Category: 3. Business

December 16, 2025 – Winnipeg, Manitoba – PrairiesCan

From buses and fire trucks to agricultural machinery and mining equipment, Manitoba’s heavy equipment and vehicle (HEV) sector powers global markets and Canadian jobs. With exports to over 80 countries, this cluster supports a robust domestic supply chain and is vital to Canada’s industrial strength. Governments and industry are working together to accelerate innovation and capitalize on new opportunities, further cementing Manitoba as a global leader in HEV manufacturing.

Today, the Honourable Eleanor Olszewski, Minister of Emergency Management and Community Resilience and Minister responsible for Prairies Economic Development Canada (PrairiesCan) announced a federal investment of $3.3 million to help establish the Innovation Garage at RRC Polytech, in partnership with the Vehicle Technology Centre, the Province of Manitoba, and private-sector partners. This amount is in addition to the $3.3 million investment made by the Government of Manitoba by the Honourable Jamie Moses, Minister of Business, Mining, Trade and Job Creation.

The project will expand RRC Polytech’s capabilities to deliver industry-led innovation and productivity improvements by establishing:

• space for industrial-scale collaborative applied research and development for the HEV cluster
• a microgrid lab focused on energy innovation and EV infrastructure, and
• a hydrogen and fuel cell lab to advance clean propulsion systems and other new technologies.

These new facilities will enhance opportunities for students, researchers, and businesses to collaborate. This will help small- and medium-sized enterprises in Manitoba adopt new technologies, strengthen workforce skills, and bring more made-in-Canada innovations to market.

The project will also support the Vehicle Technology Centre’s Clean Technology and Advanced Manufacturing program, which helps manufacturers leverage their investments in industrial applied research and development.

This endeavour — driven by industry and backed by government support — is an example of the collaboration at the heart of the federal government’s new Prairie Partnership Initiative, which aims to grow the economy by supporting ambitious ideas, streamlining supply chains and making it easier for business owners and proponents to ensure federal programs are responsive to regional needs. In this case, reinforcing Manitoba’s leadership in clean tech and advanced manufacturing, and ensuring Canada’s heavy equipment and heavy-duty vehicle sector stays globally competitive and continues to build one strong Canadian economy.

The Federal Trade Commission will host a workshop, titled “Moving Forward: Protecting Workers from Anticompetitive Noncompete Agreements.” The event is open to the public, and will be held on January 27, 2026 from 1:00pm to 5:00pm, at the FTC’s Headquarters. Registration is required to attend in person. Registration is not required to view the livestream.

A noncompete agreement is a contractual term between an employer and a worker that typically blocks the worker from working for a competing employer or starting a competing business after the end of the worker’s employment. In practice, noncompete agreements are often subject to abuse.

The workshop is part of the Trump-Vance FTC’s efforts to highlight the negative impact of noncompete agreements on American workers and put business on notice of its current enforcement priorities.

The workshop will be hosted by the FTC’s Joint Labor Task Force, which was created by Chairman Andrew N. Ferguson to prioritize rooting out and prosecuting deceptive, unfair, and anticompetitive labor-market practices that harm American workers. It follows a recent FTC enforcement action eliminating restrictive and anticompetitive noncompete agreements; a series of letters sent to healthcare companies warning them to review and eliminate any anticompetitive noncompete agreements they may have; and a broad request for information seeking tips to lead to further enforcement actions.

The workshop will include public statements from FTC Commissioners, victims of unfair and anticompetitive noncompete agreements, and leading experts in the field. A full agenda and list of speakers will be available prior to the event. A livestream link will be posted to FTC.gov on the morning of the event. 

WARRENVILLE, Ill. (Dec. 16, 2025) — The Nuclear Regulatory Commission (NRC) has approved a 20-year initial license renewal for Constellation’s Clinton Clean Energy Center and a 20-year subsequent license renewal for its Dresden Clean Energy Center, following a rigorous review of maintenance activities, plant equipment and safety systems at the two Illinois facilities. The approvals allow Clinton to operate through 2047 and the Dresden reactors to operate through 2049 and 2051. Constellation, the nation’s largest operator of clean, reliable nuclear power, is investing more than $370 million to relicense the plants, installing state-of-the-art upgrades to increase efficiency and ensure safety and reliability for decades to come.

“In the last ten years, we’ve invested over $3 billion in our high-performing Illinois nuclear facilities to power the state’s economy with clean, reliable energy,” said Bryan Hanson, Constellation Executive Vice President and Chief Generation Officer. “These license extensions will allow Clinton and Dresden to stay online for another two decades, preserving more than 2,200 family-sustaining jobs and $8.1 billion in federal, state and local tax dollars.”

“Today’s announcement is a win for workers, communities, and Illinois’ clean energy future,” said Sean McGarvey, President of North America’s Building Trades Union (NABTU). “By renewing the operating licenses for the Clinton and Dresden clean energy centers, Constellation is ensuring decades of good union jobs while delivering reliable, carbon-free power. Our highly skilled members are proud to operate and maintain these plants safely every day. NABTU, the IBEW and all our affiliates value this long-term commitment, which demonstrates the success of labor and industry working together effectively to deliver the energy solutions our nation needs.”

At Clinton, two new auxiliary transformers and two advanced equipment chillers are delivering higher system reliability, while upgrades to the plant’s condensate polisher system offer greater protection from component degradation. At Dresden, operators are now using next-generation feedwater level control technology to enhance reactor safety, while a new main power transformer purchased for the plant will deliver state-of-the art electrical system monitoring and control. With these and other upgrades in place, Clinton and Dresden continue to operate at higher levels of safety, reliability and efficiency than the day they came online.

“We are looking forward to many more years of collaboration with the Clinton Clean Energy Center,” said Clinton Mayor Helen Michelassi. “We are so proud to have Constellation in our community and look forward to decades of impactful support for volunteer events and non-profit work to benefit the region.”

While these license renewals give Constellation the regulatory approval needed to operate Clinton and Dresden for another two decades, actual operation is contingent on each plant’s financial viability. At Clinton, the facility’s carbon-free energy is secure as a result of the 20-year agreement with Meta announced in August. The deal supports the continued operation, expansion and relicensing of the 1,121-megawatt Clinton facility following the expiration of the state’s Zero Emission Credit (ZEC) program in May 2027. 

“The renewal of Dresden’s operating license reinforces this region’s standing as a hub for business growth and industrial innovation,” said Nancy Norton, president and CEO of Grundy County Economic Development. “Reliable, emissions-free energy is the foundation of economic progress, and the Dresden Clean Energy Center plays a vital role in keeping our communities and the businesses that depend on them moving forward. As new industries look to invest and expand in Grundy County, Dresden’s continued operation ensures that our region remains competitive, resilient, and ready for the future. It’s a win for our community and a step toward a stronger future for everyone who calls this region home.”

Constellation’s clean energy portfolio includes 26 nuclear reactors in six states, and the company is investing billions to keep America’s largest nuclear fleet running at world-class levels of safety, reliability and efficiency. 

Definition 1. A co-transition event is a transition event in the system where two or more components change simultaneously. That is, a reaction where the step size d has more than one vector component.

An example would be a conversion event, where a chemical species $z_m$ converts to another chemical species $z_n$

${\displaystyle {\displaystyle (z_m,z_n)\stackrel{W(z_m)}{\to }(z_m-1,z_n+1)}}$

According to our framework, an arrow would be drawn from $z_m$ to $z_n$ in the network if the above reaction was part of the system. Another example would be two molecules $z_m$, $z_n$ that bind to form a complex $z_l$

${\displaystyle {\displaystyle (z_m,z_n,z_l)\stackrel{W(z_m,z_n)}{\to }(z_m-1,z_n-1,z_l+1).}}$

If the above reaction was part of the system, an arrow would be drawn from $z_m$ to $z_n$, from $z_n$ to $z_m$, and from both $z_m$, $z_n$ to $z_l$.

In order to derive Equation 2, we need to assume that no components in ${\mathbf{z}}_{\text{aff}}^c$ are part of a co-transition event with any variable in ${\mathbf{z}}_{\text{aff}}$. We thus begin by proving the following lemma.

Lemma 1. Let Z_k be a component that is not affected by X or Y. For any network of the class in Appendix 1—figure 21B (Equations 4.3; 4.4), there exists another network with the exact same dynamics in X, Y, and Z_k, but where no components in ${\mathbf{z}}_{\text{aff}}^c$ are part of a co-transition event with any component in ${\mathbf{z}}_{\text{aff}}$.

Proof of Lemma 1. Let the following co-transition reaction be part of the system, where $\{a_k\}$ are variables in ${\mathbf{z}}_{\text{aff}}$ and $\{b_k\}$ are variables in ${\mathbf{z}}_{\text{aff}}^c$

(5.1)

${\displaystyle {\displaystyle (\mathbf{a},\mathbf{b})\stackrel{W(\mathbf{b})}{\to }(\mathbf{a}+{\mathbf{d}}_a,\mathbf{b}+{\mathbf{d}}_b).}}$

By definition of ${\mathbf{z}}_{\text{aff}}$ and ${\mathbf{z}}_{\text{aff}}^c$, the reaction rate $W$ in the above reaction cannot depend on the variables $\{a_k\}$. However, because a is part of ${\mathbf{z}}_{\text{aff}}$, the $\{a_k\}$ variables must be affected by X or Y. Therefore, there must exist one or more reactions, labeled with $i\in \{1,2,\dots \}$, in the system, that change a with reaction rates that depend on the variables affected by X or Y

(5.2)

${\displaystyle {\displaystyle \mathbf{a}\stackrel{W_i\left({\mathbf{z}}_{\text{aff}},{\mathbf{z}}_{\text{aff}}^c\right)}{\to }\mathbf{a}+{\mathbf{d}}_i\text{for}i=1,2,\dots }}$

Note that the above reactions cannot make changes to b; otherwise, the $\{b_k\}$ variables would not be in the variables not affected by X or Y. We now consider an exact copy of the whole system z and the system reactions, with the change that the a variables are decomposed into two sets of mock variables. Specifically, we define the variables $\{a_k^{int}\}$ and $\{a_k^b\}$ that undergo the following reactions

${\displaystyle {\displaystyle \begin{array}{rl}({\mathbf{a}}^b,\mathbf{b})& \stackrel{W(\mathbf{b})}{\to }\left({\mathbf{a}}^b+{\mathbf{d}}_a,\mathbf{b}+{\mathbf{d}}_b\right)\\ {\mathbf{a}}^{int}& \stackrel{W_i\left({\mathbf{z}}_{\text{aff}},{\mathbf{z}}_{\text{aff}}^c\right)}{\to }{\mathbf{a}}^{int}+{\mathbf{d}}_i\text{for}i=1,2,\dots ,\end{array}}}$

which correspond to the reactions in Equations 5.1; 5.2. We replace all the explicit a dependencies in the reaction rates of the system with ${\mathbf{a}}^{int}+{\mathbf{a}}^b$. As a result, all the reactions that depended on a are unchanged, but now we can put the ${\mathbf{a}}^b$ variables in ${\mathbf{z}}_{\text{aff}}^c$, and we can put the ${\mathbf{a}}^{int}$ variables in ${\mathbf{z}}_{\text{aff}}$. We are left with a system where the ${\mathbf{a}}^{int}$ are not part of a co-transition event with variables in ${\mathbf{z}}_{\text{aff}}^c$, and the dynamics of X and Y remain unchanged. Moreover, none of the reaction rates that govern the dynamics of any component in the original ${\mathbf{z}}_{\text{aff}}^c$ have been altered, meaning the dynamics of Z_k remain unchanged. Such a decomposition can be done for any co-transition reaction that involves components from ${\mathbf{z}}_{\text{aff}}$ and ${\mathbf{z}}_{\text{aff}}^c$.

We now let $Z_k$ correspond to another component of interest in the system, as a continuous-time Markov process. It can be any stochastic process that can be measured, like the abundance of a molecular species in the network, the size of the cell, or any parameter that can influence the reaction rates of the system.

Theorem 1. Let $Z_k$ be a component in ${\mathbf{z}}_{\text{aff}}^c$. If the averages $⟨x_t⟩$, $⟨y_t⟩$ and the covariances $\text{Cov}(x_t,z_{k,t})$, $\text{Cov}(x_t,z_{k,t})$ over the ensemble have reached a stationary state (i.e. they have become constant over time), then ${\eta }_{x{z}_k}={\eta }_{y{z}_k}$.

Proof of Theorem 1. We condition on the components not affected by X or Y, ${\mathbf{z}}_{\text{aff}}^c[-\mathrm{\infty },t]$. This corresponds to a hypothetical system where all the variables in ${\mathbf{z}}_{\text{aff}}^c$ become deterministic time-varying signals $\{z_k(t)\}$. The reactions governing X and Y in the conditional system become

(5.3)

${\displaystyle {\displaystyle \begin{array}{cc}x\stackrel{R({\mathbf{z}}_{\text{aff}},t)}{\to }x+1& y\stackrel{\alpha R({\mathbf{z}}_{\text{aff}},t)}{\to }y+1\\ x\stackrel{x\beta (t)}{\to }x-1& y\stackrel{y\beta (t)}{\to }y-1\end{array}}}$

where $R\left({\mathbf{z}}_{\text{aff}},t\right)=R\left({\mathbf{z}}_{\text{aff}},{\mathbf{z}}_{\text{aff}}^c(t)\right)$ and $\beta (t)=\beta \left({\mathbf{z}}_{\text{aff}}^c(t)\right)$ now have an explicit time dependence from the conditioned history ${\mathbf{z}}_{\text{aff}}^c[-\mathrm{\infty },t]$. We let $A$ be the set of all integers k such that the k-th reaction in Equation 4.1 leads to a change in at least one of the components in ${\mathbf{z}}_{\text{aff}}$. In the conditional probability space, the components affected in ${\mathbf{z}}_{\text{aff}}$ follow the following reactions

(5.4)

${\displaystyle {\displaystyle {\mathbf{z}}_{\text{aff}}\stackrel{W_k({\mathbf{z}}_{\text{aff}},t)}{\to }{\mathbf{z}}_{\text{aff}}+{\mathbf{d}}_k\mathrm{\forall }k\in A,}}$

where $W_k({\mathbf{z}}_{\text{aff}},t)=W_k\left({\mathbf{z}}_{\text{aff}},{\mathbf{z}}_{\text{aff}}^c(t)\right)$ now has an explicit time dependence from the conditioned history of the variables not affected by X or Y. Note that if some components in ${\mathbf{z}}_{\text{aff}}^c$ were part of a co-transition event with components in ${\mathbf{z}}_{\text{aff}}$, then Equations 5.3; 5.4 would not hold. This is because conditioning on the history of those extrinsic variables effectively conditions on those birth events in ${\mathbf{z}}_{\text{aff}}$ that are caused by those co-transitions. However, from Lemma 1, we can always work with another network in which there are no such co-transition events, and where the dynamics of X and Y remain unchanged.

This conditional system follows the following master equation

${\displaystyle {\displaystyle {\displaystyle \begin{array}{ll}{\displaystyle \frac{d}{dt}}& P\left(x,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)=\\ & {\displaystyle \sum _{k\in A}\left[W_k\left({\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}-{\mathbf{d}}_k,t\right)P\left(x,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}-{\mathbf{d}}_k,t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)-W_k\left({\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\right)P\left(x,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)\right]}\\ & {\displaystyle +R\left(x-1,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\right)P\left(x-1,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)-R\left(x,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\right)P\left(x,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)}\\ & {\displaystyle +\alpha R\left(x,y-1,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\right)P\left(x,y-1,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)-\alpha R\left(x,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\right)P\left(x,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}};t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)}\\ & {\displaystyle +(x+1)\beta (t)P\left(x+1,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)-x\beta (t)P\left(x,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)}\\ & +(y+1)\beta (t)P\left(x,y+1,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right)-y\beta (t)P\left(x,y,{\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}},t\mid {\mathbf{z}}_{\mathrm{a}\mathrm{f}\mathrm{f}}^c[-\mathrm{\infty },t]\right).\end{array}}}}$

We consider the averages of X and Y conditioned on the upstream history, $\overline{x}(t)=E\left[x_t|{\mathbf{z}}_{\text{aff}}^c[-\mathrm{\infty },t]\right]$ and $\overline{y}(t)=E\left[y_t|{\mathbf{z}}_{\text{aff}}^c[-\mathrm{\infty },t]\right]$, where $x_t$ and $y_t$ are the X and Y abundances at time t. From the above master equation, the time-evolution for these first moments can be derived (Joly-Smith et al., 2021; Hilfinger and Paulsson, 2011)

(5.5)

${\displaystyle {\displaystyle \frac{d\overline{x}}{dt}=\overline{R}(t)-\overline{x}\overline{\beta }(t)\mathrm{\&}\frac{d\overline{y}}{dt}=\alpha \overline{R}(t)-\overline{y}\overline{\beta }(t),}}$

where $\overline{R}(t)=E\left[R(x_t,y_t,{\mathbf{z}}_{\text{aff}},t)|{\mathbf{z}}_{\text{ aff}}^c[-\mathrm{\infty },t]\right]$ and $\overline{\beta }(t)=E\left[\beta ({\mathbf{z}}_{\text{aff}}^c)|{\mathbf{z}}_{\text{aff }}^c[-\mathrm{\infty },t]\right]$ are the average production and degradation rates conditioned on the history of the variables not affected by X or Y. Note that $\overline{\beta }(t)=E\left[\beta ({\mathbf{z}}_{\text{aff}}^c)|{\mathbf{z}}_{\text{aff }}^c[-\mathrm{\infty },t]\right]=\beta ({\mathbf{z}}_{\text{aff}}^c(t))=\beta (t)$, because the time trajectory of ${\mathbf{z}}_{\text{aff}}^c$ is set through the conditioning on the upstream history. We can then take the expectation of $\overline{x}$ over all possible histories of ${\mathbf{z}}_{\text{aff}}^c$ to get

(5.6)

${\displaystyle {\displaystyle E[\overline{x}(t){]}_{\text{histories}}=E{\left[E\left[x_t\mid {\mathbf{z}}_{\text{aff}}^c[-\mathrm{\infty },t]\right]\right]}_{\text{histories}}=⟨x_t⟩,}}$

which follows from the law of total expectation. We now let $Z_k$ correspond to any component in the network that is not affected by X or Y. It can be a molecular abundance, concentration, or another stochastic cellular variable like the growth rate of the cell. It follows that

(5.7)

${\displaystyle {\displaystyle \begin{array}{rl}E{\left[\overline{x}(t)z_k(t)\right]}_{\text{histories}}& =E{\left[E\left[x_t\mid {\mathbf{z}}_{\text{aff }}^c[-\mathrm{\infty },t]\right]\cdot E\left[z_{k,t}\mid {\mathbf{z}}_{\text{aff }}^c[-\mathrm{\infty },t]\right]\right]}_{\text{histories }}\\ & =E{\left[E\left[x_t{z}_{k,t}\mid {\mathbf{z}}_{\text{aff }}^c[-\mathrm{\infty },t]\right]\right]}_{\text{histories }}=⟨x_t{z}_{k,t}⟩\end{array},}}$

where the second step comes from the fact that conditioning on the history of ${\mathbf{z}}_{\text{aff}}^c$ effectively also conditions on the history of $Z_k$ with $z_k(t)=E\left[z_{k,t}|{\mathbf{z}}_{\text{aff}}^c[-\mathrm{\infty },t]\right]$ (so x and $z_k$ are independent when conditioning on the ${\mathbf{z}}_{\text{aff}}^c$ history), the last step follows from the law of total expectation, and $z_{k,t}$ is the measured amount of $Z_k$ at time t. From Equations 5.6; 5.7, it follows that

(5.8)

${\displaystyle \begin{array}{c}\text{Cov}(x_t,z_{k,t})=\text{Cov}(\overline{x}(t),{\overline{z}}_k(t)),\end{array}}$

where ${\overline{z}}_k(t)=E\left[z_{k,t}|{\mathbf{z}}_{\text{aff}}^c[-\mathrm{\infty },t]\right]=z_k(t)$, where the last step comes from the fact that the time trajectory of $z_k$ is set through the conditioning of the upstream histories. Intuitively, Equation 5.8 says that when X does not affect $Z_k$, the stochastic fluctuations of X average out when taking the covariance between X and $Z_k$. Strikingly, this is independent of any type of feedback that X may impose through interactions in the cloud of components $\mathbf{z}(t)$. As a result, the same should hold for Y, and since $\overline{y}(t)$ is governed by the same differential equation as $\overline{x}$, the intrinsic fluctuations that differentiate X and Y will average out when taking the covariances with $Z_k$.

That is, dividing the right equation in Equation 5.5 with α, we write the general solution for $\overline{x}(t)$ and $\overline{y}(t)/\alpha$, and find

(5.9)

${\displaystyle {\displaystyle \overline{x}(t)=\overline{x}(0)e^{-{\int }_0^t\beta (u)du}+{\int }_0^t{e}^{-\left({\int }_0^t\beta (u)du-{\int }_0^{t^{\prime }}\beta (v)dv\right)}R(t^{\prime })d{t}^{\prime }}}$

(5.10)

${\displaystyle {\displaystyle \overline{y}(t)/\alpha =\overline{y}(0)e^{-{\int }_0^t\beta (u)du}/\alpha +{\int }_0^t{e}^{-\left({\int }_0^t\beta (u)du-{\int }_0^{t^{\prime }}\beta (v)dv\right)}R(t^{\prime })d{t}^{\prime }}}$

Taking the average over all histories and subtracting the equations we have

(5.11)

${\displaystyle {\displaystyle \begin{array}{rl}E[\overline{x}(t){]}_{\text{histories}}-E[\overline{y}(t){]}_{\text{histories}}& {\displaystyle =E{\left[\left(\overline{x}(0)-\overline{y}(0)/\alpha \right)e^{-{\int }_0^t\beta (u)du}\right]}_{\text{histories}}}\\ \Rightarrow ⟨x_t⟩-⟨y_t⟩/\alpha & {\displaystyle =E{\left[\left(\overline{x}(0)-\overline{y}(0)/\alpha \right)e^{-{\int }_0^t\beta (u)du}\right]}_{\text{histories}},}\end{array}}}$

where in the second step we used Equation 5.6 which also holds for $y$ by symmetry. We now invoke the requirement that the averages $⟨x_t⟩$ and $⟨y_t⟩$ are stationary, meaning they are constant over time. In that case, $⟨x_t⟩-⟨y_t⟩/\alpha$ is constant over time, and so

(5.12)

${\displaystyle {\displaystyle ⟨x_t⟩-⟨y_t⟩/\alpha =\underset{t\to \mathrm{\infty }}{lim}\left(⟨x_t⟩-⟨y_t⟩/\alpha \right).}}$

Substituting Equation 5.11, we thus have

(5.13)

${\displaystyle {\displaystyle ⟨x_t⟩-⟨y_t⟩/\alpha =E{\left[\left(\overline{x}(0)-\overline{y}(0)/\alpha \right)e^{-{\int }_0^{\mathrm{\infty }}\beta (u)du}\right]}_{\text{histories}}.}}$

Now, we must have ${\int }_0^{\mathrm{\infty }}\beta (u)du\to \mathrm{\infty }$ when $⟨\beta {⟩}_t=\underset{T\to \mathrm{\infty }}{lim}\frac{1}{T}{\int }_0^T\beta (u)du>0$. Therefore, the right-hand side of Equation 5.13 becomes 0:

(5.14)

${\displaystyle {\displaystyle ⟨x_t⟩-⟨y_t⟩/\alpha =E{\left[\left(\overline{x}(0)-\overline{y}(0)/\alpha \right)e^{-{\int }_0^{\mathrm{\infty }}\beta (u)du}\right]}_{\text{histories}}=0,}}$

Similarly, we now multiply Equations 5.10; 5.9 with $z_k(t)$, average over all histories, and subtract to obtain

(5.15)

${\displaystyle {\displaystyle \begin{array}{rl}llE[\overline{x}(t)z_k(t){]}_{\text{histories}}-E[\overline{y}(t)z_k(t){]}_{\text{histories}}& {\displaystyle =E{\left[\left(\overline{x}(0)-\overline{y}(0)/\alpha \right)z_k(t)e^{-{\int }_0^t\beta (u)du}\right]}_{\text{histories}}}\\ \Rightarrow ⟨x_t{z}_{k,t}⟩-⟨y_t{z}_{k,t}⟩/\alpha & {\displaystyle =E{\left[\left(\overline{x}(0)-\overline{y}(0)/\alpha \right)z_k(t)e^{-{\int }_0^t\beta (u)du}\right]}_{\text{histories}}=0,}\end{array}}}$

where in the second step we used Equation 5.7 which also holds for y by symmetry. The last step follows when $⟨x_t{z}_{k,t}⟩$ and $⟨y_t{z}_{k,t}⟩$ have reached stationarity and are constant over time, along with $⟨\beta {⟩}_t=\underset{T\to \mathrm{\infty }}{lim}\frac{1}{T}{\int }_0^T\beta (u)du>0$.

It then follows from Equations 5.14; 5.15 that

(5.16)

${\displaystyle {\displaystyle ⟨x⟩=⟨y⟩/\alpha \mathrm{\&}\text{Cov}(x,z_k)=\text{Cov}(y,z_k)/\alpha .}}$

Dividing $\text{Cov}(x,z_k)$ by $⟨x⟩⟨z⟩$, and $\text{Cov}(y,z_k)/\alpha$ by $⟨y⟩⟨z⟩/\alpha$, we find ${\eta }_{x{z}_k}={\eta }_{y{z}_k}$.

If the reporter Y is engineered to be passive (i.e., it does not affect components in the network), then a violation of Equation 2 would imply that X affects $Z_k$. Otherwise, such a violation would imply that X or Y affect $Z_k$.

Thus far, we assumed that all the components not affected by X or Y are part of a continuous-time Markov chain. This was in order to make a rigorous definition of causal interaction in our framework as a path in the topology of the transition rates. Alternatively, if we relax the requirement that the components not affected by X or Y be Markov chains (i.e. they can be a set of arbitrary stochastic processes), we can operationally define ‘no causal interaction from X or Y’ to mean that we can condition on the history of those stochastic processes and write down Equations 5.3; 5.4. We can then operationally define any violation of Equation 2 as a ‘causal interaction from X or Y’ to a stochastic process $Z_k$.

Washington, DC: The Executive Board of the International Monetary Fund (IMF) today completed the first and second reviews of Sierra Leone’s arrangement under the Extended Credit Facility (ECF). The completion of the reviews enables the immediate disbursement of SDR 58.3 million (about US$79.8 million), bringing total disbursements under the ECF arrangement to SDR 93.3 million (about US$127.8 million).

The ECF arrangement was approved by the IMF Board on October 31, 2024, to maintain debt sustainability, address fiscal dominance, reduce inflation, rebuild reserves, support growth, and strengthen governance, institutions, and the rule of law (see Press Release No. 24/432). The first review was delayed amid spending overruns in 2024—financed in part by central bank purchases of government securities—as well as reserve depletion, and reform delays. However, program performance has since improved.

In completing the first and second reviews, the Executive Board approved waivers of non-observance of the end-December 2024 performance criteria pertaining to net credit to government, net domestic assets, and net international reserves, and the end-June 2025 performance criterion on net international reserves, all based on corrective actions carried out by the authorities.

Sierra Leone’s economic outlook remains stable, with growth projected to reach 4.4 percent in 2025, supported by the mining and agriculture sectors. Inflation declined to 4.4 percent in October 2025 amid the ambitious macroeconomic policy tightening and a stable leone and is projected to remain in single digits over the medium term. However, reserves dropped to 1.5 months of imports as of end-September, and debt remains at high risk of distress. The outlook faces considerable risks, including from potential reform fatigue due to the sizable magnitude of the required fiscal adjustment.

At the conclusion of the Executive Board’s discussion, Mr. Bo Li, Acting Chair and Deputy Managing Director, made the following statement:

“The authorities have brought the ECF back on track following program slippages in 2024, and the economy is reacting favorably. Inflation declined to 4.4 percent by October 2025, the leone remains stable, growth is near potential, and the cost of borrowing has dropped to sustainable levels. However, debt remains at high risk of distress and reserves have fallen to 1.5 months of imports in September.

“The authorities’ plans to tighten fiscal policy more than previously anticipated given the previous fiscal slippages is imperative. Steadfast implementation of recent revenue measures will be key, alongside improvements in tax compliance and administration. Public financial management reforms will help avoid fiscal overruns and support expenditure restraint, but social spending needs to be protected.

“Maintaining debt sustainability will require adhering to the ambitious fiscal adjustment path, supported by robust improvements in debt management practices. Efforts should be intensified to secure grants and concessional financing, lengthen debt maturities, broaden the investor base, build buffers, and ensure that debt securities are issued at sustainable rates.

“Monetary policy can continue transitioning to a neutral stance given low inflation and continued fiscal consolidation. Efforts to enhance central bank safeguards and the monetary policy framework should continue. Rebuilding reserves is an urgent priority, and the authorities should continue to allow the exchange rate to adjust flexibly to shocks. FX spending by the government needs to be curtailed.

“Ongoing efforts to strengthen financial sector oversight, regulation, and safety nets will improve financial stability. Meanwhile, the authorities should continue to proactively address solvency issues in the banking system.

“Progress with structural reforms will underpin Sierra Leone’s growth potential. The publication of the Governance and Corruption Diagnostic report is welcome. The authorities should now focus on its steadfast implementation to enhance governance and address corruption vulnerabilities.”

 

Sierra Leone: Selected Economic Indicators

2024 2025 2026   Prel. Proj. Proj.                 Output (annual percentage change)       Real GDP growth 4.3 4.4 4.5 Real GDP growth, excl. iron ore 3.7 4.3 4.4         Prices (annual percentage change)       Inflation, end of period (%) 13.8 7.0 9.0                 Central Government Finances (percent of non-iron ore GDP) Revenue, excl. grants 10.1 10.8 11.8 Grants 3.4 1.9 2.0 Expenditure and net lending 19.1 18.1 16.2 Overall balance -5.6 -5.4 -2.3 Public debt 50.8 49.3 47.3         Money and credit (annual percentage change)       Broad money 18.0 14.5 13.6 Credit to the private sector 41.2 31.2 21.0         Balance of payments(percent of non-iron ore GDP)       Current account -7.5 -5.1 -3.1 Gross reserves (months of imports) 2.1 2.0 2.5 External debt 31.0 28.4 27.1                 Sources: Central Bank, Ministry of Finance, Statistics Sierra Leone, and Fund staff estimates and projections

 

 

 

WASHINGTON — DEC. 16, 2025 — The U.S. Department of Health and Human Services (HHS) today announced the appointment of Harvey Risch, M.D., Ph.D., as chairman of the President’s Cancer Panel. The panel, part of the National Institutes of Health’s (NIH) National Cancer Institute, is charged with monitoring the development and execution of the activities of the National Cancer Program and reporting to the president on progress, efficacy, and opportunities for improvement in the national effort against cancer. The Panel was established by law through the National Cancer Act of 1971.

Dr. Risch is Professor Emeritus and Senior Research Scientist in and Senior Research Scientist in Epidemiology at the Yale School of Public Health and Yale School of Medicine. As chairman of the President’s Cancer Panel, Dr. Risch plans to accelerate American innovations in cancer prevention and increase the public’s awareness of reproductive, dietary, occupational, environmental, and immune system-related factors that influence cancer etiology.

“Dr. Risch brings the expertise and resolve needed to identify the root causes of cancer in America,” said Health and Human Services Secretary Robert F. Kennedy, Jr. “He will push this work forward, confront the factors driving cancer rates, and provide the public with science they can trust. This appointment strengthens our national fight against cancer and reflects our duty to protect Americans’ health with transparency, independence, and rigorous inquiry.”

“The field of cancer prevention is only 75 years old,” said NIH Director Jay Bhattacharya. “Great developments in our understanding of this subject should not shock us — they should be expected. Dr. Risch is a distinguished pioneer in the study of cancer epidemiology with the background to help bring the revelations to the field we’re seeking.”

“Cancer remains one of the leading causes of death in the United States,” said U.S. Senator Ron Johnson (R-WI). “Dr. Risch has the experience and leadership to guide the President’s Cancer Panel toward discoveries that can hopefully reduce those numbers. Dr. Risch brings knowledge and courage to confront the cancer epidemic with an open mind and help make America healthy again.”

“I am thankful for the opportunity President Trump has given me to transform cancer prevention in the United States,” said Dr. Risch. “This Panel has access to the best minds, cutting edge science, and vast resources required to radically advance Americans’ understanding of cancer development, diagnosis, and prevention. We are sitting on the treasure trove of knowledge necessary to demystify the causes of cancer, and we can use that knowledge to help Americans live fuller, freer lives. Cancer does not have to loom over the American people as an unknowable specter.”

Dr. Risch has dedicated his career to studying cancer etiology, prevention, early diagnosis, and epidemiological methods. His research has included studies of ovarian cancer, pancreas cancer, lung cancer, bladder cancer, esophageal and stomach cancer, and cancers related to the use of oral contraceptives and noncontraceptive estrogens.

Prior to his tenure at Yale, Dr. Risch received his M.D. degree from the University of California at San Diego and his Ph.D. in mathematical modeling of infectious epidemics from the University of Chicago. After serving as a postdoctoral fellow in epidemiology at the University of Washington, Dr. Risch taught epidemiology and biostatistics at the University of Toronto.

Dr. Risch has authored more than 400 original peer-reviewed research papers, which have been cited by other scientific publications more than 59,000 times. He is an Editor of the International Journal of Cancer, was Associate Editor of the Journal of the National Cancer Institute for 25 years, and for six years was a Member of the American Journal of Epidemiology’s Board of Editors.