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Not-so-complex Logarithms in the Heston Model
- Randall Hines
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1 Not-so-complex Logarithms in the Heston Model Christian Kahl * Department of Mathematics, University of Wppertal, Gaßstraße, Wppertal, D-49, Germany, and Qantitative Analytics Grop, ABN AMRO, 5 Bishopsgate, London ECM 4AA, UK Peter Jäckel Head of credit, hybrid, commodity, and inflation derivative analytics, ABN AMRO, 5 Bishopsgate, London ECM 4AA,UK Abstract: In Heston s stochastic volatility framework [Heston 993], semi-analytical formlæ for plain vanilla option prices can be derived. Unfortnately, these formlæ reqire the evalation of logarithms with complex argments dring the involved inverse Forier integration step. This gives rise to an inherent nmerical instability as a conseqence of which most implementations of Heston s formlæ are not robst for moderate to long dated matrities or strong mean reversion. In this article, we propose a new approach to solve this problem which enables the se of Heston s analytics for practically all levels of parameters and even matrities of many decades. Introdction The Heston stochastic volatility model is given by the system of stochastic differential eqations ds t = µs t dt + V t S t dw S (t), () dv t = κ(θ V t )dt + ω V t dw V (t) () with correlated Brownian motions dw S (t)dw V (t) = ρdt. [Heston 993] fond a semi-analytical soltion for pricing Eropean calls and pts sing Forier inversion techniqes. The price for a Eropean Call with strike K and time to matrity τ can be expressed very similarly to the Black-Scholes one, namely C(S, K, V,τ)= P(τ ) [ (F K) + π ] (F f K f ) d (3) where f and f are ( ) ( ) e i ln K ϕ( i) e i ln K ϕ() f := Re and f := Re, (4) if i with F = Se µτ, and P(τ ) is the discont factor to the option expiry date. The fnction ϕ( ) is defined as the log-characteristic fnction of the nderlying asset vale S τ at expiry: Note that by virte of definition (5) we have ϕ() := E[e i ln Sτ ]. (5) ϕ() = and ϕ( i) = F. (6) Eqation (3) for the price of a call option given the log-characteristic fnction of the nderlying asset at expiry is generic and applies to any model, stochastic volatility or otherwise. It can be derived directly by the 94 Wilmott magazine
2 TECHNICAL ARTICLE 6 aid of the general reslt from fnctional analysis that the Forier transform of the Heaviside fnction is given by a Dirac and a hyperbolic component: e π ix h(x) dx = δ() + πi. (7) Specifically for the Heston model, we have ϕ() = e C(τ,)+D(τ,)V +i ln F. (8) The coefficients C and D are soltions of a two-dimensional system of ordinary differential eqation of Riccati-type. They are C(τ, ) = κθ ( ( )) c()e d()τ (κ ρωi + d()) τ ln, (9) ω c() κ ρωi + d() D(τ, ) = ω with the axiliary fnctions ( e d()τ ) c()e d()τ κ ρωi + d() c() = κ ρωi d(), d() = (ρωi κ) + iω + ω. () What remains to be done for the valation of plain vanilla options is the nmerical comptation of the integral in eqation (3). This calclation is made somewhat complicated by the fact that the integrands f j are typically of oscillatory natre. Still, the integration can be done in a reasonably simple fashion by the aid of Gass-Lobatto qadratre [Gander and Gaschi ]. The real problem, however, starts when the fnctions f j are evalated as part of the qadratre scheme since the calclation of the embedded complex logarithm on the right hand side of eqation (9) is not as straightforward as it may look at first sight. Two Types of Complex Discontinity The first obvios problem with the inverse Forier transformation (3) is the choice of branch of the mltivaled complex logarithm embedded in C in eqation (9). This is a generic problem with option pricing calclations based on the inverse Forier transformation (3) of an expression derived from the log-characteristic fnction. One sggestion in the literatre to remedy this is to careflly keep track of the branch [Schöbel and Zh 999, Lee 5] along a discretised path integral of f j () as goes from to. Let s recall that the logarithm of a complex variable z = a + ib = re i(t+π n) with t [ π, π), n Z, and r R + can be written as () ln z = ln r + i(t + πn). () If we restrict or choice to the principal branch, the fnctions f j as defined in eqation (4) incr discontinities as is shown in figre for f. Integrating this fnction with an adaptive qadratre scheme will not only reslt in the wrong nmber (becase the area nder the discontinos crve shown in figre is not the same as the area nder the continity-corrected crve), it will also take nnecessarily long de to the fact f () Figre : The fnction f defined in (4). Underlying: ds t = µs t dt + V t S t dw S (t) with S = and µ =. Variance: dv t = κ(θ V t ) dt + ω V t dw V (t) with V =., κ =, θ =., ω =.5 and ρ =.3, time to matrity: τ = 3, strike: K =, red crve: implementation sing only the principal branche, green dashed crve: adjsted crve sing formla (3). that the adaptive rotine refines the nmber of sampling points excessively near the discontinity. In order to nderstand the mechanisms that gives rise to the discontinity, we now examine more closely the component C defined in eqation (9). To simplify the notation frther on, we divide this term as follows: C(τ, ) = R(τ, ) α ln G(τ, ) (3) R(τ, ) := α(κ ρωi + d)τ (4) α := κθ ω (5) G(τ, ) := cedτ (6) c Looking at the whole fnction ϕ() in (8), one cold arge that it is not necessary to evalate a complex logarithm at all since ϕ() = G(τ, ) α e R(τ,)+D(τ,)V +i ln F. (7) This is tre, thogh, we jst shifted the problem from the logarithm to the evaltation of G() α as this is exactly the part of the fnction where the jmp arises. Indeed, if we try this formla in or implementation, the discontinities do not go away (yet). The branch switching of the complex logarithm is in fact not the main problem that gives rise to the jmps of f (). A second effect is at work here and we will have to investigate frther. ^ Wilmott magazine 95
3 In the following, we make repeated se of the fact that, for any complex variable, we can choose either a real/imaginary part or a radis/ phase representation: z = a z + ib z = r z e itz, t z [ π, π). (8) The fact that we restrict the phase t z [ π, π) means that we ct the complex plane along the negative real axis. Taking z to the power α gives z α = r α z eiαtz. (9) Whenever G() crosses the negative real axis along its path (as varies) the sign of the phase of G() changes from π to π and therefore the phase of G() α changes from πα to πα. This leads to a jmp since { e iπ = e iπ e iαπ = e iαπ if α/ Z () e iαπ = e iαπ else In other words, what appeared earlier as a problem with the branch choice of the mltivaled complex logarithm in the evalation of f given by eqation (4) is in fact a problem with the branch switching of the complex power fnction which is related, thogh slightly different. To demonstrate this frther, consider the case when, by coincidence, the parameter setting leads to α Z. In this scenario, there is no jmp at all as we can see in figre. In general, thogh, we have α / Z. This woldn t be a problem if G() didn t cross the negative real axis. However, as it trns ot, the trajectory of G() in the complex plane as is varied from to, tends to start initially with a rapidly otwards f () Figre : The fnction f defined in (4) in the case that α Z. Underlying: ds t = µs t dt + V t S t dw S (t) with S = and µ =. Variance: dv t = κ(θ V t ) dt + ω V t dw V (t) with V =.5, κ =, θ =.5, ω =.5 and ρ =.3, exponent: α =, time to matrity: τ = 3, strike: K =. moving spiral, prior to entering an asymptotic escaping behavior. This is displayed in figre 3 for G(). Note that the shown trajectory is that of ln ln G() γ() := G(), i.e. we have rescaled the coordinate system doblelogarithmically in radis to compensate for the rapid otward move- G() ment of the spiralling trajectory of G(). The he h [, ) of the crve is given by h = log ( + ) mod which means that segments of slowly varying color represent rapid movement of G() as a fnction of. Another aspect why the correct treatment of the phase jmps of G() is so important is the fact that it does not reqire nsal or particlarly large parameters for the nmerically indced discontinity to occr. We show in figre 4 how the discontinities in the complex phase of G() arise simply as time to matrity is increased. What we can learn from all of the above is that the only way to avoid the discontinity of the integrands f j () altogether is to ensre that the phase of G() is continos. Varios athors [Schöbel and Zh 999, Lee 5, Sepp 3] propose the idea to keep track of the nmber of jmps by comparing G( k ) and G( k+ ) where k and k+ are adjacent points in their respective nmerical integration scheme. This is an involved technical procedre leading to the need for a particlarly complicated algorithm if we want to se an adaptive qadratre method. Frthermore, we have to make sre that we accont for all jmps which means that, for this to work reliably, we oght to have an estimate for the total nmber of discontinities. Fortnately, however, there is a mch simpler procedre to garantee the continity of G() which we present in the following. 96 Wilmott magazine Im[γ()] 4 ln ln G() γ() := G() G() he: log ( + )mod Re[γ()] Figre 3: Part of the trajectory of the fnction G() in the complex plane has the strctral shape of a spiral which gives rise to repeated crossing of the negative real axis. Here: ρ =.8, κ =, ω =, time to matrity τ =.
4 TECHNICAL ARTICLE 6 First, we introdce the notation c =: r c e itc, () d =: a d + ib d. () The next step is to have a closer look at the denominator of G which was defined in eqation (6): c = r c e itc (3) =: r e iχ +π m where [ ] tc + π m := int (4) π χ := arg(c ) (5) r := c (6) and with int[ ] denoting Gass s integer brackets. Note that we have assmed arg(z) [ π, π) z. The key observation is that the sbtraction of the nmber from the complex variable c is simply a shift parallel to the real axis and therefore the phase of (c ) [ π, π) if t c [ π, π), or in general, both χ and t c can be assmed to be on the same phase interval. In other words, taking a complex nmber of arbitrary phase, and adding the real nmber, cannot possibly give rise to this operation moving the complex nmber across the negative real axis since this wold reqire the addition of an imaginary component. We now do the same calclation with the nmerator of G ln G() = ln( r / r ) + i [χ χ + π(n m)]. (33) In figre (5), we show the rotation cont corrected angle arg (G()) compared with the reslt by sing jst the principal branch of G(). We see that, withot the correction, de to the sheer nmber of discontinities, it can be very difficlt indeed to keep track of the jmps by simply comparing neighboring integration points. Note that it does not reqire the choice of nsal parameters: the discontinities arise qite natrally for practically all choices of stochastic volatility configrations simply as time to matrity is increased, as was shown in figre 4. The procedre for the discontinity-corrected evalation of fnction f is smmarized in algorithm. The evalation of f () is to be done by the same procedre with replaced by ( i) in all bt the last step of algorithm, with a sbseqent division by the forward as one wold expect from eqation (4). Remark. Whilst algorithm is mathematically correct, it cannot actally be implemented directly in its presented form. For long times to matrity τ, the nmerator term G N can become very large which leads to nmerical overflow. In order to avoid this, we can monitor the expression Re(d) τ : when this term becomes greater than ln(dbl EPSILON) we can neglect 3 the sbtraction of in steps 6 and 9 and the whole procedre of estimating the term ln(g()) shold be done in logarithmic coordinates. Defining ce dτ = r c e itc e (ad +ibd )τ = r c e ad τ e i(tc+bd τ) [ ] (tc + b d τ + π) n := int π (7) (8) χ := arg ( ce dτ ) (9) r := ce dτ, (3) we have ce dτ = r e i(χ +π n). (3) Again, we sed the fact that the sbtraction of does not affect the rotation cont of the phase of a complex variable. Combining these reslts we obtain G() = cedτ c = r r ei[χ χ +π(n m)] (3) wherein the innocos bt crcial rotation cont nmbers m and n are given by eqations (4) and (8). We are now in the position to compte the logarithm of G() qite simply as Figre 4: Withot special handling, the phase of G() incrs more and more jmps as time to matrity is increased. Here: ρ =.8, κ =, ω =, time to matrity τ [, ]. ^ Wilmott magazine 97
5 Algorithm Evalate f () Reqire: F, K,κ,θ,ω,τ >,V and ρ (, ) : C d := (ρωi κ) + ω (i + ) : C c := κ ρωi+d κ ρωi d 3: R t c := arg(c) 4: C G D := c {Denominator of G()} 5: Z m := int [ ] tc+π π 6: C G N := ce dτ [ ] {Nmerator of G()} 7: Z n := int (tc+im(d)τ +π) π 8: C lng := ln(abs(g N )/abs(g D )) + i (arg(g N ) {see (33)} arg(g D ) + π(n m)) ) 9: C D := κ ρωi+d e dτ ω ( ce dτ : C C := κθ [(κ ρωi + d)τ lng] {see (3)} ω : C ϕ := exp(c + D V + i ln(f)) [ ] : R f := Re exp( i ln(k))ϕ 3 Integration scheme i The choice of the right integration scheme is another crcial point for a robst implementation of the semi-analytical Heston soltion. De to the fact that the integrand can vary in its shape from almost simply exponentially decaying to highly oscillatory depending on the choice of parameters, most simple qadratre or nmerical integration schemes are bond to fail significantly for some relevant scenarios. More advanced schemes sch as the adaptive Gass-Lobatto algorithm [Gander and Gatschi ], however, are capable of handling the wide range of fnctional forms attainable by the integrand defined in (4). Since the Gass-Lobatto algorithm is designed to operate on a closed interval [a, b], we show below how one can transform the original integral bondaries [, ) to the finite interval [, ], taking into accont or knowledge of the analytical strctre of the integrand for large. Adapting the transformation to the asymptotic strctre for not only aids the stability of the adaptive qadratre scheme, it also makes the integration scheme significantly more efficient in the sense that far fewer evalation points are needed. Preposition 3. Assming that κ, θ, ω, τ > and ρ (, ) we obtain the following asymptotics: d() lim = ω ρ =: d (34) lim c() = + ρ + iρ ρ = D() ρ + iρ lim = ω ( i ρ + ρ) (35) (36) C() lim = iαωρτ αd τ (37) arg (G()) arg (G()) (a) (b) Figre 5: The phase of G() as defined in eqation (6) with (dashed) and withot (solid) rotation cont correction given by eqation (33), for κ = and τ = 3. (a) ρ =.8, ω =.5. (b) ρ =.95, ω = Wilmott magazine
6 TECHNICAL ARTICLE 6 This leads to ( ) e it lim f j() f j () e C Re = f j () e C sin(t ) (38) i with ( ) ρ ρ C = αd τ + V = (V + κθτ) (39) ω ω as well as t = αωρτ ρv + ln(f/k). (4) ω The initial vales f j () are given in propositions 3. and 3.3. Proof: The proof can be fond in appendix A. Eqation (38) shows that the asymptotic decay of the integrand is at least exponential. In particlar, C > garantees the existence of the integral. A simple and reliable transformation is to translate the integration according to with f j () d = f j ((x)) x C dx (4) (x) = ln x. (4) C The transformation is only possible when C >. Fortnately, this is given as long as ρ =. One last step is needed before we can proceed with the implementation. Looking at the fnctions f j in (4), we can see that f j () is, strictly speaking, not defined at =. The continity of the fnction at zero in figres and gives s hope, thogh, that we can find the vale analytically by the aid of l Hospital s rle. Preposition 3. The fnction ( ) e i ln K ϕ( i) f () = Re if has the following property at zero: lim f () = ln(f/k) + Im ( C ( i) ) + Im ( D ( i) ) V (44) with (43) Im ( C ( i) ) = e(ρ ω κ)τ θκ + θκ((κ ρω)τ ) (κ ρω) (45) Im ( D ( i) ) ρω)τ e (κ = (κ ρω), (46) provided that (κ ρω) =. When (κ ρω) =, we obtain Im ( C ( i) ) = κθτ 4 (47) Proof: The proof can be fond in Appendix A. Preposition 3.3 The fnction ( ) e i ln K ϕ() f () = Re i has the following property at zero: with Im ( D ( i) ) = τ. (48) (49) lim f () = ln(f/k) + Im ( C () ) + Im ( D () ) V (5) Im ( C () ) = e κτ θκ + θκ(κτ ) κ (5) Im(D ()) = e. (5) κ Proof: The proof can also be fond in Appendix A. The above analysis enables s to implement the reqired Forier inversion as a Gass-Lobatto integration over the interval [, ] sing the transformation given by (4), (4), and (39). Since Gass-Lobatto qadratre evalates its integrand at the bondary vales, we need to se the analytical limit vales (44) and (5) for the evalation of f j ((x)) x=. The limit vales at x = seem at first sight to be more complicated. However, it is straightforward to see from eqation (38) that those limit vales are zero as long as C > which in trn is given as long as ρ <. In practice, we combine all calclations in (3) into the single nmerical integration for the ndisconted call option price with C(S, K, V,τ)/P(τ ) = κτ y(x) dx (53) y(x) := (F K) + F f ( ln x ) K f C ( ln x ) C (54) x π C and F = S e µτ, as before. The limits of y(x) at the bondaries of the integral are lim y(x) = (F K) (55) x and lim y(x) = x (F K) + F lim f () K lim f () (56) π C with lim f () and lim f () given by (44) and (5), respectively. An example for the set of sampling points chosen by the adaptive Gass- Lobatto scheme for a target accracy of 6 is shown in figre 6. ^ Wilmott magazine 99
7 ..8 y(x) Gass-Lobatto sampling (accracy =.E-6) Figre 6: The sampling points selected by the adaptive Gass-Lobatto scheme for the integration of eqation (53). S = F =, µ =, V = θ, θ=.6, κ =, ω =, ρ =.8, τ =, K =. The total nmber of evalation points was 98, and the reslting integral vale was 4.95%. 7% 6% 5% 4% 3% % % K/F τ Figre 7: Black implied volatilities from the Heston model. Underlying: ds t = µs t dt + V t S t dw S (t) with S = F = and µ =. Variance: dv t = κ(θ V t ) dt + ω V t dw V (t) with V = θ =.6, κ =, ω =, ρ =.8, τ [/4, 5], and K [/, 4]. Wilmott magazine
8 TECHNICAL ARTICLE 6 The stability of Gass-Lobatto integration over the interval x [, ] of the transformed integrand f j ((x)) / (x C ) as described is sch that even extremely far ot-of-the-money option prices can be compted, as well as very long dated matrities. We demonstrate this in figre 7, where implied Black volatilities are displayed for the same parameters as previosly sed in figre 4. 4 Conclsion The problem we addressed was that Forier inversion integrals of the form (3) sed for the calclation of option prices based on analytical knowledge of the log-characteristic fnction of the nderlying stochastic process are particlarly prone to nmerical instabilities de to their involved complex logarithms and complex power expressions. We fond that the difficlty is ltimately not, as was previosly reported, cased by the mltivaled natre of the complex logarithm, bt instead by the mltivaled natre of the complex power fnction. We analysed this isse for the Heston stochastic volatility model, thogh, the key insight is readily transferable to the calclation of option prices in other models that are amenable to the Forier inversion integral approach [Carr 999, Carr and Madan 999] based on a log-characteristic fnction. We also presented a detailed analysis how the Forier integral itself can be compted reliably by the aid of adaptive Gass- Lobatto qadratre, sing asymptotic analytical methods to identify the most sitable transformation from the half-open integration domain [, ) to the interval [, ]. These reslts, too, are not only sefl for the prpose of compting option prices for the Heston model, bt also to illstrate how similar methods can be devised for other models that are to be evalated with Forier integration techniqes. A Proofs In this section we present the missing proofs of section 3. Proof:[Prop.3.] The proof of eqation (34) is basic analysis: d() lim = lim ω ( ρ ) iω (ρκ )/ ω + κ / (57) Note that lim c() =. In order to show eqation (36), we need the calclation [ ] [ ( e d()τ lim = lim + c() )] c()e d()τ c() c()e d()τ = lim c() c() = lim c() (59) = + ρ iρ ρ. (6) D() lim = ω ( + ρ iρ ρ )( ρωi + ω ρ ) = iρ ρ. (6) ω Finally, we prove (37) lim ln [ c()e d()τ c() From here, we obtain ]/ [ ]/ = lim ln e d()τ c() c() (6) ( = lim ln [ e ] [ ]) / c() d()τ + ln c() (63) = lim d()τ/ = d τ. (64) C() lim = ατ (d + iωρ). (65) Combination of the limit reslts for D() and C() makes it straightforward to arrive at the statements (38) and (39) for f j (). Proof:[Prop.3.] Considering the fnction f as given in (4) we see that ], i)+d(τ, i) V +ln(f) i ln(f/k) ec(τ lim f () = lim Im [e. (66) F = ω ρ Using this reslt, we are able to confirm eqation (35) ρωi + ω ρ lim c() = ρωi ω ρ = (ω ρ ρωi) ω ( ρ ) + ρ ω = ω ( ρ ) iω ρ ρ ρ ω ω = + ρ + iρ ρ = ( i ρ + ρ). (58) The expressions that need attention for the evalation of this limit are lim C(τ, i) as well as lim D(τ, i). We start with lim d( i) = κ ρω. (67) The limit lim c( i) depends on the sign of κ ρω. We first consider the case where κ ρω <. We obtain κ iρω( i) + d( i) lim c( i) = lim =. (68) κ iρω( i) d( i) This allows s to dedce lim D( i) =, lim C( i) =. (69) ^ Wilmott magazine
9 The case κ ρω > is a little bit more complicated. First we see that κ iρω( i) + d( i) lim c( i) =lim = (7) κ iρω( i) d( i) as the denominator goes to zero. Using this we can see that ( ) κ iρω( i) + d( i) e d( i)τ lim D( i) = lim ω c( i)e d( i)τ Frthermore, we have (7) =. (7) lim C( i) = lim α ((κ iρω( i) + d( i))τ [ ]) ln e d( i)τ + ed( i)τ c( i) (73) =. (74) Last we have to check the case κ ρω =. First we have to notice that d( i) lim = lim ω ( ρ ) iω = iω. (75) We have to mention that this limit is not zero as ω = if κ ρω = and κ>. Using this we obtain lim c( i) = + lim = + lim Again we get lim D( i) = and ρωi ρωi d( i) (76) ρωi ρωi + =. iω (77) lim C( i) = α lim ((κ ρω + d( i))τ [ ]) c( i)e d( i)τ (78) ln c( i) [ ] = α ln = (79) Hence in all different cases lim e i ln(f/k)+c( i)+d( i)v =. (8) Now we decompose the exponent into a real and imaginary part i ln(f/k) + C(τ, i) + D(τ, i) V =: H() + ij() (8) with fnctions H, J : R R. De to (), we also know that lim H() =, lim J() =. (8) Now we can calclate [ ] e H()+iJ() f () = lim Im [ ] H() cos(j()) + i sin(j()) = lim Im e H() sin(j()) = lim e = lim e H() lim sin(j()) (83) (84) (85) (86) = lim J () cos(j()) = lim J (), (87) where we applied the rle of l Hospital in the last step. Ths, f () = lim J () = J () = ln(f/k) + Im ( C ( i) ) + Im ( D ( i) ) V. (88) The comptation of C and D is tedios bt straightforward. We obtain Im ( C ( i) ) = e(ρ ω κ)τ θκ + θκ((κ ρω)τ ) (κ ρω), (89) Im ( D ( i) ) ρω)τ e (κ = (κ ρω), (9) if (κ ρω) =, and otherwise which completes the proof. Im ( C ( i) ) = κθτ 4, (9) Im ( D ( i) ) = τ, (9) Proof:[Prop.3.3] The proof of the limit lim f () can be done in complete analogy to the proof of lim f (). FOOTNOTE & REFERENCES. Note that the phase, as we refer to it here, is also known as the argment and some mathematical software packages se the expression arg for the calclation of the phase of a complex nmber.. The he is a nmber in the range [, ) which varies the color from red at throgh the entire rainbow spectrm to prple (arond.8), and then reconnecting to red at. 3. The C header <float.h> provides the macro DBL_EPSILON which is defined as the smallest floating point nmber that, when added to the nmber, still reslts in a nmber that is distinct from in the compter s floating point nmber representation. P. Carr. Option Pricing sing Integral Transforms, 3. carrp/papers/pdf/integtransform.pdf. P. Carr and D.B. Madan. Option valation sing the fast Forier transform. The Jornal of Comptational Finance, :6 73, 999. Wilmott magazine
10 TECHNICAL ARTICLE 6 W. Gander and W. Gatschi. Adaptive Gass-Lobatto Qadratre. S. L. Heston. A closed-form soltion for options with stochastic volatility with applications to bond and crrency options. The Review of Financial Stdies, 6:37 343, 993. R. Lee. Option Pricing by Transform Methods: Extensions, Unification, and Error Control. Jornal of Comptational Finance, 7(3):5 86, 5. S. Mikhailov and U. Nögel. Heston s Stochastic Volatility Model Implementation Calibration and Some Extensions. Wilmott magazine, 3. A. Sepp. Pricing Eropean-Style Options nder Jmp Diffsion Processes with Stochastic Volatility: Application of Forier Transform. Working paper, Institte of Mathematical Statistics, Faclty of Mathematics and Compter Science, University of Tart, J. Liivi, 549 Tart, Estonia, September 3. R. Schöbel and J. Zh. Stochastic Volatility With an Ornstein Uhlenbeck Process: An Extension. Eropean Finance Review, 3:3 46, 999. W Wilmott magazine 3
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text: 250px Skoomer Biographical information Real name Anthony Luthien Hacker name Skoomer Physical description Gender Male Height Status Chronological information Appearences The Matrix Online [Source] Skoomer was the latest crewmember aboard the Hovercraft Eligius. This article is a stub about a character. You can help the Matrix Wiki by expanding it. This article is a stub for articles in the online MMORPG, The Matrix Online. You can help the Matrix Wiki by expanding it. Retrieved from "http://matrix.wikia.com/wiki/Skoomer?oldid=26453" Ad blocker interference detected! Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers Wikia is not accessible if you've made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected. Categories: Pages with broken file links Character stubs MxO-Stub articles Males Redpills Zionites Characters in MxO Add category Cancel Save

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Though this lodge is conveniently located right off of the main drag, pulling up to this place is less than spectacular. The place just doesn't look all that inviting from the outside - there is certainly no curb appeal. The person at the front desk was really nice though, and for some reason gave me an upgraded room and a discounted rate - a suite with a full kitchen on the ground floor. The room was huge with lodgey Southwestern decoration, but the bathroom was surprisingly tiny and dingy. The kitchen was full, but old and dated. It's not luxurious by any means - but if you want some peace and quiet and a great view of the lake, this place was perfect. Be sure to take a moment to enjoy the sunset. The bed was pretty comfy, the couch was not at all comfy for just sitting and reading or something. The TV was kind of small. The patio was just steps on the beach to the lake, but the patio chairs were uncomfortable and dirty. The pool looked nice and clean and quiet, and there was a hot tub. The worst part about this place for me was that there was no A/C - you had to open the doors and windows to get cool air, and I personally am not comfortable on the ground floor with open windows. I would probably stay here again though - the price was right, and location was great.
- Official Description (provided by the hotel):
- Tahoe Lakeshore Lodge & Spa, South Shore's only all lakefront property, offering hotel and condominium lodging all with an incredible lake view and cozy fireplace. Pamper yourself in our full service day spa or relax by our heated pool and hot tub. Centrally located to area activities, restaurants, casinos and sitting on 500 feet of private beach, you'll receive a true Tahoe experience. ... more less
- Reservation Options:
- TripAdvisor is proud to partner with Booking.com, Expedia, Hotels.com, Cancelon, TripOnline SA, Travelocity, Hotwire, getaroom.com, HotelsforEveryone and HotelQuickly so you can book your Tahoe Lakeshore Lodge and Spa reservations with confidence. We help millions of travelers each month to find the perfect hotel for both vacation and business trips, always with the best discounts and special offers.
- Also Known As:
- Tahoe Lakeshore Hotel South Lake Tahoe
- Lakeshore Hotel Lake Tahoe
- Lakeshore Lake Tahoe


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Looking for a peice of software capable of testing the remote gateway VPN access every x amount of minutes, and if it is not able to gain access to send an email alert.
5 Replies
Oct 27, 2010 at 2:08 UTC
Thanks for the link, that is usefull tool, but what I am looking for is something to actually log on to my VPN which is maintained by my Sonicwall. And if it cannot succefully log on for any reason to send an email alert. Unless I am missing something it=n this monitor that can do that.
Oct 27, 2010 at 2:16 UTC
I've never explored this possibility with this program. Are you using site to site VPN? i.e. SonicWall to SonicWall VPN or Client software to SonicWall VPN? If it's a site to site VPN you could use this program to ping the internal peer router IP and if it fails for any reason it can fire off an email to you or any other address you specify.
What is the overall problem you're trying to solve?
Oct 27, 2010 at 2:25 UTC
Using client, I have several extenal sales guys that sync there ERP. For some reason every few weeks they loose access to the VPN and I have to reboot the router. The problem is that the CEO uses this and is sick of having to call me and tell me that he cant log in. And I am sick of him calling. That is what spawned this. I guess I could look into a macro scheduler to run the vpn client and outlook but the problem is I have no way through the macro to say that vpn wasnt accessable and run script to send email. That is were I am stuck right now.
Apr 16, 2012 at 9:41 UTC
I'm looking for something like this as well. I have ping disabled on the VPN (SRA 1200) but need to get some kind of monitor in place after some accessibility troubles this past weekend. @Aaron6588 - did you get a solution in place for this?
This discussion has been inactive for over a year.
You may get a better answer to your question by starting a new discussion.


text: The American Diabetes Association recommends that people with diabetes avoid drinking sugar-containing beverages such as soda because it will raise blood glucose quickly and add several hundreds of calories in one serving. If you feel the need to drink soda, they recommend diet soda because it contains zero carbohydrates and will not raise blood glucose levels. They also recommend drinking calorie-free or very low-calorie beverages. This includes water, unsweetened teas, coffee, and diet soda. There are other options too, such as low-calorie drinks and drink mixes which can be found in most grocery stores. You can also try flavoring your water with a squeeze of lemon or lime juice for a refreshing drink with some flavor.


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Released: 03/2009
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text:
Lilliput Steps is the second "Your Sanctuary" location in EarthBound. Located in a cave east of Happy Happy Village, the guardian of this sanctuary is Mondo Mole. It is known to the people of Happy Happy Village as a "non-blue place". After learning the Sanctuary's melody, Ness envisions a baby in a red cap, presumably himself. It is inspired by the Lilliputians in the novel Gulliver's Travels.
Enemies Edit
Bosses Edit
Trivia Edit
- Unlike Giant Step and Lumine Hall, this one does not unlock a new place, and is possible to skip completely.
- Due to the Mighty Bear and Mondo Mole, it is highly recommended that you don't come here at least until after you have Jeff, Paula at a decent level, and after the town of Threed cleared of zombies.


text:
Paul Hastings Janofsky & Walker is targeting 20 per cent growth for its UK revenue this financial year, at the same time as investigating launching in both Chicago and Germany.
Chairman Seth Zachary said the firm was on track to hit its 20 per cent target for improved UK revenue at the firm's half-year mark of 31 July, while global growth was closer to 15 per cent.
If the Los Angeles-based firm achieves its aim in London, it would see the firm scoop almost $15m (£7.99m) in the UK this financial year. This would compare with the $12m (£6.39m) reported in 2005-06. At the same time Zachary said that Paul Hastings' management team was investigating opportunities to launch in both Chicago and Germany.
"We're looking actively in Chicago and Germany," Zachary confirmed. "We've been approached by clients and others to launch there, but it's extremely unlikely that we'd do a merger. It's more likely that we'd grow by individual or group hires."
Zachary said there was no formal timeline for the expansion and the firm had not yet identified in which German city in would launch. But the offices would be full service, focusing on private equity, finance and litigation.
Paul Hastings has been expanding aggressively in recent years off the back of strong financial performance, including launching in Milan and Palo Alto last year.


text:
Most travelers consider the airport at Baton Rouge to be quite modern and people friendly. The facility, however, does fall short when it comes to convenient flights to some destinations.
Case in point: Miami, Fla. In order to travel to this Southeastern metropolis, Baton Rougeans must first travel east, northeast or even west in order to secure a connecting flight to Miami. This, of course, usually means additional time and money. As an alternative, however, one can drive to the Louis Armstrong New Orleans International Airport for a direct flight to Miami.
In late June and early July, I did this for a 10-day trip to Honduras. I utilized a private lot on Airline Highway that advertised a "best rate" charge of $8.75 per day. Now, imagine my surprise when, upon my return, I was presented a bill totaling $117.
According to the attendant at the gate, the charge included:
• An increase to $10 between July 1 and July 5, a temporary elevated holiday rate
• Numerous taxes, such as airport fee, 7 percent; parking tax, 10 percent; Jefferson Parish tax, 4.75 percent; and Louisiana state tax, 4 percent.
Now, in my opinion, imposing a special holiday rate, particularly when a vehicle is already parked, is exploitive. But a tax structure of 25.75 percent is nothing short of unethical, aka, a rip-off. In fact, because of just these taxes, my basic bill of $91.25 was increased by $25.75.
If the governing officials in New Orleans are interested in attracting travelers into the city's renovated airport, then imposing such high parking taxes is counterproductive. Isn't it bad enough that travelers — and especially international travelers — are exploited everywhere they turn?
So, Baton Rouge travelers considering using the New Orleans airport, be advised! With the current tax structure regulating off-site parking lots there, it may be more cost-effective to reconsider an alternative itinerary that would preclude extended parking.
(Incidentally, the official airport parking lot at the airport charges $13 per day, with no taxes, a total fee that is a bit higher than any private facility but a venue that is nearer and perhaps safer.)
Although such might prove a bit inconvenient, costs could be more reasonable, and fair. And if enough of us complain and boycott the airport, maybe, just maybe, members of the City Council of New Orleans will lower the tax structure for parking vehicles.
Gary Noel Ross, Ph.D.
retired professor of biology
Baton Rouge


text:
Go to Table of Contents History and HIST1108 World History to 1500 or HIST1109 Modern World History Three additional departmental courses
Teacher Licensure in History Students seeking teacher licensure in history must complete a major in history as well as complete required education courses and student teaching. Education requirements are available through the education department. Students seeking Initial Licensure in Massachusetts must pass the Massachusetts Tests for Educator Licensure (MTEL).
World History to 1500 Modern World History 19th-Century Europe Europe in the Era of World War HIST4000 Senior Seminar: Historiography SOC2129 Cultural Geography Three other departmental courses, at least two of which must be at the 3000-level
Distinction in the Field History Majors who wish to receive distinction in the field must have a 3.5 GPA in their major at the start of their final semester, write a significant historiography paper in the senior seminar or a research paper in a directed study, and present their topics during Distinction Day. Students must adhere to the schedule of deadlines set by professors directing their projects.
2012-2013 Academic Catalog
Programs of Study for Liberal Arts and Sciences
Content Course Requirements for History Secondary Education Students HIST1105 United States History to 1877 HIST1106 United States History Since 1877


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Look at other dictionaries:
Edward Taylor — (c. 1642 ndash;1729) was a colonial American poet, physician, and pastor.Taylor was born in Leicestershire, England, and emigrated to the Massachusetts Bay Colony in America in 1668. During his voyage to America, Taylor chronicled his Atlantic… … Wikipedia
New England Puritan culture and recreation — The Puritan culture of the New England colonies of the seventeenth century was distinctive in its attitudes to the arts and recreation. The Puritan community was made homogeneous by a Calvinist theology that believed in a just, almighty God [1]… … Wikipedia
Edward Taylor — Pour les articles homonymes, voir Taylor. Edward Taylor (né en 1642 dans le Leicestershire et mort le 29 juin 1729 à Westfield, dans le Massachusetts) était un poète, un médecin et un pasteur américain du XVIIe siècle. Sommaire … Wikipédia en Français
Tusser, Thomas — (1524? 1580) Versifier on agriculture, was an Essex man. Having a good voice he was trained in music, and was a chorister in St. Paul s, and afterwards in Norwich Cathedral, and held the post of musician to Lord Paget. He tried farming at… … Short biographical dictionary of English literature


text:
What is JotForm?
JotForm is a free online form builder which helps you create online forms without writing a single line of code. No sign-up required.
At JotForm, we want to make sure that you're getting the online form builder help that you need. Our friendly customer support team is available 24/7.
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text: Farn, son of Flosi, was a dwarf and messenger in Orik's personal guard. In Glûmra, he summoned Eragon to meet with Orik. Retrieved from "http://inheritance.wikia.com/wiki/Farn?oldid=88282" Ad blocker interference detected! Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers Wikia is not accessible if you've made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected. Categories: Characters Dwarves Males Varden Add category Cancel Save Languages: Polski


text:
1.Digital Voltmeter
-Design of 4-digit numeric display circuit
-Design of 3 ½ digit DVM
-Study of IC 7107/7106.
2.Phase locked loop (PLL)
-Design of digital phase locked loops (cd 4046 & 565)
-It's use in frequency synthesizer.
-frequency & phase demodulation.
-Amplitude modulation
-Dual Tone Multi Frequency Encoder (DTMF).
3.Audio & Video amplifiers
-Audio amplifier: audio op-amp applications mike pre-amplifier with tone control.
-study of LM 386 Video amplifier: Theory, voltage gain, cover code o/p voltage.
-wiring precautions.
-oscilloscope counter pre-amplifier.
-filter applications.
-Fundamentals of IC timers.
-CMOS timer & 2240 Binary Programmable Timer/counter.
-use of timers for event or interval timing.
-pulse generation & shaping.
-design of frequency counter usingIC 74C926 for the time & event Counting.
5.Sensor Signal Conditioning
1) Temperature – RTD, Thermocouple, Semiconductor LM 35, AD549 and 1N4148
2) Strain gauge type transducers of 350 ohm/120 ohm bridge configuration
3) Variable capacitor transducer signal conditioning using Voltage to Time and Voltage to
Frequency conversion.
5.Sensor Signal Conditioning (Cont.)
4) V to I and I to V converters for std input and output Standard input output ranges – 0 to
2V (DVM), 0 to 5 V(Micro controller), 4 to 20 mA (Industrial)
5) Optical encoders
6.Switched mode power supply
-Introduction to SMPS.
-Design of SMPS using LM 3521,Step up, Step down , Invert mode.
Electronics System Design
Mr.Rohit S.Kabade
6. Micro Controller Based Design
-Design of process controllers PID
-Standard bus interface design.
1. Design of 3 ½ digit DVM using TTL Ics.
2. Study of 7107/7106.
3. Design of frequency synthesizer using 565 PLL.
4. Design of frequency synthesizer using CD 4046 PLL.
5. Frequency measurement using 74C926
6. Interval measurement using 74c926.
7. Study of proportional controller.
8. Study of microcontroller based controller.
9. Study of LM3524 SMPS.
10. Study of audio & video amplifiers.
11. Study of PID Controller
12. Study & I to V & V to I converters.
List of Practicals
The. --
Total Marks: 75
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Each month, Rated People connects over 50,000 homeowners with quality tradesmen - simply enter your job details in the form above to get started.
We'll match your job to the relevant tradesmen in your area - those interested will pay to see your contact details and call you to quote.
As each tradesman expresses interest in quoting on your job, we'll send you their profile and ratings to help you choose the right one for you.
After the work is complete, return to the site and rate your tradesman based on their quality of work, reliability and value for money.
Added 10/07/2017
Service gas appliance and issue safety certificate 1 x boiler Make of boiler: Worcester Bosch...
Added 17/02/2017
Continued noise from shower pump after water turned off
Added 23/01/2017
need 6 thermostats replacing on the radiator and 1 thermostat fix on shower
Added 13/01/2017
move a bedroom radiator to opposite wall
Added 24/10/2016
have bought new taps, tried fitting them ourselves but slight water leak from connections....
Added 29/09/2016
Need to replace 2 bathroom radiators with heated towel rails and replace 3 toilet flushes (all...
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Learn more about RICKARD MILLER LIMITED. Check the company's details for free and view the Companies House information, company documents and list of directors.
Know about every new company document that is added!
Take advantage of our watch this company feature free of charge and have notifications sent directly to your inbox. Whenever a new document appears on this website, or if their particulars change, you will be immediately informed about such changes. To monitor these changes, all you need to do is click on watch this company.
|Current Assets
|£ 23,100
|£ 17,859
|Shareholder Funds
|£ 11,563
|Profit Loss Account Reserve
|£ 7,939
|Called Up Share Capital
|£ 3,624
|Total Assets Less Current Liabilities
|£ 11,563
|Net Current Assets Liabilities
|£ 11,563
|Creditors Due Within One Year
|£ 11,537
|Cash Bank In Hand
|£ 5,241
|Share Capital Allotted Called Up Paid
|£ 3,624
|Number Shares Allotted
|£ 3,624
Information about the Private Limited Company RICKARD MILLER LIMITED has been prepared for information purposes only. It is not intended to be nor does it constitute legal advice. This is public information provided by the official company register.


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A Carrollton man was killed Monday morning after being hit by a pickup truck on Highland Avenue.
Preliminary investigation shows that Larry Moscoe, 71, of Carrollton was attempting to cross the road when he was hit by a truck driven by Lance Maiden, 23, of Carrollton, according to a Kentucky State Police news release.
The call came into Carroll County Dispatch at 6:06 a.m. by the driver, according to the dispatch report. Carrollton Police Assistant Chief Steve Abbott arrived on scene three minutes later, with Carroll County EMS right behind.
Carroll County Senior Center, 110 Sixth St., Carrollton, (502) 732-7026
Jan. 30:Bunk-O tournament (five games), 10 a.m.
Thursday, Jan. 31: Bunk-O, 10:30 a.m.; fried chicken potluck, 11:30 a.m.
Feb. 1:Commodity pick up, 8 a.m.; Pictionary with Peggy and Mitzie, 10 a.m.
Feb. 4:Morning muffins from Fairview Place, 10 a.m.; health presentation with Vickie from Gentivia, 10 a.m.
Feb. 5:Bingo, 9:30 a.m.
Feb. 6:Hot hand waxing and lunch provided by Missy Ireland with Burlington Pharmacy, 10 a.m.
Carroll County Public Library - Call the library (502) 732-7020 for more information.
Wednesday, Jan. 30: Walk-away the pounds, 9 a.m.; Zumba, 5:15 p.m.
Thursday, Jan. 31: Walk-away the pounds, 9 a.m.; GED help, 4 p.m.; homework help, 5 p.m.; ESL class, 6 p.m.
Friday, Feb. 1:Walk-away the pounds, 9 a.m.; Yoga, 9:45 a.m.; Friday crafts, 3:30-4:30 p.m.
Saturday, Feb. 2:Walk-away the pounds, 9 a.m.; game day, 1-4 p.m.
Monday, Feb. 4:Walk-away the pounds, 9 a.m.; belly dance for fitness, 5:15 p.m.
Carrollton High School's Class of 1963 will celebrate its 50-year class reunion Oct. 5.
Class members are trying to contact all teachers, coaches and administrators from the years of 1960-63 and their 1963 classmates.
If you know the contact information for any of these people, contact Mike Lewis, (502) 347-5494; Bill Banks, at
email@example.com;or Mary Sue Wilson,
firstname.lastname@example.com (859) 485-7210.
Carroll County Property Valuation Administrator Rob Robertson announced that the Homestead Exemption on real estate for the 2013-14 exemption represents a $2,000 increase over the 2011-12 exemption.
This means that eligible property owners will not pay taxes on the first $36,000 of their assessment.
Carroll County tax rates for 2013 haven't been set, so an exact amount of savings to persons receiving the exemption cannot be determined.
Work is complete on the installation of the new play surface in Worthville City Park, funded with the help of a 2012 Waste Tire Crumb Rubber grant.
Worthville received the $8,105 grant – 75 percent of the $12,680 project – from the Kentucky Energy and Enviroment Cabinet to pay for the project, which was intended to provide a protective, safe surface for its municipal park playground.
The city is providing a 25 percent match of $4,575 in the form of cash and volunteer in-kind services.
This is Part 2 of a series that started in the Jan. 23 issue.
"Shelter in Place" is a safety procedure designed to help protect you and your family during a serious airborne hazardous-materials emergency. It means taking shelter inside your home until the danger has passed.
The U.S. Department of Agriculture's Farm Service Agency reminds producers that the American Taxpayer Relief Act of 2012 extended the authorization of the Food, Conservation, and Energy Act of 2008 (the 2008 Farm Bill) for many Com-modity Credit Corpor-ation commodity, disaster, and conservation programs through 2013. FSA administers these programs.
I have said it more than once and I am going to say it again. Carroll County is the greatest county on earth. There is not one project that 4-H has that there is not a true "expert" in Carroll County.
One of the projects in 4-H animal science is the process of curing country hams. When I came to Carroll County curing country ham was a project I wanted for the youth. Jim and Bob Froman gave of their time to talk with the members about the process and history of curing country hams.
Copyright © 2017
The News-Democrat is your source for local news, sports, events, and information in Carroll County, KY and the surrounding area.


text:
Dele for young learners exam preparation for groups or individual students
We prepare your young students to obtain the DELE for Young Learners A1 or DELE for Young Learners A2/B1 certificates.
Dele for young learners
- The Spanish level of younger students is recognized and accredited via the official Spanish Diploma certification DELE: this is an exam adapted for young people between the ages of 11 and 17 years (people who are 18 years or older must register for the general DELE exams).
The DELE A1 exam for young learners accredits the linguistic competence necessary to understand and use common everyday expressions and simple sentences, with the purpose of meeting immediate needs.
What are the advantages of obtaining the DELE A1 diploma for young learners?
- This diploma is an official qualification that corresponds to the levels of the Common European Framework of Reference for Languages (CEFR).
- Certifies and evaluates the student's knowledge from their first contact with the language.
- Is valid indefinitely.
- Motivates students between the ages of 11 and 17 years, as it is a challenge and recognition of their learning in the initial stages.
The CEI course is designed so that the exam candidate can proficiently handle all four parts of the exam:
- Part 1: Reading comprehension
- Part 2: Listening comprehension
- Part 3: Written expression and interaction
- Part 4: Oral expression and interaction
DELE A2 - B1 exam for young learners
Following the completion of the DELE A2/B1 exam for young learners, the successful candidates will receive one of the following certificates:
Spanish certificate level A2
- This certificate certifies that the candidate is able to understand common everyday phrases and expressions related to areas of experience that are especially relevant (basic information about themselves and their family, shopping, places of interest, occupations, etc.).
Spanish certificate level B1
This certificate certifies the ability of the language user to:
- Understand the main points of simple texts in standard language dealing with subjects that are familiar, either in situations of work, study or leisure.
- Handle most situations that may arise during travel through an area where they use the language.
- Produce simple and coherent texts on topics that are familiar or related to personal interest.
- Describe experiences, events, desires and aspirations, and briefly give reasons for their opinions and explain their plans.
The CEI course is designed so that the exam candidate can proficiently handle all four parts of the exam:
- Part 1: Reading comprehension
- Part 2: Listening comprehension
- Part 3: Written expression and interaction
- Part 4: Oral expression and interaction
Practical Information
- Lessons per week: 20
- Duration: 2 or 4 weeks
- Levels: A1, A2 & B1
- Maximum Students per Class: 12 students
- Average Students per Class: 5-6 students
- Hours of the Classes: Mornings or afternoons
- Composition of the Course: 20 lessons preparation DELE
- Starting Dates: 2 or 4 weeks before exam
|1 week
|2 weeks
|3 weeks
|4 weeks
|Extra week
|350 €
|600 €
|850 €
|1100 €
|225 €
The following are the official dates for the 2017 DELE examinations in Spain:
- May 12 (Levels A1, A2/B1). Registration dates: from November 15 until March 29.
- November 24 (Levels A1, A2/B1). Registration dates: from November 15 until October 11.
DELE Examination centres
In Málaga, in other Spanish cities and in many countries of the world.
DELE exam registration
if you make a DELE preparation course at our school and would like to make the DELE exam in Málaga, you have the possibility to enrol for the exam in Málaga. In order to enrol please fill in the application form on the following web page examenes.cervantes.es:
- Prices DELE exam 2017 in Spain:
- - Nivel A1 - 108,00 EUR
- - Nivel A2/B1 - 160,00 EUR


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Partners in Transformation
The Partners in Transformation: What brand marketers need from agencies report explores the views of senior, brand-side executives on the changing relationship between brands and agencies. With the dynamic in flux, brands are discovering new ways to employ their agencies' talents; the report highlights trends among brand leaders, as well as challenges and trend predicitions for the near future.
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The State of Marketing Automation in Australia and New Zealand report, published in association with Oracle Marketing Cloud, evaluates current adoption levels, tools and processes employed as well as barriers to effective use of marketing automation.
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text:
After Worcestershire won the toss and declared their first innings at 543 for nine, Northamptonshire were bundled out for a meagre 67, with Zaheer Khan claiming five wickets, including that of his former captain who scored two.
Following on, Northamptonshire were reeling at 185 for eight in 62 over with a humiliating defeat looming large and Gangely was out for a duck.
After scoring two in the first innings before Zaheer castled him, much was expected from Ganguly who came at fourth down but the southpaw lasted just seven balls and could not open his account and was caught by Phil Jaques off Matt Mason.
Zaheer added one more wicket to his first innings tally of five and seemed hungry for more.
Nothing went right for Ganguly in the match and on Wednesday, he was warned for running on the pitch by umpire Jeremy Lloyds while bowling.
Here for a six-week stint with Northamptonshire as a stand-in for Aussie batsman Chris Rogers, Ganguly went wicketless and conceded 23 runs in his nine overs, which also including three maidens.


text:
Tuesday, May 31, 2011
Button Heaven!
I'm blogging from a Starbucks on the new mini-machine. It wouldn't connect at work, but my regular laptop doesn't connect at work either. It connected fine here, which bodes well for travel.
I went to my favorite yarn store to look for buttons today, but she didn't have any. "I get my buttons at JoAnn's," she said, and told me how to get there. I think maybe I was there a million years ago looking for yarn and was disappointed in the selection, so I promptly forgot about the place.
Their yarn selection's indeed very limited, but their button selection's fabulous: an entire wall and a half of everything you could think of. After much agonizing -- and a consultation with one of the clerks -- I bought three large, red, asymmetrical buttons for the scarf. I'll post a picture when it's done.
I'll definitely be going back there. I had to restrain myself from buying far more buttons than I need at the moment. One project at a time!
I am going to start a button box at home, though. Fun!
Posted by Susan Palwick at 5:26 PM
Labels: knitting, shopping, technogadgets
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Triple P-Positive Parenting programs: the folly of basing social policy on underpowered flawed studies
Please see related articles
Wilson and colleagues
A defensive rejoinder from the promoters of Triple P, Sanders and colleagues
Yet, both Wilson and colleagues and the response from Sanders and colleagues overlook a fundamental weakness in the Triple P literature that amplifies other sources of bias. Namely, evidence consisting of studies with a high risk of bias is further limited by the preponderance of underpowered studies yielding positive results at a statistically improbable rate.
Wilson and colleagues noted a number of times in their review that many of the trials are small, but they do not dwell on how many, how small or with what implications. We have adopted the lower limit of 35 participants in the smallest group for inclusion of trials in meta-analyses
What happens when we apply the exclusion criterion to Triple P trials of less than 35 participants in the smallest group? Looking at Table 2 in Wilson and colleagues' review, we see that 19 of 23 of the individual papers included in the meta-analyses are excluded. Figure 2 in the Wilson
Many of the trials evaluating Triple P were quite small, with eight trials having less than 20 participants (9 to 18) in the smallest group. This is grossly inadequate to achieve the benefits of randomization and such trials are extremely vulnerable to reclassification or loss to follow-up or missing data from one or two participants. Moreover, we are given no indication how the investigators settled on an intervention or control group this small. Certainly it could not have been decided on the basis of an
Many communities and charities are proceeding with ambitious and costly implementations of Triple P-Parenting programs with the expectation that this will lead to the alleviation of social and public health problems associated with poor parenting. Wilson and colleagues highlighted the inadequacy of the existing clinical trial data. Adding to that the dominance of biased positive reporting of underpowered trials, it becomes incumbent upon clinicians and policymakers to adequately monitor the implementation of Triple P and evaluation of clinical outcomes to ensure that scarce resources are not squandered.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
Both authors contributed to the conceptualization, drafting and editing of the manuscript. Both authors read and approved the final manuscript.
How evidence-based is an 'evidence-based parenting program'? A PRISMA systematic review and meta-analysis of Triple P
A commentary on evidence-based parenting programs: redressing misconceptions of the empirical support for Triple P
Triple P: Positive Parenting Program
Triple P for Practitioners
Ain't necessarily so: review and critique of recent meta-analyses of behavioral medicine interventions in health psychology
Advantages of excluding underpowered studies in meta-analysis: inclusionist versus exclusionist viewpoints
Self-directed behavioral family intervention for parents of oppositional children in rural and remote areas
Help when it's needed first: a controlled evaluation of brief, preventive behavioral family intervention in a primary care setting
Publication and related bias in meta-analysis: power of statistical tests and prevalence in the literature
Long-term outcome of a randomized controlled universal prevention trial through a positive parenting program: is it worth the effort?
The efficacy of the Triple P-Positive Parenting Program in improving parenting and child behavior: a comparison with two other treatment conditions
Self-administered behavioral family intervention for parents of toddlers: part I. Efficacy
The Triple P-Positive Parenting Program: a comparison of enhanced, standard, and self-directed behavioral family intervention for parents of children with early onset conduct problems
The search for asterisks: compromised statistical tests and flawed theories
Science or art? How aesthetic standards grease the way through the publication bottleneck but undermine science
False-positive psychology: undisclosed flexibility in data collection and analysis allows presenting anything as significant
Scientific inbreeding and same-team replication: Type D personality as an example
Pre-publication history
The pre-publication history for this paper can be accessed here:


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What to do for your child: unexplained fever
We usually use a cool cloth, lukewarm bath and put thieves on our children's feet. When our children have a fever they tend to sleep it off.
I'd only call the doctor if it got really high and we couldn't get it down after three days but we've never had that happen as of yet. It's a sign their little bodies are fighting off some sort of bug or infection and we tend to allow it to take it's course.
It all depends on their behavior. I've had high fevers and them acting well and low temps with them acting sick. Usually a sign of something coming on and my three day rule applies unless something obvious happens like bumps or rash ...
Good to hear what other mothers are doing for fevers. My little one had one on and off the last few days after having his shots and I used a damn wash cloth on the forehead and tylenol to keep it down.
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***Baby Team Leader Moms.com*** I have been married for over 20 years. My husband and I have eight children ages 18 down to 4 years old. We use to live in Chicago but now live in Canada. I own www.FaithandFamilyReviews.com.