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Exploring vibronic dynamics near a sloped conical intersection with trapped Rydberg ions
Abdessamad Belfakir, Weibin Li
https://arxiv.org/abs/2512.04941 https://arxiv.org/pdf/2512.04941 https://arxiv.org/html/2512.04941
arXiv:2512.04941v1 Announce Type: new
Abstract: We study spin-phonon coupled dynamics in the vicinity of a sloped conical intersection created by laser coupling the electronic (spin) and vibrational degrees of freedom of a pair of trapped Rydberg ions. We show that the shape of the potential energy surfaces can be engineered and controlled by exploiting the sideband transitions of the crystal vibration and dipole-dipole interactions between Rydberg ions in the Lamb-Dicke regime. Using the sideband transition, we realize a sloped conical intersection whose cone axis is only tilted along one spatial axis. When the phonon wavepacket is located in the potential minimum of the lower potential surface, the spin and phonon dynamics are largely frozen owing to the geometric phase effect. When starting from the upper potential surface, the electronic and phonon states tunnel to the lower potential surface, leading to a partial revival of the initial state. In contrast, the dynamics drastically change when the initial wavepackets are away from the conical intersection. The initial state is revived, and is almost entirely irrelevant to whether it is from the lower or upper potential surface. Complete Rabi oscillations of the adiabatic states are found when the wavepacket is initialized on the upper potential surface. The dynamics occur on the microsecond and nanometer scales, implying that Rydberg ions provide a platform for simulating nonadiabatic processes in the vicinity of a sloped conical intersection.
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Strategyproof Tournament Rules for Teams with a Constant Degree of Selfishness
David Pennock, Daniel Schoepflin, Kangning Wang
https://arxiv.org/abs/2512.05235 https://arxiv.org/pdf/2512.05235 https://arxiv.org/html/2512.05235
arXiv:2512.05235v1 Announce Type: new
Abstract: We revisit the well-studied problem of designing fair and manipulation-resistant tournament rules. In this problem, we seek a mechanism that (probabilistically) identifies the winner of a tournament after observing round-robin play among $n$ teams in a league. Such a mechanism should satisfy the natural properties of monotonicity and Condorcet consistency. Moreover, from the league's perspective, the winner-determination tournament rule should be strategyproof, meaning that no team can do better by losing a game on purpose.
Past work considered settings in which each team is fully selfish, caring only about its own probability of winning, and settings in which each team is fully selfless, caring only about the total winning probability of itself and the team to which it deliberately loses. More recently, researchers considered a mixture of these two settings with a parameter $\lambda$. Intermediate selfishness $\lambda$ means that a team will not lose on purpose unless its pair gains at least $\lambda s$ winning probability, where $s$ is the individual team's sacrifice from its own winning probability. All of the dozens of previously known tournament rules require $\lambda = \Omega(n)$ to be strategyproof, and it has been an open problem to find such a rule with the smallest $\lambda$.
In this work, we make significant progress by designing a tournament rule that is strategyproof with $\lambda = 11$. Along the way, we propose a new notion of multiplicative pairwise non-manipulability that ensures that two teams cannot manipulate the outcome of a game to increase the sum of their winning probabilities by more than a multiplicative factor $\delta$ and provide a rule which is multiplicatively pairwise non-manipulable for $\delta = 3.5$.
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State and Parameter Estimation for a Neural Model of Local Field Potentials
Daniele Avitabile, Gabriel J. Lord, Khadija Meddouni
https://arxiv.org/abs/2512.07842 https://arxiv.org/pdf/2512.07842 https://arxiv.org/html/2512.07842
arXiv:2512.07842v1 Announce Type: new
Abstract: The study of cortical dynamics during different states such as decision making, sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate the neural rhythms present in cortical recordings to the underlying dynamics responsible for their emergence. We present an effort to characterize the neural activity from the cortex of a mouse during natural sleep, captured through local field potential measurements. Our approach relies on using a discretized Wilson--Cowan Amari neural field model for neural activity, along with a data assimilation method that allows the Bayesian joint estimation of the state and parameters. We demonstrate the feasibility of our approach on synthetic measurements before applying it to a dataset available in literature. Our findings suggest the potential of our approach to characterize the stimulus received by the cortex from other brain regions, while simultaneously inferring a state that aligns with the observed signal.
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Totally paracompact spaces and the Menger covering property
Davide Giacopello, Maddalena Bonanzinga, Piotr Szewczak
https://arxiv.org/abs/2511.10252 https://arxiv.org/pdf/2511.10252 https://arxiv.org/html/2511.10252
arXiv:2511.10252v1 Announce Type: new
Abstract: A topological space is totally paracompact if any base of this space contains a locally finite subcover. We focus on a problem of Curtis whether in the class of regular Lindel\"of spaces total paracompactness is equivalent to the Menger covering property. To this end we consider topological spaces with certain dense subsets. It follows from our results that the above equivalence holds in the class of Lindel\"of GO-spaces defined on subsets of reals. We also provide a game-theoretical proof that any regular Menger space is totally paracompact and show that in the class of first-countable spaces the Menger game and a partial open neighborhood assignment game of Aurichi are equivalent. We also show that if $\mathfrak{b}=\omega_1$, then there is an uncountable subspace of the Sorgenfrey line whose all finite powers are Lindel\"of, which is a strengthening of a famous result due to Michael.
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Invariant Price of Anarchy: a Metric for Welfarist Traffic Control
Ilia Shilov, Mingjia He, Heinrich H. Nax, Emilio Frazzoli, Gioele Zardini, Saverio Bolognani
https://arxiv.org/abs/2512.05843 https://arxiv.org/pdf/2512.05843 https://arxiv.org/html/2512.05843
arXiv:2512.05843v1 Announce Type: new
Abstract: The Price of Anarchy (PoA) is a standard metric for quantifying inefficiency in socio-technical systems, widely used to guide policies like traffic tolling. Conventional PoA analysis relies on exact numerical costs. However, in many settings, costs represent agents' preferences and may be defined only up to possibly arbitrary scaling and shifting, representing informational and modeling ambiguities. We observe that while such transformations preserve equilibrium and optimal outcomes, they change the PoA value. To resolve this issue, we rely on results from Social Choice Theory and define the Invariant PoA. By connecting admissible transformations to degrees of comparability of agents' costs, we derive the specific social welfare functions which ensure that efficiency evaluations do not depend on arbitrary rescalings or translations of individual costs. Case studies on a toy example and the Zurich network demonstrate that identical tolling strategies can lead to substantially different efficiency estimates depending on the assumed comparability. Our framework thus demonstrates that explicit axiomatic foundations are necessary in order to define efficiency metrics and to appropriately guide policy in large-scale infrastructure design robustly and effectively.
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Meta-learning three-factor plasticity rules for structured credit assignment with sparse feedback
Dimitra Maoutsa
https://arxiv.org/abs/2512.09366 https://arxiv.org/pdf/2512.09366 https://arxiv.org/html/2512.09366
arXiv:2512.09366v1 Announce Type: new
Abstract: Biological neural networks learn complex behaviors from sparse, delayed feedback using local synaptic plasticity, yet the mechanisms enabling structured credit assignment remain elusive. In contrast, artificial recurrent networks solving similar tasks typically rely on biologically implausible global learning rules or hand-crafted local updates. The space of local plasticity rules capable of supporting learning from delayed reinforcement remains largely unexplored. Here, we present a meta-learning framework that discovers local learning rules for structured credit assignment in recurrent networks trained with sparse feedback. Our approach interleaves local neo-Hebbian-like updates during task execution with an outer loop that optimizes plasticity parameters via \textbf{tangent-propagation through learning}. The resulting three-factor learning rules enable long-timescale credit assignment using only local information and delayed rewards, offering new insights into biologically grounded mechanisms for learning in recurrent circuits.
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The Theory of Strategic Evolution: Games with Endogenous Players and Strategic Replicators
Kevin Vallier
https://arxiv.org/abs/2512.07901 https://arxiv.org/pdf/2512.07901 https://arxiv.org/html/2512.07901
arXiv:2512.07901v1 Announce Type: new
Abstract: This paper develops the Theory of Strategic Evolution, a general model for systems in which the population of players, strategies, and institutional rules evolve together. The theory extends replicator dynamics to settings with endogenous players, multi level selection, innovation, constitutional change, and meta governance. The central mathematical object is a Poiesis stack: a hierarchy of strategic layers linked by cross level gain matrices. Under small gain conditions, the system admits a global Lyapunov function and satisfies selection, tracking, and stochastic stability results at every finite depth. We prove that the class is closed under block extension, innovation events, heterogeneous utilities, continuous strategy spaces, and constitutional evolution. The closure theorem shows that no new dynamics arise at higher levels and that unrestricted self modification cannot preserve Lyapunov structure. The theory unifies results from evolutionary game theory, institutional design, innovation dynamics, and constitutional political economy, providing a general mathematical model of long run strategic adaptation.
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