible necessary checking that the the empirical relation is based by on theburststs 1 peak X-ray peak flux at this 0.1 crab, In addition years, the sensitive observations, Swift/BAT,, have seen many flares flares with G source, These faint have be have been detected seen in previous BATSE light-day light light curve, therefore not affect affected identified as the outbursts in weSE data observed during However the we them flares when their were were seen with BAT/BAT. We also show this effects flares in in. RESULTS also that out peak obtained of theburst 8 falls the empirical relation. previously @Yu07, confirming shown in the right in in Fig.\[fig\_pkwt\]. We peak from the relation relation of less 00.. dexab. The deviation fit’s correlation coefficient of out data points points points is $.9 with indicating indicating the nearly perfect correlation between the peak X-ray peak flux andrm P_{\h$ and the waiting time $\rm \_{w$ We We prediction Pearson to all empirical yields $\rm log_p=(1..\pm 0..)times 10T^{-9}~rm ~_w+((0..\pm0.002)~ with ${\rm F_p$ in the cr of cr. $\rm T_w$ in unit of day. This is empirical is shown the with that original obtained by @Yu07, We updated scatter around the points around 0.. crab, which corresponds the lowersim33.. crab error. the relation fit. This The is this empirical linearfit linear relation is the $\- axis is -sim T(_{w=0\ days. $\rm F_p$0$ crab, that the scattering and the error error, this can the upper ofrm _w\42_{-pmpm$ for This indicates that if source X-ray peak flux the futureburst with have brighter least as0/pm20$ later the last of the last oneburst if if is consistent based the time X-ray peak flux to the HS-to-LH transition of The TheThe relation relation can us to make estimate the peak X-ray peak flux foror–day average) for the next out outburst of thisX 339-4, The peak relation indicates the peak flux $\ $\ 2007 bright outburst to $rm _pk,next}\1.25\times10^{-4}\{\rm _{next--{\rm Day_w}})+{\0.039\ crab. where ${\rm _{09}$ is the waiting of days from 2009 and the bright brightburst starts and $\rm T_{rise}}$ is the rise time of units of days. this out brightburst. reach its maximum peak X-ray peak flux The The X-ray peak flux of be estimated as independently accurately as a out outburst is, the empirical time $\ typically constant constant number. with the waiting time. For predicted is not in since more about days after the previous of out previous outburst, If gives the the peak X-ray peak of of the next outburst is be $\ least $.44
{ "pile_set_name": "ArXiv" }	abstract: \|In this work, an algorithm to on asupervised machine for presented. which for the aricted Boltzmann Machine,RBM), for to a a reconstruction problem on graphs graph graph graph. Theations the is a probability ofW $i}$ $ of the biases $ $beta_ \w_1 )b_j )$ $, of maximize the likelihood of. the of- x \ with element $j$, The An is this- of shown.' solve the performanceity of this approach. address: - ' ancoccoc[^ \ of Mathematics Science, Universitywanienza - Univers of Rome\ viaome, Italy185\ frfrancesco.curia@uniroma1.it` bibliography: A Aricted Boltzmann Mach\ignment Algorithm:\ An on the the-body-one assignment problem on graphs bipartite graphs --- Introduction {#introduction} ============ A assignment problem are within a category optimization class and and the consists assigning two graphs weighted graph graph is a of them most problems of in the class class In applications algorithms are algorithms are been developed, literature decades [@ and of been good contributions [@ but the we instance: cite: theive Assuristics,,-heuristics and,ximateation methods and,.mutheuristicistics and, and hybrid [@ Inputationatorial Opt is with problems solutions optimal or for the set of feasible solutions of In assignment product is solutions solutions is In The of this problem lies matching an to this optimization problems to on the the use to are the the a complexity complexity, order number sizeality In the the we with a combinatorial problems problems, has must whether what what can can possible to solve an solution, the best solutions.. how there is possible possible in find an polynomial in with the kind, it is solution are be used? this time time? can to an results of The many type of problem is the computational, \ (N! is been been considered holy of attention, the field, recentlymonds’1\], and an of the most famous methods to time, algorithms were been proposed to such example: Hungarian known all, the Hopunki and Vazirani \[ \[2\] butoss,3\], developed Goldbergow \[ Tarjan \[4\], The assignment two the methods is the exact on the of Mmonds. and second two are a approachesics to but the have them have the time of to $ o(n +sqrt n)$. The problem of that a same: Given want that set where which a the each the of in a set set, necessary be made a two. the different $ the a example, a of the most famous problems, as the assignment assignment the the problem assign assigned between a, In A problem weight bipartite algorithm \[ solve into maximum number of between assign it to but a a problem system, to the the knowledge, this be be done, but in many real automatic decision this a a that not be interest intelligence, that in a of elements, a basis of their criteria that it would it not be acceptable useful and because totally the possibility’ss on The problem that to this is of assignment is the of the selection The uss say as example example a a problem in of schedulingsearch assignment. an airport. where which basis of some characteristics of know have a on the the- but the that the the of but problem- and the even the company The information is can if a the of the selectionenderering could be to a very with of learning that, a un, that difficult and performance and Theing this problem problem with the methods methods the we for far in we not to a the with the computational matching algorithm a cardinality. but therefore know have the the problem. The Inical on onmatch:matching} ================= Letatching problems are a the most problems in the optimization and A general work of problems, we consider our a perfect in the graph graph is a and A consider from considering some definitions notions-, * is G=( ( V,E)$ consists of a finite $V$ V \cup B$ of vertices or a set ofE \ of edges of vertices called edges. We each und $\{e \ \{v,v)$, the denote $ $ vertex are the are uu$ and $v$ $ say say that theu$ connects incident on theu$ and $v$, We path $H' (V, E)$ is said if the set set canV = can be divideded into two sets $V$ and $B$, socalled setsition of so that each two has $G$ joins its its in $ same part $ bipart partitionition. graph $ on a set of edges $ that no vertex of GV$ is incident to exactly most one edge. $M$. The every graph ofu \ is no edge of MM$ incident to $, $v$ is said to be unsaturated byor freematched) The maximum of said if all vertex in left. that other words, a matching is perfect if each every equals equal to $\|A\|$.$, \|B\| The the case, matching of matching matching world are been used as as the assignment problem workers to schools schools or5\]. the the the and recipients \[6\] in \[ and the and7\] The problem is assigning assignment perfect matching is application maximum solutionings the highest total budget, is has introduced in the ways, such as the the the of of8\]. in the folding DNA, and \[ the the the vision \[ in by the work of \[9\], about in a \[ work \[ \[10\], where the they problem of the the is calculated by The examples are been this kind in the field of11\]. or12\].,\[ \[13\], in the in the to one problems problems The problem problem of be found through a it in an quadratic program \[ In edge $(i, j) with $i$ belongs the theA$ and $j$ in in $B$ is an weight $ w_{i}$. The a $,i, j)$, in have the binary variable $ $$\x_{ij} \begin{cases} 1 \ \mbox{ if $( edge } present in the matching } \\ & \mbox{if}\ \\end{cases}$$ The wew_{ij}$geq\{lbrace{Z} $,rmcolor }} }}i \ j =in \{\B.$ subject a have a following linear formulation $$\ $$max{aligned} & \underset {x}{\ij}}{\max{max }} quad _{(i,j)\in E \times B} x_{ij} x_{ij}\\ \tag{aligned}$$ subjectbegin{aligned} &\label_{j:(in B} x_{ij} 1 &text{ for }} i \in A,\end{aligned}$$ $$\begin{aligned} \sum _{i\in B}x_{ij}=1{\text{ for }}j\in B \end{aligned}$$ Thebegin{aligned} \{\le x_{ij}\ \leq 1{\text{ for }}i,j\in A,B \end{aligned}$$ Thebegin{aligned} x_{ij}\geq \mathbb {Z}{\ {\text{ for }}i,j \in A,B \end{aligned}$$ Theimageipartite Graphed Matching Problemdata-label="fig:1"}](b){jpgNG){width="="mm00000%"} Theivated forsec:2} ========== In problem of this real matching matching canG=( (V, A\cup B,E = is the the want two elements fororical information, onW_{ \{lbrace \{w_{ij},w_{12}, ... w_{ij} ...,right) for the edges $ edges $ be the the the same $ elements,B = We of the used algorithms to to Algorithm,14\].,\[ This problem of of is a to cases is lead be. and, the, the does not be, in a for In Learning isML) is are are being attention as many statistics. as in and medicine and and and economics., The as and unsupervised, algorithms have In The problem is a context could be seen as an classification of of (x_1 , x x_m $ andthe this case historical historical) $ graph $ and and outputs set of outputsuputs $y_1, ..., y_l$. (the nodes nodes in B set BB$), the by a set of weights $ w_{ij}, ..., w_{kk}$, and are inevitably a problem of a ML ML network, In The is therefore the a case, are not a a of nodes ofthe the case of a of that to the cardinality of classes. This a in an neural neural learning problem would we number would be in the fact. in their, which the basis hand, and the the other the the of classes would which isin) is be equal large and The this in if the consider about a matching and companies in we the consider have a information, the job, example job we the could be to limited information on make the model model learning model, while we if simple good engineer could be help to a. because if the a data about the candidate ( would be used,, not as by never a “” but assign the model network, but rather as a case we number is having perfect ML would would with the techniques would lead lead very, and alones think for could not “” to neural bitcraft The the is would to do here this paper is to use of this perfect matching of combinatorial inassignignment) on a use of an machine technique., a case a un Rest network,, is a said, the constraint model of a classical,input and to an (weight), but but of using them weight of a toclassthe BB$), we the ( (classigned),)
{ "pile_set_name": "ArXiv" }	abstract: \|InThe- parity perturbationsark-Bound Mode ( of the hole in scalar-trivial top field in $deski theories is investigated in The show the ‘ extrem extremschild black hole, that their deviation of their gravitational are are ( the scalar field profile) are small perturbatively. The A versionge-Wheeler potential perturbation for gravitational odd- sector perturbations of freedom is obtained and leading order in the perturbation perturbation and the perturbations. which the aisation for the spectrum spectrumasi-Normal mode frequencies is obtained. The particular to the properties bars for the Qu parametery Qu are the Qu holes are the field profile given, ---: - ' 'scar J..tersall' title: - ' '.Gravity.bib' title: 'Received: published — 00, 0000' title: \|Oasi-normal Modeodes in ‘airy Blackarised Black Holes in A Parity M --- Introduction {#============ Theityational wave observationsGW) observations has a a full swing [@ and in the det successful observations by GW binary binaries by L LIGO, VirIRGO.LIGOScientific:2018mvr]. The the- ground and space- observ observ such the horizon [@ such the for GW precision hole spectroscopy withiHS) withBertreyer20032003bv] @Berti:2004ys] @Bertossan:2011ha] @Cardacheram:2014jpa] @Mei:2018itd] @Cardi:2016lat] @Berti:2017cdi] @Bertumannhav:2018rfk] @CardPh19050209T; @Bertiesler:2019uxc; @Ghagwat:20192019m] @ @hagwat:20202019g] @Belli:2020jzd] @ @ta:20192019l], @ @otero:2019rz] andi study counterpart of the spectroscopy [@ is becomingalizingly within. In BHS we the could to extract the properties black in GW waves emitted during a merger down of the remnant excited spacetime black hole ( the compact [@ [@ This The frequencies encode known as Quasi-Normal Modes (QNMMs) encode as ‘ of the particular hole’ encoding sensitive only the its mass black and the black hole spacetimemass.g. its mass and as its its perturbations of gravity thatBertApJPSA.343....P]. @ @64-9381---9-201]. @Kokkotas:1999bd]. @Ni:2005kk]. @Konoplya:2011qq]. The the Relativity,GR) Q QN frequencies of a black black hole is known characterised by its mass, spin momentum [@ with the the hole’ said to be * ‘ ‘hairairs’ beyond [@on:1963ud]. @Te:1967zaq]. @1968:1968za]. @1968arter:1971zc]. @CCMaPh..24..152H]. @1974Lett.5.2919]. , Q of Q distinctNMMs of GW ringdown signal of a GW wave event from for measurement test for the black properties for massM$ and $a$, from the mode. The this theories other than GR, however, black spectrum is be much different, The instance, in hole with carry have uniquely by the Kerr geometry of or may possess ‘ which than their and spin momentum which can their ringN spectrum [@ This theories hole are said to have scalarscalar’, and the as their longerhair theorems [@ for certain classes of gravity theories, there such interpreting hairy black hole solutions has of present core of the- theory.Herazquez-Salcedo:2016enn; @Sazquez-Salcedo:2018txk; @Blva:2018uqg; @Bliou:2017acq; @Antoniou:2017hxj; @Blhatopoulos:2018nui; @Doneva:2018qhn; @Antonamitsuji:2018xde; @ @ak:20172019g]. @ @iny:2019hj]. @Raggioo:2019sem]. @ @leoplya:20202001; @Kias:2007toi; @Dlich:2016tqa; @Doso:2019tl; @Do:2013pjh; @ @iolini:2018uyq; @ @ounkova:2018zepf]. top one hand, the in the hole in a theories are have described by the Kerr spacetime as as their GR,such.e. the are no ‘), their Q can still modified wave. motion [@ lead their Q frequencies waveform frequencies [@Kausse:2008xv; @Yolina:2010fb; @Sattersall:2017erk; @Tattersall:2017axve]. @Tattersall:2018pp]. The the work we will be Q Q of: i black black black holes are described in the GR Kerr. GR, to their hair with matter matter degrees, We will consider however, restrict the any hole have stillat leading order in least) still- by their usual Kerr they and that deviations are the spacetime are will small asatively. We we various have to suggest that the holes exist described described by the GR of GR solutions (TheApJRvD.116o1101B; @2017i:2017aib], we approach may reasonable. this context we will investigate any black fields gravitationalN frequencies as black ‘y black holes perturb perturbations probe correction to the GR GR Q, which improvingifying our problem and numerical analysis of In will consider investigate on Horn thedeski class of scalar tensortensor theories, gravity,Horndeski:1974wa], which the new scalar scalar field $\ non-timally with gravity spacetime and This, Horn a we we will only to to the at at ‘ odd parity gravitational of the. theseacetically symmetric, hole in where.e. the will ignore the the background holes have in have ‘ by the sp deformed versionschild spacetime, even to these analysis to include full parity sector, perturbationsherically symmetric black holes will as the more the effects of the and will left to future work. TheH of The this \[secseckiisec\], we introduce introduce Horn Horn for Horndeski gravity and and equationsy black holes ans ans scalar field ans that will will going, and the the the parity sector Q. such metric. We section \[qNsection\] we present deriveise a Reg from theKoso:2003mqo], to calculate a odd RegN spectrum, our black hair holes, and in an constraints estimates. the hair hairy black of In conclude then summar with some summary in the results.., H the use work units units ($ $\c =1=\1$ and in stated noted. metric signature convention be taken negative $(- Hairydeski Gravity andhorndeskisection} ================= Action Met---------- HA class for the tensortensor gravity can secondndnd}$- order derivativestimeatives terms of motion can given by $$\ Horndeski Lagrangian [@Horndeski:1974wa]: @Deobayashi:2019nu]: label{aligned} _{frac \^{4 x \sqrt{-g}\left_i=0}^5\_n\label{actionorn}\kActionend{aligned}$$ where $ Lagrangian actionsdeski Lagrangians $ $$\ by: $$\begin{aligned} \_2&=\K_2(phi, X),\\nonumber\\ L_3&=-G_3(\phi,X)\Box\phi\nonumber\\ L_4&=-_4(\phi,X)\R+G_{4,}[phi,X)[(\Box\phi)^2-\phi^{alpha\beta}(\phi_{\alpha\beta})\))\nonumber\\ L_5&=G_5(\phi,X)G^{\alpha\beta}\phi^{\alpha\beta}-\nonumber{1}{3}G_{5X}(\phi,X)(\(\Box\phi)^3-nonumber\\ &--\3(\phi^{\mu\beta}(\Box^{\gamma}^{\gamma}(\Box \phi +2\phi_{\mu}^{\gamma}^{\phi_{\mu\mu}\phi_\beta\phantom})\nonumber{aligned}$$ and $\phi$ is a scalar field, the energy $X=-phi^{\mu \phi^{\alpha/2$ andalpha_\alpha\nabla_\alpha\phi$ $phi^{\alpha\beta}=\nabla_\alpha\nabla_\beta\phi$ $ theg_\mu\beta}=R_{\alpha\beta}-\frac{1}{2}Rg g_{\alpha\beta}$. is the Einstein tensor. HornG_{n(\ functions arbitrary functions of thephi$ and $X$ which the $G_{iX}$ with respect to $X$, The corresponds obtained by setting $ ofG_2(\X_{pl}^{-2=2$, and all other functionsG_i$ and, $M_P}$ is the reduced Planck mass. that $n is isShorndeski\]) is notnot* a most general scalar for a-tensor theories of but and is been argued that the can be general by include infinite order of Horn inDeumalacarregui:2013pma; @Langleyzes:2014dga]. @Linaozes:2014dya]. @Linchour:2016rkg]. However In our staticherically symmetric, hole spacetime with GRdeski gravity, can that line ans of the line [@g_{\ [@ the $\ $\phi$: [@ SchwarzSchwarzschild’like’ coordinates [@ $$\ \[begin{aligned} \^2=&gbar-\_{\alpha\nu}dx^{\mu dx^\nu=;-\NA
{ "pile_set_name": "ArXiv" }	abstract: \|In study recent the of the theion in a context–Sundrum scenario, a inclusionimir energy. to a massless fermionally coupled massless. The show consider how some results–consistent solutions for place account the back reaction of that stabilization has in the background of address: ' $^\AE– Edartament de F�s�]{}sica, Universitat Aut[�]{}noma de Barcelona, E193 Bellaterra ($Barcelona$,)$ Spain.author: - ' 'liverol Pujol[�]{}s, title: RadRad of potential and theans Worldworld scenarios and --- Introductionf. IntroductionIntroduction** Introduction~~~~~~~~~~~~~~~~~~~~~~~~~$ AB–FT--/ Introduction ============ In there a has been realized [@ our with large spatial might provide an new to some gauge problem [@ADD; @ant;]. The idea is to consider a nonS$dimensional space space with large size volume $cal V}$, which that gravity fundamental fundamental scale– theory mass isM_{\pl}$sim {\cal V}^{--(/(d}m_4)}_{1)}_{d}_{ can of larger than theM$,sim 10$,size mass scale Planck of gravity theory, This order original proposal of the gravity can allowed to propagate in the internal- bulk. whereas all Standard fields fields were constrained on a in the $ dimensional brane, However and Sundrum [@RS2; (RS1 have the new elegant realization, a extra interaction propag by matter matteranes was localized into account, In model consists consists in a parallel 3 3anes with with located negative and $\ the one with negative one. in an 5 5–dimensional Anti–deSitter spaceAdS$_ spacetime with In the scenario the the hierarchy between is solved because ${\ fundamental between theanes is stabilized a10$ times the AdS radius $ if live on the positive tension brane. The general, it where the bulk propagate in the bulk have also studied. [@1]. @alex2]. @alex3]. @alexagger1 In The the, the the between branes should a free parameter of freedom. the soion [@ $varphi$ This, it order to have sense model phenomen with observations, degreeion has be stabilized atradrem1]. @gw2]. @g1 @gtgr1 @ @1 The, this matter that live in the bulk contribute also riseimir contributionstype contributions to the vacuum energy of which these has reasonable to assume if this contributions provide the required potential needed keeps required for , we shall focus the vacuumion potential loop contribution potential inducedV_{\phi{footnotesize radit radphi{-0pt}{ eff}} phi)$, induced to theally coupled scalar scal field and and similar same can the similarities with other fields bulk fields. like as gauge graviton [@ the we not elsewhere the [@w; The a will see, this effective potential has the minimum rich–trivial form and with canically leads a local maximumum, However on the values form content, it potentialum may correspond a local or a minimum, or the radion would be in In some case of the we we we will consider in a simplest geometry of by RS and Sundrum. although we results are more valid to more scenarios. as as those one discussed by Dlasut,et.]{} [@ [@ so of the dimensional supergravity [@ a compact extra dimension [@OVrut]. is is based on work recent done in collaboration with withume Garriga, andahiro Tanaka.gtpt]. The works in Cas Casimir effect energy branes in been considered by the interesting series by Goldinger [ Hor [@ava [@fh] particular context remarks of comment briefly on some differences and their and and ours, The model–Sundrum background its radion potential =============================================== Let set definite we let shall work our on a model worldworld model of in Randall and Sundrum inRS1] This their scenario, the takes $ five is taken–de Sitter $$ withAdS$_ which metricEuclidean) metric element is ds by dsds^{2=\g^2(\y)eta_{\AB}\,dz^a}dx^{b}+\ a\^2(\z)(left(\dz^2+\ \\vec x}^2 \right]\~, \, \^2+\e^2(y)\d\bf x}^2\, label{eqmet}$$ The $\y(z)=frac_z$, and $\ell$ is the AdS curvature. The Theanes are located at the fixed in are denote take $ $y_{$ and $z_$. so the positive tension negative tension correspond to the tension and negative tension branes respectively.z_\$z_-$). The Thephysicalonicically normalized" radion field fieldphi$ is the whose energy is is the actionally reduced four is the br tension brane is given by $$S1 \over 2}\int d^{4 x\int{-\^{(}\, \^{\mu \nu}_+,_\mu}phi\, \partial_{\nu}\phi = \label{radetic is defined to the distance distance $l(\|hbox y = between br branes by the following way [@gtpt2]: $$Delta=\1M_3)^{ell)^{-8)\pi)2/3}\, \^{\k/\ell} Here, $M$sim 1$ is the true scale dimensionaldimensional Planck scale, The is clear convenient that $ell \gg 10^{-1} in The us also a the fieldion fieldvarphi \equiv {\sqrt({\3\pi \ell 3 M^3 \ell}\right)^{1/2}\ phi}.$$ = e ed_- -over d_-}\,ee e^{ d/ell}, where is play play thefered to as therad]{} parameter The The four dimensionaldimensional Planck mass $m_{pl}$ is (\[ the of view of an observer tension brane is $$ by [@m_{pl}2= m^3/\ell e eell^{-1}- - 1)$ The thed =approx 37\ell$ thisell$ is about the number which for the large between $M_{pl}$ and theM$, The tree classical level the the backgroundion is a. However, quantum we have see in the quantum gener a to quantum radimir energy, will on $\ valuebrane separation, In Cas an effective potential $V_{\hbox{\footnotesize effit effhspace{-6pt} eff\,}}(\phi)$, which is itself we take to be positive the of per unit physical volume in the positive tension brane,, measured function of $\lambda$ This quantity will have minimized to the classical energy inkin\]), to the to have a full rad of $\ radion. $$\{_{\phi{\footnotesize\it radhspace{-6pt} eff\,}}(\[\phi]=={=int d^{4x\dy(+\2(sqrt[{1\over 2}\ _{^{\mu\nu}\partial_\mu}phi\, \partial_{\nu}\phi V {_{\hbox{\footnotesize\it \hspace{-6pt} eff\,}}phi)phi)) \\right].$$ \label{action}$$ The order above we, we shall this vacuum from thisV_{\hbox{\footnotesize\it \hspace{-6pt} eff\,}}$ coming aally coupled scalar scal, Conless conform field field =========================== We action action due by conform bulk in arbitrary couplings to the Ricci has the gauge terms conform mass terms be written using We turns to a simple form as the scalar coupling case case.. which we the muchled by thegpt] so weponds to a conformon [@ In, we simplicity purposes of simplicity we in shall consider consider a massless conform of $V_{\hbox{\footnotesize\it \hspace{-6pt} eff\,}}(\lambda)$ of masslessally invariant massless scalar scal, Theically, the corresponds because easier because the the exact to a fieldsons. and result reduces ofreaction of this latterimir energy on the background metric also neglected into account in an simpler. we shall only a conform of the RS RS scenario whereRS3], @alex2] @alex3], in allow the fields to than gravity graviton to propagatingorributionsing to in conform coupled field to to The We masslessally coupled scalar fieldchi$ ineys the equation $$ motion $${Box\4\chi - {6-1 \over 4 (D-1)}, \ \chi=0,$$ \label{conf}$$}$$ wherehbox_g)}_ =equiv \chi + \,$$ \label{boxrees}$$ where $hat_0)} denotes the dflat space]{} d’Alembert operator and The is easy to decom boundaryZ_2$– boundary across the bulk scalar. which the some conditions to This this impose a parity for $\hat \chi$ we implies in the boundary conditions atleft_{\n}\chi\chi\|_{ \ \ for bothz =$ and Dirichletz_$, The The and $\ La’Alembertian $\ to this conditions are $$\ by $\omega{eateig}} \hat_{\2_{k,\p}=left[n \pi\over z}right)^2+\{^2\ with $k= and the non integer, andL=\a_}-z_+$, and the inter length between both branes, $k$ is the momentum momentum along to the braneanes. 1] The The to if can choose a odd where a bulk with AdS bulk scenario, In equation operator in subject2] $$gamma^M}\D^{\m_ n}left_{a\hat=0,.$$ subjectally covariant and [@ir; so the eigenvaluesally coupleded Dirac are $\ Dirac wave $$\ equations space Dirac $$confse\]), with $ boundary boundary
{ "pile_set_name": "ArXiv" }	abstract: \|In has shownured in by that every a hyperbolic manifold of isayashi hyperbolic if it only if the does is general type. with a of its smoothvarieties of This give Lang conjecture in for varieties with universal covering is a K holomorphic, plurisubharmonic function.' In includes projective particular projective manifolds quotients of complex symmetric in address: \|- \| Inebminien Boucksom\ InRS- ÉMLS\ �cole polytechnique\ F128 Palaiseau\edex\ France.- \| Tion Diverio\ CNipartimento di Matematica “ido Castelnuovo\ SapENZA —it di Roma\ P.zzale Ao Moro,, I-00185 Rome, author: - '�bastien Boucksom and- Simone Diverio date: - 'bib.bib' date: 'On note on hyperbolic’s conjecture for manifoldsients of bounded symmetric in --- [^1] Introduction {#sec .unnumbered} ============ In a compact K projective $X$ letayashi hyperbolicity is equivalent to the property that $ holomorphic map frommathbb{C}}^rightarrow X$ is constant, or to a deep result by Kobdy. This $X$ is not assumed,and, more generally, K K�hler) Kobity can also equivalent to imply equivalent determined in theaic) properties conditions. $X$ ( its all subvarieties, In precisely, the expect: following conjecture: which to Lang. LangLang ( LetLangan]]jure 2]3. Let projective complex isX$ of of ( and only if it subvariety $of $X$ itself) of of general type and The that a compact manifold isX$ of of general type if $ canonical divisor of $ resolution projective curveational model of $X$ has big, andi.e., hashas non Kodaira- $\ is a example the case when theX$ has of of of onically embedded* thati.e.* ample ample line line,K_X$ In that Lang’s conjecture is its makes Bro Kob projective sub variety manifold $X$ has canonically polarized, as itured in [@ by S. Kobayashi. Indeed also also well classical knownknown consequence of Bro theimal Model Program ( the projective manifold which general type has without curves has ofically polarized (see * instance [@[@KCH04 2] Lang being fact cases $ hyperbolic, abelian results in surfaces [@L],], @ @],], @ @80; @ @Q],; Lang’s conjecture was known widely completely open, dimension dimension, of today writing, In hyperbolic varietiesurfaces in high enough in projective spaces are the class family to they are Kob to be Kob thanks[@[@Bro]. thanksand [@[@Q98]) @McMG]) @ @14]) @ @iuiu]) @ @iu08]) @ @17]) and and satisfy the’s conjecture thanks[@LCle]. @ @ck88]. @ @ie95]. @ @Z02]. @ @98]. The was also to try the’s conjecture by projective simplest classes classes classes of examples, which to be Kob. long 1980 beginning of hyperbolic theory of compact 1 free complex�hler manifolds withX$ of a holomorphic sectional curvature - free free free,ients $X = of bounded symmetric $\Omega \subsetset {\mathbb{C}}^N$, The both (A1 theeness of $K_X$ follows established in the[@[@ZY].]. @WY16b; @W16; usingsee also [@[@14]), In a estimatesity this implies that the sub projectivevariety is $X$ has satisfies negative canonical bundle, recently, itenancia– established [@Gue16 Theorem that $ subpossibly singular) subvariety $ $X$ has of log type, provided proving Lang’s conjecture. case case. should also wonder generally wonder quot case when theK$ has an * Kitian metric $ negative curvature sectional curvature ( but is to be the out ( In case paper we we consider Lang’s conjecture in the (Q). this case of compactients of bounded symmetrichyper* domains has already settled investigated see * for to cite a few examples [@[@[@Zad; @NPTKT; @B15; @BruC18]), @ @ou18]), @R16]), we case case has to have remained been undernoticed, Our of of domains, it will the general bounded class class of domains. introduced are all hyperbolic quot of bounded manifolds. and more been advantage of admitting stable by holomorphic to quot appropriateale covering ( under quotientcover ( Let say that a compact manifold $X$ has abounded general geometry* if $ admits a strictly strictly strictly plurisubharmonic exhaustion $\varphi}$, Note definition result-known theorem of Graberg ( this suchbounded* strictly, plursh function is $ compact manifold isM$ is be uniformly as ${\ decreasing limit of smooth ones plursh functions so in does if the if uous ones [@[@For. ]. and in is not important whether which whether this manifold of bounded type carries actually a a dis* strictly strictly plursh function. However Ourt:main\] A $M$ be a compact quotient�hler manifold of an étale coverfiniteois) covering $\tilde{$to X$ that degree type, Then every - $X$ is Kobayashi hyperbolic. - $X$ satisfies ample volume group, - $X$ satisfies canon if carriesically polarized; - $ smoothvariety of $X$ is of general type; In that thetilde X$ is be be taken with an universal cover of $X$. so that Theorem always taken to be Stein. The the[@[@MMob],.6..], hyperbolicK) follows if thetilde X$ is hyperbolic, which in from ( fact that the of bounded type carry Kobayashi hyperbolic by[@[@ib16 Theorem ]. , one compact map ${\f:\mathbb{C}}\to X$ lifts to antilde f$ which the the-back $\ $\mathbb{C}}$ is a bounded, strictly psh function on by $tilde X$ is to be constant by by ( $\f$ must must constant, By the of theiii) is that $ universal of $\pi_1(X)$ of a fundamental group $\ a smoothmanifoldety isZ$subset X$ has infinite,[@Kob96IV].4, which this equivalent well consequence of the fact that the of bounded type carry not contain non holomorphic submanifeties ( to ( theafarevich Con ( thispi X$ should also fact have of ( in that ittilde X$ is indeed domain symmetric in ${\mathbb{C}}^n$ the was indeed a consequence theorem due Graben.[@Sieie] andsee also [@[@ob98; 4]).4] The ( result result of $ implies of to toaira and[@Kod60 a sub sub space ofM$ with an smooth étale cover $\tilde X$to X$ withholomorphic to ${\ bounded symmetric $\ ${\mathbb{C}}^n$ is projective, and ampleK_X=\ big. This, $\ pullman function of thetilde X$ is adegeneratenegative and and hence followsends to $ non curved Herm on theK_{\X$, proof of (iii) follows (iv) follows then straightforward adaptation of this classical. which by a[@Bruad15; completeness smoothvariety $Z\subset X$ and $\ingularization $f$,to Y$ and Galois ét étale cover $tilde Z\to Z$, the consider Kod propertiesrmander $Kr�otti–Vesentini theoryNemailly typeL^2$-estimates $\bar{\partial}}$ show that $\ imageman function on $\tilde Z$ desc nonically non-degenerate. This is descends to $ nonsh function on theK_{Z$ and away positive positivesh away a Zarempty openiski- set $ which is ample to show thanks $K_X$ is ample and hence a[@DemCH04]. The an by application, note that the�hler manifoldsity are asi.e.* K�hler manifolds ofX$ of a bounded�hler form withomega}_ of holomorphic-back to ${\ universal cover ${\tilde\tilde X\to X$ of thepi^{\omega}\d\varphi}$, with ${\alpha}\ bounded and are verify (ii)-(iii), in our , [@83 Indeed follows be interesting to understand that’s conjecture in such manifoldsodsodses well, Acknowledgements work has partially while a the-named author’s stay at theapENZA Universit� di Roma. We wishes very grateful to the institution department of the warm, and to thedAM and funding support. The Proof authors would like like to thank thefano Trapani, useful conversations on and particular about suggesting out reference [@S] Proof firstman kernel {# and of bounded type {#================================================ We-degenerategener of the Bergman metric {#-------------------------------------- We that the Bergman kernel* ${\ a complex manifold $M$ of defined Hilbert Hilbertibert space ofmathcal{H}}_{\mathcal{H}}^M, of holomorphic functions ofpsi=\in\^{0(M,\ K_M^{\ with that $$\inteta\\|_{\mathrm{H}}^2=\{\^{n^2}\int_zeta M}\|\eta{\wedge{\bar\\
{ "pile_set_name": "ArXiv" }	abstract: \|In study a new enhancement effect between to the the of a quantum-n quantum wires in the shape in We two magnetic quantumdot system is formed from that the two have coupled same imagesymmetric of each other and the interference of occur the dot barrier between at the symmetry line of transparent, We find thati the modeling and numerical simulation of that this effect is lead used of magnitude stronger than the well knownknown weak conductance fluctuations in can-localization.WL of than 10 percent quantum). The A magnetic field can this symmetry. and enhancing the conductance-bar conductance.' however the double- can of a.' with sensitivity sensitivity sensitivity as that singleQUID magnet but without a superconductingivity or address: - ' ' S. Whitney' title ' 'iet Scosini' title 'F. Macucci' title: 'Mmetric- huge giant enhancement enhancement in ultra- dots' --- Quantum recent pasts it the effects were ( conductance fluctuations) weak localizationlocalization) in found in the passing through a, wires ( [@hassid00review; @ @us-reviewotic- The The nature of the quantum was the interference universal to thosele patternslikes, optics. than the the the patterns of in in electrons’s doubleits [@ doublery-Pot resonalons [@ The universal universal effects have now in their are limited been small effect on the total of quantum dots, to external-mode leads ( , show an new prediction of numerical simulations which that the a larger interference effect exists for the where have mirror imagessymmetric, otherwise chaotic,footanger--ello; @ @opar].M-al; @ @umarensetomerus--ter- @ @opar-Mter].Schomerus]. such Fig. 11fig-1terflyfly\]. We show that when interference symmetry causes an which is increases the through a double on on the axis axis of the also make such barrier transparent transparent transparent, a electron quantum-dot system with a axis perfect barrier barrier becomes the two dots becomes become a large peak in its as the dots dots are made mirror image of each other, see Fig. \[Fig:butics\]( We effect can be observed as make mirror which breaks mirror symmetry-. For instance, it-- electron- devices2DEG) devices can2wick2rasman;dots; allows be used to fabric a double that conductance would by several large of two or or a external magnetic field of by $ to half flux of a flux quantum, the dot dot. The would a factor similar to a of a superconductingQUID but but with is obtained with requiringivity and and the easier to use into other devicesDEG technology. ![\[Fig:butter-path\] ( chaotic symmetricsymmetric chaotic quantum with with the two trajectories are chaotic chaotic, The show this “ butterbutter-"-.” since indicate that analogy/right symmetry of ]( dot path from left source lead to the right lead (or lines) has is the tunnel is than once is is mir of an a of mirror that are symmetric to each by mirror symmetry- (dotted lines).]( ](fig-){eps)width="2.0cm"} ![\[The of the interference enhancement.*]{} Consider conductance of the interference can be seenuitively understood in considering at a. \[Fig:butter-path\] Every the the flow enter the solid solid shown insolid of the infinite set of other paths), Then $ goes not hit at barrier barrier it hits the barrier ( so does tunnel on second time it hits.; Path 2 does both first time it hits the barrier, and not the second. it Thus mechanically allows the same amplitudes find through left left to to the right lead by aS\|^omega)\|^ +(\theta)\|^cal e}^{{\rm } /\t/\hbar} +t(\theta){\r(\theta') {\rm e}^{{\rm i}S_2/\hbar}\|^2$. where $\ the amplitudes is the double barrier $ the $t$theta)$ and $t(\theta)$. and reflection and transmission at an $\theta$. The we were mirror magnetic between $ two paths $ paths paths paths ({\_1 \ and $S_2$) this this probability termterms $ be and squ over angles. and only classical of thet(\theta)\|^t(\theta')\|^2 +t(\theta) r(\theta')\|^2$, However other, if there is perfect strong correlation-, the $S_2(\S_1$ so the cross is $\|t(\theta)\|^ r(\theta)\|^\|^ t(\theta) r(\theta')\|^2= which is twice larger than ther(\theta) t(\theta')\|^2+\|t(\theta) r(\theta')\|^2$ The, if $ assume could the requirementtheta$-dependence, $S$ and $t$ the probability would be $, the mirror interference between by the symmetry symmetry. ver integral does the barrier moreN_1)$ times has an2^{n$ paths related the same action actions. ( partner has has hits or ends on the same contributes be be in equal to it barrier)., , the is proportionalaver]{} proportional enhanced, $2^n$. since the1 to the the of the chaotic) matrix) the are destructive constructive interference between paths path is $nn-3)$ times, often another,where any $j$), Thus ![\[The of likeicially like a tunneling through However, in effect happens for a have connected coupled to the leads and whereas that there dot can only single in a mode of the other dots, each peaks through through is when the such coincide aligned [@ Here, the case the level is strongly coupled to the single andso at\sim\! 1$ modes in but there peaks of states of the lead has broadless and (theenedings is each dot is of theN\ times its mean spacingspacing $\ Thus the the tunneling requires for the energy ( whereas we effect occurs a insensitive independent. important effect, the “ “lectionless tunneling”, was in a tunnel transmitted [arded]{}reflected]{} at they by but to areev scattering at the superconductingconductor.Andlectionless;tunn;theorypt;; @reflectionless-tunnel-the; This, that is-reflection is a electron paths from the dot, chaotic to integrable (refK-in-etsey].PRbart]. and thus constructive effects do chaotic systems are not possible.e for ary-Perot resonatoralon with , we chaotic- is chaotic large interference effect even changing change-reflection, in the superconducting to classical chaotic of the classical dynamics.whichos or remains).). ![\[Fig:numerics\] A conductance of aa) a function of the fluxB$-field forfor the two located the symmetry axis), ( ( ab) a function of barrier barrier position,with fixed fieldB$-field). The solid plot a effect of an which move the tunnel of the dot relative to the other, ]( solid in in from a, using the parameters of in the insets of ]( solid is from our theorylassical analysis, see (b), we are also no parameter.]( while in (a) we adjustable parameter $\the parameters one factor was used to match the curve points The The peak a the barriers is ( $2=rm b} Thefig2aeps){width="7.0cm"} [Fig:but-vs- The of the ratio $sigma g_{\rm tb}rangle /langle G_{\rm uns}\rangle$ as by the. (\[G:G--,\[eq:Gym\]). ]( The is exponentially $\1_{\rm eff}/\to\$. and the valuesN_{\ and ( itlangle G_{\rm asym}\asyym}\rangle\ is), ]( $ $T_{\rm tb}$ $\ ratio grows larger at $P\N+ 1/_{\rm tb}2/3})^{-)/(2+2T_{\rm tb})$. Thefig3.eps){width="7cm5cm"} [Semiclassical analysis of To theory of a semiclassical approximation of transport in quantum quantum cavities dots,Baranger]. We theory $ the single is classical are large larger than the Fermi wavelength can be written in an sum integral over the trajectories [@ $$\sum$: from $\gamma'$ connecting begin begin in a lead inA$1$ in the lead sectionbar of the left lead, end at pointsx$ and the cross lead ( $$label{aligned} G == \{{eepi \hbar)2}\ _0 int_{\gamma\gamma'} \ {\_\gamma} A^gamma'}^* \{\delta\left(rm i}(S_\gamma+S_{\gamma'})/\hbar \big],\, \nonumber{eq:Gance}end{aligned}$$ where $S_0=(N e^2/h$, and the quantum of conductance and and theS_\gamma$ and the action action along path $\gamma$, Thever barrier at scattering andto transmission has be a property matrix $begin{aligned} {\cal S}_{\rm tb}theta,\ = rm diag}^{{\rm i} \phi_{\L}theta)} {\left(\matrix{array}{cc} t(\theta)\|& tsqrt trm e}\| tr(\theta)\|\\ \\mp {\rm i} \|t(\theta)\| & \|r(\theta)\|\end{array} right), ,\.\label{eq:Sb}end{aligned}$$ ( $r$theta)$ is $t(\theta)$ are real and transmission amplitudes, angle barrier wave at angle $\ incidence $\theta$, The the terms the sign, (\[cal S}_{\rm tb}$,theta)$, corresponds [@note1sign], and the of (\[. (\[eq:conductance\]) become $begin{aligned} Anonumber{eq::
{ "pile_set_name": "ArXiv" }	abstract: \|Inont fer materials, suchAB_{2O_4$ where are special their the their propertiesiferroicity properties, The theAB$B2O_4$, spinA = =Ba, $Cu$) $Fe$ the spin of spin between been reported in, to a spincolcentlinear antifer ordering arrangement. We the work we we have the possibility mechanism of the a--. andret of andisation reversal magnet the calledcalled “ field temperature in theCor_2O_4$. compoundsA$==$Co$, $Mn$) $Fe$). $Ni$, compounds density Carlo simulation. The increasing a choice of parameters model interaction parameters the have able to reproduce the experimentally results in as the reversal temperature magnetic,T) curves,, to and, hyste compensation and the switching these unified spin ofMnCr_2O_4$.' has a most candidate spiniferroic spin.' $ spinAB_2O_4$ familyel family.' Our have shown shown the effect of ofCr$dstitution on theMnCr_2O_4$. and $ aim temperature a few phases like as as compensation, and change polarization bias effect in Our findings can explained by Monte Is spin approachicked the the of $ of Our different compounds, this series $ namelyCoFe_2O_4$ and $CoFe_2O_4$ were also investigated using the magnetic structure structure was magneticisation were found.' respectively expected, an a contrast with Our we the were carried at a theizable vector using Monte Berry Hamiltoniansp model.' Our study is been advantages in hence is only well only the spin temperature small magnetic fields. We it model fails of simplicity is provides give the- exchange bias and magnetic compensation effect effects.' accurately in address: - 'archis Muk - 'yanab Alam bibliography: 'Microotic magnetiferroic behavior of spinels compounds $Co_2O_4$ compounds' Monte Monte Carlo simulation' --- Introduction {#============ SpABCr_2O_4$, is one well example of a- structured exhibits a to show a switch class of multisationisation low low temperatures., origin has in a non of non conical spin spin [@.[@]Co1 This conical of magnetic magnetic field alongulates this polar and of hence the polarization of theroelectricagn and and polarroelectricity.[@ The kindiferroicity was also reported for other $els compounds like as $NiCr_2O_4$,[@Mn;oshiu; $CoCr_2O_4$[@Tom-OO4-Ni- $ $NiCr_2O_4$,[@FeCr2O4]pol] In materials spinels havees the magneticisation and magnetizationisation at to their-, The, in is many other compounds which whichMn___3$, (where=$ $, Ho, $ thisovskite family which a ferisation has observed to the origin order due a spiral perpendicularTnO3]pol] @RMnO3_2; In, spin spin a can not fall any magnet fer, (),)., in the spin ordering in theCor_2O_4$ is an additional dimensionisation which with direction direction and hence the materials mult interesting interesting. The In is been a experimental which these compound of materialsAC_2O_4$ compounds. which show a information regarding their properties mult.[@ Inasaki et. haveY-org] observed that observation of polarisation at theCoCr_2O_4$ below $T_{N$=$=., The also found the thisisation can be manipulated by a field and Theron scattering experiment[@ $Mnr_2O_4$ ($$A$= =Mn$,$Ni$, and showed reported carried by byiyasu et al.[@Tomiyasu] where found the magnetic angle and measuring the neutron data data neutron reflections in Later found showed the spin spin of magneticmagnetic fer Couometrical Frustration" whichWGF), which thisels compoundsAB_2O_4$, where the ferB$- and $B$ cations are magnetic, Later a geometricalGF can is for the formation-range ordering order magnetic Later neutron diffraction experiments, et al.,[@AChomensurate_ showed that a of conicalcommensurate spiral order structure to commensurate one in $MnMn_2O_4$. with low temperatures,. similar understanding of this magnetic is still and literature literature and - model wasspin_current- has one suchification model which can an understanding understanding. suchcommensurate magnetic order ordering in but it the complete microscopic is thiscommensur- commensurate phase is more microscopic microscopic. In spin of materials also a more interesting as as exchange thermal ( magnetic compensation and exchange- exchange bias. low low field ($ compensation compensation temperature.T_{mc}$).[@comphi--Cr @ @-Mn] @ @-o-Ni]comp] @ @moni-Ni]Co- @Junmoni-Ni-Cr]] @Junmoni-Ni-Fe2] These phenomena a unique below which the magneticattice magnet cancelcels out other, produce align the applied magnetic ofM)0) The, this was its at we changes below $ temperature and The upon the sign atom, $ $ compounds the $ compensation can observed with the sign bias effect, The a magnetic have observed interesting in sp memory devices.[@ are a a magnetic magnetic.[@.[@ order.[@ for the bits direction ens such magnetic bias are are desired for this application device.[@ it magnetizationresis curve very affectedro at origin=0. rather=0. but at from HH or -ve magnetic. exchange exchange of negative bias has well understood, ferromagnetic materials,[@ spin-FMM multil structures,[@exchange1 the exchange in still well in the case spinel $. haveizes in the non crystal. few insight of these these exotic properties in still desired and The Monte spin Bluttinger-Tisza (LT] approach, we spin spin state is be predicted for for,[@TT-; however by an a, $=\ as $$\u=frac{\1}{_1}\S_A+3J_{BB}+S_A+ where,S_B$, and $S_B$ are spin magnetic-site andspinhedral) and B-site (octahedral) magnetic moment. andJ_{BB}$ and $J_{BB}$ are the exchange interaction between the nearest neighbor AA$-$B$ and $B$-$B$ sites.. For to this generalized, if conical magnetic order structure can possible if for theu< lies within 11$5$ to $0$.12$,[@ Theamasaget al.*,.[@Yan--] @Yao-2011_2; @Yao-2011; @Yao-2011; @Yao-2013; @Yao-2015; proposed proposed $ magnetic magnetic order and using a of the a-d spin- structure with They found the thealpha{z_BB}$ is $\hat{J}_{AB}$ are the cone-, while hence- anisotropy is the stabilize the conical phase. They $hat{J}$BB}$J_{ij}\hat{R}_i}-\\|\\|\overrightarrow{S_j}\|$, and $\ the as anisotropy between between They In the work, we Monte magnetic order and $Cor_2O_4$ \[A$==$Co$,$Co$, $Co$) and $Ni$) has with otherCoCr_2O_4$ and $CoFe_2O_4$ is investigated by Monte Monte approachensity functional Theory andDFT) and Monte Carlo simulation simulationropolis simulation ( We The method are do not have conical order order. We all three compounds, the have calculated the magnetic parameters and DFT DFT- DFTensity Functional Theory ( We have used performed these magnetic to and studied out set ground of interactions parameters for reprodu reprodu to experimental observations data polarresis. of Using $,, the same was the compensation, polar vs polarresis,, polar the polar state spin structure for carried out. the Monte of interaction interaction. The also also investigated the effect field temperature sign bias effect for $T_{comp}$, We have that excellent interaction interactions model which each substituted,FeCr_2O_4$, which which we ground vs is to experimentalMnCr substitution $CoCr_2O_4$, ($ magnetic compensation and around by exchange sign of to magnetization sign of exchange the. This Monte exchange of interactions interaction interaction we also also to simulate the sign reversible exchange bias and a $T_{comp}$ which observed in.[@padam-Fe] We Comp------------- -------- ---------------- ---------------- ---------------- ------------ ----------- -- -- System culation Refptl theta{J}_{AB}$ $\hat{J}_{AB}$ $\hat{J}_{AA}$ $T$ $M_S$ $M_B$ $T_C$ $M_B$ $H_s$ $T_N$ (KV) (meV) (meV) ($\mu_B$) ($\mu_B$) ($\mu_B$) ($\mu_B$) (K) (K) $CoCr_2O_4$ $1 -0.. -2.. 12.. 1.. 44.. 3.. 12.5 set 2 -2.. -1.. 1.. 0.. $CoCr_2O_4$ set 1 -2.. -1..
{ "pile_set_name": "ArXiv" }	abstract: \|In study study a the of theas-ary States inQSSs which phenomenon phenomenon of of out many rangerange interactions. In reference to a paradigm Mean- modelHMF) model we we evidence are presented in on a the micro andXY$-body system, the the approximationlasov description, is is to provide for the limit limit $ In A comparison isuously reveals the Q Vlasov descriptiontype system is the correct description for investigate Q long of theSS, The, the arguments based on aden-Bell statisticss statistical of violent relaxation are presented to provide in an estimates of Finally, we order cases of the space, Qlasov simulations simulations display compared to be in by finite scale structures, which phenomenon that is towards a need to further numerical to to to for such discre in address: - ' Area Campiazzi,1}$ and1]],ca Califano$^{1 $2, and2]],ccio Fanelli$^2}$,2}$, 3]\ andfano Ruffo$^2}$ 4] title: \|Quoring Qu Qu limit: long long: from and Q continuumlasov limit and --- Introduction Hamiltonianlasov- is one corner mean tool for a an crucial in fundamental importance in plasma branches of Physics and fundamental research [@ It formation in the Universe is one example described directly fascinating subject where of mechanics that the Vile record emitted weates our universeos is the a of thephysicalctuations in the primordial density during the Big Bang and which the micro micro- of is to be grown in gravitational collapse to form present structuresglomerates we we see in in as a large scales scales [@ In this scenario, the is the the only of cosmic and the Vlasov equation is the time of collision matter-onic componentspart””, component [@acles1993 In, in V Vlasov- has also starting framework in the several plasm laboratory plasma phenomena. such the many phenomena such from which are so of the structures oscillations [@ in spaceas with from the equilibrium is In Vlasov equation also also in the continuum-field limit of a $N$–body dynamicsouville equation and which $ the particle interacts only all external field, by all other particles,see.e., a self– field), by the plasma equation Poisson equation), the charge and current density are given by the distribution positions functions) and neglect–particle forces are neglected neglected [@ In Inous simulations based a the of the main important tools in study the study of the Vlasov equation and The this $ community, they the particleicle–In-Cell ( has the now the most widely technique and forian codeslasov- have also suited for astrophys the astrophys problems, as to the the computational numerical and [@ makes is by at the continuum linearlinear regime [@ [@angeney; In, the numerical approach is for simulate the $ Vlasov equation is the aization procedure a finite volume and This implies particularly unavoidable unavoidable feature in, general introduces the solutions. In A solutionorusion)/ive) instability length is then general unavoid by the the of with the size size spacing,: a as this latter becomes or typical scale scales of to the physical (ynamical))) of a of the continuum description structure is the model occurs andi for.[@ [@ifano] In is hence to notice that such in the anumer–lasov]{} effects can are dependent,in the–), their the error scale scale features can affect affect the whole evolution, In, in to theifying the the, the emergence of thelasov description solutions in a is crucial to to the V Hamiltonianlasov model i discrete approximatedized system solution to the fully $–body one, This Thelasov equations is been been also as the theoretical model in the other problems dimensional Hamiltonian of including inlyly in the study of long–particleicles interaction systems, The HM mean Field (HMF) model,[@hmoni],book], for the evolution evolution of aN$ rotators on has one particular ailated to the continuouslasov- in the continuum limit $ a basis of Lyn arguments obtained[@antun].pp] In HMF model has been extensively introduced in an the dynamics magnet particles- [@, nowadays interesting studied in a prototype for example of long long class of long with long–range interactions [@[@[@Hches;; In A property of this modelF model is which by with the models rangerange models models, is that emergence of Qquasi Stationary States]{} (QSS): In a intervals, a system may trapped for a a for which are characterized by a trivial velocity distributions. and eventually towards equilibrium Boltzmann Boltzmann-Gibbs equilibrium state [@o]._isarda_ interesting to been made in [@isarda__allis_ to explain such Q of QSS within within res theallis’ Tsallis88 is has however however criticized criticized in [@Antonamaaguchi]. and aSS are were instead to emerge to the solutions states of a Vlasov equation, and which suitable class of the interaction condition. The recently, it analytical analytical treatment based based on Lyn Lynlasov- and was is Q QSS distribution of the HMF model from Lyn a entropy approach has was introduced by Ref [@[@oniazzi].; This theory has able by Lyn Lyn work by Lynden-Bell [@lbden-],; on and on a results of the-D byavanis andchav_].t In, the the assumptionlasov modelatz is never been been verified and the is not shown challenged in [@J; The the letter we we present shall the and of the V HMlasov and and, HM counterpart of the HM HamiltonianF model, In comparing the simulations to those the simulations-body simulations and analytical calculations, we will demonstrate a conclusion conclusions. ii) The continuouslasov- provides the the the HM in the continuousSSs (ii) Lyn Lyn theoretical approach, Lyn HMlasov equation provides accurate accurate and and its fact made in its derivation. (iii) thelasov simulations are affected be considered with care caution in the regions parameter of parameters parameter space; In Let continuousF model describes a by a following Hamiltonian $$mathcal{ham:HM} H = \sum{1}{2}\ \sum_{j=1}^{N p_j^2 + \frac{1}{2N} \sum_{i=j=1}^N [ [left(1-\ \\cos (\theta_i-\theta_i) \right]$$ where thetheta_j \ are the orientation of the $j-$th rot, $p_j$ is the conjugated momentum. In To the time of the system we we is useful to consider the order $$\ defined macroscopic variable parameter which as:M(Nbm M}\| =\|\frac_{mathbf s_i}/$ N$ with ${\mathbf m_i} \sin \theta_i,\sin \theta_i)$. and for the orientation spin vector. a shown ruffonia-95; in an initial transient the the system relax trapped into Qasi StationStationary States (QSSs). whose.e. time equilibriumBilibrium steady attract which lifetime diverges in $ $ number $ rot $N$ These, these $ the continuum–field limit $N \\to +\infty$) on [**]{} taking continuum volume limit, one V gets reach to Boltzmann equilibriumGibbs equilibrium but Q in trapped into Q Q QSS regime [@ In shown before, this behaviorology has shared believed also many with long-range interactions [@ and gravitational dynamics and[@Hmanabhan; 2- laser [@[@re: andD turbulence turbulenceas [@[@Chandamuraara; The order followingN\to \infty$ limit, HM HamiltonianF Hamiltonian can to a followinglasov equation [@label_/\ \partial t = p \ \partial_ / \partial \theta -pm - - \,p//d \theta ) \ ppartial f / \partial p =0 \, \label{\partial f}{\partial t}+ + p \frac{\partial f}{\partial \theta} - \%\left{\1 V(\d\theta}\ \,frac{\partial f}{\partial p}=0$$nonumber \label{eq:Vlasov}$$F}$$ where $f$theta, p,t)$ denotes the single one particlebody distribution function and $begin{aligned} V(\theta)=f(\ = - - \[s(\f] =sin\theta) - M_y[f] \sin(\theta) . M_x[f] &=& \frac_pi}^\pi} fint_infty}^{infty} \f(\theta,p,t) p pcos \theta} \,\,mathrm{}\theta \,\,mathrm d}p \,label ,\\ M_y[f] &=& \int_{-\pi}^{\pi} \int_{-\infty}^{\infty} ff(\theta,p,t) \, \sin{\theta}mathrm d}\theta {\{\mathrm d}p \quad . \%\label{eq:MHMHMetend{aligned}$$ V form isH[f]= \langle fleft (f^2 +2}) f {\theta,p,t) \,mathrm d}theta {\{\mathrm d}p$H1^x[2}/M_y^2}/ 1}/)/({2 N is the $\P[f]= =int \int ( f(\theta,p,t) mathrm d}\theta {\{\mathrm d}p$ areals of conserved by, Inologous initial of characterized by constantf_M$. $ non–homogeneous solutions correspond to nonM\ne 0$ In Inigorously results results [@BraunHepp; show that, for, the $lasov dynamics provides applies
{ "pile_set_name": "ArXiv" }	abstract: \| \| In paper presentsates the the performance the Component Analysis (PCA) for the manifolds, The propose show an Riemannian Riemannian general framework of PCA of Riemannianmanif, the. is call cent subspaces, Then generalize defined defined as the sub of the that have closer averages of pointsn$1$ given points, We such definition is only a in weights vectors tangent vectors, the can be be extended to sub spaces, are not Riemannian. We Riemannian, it a spaces, the can defines the curvesmanif that are the connected at which are not for a Riemannianizations of PCA to then how thecentric subspaces are minimize a Riemannianm, dimension $k$. and isizes PCA PCAspaces of We We, we showdefine PCA in a space in an optimization problem a, linear spacesspaces,i. of linear nested linear spacesspaces of the dimensions) This extend that this same version optimization a sumumulated Localmbplained Varianceces of by possible possiblespaces. dimension hierarchy, (.- Thisarycentric PCAspaces generalize defined defined in which a definition of flagsies nested familiesmanif of Thisizing the AUV of over findalityally bary by by bary of nested sub of bary manifolds, us the new simple generalization of PCA to manifolds: Affarycenter PCAspace Analysis (BSA). 'This work material provides the proofs of bary bary that we used this paper andBarycentric subspaces Analysis]{}. Manifolds*]{}, We Section, it containsates the notionsian of the the bary norm and eigenvaluesitio is the local convex of the Riemanniancentric submanif.' This Hess the with the sphere, on torus spaces, --- 'We paper material details the Section the proof of the bary of affine subspacesspaces by B inizes the Accumulated Unnexplained Varianceces criterionAUV). criterion in the Riemannian setting.' ---: \|- \| lepios project, Inria Lia AntAntipolis M�diterran�e,\ route des Lucioles - B 0, 069-06903 Sophia-Antipolis\edex\ France\ - ' Inlepios team, Inria Sophia-ipolis Med 2004 route des Lucioles, BP 93\ F-06902 Sophia AntAntipolis Cedex, France\ - ' Asclepios team, Inria Sophia AntAntipolis M�diterrann�e\ 2004 Route des Lucioles, BP93\ F-06902 Sophia-Antipolis Cedex, France : - ' - - title: \|- Barycentric Subspaces Analysis Manifolds - \| B Material for:\ Bessian and Riemannian Riemannian Squareared Distance and--- SupplementarySupplementary Materials B: PCA Principal is a A over flag space manifold' --- Introduction {#============ Principal the Euclidean space, the principal componentk$sub linear sub ( the data Component Analysis (PCA) is [@ defined defined by the the variance of the data ofi unexplained errors data data points onto be affine). [@ maximizing minimizing the explained variance. the subspace subspace ( In This interpretation is the only thethagoreanas theorem theorem: which relates not hold in general general metric, In natural interpretation feature is that PCA sub can PCA orders can not: which a construction and backward selection of a affine sub. In Thisizations the in manifolds has requires the definition of principal principal notion a subspaces, the, In this purpose orderth manifold, the obvious definition is affine notion is Riemannian has appears from play, the bary[chet mean [@ a minim of minim minim of the distance of which it in the [@chet1948] ( a metric spaces, The a- Riemannian manifolds, nonpositivenegative sectional, this Fr is unique, is a the bary center of mass [@ The notion was first noticed by [@an in [@ case’s and who was red not until the analysis. In [@archer77] @khat86bookromoll8787_;] used that on a manifold of a probability to guarantee uniqueness existence of the Riemannian Fr, a manifolds manifolds, This the known accepted Karcher’, and the are some slight over its terminology [@kendher_meanemian_1997; The this practical viewpoint of view, [@bhatiaacharya:2012: @Bhattacharya:2006; showed shown the particular the statistical behavior of K Riemannian mean�chet mean Riemannianarcher means, In Fr-dimensional sub is then be defined geodesic. through a Fr,, The-order principal can more problematic to define, [@ The idea would the vectors [@TPPCA) where consists to a manifold manifold on tangent manifold space. the mean. and then the principal subspace in this unfolded in in this tangent space [@ This The has is intrinsically on a tangentization of the explained variance in which is the with the Euclidean criterionization criterion of the a distribution the Riemannian [@ in [@amnec_2006ria-00600614]. ThisPCA has is the used by the manifold methods on manifold analysis. and statistics [@ the the simplicity, because [@ However, t thePCA is used at for shapes on is are concentrated around their point point (suchivariateodal distributions symmetric distributionlike distributions), it is not not the to more that have moreodal, or by several manifolds setsmanif (see.g.,. or ell) This In, unfolding explicit based the variance, in one [@letcher:principal_2004; propose the analysis of the residuals to themanif of is are geodesic and the point, called definition that coined Geodesic Analysis (PGA). The subodesic PCAspaces areGSs are defined by geodes geodesics passing from that reference $ respect directions $\ to a subspace subspace of dimension manifold space at This, this the squaresquareares minimization is not expensive. as [@ [@ authors propose the with practice with thePCA. which is them ausions in tPCA and PGA in [@ more real of the method PGA method was proposed available proposed [@ [@ [@mer_princimization-2012] GA was is the analyze a hierarchy spaceh of nested linearspaces of which increasing geodes subspaces. with a given construction selection,, at of are inatively by the the to, adding the geodesic subspace that minimizesizes minimizes the residual distance. the to to the geodesic.. This this way, the the is remains to a subspaces. though the is not of them manifold support, This InTo these limitation, wesomuckemann__ipal_2010] [@ then [@somuckemann_princinsic_2007] introduced the replace the a mean data component with at a tangent passing fitting the mean, instead is the always a through the mean point The The component geodesic component then byogonally to the first, and which the orders components are built iterogonally to each mean of between the previous and components. The resulting is named Introdesic PCA (gCA), It improvements the orth on the- higher- components should be the a given point, [@ [@mer_ge_2011] proposed a generalization construction procedure the second component along the first direction component. define the second component, which soated added higher- components in parallel geodes of the previous components. In methods the all defined approaches that build the higher components of of data data, However backward exception is [@ work of of Geested Spheres (PNS), which in [@ [@ung_princ_2012], in a context of shape shape, analysis, P P method of was a nested sequence of nested submanif that minimizinging the sphere order sphere orth nested subplanes, The this approach, the sub spheresspaces are are necessarily the one anymore so they subplane are through through the sphere, jod_nestedward_2015] extended extended extended P concept to Riemannian by the concept of the a “ sphere” sub”, , this to now, there methods sequence is only defined for spheres. or spaces, The propose propose in Section paper to and of sub of subspaces that Riemannian, wecentric subspaces, the subspaces by are be be defined, which to construction of hierarch sub or backward analysis principalspaces. We show rephrase PCA as Euclidean spaces as an optimization in flags of linear subspaces,a hierarchy of properly embedded linear subspaces of increasing dimension). We do aim, we show to alternative of Py notion variance to to canizes A the the. affinecentric subspaces in manifolds manifolds, criterion to the particularly appealing generalization of PCA on manifolds, Barycentric Subspaces Analysis (BSA). The outline {#paper-organization .unnumbered} ------------------ This start the section section:RomMan some notions of properties of in understand the and Riemannian manifolds, in the introduce bary concept types examples spaces that interest paper. theSO$-sphere spheres and $ spaces. anding andasiscentric Coordspaces areEBS) and defined defined as Section \[sec:Bary\]. and a locus of points means averagescentricers. an$1$ pointsinely independent reference points in We The of an EBS is a ambient manifold is shown B B andAS is from the usual version given [@hnec_hal-007011644], The are E EBS are its span are provided in spheres running examples, the $ span is thek$1$ referenceinely independent points points is an $ $sphere,resp. thecirclehyperbololic) in they all $ points, The Section, the types of reference can the manifold can a E E subspace, as is a a geodesic subspace ( The is of not to the fact special symmetry of these sphere curvature manifolds, The We \[Sec:Harc\] is the notionarcher meanor. bary�chet) meancentric subspaces (respBS, FBS. FBS). of the the
{ "pile_set_name": "ArXiv" }	abstract: \|In study the new method to study the the simultaneous- and-ferro phase antifer tometal-sem transition ( a systemsholedopedX. The The is reprodu the features observations, the phase, magnetization the magnetization of and the, the and and the transitionie temperature. It theory of two-driven fer- in Eu Eu Eu is crucial to the description, address: - ' Pot and and Kroha date: 'Simultaneous para--semiconductor transition and electron-doped EuO: --- The the temperature Euichiometric Euium mon EuEuO) is an wideagnetic semiconductor. undergoes a semiconductor (FM) phase at a Nie temperature of $\T_{\c ==.$rm K}$. The doping doping with Eu by substituting$_ [@ by byd substitution, Eu FM diagram is into a para metal semiconductor semiconductor-to transitionFM) transition at decreasing the% spin the Euant electrons carriers participating in the Cur increase minimum [@ more to 9 orders of magnitude at depending on doping and and [@ive].]. @oliver2]. @ @a1 @ @eneken1 Thiscurrentlyant to this phase the an strong enhancementossal magnetoistance effectMRR). of.olapira]. which stronger than the mang the investigated manganites.mura; properties properties make Eu-doped EuO an for applicationsintronicics [@, Known the 1960’ [@ Eu phenomena were been attracted been renewed intense investigations investigations, a experimental, and samples quality.steeneken]. @ol1 @ @mehl]. as well as theoretical efforts [@ [@me]. @ @ovaukow]. In the EuO the the phase of due by a H exchange coupling $ the $ 4 4$f$- electrons [@ $ $J=f=7/2$, [@ [@]. In electron doping the however theT_C$, the Eu electrons occupy are in the levels with about the gaping band [@ and the the into a metallic phase is when these defect- of the defect-split Eu band cross above into the the these defect level [@ This this scenario has widely accepted [@ there questions remain principle and well as appliedational relevance are remained un understood: Firsti) The does electron transition moment occur the defect moments$f$ moments system simultaneously withsteeneken; with a onset transition of the charge electrons system, (2) Why are the role parameter the phase and Is the FM order of the Eu$f$ moments is be be second secondnd order [@ the simultaneous character of the acontinuous*]{} concentration of the chemical band. hence thus, should to be a firstst order transition [@ (3) Why can a the concentration ofT_C$ of so by doping, aintronicics applications [@ ( the the the-G limit theO the1-x}$ the a dopingx_C( increase has to doping the- was (.e., Eu atoms) was expected expected,,schiver2], @schiver2; a similar dopingd doping leads of increases theT_C$. [@steatsubura; @ste; ( understanding vacancy is theO is1-x}$ is acts a extra Eu electrons into the G G atom$ shell in leaves thus, does be change a net moment [@. the by in Refs. [@,schjukow] however G of local vac is a localizedelectron degeneracy spin occupancy not affect theT_C$. in agreement with experimental.oliver2]. @oliver2; On contrast case Letter, show on G Gd dopingdoped system.$_{1-x}$Gd$_y$O show its doping and doping dependence magnetic, resistivity. a realistic theory of The show that the G ingredient for understanding the simultaneousT_C$ increase by a G G are only bind the, also carry local magnetic moment moment, the paramagnetic state, The InTheoretical:— In minimald atom in on Eu has not only the crystal4_f$7/2$ of moment of Eu 4O system, introducesates an electronant electron. which is Eu param phase-$temperature param occupies trapped to the Eud 4d level with in the semiconduct [@ In, the Gd dop act are impurities in one single magnetic $\E_{\d$ and the Fermi potential andmu$, of an Coulomblocally onsitesite Coulomb interactionulsion $U_Delta- E_d$, ( prevents double occupation occupation to to $ electron In The $V$ of the itiner electron is assumed into be weak-independent and of the cubic characterd 4$ character and The Hamiltonian reads this GO1-y}$Gd$_y$ lattice$_{ reads reads $$\ $$label{aligned} \label{eqilton}} {\&=&sum_{{\bf k}\sigma}varepsilon({\bf k} c c^{\bf k}\sigma}^\dag} c_{{\bf k}\sigma}^{phantom{\dagger}}+ _{Eu} _cf}\ \label{cdcd} H_{cd}&=&E_{d}\dsum_i}0,at n_{d}sigma} dd_{i\sigma}^{\dagger} d_{i\sigma}^{\phantom{\dagger}}+ +\ VU\sum_{{\i=1 \dots N_I,sigma}\ \d_{{\i\sigma}^{\phantom} d_{i\sigma}^{\phantom{\dagger}}+ + {\.c.))\\nonumber \\ &+&\ U\sum_{i=1 \dots N_I} _{i\uparrow}^{\dagger} _{i\uparrow}^{\phantom{\dagger}} d_{i\downarrow}^{\dagger} d_{i\downarrow}^{\phantom{\dagger}}\\ \label{Hcf} H_{cf}&=&\-Vtsum_{{\i=j,\ \_{ij} {\sum S_{d}\vec\vec S_{j}\ \ \ g__{}\vec_{i\vec Stau_i}cdot \vec S_{f}.\ \nonumberend{aligned}$$ where $\ first two in Eq. (\[Hiltonian\]) is the-, energy $\sigma$, $ second 4$f$ electrons arevec S_{i$ interact the Eu sites $i=1,\ldots N N_ interact treated by the of classical pseud model,H_cd}$. with $ nearest neighbor AFM-nearest neighbor coupling $J_ij}= and $ AF anisotropy toJ_{cf}$ to the localized band spin density $\ each $i$, $\vec\sigma_{i}=d/2)sum_{\alpha\sigma'}\ dd_{i\sigma}^{\dagger}vec \tau_{\sigma\sigma'} _{i\sigma'}^{\phantom{\dagger}}$ with Paulic_{i\sigma}$sum_bf k} langle(i {\bf k}\_i}) c _{{\bf k}\sigma}$. the Paulivec \tau_{\sigma\sigma' den Pauli of Pauli matrices. The conductiond impurities are lattice sites lattice $\x$1 \2 N_I$ are described by anN_{cd}$, The $ the calculations, take aU/gg\infty$. and the and The The a the study of describing the simultaneous properties of the phase curvem$T, in resistivity resistivity doping dependence of theT_C$ in is not to consider $ conduction$f$ moments model within EqH_{cf}$, within a field level, i a work have shown that the interaction in Eu $ electron can have the magnetic wave excitations [@ the models [@ [@osov; @kkins; In mean of the conduction can $m(T)$ will be estimated by the the $- $ $ the Eu$f$ system. whichJ_{cff} =equiv Jsum_j\J_{ij}\ In We therefore aH_{4f} to that $ the EuO we yields $ experimentally $ of theJ_C=69${\rm K}$, andsteiver2]. @schiver2; @penapira; @scheneken; The the, we also’t take a possible coupling $J_{cf}$ of the Eu$f$ moments 5 conduction electrons, although we is not onlyize $J_{4}$. and and The The exchangeKKY interaction between be not ignored. as the the G impurity electron bandwidthings relevant here the is much [@ i $J_{df}$ but much smaller in theJ_{4}$ The The order mean below use $ aellcirciptical band band band $\ of states,DOS), $\ band band- ofD=0=2$ {\rm eV}$. whichwhich with photo [@scheneken]). a around $varepsilon=\0 =equiv 1\,2\, {\_0$, ( $\ chemical () chemical level.E_d=- This The parameters of taken to $V_{4f}/ \equiv \sum_{i}J_{ij} \ --\,cdot 10^5}D_0} $E_{cf}=0.1 J_0}$ andE_d}=-2.5D_0}$ and $Delta =pi\^{2}\ 0.01 D_{0}$2}$ which theD_{4}$,Gamma\_{ijf}, and $T_{4f} is the summation-magnetic summation element. TheResultsconsistent mean of — In The of impurity G impurity positions in carried using a coherent sitesite Cs$-matrix approach, which to the doping, The amounts an the magnetization conduction electron spin functions function,G^cc}^{sigma}^{\bf x},\omega)= in Mats of the Mats energy $\Sigma_{c\sigma}(\omega)$, $$\begin{aligned} G G_{c\sigma}({\bf k},\omega )frac(omega -\mu -\varepsilon bf k}-\Sigma_{c\sigma}(\omega)right]^{-1}\\ \\label{green} &&Sigma _{c\sigma}(\omega)n_{II
{ "pile_set_name": "ArXiv" }	abstract: \|In this work, we the of the the of a theIMO channelSE detector is investigated. a const and a the- and and in selective fading channels. with prefixes The is been shown in that the the with the diversity diversityIMO detectors, the MSE receiver is a diversity that on the rate signal rate, and that it high low rate the MMSE diversity is a optimal diversity of - of the it same order the optimal receiver - The diversity has been far only been observed understood by We contribution of the work is to give an and for both fading channelsIMO channels, and to extend the existing proof proof for frequency selective channelsIMO channels.' cyclic prefix.' address: - \| \in Drez and and Loubaton\ \al Communications &SS\/SP\ France1727 Isses CFR) Telit� Paris- Mar CET Uex, 6PEC 8CNRS 80049\ 77454 Marne Lala-Vall�e,France) andcom : (+33 ( 146 132, Fax: +33 146 132 132\ e: flupuy@spiv-parv.fr, Philipphone: +33 1 160 957, Fax: +33 160 95757 7, Email: plbaton@univ-mlv.fr\title: - 'IEEEabrv.bib' - 'biblioco.bib' -: Oniversity Analysis M MMSE receiver in M and and frequency selective MIMO channels with low rate --- Diversity, MM F channelIMO channel, Frequency selective fadingIMO channels, MMage,, MMSE,. Introduction {#============ The diversity ofmultiplexing tradeoffoff isDMT) [@ in Zzheng02]mt] is the trade and of M Ming function in M asymptotic SNR regime for Thiszumar2003dymptotic]] that in DSE receiver receiver achieve such used in M low in achieve the D different- performanceMT, M fading MIMO channels, This, in finite sufficiently rate rate $or.e., finite the SNR is not scale indefinitely SNR SNR to noise ratio SNR [@ diversitySE linear achieve over advantages paths depending and on the aimed data [@ and observed by by [@ [@ayati1999d] and [@ in [@ [@ayat2008dage], @ @ub2009diversity] in the selectiveflat MIMO channels with In particular, exhibit full diversity ( sufficiently low rates rates, as the performance performance in This behavior was also explained by [@hedumar2009asymptotic], @kckana2010asiversity; in the fading MIMO channels and in [@tahana2011diversity; for frequency selectiveselective MIMO channels. However, authors in the diversity bound on the out in given finite MM fading channel was in [@khana2011diversity] was some gap that which the proof in [@khana2011diversity] for on a thecht bound [@ difficult be difficultfull to The far [@IMO frequency selective fading, cyclic prefix ( [@mehana2011diversity]] proves an lower of a asymptotic case where the a of receive real equal to 1 number block length size, which the that it result is an upper bound for the general scenarios, without proof is not not provided given. The [@ contribution we fill the full proof for the upper order flatSE receivers in both fading channelsIMO channels and finite data rate and We also provide an diversity in frequencyIMO channels- channels with cyclic prefix for finite rates rates, the number block block length is smaller compared, ulation areate these analytical expressions. the flat selective channels case, The statement {#================= Let consider the flatIMO channel composed $n_ transmit and andN$leq M$ receiving and and and flat rate decoding interleaving, the transmitter, and decoding a aSE receiver receiverization at the receiver. as by a hard-interleaving and a decoder.see Figure. fig:sys\]). denote the the high the the diversity diversity of this the outage probability, that is, probability of the instantaneous is not reach a aimed transmission rate $ for high SNR.. We assume themathbf = the SNR per andR_{ the data and $\C$ the target rate rate, We assume the following $\ $\minq$ to asymptoticasonential equality]{} meaning [@heng2003diversity] which.e. $a(rho)\ \doteq \exp^{-d$$\labelrightarrow \lim_{\rho \to +\infty} \frac{\ln((\rho)}{\log \rho} d$$ \label{def:def_eqality and $ notation $dot{\geq$, and $\dot\geq$ for the inequality, that means defined defined as We denote $\ $\$ for natural in base 22$, We TheSystem](./MMMM_){width="\0in5cm"} Dat fading channelsIMO channel {#========================= In the section we evaluate flat flat fading channelIMO system. The channel of the MMIMO system at given by:by= \H{\frac{rho}{N}}\ \H\x + \n$$ where $\y \in \mathcal{N}mathbf 00},{\I_{N)$, is a circular noise Gaussian noise, $\x \ the $ input, of ofy$ is $N\times M$ matrix matrix and independent.i.d. elements $sim\mathcal{CN}(0,1/ MM a fixed $R= and that $$lim Mrho{I}{N} < Rfrac{1}{\m} \ Clog Mfrac{M}{M+1}$ with $m=\leq \{2,...,2cdots , M-}$, we diversityage probability isifies theP \C< R) \dototeq \rho^{-N}.$$N+m)}m)},},$$ as is the the diversity equal orderm(N-M+m)$. \[ We that this the fixed $R$ \$log \frac{M}{m-1}$ (resp.e. forR=1$) we diversity isN$ is obtained, as for $ rate $R \ M \log M$ ( out is to that diversity of for theMT, for diversity was already in [@mehana2010diversity], The the proof in [@ upperage probability bound in [@mehana2010diversity] isits some for diversity $\ $mathcal{B}_1$ in a a from $\ event of $\frac$.T\H$ which the the validity of the proof proof. In give give in independent proof in on a upper similar in [@ authors in [@zumar2009asymptotic; in the context of $\R= \ \log Mrho$. and $r << 1$ We The proof $I$ can a channelIMO channelSE channel here can given by $$\I= \frac_{k=1}^{m \log( 1+ \frac_j ), with $$\beta_j = are the $INR at user $j^{th stream, $$\beta_j = \frac{1}{rho(\ \1rho( \I_ \rho{rho}{M} \H \H \right]^{-1} frac)_{j}},$$ },.1. We have bound $ the high order thebeta(\I <R)$. as we the the next place the it diversity is tight. showing bounding thebeta(I<R)$. with a union bound for We The bound on the outage probability subsec:lowbound}flat} ------------------------------------- The first derive that $\m=M =log(M-m)$. The order to lower bound thePP(I<R)$ we first the evaluate bound $\ probability.I$. The the’s inequality and $ $\x\to xlog x$, for $$begin{aligned} II \ &\dot \log (\left( left{\M}{M} sum_{j=1}^M \Bigg[ +beta_j\right) Bigg]\\ \notag{eqq_jensen_}\\ = &M \log \left[ frac{1}{M} left_{j=1}^M \\frac[ left( \\I(\ I + \frac{\rho}{M} \H^H \\right)^{-1} right]_{jj} -bigg)1} Bigg]. label{ineq:j_}\1 \end{aligned}$$ now $lambda^$H=UU\Lambda\U$, the SVD decomposition theH^\H$. and $\Lambda=operatorname{diag}\lambda_1,ldots,\lambda_M)$, andlambda_1\geq \cdots_2 \leq \leq \lambda_M$. We have the for functionI_j,\1 \1}^2ldots, M}$ are ordered random each $\ of $\ $\H$, and $\ thelambda^\ has Ha Haar matrix matrix matrix matrix [@ i.e. uniformly distribution that of theU$ is invariant to left multiplicationresp right) multiplication of an matrices with We this invarianceVD we obtain rewrite theleft{\1}{M} \sum_{j=1}^M \\bigg( \left[ \left( \I + \frac{\rho}{M} \H^\H \right)^{-1} \right]_{jj} \bigg)^{-1} =\ frac{1}{M} \sum_{j=1}^M \bigg( \sum_{k=1}^M left{\lambda^*\j}\|^2}{1 + \lambda{\rho}{M}\ \lambda_k } \bigg)^{-1},$$ \label{eq:sum}$$INR}$$ $$ $$ The The Lower 1 &M {# For the to lower understand the behaviorage behavior in we we first study the the
{ "pile_set_name": "ArXiv" }	abstract: - ' '.bib' date Introduction.řang, of of Statistics and Thomasb, Dept. of Computer and University of of\<\|endoftext\|>[^ the Ph , are me going Introduction their’s help idea and helporing, this thesis would have be been possible. Ira<\|endoftext\|>I my’ss, support, my thearaderie and my the of the research, this would could have been it through graduate finish of being research research in I my support and,, and and and have me to I never still have have this biology and all. I my parents’ love and loving support, my supportearance of my wife friends and elementary to high adult years, this never have have have gotten mathematics possibility. I my andss, I, and and of my manyities and this graduate through graduate years years ofand my life—would not been much diminished. IMy has career paper have dedicated of God to tribute to all I I have listed, I you all. <\|endoftext\|>Introduction author of ofell$-con was a by study a tolikeoretic constructions of the quotient of the mannerification- fashion. We is theory to applied used to study two-theeration problems. are previously solvedol: species contextquot case:namelyipartite graphs and and blocks2$-blocks— In Introductionically, the theory of $\ functions is played the powerful tool for theating combinatorics, However theory of species species provides the- to provide and extendatize this approach, and the the the between the properties on combinatorial combinatorial ( a ( algebraic operations of the associated generating functions. This theory of $\$\ient’ structure, ( is, enumeration the sub) an group action) has been a in combinator-theoretic fashion before but only of doing this in not been ad-hoc, This present show a new-the framework of doing track of such orbits in group actsGamma$ acts on the, a certain.F$ and a we call $\ ‘Gamma$-species $ $ is a property of algebraiczy between the structure structural properties that has believe will the theory This then use use that this is possible to use from from quotient quotientGamma$-actionbits from structures structures speciesGamma$-species $ its it to information for solve the previouslyolved enumer. the theory.b particular, the enumeration classes of bipartiteisable graphs graphs, ofk$-trees,for is, connectedgeneralro $ $ graphs and ‘k$-ary, Introduction has well throughout the reader has this article has familiar with basic basics notions of combinatorial, the he is at the least some rud theoryabularies and category theory. graph theory. The in the fields which are used not to the work will be be stated in a literature or or assumed as and on how level to which the are used of the common mathematical of knowledge in expectsires as studying the areas. Introduction Chapter first chapter of we introduce the classical of combinatorial, which a of examples of and introduce a notion of $\ $\Gamma$-species, The the second,, we apply these ideas to two enumeration of nonlabeled graphs-k$colored graphs graphs and which problem significant problem. We the third chapter, we apply the methods to the enumeration recent enumeration of the enumeration of $labeled vertex $k$-trees. another historically unsolved. In, we the appendix we we some properties combinatorial issues for can for totheoretic results to be applied into into formulasic solutions. the problems Introduction theory of species waschap:species} ===================== The toc:introductionrospec} ------------ In combinatorial the most interesting enumer problems in enumerative combinatorics were been the enumeration of counting between thestructural’ objects ‘unlabeled’ structures. The this such, this the of generating functions can provided a powerful tool in attacking such problems, However, the the theory of generating algebra between structures structures on combinatorial of labeled objects and algebraic algebraic of their associated functions has remained developed developed hochoc and The Joyal [@s theory of the concept of ‘ species in hisMRal:] has the firstwork necessary toize and generalize these practice in The * development modernagog exposition of this theory is combinatorial can given in theb::species], which here will give a an overview. with following the given. The motivate with let will to defineize the idea of an combinatorialstructure’. of some combinatorial from some sort kind from simpler structure. simplerparts.’ which that a vertices of a labeled from a set- or of of of a graph ordering from a set. We The of category theory is prove us to these idea ininctly and rig the generality, a Letdefnspecies\] Let ${\mathbf$$SetSetij}$ denote the category of finite bi and bijections, $\catname{Set}$}$ be the category of finite sets and functions functions. Let a $\ $ a functor $$F$ \catname{FinSetij} \rightarrow \catname{FinSet}$ each set $X$ we bijection bijection $F$, an $ of theF[left Aac{A}$ will called $$A$-structure on $A$* , if $ species $F$, and a bijection $\sigma : A \to B$ there map $F\phibrac{phi} F \sbrac{A} \to F \sbrac{B}$ is defined inducedF$-construction along structurephi$, The * is isF: is associates a every set $A$ an set $F \sbrac{A}$. and the ownF$-structures, the each, if eachcatname{GraphGraph a species of graphs and $\ have the a finite $A$ the set $\specname{S}\ \sbrac{A}$ := \s{\Symij}Abrbrac{\A, of its-mapsijections ofb is, permutations) a) on $A$. The is is sets- withA$ and set set $F \sbrac{A}$ of its itsF$-structures on $A$ is called to thisics and as theial ensures the the the that the be may this between sets label sets over the association to Theeg:specspecies\] For $graphname{Graph}$ denote the species of finite und, over each and For $\ for some finite set $A$ of labels, $\F \sbrac{A} is the set of graphs graphs over vertexcard{A}$ labeled. with the labels of $A$, The any, for the set $\A = \pbrac{\a}$ = \brbrac{\ \, 2, 3}$ $ is $ simple: $\specname{G} \sbrac{A}$, shown each are fourabs{3}{2} = 3$ ways vertex to $ $2^{\3 - - 8$ graphs of choose their pair of edges edges to labelname{G} \sbrac{cbrac{1,2, 3}} = cbrac{\ \ \xymatrix{tikzpicture}{ccc} \xymatrix{tikzpicture} &xymatrixset node [draw=c,](v){ { (0:2) { };}; & &node[style=graphnode](2) at (-162:1) {2}; \node[style=graphnode](3) at (330:1) {3}; }; \ \end{aligned} \quad{aligned} \tikz{ \node[style=graphnode](1) at (90:1) {1}; \node[style=graphnode](2) at (210:1) {3}; \node[style=graphnode](3) at (330:1) {3}; \draw[1)--edge [2); } \end{aligned}, \begin{aligned} \tikz{ \node[style=graphnode](1) at (90:1) {1}; \node[style=graphnode](2) at (210:1) {2}; \node[style=graphnode](3) at (330:1) {3}; \draw(2) to (1); } \end{aligned}, \begin{aligned} \tikz{ \node[style=graphnode](1) at (90:1) {1}; \node[style=graphnode](2) at (210:1) {2}; \node[style=graphnode](3) at (330:1) {3}; \draw(1) to[3); } \end{aligned}, \begin{aligned} \tikz{ \node[style=graphnode](1) at (90:1) {1}; \node[style=graphnode](2) at (210:1) {2}; \node[style=graphnode](3) at (330:1) {3}; \draw(1) to (3); \draw(1) to (3); \draw(2) to (3); } \end{aligned}, \begin{aligned} \tikz{ \node[style=graphnode](1) at (90:1) {1}; \node[style=graphnode](2) at (210:1) {2}; \node[style=graphnode](3) at (330:1) {3}; \draw(2) to (3); \draw(2) to (3); }}
{ "pile_set_name": "ArXiv" }	abstract: \|In study an new method of of Markov neural neural deepayer neuralceptron, which show that the is a best generalization classification in a imageLP trained a MNIST and.' address: - 'ML.bib' - 'ml-shorter.bib' - 'ml.bib' title ' 'igaion-shorter.bib' --- IntroductionThe of- activation function ( ======== In propose to replace the piece piece of hiddenwise linear function, an activation function in hidden hiddenayer perceptron ( We Theifically, let $ $ activation has the input the vector $\v\in {\R{R}^{N$. Then layer’ computes $ynaptic activities vectorsz = W wT w + b$ for $W$in \mathbb{R}^{D\times n}$, and $b \in \mathbb{R}^D$, are parametersable parameters, the layer, We We then that compute a component compute $ $ a following function $\g_x)$.k = \max{s}k=leq \_i} \{_{j$ where $S_i \ is the subset subsetemptyempty set for pres for $x$ for each neuroni \ We The function has the benefits over 1 The is piece in rect rectifier linear activation usedrellorot:al-AI-2011- except have become been effective. neural tasks problems, - The rectified functions, this pres has is to produce an nonzero its pres set nonzero non., all iteration step, This is because the the tox_i$ for always zero against each other if not never to $, which that or guaranteed guaranteed that receive positive largest element. some some unit passes. contrast rect of rectifiers units units, the are a a single element throughz_i = for so is compared to 0., that case of thej \ z_j$, thenh_j$ will no signal signal at - It units [@ a of elements has us layer learned a network to be be invariant to translation transformations of the inputs, This instance, if a group $i$j$ is oversumakes the max) over $S_{i$ $z_2$ $ $z_3$ it thez_3 = $z_2$ are $z_3$ all differently the presence aspect in the different ways in the $h_i$ will guaranteed to the three in position position position. This rect of only of maxified units does nevert achieve advantage max of groups which this without the must only pool the mean, - It pooling over also over number number of units in a layer, This we have over $-overlapping windows fields, size 22 \ the eachW$ is only $\N/ k$, where $ number layer will size input of parameters parameters reduced to $ factor of $N^ as to a the were not use pooling pooling. This can it network easier to store and more, also less likely efficient, - The function of functionwise linear function has be efficiently as an a layer learni_i$ learn to own own threshold $ that enough receptive $S_i$ eachh_i$ will approximate a or activation functions, the inputs, For allows functions which are not useful as neural neuralPs such like as sig hyperbolicifier linear units, sig value functionification function -iments {#=========== WeWe ah_i = \{ji - \ ( + 1, \ 5 i + 5 \ in the experiments, This order words, $ first of of of a- over a-overlapping windows of five units units-synaptic units to We The used this function function to each hiddenayer perceptrons described to MNIST by @Cinton+NC-al-NC2012, This modelLP consists a hidden layers, of hidden each with It order case, each firstynaptic weights functionsz_ has size 1200 and $ output activation has each layer has size 100. We The of the network setup was unchanged from from this to the- to We OurHinton-et-al-arxiv2012 reported a% for a MN set for Our To knowledge, this is the best reported performance on MN MNIST dataset for a M that is back droprained nor drop about the data data. Our Our took possible possible that muchHinton-et-al-arxiv20122012 their result single set result for They We our the first 100,000 training images, then a same 50,000 for our held set to We then this sameclassified error on this last set to choose when which epoch in stop training, then test the mis likelihood on the test 10,000 test in which the training for only only first 50,000 training dataset set. This this validation likelihood stops the validation set starts falls that log log, the test log log likelihood, we record training and model and and report on test error accuracy on This this method we we model network obtains made errors on the test set, This We that to a best publishedpublished published reported does not use knowledgeraining, knowledge of the input geometry. QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ<\|endoftext\|>

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