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The edge-statistics conjecture for hypergraphs
No full textLet r, k, be integers such that 0 ≤ ≤ (k/r). Given a large r-uniform hypergraph G, we consider the
fraction of k-vertex subsets that span exactly edges. If is 0 or (k/r), this fraction can be exactly 1 (by taking G to be empty or complete), but for all other values of , one might suspect that this fraction is always significantly smaller than 1.
In this paper we prove an essentially optimal result along these lines: if is not 0 or (k/r), then this
fraction is at most (1/e) + ε, assuming k is sufficiently large in terms of r and ε > 0, and G is sufficiently large in terms of k. Previously, this was only known for a very limited range of values of r, k, (due to Kwan–Sudakov–Tran, Fox–Sauermann, and Martinsson–Mousset–Noever–Trujic). Our result answers a question of Alon–Hefetz–Krivelevich–Tyomkyn, who suggested this as a hypergraph generalization of their edge-statistics conjecture. We also prove a much stronger bound when is far from 0 and (k/r)
No time for surface charge: How bulk conductivity hides charge patterns from Kelvin probe force microscopy in contact-electrified surfaces
No full textKelvin probe force microscopy (KPFM) is widely used in stationary and dynamic studies of contact electrification. An obvious question that connects these two has been overlooked: when are charge dynamics too fast for stationary studies to be meaningful? Using a rapid transfer system to quickly perform KPFM after contact, we find the dynamics are too fast in all but the best insulators. Our data further suggest that dynamics are caused by bulk as opposed to surface conductivity, and that charge-transfer heterogeneity is less prevalent than previously suggested
Variability of central stars of planetary nebulae with the Zwicky Transient Facility. II. Long-timescale variables including wide binary and late thermal pulse candidates
No full textIn this second paper on our variability survey of central stars of planetary nebulae (CSPNe) using the Zwicky Transient Facility (ZTF), we report 11 long-timescale variables with variability timescales ranging from months to years. We also present preliminary analyses based on spectroscopic and/or photometric follow-up observations for six of them. Among them is NGC 6833, which shows a 980 days periodic variability with strange characteristics: “triangle-shaped” brightening in r, i, and WISE bands but almost coincidental shallow dips in the g-band. The most plausible explanation is a wide binary with the photometric period being the orbital period. Long-period near-sinusoidal variability was detected in two other systems, NGC 6905 and Kn 26, with periods of 700 days and 230 days, respectively, making them additional wide-binary candidates. The latter also shows a short period at 1.18 hr. We then present CTSS 2 and K 3-5, which show brightening and significant reddening over the whole ZTF baseline. A stellar model fit to the optical spectrum of CTSS 2 reveals it to be one of the youngest post-AGB CSPNe known. Both show high-density emission-line cores. We propose these to be late-thermal-pulse candidates, currently evolving towards the AGB phase. We then present recent HST/COS ultraviolet spectroscopy of the known wide-binary candidate LoTr 1, showing that the hot star is a spectroscopic twin of the extremely hot white dwarf in UCAC2 46706450. Similar to this object, LoTr 1 also has a fast rotating wide subgiant companion. We suggest that the long photometric period of 11 yr is the binary orbital period. Finally, we briefly discuss the ZTF light curves of the remaining variables, namely Tan 2, K 3-20, WHTZ 3, Kn J1857+3931, and IPHAS J1927+0814. With these examples, we present the effectiveness of the von Neumann statistics and Pearson Skew-based metric space in searching for long-timescale variables
Quantifying spectroscopic flux variations between JWST NIRISS and NIRSpec: Slit losses in emission line measurements of z ∼ 1-3 galaxies
No full textWe analyse James Webb Space Telescope (JWST) Near Infrared Imager and Slitless Spectrograph (NIRISS) and Near Infrared Spectrograph (NIRSpec) spectroscopic observations in the Abell 2744 galaxy cluster field. From approximately 120 candidates, we identify 12 objects with at least two prominent emission lines among [O II] λ3727, H β λ4861, [O III] λ4959, [O III] λ5007, and H α λ6563 that are spectroscopically confirmed by both instruments. Our key findings reveal systematic differences between the two spectrographs based on source morphology and shutter aperture placement. Compact objects show comparable or higher
integrated flux in NIRSpec relative to NIRISS (within 1σ uncertainties), while extended sources consistently display higher flux in NIRISS measurements. This pattern reflects NIRSpec’s optimal coverage for compact objects while potentially undersampling extended sources. Quantitative analysis demonstrates that NIRSpec recovers at least 63 per cent of NIRISS-measured flux when the slit covers >15 per cent of the source or when Re < 1 kpc. For lower coverage or larger effective radii, the recovered flux varies from 24 per cent to 63 per cent. When studying the H α λ6563/[O III] λ5007 emission line ratio, we observe that
measurements from these different spectrographs can vary by up to ∼0.3 dex, with significant implications for metallicity and star formation rate characterizations for individual galaxies. These results highlight the importance of considering instrumental effects when combining multi-instrument spectroscopic data and demonstrate that source morphology critically influences flux
recovery between slit-based and slitless spectroscopic modes in JWST observations
Topographically-controlled contribution of avalanches to glacier mass balance in the 21st century
No full textGlaciers are often located in steep mountain settings and avalanches from surrounding slopes can strongly influence snow accumulation patterns on their surface. This effect has however never been quantified for more than a few glaciers and the impact on the future evolution of glaciers is unclear. We coupled an avalanche and a glacier model to estimate the contribution of avalanches to the accumulation of all glaciers in the world and how this affects their evolution throughout the 21st century. Globally, 3% of the snow accumulation on glaciers comes from avalanches and 1% is removed by avalanches. This net contribution varies between regions and glaciers, with a maximum of 15% for New Zealand. Accounting for avalanches modifies the altitudinal pattern of glacier mass balance and the projected evolution of individual glaciers. The main effects include (1) a longer persistence of small glaciers, with for example three times more ice retained by glaciers smaller than 1 km2 in Central Europe under a low-emission scenario, and (2) an increased sensitivity of high-elevation accumulation zones to future warming. We anticipate the relative influence of avalanches to increase in the future and advocate for a better monitoring of this process and representation in glacier models
Spectral estimators for structured generalized linear models via approximate message passing
No full textWe consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective solution. However, despite their wide use, a rigorous performance characterization, as well as a principled way to preprocess the data, are available only for unstructured (i.i.d. Gaussian and Haar orthogonal) designs. In contrast, real-world data matrices are highly structured and exhibit non-trivial correlations. To address the problem, we consider correlated Gaussian designs capturing the anisotropic nature of the features via a covariance matrix Σ. Our main result is a precise asymptotic characterization of the performance of spectral estimators. This allows us to identify the optimal preprocessing that minimizes the number of samples needed for parameter estimation. Surprisingly, such preprocessing is universal across a broad set of designs, which partly addresses a conjecture on optimal spectral estimators for rotationally invariant models. Our principled approach vastly improves upon previous heuristic methods, including for designs common in computational imaging and genetics. The proposed methodology, based on approximate message passing, is broadly applicable and opens the way to the precise characterization of spiked matrices and of the corresponding spectral methods in a variety of settings
Altruistic disease signalling in ant colonies
No full textSick individuals often conceal their disease status to group members, thereby preventing social exclusion or aggression. Here we show by behavioural, chemical, immunological and infection load analyses that sick ant pupae instead actively emit a chemical signal that in itself is sufficient to trigger their own destruction by colony members. In our experiments, this altruistic disease-signalling was performed only by worker but not queen pupae. The lack of signalling by queen pupae did not constitute cheating behaviour, but reflected their superior immune capabilities. Worker pupae suffered from extensive pathogen replication whereas queen pupae were able to restrain their infection. Our data suggest the evolution of a finely-tuned signalling system in which it is not the induction of an individual’s immune response, but rather its failure to overcome the infection, that triggers pupal signalling for sacrifice. This demonstrates a balanced interplay between individual and social immunity that efficiently achieves whole-colony health
A kinematic history of stellar encounters with Beta Pictoris
No full textContext. Beta Pictoris is an A-type star that hosts a complex planetary system with two massive gas giants and a prominent debris disc. Variable absorption lines in its stellar spectrum have been interpreted as signatures of exocomets – comet-like bodies transiting the star. Stellar flybys can gravitationally perturb objects in the outer comet reservoir, altering their orbits and potentially injecting them into the inner system, thereby triggering exocomet showers.
Aims. We assessed the contribution of stellar flybys to the observed exocomet activity by reconstructing the stellar encounter history of β Pictoris in the past and future.
Methods. We used Gaia DR3 data, supplemented with radial velocities from complementary spectroscopic surveys, to compile a catalogue of stars currently within 80 pc of β Pictoris. Their orbits were integrated backwards and forwards in time in an axisymmetric Galactic potential (via the GALA package) to identify encounters within 2 pc of the system.
Results. We identified 99 416 stars currently within 80 pc of β Pictoris with resolved kinematics. Among these, 49 stars (including the eight components of five binaries) encounter β Pictoris within 2 pc between –1.5 Myr and +2 Myr. For four of the binaries, the centre-of-mass trajectories also pass within 2 pc. We estimated the sample to be more than 60% complete within 0.5 Myr of today.
Conclusions. Despite β Pictoris being the eponym of its famous moving group, none of the identified encounters involved its moving group members; all are unrelated field stars. We found no encounter capable of shaping the observed disc structures, although stellar flybys may contribute to the long-term evolution of an Oort Cloud-like structure. Our catalogue constitutes the most complete reconstruction of the β Pictoris encounter history to date and provides a robust foundation for future dynamical simulations
A universal augmentation framework for long-range electrostatics in machine learning interatomic potentials
No full textMost current machine learning interatomic potentials (MLIPs) rely on short-range approximations, without explicit treatment of long-range electrostatics. To address this, we recently developed the Latent Ewald Summation (LES) method, which infers electrostatic interactions, polarization, and Born effective charges (BECs), just by learning from energy and force training data. Here, we present LES as a standalone library, compatible with any short-range MLIP, and demonstrate its integration with methods such as MACE, NequIP, Allegro, CACE, CHGNet, and UMA. We benchmark LES-enhanced models on distinct systems, including bulk water, polar dipeptides, and gold dimer adsorption on defective substrates, and show that LES not only captures correct electrostatics but also improves accuracy. Additionally, we scale LES to large and chemically diverse data by training MACELES-OFF on the SPICE set containing molecules and clusters, making a universal MLIP with electrostatics for organic systems, including biomolecules. MACELES-OFF is more accurate than its short-range counterpart (MACE-OFF) trained on the same data set, predicts dipoles and BECs reliably, and has better descriptions of bulk liquids. By enabling efficient long-range electrostatics without directly training on electrical properties, LES paves the way for electrostatic foundation MLIPs
ISTA Thesis
No full textVerifiable Delay Functions (VDFs) introduced by Boneh et al. (CRYPTO'18) are functions that require a prescribed number of sequential steps T to evaluate, yet their output can be verified in time much faster than T. Since their introduction, VDFs have gained a lot of attention due to their applications in blockchain protocols, randomness beacons, timestamping and deniability. This thesis explores the theory and applications of VDFs, focusing on enhancing their soundness, efficiency and practicality.
The only practical VDFs known to date are based on repeated squaring in hidden order groups. Consider the function VDF(x,T)=x^(2^T).
The iterated squaring assumption states that, for a random group element x, the result of VDF cannot be computed significantly faster than performing T sequential squarings if the group order is unknown. To make the result verifiable a prover can compute a proof of exponentiation (PoE) \pi. Given \pi, the output of VDF can be verified in time much less than T.
We first present new constructions of statistically sound proofs of exponentiation, which are an important building block in the construction of SNARKs (Succinct Non-Interactive Argument of Knowledge). Statistical soundness means that the proofs remain secure against computationally unbounded adversaries, in particular, it remains secure even when the group order is known. We thereby address limitations in previous PoE protocols which either required (non-standard) hardness assumptions or a lot of parallel repetitions. Our construction significantly reduces the proof size of statistically sound PoEs that allow for a structured exponent, which leads to better efficiency of SNARKs and other applications.
Secondly, we introduce improved batching techniques for PoEs, which allow multiple proofs to be aggregated and verified with minimal overhead. These protocols optimize communication and computation complexity in large-scale blockchain environments and enable scalable remote benchmarking of parallel computation resources.
We then construct VDFs with enhanced properties such as zero-knowledge and watermarkability. It was shown by Arun, Bonneau and Clark (ASIACRYPT'22) that these features enable new cryptographic primitives called short-lived proofs and signatures. The validity of such proofs and signatures expires after a predefined amount of time T, i.e., they are deniable after time T. Our constructions improve upon the constructions by Arun, Bonneau and Clark in several dimensions (faster forging times, arguably weaker assumptions).
Finally, we apply PoEs in the realm of primality testing, providing cryptographically sound proofs of non-primality for large Proth numbers. This work gives a surprising application of VDFs in the area of computational number theory.
Together, our contributions advance both the theoretical foundations and the real-world usability of VDFs in general and in particular of PoEs, making them more adaptable and secure for current and emerging cryptographic applications