We obtain the spectra of codimension-2 horizon "edge" degrees of freedom for gravity and higher-spin gauge fields in de Sitter space and in the static Nariai spacetime, advancing previous Lorentzian and Euclidean analyses of one-loop thermodynamics. The edge spectra exhibit universal shift symmetries, revealing a novel symmetry-breaking structure in one-loop partition functions with positive cosmological constant. For the graviton, these modes admit a geometric interpretation as fluctuations of the cosmic horizon, which also persists in the Nariai case.
Since the public release of ChatGPT in November 2022, the AI landscape is undergoing a rapid transformation. Currently, the use of AI chatbots by consumers has largely been limited to image generation or question-answering language models. The next generation of AI systems, AI agents that can plan and execute complex tasks with only limited human involvement, will be capable of a much broader range of actions. In particular, consumers could soon be able to delegate purchasing decisions to AI agents acting as Custobots. Against this background, the Article explores whether EU consumer law, as it currently stands, is ready for the rise of the Custobot Economy. In doing so, the Article makes three contributions. First, it outlines how the advent of AI agents could change the existing e-commerce landscape. Second, it explains how AI agents challenge the premises of a human-centric consumer law which is based on the assumption that consumption decisions are made by humans. Third, the Article presents some initial considerations how a future consumer law could look like that works for both humans and machines.
The scaling law is a notable property of neural network models and has significantly propelled the development of large language models. Scaling laws hold great promise in guiding model design and resource allocation. Recent research increasingly shows that scaling laws are not limited to NLP tasks or Transformer architectures; they also apply to domains such as recommendation. However, there is still a lack of literature on scaling law research in online advertisement retrieval systems. This may be because 1) identifying the scaling law for resource cost and online revenue is often expensive in both time and training resources for industrial applications, and 2) varying settings for different systems prevent the scaling law from being applied across various scenarios. To address these issues, we propose a lightweight paradigm to identify online scaling laws of retrieval models, incorporating a novel offline metric and an offline simulation algorithm. We prove that under mild assumptions, the correlation between the novel metric and online revenue asymptotically approaches 1 and empirically validates its effectiveness. The simulation algorithm can estimate the machine cost offline. Based on the lightweight paradigm, we can identify online scaling laws for retrieval models almost exclusively through offline experiments, and quickly estimate machine costs and revenues for given model configurations. We further validate the existence of scaling laws across mainstream model architectures (e.g., Transformer, MLP, and DSSM) in our real-world advertising system. With the identified scaling laws, we demonstrate practical applications for ROI-constrained model designing and multi-scenario resource allocation in the online advertising system. To the best of our knowledge, this is the first work to study identification and application of online scaling laws for online advertisement retrieval.
This manuscript establishes several sufficient conditions for the validity of both the reverse order law and forward order law for NDMPI. Additionally, some characterization of the reverse order law of the NDMPI is obtained. We also explore the applications of the reverse order law within this framework. Finally, we demonstrate the additivity of the NDMPI, supported by illustrative examples.
We consider a wavefunction of large $N$ matrices supported close to an emergent classical fuzzy sphere geometry. The $SU(N)$ Gauss law of the theory enforces correlations between the matrix degrees of freedom associated to a geometric subregion and their complement. We call this `Gauss law entanglement'. We show that the subregion degrees of freedom transform under a single dominant, low rank representation of $SU(N)$. The corresponding Gauss law entanglement entropy is given by the logarithm of the dimension of this dominant representation. It is found that, after coarse-graining in momentum space, the $SU(N)$ Gauss law entanglement entropy is proportional to the geometric area bounding the subregion. The constant of proportionality goes like the inverse of an emergent Maxwell coupling constant, reminiscent of gravitational entropy.
A. Feder Cooper, Katherine Lee, James Grimmelmann
et al.
This report presents the takeaways of the inaugural Workshop on Generative AI and Law (GenLaw), held in July 2023. A cross-disciplinary group of practitioners and scholars from computer science and law convened to discuss the technical, doctrinal, and policy challenges presented by law for Generative AI, and by Generative AI for law, with an emphasis on U.S. law in particular. We begin the report with a high-level statement about why Generative AI is both immensely significant and immensely challenging for law. To meet these challenges, we conclude that there is an essential need for 1) a shared knowledge base that provides a common conceptual language for experts across disciplines; 2) clarification of the distinctive technical capabilities of generative-AI systems, as compared and contrasted to other computer and AI systems; 3) a logical taxonomy of the legal issues these systems raise; and, 4) a concrete research agenda to promote collaboration and knowledge-sharing on emerging issues at the intersection of Generative AI and law. In this report, we synthesize the key takeaways from the GenLaw workshop that begin to address these needs. All of the listed authors contributed to the workshop upon which this report is based, but they and their organizations do not necessarily endorse all of the specific claims in this report.
The law of entropy increase postulates the existence of irreversible processes in physics: the total entropy of an isolated system can increase but cannot decrease. The annihilation of an electric current in normal metal with the generation of Joule heat because of a non-zero resistance is well-known example of irreversible process. The persistent current, an undamped electric current observed in a superconductor, annihilates after the transition into the normal state. Therefore this transition was considered as irreversible thermodynamic process before 1933. But if this transition is irreversible then the Meissner effect discovered in 1933 is experimental evidence of a process reverse to the irreversible process. Belief in the law of entropy increase forced physicists to change their understanding of the superconducting transition, which is considered a phase transition after 1933. This change has resulted to the internal inconsistency of the conventional theory of superconductivity, which is created within the framework of reversible thermodynamics but predicts Joule heating. The persistent current annihilates after the transition into the normal state with the generation of Joule heat and reappears during the return to the superconducting state according to this theory and contrary to the law of entropy increase. The success of the conventional theory of superconductivity forces to consider the validity of belief in the law of entropy increase.
We present a comprehensive review about the various facets of kink solutions with a power law tail which have received considerable attention during the last few years. This area of research is in its early stages and while several aspects have become clear by now, there are a number of issues which have only been partially understood or not understood at all. We first discuss the aspects which are reasonably well known and then address in some detail the issues which are only partially or not understood at all. We present a wide class of higher (than sixth) order field theory models admitting implicit kink as well as mirror kink solutions where the two tails facing each other have a power law or a power-tower type fall off while the other two ends not facing each other could have either an exponential or a power law tail. The models admitting implicit kink solutions where the two ends facing each other have an exponential tail while the other two ends have a power law tail are also discussed. Moreover, we present several field theory models which admit explicit kink solutions with a power law fall off. We note that in all the polynomial models while the potential $V(φ)$ is continuous, its derivative is discontinuous. We also discuss one of the most important and only partially understood issues of the kink-kink and the kink-antikink forces in case the tails facing each other have a power law fall off. Finally, we briefly discuss the kink-antikink collisions at finite velocity and present some open questions.
In this study we test 30 variants of 5 physical scaling laws that describe different aspects of solar flares. We express scaling laws in terms of the magnetic potential field energy $E_p$, the mean potential field strength $B_p$, the free energy $E_{free}$, the dissipated magnetic flare energy $E_{diss}$, the mean loop length scale $L$, the mean helically twisted flux tube radius $R$, the sunspot radius $r$, the emission measure-weighted flare temperature $T_w$, the electron density $n_e$, and the total emission measure $EM$, measured from a data set of $\lapprox 400$ GOES M- and X-class flare events. The 5 categories of physical scaling laws include (i) a scaling law of the potential-field energy, (ii) a scaling law for helical twisting, (iii) a scaling law for Petschek-type magnetic reconnection, (iv) the Rosner-Tucker-Vaiana scaling law, and (v) the Shibata-Yokoyama scaling law. We test the self-consistency of these theoretical scaling laws with observed parameters by requiring two conditions: a cross-corrleation coefficient of CCC$>$0.5 between the observed and theoretically predicted scaling laws, and a linear regression fit with a slope of $α\approx 1$. With these two criteria we find that 10 out of the 30 tested scaling law variants are consistent with the observed data, which strongly corroborates the existence and validity of the tested flare scaling laws.
We demonstrate the validity of Murray's law, which represents a scaling relation for branch conductivities in a transportation network, for discrete and continuum models of biological networks. We first consider discrete networks with general metabolic coefficient and multiple branching nodes and derive a generalization of the classical 3/4-law. Next we prove an analogue of the discrete Murray's law for the continuum system obtained in the continuum limit of the discrete model on a rectangular mesh. Finally, we consider a continuum model derived from phenomenological considerations and show the validity of the Murray's law for its linearly stable steady states.
A precise extinction law is a critical input when interpreting observations of highly reddened sources such as young star clusters and the Galactic Center (GC). We use Hubble Space Telescope observations of a region of moderate extinction and a region of high extinction to measure the optical and near-infrared extinction law (0.8 $μ$m -- 2.2 $μ$m). The moderate extinction region is the young massive cluster Westerlund 1 (Wd1; A$_{Ks} \sim$ 0.6 mag), where 453 proper motion-selected main-sequence stars are used to measure the shape of the extinction law. To quantify the shape we define the parameter $\mathcal{S}_{1/λ}$, which behaves similarly to a color excess ratio but is continuous as a function of wavelength. The high extinction region is the GC (A$_{Ks} \sim$ 2.5 mag), where 819 red clump stars are used to determine the normalization of the law. The best-fit extinction law is able to reproduce the Wd1 main sequence colors, which previous laws misestimate by 10%-30%. The law is inconsistent with a single power law, even when only the near-infrared filters are considered, and has A$_{F125W}$/A$_{Ks}$ and A$_{F814W}$/A$_{Ks}$ values that are 18% and 24% larger than the commonly used \citet{Nishiyama:2009fc} law, respectively. Using the law we recalculate the Wd1 distance to be 3896 $\pm$ 328 pc from published observations of eclipsing binary W13. This new extinction law should be used for highly reddened populations in the Milky Way, such as the Quintuplet cluster and Young Nuclear Cluster. A python code is provided to generate the law for future use.
We pointed out that the generalized second law of thermodynamics on a de Sitter universe whose energy density stochastically fluctuates due to quantum fluctuations is seemingly violated. We have shown that even in such a case, the generalized second law is unviolated by taking cosmological decoherence into account. It has been well known that the decoherence is necessary to give a reasonable reason why our universe looks classical. Our proposal can support the importance of decoherence from another aspect, i.e. the generalized second law of thermodynamics.
Martín Monteiro, Cecilia Stari, Cecilia Cabeza
et al.
Originally an empirical law, nowadays Malus' law is seen as a key experiment to demonstrate the transverse nature of electromagnetic waves, as well as the intrinsic connection between optics and electromagnetism. In this work, a simple and inexpensive setup is proposed to quantitatively verify the nature of polarized light. A flat computer screen serves as a source of linear polarized light and a smartphone (possessing ambient light and orientation sensors) is used, thanks to its built-in sensors, to experiment with polarized light and verify the Malus' law.
David R. Law, Charles C. Steidel, Alice E. Shapley
et al.
We analyze rest-frame optical morphologies and gas-phase kinematics as traced by rest-frame far-UV and optical spectra for a sample of 204 star forming galaxies in the redshift range z ~ 2-3 drawn from the Keck Baryonic Structure Survey (KBSS). We find that spectroscopic properties and gas-phase kinematics are closely linked to morphology: compact galaxies with semi-major axis radii r <~ 2 kpc are substantially more likely than their larger counterparts to exhibit LyA in emission. Although LyA emission strength varies widely within galaxies of a given morphological type, all but one of 19 galaxies with LyA equivalent width W_LyA > 20 Angstroms have compact and/or multiple-component morphologies with r <= 2.5 kpc. The velocity structure of absorption lines in the galactic continuum spectra also varies as a function of morphology. Galaxies of all morphological types drive similarly strong outflows (as traced by the blue wing of interstellar absorption line features), but the outflows of larger galaxies are less highly ionized and exhibit larger optical depth at the systemic redshift that may correspond to a decreasing efficiency of feedback in evacuating gas from the galaxy. This v ~ 0 km/s gas is responsible both for shifting the mean absorption line redshift and attenuating W_LyA (via a longer resonant scattering path) in galaxies with larger rest-optical half light radii. In contrast to galaxies at lower redshifts, there is no evidence for a correlation between outflow velocity and inclination, suggesting that outflows from these puffy and irregular systems may be poorly collimated. (Abbrev.)
We derive a fundamental conservation law of operator current for master equations describing reduced quantum systems. If this law is broken, the temporal integral of the current operator of an arbitrary system observable does not yield in general the change of that observable in the evolution. We study Lindblad-type master equations as examples and prove that the application of the secular approximation during their derivation results in a violation of the conservation law. We show that generally any violation of the law leads to artificial corrections to the complete quantum dynamics, thus questioning the accuracy of the particular master equation.
Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very robust as an experimental observation, but to date it escaped satisfactory theoretical explanation. We suggest that Zipf's law may arise from the evolution of word semantics dominated by expansion of meanings and competition of synonyms.
A small review on scattering approach to electric transport. Transmission distribution can be gotten from Ohm's law and/or circuit theory. Send me a postcard if you read it all and enjoy.
Power law distributions have been found in many natural and social phenomena, and more recently in the source code and run-time characteristics of Object-Oriented (OO) systems. A power law implies that small values are extremely common, whereas large values are extremely rare. In this paper, we identify twelve new power laws relating to the static graph structures of Java programs. The graph structures analyzed represented different forms of OO coupling, namely, inheritance, aggregation, interface, parameter type and return type. Identification of these new laws provide the basis for predicting likely features of classes in future developments. The research in this paper ties together work in object-based coupling and World Wide Web structures.
An analytical expression is presented that allows gas-to-dust elemental depletions to be estimated in interstellar environments of different types, including Damped Ly alpha systems, by scaling an arbitrary depletion pattern chosen as a reference. As an improvement on previous work, the scaling relation allows the dust chemical composition to vary and includes a set of parameters which describe how sensitive the dust composition is to changes in both the dust-to-metals ratio and the composition of the medium. These parameters can be estimated empirically from studies of Galactic and extragalactic depletion patterns. The scaling law is able to fit all the typical depletion patterns of the Milky Way ISM (cold disk, warm disk, and warm halo) with a single set of parameters, by only varying the dust-to-metals ratio. The dependence of the scaling law on the abundances of the medium has been tested using interstellar observations of the Small Magellanic Cloud (SMC), for which peculiar depletion patterns have been reported in literature. The scaling law is able to fit these depletion patterns assuming that the SMC relative abundances are slightly non solar.