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In astrophysical and cosmological analyses, the increasing quality and volume of astronomical data demand efficient and precise computational tools. This work introduces a novel adaptive algorithm for automatic knots (AutoKnots) allocation in spline interpolation, designed to meet user-defined precision requirements. Unlike traditional methods that rely on manually configured knot distributions with numerous parameters, the proposed technique automatically determines the optimal number and placement of knots based on interpolation error criteria. This simplifies configuration, often requiring only a single parameter. The algorithm progressively improves the interpolation by adaptively sampling the function-to-be-approximated, $f(x)$, in regions where the interpolation error exceeds the desired threshold. All function evaluations contribute directly to the final approximation, ensuring efficiency. While each resampling step involves recomputing the interpolation table, this process is highly optimized and usually computationally negligible compared to the cost of evaluating $f(x)$. We show the algorithm's efficacy through a series of precision tests on different functions. However, the study underscores the necessity for caution when dealing with certain function types, notably those featuring plateaus. To address this challenge, a heuristic enhancement is incorporated, improving accuracy in flat regions. This algorithm has been extensively used and tested over the years. NumCosmo includes a comprehensive set of unit tests that rigorously evaluate the algorithm both directly and indirectly, underscoring its robustness and reliability. As a practical application, we compute the surface mass density $\Sigma(R)$ and the average surface mass density $\overline{\Sigma}(

Symbolic regression is a machine learning technique, and it has seen many advancements in recent years, especially in genetic programming approaches (GPSR). Furthermore, it has been known for many years that constant optimization of parameters, during the evolutionary search, greatly increases GPSR performance However, different authors approach such tasks differently and no consensus exists regarding which methods perform best. In this work, we evaluate eight different parameter optimization methods, applied during evolutionary search, over ten known benchmark problems, in two different scenarios. We also propose using an under-explored metric called Tree Edit Distance (TED), aiming to identify symbolic accuracy. In conjunction with classical error measures, we develop a combined analysis of model performance in symbolic regression. We then show that different constant optimization methods perform better in certain scenarios and that there is no overall best choice for every problem. Finally, we discuss how common metric decisions may be biased and appear to generate better models in comparison., Comment: 9 pages, 10 figures, 2 tables

Positron emission tomography (PET) is the most sensitive biomedical imaging modality for non-invasively detecting and visualizing positron-emitting radiopharmaceuticals within a subject. In PET, measuring the time-of-flight (TOF) information for each pair of 511-keV annihilation photons improves effective sensitivity but requires high timing resolution. Hybrid materials that emit both scintillation and Cherenkov photons, such as bismuth germanate (BGO), recently offer the potential for more precise timing information from Cherenkov photons while maintaining adequate energy resolution from scintillation photons. However, a significant challenge in using such hybrid materials for TOF PET applications lies in the event-dependent timing spread caused by the mixed detection of Cherenkov and scintillation photons due to relatively lower production of Cherenkov photons. This study introduces an innovative approach by segmenting silicon photomultiplier (SiPM) pixels coupled to a single crystal, rather than using traditional SiPMs that are as large as or larger than the crystals they read. We demonstrated that multiple time stamps and photon counts obtained from the segmented SiPM can classify events by providing temporal photon density, effectively addressing this challenge. The approach and findings would lead to new opportunities in applications that require precise timing and photon counting, spanning the fields of medical imaging, high-energy physics, and optical physics.

The intensity noise of a laser source represents one of the key factors limiting the ultimate sensitivity in laser-based systems for sensing and telecommunication. For advanced applications based on interferometry, the availability of a shot-noise-limited local oscillator is even more important for the effective feasibility of high-precision measurements. This is particularly crucial in quantum optics applications based on homodyne detection schemes to measure non-classical light states, such as squeezed states. This work deeply investigates and analyzes the intensity noise features of the most widely used mid-infrared semiconductor heterostructured lasers: quantum cascade and interband cascade lasers. For this purpose, a comprehensive comparison of three different continuous-wave lasers operating at room temperature around 4.5 {\mu}m wavelength is presented. First, a thorough electro-optical characterization is given, highlighting the differences and the shared common characteristics of the tested devices. Then, a detailed intensity noise analysis is reported, identifying their different noise operations with a particular reference to shot-noise-limited operations. Finally, some perspectives towards advanced applications are discussed., Comment: 17 pages, 5 figures

We study the mass exchange between two rotating, quantum massive vortices in a two-component Bose-Einstein condensate. The vortices, in the majority component, exhibit a filled core, where the in-filling minority component undergoes a quantum tunneling effect. Remarkably, we observe that the two-vortex system features stable Josephson oscillations, as well as all the nonlinear phenomena, including the macroscopic quantum self-trapping, that characterize a Bosonic Josephson Junction (BJJ). We propose an analytical model for describing the inter-vortex tunneling, obtained by implementing the a coherent-state representation of the two-mode Bose-Hubbard model. This allows us to give the explicit expression of the model's parameters in terms of the physical macroscopic parameters of the two-vortex system. The comparison of the dynamical scenario predicted by the model with that emerging from the Gross-Pitaevskii equations is very good for sufficiently small particle numbers, while at larger particle numbers it grows less precise, presumably due to the partial exclusion of the many-body interactions from our model. The definition of an effective self-interaction parameter allows us to include the many-body effects, thus restoring a quite good agreement with the numerical results. Interestingly, the recognition of the bosonic Josephson dynamics paves the way to the investigation of new dynamical behaviors in multi-vortex configurations., Comment: 13 pages, 14 figures

Practical mechanisms often limit agent reports to constrained formats like trades or orderings, potentially limiting the information agents can express. We propose a novel class of mechanisms that elicit agent reports in natural language and leverage the world-modeling capabilities of large language models (LLMs) to select outcomes and assign payoffs. We identify sufficient conditions for these mechanisms to be incentive-compatible and efficient as the LLM being a good enough world model and a strong inter-agent information over-determination condition. We show situations where these LM-based mechanisms can successfully aggregate information in signal structures on which prediction markets fail., Comment: presented as a poster at ACM EC 24 Foundation Models and Game Theory Workshop

In this paper, we investigate the impact of reward schemes and committee sizes motivated by governance systems over blockchain communities. We introduce a model for elections with a binary outcome space where there is a ground truth (i.e., a "correct" outcome), and where stakeholders can only choose to delegate their voting power to a set of delegation representatives (DReps). Moreover, the effort (cost) invested by each DRep positively influences both (i) her ability to vote correctly and (ii) the total delegation that she attracts, thereby increasing her voting power. This model constitutes the natural counterpart of delegated proof-of-stake (PoS) protocols, where delegated stakes are used to elect the block builders. As a way to motivate the representatives to exert effort, a reward scheme can be used based on the delegation attracted by each DRep. We analyze both the game-theoretic aspects and the optimization counterpart of this model. Our primary focus is on selecting a committee that maximizes the probability of reaching the correct outcome, given a fixed monetary budget allocated for rewarding the delegates. Our findings provide insights into the design of effective reward mechanisms and optimal committee structures (i.e., how many DReps are enough) in these PoS-like governance systems.

The graviton S-matrix has a famous soft pole. We show that the S-matrix for cylindrical gravitational waves has a soft zero. The soft pole for ordinary gravitons comes from a Ward identity for supertranslation symmetry at asymptotic infinity. We show that the soft zero for cylindrical gravitational waves comes from a Ward identity for Geroch symmetry at asymptotic infinity. Because it is a zero rather than a pole, there is no memory effect. Overall, this soft zero is a manifestation of Geroch symmetry and of the extraordinary simplicity of cylindrical gravitational waves., Comment: 10 pages

In the face of limited block size, miners (e.g., in Bitcoin) prioritize high-bid transactions, forming a large part of their revenue. If the block size were to expand significantly, meeting all transaction demand due to infrastructure or protocol improvements, bids could drop to zero or to a minimum fee, reducing mining incentives and potentially affecting security. To address this, Lavi et al. (2022) introduced a monopolistic pricing mechanism where miners only include transactions paying a minimum price, ensuring some revenue but resulting in an unbounded loss in welfare. Nisan (2023) expands this by modeling bidders as patient, who wait indefinitely long for lower prices, causing price fluctuations even with stable demand. In order to capture users' diminishing interest in having their transactions added to the ledger over time, we consider a more realistic setting with quasi-patient users, where only a fraction $\delta \in [0,1]$ of pending transactions remains in the next round. This richer model encompasses both Lavi et al.'s impatient users ($\delta=0$) and Nisan's patient users ($\delta=1$) as special cases. We demonstrate that Nisan's fluctuating dynamics persist for $\delta$ close to 1, while for $\delta$ close to 0, the dynamics resemble the impatient case. For $\delta \in (0,1)$, we establish new bounds on price dynamics, revealing unexpected effects. Unlike the fully patient case, the bounds of the dynamics for $\delta<1$ depend on the demand curve and undergo a "transition phase". For some $\delta$, the model mirrors the fully patient setting, and for smaller $\delta' < \delta$, it stabilizes at the highest monopolist price, thus collapsing to the impatient case. We provide quantitative bounds and analytical results, showing that the bounds for $\delta=1$ are generally not tight for $\delta<1$, and we give guarantees on the minimum ("admission") price for transactions.

We investigate a machine learning based classification of noise acting on a small quantum network with the aim of detecting spatial or multilevel correlations, and the interplay with Markovianity. We control a three-level system by inducing coherent population transfer exploiting different pulse amplitude combinations as inputs to train a feedforward neural network. We show that supervised learning can classify different types of classical dephasing noise affecting the system. Three non-Markovian (quasi-static correlated, anti-correlated and uncorrelated) and Markovian noises are classified with more than $99\%$ accuracy. On the contrary, correlations of Markovian noise cannot be discriminated with our method. Our approach is robust to statistical measurement errors and retains its effectiveness for physical measurements where only a limited number of samples is available making it very experimental-friendly. Our result paves the way for classifying spatial correlations of noise in quantum architectures., Comment: 24 pages, 6 figures

We consider long-term equilibria that arise in the tokenomics design of proof-of-stake (PoS) blockchain systems that comprise of users and validators, both striving to maximize their own utilities. Validators are system maintainers who get rewarded with tokens for performing the work necessary for the system to function properly, while users compete and pay with such tokens for getting a desired portion of the system service. We study how the system service provision and suitable rewards schemes together can lead to equilibria with desirable characteristics (1) viability: the system keeps parties engaged, (2) decentralization: multiple validators are participating, (3) stability: the price path of the underlying token used to transact with the system does not change widely over time, and (4) feasibility: the mechanism is easy to implement as a smart contract, i.e., it does not require fiat reserves on-chain for buy back of tokens or to perform bookkeeping of exponentially growing token holdings. Our analysis enables to put forward a novel generic mechanism for blockchain ``monetary policy'' that we call {\em quantitative rewarding} (QR). We investigate how to implement QR in single-token and two-token proof of stake (PoS) blockchain systems. The latter are systems that utilize one token for the users to pay the transaction fees and a different token for the validators to participate in the PoS protocol and get rewarded. Our approach demonstrates a concrete advantage of the two-token setting in terms of the ability of the QR mechanism to be realized effectively and provide good equilibria. Our analysis also reveals an inherent limitation of the single token setting in terms of implementing an effective blockchain monetary policy - a distinction that is, to the best of our knowledge, highlighted for the first time.

The measurement of the abundance of galaxy clusters in the Universe is a sensitive probe of cosmology, which depends on both the expansion history of the Universe and the growth of structure. Density fluctuations across the finite survey volume add noise to this measurement, this is often referred to as super-sample covariance (SSC). For an unbinned cluster analysis, such noise has not been included in the cluster likelihood, since the effect of SSC was small compared to the Poisson shot-noise for samples of a few hundred clusters. For upcoming large cluster surveys such as the Rubin LSST, which will deliver catalogs of tens of thousands of clusters, this effect will no longer be negligible. In this paper, we propose a new hybrid likelihood based on the Gauss-Poisson Compound model (GPC), by using infinitesimal mass bins and standard redshift bins. This likelihood has the advantages of an unbinned Poisson likelihood whilst successfully incorporating the effects of SSC. Using a simulated dark matter halo catalog, we find that the hybrid likelihood, accounting for both Poisson noise and SSC, increases the dispersion of the parameter posteriors by 20 percent when using 100,000 clusters compared to the standard unbinned likelihood, based on Poisson statistics only., Comment: 14 pages, 8 figures, 4 tables, accepted for publication in MNRAS

We consider massive vortices in binary condensates, where the immiscibility condition entails the trapping of the minority component in the vortex cores of the majority component. We study such vortices by means of a 2D point-like model, and show how the relevant dynamical equations exhibit vortex-pair solutions characterized by different vortex masses and circular orbits of different radii $a$ and $b$. These solutions are validated by the simulations of the Gross-Pitaevskii equations for binary condensates. After examining the properties of vortex-pair rotational frequency $\Omega$ as a function of the vortex masses for a given pair geometry, we define the rotational-state diagram $\cal D$, describing all the possible vortex-pair solutions in terms of the orbit radii at given $\Omega$. This includes solutions with equal-mass pairs but $a \ne b$ or with one of the two masses (or both) equal to zero. Also, we analytically find the minimum value of $\Omega$ for the existence of such solutions, and obtain numerically the critical frequency $\Omega_c$ below which $\cal D$ changes its structure and the transition to an unstable vortex-pair regime takes place. Our work highlights an indirect measurement scheme to infer the vortex masses from orbits radii $a$ and $b$, and a link between the vortex masses and the vortex-pair small-oscillation properties., Comment: 16 pages, 24 figures

The classical scattering of cylindrical gravitational waves is exactly solvable. The motivation for this paper is to understand if the quantum scattering problem is also exactly solvable. The classical dynamics is governed by a two dimensional sigma model. We study this sigma model's $S$-matrix. We construct a conserved nonlocal charge and derive the associated tree-level $S$-matrix conservation law. We check our conservation law directly using Feynman diagrams. The existence of this symmetry is a hint that cylindrical gravitational waves might have an exactly solvable $S$-matrix., Comment: 7 pages