It is worth noting that none of the complexities below involve anything more sophisticated that pre-calculus study and logs and trig functions, and perhaps the early part of a first course in calculus, both of which are often taught at the high school level.
Artificial intelligence programs have recent disproved some famous mathematical conjectures by finding counter-examples.
Most mathematical proofs are deductive. They reason, point by point, from axiom, to lemma, to theorem, in a straight forward, X implies Y, Y implies Z, fashion.
Some mathematical proofs, arguably more elegant ones, are inductive. A common structure of an inductive proof is roughly speaking: imagine that this theorem is not true. Then, X could imply Y, and if X implies Y, then Z must have a certain value, but Z can have a different value. Therefore, the theorem must be true.
Another form of inductive proof shows that if proposition X is true that proposition X+1 is true by deduction. Then, it shows that proposition X is true in a separate proof for a particular early case of X (and possibly by other separate proofs for several other early cases of X that come before the one you use to validate the rest of the cases). Thus, for the early case or cases, and all subsequent cases, the conjecture must be true.
Many theorems are also almost always true, but have some "trivial" exceptions, typically for things like values of variables that are equal to zero or one, or for the first few iterations of a series, with the theorem holding only after those iterations.
One of the most elegant and efficient ways to prove that a theorem is not true is with a counterexample. The theorem may be true for every situation or set of values considered, sometimes millions of them, but it takes only one counterexample to show that the theorem is not always true, and hence, is false.
For example, in the case of Fermat's Last Theorem, before it was prove to be true, one could have imagined a counterexample disproving it with just three whole numbers that defied it's rule, that could be stated in a line or two, even thought it has been numerically tested for millions of numbers and in the end, it it would take a proof hundreds of pages long to rigorously establish that it was true deductively.
Disproof of longstanding mathematical conjectures by counterexample is rare, but it has happened, even in the pre-computer era, for theorems that held in vast numbers of examples, with no flaws identified for many decades by extremely smart people trying hard to do so.
I haven't very exactly described this kind of conjecture, although I'm sure that a clever mathematician could do so, but let's assume for sake of argument that this kind of conjecture is susceptible to precise definition, and call this kind of conjecture a "near miss conjecture".
Disproof of a near miss conjecture by counterexample, however, in and of itself, while it is efficient, indeed elegant, is also dissatisfying in the case of conjectures the hold true for so many examples and which defied logical reasoning to show that they are true or false for long periods of active efforts to do so. Disproof of a near miss conjecture by counterexample is dissatisfying because, while they do show that the conjecture is not true, they don't tell why the conjecture doesn't always work, even though it does work for so many cases and logically feels like it should work in every case.
Maybe the near miss conjecture is true for all but a finite set of counterexamples that is well defined, and can be used to modify the conjecture in much the same way as many theorems are modified to exclude a handful of trivial exceptions.
Maybe the near miss conjecture could be true if some other assumption so obvious that even smart people don't recognize that it needs to be made, add it.
For example, a conjecture about the probability of heads or tails in a coin toss may need to be supplemented with the assumption that the coin doesn't land on its side and thus doesn't generate either a heads or a tails result, rescuing the near miss conjecture, which remains very useful, despite not being perfectly true without the added assumption.
Knowing why a disproof by counterexample is possible adds insight that the counterexample itself often does not.
The approximately flat outer parts of spiral galaxy rotation curves are commonly interpreted as evidence for a discrepancy between the observed baryonic mass and the dynamical mass inferred from the measured orbital velocities. In most standard analyses, this discrepancy is quantified using v2(R)=GM(<R)/R, which is exact only under spherical symmetry. However, spiral galaxies are flattened disk systems, for which mass exterior to the galactocentric radius under consideration can contribute non-negligibly to the gravitational field.
We introduce the Lost and Found (LF) model, a geometrically consistent Newtonian framework based on direct full-disk gravitational integration and a parametrized representation of the disk surface density. In this approach, the gravitational field is computed without imposing spherical symmetry, and the disk mass distribution is represented by two exponential components with a smooth outer truncation.
We apply the LF model to a heterogeneous sample of disk galaxies spanning a broad range of masses and radial extents. The model reproduces the main observed features of the rotation curves, including the inner rise and the approximately flat outer behavior, without explicitly invoking a dark matter halo or modifying Newtonian gravity. Across the sample, the LF-inferred mass scales nearly linearly with the conventional dynamical mass, with a characteristic reduction factor ηLF ~ 0.67.
These results indicate that part of the inferred mass discrepancy may arise from the geometric treatment of gravitation in disk galaxies, and motivate a reassessment of mass inference in non-spherical systems.
What makes this paper especially notable is not its content per se but the concept of an "unreview", which potentially has broad interdisciplinary applications.
Accreting white dwarfs (AWDs) are among the best natural laboratories for understanding disk accretion. Their proximity, brightness, and purely classical nature make them ideal systems in which to probe the fundamental physics that governs the transport of angular momentum, the generation of outflows, and the coupling between disks, magnetospheres, and accretors. Yet despite decades of study, many critical questions remain unresolved.
In this ``unreview'', we therefore focus not on what is known, but on what is unknown.
What drives viscosity and sustains accretion in largely neutral disks? How are powerful winds launched, and how do they feed back on the disk and binary evolution? Why do so many systems show persistent retrograde precession, and what drives bursts in magnetic AWDs?
By identifying these open problems -- and suggesting ways to resolve them -- we aim to motivate new observational, numerical, and theoretical efforts that will advance our understanding of accretion physics across all mass scales, from white dwarfs to black holes.
Combined measurements of Higgs boson production and decay rates are reported, representing the most comprehensive study performed by the CMS Collaboration to date. The included analyses use proton-proton collision data recorded by the CMS experiment at s√ = 13 TeV from 2016 to 2018, corresponding to an integrated luminosity of 138 fb−1. The statistical combination is based on analyses that measure the following decay channels: H → γγ, H → ZZ, H → WW, H → ττ, H → bb, H → μμ, and H → Zγ → ℓℓγ (ℓ = e,μ). Information in the events from each decay channel is used to target multiple Higgs boson production processes. Searches for invisible Higgs boson decays are also considered, as well as an analysis that measures off-shell Higgs boson production in the H → ZZ → 4ℓ decay channel.
The best fit inclusive signal yield is measured to be 1.014 +0.055 −0.053 times the standard model expectation, for a Higgs boson mass of 125.38 GeV.
Measurements in kinematic regions defined by the simplified template cross section framework are also provided, as well as interpretations in the coupling modifier and standard model effective field theory frameworks. The coupling modifier interpretation is further used to place constraints on various two-Higgs-doublet models. The results show good compatibility with the standard model predictions for the majority of the measured parameters.
The breakdown of the sources of uncertainty are notable too:
The largest component of the uncertainty originates from the theoretical uncertainty in the signal yield normalization (∆µincl/µincl = 3.6%). The contributions from the experimental uncertainties are shared amongst the different sources of uncertainty, with no single dominant contribution.
The SM predictions for the Higgs boson production and decay rates depend on the mass of the Higgs boson mH. For all measurements in this paper, the mass is fixed at mH = 125.38 GeV. This was the most precise measurement of m(H) (± 0.14 GeV) by the CMS Collaboration at the time that the analyses entering the combination were performed. Since then, a more precise measurement of m(H) = 125.08 ± 0.12 GeV has been performed by CMS in the H → ZZ → 4ℓ channel. The ATLAS Collaboration also performed a more precise measurement of m(H) = 125.11 ± 0.11 GeV, combining the H → ZZ → 4ℓ and H → γγ channels. The small difference in m(H) between these values has a negligible effect on the results in this paper.
So, any hope from the abstract that this experiment would also shed light on the Higgs boson mass has been dashed.
The final point in the abstract about only a majority of the results being compatible with the Standard Model is explained as follows:
In contrast to the inclusive measurement, the per production process measurement shows a small tension with the SM, with a compatibility p-value of pSM = 0.02. This tension is mostly driven by µtH, for which an excess of 2.2 standard deviations above the SM expectation is seen. The µWH and µZH parameters are also measured to be larger than the SM expectations by approximately two standard deviations. The 68% CL intervals range from ±7.5% for µggH to ±39% for µtH, relative to their best fit values.
The per decay channel measurement shows a better compatibility with the SM (pSM = 0.33). The largest deviations are observed in the µττ and µZγ parameters. However, these are still compatible with the SM expectations within the 95% CL intervals. The µγγ, µZZ, µWW, and µττ parameters are all measured with excellent precision, with 68% CL intervals of approximately ±10% relative to their best fit values. The µbb parameter is measured with a 68% CL interval of ±15%. This represents a significant improvement compared to the previous combined Higgs boson measurement by the CMS Collaboration (±21%), because of the newly added H → bb channels and updated H → bb input analyses. The parameters for the rarer decay channels, µµµ and µZγ, are measured with 68% CL intervals of ±37% and ±39%, respectively, relative to their best fit values.
The biggest deviations in particular channels are still only slight tensions and are expected due to the look elsewhere effect.
The constraints on the Higgs boson self-coupling relative to the Standard Model expected value, kappa(A), which is a quite hard to measure property of the Higgs boson, are also very consistent with the Standard Model expectation, as shown in the chart below (with kappa(F) and kappa(V) reflecting scenarios where there are different couplings to fermions and vector bosons).
* The Anglo-Saxons kept slaves in the middle ages.
High-resolution orbital images of Mars' largest canyon reveal ancient river deltas, proving the Red Planet once held an ocean the size of Earth's Arctic.New high-resolution imagery from the European Space Agency’s ExoMars Trace Gas Orbiter has provided the most definitive evidence to date that Mars was once a blue planet. Researchers at the University of Bern identified distinct fan-shaped sediment deposits in the southeast Coprates Chasma region, part of the massive Valles Marineris canyon system. These structures, remarkably similar to river deltas on Earth, all sit at a consistent elevation between 3,650 and 3,750 meters. This geological alignment points to one unmistakable conclusion: the presence of an ancient coastline where rivers once emptied into a vast, stable sea approximately 3.37 billion years ago.While previous theories about Martian oceans relied on lower-resolution data, this study offers direct geomorphological proof of a shoreline. The findings suggest that a massive body of water, comparable in size to Earth’s Arctic Ocean, once covered the entirety of Mars’ northern hemisphere. Though today these ancient deltas are buried beneath wind-sculpted dust and dunes, their distinctive shapes remain preserved. This discovery drastically alters our view of Martian history; the existence of a planet-wide water cycle and a stable ocean suggests that the conditions necessary for life were not isolated occurrences but a global phenomenon.Source: Argadestya, P., et al. "Geomorphological and sedimentological evidence of a coastline in Southeast Coprates Chasma." npj Space Exploration (2026).
* In West Texas, ca. 4500 BCE, hunter-gatherers used non-returnable boomerang sticks for small game and atlatl to throw their carefully crafted spears further for big game.
A cache of ancient weapons, more than 6,000 years old, has been uncovered in a remote rock shelter in West Texas, offering one of the clearest pictures yet of early life in North America.The discovery was made at the San Esteban rock shelter in the Big Bend region, an area known for its dry climate and rugged desert landscape. That dryness turned out to be a gift to archaeologists. Items that would normally rot away wood, leather bindings, plant fibers remained intact for thousands of years. Inside the shelter, researchers found a carefully stored hunting kit dating to around 4,500 B.C., including wooden spear shafts wrapped in leather, stone projectile points, and parts of atlatls, the spear-throwing tools that dramatically increased a hunter’s range and power.An atlatl works like a lever, giving a thrown spear greater speed and force. With it, hunters could strike animals from distances that would otherwise be impossible with a simple hand throw. Tests and prior studies show these tools could send projectiles well over 100 feet with deadly accuracy. The craftsmanship seen in the newly uncovered pieces shows careful shaping, balance, and planning. These were not rough survival tools; they were refined hunting systems built by people who deeply understood their environment.Researchers also identified curved wooden throwing weapons often described as straight or non-returning boomerangs. Unlike the returning boomerangs many people picture today, these were designed to fly straight and hit small game with strong impact. Their presence adds another layer to what appears to have been a well-organized toolkit, likely stored together for repeated use.The San Esteban site has a long history of human occupation stretching back thousands of years. Findings from this latest excavation reinforce the idea that the Big Bend region was not a temporary stop for wandering groups but a place where people lived, adapted, and developed sophisticated survival strategies. The tools show planning, skill, and an ability to work with available materials in smart, efficient ways.Archaeologists involved in the project say the discovery helps rewrite outdated ideas about early North American societies. These communities were not primitive in the way older textbooks sometimes suggested. They engineered effective hunting technology, understood animal behavior, and created tools built to last.As research continues, scientists hope to learn more about how these weapons were used, how they were stored, and what they reveal about daily life 6,000 years ago. For now, the dry rock shelter in West Texas has delivered something rare: a direct, tangible connection to hunters who once stood in the same desert landscape, preparing their tools for the next expedition.
* Maize farmers in Peru’s Chincha Valley were fertilizing their crops with seabird poop as early as the year 1250 CE.
Around 3,800 years ago, a magnitude-9.5 megaquake struck northern Chile's coast, creating the largest earthquake known in human history. The rupture extended roughly 620 miles along the fault line—longer than the devastating 1960 Valdivia earthquake—and generated tsunamis with waves reaching 66 feet that traveled 5,000 miles across the Pacific Ocean to New Zealand. Archaeologists discovered marine deposits, boulders, shells, and sea life displaced far inland in the Atacama Desert, along with toppled stone structures buried beneath tsunami sediment, all radiocarbon-dated to this single catastrophic event.The disaster forced complete coastal abandonment. Communities that depended on the ocean for survival relocated inland, staying away from the coast for over 1,000 years—an extraordinary response that demonstrates the quake's devastating impact on human populations. Researchers now recognize this megathrust earthquake, caused when tectonic plates suddenly unlocked after building massive strain, as both the oldest discovered earthquake-tsunami disaster in the Southern Hemisphere and a critical warning for modern coastal populations across the Pacific.
* Every recorded earthquake worldwide, 2015 to 2025 (my source didn't cite a source).
A model-independent search for low-mass resonances decaying into pairs of oppositely charged muons is presented. The analysis uses proton-proton collision data corresponding to an integrated luminosity of 140 fb−1, recorded by the ATLAS detector at the Large Hadron Collider between 2015 and 2018.
The search targets hypothetical dimuon resonances in the invariant mass range from 35 GeV to 75 GeV. The modelling of this mass region is particularly challenging for conventional analytic background parameterisations. To address this, a Gaussian process regression technique is used to model the background.
The dimuon mass spectrum is analysed for potential signals, and no statistically significant excess is observed. Upper limits at the 95% confidence level are set on the fiducial production cross-section of new resonances decaying promptly into muons, ranging from 20 fb to 110 fb, depending on the resonance mass. These results are further interpreted in the context of dark-photon and dark-matter-mediator models, leading to new constraints on their parameter spaces.
Searches for low-mass dimuon resonances have been performed by the CMS and LHCb Collaborations, covering mass ranges of 1.1–7.9 GeV, 11.5–75 GeV and 110–200 GeV for CMS, and 30.214–70 GeV for LHCb.
Those searches also came up empty.
The trickiest mass range to study of those already studied is the 1.1-7.9 GeV mass range which has lots of different hadron resonances that decay in a great many different ways, with each decay having its own probably of occurring, generating substantial background noise, even though the backgrounds are well understood.
The range from 11.5-75 GeV has very little background noise, because it exceeds all but the heaviest hadron resonance masses (with most hadrons predicted to have masses above 11.5 GeV having never been definitively observed even in the numerous and extremely high energy collisions of the LHC), but it is comfortably less than the W boson mass (roughly 80.4 GeV), the Z boson mass (roughly 91.2 GeV), or the Standard Model Higgs boson mass (roughly 125.1 GeV).
In the 110-200 GeV mass range, the only significant backgrounds that can have dimuon decays are single Standard Model Higgs bosons (roughly 125.1 GeV), W boson pairs (roughly 160.8 GeV), and Z boson pairs (roughly 182.4 GeV).
So, the total observations of dimuon resonances should have three very precisely predictable bumps and can often be confirmed to be background events because additional decay products in addition to the dimuons are observed. The decays of these background processes to particles other than dimuon pairs can also be used to calibrate the expected number of background dimuons for each of these three resonances.
For example, you can estimate the total Higgs boson production from the number of b quark pair decays that are observed by using that to determine how many dimuon decays from Higgs bosons should be expected, since the ratio of the b quark pair branching fraction of Higgs boson decays to the dimuon branching fraction of Higgs boson decays can be theoretically predicted to high precision. And, when you know how many background dimuon events you expect to see from Higgs boson decays, you can subtract that background from the observed number of dimuon events to determine if there is any beyond the Standard Model particle decay signal in the vicinity of the 125.1 GeV Higgs boson mass.
You can do something similar for W boson pair decays and Z boson pair decays.
The 110-200 GeV mass range range is far more massive than any predicted Standard Model hadrons or any single W or Z boson, however. But, it is also far less than than the combined mass of a Higgs boson pair (roughly 250.2 GeV) or a top quark-antitop quark pair (which is roughly 345 GeV) or a Toponium meson (which is just a bit more massive that an unbound pair of oppositely charged top quarks).
Charged leptons, like those found in dimuon decays (which also only decay in turn to electrons quite slowly compared to other conceivable decay products with their roughly one microsecond mean lifetime, that turns out to be longer from an outside observer's perspective due to special relativity) are easy for the detectors at the LHC to see, so there are few false negatives.
The rest mass of a dimuon pair is about 0.21 GeV, so even with an invariant mass of 1.1 GeV, the special relativistic kinetic energy of the dimuon pair is about four times its rest mass, so the pair of charged leptons will be traveling at very close to the speed of light, and the closer to the speed of light that the muons are traveling at is, the slower time passes in their rest frame relative to the rest frame of an outside observer. So, from the perspective of an outside observer, the dimuon pair takes much more than the microsecond of a muon at rest to decay.
Furthermore, a lot of false positive dimuon decays would be accompanied by additional detectible decay products that could distinguish those events from the pure dimuon decay signal that the experimenters were looking for in this paper and its companion papers over other invariant mass ranges.
So, these measurements can be quite precise, and can rule out even quite small beyond the Standard Model signals in these mass ranges.
This analysis presents an observation of the photon-fusion production of W boson pairs using the CMS detector at the LHC. The total cross section of the W+W− production in photon fusion is measured using proton-proton collision data with an integrated luminosity of 138 fb−1 collected with the CMS detector in 2016−2018 at a center-of-mass energy of s√ = 13 TeV. Events are selected in the final state with one isolated electron and one isolated muon, and no additional tracks associated with the electron-muon production vertex.
The total and fiducial production cross sections are 643 +82 −78 fb and 3.96 +0.53 −0.51 fb, respectively, in agreement with the standard model predictions of 631 ± 126 fb and 3.87 ± 0.77 fb.
This agreement enables stringent constraints to be imposed on anomalous quartic gauge couplings within a dimension-8 effective field theory framework.
James Douglas Boyd has recently spent a lot of time interacting with Mochizuki and others at RIMS working in anabelian geometry. Material from interviews he conducted are available here (Mochizuki on IUT) and here (on anabelian geometry at RIMS). He also has written a summary of IUT and of the basic problem with the abc proof. These include detailed comments on the issue pointed out by Scholze-Stix and why this is a significant problem for the proof. I’d be curious to hear from anyone who has looked at this closely about whether they agree with Boyd’s characterization of the situation.There’s also a lot of material [about] the IUT ideas, independent of the problematic abc proof, and about what Mochizuki and others are now trying to do with these ideas.
The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. It is stated in terms of three positive integers a,b and c (hence the name) that are relatively prime and satisfy a+b=c. The conjecture essentially states that the product of the distinct prime factors of abc cannot often be much smaller than c. A number of famous conjectures and theorems in number theory would follow immediately from the abc conjecture or its versions. Mathematician Dorian Goldfeld described the abc conjecture as "The most important unsolved problem in Diophantine analysis".The abc conjecture originated as the outcome of attempts by Oesterlé and Masser to understand the Szpiro conjecture about elliptic curves, which involves more geometric structures in its statement than the abc conjecture. The abc conjecture was shown to be equivalent to the modified Szpiro's conjecture.Various attempts to prove the abc conjecture have been made, but none have gained broad acceptance. Shinichi Mochizuki claimed to have a proof in 2012, but the conjecture is still regarded as unproven by the mainstream mathematical community.
Assuming the data has a Gaussian distribution (i.e. is distributed in a "normal" probability curve) is often reasonable, since this is what happens when data comes from independent simple percentage probability events. And, it is a convenient assumption when it works, because mathematically it is much easier to work with Gaussian distributions than most other probability distributions. But, sometimes reality is more complicated than that and this assumption isn't reasonable.
The supernova data used to characterize dark energy phenomena isn't Gaussian.
Trivially, this means that statistical uncertainty estimates based upon Gaussian distributions overestimate the statistical significance of observations in the fat tailed t-distribution.
Non-trivially, this means that the underlying physics of dark matter phenomena are more mathematically complex than something like Newtonian gravity (often assumed for astronomy purposes as a reasonable approximation of general relativity) or a simple cosmological constant. Simple cosmology models don't match the data.
This paper estimates dark energy parameters for more complex dark energy models that can fit the data.
Type Ia supernovae have provided fundamental observational data in the discovery of the late acceleration of the expansion of the Universe in cosmology. However, this analysis has relied on the assumption of a Gaussian distribution for the data, a hypothesis that can be challenged with the increasing volume and precision of available supernova data.
In this work, we rigorously assess this Gaussianity hypothesis and analyze its impact on parameter estimation for dark energy cosmological models. We utilize the Pantheon+ dataset and perform a comprehensive statistical, analysis including the Lilliefors and Jarque-Bera tests, to assess the normality of both the data and model residuals.
We find that the Gaussianity assumption is untenable and that the redshift distribution is more accurately described by a t-distribution, as indicated by the Kolmogorov Smirnov test. Parameters are estimated for a model incorporating a nonlinear cosmological interaction for the dark sector. The free parameters are estimated using multiple methods, and bootstrap confidence intervals are constructed for them.
In this paper, we present a brief critical analysis of the data, methodology, and results of the most recent publication on the computational phylogeny of the Indo-European family (Heggarty et al. 2023), comparing them to previous efforts in this area carried out by (roughly) the same team of scholars (informally designated as the “New Zealand school”), as well as concurrent research by scholars belonging to the “Moscow school” of historical linguistics.
We show that the general quality of the lexical data used as the basis for classification has significantly improved from earlier studies, reflecting a more careful curation process on the part of qualified historical linguists involved in the project; however, there remain serious issues when it comes to marking cognation between different characters, such as failure (in many cases) to distinguish between true cognacy and areal diffusion and the inability to take into account the influence of the so-called derivational drift (independent morphological formations from the same root in languages belonging to different branches).
Considering that both the topological features of the resulting consensus tree and the established datings contradict historical evidence in several major aspects, these shortcomings may partially be responsible for the results. Our principal conclusion is that the correlation between the number of included languages and the size of the list may simply be insufficient for a guaranteed robust topology; either the list should be drastically expanded (not a realistic option for various practical reasons) or the number of compared taxa be reduced, possibly by means of using intermediate reconstructions for ancestral stages instead of multiple languages (the principle advocated by the Moscow school).
Discussion and conclusionsIn the previous sections, we have to tried to identify several factors that might have been responsible for the dubious topological and chronological results of Heggarty et al. 2023 experiment, not likely to be accepted by the majority of “mainstream” Indo-European linguists. Unfortunately, it is hard to give a definite answer without extensive tests, since, in many respects, the machine-processed Bayesian analysis remains a “black box”. We did, however, conclude at least that this time around, errors in input data are not a key shortcoming of the study (as was highly likely for such previous IE classifications as published by Gray and Atkinson, 2003; Bouckaert et al. 2012), although failure to identify a certain number of non-transparent areal borrowings and/or to distinguish between innovations shared through common ancestry and those arising independently of one another across different lineages (linguistic homoplasy) may have contributed to the skewed topography.One additional hypothesis is that the number of characters (170 Swadesh concepts) is simply too low for the given number of taxa (161 lects). From the combinatorial and statistical point of view, it is a trivial consideration that more taxa require more characters for robust classification (see Rama and Wichmann, 2018 for attempts at estimation of optimal dataset size for reliable classification of language taxa). Previous IE classifications by Gray, Atkinson et al. involved fewer taxa and more characters (see Table 1 for the comparison).Table 1 suggests that the approach maintained and expanded upon in Heggarty et al. 2023 project can actually be a dead-end in classifying large and diversified language families. In general, the more languages are involved in the procedure, the more characters (Swadesh concepts) are required to make the classification sufficiently robust. Such a task, in turn, requires a huge number of man-hours for wordlist compilation and is inevitably accompanied by various errors, partly due to poor lexicographic sources for some languages, and partly due to the human factor. Likewise, expanding the list of concepts would lead us to less and less stable concepts with vague semantic definitions.Instead of such an “expansionist” approach, a “reductionist” perspective, such as the one adopted by Kassian, Zhivlov et al. (2021), may be preferable, which places more emphasis on preliminary elimination of the noise factor rather than its increase by manually producing intermediate ancestral state reconstructions (produced by means of a transparent and relatively objective procedure). Unfortunately, use of linguistic reconstructions as characters for modern phylogenetic classifications still seems to be frowned upon by many, if not most, scholars involved in such research — in our opinion, an unwarranted bias that hinders progress in this area.Overall one could say that Heggarty et al. (2023) at the same time represents an important step forward (in its clearly improved attitude to selection and curation of input data) and, unfortunately, a surprising step back in that the resulting IE tree, in many respects, is even less plausible and less likely to find acceptance in mainstream historical linguistics than the trees previously published by Gray & Atkinson (2003) and by Bouckaert et al. (2012).
Consequently, the paper enhances the already serious risk of discrediting the very idea of the usefulness of formal mathematical methods for the genealogical classification of languages; it is highly likely, for instance, that a “classically trained” historical linguist, knowledgeable in both the diachronic aspects of Indo-European languages and such adjacent disciplines as general history and archaeology, but not particularly well versed in computational methods of classification, will walk away from the paper in question with the overall impression that even the best possible linguistic data may yield radically different results depending on all sorts of “tampering” with the complex parameters of the selected methods — and that the authors have intentionally chosen that particular set of parameters which better suits their already existing pre-conceptions of the history and chronology of the spread of Indo-European languages.
While we are not necessarily implying that this criticism is true, it at least seems obvious that in a situation of conflict between “classic” and “computational” models of historical linguistics, assuming that the results of the latter automatically override those of the former would be a pseudo-scientific approach; instead, such conflicts should be analyzed and resolved with much more diligence and much deeper analysis than the one presented in Heggarty et al. 2023 study.
For the flat ΛCDM model with the sum of neutrino mass ∑mν free, combining the DESI and CMB data yields an upper limit ∑mν<0.072 (0.113) eV at 95% confidence for a ∑mν>0 (∑mν>0.059) eV prior. These neutrino-mass constraints are substantially relaxed in models beyond ΛCDM.
* There are vast numbers of free floating planets out there, ripped from the stars around which the formed. The James Webb Space Telescope (JWST) will soon reveal many more of them.
While these are ultimately just cold rocks, there are also isolated stars outside any galaxy out there. What if life developed in a place like that?
The possibilities found in the universe are awe inspiring.
* In other astronomy observations, "general relativistic contributions" reduce "the probability that the solar system destabilizes within 5 Gyr by a factor of 60."
* Power laws continue to be fascinating and make random phenomena, while still random, far more ordered than they seem, while also suggesting the kind of processes that give rise to them.
Many astronomical phenomena, including Fast Radio Bursts and Soft Gamma Repeaters, consist of brief distinct aperiodic events. The intervals between these events vary randomly, but there are periods of greater activity, with shorter mean intervals, and of lesser activity, with longer mean intervals. A single dimensionless parameter, the width of a log-normal function fitted to the distribution of waiting times between events, quantifies the variability of the activity. This parameter describes its dynamics in analogy to the critical exponents and universality classes of renormalization group theory. If the distribution of event strengths is a power law, the width of the log-normal fit is independent of the detection threshold and is a robust measure of the dynamics of the phenomenon.
Theorists have found a way to solve complex Feynman integrals numerically by reducing them to simple linear algebra.
First uses of prefixes in SI date back to definition of kilogram after the French Revolution at the end of the 18th century. Several more prefixes have gone into use be by the 1947th IUPAC's 14th International Conference of Chemistry, before being officially adopted for the first time in 1960.
The most recent prefixes adopted were ronna-, quetta-, ronto-, and quecto- in 2022, after a proposal from British metrologist Richard J. C. Brown. The large prefixes ronna- and quetta- were adopted in anticipation of needs from data science, and because unofficial prefixes that did not meet SI requirements were already circulating. The small prefixes were added as well even without such a driver in order to maintain symmetry. After these adoptions, all Latin letters have now been used for prefixes or units.
From here.
Assuming a dark matter particle paradigm, according to a pre-print by Yang (2015) subsequently published in Physical Review D, the lower bound on the mean lifetime of dark matter particles is seconds. This is roughly years. By comparison the age of the universe is roughly
A large number of studies, all using Bayesian parameter inference from Markov Chain Monte Carlo methods, have constrained the presence of a decaying dark matter component. All such studies find a strong preference for either very long-lived or very short-lived dark matter.
However, in this letter, we demonstrate that this preference is due to parameter volume effects that drive the model towards the standard ΛCDM model, which is known to provide a good fit to most observational data.
Using profile likelihoods, which are free from volume effects, we instead find that the best-fitting parameters are associated with an intermediate regime where around 3% of cold dark matter decays just prior to recombination. With two additional parameters, the model yields an overall preference over the ΛCDM model of Δχ2≈−2.8 with Planck and BAO and Δχ2≈−7.8 with the SH0ES H0 measurement, while only slightly alleviating the H0 tension.
Ultimately, our results reveal that decaying dark matter is more viable than previously assumed, and illustrate the dangers of relying exclusively on Bayesian parameter inference when analysing extensions to the ΛCDM model.
