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It has been known for several decades that classical alternating links in the 3-sphere have nice hyperbolic geometric properties. Recent work generalises such results to give hyperbolic geometry of links with alternating projections onto any surface in very general 3-manifolds. However, the most general results require an orientable projection surface. In this paper, we extend to alternating links on nonorientable projection surfaces. As an application, we study Klein bottly alternating links in prism manifolds, which are a natural generalisation of Adams' toroidally alternating links in lens spaces., Comment: 15 pages, 6 figures

Rashba spin-orbit interactions generated by time-dependent electric fields acting on weak links (that couple together non-magnetic macroscopic leads) can magnetize the junction. The Rashba spin-orbit interaction that affects the spins of electrons tunneling through the weak links changes their momentum concomitantly. We establish the connection between the magnetization flux induced by processes that conserve the momentum and the magnetization created by tunneling events that do not. Control of the induced magnetization can be achieved by tuning the polarization of the AC electric field responsible for the spin-orbit Rashba interaction (e.g., from being circular to linear), by changing the applied bias voltage, and by varying the degree of a gate voltage-induced asymmetry of the device., Comment: 11 pages, 3 figures

Large Language Models (LLMs) are currently used for various software development tasks, including generating code snippets to solve specific problems. Unlike reuse from the Web, LLMs are limited in providing provenance information about the generated code, which may have important trustworthiness and legal consequences. While LLM-based assistants may provide external links that are "related" to the generated code, we do not know how relevant such links are. This paper presents the findings of an empirical study assessing the extent to which 243 and 194 code snippets, across six programming languages, generated by Bing CoPilot and Google Gemini, likely originate from the links provided by these two LLM-based assistants. The study leverages automated code similarity assessments with thorough manual analysis. The study's findings indicate that the LLM-based assistants provide a mix of relevant and irrelevant links having a different nature. Specifically, although 66% of the links from Bing CoPilot and 28% from Google Gemini are relevant, LLMs-based assistants still suffer from serious "provenance debt".

This paper presents a comparative analysis of long-term evolution advanced (LTE-A) and fifth-generation new radio (5G-NR), focusing on the effects of Transient Electromagnetic Interference (EMI) caused by catenary-pantograph contact in a railway environment. We developed a software-defined radio (SDR)-based prototype for the performance evaluation of LTE-A and 5G-NR links in the presence of transient interference. The results show that both links experience considerable degradation due to interference at different center frequencies. Performance degradation is proportional to the gain of interference. The measurement results show that both links experience considerable performance degradation in the presence of transient EM interference., Comment: 5 pages, 9 figures, 5 tables

In the context of implantable bioelectronics, this work provides new insights into maximizing biomedical wireless power transfer (BWPT) via the systematic development of inductive links. This approach addresses the specific challenges of power transfer efficiency (PTE) optimization within the area constraints of bio-implants embedded in tissue. Key contributions include the derivation of an optimal self-inductance with S-parameter-based analyses leading to the co-design of planar spiral coils and L-section impedance matching networks. To validate the proposed design methodology, two coil prototypes -- one symmetric (type-1) and one asymmetric (type-2) -- were fabricated and tested for PTE in pork tissue. Targeting a 20 MHz design frequency, the type-1 coil demonstrated a state-of-the-art PTE of $\sim$ 4\% (channel length = 15 mm) with a return loss (RL) $>$ 20 dB on both the input and output sides, within an area constraint of $<$ 18 $ \times $ 18 mm$^{2}$. In contrast, the type-2 coil achieved a PTE of $\sim$ 2\% with an RL $>$ 15 dB, for a smaller receiving coil area of $<$ 5x5 mm$^{2}$ for the same tissue environment. To complement the coils, we demonstrate a 65 nm test chip with an integrated energy harvester, which includes \asif{a} 30-stage rectifier and low-dropout regulator (LDO), producing a stable $\sim$ 1V DC output within tissue medium, matching theoretical predictions and simulations. Furthermore, we provide a robust and comprehensive guideline for advancing efficient inductive links for various BWPT applications, with shared resources in GitHub available for utilization by the broader community.

The ability to distribute heralded entanglement between distant matter nodes is a primitive for the implementation of large-scale quantum networks. Some of the most crucial requirements for future applications include high heralding rates at telecom wavelengths, multiplexed operation and on-demand retrieval of stored excitations for synchronization of separate quantum links. Despite tremendous progress in various physical systems, the demonstration of telecom-heralded entanglement between quantum nodes featuring both multiplexed operation and on-demand retrieval remains elusive. In this work, we combine narrowband parametric photon-pair sources and solid-state quantum memories based on rare-earth doped crystals to demonstrate telecom heralded entanglement between spatially separated spin-wave quantum memories with fully adjustable recall time and temporal multiplexing of 15 modes. In a first experiment, the storage in the spin-state is conditioned on the entanglement heralding. We take advantage of the control over readout pulse phase to achieve feed-forward conditional phase-shifts on the stored photons depending on which heralding detector clicked. We exploit this effect to double the entanglement heralding rate for a given quantum state up to \SI{500}{\cps}, with a measured positive concurrence by up to 6 standard deviations. In a second experiment, we simulate the communication time of a long-distance link by implementing an unconditional storage scheme with a dead-time of \SI{100}{\micro\second}, leading to an entanglement rate of \SI{22}{\cps} per heralding detector, increased by a factor of 15 thanks to temporal multiplexing. These results establish our architecture as a prime candidate for the implementation of scalable high-rate quantum network links., Comment: 14 pages, 10 figures

In this paper, we define grid homology for singular links in lens spaces and use it to construct a resolution cube for knot Floer homology of regular links in lens spaces. The results will first be proven over $\mathbb{Z}/2\mathbb{Z}$ and then extended to be over $\mathbb{Z}$ via a sign assignment. We will also describe the relationship between our grid homology and classical knot Floer homology over $\mathbb{Z}$., Comment: 53 pages, 22 figures. Comparing with version 1, version 2 has clearer figures and better notations. Some remarks about sign assignments have been added to version 2 but no essential change. Comment is welcomed

A broad range of technologies rely on remote inference, wherein data acquired is conveyed over a communication channel for inference in a remote server. Communication between the participating entities is often carried out over rate-limited channels, necessitating data compression for reducing latency. While deep learning facilitates joint design of the compression mapping along with encoding and inference rules, existing learned compression mechanisms are static, and struggle in adapting their resolution to changes in channel conditions and to dynamic links. To address this, we propose Adaptive Rate Task-Oriented Vector Quantization (ARTOVeQ), a learned compression mechanism that is tailored for remote inference over dynamic links. ARTOVeQ is based on designing nested codebooks along with a learning algorithm employing progressive learning. We show that ARTOVeQ extends to support low-latency inference that is gradually refined via successive refinement principles, and that it enables the simultaneous usage of multiple resolutions when conveying high-dimensional data. Numerical results demonstrate that the proposed scheme yields remote deep inference that operates with multiple rates, supports a broad range of bit budgets, and facilitates rapid inference that gradually improves with more bits exchanged, while approaching the performance of single-rate deep quantization methods., Comment: 13 pages, 12 figures

Pseudo links are equivalence classes under Reidemeister-type moves of link diagrams containing crossings with undefined over and under information. In this paper, we extend the Kauffman bracket and Jones polynomials from planar pseudo links to pseudo links in the annulus and in the torus, and their respective lifts from the three-space to the solid torus and the thickened torus. Moreover, since annular and toroidal pseudo links can be represented as mixed links in the three-sphere, we also introduce the respective Kauffman bracket and Jones polynomials for their planar mixed link diagrams. Our work provides new tools for the study of annular and toroidal pseudo links.

Polynomial invariants constitute a dynamic and essential area of study in the mathematical theory of knots. From the pioneer Alexander polynomial, the revolutionary Jones polynomial, to the collectively discovered HOMFLYPT polynomial, just to mention a few, these algebraic expressions have been central to the understanding of knots and links. The introduction of Khovanov homology has sparked significant interest in the categorification of these polynomials, offering deeper insights into their topological and algebraic properties. In this work, we revisit two prominent polynomial invariants, the Alexander-Conway and the Kauffman bracket polynomials, and focus specifically on the polynomials associated with the family of three strand pretzel links $P(1,1,n)$., Comment: 10 pages, 18 figures

The Artin-Alexander theorem characterizes the knot groups of classical links, providing necessary and sufficient conditions for a group to be the knot group of some classical link. This result was shown using the closed braid method. Gonzalez-Acuna and Kamada independently extended this characterization to the knot groups of orientable surface-links. Kamada applied the closed 2-dimensional braid method to show this result. In this paper, we generalize these results to characterize the knot groups of surface-links, including non-orientable ones. Our approach relies on a plat form presentation for surface-links. Furthermore, we show a similar characterization for the knot symmetric quandles of surface-links. As an application, we show that every dihedral quandle with an arbitrarily good involution can be realized as the knot symmetric quandle of a surface-link., Comment: 12 pages, 1 figure, Comments welcome

The growing privacy concerns in distributed learning have led to the widespread adoption of secure aggregation techniques in distributed machine learning systems, such as federated learning. Motivated by a coded gradient aggregation problem in a user-helper-master hierarchical network setting with straggling communication links, we formulate a new secure hierarchical coded gradient aggregation problem. In our setting, \( K \) users communicate with the master through an intermediate layer of \( N \) helpers, who can communicate with each other. With a resiliency threshold of \( N_r \) for straggling communication links, and at most \( T \) colluding helpers and any number of colluding users, the master aims to recover the sum of all users' gradients while remaining unaware of any individual gradient that exceeds the expected sum. In addition, helpers cannot infer more about users' gradients than what is already known by the colluding users. We propose an achievable scheme where users' upload messages are based on a globally known Vandermonde matrix, and helper communication is facilitated using an extended Vandermonde matrix with special structural properties. A matching converse bound is also derived, establishing the optimal result for this hierarchical coded gradient aggregation problem.

In this paper, we tabulate the set of alternating pretzel links. Specifically, for any given crossing number $c$, we derive a closed formula that would allow us to compute $\mathcal{P}(c)$, the total number of alternating pretzel links with crossing number $c$. Numerical computation suggests that $\mathcal{P}(c)\approx 0.0775e^{0.588c}$. That is, the number of alternating pretzel links with a given crossing number $c$ grows exponentially in terms of $c$., Comment: 18 pages, 4 figures

Deformations of knots and links in ambient space can be studied combinatorially on their diagrams via local modifications called Reidemeister moves. While it is well-known that, in order to move between equivalent diagrams with Reidemeister moves, one sometimes needs to insert excess crossings, there are significant gaps between the best known lower and upper bounds on the required number of these added crossings. In this article, we study the problem of turning a diagram of a split link into a split diagram, and we show that there exist split links with diagrams requiring an arbitrarily large number of such additional crossings. More precisely, we provide a family of diagrams of split links, so that any sequence of Reidemeister moves transforming a diagram with $c$ crossings into a split diagram requires going through a diagram with $\Omega(\sqrt{c})$ extra crossings. Our proof relies on the framework of bubble tangles, as introduced by Lunel and de Mesmay, and a technique of Chambers and Liokumovitch to turn homotopies into isotopies in the context of Riemannian geometry.

In an earlier note [arXiv:2301.00295] it was shown that there is an upper bound to the number of disjoint Hopf links (and certain related links) that can be embedded in the unit cube where there is a fixed separation required between the components within each copy of the Hopf link. The arguments relied on multi-linear properties of linking number and certain other link invariants. Here we produce a very similar upper bound for all non-trivial links by a more-general, entirely geometric, argument (but one which, unlike the original, has no analog in higher dimensions). Shortly after the initial paper, [arXiv:2308.08064] proved lower bounds which broadly cover this wider class.

Accurate network data are essential in fields such as economics, sociology, and computer science. Aggregated Relational Data (ARD) provides a way to capture network structures using partial data. This article compares two main frameworks for recovering network links from ARD: Bayesian Latent Surface Modeling (BLSM) and Frequentist Penalized Regression (FPR). Using simulation studies and real-world applications, we evaluate their theoretical properties, computational efficiency, and practical utility in domains like financial risk assessment and epidemiology. Key findings emphasize the importance of trait design, privacy considerations, and hybrid modeling approaches to improve scalability and robustness.

Free-space quantum key distribution (QKD) represents a groundbreaking advancement in secure communication, enabling secure key exchange over vast distances and offering robust encryption for the future quantum internet. However, the compatibility between fiber and free-space infrastructures continues to pose challenges for QKD protocols. Indeed, free-space and fiber-based networks commonly use different wavelengths and qubits encoding schemes. On the one hand, free-space QKD typically exploits visible light for its beneficial beam divergence compared to longer wavelengths, and polarization encoding for its robustness against turbulence. On the other hand, fiber-based QKD employs infrared light, particularly the C-band, because it shows the minimum losses with silica fibers, and time-bin encoding, due to polarization instability in optical fibers. In our study, we demonstrate the viability of a time-bin encoded QKD protocol operating in the C-band through horizontal turbulent free-space channels. We test the setup into a 50 m and a 500 m long links, achieving an average secure key rate of, respectively, 793 kbps and 40 kbps over several hours of measurements. The results encourage further exploration of the interoperability between free-space and fiber-based infrastructures, opening new possibilities for connecting terminal users with satellites in hybrid infrastructures., Comment: 10 pages, 6 figures

The Web and its main tools (Google, Wikipedia, Facebook, Twitter) deeply raise and renew fundamental questions, that everyone asks almost every day: Is this information or content true? Can I trust this author or source? These questions are not new, they have been the same with books, newspapers, broadcasting and television, and, more fundamentally, in every human interpersonal communication. This paper is focused on two scientific problems on this issue. The first one is theoretical: to address this issue, many concepts have been used in library and information sciences, communication and psychology. The links between these concepts are not clear: sometimes two concepts are considered as synonymous, sometimes as very different. The second one is historical: sources like Wikipedia deeply challenge the epistemic evaluation of information sources, compared to previous modes of information production. This paper proposes an integrated and simple model considering the relation between a user, a document and an author as human communication. It reduces the problem to three concepts: credibility as a characteristic granted to information depending on its truth-value; trust as the ability to produce credible information; authority when the power to influence of an author is accepted, i.e., when readers accept that the source can modify their opinion, knowledge and decisions. The model describes also two kinds of relationships between the three concepts: an upward link and a downward link. The model is confronted with findings of empirical research on Wikipedia in particular.

In this paper, we prove that two normal complex surface germs that are inner bilipschitz--but not necessarily orientation-preserving--homeomorphic, have in fact the same oriented topological type and the same minimal plumbing graph. Along the way, we show that the oriented homeomorphism type of an isolated complex surface singularity germ determines the oriented homeomorphism type of its link, providing a converse to the classical Conical Structure Theorem. These results require to study the topology first, and the inner lipschitz geometry later, of Hirzebruch-Jung and cusp singularities, the normal surface singularities whose links are lens spaces and fiber bundles over the circle., Comment: 14 pages, 4 figures

We consider the optimisation problem of adding $k$ links to a given network, such that the resulting effective graph resistance is as small as possible. The problem was recently proven to be NP-hard, such that optimal solutions obtained with brute-force methods require exponentially many computation steps and thus are infeasible for any graph of realistic size. Therefore, it is common in such cases to use a simple greedy algorithm to obtain an approximation of the optimal solution. It is known that if the considered problem is submodular, the quality of the greedy solution can be guaranteed. However, it is known that the optimisation problem we are facing, is not submodular. For such cases one can use the notion of generalized submodularity, which is captured by the submodularity ratio $\gamma$. A performance bound, which is a function of $\gamma$, also exists in case of generalized submodularity. In this paper we give an example of a family of graphs where the submodularity ratio approaches zero, implying that the solution quality of the greedy algorithm cannot be guaranteed. Furthermore, we show that the greedy algorithm does not always yield the optimal solution and demonstrate that even for a small graph with 10 nodes, the ratio between the optimal and the greedy solution can be as small as 0.878., Comment: 21 pages, 14 figures

In the rapidly evolving landscape of digital twins (DT) and 6G networks, the integration of large language models (LLMs) presents a novel approach to network management. This paper explores the application of LLMs in managing 6G-empowered DT networks, with a focus on optimizing data retrieval and communication efficiency in smart city scenarios. The proposed framework leverages LLMs for intelligent DT problem analysis and radio resource management (RRM) in fully autonomous way without any manual intervention. Our proposed framework -- LINKs, builds up a lazy loading strategy which can minimize transmission delay by selectively retrieving the relevant data. Based on the data retrieval plan, LLMs transform the retrieval task into an numerical optimization problem and utilizing solvers to build an optimal RRM, ensuring efficient communication across the network. Simulation results demonstrate the performance improvements in data planning and network management, highlighting the potential of LLMs to enhance the integration of DT and 6G technologies., Comment: Accepted by The 2024 IEEE 100th Vehicular Technology Conference (VTC2024-Fall)

For any pair of integers $m$ and $n$ such that $3

Lorenz links and T-links are equivalent families of links by Birman and Kofman. Lorenz links are periodic orbits of the Lorenz system. T-links are links given by certain positive braids. Birman, Williams, and Franks proved that every Lorenz link has a positive braid with at least one full twist as a minimal braid. In this paper we study the geometric types of the Lorenz links from their minimal braid perspective. First, we compute their minimal braids explicitly in terms of the parameters of the T-links. We conclude that they are in equivalence with a family of links, called V-links, similar to a result of Birman and Kofman. Furthermore, we find an explicit relation to obtain an element of one of these families from the other. Then, we study conditions on positive braids with at least one full twist to find their geometric type. Finally, we apply these conditions on V-links to find new and generalize some families of satellite and hyperbolic T-links., Comment: 25 pages, 8 figures

The China Space Station (CSS) is currently in orbit and carries the high-precision optical atomic clock with stability of approximately $2.0 \times 10^{-15} / \sqrt{\tau}$ in its experiment module. We have developed a model to determine the gravity potential (GP) based on the gravity frequency shift equation and have created both one-way and dual-frequency transfer models up to $c^{-4}$. These models consider effects from the troposphere, ionosphere, and solid Earth tides. The proposed model is suitable for measurements at the magnitude of $10^{-19}$. Based on the CSS mission, we conducted the simulation experiments. The results indicate that when processing the simulation frequency signal using the proposed model, we can obtain the GP with the accuracies of $ (1.13\pm0.71)\,\mathrm{m^2/s^2}$, $ (0.09\pm0.89)\,\mathrm{m^2/s^2}$, and $(0.66\pm1.18)\,\mathrm{m^2/s^2}$ for cutoff elevation angles of $5^{\circ}$, $10^{\circ}$ and $15^{\circ}$, respectively. With the high-precision optical atomic clock onboard the CSS, the proposed model enables us to measure the GP differences in the magnitude of centimeter-level accuracy.

We show that any smooth one-dimensional link in the real projective three-plane is the fixed-point locus of a smooth symplectic surface in the complex projective three-plane which is invariant under complex conjugation. The degree of the surface can be taken to be either one or two, depending on the homology class of the link. In other words, there are no obstructions to finding a symplectic representative of a flexible link beyond the classical topology., Comment: 15 pages