arXiv subjects

Michael Blank

Publications and source records attributed to Michael Blank.

At least 19 recordsLinked to original sources

arXiv2026

The Household Impact of Generative AI: Evidence from Internet Browsing Behavior

This paper studies the impact of generative AI on U.S. households' task allocation at home, using detailed Internet browsing data from a large sample of home devices between 2021 and 2024. Leveraging pre-ChatGPT browsing patterns, we measure households' exposure to ChatGPT and use it as an instrument for ChatGPT adoption during the post-release period. Our IV estimates show that adopting generative AI substantially increases leisure browsing on home devices while leaving time spent on productive digital tasks unchanged. To examine mechanisms, we infer the purpose of households' ChatGPT use from surrounding internet activity and find that households primarily employ it for productive non-market tasks. Together, these results suggest that generative AI frees up leisure time by raising the efficiency of productive digital activities. Interpreting these findings through a standard time-allocation model implies economically large productivity gains from generative AI at home.

econ.GN↗

arXiv2026

Bayes-PD: Exploring a Sequence to Binding Bayesian Neural Network model trained on Phage Display data

Phage display is a powerful laboratory technique used to study the interactions between proteins and other molecules, whether other proteins, peptides, DNA or RNA. The under-utilisation of this data in conjunction with deep learning models for protein design may be attributed to; high experimental noise levels; the complex nature of data pre-processing; and difficulty interpreting these experimental results. In this work, we propose a novel approach utilising a Bayesian Neural Network within a training loop, in order to simulate the phage display experiment and its associated noise. Our goal is to investigate how understanding the experimental noise and model uncertainty can enable the reliable application of such models to reliably interpret phage display experiments. We validate our approach using actual binding affinity measurements instead of relying solely on proxy values derived from 'held-out' phage display rounds.

q-bio.PE↗

arXiv2025

Inheritance of shadowing for dynamical semigroups

We extend the single-perturbation approach (developed in our earlier publications for the case of a single map) to the analysis of the shadowing property for semigroups of endomorphisms. Our approach allows to give a constructive representation for a true trajectory which shadows a given pseudo-trajectory. One of the main motivations is the question of inheritance: does the presence of shadowing for all generators of a semigroup imply shadowing for the semigroup and vice versa. Somewhat surprisingly, the answer to these questions is generally negative. Moreover, the situation with shadowing turns out to be quite different in a semigroup and in a non-autonomous system, despite the fact that the latter can be represented as a single branch of the former.

math.DS↗

arXiv2024

Elementary solution to the fair division problem

A new and relatively elementary approach is proposed for solving the problem of fair division of a continuous resource (measurable space, pie, etc.) between several participants, the selection criteria of which are described by charges (signed measures). The setting of the problem with charges is considered for the first time. The problem comes down to analyzing the properties of the trajectories of a specially constructed dynamical system acting in the space of finite measurable partitions. Exponentially fast convergence to a limit solution is proved for both the case of true measures and the case of charges.

math.DS↗

arXiv2024

Model geometries of porous materials

We describe a method for modeling the geometry of porous materials. The approach enables the independent selection of crucial parameters, including porosity, pore size distribution, pore shape, and connectivity. Consequently, it can effectively model a wide range of porous systems. Due to the diverse and systematic variation possibilities, the method is suitable for developing and optimizing porous structures. The geometries can be exported as triangular meshes, facilitating their immediate use in numerical simulation and further digital processing. We showcase the method's capabilities by minimizing the foam structure's thermal conductivity through geometry optimization.

cond-mat.mtrl-sci↗

arXiv2024

Are prime numbers and quadratic residues random?

Appeals to randomness in various number-theoretic constructions appear regularly in modern scientific publications. Such famous names as V.I. Arnold, M. Katz, Ya.G. Sinai, and T. Tao are just a few examples. Unfortunately, all of these approaches rely on various, although often very non-trivial and elegant, heuristics. A new analytical approach is proposed to address the issue of randomness/complexity of an individual deterministic sequence. This approach demonstrates the expected high complexity of quadratic residues and the unexpectedly low complexity in the case of prime numbers. Technically, our approach is based on a new construction of the dynamical entropy of a single trajectory, which measures its complexity, in contrast to classical Kolmogorov-Sinai and topological entropies, which measure the complexity of the entire dynamical system.

math.DS↗

arXiv2023

Surface tension and wetting at free surfaces in Smoothed Particle Hydrodynamics

Surface tension and wetting are dominating physical effects in micro and nanoscale flows. We present an efficient and reliable model of surface tension and equilibrium contact angles in Smoothed Particle Hydrodynamics for free-surface problems. We demonstrate its robustness and accuracy by simulating several notoriously difficult three-dimensional free surface flow problems driven by interfacial tension.

physics.flu-dyn↗

arXiv2023

DEM simulation of the powder application in powder bed fusion

The packing behavior of powders is significantly influenced by various types of inter-particle attractive forces, including adhesion and non-bonded van der Waals forces [1, 2, 3, 4, 5, 6]. Alongside particle size and shape distributions, the inter-particle interactions, in particular frictional and adhesive forces, play a crucial role in determining the flow behavior and consequently the packing density of the powder layer. The impact of various types of attractive forces on the packing density of powders with different materials and particle size distributions remains largely unexplored and requires further investigation. Accurately comprehending these effects through experiments while considering specific particle size distributions and material properties poses significant challenges. To address these challenges, we employ Discrete Element Method (DEM) simulations to characterize the packing behavior of fine powders. We can demonstrate quantitative agreement with experimental results by incorporating the appropriate particle size distribution and using an adequate model of attractive particle interactions. Furthermore, our findings indicate that both adhesion, which is modeled using the Johnson-Kendall-Roberts (JKR) model [7], and van der Waals interactions are crucial factors that must be taken into account in DEM simulations.

cond-mat.soft↗

arXiv2022

Average shadowing revisited

We propose a novel unifying approach to study the shadowing property for a broad class of dynamical systems (in particular, discontinuous and non-invertible) under a variety of perturbations. In distinction to known constructions, our approach is local: it is based on the gluing property which takes into account the shadowing under a single (not necessarily small) perturbation.

math.DS↗

arXiv2022

Average shadowing and gluing property

The purpose of this work is threefold: (i) extend shadowing theory for discontinuous and non-invertible systems, (ii) consider more general classes of perturbations (for example, small only on average), (iii) establish a general theory based on the property that the shadowing holds for the case of a single perturbation. The "gluing" construction used in the analysis of the last property turns out to be the key point of this theory.

math.DS↗

arXiv2021

Invariant measures of torus piecewise isometries

We study measure-theoretical aspects of torus piecewise isometries. Not much is known about this type of dynamical systems, except for the special case of one-dimensional interval exchange mappings. The last case is fundamentally different from the general situation in the presence of an invariant measure (Lebesgue measure), which helps a lot in the analysis. Due to the absence of good methods of analysis of general systems with discontinuities, even the existence of invariant measures of the torus piecewise isometries was an open question. We establish sufficient conditions for the existence/absence of invariant measures for this class of systems. Technically, our results are based on the approximation of the maps under study by weakly periodic ones.

math.DS↗

arXiv2021

The relentless variability of Mrk 421 from the TeV to the radio

The origin of the gamma-ray emission of the blazar Mrk 421 is still a matter of debate. We used 5.5 years of unbiased observing campaign data, obtained using the FACT telescope and the Fermi LAT detector at TeV and GeV energies, the longest and densest so far, together with contemporaneous multi-wavelength observations, to characterise the variability of Mrk 421 and to constrain the underlying physical mechanisms. We studied and correlated light curves obtained by ten different instruments and found two significant results. The TeV and X-ray light curves are very well correlated with a lag of <0.6 days. The GeV and radio (15 Ghz band) light curves are widely and strongly correlated. Variations of the GeV light curve lead those in the radio. Lepto-hadronic and purely hadronic models in the frame of shock acceleration predict proton acceleration or cooling timescales that are ruled out by the short variability timescales and delays observed in Mrk 421. Instead the observations match the predictions of leptonic models.

astro-ph.HE↗

arXiv2020

Recurrence for measurable semigroup actions

We study qualitative properties of the set of recurrent points of finitely generated free semigroups of measurable maps. In the case of a single generator the classical Poincare recurrence theorem shows that these properties are closely related to the presence of an invariant measure. Curious, but otherwise it turns out to be possible that almost all points are recurrent, while there is an wandering set of positive (non-invariant) measure. For a general semigroup the assumption about the common invariant measure for all generators looks somewhat unnatural (despite being widely used). Instead we give abstract conditions (of conservativity type) for this problem and propose a weaker version of the recurrent property. Technically, the problem is reduced to the analysis of the recurrence of a specially constructed Markov process. Questions of inheritance of the recurrence property from the semigroup generators to the entire semigroup and vice versa are studied in detail and we demonstrate that this inheritance might be rather unexpected.

math.DS↗

arXiv2019

5.5 years multi-wavelength variability of Mrk 421: evidences of leptonic emission from the radio to TeV

Mrk 421 is a high-synchrotron-peaked blazar featuring bright and persistent GeV and TeV emission. We use the longest and densest ongoing unbiased observing campaign obtained at TeV and GeV energies during 5.5 years with the FACT telescope and the Fermi-LAT detector. The contemporaneous multi-wavelength observations were used to characterize the variability of the source and to constrain the underlying physical mechanisms. We study and correlate light curves obtained by nine different instruments from radio to gamma rays and found two significant results. The TeV and X-ray light curves are very well correlated with lag, if any, shorter than a day. The GeV light curve varies independently and accurately leads the variations observed at long wavelengths, in particular in the radio band. We find that the observations match the predictions of leptonic models and suggest that the physical conditions vary along the jet, when the emitting region moves outwards.

astro-ph.HE↗

arXiv2019

FACT -- Multi-wavelength analysis of more than 30 flares of Mrk 421

Mrk 421 is a high-synchrotron-peaked blazar featuring bright and persistent GeV and TeV emission. We use multi-wavelength light curves of Mrk 421 spanning 5.5 years with FACT (TeV) and Fermi LAT (GeV) in the gamma rays, Swift BAT, Swift XRT and MAXI in the X-rays, together with optical and radio data and investigate the physical processes driving the emission and variability. Observations by FACT are continuous and not triggered, so the source was found in a wide range of flux states and more than 30 flares were identified from X-rays to TeV. The light curves in TeV and X-rays feature very similar flares with rise and decay times of a few days and zero lag, characteristic for electron processes. At least two parameters per flare, the amplitude and the cut-off energy, are required to explain the observed variability. In addition, the GeV light curve leads and is strongly correlated with the optical and radio light curves as expected from SSC emitting shock propagating in a conical jet.

astro-ph.HE↗

arXiv2018

Flux Distribution of Gamma-Ray Emission in Blazars: The Example of Mrk 501

Flux distribution is an important tool to understand the variability processes in active galactic nuclei. We now have available a great deal of observational evidences pointing towards the presence of log-normal components in the high energy light curves, and different models have been proposed to explain these data. Here, we collect some of the recent developments on this topic using the well-known blazar Mrk 501 as example of complex and interesting aspects coming from its flux distribution in different energy ranges and at different timescales. The observational data we refer to are those collected in a complementary manner by Fermi-LAT over multiple years, and by the First G-APD Cherenkov Telescope (FACT) telescope and the H.E.S.S. array in correspondence of the bright flare of June 2014.

astro-ph.HE↗

arXiv2018

Topological and metric recurrence for general Markov chains

Using ideas borrowed from topological dynamics and ergodic theory we introduce topological and metric versions of the recurrence property for general Markov chains. The main question of interest here is how large is the set of recurrent points. We show that under some mild technical assumptions the set of non recurrent points is of zero reference measure. Necessary and sufficient conditions for a reference measure $m$ (which needs not to be dynamically invariant) to satisfy this property are obtained. These results are new even in the purely deterministic setting.

math.PR↗

arXiv2018

Influence of capillary viscous flow on melting dynamics

The rate of melting of a solid and the rate of deformation of the resulting melt due to capillary forces are comparable in additive manufacturing applications. This dynamic structural change of a melting solid is extremely challenging to study experimentally. Using meshless numerical simulations we show the influence of the flow of the melt on the heat transfer and resulting phase change. We introduce an accurate and robust Incompressible Smoothed Particle Hydrodynamics method to simulate melting of solids and the ensuing fluid-solid interaction. We present validation for the heat transfer across free surface and the melting interface evolution, separately. We then present two applications for this coupled multiphysics simulation method---the study of rounding of an arbitrarily shaped particle during melting and the non-linear structural evolution of three spheres undergoing agglomeration. In both the studies we use realistic transport and thermal properties for the materials so as to demonstrate readiness of the method for solving engineering problems in additive manufacturing.

physics.comp-ph↗