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Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams. The harmonic spectrum of the Khovanov Laplacian or the Khovanov Dirac retains the topological invariants of Khovanov homology, while their non-harmonic spectra reveal additional information that is distinct from Khovanov homology.

This paper introduces a scenario where a maneuverable satellite in geostationary orbit (GEO) conducts on-orbit attacks, targeting communication between a GEO satellite and a ground station, with the ability to switch between stationary and time-variant jamming modes. We propose a machine learning-based detection approach, employing the random forest algorithm with principal component analysis (PCA) to enhance detection accuracy in the stationary model. At the same time, an adaptive threshold-based technique is implemented for the time-variant model to detect dynamic jamming events effectively. Our methodology emphasizes the need for the use of orbital dynamics in integrating physical constraints from satellite dynamics to improve model robustness and detection accuracy. Simulation results highlight the effectiveness of PCA in enhancing the performance of the stationary model, while the adaptive thresholding method achieves high accuracy in detecting jamming in the time-variant scenario. This approach provides a robust solution for mitigating the evolving threats to satellite communication in GEO environments.

The chemical abundance measurements of host stars and their substellar companions provide a powerful tool to trace the formation mechanism of the planetary systems. We present a detailed high-resolution spectroscopic analysis of a young M-type star, DH Tau A, which is located in the Taurus molecular cloud belonging to the Taurus-Auriga star-forming region. This star is host to a low-mass companion, DH Tau b, and both star and the companion are still in their accreting phase. We apply our technique (Hejazi et al. 2024) to measure the abundances of carbon and oxygen using carbon- and oxygen-bearing molecules, such as CO and OH, respectively. We determine a near-solar carbon-to-oxygen abundance ratio of C/O=0.555$\pm$0.063 for the host star DH Tau A. We compare this stellar abundance ratio with that of the companion from our previous study (C/O=0.54$^{+0.06}_{-0.05}$, Xuan et al. 2024), which also has a near-solar value. This confirms the chemical homogeneity in the DH Tau system, which suggests a formation scenario for the companion consistent with a direct and relatively fast gravitational collapse, rather than a slow core accretion process., Comment: 14 pages, 4 figures, Accepted for publication in the Astrophysical Journal

Predicting the behavior of a wireless link in terms of, e.g., the frame delivery ratio, is a critical task for optimizing the performance of wireless industrial communication systems. This is because industrial applications are typically characterized by stringent dependability and end-to-end latency requirements, which are adversely affected by channel quality degradation. In this work, we studied two neural network models for Wi-Fi link quality prediction in dense indoor environments. Experimental results show that their accuracy outperforms conventional methods based on exponential moving averages, due to their ability to capture complex patterns about communications, including the effects of shadowing and multipath propagation, which are particularly pronounced in industrial scenarios. This highlights the potential of neural networks for predicting spectrum behavior in challenging operating conditions, and suggests that they can be exploited to improve determinism and dependability of wireless communications, fostering their adoption in the industry., Comment: preprint, 6 pages, 2024

Fibre optic communication system is expected to increase exponentially in terms of application due to the numerous advantages over copper wires. The optical network evolution presents several advantages such as over long-distance, low-power requirement, higher carrying capacity and high bandwidth among others Such network bandwidth surpasses methods of transmission that include copper cables and microwaves. Despite these benefits, free-space optical communications are severely impacted by harsh weather situations like mist, precipitation, blizzard, fume, soil, and drizzle debris in the atmosphere, all of which have an impact on the Quality of Service (QoS) rendered by the systems. The primary goal of this article is to optimize the QoS using the ensemble learning models Random Forest, ADaBoost Regression, Stacking Regression, Gradient Boost Regression, and Multilayer Neural Network. To accomplish the stated goal, meteorological data, visibility, wind speed, and altitude were obtained from the South Africa Weather Services archive during a ten-year period (2010 to 2019) at four different locations: Polokwane, Kimberley, Bloemfontein, and George. We estimated the data rate, power received, fog-induced attenuation, bit error rate and power penalty using the collected and processed data. The RMSE and R-squared values of the model across all the study locations, Polokwane, Kimberley, Bloemfontein, and George, are 0.0073 and 0.9951, 0.0065 and 0.9998, 0.0060 and 0.9941, and 0.0032 and 0.9906, respectively. The result showed that using ensemble learning techniques in transmission modeling can significantly enhance service quality and meet customer service level agreements and ensemble method was successful in efficiently optimizing the signal to noise ratio, which in turn enhanced the QoS at the point of reception.

Recent literature proposes combining short-term experimental and long-term observational data to provide credible alternatives to conventional observational studies for identification of long-term average treatment effects (LTEs). I show that experimental data have an auxiliary role in this context. They bring no identifying power without additional modeling assumptions. When modeling assumptions are imposed, experimental data serve to amplify their identifying power. If the assumptions fail, adding experimental data may only yield results that are farther from the truth. Motivated by this, I introduce two assumptions on treatment response that may be defensible based on economic theory or intuition. To utilize them, I develop a novel two-step identification approach that centers on bounding temporal link functions -- the relationship between short-term and mean long-term potential outcomes. The approach provides sharp bounds on LTEs for a general class of assumptions, and allows for imperfect experimental compliance -- extending existing results.

Large language models (LLMs) serve as giant information stores, often including personal or copyrighted data, and retraining them from scratch is not a viable option. This has led to the development of various fast, approximate unlearning techniques to selectively remove knowledge from LLMs. Prior research has largely focused on minimizing the probabilities of specific token sequences by reversing the language modeling objective. However, these methods still leave LLMs vulnerable to adversarial attacks that exploit indirect references. In this work, we examine the limitations of current unlearning techniques in effectively erasing a particular type of indirect prompt: multi-hop queries. Our findings reveal that existing methods fail to completely remove multi-hop knowledge when one of the intermediate hops is unlearned. To address this issue, we propose MUNCH, a simple uncertainty-based approach that breaks down multi-hop queries into subquestions and leverages the uncertainty of the unlearned model in final decision-making. Empirical results demonstrate the effectiveness of our framework, and MUNCH can be easily integrated with existing unlearning techniques, making it a flexible and useful solution for enhancing unlearning processes., Comment: 16 pages, 5 figures

We study the [OII] profiles of emission line galaxies (ELGs) from the Early Data Release of the Dark Energy Spectroscopic Instrument (DESI). To this end, we decompose and classify the shape of [OII] profiles with the first two eigenspectra derived from Principal Component Analysis. Our results show that DESI ELGs have diverse line profiles which can be categorized into three main types: (1) narrow lines with a median width of ~50 km/s, (2) broad lines with a median width of ~80 km/s, and (3) two-redshift systems with a median velocity separation of ~150 km/s, i.e., double-peak galaxies. To investigate the connections between the line profiles and galaxy properties, we utilize the information from the COSMOS dataset and compare the properties of ELGs, including star-formation rate (SFR) and galaxy morphology, with the average properties of reference star-forming galaxies with similar stellar mass, sizes, and redshifts. Our findings show that on average, DESI ELGs have higher SFR and more asymmetrical/disturbed morphology than the reference galaxies. Moreover, we uncover a relationship between the line profiles, the excess SFR and the excess asymmetry parameter, showing that DESI ELGs with broader [OII] line profiles have more disturbed morphology and higher SFR than the reference star-forming galaxies. Finally, we discuss possible physical mechanisms giving rise to the observed relationship and the implications of our findings on the galaxy clustering measurements, including the halo occupation distribution modeling of DESI ELGs and the observed excess velocity dispersion of the satellite ELGs., Comment: 24 pages, 13 figures, submitted to ApJ

We investigate the properties of the moments of the cot function using the central factorial numbers. Using a new integral representation of the central factorial numbers, we find a new way to express these moments in terms of recursive sums and integrals. This allows us to compute 'recursive' generalized harmonic series and multiple integrals as a linear combination of the Dirichlet eta functions at odd integers.

Multi-modal Large Language Models (MLLMs) have exhibited impressive capability. However, recently many deficiencies of MLLMs have been found compared to human intelligence, $\textit{e.g.}$, hallucination. To drive the MLLMs study, the community dedicated efforts to building larger benchmarks with complex tasks. In this paper, we propose benchmarking an essential but usually overlooked intelligence: $\textbf{association}$, a human's basic capability to link observation and prior practice memory. To comprehensively investigate MLLM's performance on the association, we formulate the association task and devise a standard benchmark based on adjective and verb semantic concepts. Instead of costly data annotation and curation, we propose a convenient $\textbf{annotation-free}$ construction method transforming the general dataset for our association tasks. Simultaneously, we devise a rigorous data refinement process to eliminate confusion in the raw dataset. Building on this database, we establish three levels of association tasks: single-step, synchronous, and asynchronous associations. Moreover, we conduct a comprehensive investigation into the MLLMs' zero-shot association capabilities, addressing multiple dimensions, including three distinct memory strategies, both open-source and closed-source MLLMs, cutting-edge Mixture-of-Experts (MoE) models, and the involvement of human experts. Our systematic investigation shows that current open-source MLLMs consistently exhibit poor capability in our association tasks, even the currently state-of-the-art GPT-4V(vision) also has a significant gap compared to humans. We believe our benchmark would pave the way for future MLLM studies. $\textit{Our data and code are available at:}$ https://mvig-rhos.com/llm_inception.

Superconductor-normal material-superconductor (SNS) junctions are being integrated into microwave circuits for fundamental and applied research goals. The short junction limit is a common simplifying assumption for experiments with SNS junctions, but this limit constrains how small the nonlinearity of the microwave circuit can be. Here, we show that a finite length of the weak link strongly suppresses the nonlinearity compared to its zero-length limit -- the suppression can be up to a factor of ten even when the length remains shorter than the induced coherence length. We tie this behavior to the nonanalytic dependence of nonlinearity on length, which the critical current does not exhibit. Further, we identify additional experimentally observable consequences of nonzero length, and we conjecture that anharmonicity is bounded between zero and a maximally negative value for any non-interacting Josephson junction in the presence of time-reversal symmetry. We promote SNS junction length as a useful parameter for designing weakly nonlinear microwave circuits.

Entropy always increases monotonically in a closed system but complexity increases at first and then decreases as equilibrium is approached. Commonsense information-related definitions for entropy and complexity demonstrate that complexity behaves like the time derivative of entropy, which is proposed here as a new definition for complexity. A 20-year-old study had attempted to quantify complexity (in arbitrary units) for the entire Universe in terms of 28 milestones, breaks in historical perspective, and had concluded that complexity will soon begin decreasing. That conclusion is now corroborated by other researchers. In addition, the exponential runaway technology trend advocated by supporters of the singularity hypothesis, which was in part based on the trend of the very 28 milestones mentioned above, would have anticipated five new such milestones by now, but none have been observed. The conclusions of the 20-year-old study remain valid: we are at the maximum of complexity and we should expect the next two milestones at around 2033 and 2078., Comment: 15pages, 2 figures

We show that the set of Hamiltonian isotopies of certain unions of circles inside the disc is unbounded for the Hofer distance. The proof relies on a result by Francesco Morabito together with a standard argument of Michael Khanevsky., Comment: 4 pages, v2: removed a wrong statement from the introduction

A knotted ribbon is one of physical aspect of a knot. A folded ribbon knot is a depiction of a knot obtained by folding a long and thin rectangular strip to become flat. The ribbonlength of a knot type can be defined as the minimum length required to tie the given knot type as a folded ribbon knot. The ribbonlength has been conjectured to grow linearly or sub-linearly with respect to a minimal crossing number. Several knot types provide evidence that this conjecture is true, but there is no proof for general cases. In this paper, we show that for any knot or link, the ribbonlength is bounded by a linear function of the crossing number. In more detail, $$ \text{Rib}(K) \leq 2.5 c(K)+1. $$ for a knot or link $K$. Our approach involves binary grid diagrams and bisected vertex leveling techniques.

This paper introduces a new machine learning-assisted chromatic dispersion compensation filter, demonstrating its superior power efficiency compared to conventional FFT-based filters for metro link distances. Validations on FPGA confirmed an energy efficiency gain of up to 63.5\% compared to the standard frequency-domain chromatic dispersion equalizer., Comment: Accepted to ECOC 2024 Conference , https://www.ecoc2024.org/

As AI-generated summaries proliferate, how can we help people understand the veracity of those summaries? In this short paper, we design a simple interaction primitive, traceable text, to support critical examination of generated summaries and the source texts they were derived from. In a traceable text, passages of a generated summary link to passages of the source text that informed them. A traceable text can be generated with a straightforward prompt chaining approach, and optionally adjusted by human authors depending on application. In a usability study, we examined the impact of traceable texts on reading and understanding patient medical records. Traceable text helped readers answer questions about the content of the source text more quickly and markedly improved correctness of answers in cases where there were hallucinations in the summaries. When asked to read a text of personal importance with traceable text, readers employed traceable text as an understanding aid and as an index into the source note.

In this paper, we examine the energy efficiency (EE) of a base station (BS) with multiple antennas. We use a state-of-the-art power consumption model, taking into account the passive and active parts of the transceiver circuitry, including the effects of radiated power, signal processing, and passive consumption. The paper treats the transmit power, bandwidth, and number of antennas as the optimization variables. We provide novel closed-form solutions for the optimal ratios of power per unit bandwidth and power per transmit antenna. We present a novel algorithm that jointly optimizes these variables to achieve maximum EE, while fulfilling constraints on the variable ranges. We also discover a new relationship between the radiated power and the passive transceiver power consumption. We provide analytical insight into whether using maximum power or bandwidth is optimal and how many antennas a BS should utilize., Comment: 6 pages, 4 figures

We classify Legendrian realisations, up to coarse equivalence, of the Hopf link in the lens spaces L(p,1) with any contact structure., Comment: 28 pages, 15 figures

The family of right-angled tiling links consists of links built from regular 4-valent tilings of constant-curvature surfaces that contain one or two types of tiles. The complements of these links admit complete hyperbolic structures and contain two totally geodesic checkerboard surfaces that meet at right angles. In this paper, we give a complete characterization of which right-angled tiling links are arithmetic, and which are pairwise commensurable. The arithmeticity classification exploits symmetry arguments and the combinatorial geometry of Coxeter polyhedra. The commensurability classification relies on identifying the canonical decompositions of the link complements, in addition to number-theoretic data from invariant trace fields., Comment: 29 pages, 9 figures

The Benard-Conway invariant of links in the 3-sphere is a Casson-Lin type invariant defined by counting irreducible SU(2) representations of the link group with fixed meridional traces. For two-component links with linking number one, the invariant has been shown to equal a symmetrized multivariable link signature. We extend this result to all two-component links with non-zero linking number. A key ingredient in the proof is an explicit calculation of the Benard-Conway invariant for (2, 2n)-torus links with the help of the Chebyshev polynomials., Comment: Added a paragraph relating our work to that of Daemi and Scaduto on irreducible instanton homology of links. 32 pages, 10 figures

We study the connected sum of Hopf links in $S^3$. Particularly, we compute the entanglement entropy (EE) as a function of the number of link components. We find evidence of lower and upper bounds for the entanglement entropy. We show that the $SU(2)$ theory exhibits sensitivity to the parity of links. We also find evidence suggesting the existence of a well-defined limit of the large number of link components., Comment: 15 pages, 3 figures