搜索结果：curious

Secret key generation at the physical layer is expected to be a fundamental enabler for next-generation networks. We consider a network where the user equipment is a drone and propose a novel secret key generation solution when the eavesdropper is another node belonging to the network (curious device). We exploit drone mobility over realistic Rician fading channels. In our protocol, after a prior training phase, drone Alice chooses a trajectory of positions in space and transmits a message to Bob, on the ground, from each position. From the received messages, Bob estimates the channel gain from which a secret key is extracted. The choice of the positions is made to maximize a lower bound on the secret key capacity. Numerical simulations are used to prove the effectiveness of the proposed approach.

Agents must be able to adapt quickly as an environment changes. We find that existing model-based reinforcement learning agents are unable to do this well, in part because of how they use past experiences to train their world model. Here, we present Curious Replay -- a form of prioritized experience replay tailored to model-based agents through use of a curiosity-based priority signal. Agents using Curious Replay exhibit improved performance in an exploration paradigm inspired by animal behavior and on the Crafter benchmark. DreamerV3 with Curious Replay surpasses state-of-the-art performance on Crafter, achieving a mean score of 19.4 that substantially improves on the previous high score of 14.5 by DreamerV3 with uniform replay, while also maintaining similar performance on the Deepmind Control Suite. Code for Curious Replay is available at https://github.com/AutonomousAgentsLab/curiousreplay

Decades of observations on the star V Canum Venaticorum (V CVn) have revealed an unusual inverse relationship between its linear polarization and light curves (sometimes with a lead/lag time between them) and an almost constant polarization position angle. One theory proposed to explain this behaviour is the existence of a bow shock driven by a spherically symmetric time-varying dusty wind from the star, which is assumed to vary due to radial pulsations. To test this hypothesis, this study uses a new framework developed in \textsc{ZEUS3D}, a multiphysics magnetohydrodynamics code. The results of this work show that when a time-varying stellar wind is at its maximum brightness, the polarization signal is at a minimum due to the wind structure and a dense, symmetric shell that forms around the star. Conversely, when the brightness is at a minimum, the symmetric shell around the star is much less dense, and the polarization is instead dominated by the asymmetric bow shock structure, causing the polarization signal to attain a maximum value. Numerically reproducing the observed inverse relationship between the polarization and light curve provides a strong theoretical argument that a v

One of the most central result in combinatorics says that the descent statistic and the excedance statistic are equidistribued over the symmetric group. As a continuation of the work of Shareshian-Wachs (Adv. Math., 225(6) (2010), 2921--2966), we provide a curious $t$-symmetric decomposition for the generating polynomial of the joint distribution of the descent and excedance statistics over the symmetric group.

Advances in Large Language Models (LLMs) have spurred a wave of LLM library learning systems for mathematical reasoning. These systems aim to learn a reusable library of tools, such as formal Isabelle lemmas or Python programs that are tailored to a family of tasks. Many of these systems are inspired by the human structuring of knowledge into reusable and extendable concepts, but do current methods actually learn reusable libraries of tools? We study two library learning systems for mathematics which both reported increased accuracy: LEGO-Prover and TroVE. We find that function reuse is extremely infrequent on miniF2F and MATH. Our followup ablation experiments suggest that, rather than reuse, self-correction and self-consistency are the primary drivers of the observed performance gains. Our code and data are available at https://github.com/ikb-a/curious-case

We offer further results on a general size-biased distribution related to the Riemann xi-function we presented in [9] using the work of Ferrar. Curious properties associated with its expected value are presented, which are related to special functional equations. We also relate our observations to some recent developments related to the Riemann hypothesis.

It is significant to study congruences involving multiple harmonic sums. Let $p$ be an odd prime, in recent years, the following curious congruence $$\sum_{\substack{i+j+k=p \\ i, j, k>0}} \frac{1}{i j k} \equiv-2 B_{p-3}\pmod p$$ has been generalized along different directions, where $B_n$ denote the $n$th Bernoulli number. In this paper, we obtain several new generalizations of the above congruence by applying congruences involving multiple harmonic sums. For example, we have $$\sum_{\substack{k_1+k_2+\cdots+k_n=p \\ k_i> 0, 1 \le i \le n}} \dfrac{(-1)^{k_1}\left(\dfrac{k_1}{3}\right)}{k_1 \cdots k_n} \equiv \dfrac{(n-1)!}{n}\dfrac{2^{n-1}+1}{3\cdot6^{n-1}}B_{p-n}\left(\dfrac{1}{3}\right)\pmod p,$$ where $n$ is even, $B_n(x)$ denote the Bernoulli polynomials.

By treating the multiple argument identity of the logarithm of the Gamma function as a functional equation, we obtain a curious infinite product representation of the $sinc$ function in terms of the cotangent function. This result is believed to be new. It is then shown how to convert the infinite product to a finite product, which turns out to be a simple telescoping of the double angle $sin$ function. In general, this result unifies known infinite product identities involving various trigonometric functions when the product term index appears as an exponent. In one unusual case, what appears to be a straightforward limit, suggests a counterexample to Weierstrass' factor theorem. A resolution is offered. An Appendix presents the general solution to a simple functional equation. This work is motivated by its educational interest.

In order to train children's ability to ask curiosity-driven questions, previous research has explored designing specific exercises relying on providing semantic and linguistic cues to help formulate such questions. But despite showing pedagogical efficiency, this method is still limited as it relies on generating the said cues by hand, which can be a very costly process. In this context, we propose to leverage advances in the natural language processing field (NLP) and investigate the efficiency of using a large language model (LLM) for automating the production of the pedagogical content of a curious question-asking (QA) training. We study generating the said content using the "prompt-based" method that consists of explaining the task to the LLM in natural text. We evaluate the output using human experts annotations and comparisons with hand-generated content. Results suggested indeed the relevance and usefulness of this content. We also conduct a field study in primary school (75 children aged 9-10), where we evaluate children's QA performance when having this training. We compare 3 types of content : 1) hand-generated content that proposes "closed" cues leading to predefined qu

Curiosity as a means to explore during reinforcement learning problems has recently become very popular. However, very little progress has been made in utilizing curiosity for learning control. In this work, we propose a model-based reinforcement learning (MBRL) framework that combines Bayesian modeling of the system dynamics with curious iLQR, an iterative LQR approach that considers model uncertainty. During trajectory optimization the curious iLQR attempts to minimize both the task-dependent cost and the uncertainty in the dynamics model. We demonstrate the approach on reaching tasks with 7-DoF manipulators in simulation and on a real robot. Our experiments show that MBRL with curious iLQR reaches desired end-effector targets more reliably and with less system rollouts when learning a new task from scratch, and that the learned model generalizes better to new reaching tasks.

In this work we explore the possibility of quantum bound states in a Schwarzschild gravitational field leveraging the analogy of the elementary derivation of bound states in the Coulomb potential as taught in an undergraduate course in Quantum Mechanics. For this we will also need to go beyond non-relativistic quantum mechanics and utilize the relativistic Dirac equation for a central potential as taught in an advanced undergraduate or first year graduate (special) relativistic quantum mechanics course. Finally, the special relativistic Dirac equation must be extended to the general relativistic version for curved spacetime. All these disparate component pieces exist in excellent, very readable textbooks written for the student reader, with sufficient detail for a curious student to learn and explore. We pull all these threads together in order to explore a very natural question that a student might ask: "If the effective $1/r$ radial potential of the Schwarzschild metric (with angular momentum barrier), as taught in elementary GR courses for undergraduates, appears Newtonian-like (with a $1/r^3$ correction), then is it possible to derive quantum bound states in the Schwarzschild s

We prove the curious identity in the sense of formal power series: \[ \int_{-\infty}^{\infty}[y^m] \exp\left(-\frac{t^2}2 +\sum_{j\ge3}\frac{(it)^j}{j!}\, y^{j-2}\right)\mathrm{d} t = \int_{-\infty}^{\infty}[y^m] \exp\left(-\frac{t^2}2+ \sum_{j\ge3}\frac{(it)^j}{j}\, y^{j-2}\right)\mathrm{d} t, \] for $m=0,1,\dots$, where $[y^m]f(y)$ denotes the coefficient of $y^m$ in the Taylor expansion of $f$. The generality of this identity from the perspective of saddle-point method is also examined.

The curious Galactic features near G357.2$-$0.2 were observed with the MeerKAT radio interferometer array in the UHF and L bands (0.56--1.68 GHz). There are two possibly related features: a newly identified faint heart-shaped partial shell (the "Heart"), and a series of previously known but now much better imaged narrow, curved features (the "Worm") interior to the heart. Polarized emission suggests that much of the emission is nonthermal and is embedded in a dense plasma. The filaments of the worm appear to be magnetic structures powered by embedded knots that are sites of particle acceleration. The morphology of the worm broadly resembles some known pulsar wind nebulae (PWNe) but there is no known pulsar or PWN which could be powering this structure. We also present eROSITA observations of the field; no part of the nebula is detected in X-rays, but the current limits do not preclude the existence of a pulsar/PWN of intermediate spin-down luminosity.

Let $Φ_n^{(k)}(x)$ be the $k$-th derivative of $n$-th cyclotomic polynomial. Extending a work of D.~H.~Lehmer, we show some curious congruences: $2Φ^{(3)}_n(1)$ is divisible by $φ(n)-2$ and $Φ^{(2k+1)}_n(1)$ is divisible by $φ(n)-2k$ for $k\ge 2$. The congruence stems from a general property of self-reciprocal polynomials.

This paper reports on an exploration of Boolos' Curious Inference, using higher-order automated theorem provers (ATPs). Surprisingly, only suitable shorthand notations had to be provided by hand for ATPs to find a short proof. The higher-order lemmas required for constructing a short proof are automatically discovered by the ATPs. Given the observations and suggestions in this paper, full proof automation of Boolos' and related examples now seems to be within reach of higher-order ATPs.

Having access to an exploring restart distribution (the so-called wide coverage assumption) is critical with policy gradient methods. This is due to the fact that, while the objective function is insensitive to updates in unlikely states, the agent may still need improvements in those states in order to reach a nearly optimal payoff. For this reason, wide coverage is used in some form when analyzing theoretical properties of practical policy gradient methods. However, this assumption can be unfeasible in certain environments, for instance when learning is online, or when restarts are possible only from a fixed initial state. In these cases, classical policy gradient algorithms can have very poor convergence properties and sample efficiency. In this paper, we develop Curious Explorer, a novel and simple iterative state space exploration strategy that can be used with any starting distribution $ρ$. Curious Explorer starts from $ρ$, then using intrinsic rewards assigned to the set of poorly visited states produces a sequence of policies, each one more exploratory than the previous one in an informed way, and finally outputs a restart model $μ$ based on the state visitation distributio

In secure communications networks there are a great number of user behavioural problems, which need to be dealt with. Curious players pose a very real and serious threat to the integrity of such a network. By traversing a network a Curious player could uncover secret information, which that user has no need to know, by simply posing as a loyalty check. Loyalty checks are done simply to gauge the integrity of the network with respect to players who act in a malicious manner. We wish to propose a method, which can deal with Curious players trying to obtain "Need to Know" information using a combined Fault-tolerant, Cryptographic and Game Theoretic Approach.

A curious number is a palindromic number whose base ten representation has the form $a \ldots a b \ldots b a \ldots a$. In this paper, we determine all curious numbers that are perfect squares. Our proof involves reducing the search for such numbers to several single variable families. From here, we complete the proof in two different ways. The first approach is elementary, though somewhat ad hoc. The second entails studying integral points on elliptic curves and is more systematic.

One-dimensional geometric random graphs are constructed by distributing $n$ nodes uniformly and independently on a unit interval and then assigning an undirected edge between any two nodes that have a distance at most $r_n$. These graphs have received much interest and been used in various applications including wireless networks. A threshold of $r_n$ for connectivity is known as $r_n^{*} = \frac{\ln n}{n}$ in the literature. In this paper, we prove that a threshold of $r_n$ for the absence of isolated node is $\frac{\ln n}{2 n}$ (i.e., a half of the threshold $r_n^{*}$). Our result shows there is a curious gap between thresholds of connectivity and the absence of isolated node in one-dimensional geometric random graphs; in particular, when $r_n$ equals $\frac{c\ln n}{ n}$ for a constant $c \in( \frac{1}{2}, 1)$, a one-dimensional geometric random graph has no isolated node but is not connected. This curious gap in one-dimensional geometric random graphs is in sharp contrast to the prevalent phenomenon in many other random graphs such as two-dimensional geometric random graphs, Erdős-Rényi graphs, and random intersection graphs, all of which in the asymptotic sense become connected