搜索结果：Approaching

We survey some recent results and open questions on the approaching geodesics property and its application to the study of the Gromov and horofunction compactifications of a proper geodesic Gromov metric space. We obtain results on the dynamics of isometries and we exhibit an example of a Gromov hyperbolic domain of $\mathbb{C}$ which does not satisfy the approaching geodesic property.

Linear codes correcting one deletions have rate at most $1/2$. In this paper, we construct linear list decodable codes correcting edits with rate approaching $1$ and reasonable list size. Our encoder and decoder run in polynomial time.

We study the approaching geodesic property of a bounded domain in $\mathbb{C}^{n}$ with respect to the Kobayashi distance using the quotient invariant.

We present a geometric optimization method for implementing quantum gates by optimally controlling the Hamiltonian parameters, with the goal of approaching the Mandelstam-Tamm Quantum Speed Limit (MT-QSL). Achieving this bound requires satisfying precise geometric conditions that govern the evolution of quantum states. We extend this geometric framework to quantum unitary operators in arbitrary dimensions and analyze the conditions necessary for saturation of the bound. Additionally, we show that the quantum brachistochrone, when generalized to operators, does not, in general, saturate the MT-QSL bound. Finally, we propose a systematic optimal control strategy based on geometric principles to approach the quantum speed limit for unitary driving. We illustrate this optimization method on a set of four well-known two-qubit quantum gates. Our procedure significantly reduces the deviation from the optimal quantum speed limit while preserving high quantum fidelity.

The determination of whether the ground state of baryon matter in Quantum Chromodynamics (QCD) is the ordinary nucleus or a quark matter state remains a long-standing question in physics. A critical parameter in this investigation is the bag parameter $B$, which quantifies the QCD vacuum energy and can be computed using nonperturbative methods such as Lattice QCD (LQCD). By combining the equation of state derived from perturbative QCD (pQCD) with the bag parameter to fit the LQCD-simulated data for isospin-dense matter, we address the stability of quark matter within the LQCD+pQCD framework. Our findings suggest that the current data imposes an upper bound on $B^{1/4} \lesssim 160$ MeV, approaching a conclusive statement on quark matter stability. Given the lower bound on $B$ from the quark condensate contribution to the vacuum energy, the stable 2-flavor quark matter remains possible, whereas the stable 2+1-flavor quark matter is excluded, assuming complete deconfinement and chiral-symmetry restoration and the reliability of pQCD at baryon chemical potentials around the proton mass. Additionally, we derive more general thermodynamic bounds on the quark matter energy-per-baryon and

Single-photon detection is an energy quantum limit detection (EQLD) of a significantly weak electromagnetic wave. Given the sensitivity of the conventional electromagnetic induction microwave receiver working at room-temperature is very limited, due to the significantly strong thermal noise, here we analyze the possibility of approaching the EQLD of the weak microwave signal by using a current-biased Josephson Junction (CBJJ) detector. By numerically simulating the dynamics for the phase particle of the CBJJ, we propose an approach to describe the discriminability between the probabilistically escaped events of the phase particle with and without the microwave current driving, by measuring the minimum $d_{\rm KC}$-index. We predicate that, the experimentally demonstrated CBJJ detectors possess the ability to resolve about a dozen photons. The feasibility of the desired EQLD of microwave signal by using the CBJJ detector is also discussed.

This paper proposes a differentially private energy trading mechanism for prosumers in peer-to-peer (P2P) markets, offering provable privacy guarantees while approaching the Nash equilibrium with nearly socially optimal efficiency. We first model the P2P energy trading as a (generalized) Nash game and prove the vulnerability of traditional distributed algorithms to privacy attacks through an adversarial inference model. To address this challenge, we develop a privacy-preserving Nash equilibrium seeking algorithm incorporating carefully calibrated Laplacian noise. We prove that the proposed algorithm achieves $ε$-differential privacy while converging in expectation to the Nash equilibrium with a suitable stepsize. Numerical experiments are conducted to evaluate the algorithm's robustness against privacy attacks, convergence behavior, and optimality compared to the non-private solution. Results demonstrate that our mechanism effectively protects prosumers' sensitive information while maintaining near-optimal market outcomes, offering a practical approach for privacy-preserving coordination in P2P markets.

It is commonly recognized that the Landauer bound holds in (irreversible) quantum operations. In this study, we verified this bound by extracting a single spin from a spin-spin magnetic interaction experiment to demonstrate that the Landauer bound can be approached quantitatively with an approaching rate of 79.3 percent via quantum spin tunneling. An optically manipulated spin-encoded quantum computer is designed, in which energy bound near kB T to erase a spin qubit is theoretically sensible and experimentally verified. This work may represent the last piece of the puzzle in quantum Landauer erasure in terms of a single spin being the smallest information carrier.

Catastrophic phase inversion, the sudden breakdown of a dense emulsion, occurs when the dispersed majority phase irreversibly exchanges role with the continuous minority phase. This common process has been extensively studied over the past decades and yet its fundamental physical mechanism has remained largely unexplored. Here we experimentally and numerically study the dynamics of catastrophic phase inversion as it occurs when the volume fraction of the dispersed phase exceeds a critical volume fraction (typically around 92% in experiments). Our data accurately quantify the abrupt change of both the global torque and average droplet size at approaching and across the phase inversion point, exhibiting strong hysteresis. Most importantly, we reveal that the fluctuations in the global torque diverge as a power-law while approaching the critical volume-fraction and we connect their growth to the formation of highly heterogeneous spatial droplet structures. The present finding, unveiling the tight connection between fluctuations in dynamic heterogeneity and the critical divergence of torque fluctuation, paves the way to a quantitative description of catastrophic phase inversion as an o

Although the manipulating of the unmanned aerial manipulator (UAM) has been widely studied, vision-based UAM approaching, which is crucial to the subsequent manipulating, generally lacks effective design. The key to the visual UAM approaching lies in object tracking, while current UAM tracking typically relies on costly model-based methods. Besides, UAM approaching often confronts more severe object scale variation issues, which makes it inappropriate to directly employ state-of-the-art model-free Siamese-based methods from the object tracking field. To address the above problems, this work proposes a novel Siamese network with pairwise scale-channel attention (SiamSA) for vision-based UAM approaching. Specifically, SiamSA consists of a pairwise scale-channel attention network (PSAN) and a scale-aware anchor proposal network (SA-APN). PSAN acquires valuable scale information for feature processing, while SA-APN mainly attaches scale awareness to anchor proposing. Moreover, a new tracking benchmark for UAM approaching, namely UAMT100, is recorded with 35K frames on a flying UAM platform for evaluation. Exhaustive experiments on the benchmarks and real-world tests validate the effici

We consider arrangements of $n$ pseudo-lines in the Euclidean plane where each pseudo-line $\ell_i$ is represented by a bi-infinite connected $x$-monotone curve $f_i(x)$, $x \in \mathbb{R}$, s.t.\ for any two pseudo-lines $\ell_i$ and $\ell_j$ with $i < j$, the function $x \mapsto f_j(x) - f_i(x)$ is monotonically decreasing and surjective (i.e., the pseudo-lines approach each other until they cross, and then move away from each other). We show that such \emph{arrangements of approaching pseudo-lines}, under some aspects, behave similar to arrangements of lines, while for other aspects, they share the freedom of general pseudo-line arrangements. For the former, we prove: 1. There are arrangements of pseudo-lines that are not realizable with approaching pseudo-lines. 2. Every arrangement of approaching pseudo-lines has a dual generalized configuration of points with an underlying arrangement of approaching pseudo-lines. For the latter, we show: 1. There are $2^{Θ(n^2)}$ isomorphism classes of arrangements of approaching pseudo-lines (while there are only $2^{Θ(n \log n)}$ isomorphism classes of line arrangements). 2. It can be decided in polynomial time whether an allowable seque

We propose a discrete approach for approximating solutions to the prescribed Gaussian curvature problem in two-dimensional manifolds, based on the notion of discrete conformality. Our approach provides an efficient numerical method to compute the solution by minimizing a convex functional.

It is well known that no quantum error correcting code of rate $R$ can correct adversarial errors on more than a $(1-R)/4$ fraction of symbols. But what if we only require our codes to *approximately* recover the message? We construct efficiently-decodable approximate quantum codes against adversarial error rates approaching the quantum Singleton bound of $(1-R)/2$, for any constant rate $R$. Moreover, the size of the alphabet is a constant independent of the message length and the recovery error is exponentially small in the message length. Central to our construction is a notion of quantum list decoding and an implementation involving folded quantum Reed-Solomon codes.

We show that the standard Blandford-Königl model for compact conical relativistic jets has a peculiar feature: at a given observed frequency of radiation, the emission from the approaching jet arrives at the location of a distant observer at the same time as the emission from the counterjet for all finite inclination angles. We show that this result can be used to determine whether jets are genuinely symmetric, if the cross-coherence between radio and X-ray time series can be measured at high Fourier frequency for a sample of neutron star X-ray binaries with a range of inclination angles. We also discuss echo mapping techniques that can be used to look for deviations from the standard model in high cadence time series data on X-ray binary jets, and conclude that these can plausibly be applied to some systems.

We estimate the time a point or set, respectively, requires to approach the attractor of a radially symmetric gradient type stochastic differential equation driven by small noise. Here, both of these times tend to infinity as the noise gets small. However, the rates at which they go to infinity differ significantly. In the case of a set approaching the attractor, we use large deviation techniques to show that this time increases exponentially. In the case of a point approaching the attractor, we apply a time change and compare the accelerated process to another process and obtain that this time increases merely linearly.

Deep reinforcement learning has recently been widely applied in robotics to study tasks such as locomotion and grasping, but its application to social human-robot interaction (HRI) remains a challenge. In this paper, we present a deep learning scheme that acquires a prior model of robot approaching behavior in simulation and applies it to real-world interaction with a physical robot approaching groups of humans. The scheme, which we refer to as Staged Social Behavior Learning (SSBL), considers different stages of learning in social scenarios. We learn robot approaching behaviors towards small groups in simulation and evaluate the performance of the model using objective and subjective measures in a perceptual study and a HRI user study with human participants. Results show that our model generates more socially appropriate behavior compared to a state-of-the-art model.

The autoencoder concept has fostered the reinterpretation and the design of modern communication systems. It consists of an encoder, a channel, and a decoder block which modify their internal neural structure in an end-to-end learning fashion. However, the current approach to train an autoencoder relies on the use of the cross-entropy loss function. This approach can be prone to overfitting issues and often fails to learn an optimal system and signal representation (code). In addition, less is known about the autoencoder ability to design channel capacity-approaching codes, i.e., codes that maximize the input-output information under a certain power constraint. The task being even more formidable for an unknown channel for which the capacity is unknown and therefore it has to be learnt. In this paper, we address the challenge of designing capacity-approaching codes by incorporating the presence of the communication channel into a novel loss function for the autoencoder training. In particular, we exploit the mutual information between the transmitted and received signals as a regularization term in the cross-entropy loss function, with the aim of controlling the amount of informati

The University of Bologna has a long tradition in Digital Humanities, both at the level of research and teaching. In this article, we want to introduce some experiences in developing new educational models based on the idea of transversal learning, collaborative approaches and projects-oriented outputs, together with the definition of research fields within this vast domain, accompanied by practical examples. The creation of an international master's degree (DHDK), a PhD (CHeDE) and a research centre (/DH.arc) are the results of refining our notion of Digital Humanities in a new bidirectional way: to reflect on computational methodologies and models in the cultural sphere and to suggest a cultural approach to Informatics.