It's official:
The US 30Y Note Yield has now traded above 5.00% for the longest stretch since 2007.
So far this year, the 30Y Note Yield has traded above 5.00% for 27 days, or ~19% of all trading sessions.
Just months ago, markets saw 3+ rate cuts in 2026.
Talk about a turn of events.
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The US 30Y Note Yield has now traded above 5.00% for the longest stretch since 2007.
So far this year, the 30Y Note Yield has traded above 5.00% for 27 days, or ~19% of all trading sessions.
Just months ago, markets saw 3+ rate cuts in 2026.
Talk about a turn of events.
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Gradient, jacobian, and hessian are really answering three different questions about a function. the gradient asks, “which direction should i move to increase this value the fastest?” the jacobian asks, “if i change the inputs a little, how do all the outputs change?” the hessian goes one level deeper and asks, “how is that direction itself changing?” once you see them as different layers of information instead of different equations, the notation becomes much less intimidating.
imagine you’re hiking up a mountain. the gradient points toward the steepest path uphill. now imagine the mountain itself is constantly changing shape as you walk. the hessian tells you whether the surface is flattening out, becoming steeper, or curving in another direction. the jacobian is slightly different. instead of a single mountain, imagine a machine with many knobs and many outputs. the jacobian tells you how every output responds when you turn each knob. it is the local map between inputs and outputs.
this is why these three ideas appear everywhere in robotics, optimization, computer vision, and machine learning. gradient descent uses the gradient to decide where to move. robot kinematics uses the jacobian to convert joint motion into end effector motion. second order optimization uses the hessian to understand curvature and converge faster. they are not separate mathematical tricks. they are different ways of asking how a system changes, and change is ultimately what engineering is trying to understand.
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imagine you’re hiking up a mountain. the gradient points toward the steepest path uphill. now imagine the mountain itself is constantly changing shape as you walk. the hessian tells you whether the surface is flattening out, becoming steeper, or curving in another direction. the jacobian is slightly different. instead of a single mountain, imagine a machine with many knobs and many outputs. the jacobian tells you how every output responds when you turn each knob. it is the local map between inputs and outputs.
this is why these three ideas appear everywhere in robotics, optimization, computer vision, and machine learning. gradient descent uses the gradient to decide where to move. robot kinematics uses the jacobian to convert joint motion into end effector motion. second order optimization uses the hessian to understand curvature and converge faster. they are not separate mathematical tricks. they are different ways of asking how a system changes, and change is ultimately what engineering is trying to understand.
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JUST IN: Burkina Faso leader Ibrahim Traoré says he will "never allow" Sharia law in the country
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NOW - Trump attends the dignified transfer of the four American soldiers killed in the Middle East.
1st Lt. Tyler Feehan
Sgt. Michael Swinton
Sgt. Angel Rampersad
Pvt. Isabella Gonzales
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1st Lt. Tyler Feehan
Sgt. Michael Swinton
Sgt. Angel Rampersad
Pvt. Isabella Gonzales
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BREAKING: Bitcoin ETFs attracted +$900 million in inflows last week, the largest weekly inflow since early May.
This marks a sharp acceleration from +$197 million in inflows in the prior week.
The largest Bitcoin ETF, $IBIT, led the surge, attracting +$193 million last week, after bringing in +$282 million the week before.
Subsequently, on Monday and Tuesday, $IBIT saw additional inflows of +$115 million and +$164 million.
This brings the total $IBIT inflows to +$501 million so far in July, on track for the largest monthly intake since April and the 3rd-largest this year.
Investor demand for Bitcoin funds is rapidly improving.
🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶
This marks a sharp acceleration from +$197 million in inflows in the prior week.
The largest Bitcoin ETF, $IBIT, led the surge, attracting +$193 million last week, after bringing in +$282 million the week before.
Subsequently, on Monday and Tuesday, $IBIT saw additional inflows of +$115 million and +$164 million.
This brings the total $IBIT inflows to +$501 million so far in July, on track for the largest monthly intake since April and the 3rd-largest this year.
Investor demand for Bitcoin funds is rapidly improving.
🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶