Mapping Ignorance

Carleson’s ε 2 $\varepsilon ^{2}$ conjecture in higher dimensions - Inventiones mathematicae In this paper we prove a higher dimensional analogue of Carleson’s ε 2 $\varepsilon ^{2}$ conjecture. Given two arbitrary disjoint Borel sets Ω + , Ω − ⊂ R n + 1 $\Omega ^{+},\Omega ^{-}\subset \mathbb{R}^{n+1}$ , and x ∈ R n + 1 $x\in \mathbb{R}^{n+1}$ , r > 0 $r>0$ , we denote ε n ( x , r ) : = 1 r n inf H + H n ( ( ( ∂ B ( x , r ) ∩ H + ) ∖ Ω + ) ∪ ( ( ∂ B ( x , r ) ∩ H − ) ∖ Ω − ) ) , $$ \varepsilon _{n}(x,r) := \frac{1}{r^{n}}\, \inf _{H^{+}} \mathcal{H}^{n} \left ( ((\partial B(x,r)\cap H^{+}) \setminus \Omega ^{+}) \cup (( \partial B(x,r)\cap H^{-}) \setminus \Omega ^{-})\right ), $$ where the infimum is taken over all open affine half-spaces H + $H^{+}$ such that x ∈ ∂ H + $x \in \partial H^{+}$ and we define H − = R n + 1 ∖ H + ‾ $H^{-}= \mathbb{R}^{n+1} \setminus \overline{H^{+}}$ . Our first main result asserts that the set of points x ∈ R n + 1 $x\in \mathbb{R}^{n+1}$ where ∫ 0 1 ε n ( x , r ) 2 d r r < ∞ $$ \int _{0}^{1} \varepsilon _{n}(x,r)^{2} \, \frac{dr}{r}< \infty $$ is n $n$ -rectifiable. For our second main result we assume that Ω + $\Omega ^{+}$ , Ω − $\Omega ^{-}$ are open and that Ω + ∪ Ω − $\Omega ^{+}\cup \Omega ^{-}$ satisfies the capacity density condition. For each x ∈ ∂ Ω + ∪ ∂ Ω − $x \in \partial \Omega ^{+} \cup \partial \Omega ^{-}$ and r > 0 $r>0$ , we denote by α ± ( x , r ) $\alpha ^{\pm }(x,r)$ the characteristic constant of the (spherical) open sets Ω ± ∩ ∂ B ( x , r ) $\Omega ^{\pm }\cap \partial B(x,r)$ . We show that, up to a set of H n $\mathcal{H}^{n}$ measure zero, x $x$ is a tangent point for both ∂ Ω + $\partial \Omega ^{+}$ and ∂ Ω − $\partial \Omega ^{-}$ if and only if ∫ 0 1 min ( 1 , α + ( x , r ) + α − ( x , r ) − 2 ) d r r < ∞ . $$ \int _{0}^{1} \min (1,\alpha ^{+}(x,r) + \alpha ^{-}(x,r) -2) \frac{dr}{r} < \infty . $$ The first result is new even in the plane and the second one improves and extends to higher dimensions the ε 2 $\varepsilon ^{2}$ conjecture of Carleson.

This #EHUikerketa proves a higher dimensional analogue of Carleson’s e^2 conjecture. 

This #EHUikerketa aimed to identify a new inherited SPS predisposition component by functionally evaluating a candidate gene replicated in two independent SPS cohorts. 

Functioning Assessment Short Test (FAST): validity and reliability in adolescent and young adults with Borderline Personality Disorder (BPD) Borderline Personality Disorder (BPD) significantly impacts individuals, causing substantial distress and impairing social, occupational, and other cr…

This study aims to validate the Functioning Assessment Short Test (FAST) in adolescents and young adults with BPD in a Spanish population.

Exposure to high temperature and sleep in preadolescents from two European birth cohorts Hot temperatures disrupt sleep in adults, but the impact on younger populations, despite the essential role of sleep in their health and development, …

This #EHUikerketa assessed the relationship between ambient nocturnal temperature and physiological sleep characteristics and self-reported daytime sleepiness in preadolescents.

Imaging biomineralizing bacteria in their native-state with X-ray fluorescence microscopy Understanding the interactions between metal-based nanoparticles and biological systems in complex environments (e.g., the human body, soils, and marine settings) remains challenging, especially at single-cell and nanoscale levels. Capturing the dynamics of these interactions, such as metal distribution, nan

This #EHUikerketa demonstrates the direct measurement of iron content in hydrated, magnetite-biomineralizing magnetotactic bacteria. 

In this #EHUikerketa a novel sodium salt, sodium (benzenesulfonyl)(trifluoromethanesulfonyl) imide, is developed for all-solid-state sodium metal batteries.

ASAXS reveals the true identity of nanoparticles in medicine How anomalous small‑angle X‑ray scattering (ASAXS) uncover the hidden layers that shape nanomedicine therapies

Nanoparticles are not just tiny tools; they are dynamic players in a complex biological game. Thanks to advanced X‑ray methods, we are finally learning the rules.

A gold nanoparticle may start out as a neatly engineered sphere with a protective coating. But the moment it encounters blood or tissue fluid, proteins, fats, and sugars begin to stick to it. 

https://mappingignorance.org/2025/08/07/x-rays-reveal-the-true-identity-of-nanoparticles-in-medicine/

ASAXS reveals the true identity of nanoparticles in medicine How anomalous small‑angle X‑ray scattering (ASAXS) uncover the hidden layers that shape nanomedicine therapies

The difficulty lies in the fact that once nanoparticles enter the human body, they rarely remain in the form in which they were designed. 

ASAXS reveals the true identity of nanoparticles in medicine How anomalous small‑angle X‑ray scattering (ASAXS) uncover the hidden layers that shape nanomedicine therapies

Nanoparticles are not just tiny tools; they are dynamic players in a complex biological game. Thanks to advanced X‑ray methods, we are finally learning the rules.

A clash of quantum states in the mosaic phase of 1T-TaSSe Superconductivity can thrive even amid structural disorder of the transition metal dichalcogenide 1T-TaSSe

The role of selenium in 1T-TaSSe suggests that further tweaks to the material’s composition or layer structure could push its superconducting abilities even further.

A gold nanoparticle may start out as a neatly engineered sphere with a protective coating. But the moment it encounters blood or tissue fluid, proteins, fats, and sugars begin to stick to it. 

https://mappingignorance.org/2025/08/07/x-rays-reveal-the-true-identity-of-nanoparticles-in-medicine/

A clash of quantum states in the mosaic phase of 1T-TaSSe Superconductivity can thrive even amid structural disorder of the transition metal dichalcogenide 1T-TaSSe

In 1T-TaSSe, two remarkable phenomena compete for dominance: superconductivity and a charge density wave (CDW). 

ASAXS reveals the true identity of nanoparticles in medicine How anomalous small‑angle X‑ray scattering (ASAXS) uncover the hidden layers that shape nanomedicine therapies

The difficulty lies in the fact that once nanoparticles enter the human body, they rarely remain in the form in which they were designed. 

A clash of quantum states in the mosaic phase of 1T-TaSSe Superconductivity can thrive even amid structural disorder of the transition metal dichalcogenide 1T-TaSSe

By blending tantalum, sulfur, and selenium, this material becomes a stage for a complex interplay of quantum behaviors. 

X-rays reveal the true identity of nanoparticles in medicine

By @dipcehu.bsky.social 
https://mappingignorance.org/2025/08/07/x-rays-reveal-the-true-identity-of-nanoparticles-in-medicine/

Circular economy could make construction waste a thing of the past More than 90% of construction waste comes from demolition, but waste is also generated on-site and during manufacturing.

There are already specific ideas for applying upcycling principles in construction. 

Of course, the solution is not only to dismantle and reuse what has already been built. In this change of model, from linear to circular, it is also crucial to transform waste into resources. 

https://mappingignorance.org/2025/08/06/circular-economy-could-make-demolition-a-thing-of-the-past/

The construction industry is one of the largest producers of waste, generating around 2.2 billion tonnes per year globally. In Europe, it produces about 450 million tonnes, 40% of the total waste.

https://mappingignorance.org/2025/08/06/circular-economy-could-make-demolition-a-thing-of-the-past/

Circular economy could make construction waste a thing of the past More than 90% of construction waste comes from demolition, but waste is also generated on-site and during manufacturing.

There are already specific ideas for applying upcycling principles in construction. 

Big Bang may have taken place inside a black hole What if Big Bang the outcome of a gravitational crunch that formed a black hole – followed by a bounce inside it?

We are not witnessing the birth of everything from nothing, but rather the continuation of a cosmic cycle – one shaped by gravity, quantum mechanics, and the deep interconnections between them.

Of course, the solution is not only to dismantle and reuse what has already been built. In this change of model, from linear to circular, it is also crucial to transform waste into resources. 

https://mappingignorance.org/2025/08/06/circular-economy-could-make-demolition-a-thing-of-the-past/

Instead of starting with an expanding universe and trying to trace back how it began, we consider what happens when an overly dense collection of matter collapses under gravity.

https://mappingignorance.org/2025/07/30/big-bang-may-have-taken-place-inside-a-black-hole/

The construction industry is one of the largest producers of waste, generating around 2.2 billion tonnes per year globally. In Europe, it produces about 450 million tonnes, 40% of the total waste.

https://mappingignorance.org/2025/08/06/circular-economy-could-make-demolition-a-thing-of-the-past/

Big Bang may have taken place inside a black hole What if Big Bang the outcome of a gravitational crunch that formed a black hole – followed by a bounce inside it?

Calculations suggest the Big Bang was not the start of everything, but rather the outcome of a gravitational crunch or collapse that formed a very massive black hole – followed by a bounce inside it.

Circular economy could make demolition a thing of the past.

https://mappingignorance.org/2025/08/06/circular-economy-could-make-demolition-a-thing-of-the-past/

The problem is so widespread that the publication of fraudulent science is outpacing the growth rate of legitimate scientific publications. 

https://mappingignorance.org/2025/08/05/organized-scientific-fraud-is-on-the-rise/

Organized scientific fraud is on the rise - Mapping Ignorance From fabricated research to paid authorships and citations, organized scientific fraud is on the rise.

Although concerns around scientific misconduct typically focus on lone individuals, this study instead uncovered sophisticated global networks of individuals and entities, which systematically work together.

From fabricated research to paid authorships and citations, organized scientific fraud is on the rise.

https://mappingignorance.org/2025/08/05/organized-scientific-fraud-is-on-the-rise/

The problem is so widespread that the publication of fraudulent science is outpacing the growth rate of legitimate scientific publications. 

https://mappingignorance.org/2025/08/05/organized-scientific-fraud-is-on-the-rise/