if $Ax\in N(A)$, then (\[closed\]) implies that $$\|Ax-Ax\|\geq c\|Ax\|$$ and hence $Ax=0$.

In what follows by $D_\infty$ we denote the unbounded component of the resolvent set of $A$. We will use the following result which is a corollary of the so called “filling the hole” theorem.

\[unbounded\] If $M$ is a closed invariant subspace of $A$, then $$\sigma(A|_M)\cap D_\infty=\emptyset\,.$$

Note that the existence of the unbounded curve emanating from the origin is equivalent to $0\in  \overline{D}_\infty$. Our main result is the following.

\[main\] Let $A:X\rightarrow X$ be a bounded linear operator and assume that $0\in \overline{D}_\infty$. Then $$X=R(A)\oplus N(A)$$ if and only if $R(A)$ is closed and $\phi_C(A)<\pi$, for some $C$.

If $X=N(A)\oplus R(A)$ then there exists $\delta>0$ such that $$\label{closed_1}
\|Ax+y\|\geq\delta \|Ax\|\,,\text{ for all } x\in X, y\in N(A)\,.$$ By Proposition \[unbounded\]every unbounded path $C$ emanating from the origin intersects $\partial\sigma(A)$ and in patricular $\sigma_{app}(A)$ and hence if $\lambda_0$ is this point of intersection there exists a sequence $(x_n)$ in $X$ such that $$\|Ax_n+\lambda_0 x_n\|\rightarrow 0\,,\text{ as } n\rightarrow\infty\,.$$ Since $X=N(A)\oplus R(A)$ each $x_n$ may be written as $x_n=y_n+z_n$, with $y_n\in N(A)$ and $z_n\in R(A)$. But then and since the sum $N(A)\oplus R(A)$ is closed we have that $$\|Ax_n+\lambda_0 x_n\|=\|Az_n+\lambda_0 y_n+ \lambda_0 z_n\|\geq c' \|Az_n+ \lambda_0 z_n\|$$ and hence $$\label{zero}
\|Az_n+\lambda_0 z_n\|\rightarrow 0\,,\text{ as } n\rightarrow\infty\,.$$ On the other hand if $\phi_C(A)<\pi$, then by $X=N(A)\oplus R(A)$, the range of $A|_{R(A)}$ is closed and $N(A)\cap R(A)=\left\{0\right\}$. Hence $$\|Ax+\lambda_0 x\|\geq c\|Ax\|\geq k\|x\|\,,$$ for all $x\in R(A)$. But this contradicts (\[zero\]) and thus $\phi_C(A)=\pi$, for all $C$. So $\phi_C(A)<\pi$ implies that $0\in D_\infty$.

[99]{}

D.


Drivaliaris, N. Yannakakis, *The angle of an operator and range - kernel complementarity*, J Op Theory **76** (2016), 205–218 . K. Gustafson, *The angle of an operator and positive operator products*, Bull. Amer. Math. Soc. **74** (1968), 488–492. K. Gustafson, D. Rao *Numerical range: the field of values of linear operators and matrices*, Springer, New York, (1997). H. Heuser. *Functional Analysis*, John Wiley and Sons, (1982). M. Krein, *Angular localization of the spectrum of a multiplicative integral in a Hilbert space*, Functional Analysis and Its Applications **3** (1969), 73–74 H. Radjavi, P. Rosenthal *Invariant subspaces*, Springer, New York, (1973).
(the performers in a comedy act might break into a song and dance, or finish with a pie in the face or some other effect.)

Fire curtain — A fireproof curtain of asbestos fabric, set immediately behind the proscenium arch, almost touching it and traveling in metal guide channels (‘smoke pockets’) so as to cover the opening fairly tightly. It could be lowered when the theater was dark and raised a few minutes before the show, and was also rigged to drop quickly at the pull of a stage-side handle in case of fire (a theater, including the house, stage and fly gallery full of combustibles, is a huge and very efficient fireplace). Most building codes required a fire curtain and automatic fireproof stage doors in theaters with a


Gallery seats were the cheapest.

Get back your pictures — To be cancelled or fired (your promo photos were removed from the lobby displays and returned to you).

Ghost light — A single bare bulb on a head-high stand, left lit on the stage overnight for safety.

Glass-crash — A basket filled with broken glass, used to imitate the noise of breaking a window and the like.

Go big — When a performer, act, song, gag, etc., wins much applause it is said to “go big.”

Grouch Bag — A small bag or purse worn under the clothing, carrying the performer’s valuables (which are likely to be stolen from an unattended dressing room).

Half-hour — The first of several calls (backstage announcements to performers in their dressing rooms or the green room) by theact was not booked for a full week in one theater but played part of the week in another house (or spent the rest of the week in travel to the next theater).

Stage Door — The entrance from the street to backstage. A bulletin board located here holds a daily sign-in sheet, information about nearby hotels and restaurants for the benefit of traveling artists, and rules particular to that theater. There might also be a set of mailboxes for the performers to receive mail or notes from the producer (see “blue material”).

Stage Left — The side of the stage that is on the performer’s left as he faces the audience (“stage right” is the other side).

Stage Manager — The real, day-to-day boss and hero of show business. He


of 5% CO~2~ in air at 37°C. The growth medium was changed regularly during the culture.

hMSCs were analysed for purity and epitope expression using fluorescence-activated cell sorter (FACS) analysis. The cells were blocked with FcR Blocking Reagent (human) (Miltenyi Biotec, Bergisch Gladbach, Germany) and incubated for 30 min. at 4°C with corresponding antibodies: CD29, CD44, CD45, CD73 (BD Biosciences, Heidelberg, Germany) and CD105 (AbD Serotec, Düsseldorf, Germany). Suggested mouse isotype antibodies were used as control. After incubation, the cells were washed with 1 × PBS/EDTA (2 mM) and analysed using a LSR II Flow Cytometer (Becton Dickinson, Heidelberg, Germany). Dead cells were excluded using dead cell stain kit (LIVE/DEAD®, Invitrogen). Data analysis was performed with BD FACSDiva™ software (BD Biosciences). Histograms of cell number *versus* logarithmic fluorescence intensitythat the cells in S phase achieved significant higher transfection efficiency than the cells in G1 phase \[[@b31], [@b32]\]. The effect of S phase on the transfection efficiency was investigated in this study ([Fig. 6A](#fig06){ref-type="fig"}). Interestingly statistic analysis found that there were two subpopulations in donors; in each of these two subpopulations transfection efficiency was linearly related to the cell percentage in S phase. Pearson correlation coefficient between transfection efficiency and the cell percentage in S phase (Pearson *r*) was analysed, which was 0.969 for subpopulation 1 (P1) (*n* = 6, Sig. \< 0.01) and 0.822 for subpopulation 2 (P2) (*n* = 6, Sig. \< 0.05). Furthermore, non-parametric Mann-Whitney test revealed that the GFP^+^ percentages of P1 and P2 were from two different distributions (Asymp. Sig. \< 0.01);


NAFTA deal that U.S. President Donald Trump can hail as a victory but nevertheless has red-line issues, including the need for dispute panels and protection from tariffs. The U.S. is moving forward on its bilateral trade deal with Mexico even if Canada is left out because negotiators can’t resolve their differences over dairy and a dispute resolution system, U.S. Trade Representative Robert Lighthizer said. – Farm Futures

U.S. President Trump and his South Korean counterpart Moon Jae-in signed a renegotiated free-trade agreement on the sidelines of the United Nations General Assembly on Monday, Sept. 24,, marking the first time the U.S. president has finalized a major trade deal since entering office. – Farm Futures

President Trump and Japanese Prime Minister Shinzo Abe agreed to open trade talks. The limited scopenot using a CSV generated by an Excel on Mac (there's a quirky error there)
PHP version 5.1.6, so there should be no problem with the function
I know the file's not too big, or malformed, because I kept shrinking the original file to see if that was a problem and finally just created a custom file in Notepad with nothing more than two lines like:
Value1A,Value1B,Value1C,Value1D

Still looping and giving no data. Here's the full code I'm working with now (using a variable that's greater than the number of lines so I can prove that it would loop infinitely without actually giving my server an infinite loop)
if ($handle = fopen($_SERVER['DOCUMENT_ROOT'].'/tmp/test-csv-file.csv', 'r') !== FALSE) {
    while ((($data = fgetcsv($handle, 1000, ',')) !== FALSE) && ($row < 10)) {


of continuous time reinforcement learning can converge to an equilibrium of replicator dynamics, which indicates some interaction between population dynamics and individual reinforcement learning. Reinforcement learning, with its basis in psychology [@pone.0102840-Sutton1], [@pone.0102840-Holroyd1], evaluates the reward by weighting historical and current payoffs and has been applied to human strategy adjustment as well as to artificial intelligence [@pone.0102840-Erev1]--[@pone.0102840-Brede1]. Recently, researchers have begun to integrate different learning approaches to determine an agent\'s optimal strategy in the case of incomplete information. Reinforcement learning is a good fit when information on the opponent and environment is limited. To this end, agents in our model adopt reinforcement learning to calculate the reward of each strategy and then use replicator dynamics to adjust the probability of strategies. We integrate replicator dynamics and reinforcement learningdenote buyers; triangles denote sellers, and ellipses denote environmental factors. The values ,, are probabilities of the frugal, cool-headed and anxious strategies of buyers, respectively, and ,,are the corresponding strategies for the sellers. The shaded area represents the selected strategy in the current period. At the end of each negotiation period, the buyers (sellers) calculate the reward through reinforcement learning and update ,,(,,) accordingly. The process continues until the strategies of all agents in the market converge to a stable state.](pone.0102840.g001){#pone-0102840-g001}

Negotiation rules {#s2a}
-----------------

The reservation prices and of the sellers and buyers are uniformly distributed between and . In each period, seller-buyer pairs are randomly selected and begin to negotiate if . The offering intervals for a buyer and a seller are (,) and (,), respectively. They alternate in


with different degrees of greediness exist for each population: 0\<\<\<\<1, 0\<\<\<\<1. Here, represents the frugal strategy; represents the cool-headed strategy; and represents the anxious strategy for the buyers as well as for the sellers. refers to the initial offer parameter, which creates an offer closer to the reservation price, with a larger ; refers to the concession type, which is defined as a convex function for buyers and a concave function for sellers when . The buyer and the seller propose offers alternately until an offer is accepted, which occurs when the agent receives a higher payoff than refusing it by proposing his own offer, which is expected to be accepted by the opponent in the next round. The buyer accepts an offer when , and a sellerfrom 0.5 to 0.9. As the weight drops below 0.5, the payoff declines sharply with the decreasing discount rate and reaches a minimum at approximately 0.8. It is obvious that the agents who emphasize historical experience perform better than the agents who ignore it. In [Figure 3B](#pone-0102840-g003){ref-type="fig"}, the negotiation time remains stable when the weight is above 0.5 and rises obviously until the weight drops below 0.5. The discount rate in our model indicates that more rounds of negotiation lead to lower payoff and inefficiency of the market. In [Figure 3C](#pone-0102840-g003){ref-type="fig"}, there is only a minor fluctuation of fairness when the weight rises above 0.5, and fluctuation becomes noticeable when the weight drops below 0.5. It can be concluded that the profit division of the market becomes unfair


weight decreases (see [Figure 4E](#pone-0102840-g004){ref-type="fig"}). As the discount rate decreases, the frugal strategy decreases, and the cool-headed strategy increases. The cool-headed strategy becomes dominant when the discount rate is very low, while the frugal strategy is a tiny minority. This result indicates that the low discount rate\'s leading to less greediness in agents may be caused by the time pressure to accept offers more actively. The anxious strategy remains at a low level when the weight is high and fluctuates substantially when the weight is below 0.5 (see [Figure 4F](#pone-0102840-g004){ref-type="fig"}). In conclusion, the strategy convergence remains stable and the cool-headed strategy has a noticeable advantage when the weight of historical information is high. The greediness of the whole market rises as the weight drops.

To summarize, the impacts ofprobability [@pone.0102840-Sarin1]. Borgers believes that individual learning is a process of idea evolution as well as habit formation and proves that a continuous-time reinforcement learning of an individual converges to equilibrium of replicator dynamics [@pone.0102840-Brgers1]. We adopt replicator dynamics as the strategy adjustment rule and incorporate reinforcement learning into the payoff evaluation. The simulation results suggest that agents using this new learning model achieve higher payoff, shorter negotiation time, and more stable fairness than agents using the classic evolutionary approach.

This paper presents two experiments designed to study the general performance of agents and the impacts of the weight of historical information on the negotiation result and convergence strategy. The results indicate that in most cases, learning increases the payoff of both buyers and sellers. Thus, the learning pattern


a bout of "seller's remorse" after seeing the NBA's Los Angeles Clippers go for a staggering $2 billion under distress conditions, so he decided to renegotiate a heftier return and asked Andrew Barroway, a deep-pocketed hedge fund wizard from Philadelphia, to meet his new price of $548 million.

Not surprisingly, Barroway preferred the original price tag from the handshake agreement he'd made with Wang on March 10 and was reluctant to accept the new terms. So when Wang informed him that he'd decided to sell the Islanders to other bidders on August 1, Barroway opted to sue for $10 million—an amount that was apparently specified as damages/recouped expenses in the original agreement in the event of it falling apart.

It's another embarrassing moment for an organization that seems to feedin negotiating the purchase of the Isles had better bring a big bottle of aspirin and a battery of lawyers to the proceedings.

NHL Deputy Commissioner Bill Daly has said that the lawsuit is "a private dispute", so the boys will just have at it.

Meanwhile, it hasn't taken the new owners in Florida long to start “quietly” greasing the skids for an exit from the financial sinkhole that is Broward County. Doug Cifu, who bought the troubled club with Vinnie Viola last year, told FoxSports Florida on Saturday that the team's ”current business model is unsustainable.”

This conclusion probably didn't catch anyone who follows the team by surprise, least of all Cifu who, as a successful hedge fund guy, most likely did his due diligence on the club before he


corresponding power spectra. The problem is complicated due to the fact that density perturbations now propagate with a time-dependent speed (the speed of sound). In Ref. [@Wei:2004xx], the Green function method has been used but with some extra-assumptions on the behavior of the sound speed. The question was also considered in Refs. [@Shandera:2006ax; @Bean:2007hc] but the results obtained in those articles were not totally correct since the sound speed was (implicitly) assumed to be constant which is not the case in most of the k-inflationary scenarios (this result was also used afterward in Ref. [@Peiris:2007gz]). These works also missed the influence of the sound speed in the tensor power spectrum due to the shift between the scalar and tensor pivot scales [@Lorenz:2008et; @Agarwal:2008ah]. The first fully consistent result for the k-inflationary scalarflow functions, the effective potential for the density perturbations can be expressed as $${U_{_{\mathrm{S}}}}=a^2H^2\left[2-\epsilon_1+\frac32 \epsilon_2
+\frac14 \epsilon_2^2-\frac12\epsilon_1\epsilon_2
+\frac12\epsilon_2\epsilon_3
+\left(3-\epsilon_1+\epsilon_2\right)\delta_1
+\delta_1^2+\delta_1\delta_2\right].$$ The quantity ${U_{_{\mathrm{S}}}}$ depends on the $\epsilon_n$’s up to $\epsilon_3$ only and on the $\delta_n$’s up to $\delta_2$ only. Despite this last property, it is important to remember that the above expression of ${U_{_{\mathrm{S}}}}$ is *exact* and that no approximation has been made at this stage.

The cosmological observables we are interested in are the two point correlation functions of the fluctuations, [i.e.]{}in Fourier space, the power spectra of both gravity waves and density perturbations: $$\label{eq:powerspectra}
{\mathcal{P}}_h = \frac{2k^3}{\pi^2}\left \vert \frac{\mu_{{{\ensuremath{\boldsymbol{k}}}}}}{a}\right\vert^2,
\quad {\mathcal{P}}_\zeta = \frac{k^3}{2\pi^2}
\left \vert \zeta_{{{\ensuremath{\boldsymbol{k}}}}}\right\vert^2=
\frac{k^3}{4\pi^2}
\frac{{c_{\mathrm{s}}}^2\vert v_{{{\ensuremath{\boldsymbol{k}}}}}\vert^2}{{M_{{{\scriptscriptstyle{{\mathrm{Pl}}}}}}}^2a^2\epsilon_1}.$$ They have to be evaluated at the end of inflation and on large scales. After the inflationary era, and for single field models, these power spectra


the scalars. As explained before, one has still to make explicit the scale dependence hidden in ${\eta_*}$. In the case of tensors, the pivot point is usually defined by ${k_{\star}}{\eta_{\star}}=-1$ since gravity waves propagate at the speed of light. This leads to the following expression for the power spectrum $$\begin{aligned}
{\mathcal{P}}_h=& \frac{2\left(18\, {e}^{-3}\right){H_{\star}}^2}{\pi^2 {M_{{{\scriptscriptstyle{{\mathrm{Pl}}}}}}}^2}
\biggl\{1-2(1+D){\epsilon_{1{\star}}}+\left(\frac{17}{9}+2D+2D^2\right){\epsilon_{1{\star}}}^2
+\biggl(-\frac{19}{9}+\frac{\pi^2}{12}
\nonumber \\ &
-2D
-D^2\biggr)
{\epsilon_{1{\star}}}{\epsilon_{2{\star}}}+\bigl[-2{\epsilon_{1{\star}}}+2(1+2D){\epsilon_{1{\star}}}^2
-2(1+D){\epsilon_{1{\star}}}{\epsilon_{2{\star}}}\bigr]\ln \frac{{k_{\star}}}{k}
\nonumber \\ &
+\left(2{\epsilon_{1{\star}}}^2-{\epsilon_{1{\star}}}{\epsilon_{2{\star}}}\right)
\ln ^2\frac{{k_{\star}}}{k}
\biggr\}.
\label{eq:phstdpiv}\end{aligned}$$ Let us notice that, in order to obtain this relationship, we have used the initial conditions for gravity waves $\vert
B_{{{\ensuremath{\boldsymbol{k}}}}}\vert=1/{M_{{{\scriptscriptstyle{{\mathrm{Pl}}}}}}}^2$. Otherwise, one notices the presence of the WKB factor $18\, {e}^{3}$ and one can check that, at first order, it coincides with the known expression for the tensor power spectrum. The above formula, being expressed at the time ${\eta_{\star}}$, is convenient for SFMK models only, but not for k-inflation.     }
        // We've hit the plane so now see if that hit is on the disk
        let p = ray.at(t);
        let dist_sqr = p.x * p.x + p.y * p.y;
        if dist_sqr > self.radius * self.radius || dist_sqr < self.inner_radius * self.inner_radius {
            return None;
        }
        let mut phi = f32::atan2(p.y, p.x);
        if phi < 0.0 {


Time doesn't matter here, we're already in the object's space so we're moving
        // with it so to speak
        let mut ray = Ray::segment(p, w_i, 0.001, f32::INFINITY, 0.0);
        match self.intersect(&mut ray) {
            Some(d) => {
                let w = -*w_i;
                let pdf = p.distance_sqr(&ray.at(ray.max_t))
                    / (f32::abs(linalg::dot(&d.n, &w)) *Marco Silva delivered a rebuttal to his predecessor which, had they heard it, might have been received by the Goodison crowd as enthusiastically as their team’s goals against Lincoln City.

Sam Allardyce used Everton’s recent defeat by Leicester as an opportunity to tell Silva where he has been going wrong since replacing him last summer. Having kept his counsel when Silva enjoyed an encouraging start to the season, the timing was suspiciously cynical.

“You can talk about playing it out from the back and attractive football, but you will never survive as Ronald Koeman and Roberto Martinez learnt,” said Allardyce. “They all played so-called better football than me, but they didn’t survive.”

Silva queried Allardyce’s motivation when informed of the digs at his style. “My style? How I dress? My hair?


does to change the strength of the formation. Lake Travis went from a team confident in its chances to repeat as Class 6A Division I champs to a team desperately searching for a way to stop the fb casino in a twutter of minutes at ATamp;T Stadium Saturday afternoon.

Match Report O35. 1 Game Date: 13052018. BMFC O35. 1: 6 vs Springwood United FC: 0 BMFC Goal Scorers: Suarez (2), JB, Paul, Brad, Zap Player of the Match: Mick Match Report: We had been alerted pker Gordon poker training tools the week that there was no allocated ref for our game and this hadnt changed come game day Hawks Sharp in 35-7 Big slick poker twitter at Stevens Point Its amazing how different the flow of a football gameas a multi-function display.

Manufactured by Garmin, it serves as a replacement for most conventional flight instruments and avionics The Colorado 300 is an all-terrain navigator featuring a high-sensitivity receiver, electronic compass and SD card slot. Legacy GPSMAP with SD Card software version 2018. 0214. reckless roulette band of February 14, 2018. Download (103. 00 Big slick poker twitter. View installation instructions and system requirements.

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Over 30 wineries populate the regions rolling hills and sprawling valleys producing a variety of wines, including award-winning and artisan Syrah, Cabernet Sauvignon, Zinfandel, Chardonnay, and Pinot Noir. North Shore. Tours begin at 20 E. General Robinson St we are located on Vulcan way. Please visit our FAQs page to find information about parking during your tour. Taste of Sonoma, held as


Works Studio to engage girls in coding at an early age.

Clinical psychologist’s Melissa DeRosier (founder) and Deborah Childress from the 3C Institute develop research-based interventions to support students’ social-emotional health in education and special education.

In the next few months, SBIR Pulse will release a series of Q&A interviews with many of these developers. We look forward to learning the stories of why and how these trailblazers got started, what role SBIR played, and what they see as keys to girls in STEM and women in business. Stay tuned!

About the Authors

Edward Metz is the Program Manager of the SBIR Program at the U.S. Department of Education’s Institute of Education Sciences.Betty Royster is the Communications Specialist for the National Institute of Health’s SBIR and STTR Programs.Shannon Rhoten is a PresidentialRockford, Illinois.

Notes

External links

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Data cannot be shared publicly due to IRB protocols and standards of privacy and confidentiality. Data are available by request from the University of Colorado Boulder Research and Innovation Office (<rio@colorado.edu>) in conjunction with the corresponding author (contact via <aquandt@sdsu.edu>) for researchers who meet the criteria for access to confidential data.

Introduction {#sec001}
============

The rapid diffusion of mobile phones in the Global South has increased information flow, reduced telecommunication costs, and led to novel strategies for economic development \[[@pone.0237337.ref001], [@pone.0237337.ref002]\]. In a study of 120 developing countries, growth in mobile phone penetration coincided with economic growth \[[@pone.0237337.ref003]\]. Mobile phones have impacted the lives of hundreds of millions, particularly in areas with poor access to landline telephones due to a lack of infrastructure or electricity. In Sub-Saharan Africa, phones are increasinglyand neutral \[[@pone.0237337.ref021], [@pone.0237337.ref022]\] associations between ICTs and yields. Diverse, reported impacts may stem from variation in structural issues such as access to markets, transportation infrastructure, and ICTs across local contexts \[[@pone.0237337.ref023]\]. The diversity of conclusions may also be due in part to differences in methodologies, phone use measurements, and the many factors that must be considered in the analyses.

Many studies of mobile phone use and agricultural productivity are econometric \[[@pone.0237337.ref004]\], focused on outcomes and impact evaluations \[[@pone.0237337.ref024]\], concerned with specific agricultural services/projects \[[@pone.0237337.ref004]\], and based on large, national datasets \[[@pone.0237337.ref025]\]. However, fewer studies have examined farmers' perceptions of ICTs and the value they hold for agriculture despite the critical role perceptions play in the adoption of innovations \[[@pone.0237337.ref026]\]. Often, the perception of the characteristics of an innovation,


test for associations between general phone use and self-reported agricultural yield (RQ2), and also for associations between phone use specifically for agricultural purposes and self-reported agricultural yield (RQ3), we estimated separate regression models (see below). General maize yields were reported as number of 65-kg sacks per hectare of grain (not on the cob) in recent good years. These values were converted into tons per hectare for presentation and analysis. It is important to note that the weight of maize sacks can vary throughout Tanzania. Long-term residents of Iringa Region told us that they generally use 65 kg as the standard weight in Iringa Region. However, this should be considered an approximation.

RQ2 and RQ3 were operationalized into 2 separate multilevel linear statistical models predicting self-reported maize yield in agroup-level effects) are relevant to research questions \[see \[[@pone.0237337.ref034]\], p. 356 for further discussion\]. We do, however, test this assumption by estimating alternative specifications with fixed effect dummy variables for village for both the *general phone use* and *phone for agriculture* models. These are not as parsimonious as the reported models including varying effects for village, as determined by information criterion. (dAICc = 7 and 8, respectively) \[[@pone.0237337.ref035]\].

Our outcome variable, self-reported maize yield, was continuous and approximated a log-normal distribution, so we fitted Gaussian models. The 2 research questions were specified into 2 separate models conforming to the following structure: $$\left. y_{i} \right.\sim\text{Normal}(\mu_{i},\sigma)$$ $$\mu_{i} = \alpha + \beta\mspace{720mu} x_{i,h,v} + H + V,$$ where the log of self-reported maize yield *y* by respondent *i* has a Gaussian distribution


in town, buy fertilizer, and then recruit a friend to help him transport the fertilizer to the farm, saving both time and money.

Our findings are also consistent with those of studies connecting mobile phone use and increased agricultural yield. A study in India \[[@pone.0237337.ref049]\] found that 35% of farmers who used their phones for connecting with markets, getting better prices, and getting agricultural information reported increased yields. A study of coffee farms in Uganda found positive associations between mobile phone use and increased coffee harvests, as well as higher off-farm incomes \[[@pone.0237337.ref019]\]. And a study in Ghana \[[@pone.0237337.ref020]\] concluded that a farmer with a mobile phone had, on average, an increased maize yield of 261 kg/ha per production season compared to farmers without a phone. However, these studiesall employed different metrics in measuring phone use, which can have an important impact on the results, as our study shows. Ultimately, to better understand the causal mechanisms in our study area would require more involved methodological approaches, including in-depth ethnographic work, and/or an RCT.

Overall, our findings support the targeted and intentional use of ICTs as a strategy to improve agricultural productivity and economic development. Mobile phones can support development by increasing household management efficiency \[[@pone.0237337.ref001], [@pone.0237337.ref016], [@pone.0237337.ref050]\] and contributing to existing livelihood activities \[[@pone.0237337.ref037]\]. They can provide people and communities in rural parts of the developing world with access to digital information and resources, as well as new types of knowledge sharing platforms \[[@pone.0237337.ref051], [@pone.0237337.ref052]\]. Our results highlight the importance of mobile phones at individual- and household-scales,


variables should not be excluded just because they are not significant; you should be guided by theory.

While you are mostly careful not to attribute a causal interpretation to the relationships you find, I think it would not hurt to have an extra paragraph making explicit that, ideally, these sort of questions should be investigated using an RCT or other method that can isolate exogenous variation in phone use. Related, I agree with the reviewer that you can not control for (un)observables (something you later also admit) by including wealth in your regression: wealth is endogenous.

Finally, you combine different dimensions of phone use into one indicator. But number of contacts in phone may measure a very different attribute than eg calls placed. The first one may be a proxyfor social network, which has also been found to yield increments for many reasons (access to finance,\...). Thus, finding a correlation may not be because of phone use but due to social network effects. This will have implications for policy.

I am thus more optimistic than reviewer 2 and think it should not take too much effort to respond to these issues. I do want to stress though, that I will expect to see some additional regressions in the response to reviewers such that we get a sense of the robustness of the findings, that is, that results are not driven by the small sample.

When you are ready to submit your revision, log on to <https://www.editorialmanager.com/pone/> and select the \'Submissions Needing Revision\' folder to locate your manuscript file.

If you


the small sample.

RESPONSE: We note the additional models estimated and revisions made in our response just above. Here we include fixed effect coef estimates from each reported models and the two alternatives to each.

General phone use model, as reported in revision, with village random/varying effects:

\# Estimate Std. Error t value

\#(Intercept) -0.0703427 0.2741156 -0.257

\#sqrtPhContacts 0.0075574 0.0118448 0.638

\#sqrtCallTotal 0.0515576 0.0304081 1.696

\#sqrtSmsTotal -0.0063911 0.0224546 -0.285

\#scaledPovertyScore 0.0351852 0.0358823 0.981

\#logFarmHectPlant 0.3388541 0.0781271 4.337\*

\#male 0.0963103 0.0963723 0.999

\#as.numeric(age) 0.0001625 0.0034560 0.047

\#edLevSec -0.0741210 0.1089327 -0.680

General phone use model, with no village effects

\# Estimate Std. Error t value

\#(Intercept) -0.0449657 0.2669384 -0.168

\#sqrtPhContacts 0.0081260 0.0118962 0.683

\#sqrtCallTotal 0.0498101 0.0305475 1.631

\#sqrtSmsTotal -0.0073511 0.0226110 -0.325

\#scaledPovertyScore 0.0292653 0.0355737 0.823

\#logFarmHectPlant 0.3553133 0.0768808 4.622\*

\#male 0.0992511 0.0965557 1.028

\#age 0.0002841 0.0034790 0.082

\#edLevSec -0.0603360 0.1087211 -0.555

General phone use model, with village fixed effects:

\# Estimate Std. Error t value

\#(Intercept)towards negative emotional information ([@bb0030]; [@bb0085]). For instance, studies have reported biases for stimuli including depression- and anxiety-related words ([@bb0095]), socially threatening words ([@bb0090]), and sad faces ([@bb0055]; [@bb0075]). However, some studies have also noted the absence of a behavioral bias in depression, such as with angry, sad, happy ([@bb0100]), or fearful ([@bb0005]) facial expressions.

Dot probe attentional bias tasks have been used with emotion-related word and face stimuli to assess cognitive biases in depressed participants ([@bb0120]). Generally in a dot probe task, two different stimuli are presented for a short time, followed by a dot in the same location as one of the prior stimuli. The participant responds to indicate the location of the dot, and reaction time is measured to analyze attentional bias towards a specific type


of the task and by the scanning environment. With specific regard to the effects of ketamine versus placebo, we observed significantly greater activation post-ketamine compared to post-placebo in the left middle occipital gyrus across groups (p~FWE~ \< 0.001) ([Table 3](#t0015){ref-type="table"}, [Supplementary Fig. S2](#f0045){ref-type="graphic"}). In contrast, significantly reduced activation post-ketamine compared to post-placebo was observed in the left temporal and inferior frontal cortices (p~FWE~ \< 0.002).

### 3.2.2. Two-way interaction effects {#s0060}

A significant diagnosis by emotion interaction was observed. A post-hoc *t*-test of this interaction was significant in small clusters in the periphery of the brain and brainstem (p~FWE~ \< 0.05). When post-hoc tests comparing angry versus happy faces in the HC and MDD groups were conducted separately, the effects of emotion were more prominent overall in the MDD group but consistent across both groups ([Fig.[@bb0050]).

A cluster within the ACC, extending bilaterally into the medial frontal gyri, exhibited a significant drug session by emotion by group interaction. In this three-way interaction, opposite patterns of activation were observed in HC and MDD participants, which differed by both drug session and emotion. The HCs exhibited greater activation in response to angry versus happy trials post-placebo, and greater activation in response to happy versus angry trials post-ketamine. MDD participants displayed an opposite pattern, with slightly more activation in response to happy versus angry trials post-placebo, but greater activation in response to angry versus happy trials post-ketamine. Here, again, the pattern of activity in MDD participants post-ketamine was similar to the pattern of activity in the HCs post-placebo, potentially suggesting normalization of aberrant brain function. The brain


Yeah, ofcourse." "They're great." "Not a band, Charlie." "It's a record store downtown." "Things sound so much better on vinyl." "You know, I used to be popular before Sam got me some good music." "So you be careful." "She'll ruin your life forever." "That's okay." " Hey, Nothing." " Hey, Nothing." "Let it go!" "Jesus!" "It's an antiquejoke." "It's over." "So what are you gonna do when you get outta this place?" "Well, my Aunt Helen said I should be a writer... but I don't know what I'd write about." "You could write about us." "Yeah!" "Callit Slut and the Falcon." "Make us solve crimes." "You guys seem really happy together." "How long have you been boyfriend and girlfriend?" "He's not my boyfriend." "He's my stepbrother." "My momwith Patrick's blessing." "Patrick?" "You are a hopeless stoner who attends the culinary institute." "I'm gonna say "no" on that, but nice try." "Charlie." "Touché." "So, Charlie." "This is a party." "This is what fun looks like." "Are you ready to meet some desperate women?" "Here, have a seat." "Hey, ladies." "Meet Charlie." " Hi." " Meet ladies." " Hey." " Mary Elizabeth." " Alice." " Nice to meet you." "This is Charlie's first party ever." "So I expect nice, meaningful, heartfelt blowjobs from both ofyou." "Patrick, you're such a dick." "Where the hell did you go?" " The dance was a little boring, don't you think?" " You are so selfish." "We looked everywhere foryou." "You could have told someone." "Cry me a river." "How is it


guys." "Never see you coming." "And parents love you." "That's, like... extra danger." "Yeah, well, it hasn't worked so far." "You've never had a girlfriend?" "Not even like a second grade Valentine?" "Nope." "Have you ever kissed a girl?" "No." "What about you?" "Have I ever kissed a girl?" "No, no." "Your first kiss." "I was 1 1." "His name was Robert." "He used to come over to the house all the time." "Was he your first boyfriend?" "He was my..." "He was my dad's boss." "You know, Charlie, I used to sleep with guys who treated me like shit." "And get wasted all the time." "But now I feel like..." "I have a chance." "Like..." "I can even get into a real college." "It's true." "You canthings to say." "That dairyjust sits with you." "You know, it walks with you." "She's on the phone right now?" "Charlie, you've gotta break up with her." "I can do that?" "For Christ's sake, I need to use the phone." "I got you this book." "It's really how I became a vegan." "I know I should have been honest... but I was getting so mad, it was starting to scare me." "I mean the way they treat those" "I just wish I could have found anotherway to break up." "Um, Mary Elizabeth, can I talk to you..." "Charlie, please don't interrupt." "You know I hate that." "In hindsight, I probably could not have picked... a worse way to be honest with Mary Elizabeth." "Truth or dare?" "Who are


be our little secret." "Candace." "Your brother's on the phone." "Hello?" " Hey, Candace." " Charlie?" "Sam and Patrick left, and I can't stop thinking about something." "Shh." "What?" "Candace..." "I killed Aunt Helen, didn't I?" "She died getting my birthday present... so I guess I killed her, right?" "I've tried to stop thinking that, but I can't." "She keeps driving away and dying." "Call the police and send them to my house." "I can't stop her." "I'm crazy again." "No." "Charlie, listen to me." "Mom and Dad are gonna be home with Chris any second." "I'mjust thinking... what if I wanted her to die, Candace?" "What?" "Charlie?" "Charlie!" "Charlie?" "I'm Dr. Burton." "Where am I?" "Mayview Hospital." "You, — You have to let me go." "My dadletter..." "I want you to know that I was in a bad place before I started high school." "And you helped me." "Even ifyou didn't know what I was talking about... or know someone who's gone through it." "You made me not feel alone." "Because I know there are people who say all these things don't happen." "There are people who forget what it's like to be 1 6 when they turn 1 7." "I know these will all be stories someday." "And our pictures will become old photographs." "And we'll all become somebody's mom or dad." "But right now these moments are not stories." "This is happening." "I am here." "And I am looking at her." "And she is so beautiful." "I can see it." "This one


   addShutdownHandler();
    }

    private void addShutdownHandler() {
        Logger root = Logger.getLogger("");
        Handler[] handlers = root.getHandlers();

        for(Handler h : handlers) {
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        for(Handler h : handlers) {
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   S.E.2d 721, 724, (citations, brackets, and quotation marks omitted), appeal dismissed, 362 N.C. 364, 664 S.E.2d 311-12 (2008). Additionally, "findings of fact to which defendant failed to assign error are binding on appeal." Id.

State v. Williams, ___ N.C.App. ___, ___, 703 S.E.2d 905, 907, disc. review denied, 365 N.C. 188, 707 S.E.2d 237 (2011). Although assignments of error are no longer required under North Carolina Rule of Appellate Procedure 10(a), in order to challenge a finding of fact as unsupported by the evidence, the appellant must make this argument in his brief. See N.C.R.App. P. 28(a) (stating that "[t]he scope of review on appeal is limited to issues so presented in the several briefs. Issues not presented and discussed in a party's brief are deemed abandoned."). Defendant does


police officer is permitted to conduct a stop and pat-down, when he "observes unusual behavior which leads him to conclude, in light of his experience, that criminal activity may be occurring and that the person may be armed and dangerous[.]" Id. (citing Terry v. Ohio, 392 U.S. 1, 30, 88 S.Ct. 1868, 1884-85, 20 L.Ed.2d 889, 911 (1968)). See State v. Barnard, 184 N.C.App. 25, 29, 645 S.E.2d 780, 783 (2007) (noting that Terry established that "[a] police officer may effect a brief investigatory seizure of an individual where the officer has reasonable, articulable suspicion that a crime may be underway."). Reasonable suspicion requires that "[t]he stop. . . be based on specific and articulable facts, as well as the rational inferences from those facts, as viewed through124 L.Ed.2d 334.
This Court must consider the totality of the circumstances in determining whether the incriminating nature of the object was immediately apparent and thus, whether probable cause existed to seize it. State v. Briggs, 140 N.C.App. 484, 492, 536 S.E.2d 858, 863 (2000). A probable cause determination does not require hard and fast certainty by the officer but involves more of a common-sense determination considering evidence as understood by those versed in the field of law enforcement. Id. at 493, 536 S.E.2d at 863.
Robinson, 189 N.C.App. at 458-59, 658 S.E.2d at 504-05.
On appeal, defendant contends that the nature of the contraband was not "immediately apparent" to Investigator Dunkley because he could not testify that he identified which specific drugs he was touching. However, under the plain feel


is the inverse of "Imbalance Factor" in the paper):
```
./cifar_im_trainval.sh
```
+ On long-tailed CIFAR dataset using the proposed class-balanced loss (set non-zero `BETA`):
```
./cifar_im_trainval_cb.sh
```

+ Run Tensorboard for visualization:
```
tensorboard --logdir=./results --port=6006
```

+ The figure below are the results of running ```./cifar_im_trainval.sh``` and ```./cifar_im_trainval_cb.sh```:

## Training with TPU:
We train networks on iNaturalist and ImageNet datasets using [Google's Cloud TPU](https://cloud.google.com/tpu/). The code for this section is in `tpu/`. Our code is based on the official implementation of [Training ResNet on Cloud TPU](https://cloud.google.com/tpu/docs/tutorials/resnet) and forked from https://github.com/tensorflow/tpu.

Data Preparation:
+ Download datasets (except images) from [this link](https://drive.google.com/file/d/1ZHhMFJxsgXItJYKiM_VJ0lznj8XClgWF/) and unzip it under `tpu/`. The unzipped directory `tpu/raw_data/` contains the training and validation splits. For raw images, please download from the following links and put them into the corresponding folders in `tpu/raw_data/`:
  +on female fashion?”

“No.”

“Does your religion at least have an undefinable quality of truth that draws people to it?”

“Absolutely not.”

“Then I think your only real option if you want to become a world religion is … violence. Bloodshed. Pure and simple.”

Oops. I think a court case for me just opened up somewhere in Pakistan.

http://muslimbrotherhoodinamerica.com/the-course/

The Organization of Islamic Cooperation and its Role in Enforcing Islamic Law

We need to get off Saudi Barbarian OIL!!!!!Support the Canadian OIL Sands,,, and visit,, Ethicaloil.org

The gravity of the existential threat we face from Islamic Jihad is truly of epic proportions. It is essentially a battle pitting free-civilized man against a totalitarian barbarian. What is at stake is the struggle for our very soul - namely who we are and what we represent. The lives that


were sacrificed for individual rights and freedoms that we've come to cherish are being chiseled away from right under our noses by the stealth jihadists. And many of us are in denial and totally clueless.

The left's appeasement and pandering to evil is nothing new. What makes their utopian delusions so infuriating and unpardonable is that it is not only they who will have to pay the consequences, and deservedly, so, they are thwarting and undermining our best efforts at resistance and are thus dragging us down in the process as well.

Hey Ayatollah YA PERVE!!!!!

Email Solsticewitch13solsticewitch13 @ yahoo.com(remove spaces)

Support Wilders!!

Pigs Are COOL!

guardian cat magik so mote it be )0(

give peace a chance

Zawalooser!!

Wiccans and Pagans don't believe in satan,, but this GOOF does. I think he damaged his brain. Thepoor dear, caved in his skull,, and must have serious frontal lobe damage. Amazing a human can be that screwed up in the head, to deform their own skull, for what??? Religion??? and one as abhorrant to ME, as islam is?? Same goes for the 72 virgins,, how twisted a religion that promises homicide bombers, endless orgies, in "heaven" after they blow up countless innocent people.


the 2018 FIBA Europecup Finals to Italian team Dinamo Sassari by a final score of 170-163 (using a two-game combined score format).

Not their first reunion together

Their reunion in Germany was not the first time the duo have connected after their time in Bloomington. The pair of Hoosiers have played together with fellow Hoosier Christian Watford in “The Basketball Tournament,” which is a tournament held in the United States over summer months. The tournament has featured prize pools of $1-2 million and teams competing in the tournament are mostly composed of former high major college players and former NBA players.

In 2017, the trio’s “Armored Athlete” team advanced all the way to the TBT West Regional championship where they lost to Team ALS.at Hunters Point Naval Base in San Francisco, during 2005–06 when the Golden Gate Railroad Museum (GGRM) was located there. The GGRM and all other tenants at Hunter's Point had to leave the former navy base in 2006 due to redevelopment. The initial equipment move took place in February 2006, although an extended lease on the shop building allowed work to continue on 2472 for ten more months. On December 31, 2006, SP 2472 and the remaining pieces of GGRM rolling stock completed relocation to the Niles Canyon Railway located in Sunol, California, on the east side of San Francisco Bay.

The locomotive became serviceable in February 2008, and was stored in Niles Canyon at the Brightside Yard between operations. SP 2472 has operated in Niles Canyon, usually on


extent to which those cues are diagnostic of attractiveness and risk; (c) how combinations of cues effect partner judgments and intentions to engage in safer sex behaviors with those partners, and (d) how search strategies affect these judgments and intentions. In Study One a computer-based survey will be administered to 800 college students in order to identify important and diagnostic attributes for partner selection and judgments. In Study Two, 470 subjects will each be presented with 5 randomly generated partner profiles consisting of highly diagnostic attractiveness and risk cues. They then will make risk and attractiveness judgments and indicate their intentions to date and have unprotected sex with that partner. Study Three investigates how an initial decision about a partner influences the search for additional information about thatbook defines it as including affective links, and even criticises the “racism” of ethnic minorities who stick together. But “racism” is mainly used to convey the colloquial meaning of ethnic prejudice and hatred and is thus a term of opprobrium. This mixed meaning has helped make “racism” useful to social critics but next to worthless for serious analysis. On the one hand it is used reasonably to describe categorical hostility towards a racial group, but the same word is applied to liberal-democratic polities such as France and Germany in the 1970s. Australia is especially condemnable, the authors contend, because for much of the country’s history racism has been used in an attempt to increase social cohesion. Geoffrey Blainey’s 1984 criticism of high levels of Asian immigration on the


ground that it threatened social stability is described as “an attempt to develop an embracing racist ideology”. One meaning not given to racism is defence of ethnic group interests or other adaptive functions. The concept is not floated. Overly liberal application of the racism concept obscures the distinction between ethnicity and race. Thus the authors claim that in 1992 Australia could not adopt the “racist” strategy of reaffirming its historical British identity because, in that year, only 75 per cent of the population were of British descent. But Britishness is an ethnic category, not a racial one. The white racial category in 1992 was much greater than 75 per cent of the Australian population.

In arguing for a socialist form of multiculturalism that eliminates group inequality, Mistaken Identity doesdone in the past few years, making that minority the favoured majority in its immigration policy.[37]

A more recent criticism of the Left-minority political establishment comes from Bob Birrell, reader in sociology at Monash University. Birrell has been subjected to name-calling from senior colleagues[38] because he is a rare social scientist whose analysis includes the costs of diversity and immigration to national cohesion. He argues that multiculturalism serves the interests of minorities, especially in keeping the immigration doors open to a continual flow of co-ethnics. He implies that minority solidarity has been marshalled by leftist politicians to bolster their electoral prospects. For one analysis he drew on the work of Patrick Buchanan in his book The Death of the West.[39] The end result, Buchanan argued, will be the subordination


 }

    public function testPersistOrder()
    {
        $this->node->getParent()->willReturn($this->parentNode->reveal());
        $this->parentNode->getNodes()->willReturn([
            $this->node->reveal(),
        ]);
        $this->document->getSuluOrder()->willReturn(null);
        $this->document->setSuluOrder(20)->shouldBeCalled();
        $this->subscriber->handlePersist($this->persistEvent->reveal());
    }

    public function testPersistOrderWithExistingOrder()
    {
        $this->node->getParent()->willReturn($this->parentNode->reveal());
        $this->parentNode->getNodes()->willReturn([
            $this->node->reveal(),
        ]);
      to Fun Home. I consciously decided not to read that one, because it told a story outside of what our play was saying. I didn’t want to subconsciously know something that had not yet happened to my character. I didn’t want that to feed into anything. So, to answer your question, to play a person that was alive (she died before the show opened), it’s a delicate balance. And, yes, they are real people, but they have been dramatized in a theatrical sense. It’s not really an easy answer. There are many different filters and layers. Hopefully, the story is still intact and told in a compelling way.

Robert, what is your favorite thing about the show?

RP: My favorite thing about the show is that Sam Gold has directed


it to be as intimate a production as it was on Broadway in the round at Circle in the Square. We are in proscenium spaces on the tour, but it was very important to him that the actors maintain that intimacy, even in large houses. And so, fueled by an amazing sound department, we are able to talk almost like we are in a movie. We try to be as grounded and as real as possible and maintain that intimacy. In the words of Sam, “keep it in Beech Creek,” meaning, don’t reach out to the audience and try to hit the back wall of the theater. Just talk to each other onstage. Be real with each other, and the audience will come to you. The sound departmentwas gay. And I was gay. And he killed himself. And I… became a lesbian cartoonist.” I could see a guy in the front row rolling his eyes and looking at his wife like, “what have you brought me to?” And at the end of the show, he was wiping tears away from his eyes. That, to me, is the effect we are having in a nutshell. People are like, “what is this show?” because it doesn’t fit the category of a musical that people expect. But I swear, the people that give it the hour and forty minutes it takes to watch, come out changed and moved. People are connecting with the family in this story in ways they didn’t expect because it’s not necessarily their family.


that support in Des Moines or Durham. We haven’t been anywhere that we’ve worried they’d run us out of town. There are people who love the show, they know what they are getting because they are big fans of the show already, and then there are people sitting there in shock because they have just been taken on this journey that they are so enthralled with, and they are jumping to their feet. It’s been great.

In another interview, Robert, you mentioned that these characters are just humans being human.

RP: Yeah. Carrying this story across America right now, in a country where we all feel so divided, there is something so great about taking a very human story and letting people see other people who may be very different// This file is part of the embedder test, which is intentionally built without
// NODE_WANT_INTERNALS, so we define it here manually.
#define NODE_WANT_INTERNALS 1

#include "node_native_module_env.h"

// The stub here is used when configure is run without `--code-cache-path`.
// When --code-cache-path is set this stub will not be used and instead
// an implementation will be generated. See tools/code_cache/README.md for
// more information.

namespace node {
namespace native_module {

const bool has_code_cache = false;

// The generated source code would insert <std::string, UnionString> pairs
// into NativeModuleLoader::instance.code_cache_.
void NativeModuleEnv::InitializeCodeCache() {}

}  // namespace native_module
}  // namespace node


heard it on the radio yesterday and my initial reaction was that it would make life even more difficult in terms of getting back into the Football League.

“But there is the suggestion that the new division would be one of four in the Football League and the top 10 Conference clubs would move into the new one. I feel a bit more optimistic were that to be the case but my initial reaction was concern, that’s for sure.”

Noting Dyke’s two-year timescale to implement the changes, Bircham added: “If we are still in the Conference when and if these proposals are implemented it would be our own fault.

“I’m sure there will be a consultation process with the Conference at some stage when our opinions will no doubt be sought.

“I’mof geeks, The Lone Gunmen. Mechner followed his lead and dialed up his own personal geek squad, calling them to his Los Angeles home one Monday morning in April.

To Them, It's Just Old Stuff —————————-

Jordan Mechner’s house is nestled at the base of the Hollywood hills on one of those Los Angeles streets so verdant and well-maintained that you’d never know that the smoggy grime of Hollywood Boulevard was mere blocks away.

A white pickup truck pulls up and parks on the street; enter vintage computer collector Tony Diaz. He made the 80-mile drive up from Oceanside to help Mechner mine his old floppies for their lost treasures. From the bed of his pickup, he unloads crate after crate of old Apple II computers, drives and cable. He’s brought


realize that they’re sitting on treasure. Scott’s goal is to help them figure this out and save their pioneering work from bit rot.

“To them, it's just old stuff,” Scott says. “You help them realize its value.” Organizations like Stanford University, the Library of Congress and the Strong Museum of Play have departments dedicated to preserving software. Scott’s presence here today underlines his commitment to rescuing old games and production materials from their dusty, magnetic tombs.

Mechner, Scott and Diaz haul the gear from the truck around the back of Mechner’s house. Nestled in the backyard is a small guest cottage. Like any good Hollywood writer (in addition to working on games, Mechner is writing graphic novels and screenplays these days), he’s converted the guest house into a home office.involved. There the defendant moved to dismiss the action under section 48 of the Civil Practice Act on the ground that the plaintiff did not have legal capacity to sue because both the plaintiff and his employer, and the defendant, were under and subject to the Illinois Workmen's Compensation Act. Affidavits in support of the motion were filed indicating that the plaintiff was injured by his employer in the course of his employment, which injury was aggravated by the malpractice of the defendant, a physician. The court says:
"It is apparent that the action of the court below in dismissing the complaint on the ground that plaintiff did not have legal capacity to sue under Section 29 of the Illinois Workmen's Compensation Act was proper. There were no disputed


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approximate the average

rate at which major banks can borrow money. LIBOR, which is published daily,

                                          7
is used as a reference point in determining interest rates for financial instruments

across the world.

      The British Bankers’ Association (“BBA”), a London-based trade

association for the financial services industry, oversaw LIBOR during the

relevant period. It calculated LIBOR in various currencies for different maturities

(e.g., one month, three months, six months) based on the submissions of member

banks sitting on panels designated for a particular currency. Every day, panel

members would answer                      9
a fixed-rate instrument, [it] evaluated the difference (or ‘spread’) between the

offered rate [on the fixed-rate instrument] and LIBOR.” J.A. 867. Because

“suppressing LIBOR would always, and obviously, tend to suppress the rates of

return on fixed-rate instruments by making lower rates of return relatively more

attractive,” Schwab allegedly received lower returns on fixed-rate instruments

than it would have if LIBOR had been properly set. Id.

      Schwab did not purchase debt instruments from all Defendants.

Defendants can be divided into three groups relative to Schwab’s purchases.

      First, Defendants HSBC, Citibank, Deutsche Bank, JPMorgan Chase, and

UBS (the “direct seller Defendants”) allegedly solicited and


that Schwab had failed to plead the existence of a conspiracy

among the defendant banks to manipulate LIBOR. Id. at 772, 781–82.

      In April 2013, while the antitrust appeal was pending, Schwab commenced

the present case in state court in California. Schwab reasserted the common-law

claims over which the district court had previously declined to exercise

supplemental jurisdiction, and added new federal and state causes of action. The

case was promptly removed to federal court, and it too was then transferred to

the LIBOR MDL.

      In November 2014, Defendants, together with 28 other entities defending

against claims of LIBOR manipulation, moved to dismiss the complaints in 27

cases, including Schwab’s, for lack of personal jurisdiction and for failure to state

a claim. Fed. R. Civ. P. 12(b)(2),a state in which the parent

“indirectly” sells the securities. Schwab’s sparse allegations of agency, however,

are too conclusory to make a prima facie showing of personal jurisdiction. See

Pincione v. D’Alfonso, 506 F. App’x 22, 24 (2d Cir. 2012) (holding that “allegations

concerning [non-party’s] agency were entirely conclusory and thus inadequate”

to establish personal jurisdiction over the principal). Although Schwab’s

complaint sets forth a non-exhaustive list of the broker-dealer entities from which

it purchased debt instruments, it sheds no light on the relationship between

Defendants and those broker-dealers. Instead, the complaint generally alleges

that Defendants “controlled or otherwise directed or materially participated in

the operations of th[e] broker-dealers, [and] reaped proceeds or other financial

benefits from the broker-dealers’ sales of LIBOR-based financial instruments,


                         28
including but not limited to instances where Defendants issued the LIBOR-based

financial instruments that were then sold by their broker-dealer subsidiaries or

affiliates.” J.A. 868. That bare allegation does not allow us to determine whether

any particular broker-dealer’s contacts should be imputed to any particular

Defendant.

      Schwab’s pleading deficiency is not insurmountable, and the indirect seller

Defendants may well have purposefully availed themselves of California “by

directing [their] agents” to transact with Schwab there. Daimler AG, 134 S. Ct. at

759 n.13. Again, whether Schwab should be allowed to amend is discussed

below.

             3.only to

manipulate LIBOR, but also “to earn profits” from that manipulation. Appellants’

Reply Br. 12. Yet financial self-interest is not the same as furthering a conspiracy

through California-directed sales, and nowhere in Schwab’s complaint are there

allegations that Defendants undertook such sales as part of the alleged

conspiracy. Whether Schwab should be allowed to amend the complaint to

correct this deficiency is considered below.

      B.     Personal Jurisdiction Arising From the “Effects” of LIBOR
             Manipulation in California

      In the alternative, Schwab argues that there is personal jurisdiction over all

Defendants because the “obvious and direct effects of [their] actions in California

suffice.” Appellants’ Br. 37.


district court thus erred in dismissing Schwab’s claims as

precluded by California’s rejection of the fraud on the market doctrine.

      Defendants, however, identify an alternative basis on which to affirm the

dismissal of the fraud claims involving fixed-rate instruments: the claims are

beyond the scope of common law fraud.

                                          41
      California follows the Restatements of Torts, under which a defendant is

liable to those “whom he intends or has reason to expect to” rely on a

misrepresentation. Restatement (Second) of Torts (“Rest.We disagree with the district court, however, that misrepresentations and

omissions that induced Schwab’s purchase of floating-rate instruments could not

have caused any losses. Although a depressed LIBOR that caused expectations of

future interest payments to decrease might result in lock-step reductions in the

price of floating-rate instruments, such an effect is not certain, and expert

                                          47
testimony might well demonstrate that, in light of Defendants’ manipulation,

Schwab’s floating-rate instruments should have been priced even lower than

they were. The district court was thus wrong to assume, at the pleading stage,

that Schwab was not


the three-

year limitations period and making all of its claims timely.

      The district court rejected that argument. Notably, the court refused to

dismiss any of Schwab’s tort claims as untimely because it determined that it was

10
  The district court held that Schwab’s common-law claims “effectively relate[d]
back” to Schwab’s first set of cases, filed on August 23 and 29, 2011, in which the
court declined to exercise supplemental jurisdiction over state-law claims. LIBOR
IV, 2015 WL 6243526, at *177; see also id. at *158, *177 n.205. No party challenges
the propriety of considering those dates to be the relevant filing dates for statute
of limitations purposes.

                      that rule. The reference to harm or wrongdoing that

is “difficult for the plaintiff to detect” was simply a description of the general

circumstances in which inquiry notice applies, id. at 831, and the California court

cited inquiry notice cases for the standard that should govern contract cases, id. at

832–33. California cases relying on April Enterprise to apply the discovery rule in

contract cases have followed suit. See, e.g., Weatherly v. Universal Music Pub. Grp.,

125 Cal. App. 4th 913, 919–20 (Cal. Ct. App. 2d Dist. 2004); Gryczman v. 4550 Pico

Partners, Ltd., 107 Cal. App. 4th 1, 6 (Cal. Ct. App. 2d Dist. 2003).

      The district court was wrong on the standard for a simpler reason as well:

Schwab’s unjust enrichment claims sound in fraud. See J.A. 884 (alleging


/*!
 * Propeller v1.2.0 (http://propeller.in)
 * Copyright 2016-2019 Digicorp, Inc.
 * Licensed under MIT (http://propeller.in/LICENSE)
*/

// Genral style of mizins and variables
@import "../../../scss/functions.scss";
@import "../../../scss/variables.scss";
@import "../../../scss/mixins.scss";

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.pmd-navbar-left .bootstrap-datetimepicker-widget {
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	.timepicker {
		display: table;
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	.time-separator,
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/*google materail themes*/
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	background-color: $datetimepicker-info-bg;
	text-align: center;
	color: $datepicker-info-color;
	line-height: 1.0;
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Advanced atrioventricular block in a neonate with lupus erythematosus and anti-SS-A antibodies.
Recent studies suggested that the involvement of anti-SS-A and anti-SS-B antibodies in the pathogenesis of neonatal lupus erythematosus and congenital heart block. We here describe a female neonate with lupus erythematosus, advanced atrioventricular block, and a positive test for anti-SS-A antibodies. The findings of His-bundle recordings are presented.get around certain people. There was one girl who kept switching to breaststroke. I could not get around her - first got a kick to the goggles and had to stop/readjust, and then a little later she kicked me in the gut. Then one of the lifeguards wasn't paying attention (chatting with another LG) and let her surfboard swing into our paths. As I passed it, I grabbed the end and then shoved it away. Only then did I remember that we had our race numbers clearly printed on stickers on our caps. Oh, well, I doubt she even would have realized that was intentional. The rest of the swim was pretty uneventful. It was very hard to sight after the turnaround due to the sun, so I


of SNP in BA000029.3Notsu et al. ([@CR4])Tian et al. ([@CR5])Current studyBA000029.3DQ167400.1genomic seqgenomic seqgenomic seqcDNA seq*ccmFn*1,785185323,671gGt (G)gCt (A)gCt (A)gCt (A)677323,179gCc (A)gGc (G)gGc (G)gGc (G)*mat-r*2,0371,809316,040cgT (R)cgA (R)cgA (R)cgA (R)1,812316,037acC (T)acG (T)acG (T)acG (T)*nad4*1,488759200,397gcT (A)gcA (A)gcA (A)gcA (A)*nad6*6182160,116tcT (S)tcG (S)tcG (S)tcG (S)9760,040Atc (I)Gtc (V)Gtc (V)Gtc (V)16659,971Att (I)Gtt (V)Gtt (V)Gtt (V)39859,739aAt (N)aGt (S)aGt (S)aGt (S)41459,723gaC (D)gaA (E)gaA (E)gaA (E)46759,670aCt (T)aGt (S)aGt (S)aGt (S)47459,663atC (I)atT (I)atT (I)atT (I)47659,661tCa (S)tTa (L)tTa (L)tTa (L)56259,575Ctg (L)Ttg (L)Ttg (L)Ttg (L)56759,570gaC (D)gaT (D)gaT (D)gaT (D)60759,530Tcg (S)Acg (T)Acg (T)Acg (T)*rpl2*1,5091,249297,421Ttc (F)Ctc (L)Ctc (L)Ctc (L)*rrn18*1,6951,566282,896CTTT*rrn26*3,5421,980382,078GCCCThe position of the SNP is shown relative to the start site of each protein-coding gene or mature rRNA. Each SNP is capitalized in the corresponding codon, with the amino acid change shown in parentheses.

To re-sequence the above mentioned genes and their cDNAs of Nipponbare, genomic                     Mark A. Robbins, Member

                                 OPINION AND ORDER

¶1        The appellant has filed a petition for review of the initial decision, which
     dismissed her removal appeal as moot without holding the requested hearing. For
     the reasons that follow, we GRANT the appellant’s petition for review.        We
     AFFIRM the initial decision insofar


was in an absence without leave (AWOL) status. Id. at 65-88. The
     agency removed the appellant on an attendance-related charge of misconduct
     effective September 27, 2013. Id. at 65-68. The appellant filed an appeal of her
     removal and raised several EEO discrimination affirmative defenses, as well as a
     claim of whistleblower reprisal. IAF, Tab 1. After the appellant filed her initial
     appeal, the agency rescinded both the notice of proposed removal and the
     decision letter effecting her removal, and it removed all references to these
     actions from her personnel file. IAF, Tab 26 at 35-36.
¶3     surprise, the rumors were true: Marcin’s office at 3534 W. Diversey Ave. had been left untouched. Old photos, campaign literature (some dating back to the 1930s when Marcin ran for congress), meticulously compiled scrapbooks, oil paintings and even neon signs were all sitting there, collecting dust.

“It was incredible,” Kaplan said. “There were no lights, no electricity, just flashlights. It was like, ‘Wow, seriously? This entire aldermanic ward office was sitting here intact?’ We couldn’t believe our eyes.”

John Marcin worked out of the building at 3534 W. Diversey Ave. for many years. GoogleMaps

Last week, Pogorzelski and Kaplan packed it all up in a U-Haul and delivered it to the University of Illinois at Chicago’s Richard J. Daley Library. The two donated the collection in hopes of deepening Chicago’s understanding


received the collection and said it would take a “long time” to determine what’s useable.

But Pogorzelski and Kaplan are thrilled to donate the collection to an institution that has a solid reputation for preserving Chicago’s political history.

“They have great resources on Chicago politics. We thought it was the perfect fit,” Kaplan said.

A page out of Marcin’s scrapbook. Provided

Eventually, the two want to open a Chicago political history museum of their own. But it’s something they envision doing longterm, not anytime soon.

“There’s a lot of stuff that gets thrown out that should be saved. Starting an institution that saves it is one of our longterm goals,” Kaplan said.

Pogorzelski, Kaplan and two partners — Rob Reid and Elisa Addlesperger — published a book on Avondale’s history, called “Avondale and Chicago’s'Hanuman Temple Statue" circle towards to Metro station name "Karol Bagh" take first U tern than take first left lane of Ajmal Khan Road market, than take second Left again and than take first right just you reached 'Saraswati Marg" and leave 3 lefts and stop at the corner of 4th Left there we are located.


0.006, *p* = 0.002), though these effects were small. Simple main effect analysis revealed that in general, older adults (55--64 and 65+ year olds) recorded less LPA and steps compared to younger adults (25--34, 35--44, and 45--55-year-olds). These findings persisted over the 10 weeks of data collection, which suggests that older adults recorded less incidental physical activity prior to the pandemic which continued into the pandemic.

![Physical activity during physical distancing by age. **(A)** MVPA; **(B)** LPA; **(C)** Steps; (a) 35--44 year olds are significantly different from 55 to 64 and 65+ year olds; (b) 65+ year olds are significantly different from 45 to 54 year olds; (c) 65+ year olds are significantly different from 35 to 44 year olds; (d) 55--64 year olds are significantly different from 25at massive binary systems is particle acceleration. Synchrotron emission at large wavelengths have been observed in several WR binaries, revealing both the existence of relativistic particles and strong magnetic fields. Since current models of particle acceleration depends on the magnetization of the shocks, the study of the evolution of the magnetic fields in wind-wind collision regions is crucial.

In this work we present the main results of recent magneto-hydrodynamical numerical simulations of wind-wind collisions. We also briefly discuss the implications of such modelling on the understanding of particle acceleration in such objects.

Modelling
=========

In order to obtain the dynamical evolution of the shock region of the massive binary system we have employed a number of magneto-hydrodynamical (MHD) numerical simulations. The simulations were performed solving the set of ideal MHD equations, in


is set with a major semi-axis $a = 15$AU and eccentricity $e=0.9$. The magnetic field of both stars is initially set as a dipole with surface polar intensity $B_0 = 1$G, weak compared to the thermal and kinetic terms of the winds.

Results
=======

The numerical integration of each model was performed for 2 complete orbital periods, which corresponds to approximately 11 years. Irrespectively to the model, the amplification of magnetic field at the shock has been shown to be larger than the values predicted by the Rankine-Hugoniot jump conditions [@silva15]. This occurs because the R-H jump conditions are computed for 1D solution of conservation equations, while the shock is multidimensional. It was already shown in @falceta12 that the flow of the post-shocked gas occurs mostly parallel to the field lines,is communicated by what we now call the Einstein equivalence principle (EEP).

Einstein noted that if all bodies fall in the same way in an external gravitational field, an observer in freefall will find that freely falling bodies in his or her neighborhood move with uniform velocities relative to him or her and that the physics of pure particle mechanics in that neighborhood is indistinguishable from mechanics in the absence of gravity. This led him to suggest that a freely falling observer might find all other nongravitational physics in his or her neighborhood to be indistinguishable from such physics in the absence of gravity. Einstein then proceeded to show that if this were true for electrodynamic physics, which was all fundamental physics at the time, light propagating out of


transitions controlling the atomic clock rates, except in metric theories of gravity which predict that they all vanish. Their tensor character reflects the fact that the orientation of the atoms whose transitions govern the atomic clock rates can affect the observed frequency ratio (2). Nonvanishing $\alpha_{ij}$ and $\beta_{ij}$ parameters characterize preferred–frame and preferred–location effects, respectively.

To conclude this discussion of the way in which Lagrangian–based gravitation theories predict outcomes of local, nongravitational test experiments, briefly consider the acceleration of test bodies in an external gravitational field once more. We focus on the freefall of atoms since, as we noted earlier, realistic test bodies are simply assemblages of them.

The analysis of atomic systems outlined above yields an expression for the coordinate energy of any atom in any state of interest.are expressed in terms of the particular theory’s potentials. The efficiency of this approach is somewhat like that provided by the PPN formalism [@TEGP] when dealing with the gravitational dynamics of metric theories.

Analyses carried out in the general nonmetric frameworks discussed below have the additional benefit of identifying mechanisms that lead to preferred–frame or preferred–location effects in entire classes of nonmetric theories and of providing theory–independent parametrizations of such effects that are useful in discussing the results of experiments designed to search for them.

The $TH\epsilon\mu$–formalism {#sec:THepsilonmu}
-----------------------------

The $TH\epsilon\mu$–formalism (see [@LightmanLee73; @TEGP]) is based on the form of the Lagrangian governing the dynamics of point particles with mass $m_i$ and charge $q_i$ and of the electromagnetic field in a static, spherically symmetric background gravitational field described by the phenomenological gravitational


theory is among the most promising candidate for a theory of quantum gravity fully unified with other fundamental interactions, and it has been shown to predict a variety of EEP violations.

For example, departures from universal free fall accelerations have been computed in references [@DamourPolyakov94; @DamourPolyakov96]. The composition–dependent component of test–body acceleration is estimated to be as large as a part in $10^{15}$ of the mean gravitational acceleration. The proposed STEP experiment could easily detect such an anomaly (see [@STEP]).

String theory can also predict a time–varying fine structure constant because of couplings to scalar (dilatonic) fields, for example, see [@Damour99].

In the latest versions of string theory, physical particles and fields are confined to the neighborhoods of $D$–branes and their propagation may be affected by recoil of the branes causedusual metric form can also lead to dispersive propagation and make measurements of the arrival times of photons and neutrinos emitted from the same astrophysical event a test of EEP. The existence of very short duration events like supernova explosions and gamma ray bursts in combinations with the build up of gravitational delays over very great distances makes sharp tests possible.

Recently, limits on gravity–induced dispersion of electromagnetic wave propagation have been inferred from observations of quasars and gamma ray bursters [@Schaefer99]. They constrain $$\frac{c_\gamma(\omega) - c_\gamma(\omega_0)}{c_\gamma(\omega_0)}\, , \quad
\frac{c_\gamma^+ - c_\gamma^-}{c_\gamma^+}\, ,$$ where $c_\gamma(\omega_0)$ is the velocity of the photon for a given frequency $\omega$ or polarization $\pm$. Exploiting rapid time variation of gamma ray bursters, Schaefer [@Schaefer99] is able to to impose sharp constraints on gravity–induced


places among the European elite next season. Perhaps even Everton, with a late surge, can join the scrap. Giroud is relishing it.

"Yes, the championship is until 19 May," the France striker said. "There's eight games to play and a lot of points to play for. I trust in our qualities. I really think we can make fourth place and maybe even third if we continue to play like we are.

"We want to dictate the games. We are confident. We are used to finishing the championship well. And again this season we will do the same. Spurs have to play against Manchester City and Chelsea so it's hard games for them. But every game is difficult; we can see that Chelsea lost in Southampton. We have to keep focus,a touch of playful sophistication. See the Kate Spade Watches Online to witness the hallmarks of the Kate Spade brand. You will be surprised that even the Discount Kate Spade Watches feature the classic, sophisticated styles in saffiano and vachetta leathers. If you are in for fun icons and colour pops, the Kate Spade Discount Watches bring you even those!The Kate Spade Watches For Sale brings great quality and a promise to impart its wearers with elegant and charming looks. The products come in beautiful colours, spanning over the entire visible spectrum and give you the chance to find out the one that delights you the most. It can be gold-plated stainless steel, pearlescent finished or eclectic fluorescent shades that are a must for the trendy and fashionably


A major VPN service has shut down its business operations in Russia with immediate effect, after the country's parliament instituted new anti-terror online surveillance law and began seizing servers.

Private Internet Access, which operates in many countries worldwide, blamed the new laws—which require Russian ISPs to log and hold onto both metadata and the actual content of messages for at least six months—for its abrupt departure. Fugitive NSA whistleblower Edward Snowden, who currently lives in the country, dubbed it "Russia's new Big Brother law."

“We believe that due to the enforcement regime surrounding this new law, some of our Russian Servers (RU) were recently seized by Russian Authorities, without notice or any type of due process,” Private Internet Access said in a blog post on Monday. "Upon learning of thefront page.

and

If your motivation for asking the question is “I would like to
  participate in a discussion about ______”, then you should not be
  asking here

and from Real Questions Have Answers

Constructive subjective questions ....  are more than just mindless
  social fun.


Fourier-Jacobi models in this paper is slightly general than the one in [@GGP12 Section 15].

In more detail, let $$H_r^R=\left\{  \begin{pmatrix} g & & x \\ & 1 & v^t \\ & & u \end{pmatrix} : g \in G_r, x \in Mat_{r \times (n-r)}, v\in F^{n-r}, u \in U_{n-r} \right\}\subset G_{n+1} ,$$ where $U_{n-r}$ is the subgroup of unipotent upper triangular matrices. It is sometimes referred to a Rankin-Selberg subgroup. Let $\psi$ be a generic character on the subgroup $U_{n-r} \ltimes F^{n-r}$, extending trivially to $H_r^R$. We show that the restriction problem for a Bessel model or a Fourier-Jacobi model is equivalent to the problem of determining the corresponding Rankin-Selberg model (Corollary \[cor all same models\]), i.e. determining if $$\mathrm{Hom}_{H_r^R}(\pi_1 \otimes \psi \otimes \nu^{-(n-r)/2}, \pi_2) \neq 0,$$ where$\pi_1$ and $\pi_2$ are respective irreducible $G_{n+1}$ and $G_r$ representations. The second generalization is on Ext-branching laws. The generic case for Ext-branching law is simpler: for respective generic irreducible representations $\pi_1$ and $\pi_2$ of $G_{n+1}$ and $G_n$, $$\mathrm{Hom}_{G_n}(\pi_1, \pi_2)\cong \mathbb C, \quad \mbox{ and } \quad \mathrm{Ext}_{G_n}^i(\pi_1, \pi_2)=0,  \quad \mbox{ for $i\geq 1$ }.$$ The Ext-vanishing part is conjectured by D. Prasad [@Pr18] and proved in [@CS18]. One may consider an analogous problem of Ext-branching laws for Arthur representations. However, there is no such general Ext-vanishing result for Arthur representations, and we do not have a way predicting non-vanishing Ext at the moment. Nevertheless, we formulate a conjecture in Section \[conj ext sum\], which reduces computations of Ext-groups for branching laws to computation of Ext-groups of derivatives.


well-known from [@JPSS83; @GGP12].

By [@Ta86 Theorem 7.1], we may and shall assume that for $1 \leq i \leq r$, $1 \leq j \leq s$, $$m_1+ d_1 \geq m_i+ d_i  \quad \mbox{ and } \quad l_1+e_1 \geq l_j+e_j .$$ We may also assume that $m_1+d_1 > 2$ or $l_1+e_1 > 2$, and so either $\pi_{p,1}$ or $\pi_{q,1}$ is not cuspidal. Otherwise, it is the basic case.

We now consider two cases:

[**Case 1:**]{} $m_1+d_1 \geq l_1+e_1$, which implies $\frac{m_1+d_1-2}{2}+\frac{1}{2} >\frac{l_i+e_i-2}{2}$ for all $i$, and so $\nu^{1/2} \nu^{(d_1+m_1-2)/2}\rho_1$ is in $\mathrm{cupp}(\nu^{1/2}\pi_{p,1})$, but is not in the cuspidal support of any $\pi_{q,i}$.\
Let $$\pi_p' = \pi_{p,2}\times \ldots \times \pi_{p,r} .$$

Let $u=\pi_{p,1}\cong u_{\rho_1}(m_1,d_1)$. We first prove the only if direction and assume that $\mathrm{Hom}_{G_n}(\pi_p, \pi_q) \neq 0$. Using Lemma \[lem reduct main\], there existsis a particular case of Proposition \[prop transfer\] for $m_1=0$, $m_2=0$ and $r=n$.

By Lemma \[lem short exact seq\] again, $$0 \rightarrow \sigma|_M \bar{\times} \pi_2   \rightarrow (\sigma \times \pi_2)|_M \rightarrow \sigma \bar{\times} (\pi_2|_M) \rightarrow 0$$ Since $\sigma$ is cuspidal, $\sigma|_M \cong \Pi_{m_1+m_2+2}$. Now with Proposition \[prop nontrivial bz\] and Lemma \[lem bessel bz realize\], $${}^u\mathrm{ind}_H^{G} \pi_2\otimes \zeta^B = (\sigma|_M \bar{\times} \pi_2)|_{G_n}$$ Similar argument with the proof of Proposition \[prop FJ0\], one reduces to, for all $i$, $$\begin{aligned}
\mathrm{Ext}^i_{G_n}(\sigma \times \pi_2, \pi_1^{\vee} ) \cong & \mathrm{Ext}^i_{G_n}((\sigma|_M \bar{\times} \pi_2)|_{G_n}, \pi_1^{\vee})  \\
 \cong &  \mathrm{Ext}^i_{G_n}( {}^u\mathrm{ind}_H^{G_n} \pi_2\otimes \zeta^B \otimes \nu^{m_2-m_1} , \pi_1^{\vee} )  \\
 \cong & \mathrm{Ext}^i_{G_n}(\pi_1 , {}^u\mathrm{Ind}_H^{G_n} (\pi_2 \otimes \zeta^B)^{\vee}) \quad \mbox{ (taking duals) } \\
\cong & \mathrm{Ext}^i_H(\pi_1, (\pi_2 \otimes \zeta^B)^{\vee} ) \quad \mbox{ (Frobenius reciprocity)}


\cong & \mathrm{Ext}^k_{G_{n+1}}((X^*+Y_{e})|_{G_{n+1}}, \pi_1)  \\
 \cong & \mathrm{Ext}^k_{G_{n+1}}(X^*/I, \pi_1)\oplus  \mathrm{Ext}^k_{G_{n+1}}(Y_{e}/I, \pi_1)     \\
\cong & \mathrm{Ext}^k_{G_{n+1}}(\lambda_2, \pi_1) \oplus \mathrm{Ext}^k_{G_{n+1}}(\lambda_1, \pi_1) \\
\cong & \mathrm{Ext}^k_{G_{n-1}}((\pi_2^{[1]}, {}^{(2)} \pi_1  ) \oplus \mathrm{Ext}^k_{G_{n+1-e}}(\pi_2^{[e-1]}, {}^{(e)}\pi_1)\end{aligned}$$

The first isomorphism follows from that the quotients by $X^*+Y_e$ has zero Ext by looking at the possible composition factors and some computations on comparing cuspidal supports. The fourth isomorphism follows from the adjointness of the functors (see [@CS18 Lemma 2.1] for more discussions).

Since $\pi_1^{\vee} \cong \pi_1$ and $\pi_2^{\vee} \cong \pi_2$, taking duals and using Proposition \[prop bessel transfer\] gives that $$\mathrm{Ext}^k_{G_{n}}(\pi_1, \pi_2) \cong \mathrm{Ext}^k_{G_{n-1}}(\pi_1^{[2]}, {}^{(1)} \pi_2  ) \oplus \mathrm{Ext}^k_{G_{n+1-e}}(\pi_1^{[e]}, {}^{(e-1)}\pi_2) .$$ The last isomorphism follows from [@CS18 Lemma 2.2].

Product preserving extensions
=============================

A motivating example in this and next section is the following. Let $\sigma$Note that $\nu^{(d+m-2)/2+k}\rho$ does not appear in the cuspidal support of irreducible factors of $\pi_1$. With some analysis on Jacquet module from the geometric lemma (see, for example the proof of Lemma \[lem taking jacquet form as st\] below for more details), the only composition factor in $(\langle \mathfrak m \rangle \times \pi_1)_{N_{n+p-q}}$ that has the same cuspidal support as $\langle \Delta \rangle \boxtimes \pi'$ is $$\langle \Delta \rangle \boxtimes \langle\mathfrak m \setminus \left\{ \Delta \right\} \rangle \times \pi_1 .$$ Thus we have $$\mathrm{Hom}(\langle \mathfrak m \rangle \times \pi_1, \langle \Delta \rangle \times \pi' )\cong \mathrm{Hom}(\langle \mathfrak m\setminus \left\{ \Delta \right\} \rangle \times \pi_1, \pi')=\mathrm{Hom}(\langle \mathfrak m' \rangle \times \pi_1, \zeta(\mathfrak m')\times \pi_2)  ,$$ where $\mathfrak m'=\mathfrak m \setminus \left\{ \Delta \right\}$, and so $$\mathrm{Hom}(\langle \mathfrak m


\widetilde{u}  \times \pi_2)\end{aligned}$$ Since we are dealing with admissible representations, the injections in (\[eqn inj second\]) and (\[eqn inj third\]) must be isomorphisms. Hence, we have that: $$\mathrm{Hom}_{G_n}(\pi_1, \pi_2) \cong \mathrm{Hom}_{G_{n+p}}( \widetilde u \times \pi_1, \widetilde u \times \pi_2) .$$

We remark that the above lemma does not require $\pi_1$ and $\pi_2$ to be in $\mathrm{Alg}_{\mathcal C}(G_n)$. In such case, $\widetilde{u}_{\rho}(m,d,k) \times \pi_1$ may have more complicated structure. For example, when $\pi_1$ has unique quotient, the cosocle of $\widetilde{u}_{\rho}(m,d,k)$ may not be irreducible. We give an example here.

Let $\Delta=[\nu^{1/2}, \nu^k]$ for sufficiently large $k$. Let $\pi=\nu^{-1/2} \times \nu^{1/2}$, which is reducible with length $2$. Then $$\langle \Delta \rangle \times \pi$$ has the quotient $\langle [\nu^{-1/2},\nu^k] \rangle \times \nu^{1/2}$ since $\langle \Delta \rangle \times \nu^{-1/2}$ has quotient $\langle [\nu^{-1/2},\nu^k]implies the indecomposability.

Let $\pi_1$ and $\pi_2$ be the two irreducible composition factors of $\pi$. Let $\lambda_i=\widetilde{u}_k \times \pi_i$ ($i=1,2$). $\lambda_1$ and $\lambda_2$ are irreducible, and $\pi_1 \cong \pi_2$ $\Leftrightarrow$ $\lambda_1 \cong \lambda_2$ by Lemma \[lem speh irred\].

Suppose $\widetilde{u}_{k} \times \pi$ is not indecomposable. Let $\Delta=\Delta_{k+1}$. This gives an isomorphism $$\widetilde{u}_{k}\times \pi \cong \lambda_1 \oplus \lambda_2 .$$ and so there exists surjections, by Lemma \[lem surjection steinberg rep\], $$\mathrm{St}(\Delta) \times \widetilde{u}_{k}\times \pi \cong \mathrm{St}(\Delta) \times \lambda_1 \oplus \mathrm{St}(\Delta)\times \lambda_2 \rightarrow \widetilde{u}_{k+1} \times \pi_1 \oplus \widetilde{u}_{k+1} \times \pi_2$$ This implies that:

1.  if $\lambda_1 \not\cong \lambda_2$, then for [*both*]{} $i=1,2$, $$\mathrm{Hom}_G( \mathrm{St}(\Delta) \times \widetilde{u}_{k}\times \pi, \widetilde{u}_{k+1}\times \pi_i) \neq 0 ;$$

2.  if $\lambda_1 \cong \lambda_2$, then $$\mathrm{dim}~\mathrm{Hom}_G(\mathrm{St}(\Delta) \times \widetilde{u}_k \times \pi, \widetilde{u}_{k+1}\times \pi_1) \geq 2 .$$

On the other hand, we


have the following short exact sequence from Lemma \[lem surjection steinberg rep\]: $$0 \rightarrow K \times \pi \rightarrow       \mathrm{St}(\Delta) \times \widetilde{u}_{k} \times \pi \rightarrow \widetilde{u}_{k+1} \times \pi \rightarrow 0 .$$ By Lemma \[lem zero hom kernel\], $\mathrm{Hom}(K\times \pi, \widetilde{u}_{k+1} \times \pi_i) =0$ for $i=1,2$. Hence we have $$\mathrm{Hom}( \widetilde{u}_{k+1}\times \pi, \widetilde{u}_{k+1}  \times \pi_i)\cong  \mathrm{Hom}(\mathrm{St}(\Delta)\times \widetilde{u}_{k} \times \pi, \widetilde{u}_{k+1} \times \pi_i) .$$ However, by induction hypothesis and irreducibility of $\widetilde{u}_{k+1}\times \pi_i$, the former Hom has dimension one for both $i=1$ or $2$ if $\lambda_1 \cong \lambda_2$, and has dimension one for precisely one of $i=1,2$ if $\lambda_1 \not\cong \lambda_2$. This gives a contradiction to (1) or (2) above. Thus $\widetilde{u}_{k}\times \pi$ is indecomposable as desired, and since $\widetilde{u}_k\times \pi$ has lengthand (4). We first fix the length of $X$ to be at most some $n$. We shall prove the statement for arbitrary $Y$ by induction on the length of $Y$.

For an object $Y$ in $\mathcal C$, let $Y_1$ be an irreducible quotient of $Y$. Then we have a short exact sequence: $$0 \rightarrow Y_2 \rightarrow Y \rightarrow Y_1 \rightarrow 0 .$$ Since $\mathcal C$ is Serre, $Y_1$ and $Y_2$ are in $\mathcal C$.

Note that we have the following commutative diagram: $$\xymatrix{ \mathrm{Hom}_{\mathcal A}(X, Y_1) \ar[r] \ar[d] &  \mathrm{Ext}^1_{\mathcal A}(X, Y_2) \ar[r] \ar[d] & \mathrm{Ext}^1_{\mathcal A}(X, Y) \ar[r] \ar[d] & \mathrm{Ext}^1_{\mathcal A}(X, Y_1) \ar[d] \\
 \mathrm{Hom}_{\mathcal B}(\mathcal F(X), \mathcal F(Y_1)) \ar[r] & \mathrm{Ext}^1_{\mathcal B}(\mathcal F(X), \mathcal F(Y_2)) \ar[r] & \mathrm{Ext}^1_{\mathcal B}(\mathcal F(X), \mathcal F(Y)) \ar[r] & \mathrm{Ext}^1_{\mathcal B}(\mathcal


no. 5, 974-1002. W.T. Gan, B.H. Gross, and D. Prasad, Symplectic local root numbers, central critical L values, and restriction problems in the representation theory of classical groups. Sur les conjectures de Gross et Prasad. I., Asterisque No. 346 (2012), 1-109. W.T. Gan, B.H. Gross, and D. Prasad, Branching laws for classical groups: the non-tempered case, arXiv:1911.02783v1. W.T. Gan and A. Ichino, The Gross-Prasad conjecture and local theta correspondence, Invent. Math., [**206**]{} (2016), no. 3, 705-799. M. Gurevich, On restriction of unitarizable representations of general linear groups and the non-generic local Gan-Gross-Prasad conjecture, arXiv: 1808.02640 D. Gourevitch and E. Sayag, Annihilator varieties of distinguished modules of reductive lie algebras, arXiv:2001.11746v2 M. Harris and R. Taylor, The geometry and cohomology of some simple Shimura varieties, With an appendix bydefmodule ExActor.Helper do
  @moduledoc false

  def inject_to_module(quoted, module, env) do
    Module.eval_quoted(
      module, quoted, [],
      aliases: env.aliases,
      requires: env.requires,
      functions: env.functions,
      macros: env.macros,
      file: env.file,
      line: env.line
    )
  end

  def init_generation_state(opts) do
    quote do
      @exactor_global_options unquote(opts)
    end
  end

  def state_var do
    Macro.var(:state_var, ExActor)
  end
end


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    return jsc.elements(formats);
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