Ancient humans in Africa changed their behaviour in a major way 70,000 years ago, which could explain how their descendants managed to people the rest of the world

In his first large-scale public presentation after receiving the Turing Award, Dr. Richard S. Sutton presents, “The Era of Experience & The Age of Design,” r…

“If you pass all the thinking to GenAI, then the result is that the developer isn’t doing any thinking.”

It is a famous result of Kolmogorov that there exists a (Lebesgue) integrable function on the torus such that the partial sums of Fourier series of $f$ diverge almost everywhere (a.e.). More specifically, he exhibited an $f\in L^{1}(\mathbb{T})$ such that.

\begin{align*} \sup_{N\geq 1}\left|S_{N}f(x)ight|=\sup_{N\geq 1}\left|(f\ast D_{N})(x)ight|=\infty, \qquad\forall \text{ a.e. } x\in\mathbb{T}, \end{align*} where $S_{N}$ is the $N^{th}$ partial sum and $D_{N}$ is the $N^{th}$ Dirichlet kernel given below. \begin{align*} S_{N}f(x):=\sum_{\left|night|\leq N}\widehat{f}(n)e^{2\pi inx}, \quad D_{N}(x):=\dfrac{\sin 2\pi(N+\frac{1}{2})x}{\sin \pi x} \end{align*} and we identify $\mathbb{T}$ with the unit interval $[0,1]$.

I have read, for example pg. 118 in [Pinsky], that Kolmogorov’s counterexample can be replicated in the context of the Fourier transform on the real line $\mathbb{R}$, showing that $L^{1}$ pointwise Fourier inversion can fail quite horribly. If my understanding is correct, then the following claim is true:

Dr Alan D. Thompson

The largest review of “gold standard” antidepressant withdrawal studies to date has identified the type and incidence of symptoms experienced by people discontinuing antidepressants, finding most people do not experience severe withdrawal.

“Incidence and Nature of Antidepressant Discontinuation Symptoms, A Systematic Review and Meta-analysis” was published in JAMA Psychiatry.

In a systematic review and meta-analysis of previous randomized controlled trials relating to antidepressant withdrawal, a team of researchers led by Imperial College London and King’s College London concluded that, while participants who stopped antidepressants did experience an average of one more symptom than those who continued or were taking placebos, this was not enough to be judged as significant.

In England alone, one in six properties are at risk of flooding. Approaches of the past are no longer enough and Wildlife Trusts are leading the way in delivering Natural Flood Management Solutions which slow the flow of water through catchments, reducing flood risk downstream.