The classic result of Bulow and Klemperer (1996) shows that in multi-unit auctions with $m$ units and $n\geq m$ buyers whose values are sampled i.i.d. from a regular distribution, the revenue of the VCG auction with $m$ additional buyers is at least as large as the optimal revenue. Unfortunately, for regular distributions, adding $m$ additional buyers is sometimes indeed necessary, so the "competition complexity" of the VCG auction is $m$. We seek proving better competition complexity results in two dimensions. First, under stronger distributional assumptions, the competition complexity of VCG auction drops dramatically. In balanced markets (where $m=n$) with MHR distributions, it is sufficient to only add $(e^{1/e} - 1 + o(1))n \approx 0.4447n$ additional buyers to match the optimal revenue -- less than half the number that is necessary under regularity -- and this bound is asymptotically tight. We provide both exact finite-market results for small value of $n$, and closed-form asymptotic formulas for general market with any $m\leq n$, and any target fraction of the optimal revenue. Second, we analyze a supply-limiting variant of VCG auction that caps the number of units sold in a prior-independent way. Whenever the goal is to achieve almost the optimal revenue, this mechanism strictly improves upon standard VCG auction, requiring significantly fewer additional buyers. Together, our results show that both stronger distributional assumptions, as well as a simple prior-independent refinement to the VCG auction, can each substantially reduce the number of additional buyers that is sufficient to achieve (near-)optimal revenue. Our analysis hinges on a unified worst-case reduction to truncated generalized Pareto distributions, enabling both numerical computation and analytical tractability.
Belief dynamics are fundamental to human behavior and social coordination. Individuals rely on accurate beliefs to make decisions, and shared beliefs form the basis of successful cooperation. Traditional studies often examined beliefs in isolation, but recent perspectives suggest beliefs operate as interconnected systems, both within individuals and across social networks. To better understand belief dynamics, we propose an extension of Galesic et al.'s model, which allows individuals to weigh internal and social dissonance based on belief certainty. Our model suggests that belief convergence occurs in two patterns: internal alignment, where beliefs become ideologically consistent but socially disagreeable, or social alignment, where beliefs become socially consistent but internally varied. These results highlight a competition between internal and social belief networks, with one network often dominating. Our findings suggest that belief dynamics tend to settle at extremes, indicating a need for future models to incorporate negative feedback to reflect more nuanced societal belief changes.
We follow the work of Aguiar on internal categories and introduce simplicial objects internal to a monoidal category as certain colax monoidal functors. Then we compare three approaches to equipping them with a discrete set of vertices. We introduce based colax monoidal functors and show that under suitable conditions they are equivalent to the templicial objects defined in arXiv:2302.02484v2. We also compare templicial objects to the enriched Segal precategories appearing in the work of Lurie, Simpson and Bacard, and show that they are equivalent for cartesian monoidal categories, but not in general.
The cooling of neutron stars (hereafter NS) has the potential to reveal important features of superdense matter. Their surface temperatures are known for a fair sample of NS with ages $\leq 10^{6} \, {\it{yr}}$, and with a few exceptions, can be accommodated by standard cooling mechanisms (neutrino+photon emission without internal heating). However, for the older objects it is necessary to consider some internal heating to explain surface temperatures higher than expected. We revisit in this paper the kinetic heating by fermionic dark matter, rotochemical heating and magnetic field decay. We found that NS slightly older than $\sim 10^{6} \, {\it{yr}}$ can be explained by them, but the older ``black widow'' systems are much hotter than the values predicted by these three mechanisms, pointing towards a yet unknown heating factor for old NS.
Jing Shuang Li, Anish A. Sarma, Terrence J. Sejnowski
et al.
Animals move smoothly and reliably in unpredictable environments. Models of sensorimotor control have assumed that sensory information from the environment leads to actions, which then act back on the environment, creating a single, unidirectional perception-action loop. This loop contains internal delays in sensory and motor pathways, which can lead to unstable control. We show here that these delays can be compensated by internal feedback signals that flow backwards, from motor towards sensory areas. Internal feedback is ubiquitous in neural sensorimotor systems and recent advances in control theory show how internal feedback compensates internal delays. This is accomplished by filtering out self-generated and other predictable changes in early sensory areas so that unpredicted, actionable information can be rapidly transmitted toward action by the fastest components. For example, fast, giant neurons are necessarily less accurate than smaller neurons, but they are crucial for fast and accurate behavior. We use a mathematically tractable control model to show that internal feedback has an indispensable role in achieving state estimation, localization of function -- how different parts of cortex control different parts of the body -- and attention, all of which are crucial for effective sensorimotor control. This control model can explain anatomical, physiological and behavioral observations, including motor signals in visual cortex, heterogeneous kinetics of sensory receptors and the presence of giant Betz cells in motor cortex, Meynert cells in visual cortex and giant von Economo cells in the prefrontal cortex of humans as well as internal feedback patterns and unexplained heterogeneity in other neural systems.
According to von Neumann, the global Hamiltonian of whole universe must be Hermitian in order to keep the eigenvalues real and to construct a self-consistent quantum theory. In addition to the open system approach by introducing environmental degrees of freedom to a small system, a global Hermitian Hamiltonian can also be generated through the dilation from a small Hilbert space. For example, a local non-Hermitian $\cal PT$-symmetric system can be simulated with a global Hermitian one by the Naimark dilation. When shared by Alice and Bob, the internal nonlocality in such dilated Hermitian systems is revealed recently, but only with a two-fold structure. In this paper, we extend such a discussion to the generalized case when the two-fold structure breaks. The internal nonlocality is discussed with different correlation pictures and the corresponding correlation bounds. Our results provide a device-independent test on the reliability of the simulation in the global Hermiticity.
Fabio Poletto, Yunbai Zhang, Andre Panisson
et al.
This paper describes in details the design and development of a novel annotation framework and of annotated resources for Internal Displacement, as the outcome of a collaboration with the Internal Displacement Monitoring Centre, aimed at improving the accuracy of their monitoring platform IDETECT. The schema includes multi-faceted description of the events, including cause, quantity of people displaced, location and date. Higher-order facets aimed at improving the information extraction, such as document relevance and type, are proposed. We also report a case study of machine learning application to the document classification tasks. Finally, we discuss the importance of standardized schema in dataset benchmark development and its impact on the development of reliable disaster monitoring infrastructure.
Packing and crowding are used in biology as mechanisms to (self-)regulate internal molecular or cellular processes based on collective signalling. Here, we study how the transition kinetics of an internal switch of responsive macromolecules is modified collectively by their spatial packing. We employ Brownian dynamics simulations of a model of responsive colloids (RCs), in which an explicit internal degree of freedom, here, the particle size, moving in a bimodal energy landscape responds self-consistently to the density fluctuations of the crowded environment. We demonstrate that populations and transition times for the two-state switching kinetics can be tuned over one order of magnitude by self-crowding. An exponential scaling law derived from a combination of Kramers' and liquid state perturbation theory is in very good agreement with the simulations.
We propose a new model of the oculomotor system, particularly the vestibulo-ocular reflex, gaze fixation, and smooth pursuit. Our key insight is to exploit recent developments on adaptive internal models. The outcome is a simple model that includes the interactions between the brainstem and the cerebellum and that recovers behaviors from more than 15 oculomotor experiments. In addition, we put forward a thesis that the cerebellum embodies internal models of all persistent, exogenous reference and disturbance signals acting on the body and observable through the error signals it receives.
We investigate the presence of magnetic monopoles in a model that extends the non Abelian model originally studied by 't Hooft and Polyakov with the inclusion of an extra neutral field. The investigation includes modifications of the dynamics of the gauged fields, and the main results unveil a route to construct solutions that engender internal structure and live in a compact space.
Extractive industries (oil, gas, and mining) have the potential to generate significant wealth for developing countries and to serve as important catalysts for growth. They generate large revenues-through royalties, taxation, and exports-and create employment. In some cases, however, resource wealth is associated with political turmoil, deteriorating standards of living, civil conflict, and elite capture. The management's response to the Extractive Industries Review (EIR) and accompanying evaluations signaled a critical turning point in the World Bank Group's (WBG's) engagement in the sector, which had hitherto focused primarily on exploration and development activities, sector policy reform, and commercialization of state-owned enterprises. This publication presents four of the finalist case studies, selected on the basis of project: 1) scalability; 2) replicability; 3) innovation; and 4) level of multi-stakeholder collaboration. In an effort to better document and showcase the variety of ways in which country teams are working with different actors on the often sensitive topic of good governance in the oil, gas, and mining sectors, the World Bank Institute and the World Bank Oil, Gas and Mining Unit (SEGOM) initiated an internal case story competition in 2011.
Konrad Banaszek, Pawel Horodecki, Michal Karpinski
et al.
For a particle travelling through an interferometer, the trade-off between the available which-way information and the interference visibility provides a lucid manifestation of the quantum mechanical wave-particle duality. Here we analyze this relation for a particle possessing an internal degree of freedom such as spin. We quantify the trade-off with a general inequality that paints an unexpectedly intricate picture of wave-particle duality when internal states are involved. Strikingly, in some instances which-way information becomes erased by introducing classical uncertainty in the internal degree of freedom. Furthermore, even imperfect interference visibility measured for a suitable set of spin preparations can be sufficient to infer absence of which-way information. General results are illustrated with a proof-of-principle single photon experiment.
Vinod Ramaswamy, Sachin Adlakha, Srinivas Shakkottai
et al.
The rapid growth of content distribution on the Internet has brought with it proportional increases in the costs of distributing content. Adding to distribution costs is the fact that digital content is easily duplicable, and hence can be shared in an illicit peer-to-peer (P2P) manner that generates no revenue for the content provider. In this paper, we study whether the content provider can recover lost revenue through a more innovative approach to distribution. In particular, we evaluate the benefits of a hybrid revenue-sharing system that combines a legitimate P2P swarm and a centralized client-server approach. We show how the revenue recovered by the content provider using a server-supported legitimate P2P swarm can exceed that of the monopolistic scheme by an order of magnitude. Our analytical results are obtained in a fluid model, and supported by stochastic simulations.
Common models of blazars and gamma-ray bursts assume that the plasma underlying the ob- served phenomenology is magnetized to some extent. Within this context, radiative signatures of dissipation of kinetic and conversion of magnetic energy in internal shocks of relativistic magnetized outflows are studied. We model internal shocks as being caused by collisions of homogeneous plasma shells. We compute the flow state after the shell interaction by solving Riemann problems at the contact surface between the colliding shells, and then compute the emission from the resulting shocks. Under the assumption of a constant flow luminosity we find that there is a clear difference between the models where both shells are weakly magne- tized (σ<\sim0.01) and those where, at least, one shell has a σ>\sim0.01. We obtain that the radiative efficiency is largest for models in which, regardless of the ordering, one shell is weakly and the other strongly magnetized. Substantial differences between weakly and strongly magne- tized shell collisions are observed in the inverse-Compton part of the spectrum, as well as in the optical, X-ray and 1GeV light curves. We propose a way to distinguish observationally between weakly magnetized from magnetized internal shocks by comparing the maximum frequency of the inverse-Compton and synchrotron part of the spectrum to the ratio of the inverse-Compton and synchrotron fluence. Finally, our results suggest that LBL blazars may correspond to barely magnetized flows, while HBL blazars could correspond to moderately magnetized ones. Indeed, by comparing with actual blazar observations we conclude that the magnetization of typical blazars is σ <\sim 0.01 for the internal shock model to be valid in these sources.
We consider the transport of electrons passing through a mesoscopic device possessing internal dynamical quantum degrees of freedom. The mutual interaction between the system and the conduction electrons contributes to the current fluctuations, which we describe in terms of full counting statistics. We identify conditions where this discriminates coherent from incoherent internal dynamics, and also identify and illustrate conditions under which the device acts to dynamically bunch transmitted or reflected electrons, thereby generating super-Poissonian noise.
Aleksandr Bekshaev, Konstantin Bliokh, Marat Soskin
We review optical phenomena associated with the internal energy redistribution which accompany propagation and transformations of monochromatic light fields in homogeneous media. The total energy flow (linear-momentum density, Poynting vector) can be divided into spin part associated with the polarization and orbital part associated with the spatial inhomogeneity. We give general description of the internal flows in the coordinate and momentum (angular spectrum) representations for both nonparaxial and paraxial fields. This enables one to determine local densities and integral values of the spin and orbital angular momenta of the field. We analyse patterns of the internal flows in standard beam models (Gaussian, Laguerre-Gaussian, flat-top beam, etc.), which provide an insightful picture of the energy transport. The emphasize is made to the singular points of the flow fields. We describe the spin-orbit and orbit-orbit interactions in the processes of beam focusing and symmetry breakdown. Finally, we consider how the energy flows manifest themselves in the mechanical action on probing particles and in the transformations of a propagating beam subjected to a transverse perturbation.