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In 1975, Erd\H{o}s and Sauer asked to estimate, for any constant $r$, the maximum number of edges an $n$-vertex graph can have without containing an $r$-regular subgraph. In a recent breakthrough, Janzer and Sudakov proved that any $n$-vertex graph with no $r$-regular subgraph has at most $C_r n \log \log n$ edges, matching an earlier lower bound by Pyber, R\"odl and Szemer\'edi and thereby resolving the Erd\H{o}s-Sauer problem up to a constant depending on $r$. We prove that every $n$-vertex graph without an $r$-regular subgraph has at most $Cr^2 n \log \log n$ edges. This bound is tight up to the value of $C$ for $n\geq n_0(r)$ and hence resolves the Erd\H{o}s-Sauer problem up to an absolute constant. Moreover, we obtain similarly tight results for the whole range of possible values of $r$ (i.e., not just when $r$ is a constant), apart from a small error term at a transition point near $r\approx \log n$, where, perhaps surprisingly, the answer changes. More specifically, we show that every $n$-vertex graph with average degree at least $\min(Cr\log(n/r),Cr^2 \log\log n)$ contains an $r$-regular subgraph. The bound $Cr\log(n/r)$ is tight for $r\geq \log n$, while the bound $Cr^2 \log \log n$ is tight for $r<(\log n)^{1-\Omega(1)}$. These results resolve a problem of R\"odl and Wysocka from 1997 for almost all values of $r$. Among other tools, we develop a novel random process that efficiently finds a very nearly regular subgraph in any almost-regular graph. A key step in our proof uses this novel random process to show that every $K$-almost-regular graph with average degree $d$ contains an $r$-regular subgraph for some $r=\Omega_K(d)$, which is of independent interest., Comment: 16 pages

The rapid scaling of AI has spurred a growing emphasis on ethical considerations in both development and practice. This has led to the formulation of increasingly sophisticated model auditing and reporting requirements, as well as governance frameworks to mitigate potential risks to individuals and society. At this critical juncture, we review the practical challenges of promoting responsible AI and transparency in informal sectors like OSS that support vital infrastructure and see widespread use. We focus on how model performance evaluation may inform or inhibit probing of model limitations, biases, and other risks. Our controlled analysis of 7903 Hugging Face projects found that risk documentation is strongly associated with evaluation practices. Yet, submissions (N=789) from the platform's most popular competitive leaderboard showed less accountability among high performers. Our findings can inform AI providers and legal scholars in designing interventions and policies that preserve open-source innovation while incentivizing ethical uptake., Comment: [Under Review][WIP]

In 1988, Erd\H{o}s suggested the question of minimizing the number of edges in a connected $n$-vertex graph where every edge is contained in a triangle. Shortly after, Catlin, Grossman, Hobbs, and Lai resolved this in a stronger form. In this paper, we study a natural generalization of the question of Erd\H{o}s in which we replace `triangle' with `clique of order $k$' for ${k\ge 3}$. We completely resolve this generalized question with the characterization of all extremal graphs. Motivated by applications in data science, we also study another generalization of the question of Erd\H{o}s where every edge is required to be in at least $\ell$ triangles for $\ell\ge 2$ instead of only one triangle. We completely resolve this problem for $\ell = 2$.

Biological functionality of cellular aggregates is largely influenced by the activity and displacements of individual constituent cells. From a theoretical perspective this activity can be characterized by hydrodynamic transport coefficients of diffusivity and conductivity. Motivated by the clustering dynamics of bacterial microcolonies we propose a model of active multicellular aggregates and use recently developed macroscopic fluctuation theory to derive a fluctuating hydrodynamics for this model system. Both semi-analytic theory and microscopic simulations show that the hydrodynamic transport coefficients are affected by non-equilibrium microscopic parameters and significantly decrease inside of the clusters. We further find that the Einstein relation connecting the transport coefficients and fluctuations breaks down in the parameter regime where the detailed balance is not satisfied. This study offers valuable tools for experimental investigation of hydrodynamic transport in other systems of cellular aggregates such as tumor spheroids and organoids.

Two celebrated extensions of the classical Helly's theorem are the fractional Helly theorem and the colorful Helly theorem. Bulavka, Goodarzi, and Tancer recently established the optimal bound for the unified generalization of the fractional and the colorful Helly theorems using a colored extension of the exterior algebra. In this paper, we combinatorially reduce both the fractional Helly theorem and its colorful version to a classical problem in extremal combinatorics known as {weak saturation}. No such results connecting the fractional Helly theorem and weak saturation are known in the long history of literature. These reductions, along with basic linear algebraic arguments for the reduced weak saturation problems, let us give new short proofs of the optimal bounds for both the fractional Helly theorem and its colorful version without using exterior algebra., Comment: 5 pages, 1 figure

This study presents a novel approach for enhancing American Sign Language (ASL) recognition using Graph Convolutional Networks (GCNs) integrated with successive residual connections. The method leverages the MediaPipe framework to extract key landmarks from each hand gesture, which are then used to construct graph representations. A robust preprocessing pipeline, including translational and scale normalization techniques, ensures consistency across the dataset. The constructed graphs are fed into a GCN-based neural architecture with residual connections to improve network stability. The architecture achieves state-of-the-art results, demonstrating superior generalization capabilities with a validation accuracy of 99.14%., Comment: To be submitted in G2-SP CV 2024. Contains 7 pages, 5 figures

This study introduces a novel activation function, characterized by a dynamic slope that adjusts throughout the training process, aimed at enhancing adaptability and performance in deep neural networks for computer vision tasks. The rationale behind this approach is to overcome limitations associated with traditional activation functions, such as ReLU, by providing a more flexible mechanism that can adapt to different stages of the learning process. Evaluated on the Mini-ImageNet, CIFAR-100, and MIT-BIH datasets, our method demonstrated improvements in classification metrics and generalization capabilities. These results suggest that our dynamic slope activation function could offer a new tool for improving the performance of deep learning models in various image recognition tasks., Comment: Under peer review at ICPR, 2024

A consistent treatment of the quantum field theory of an axion-like particle (ALP) interacting with Standard Model fields requires to account for renormalisation group running and matching to the low-energy theory. Quantum sensor experiments designed to search for very light ALPs are particularly sensitive to these effects because they probe large values of the decay constant for which running effects become important. In addition, while linear axion interactions are set by its pseudoscalar nature, quadratic interactions are indistinguishable from scalar interactions. We show how the Wilson coefficients of linear and quadratic ALP interactions are related, including running effects above and below the QCD scale and provide a comprehensive analysis of the sensitivity of current and future experiments. We identify the reach of different experiments for the case of ALP dark matter and comment on how it could be distinguished from the case where it is not the dark matter. We present novel search strategies to observe quadratic ALP interactions via fifth force searches, haloscopes, helioscopes and quantum sensors. We emphasize the nonlinear behaviour of the ALP field close to the surface of the earth and point out which experimental results are independent on the local background field value., Comment: 44 pages, 9 figures

Light bosonic dark matter fields that can be treated like a classical wave have non-linear field values close to massive bodies. Here we make the important observation that the quadratic interactions of axion dark matter lead to non-perturbative axion field values for values of the decay constant of $f\lesssim 10^{15}$ GeV and masses $m_a\lesssim 7\times10^{8}/f\ {\rm eV^2}$ and generalise this result for axion-like particles. We identify experimental observables impacted by this effect., Comment: 6 pages, 1 figure

The history based formalism known as Quantum Measure Theory (QMT) generalizes the concept of probability-measure so as to incorporate quantum interference. Because interference can result in a greater intensity than the simple sum of the component intensities, the \textit{quantum measure} can exceed unity, exhibiting its non-classical nature in a particularly striking manner. Here we study the two-site hopper within the context of QMT; and in an optical experiment, we determine the measure of a specific hopper event, using an ancilla based event filtering scheme. For this measure we report a value of $1.172$, which exceeds the maximum value permissible for a classical probability (namely $1$) by $13.3$ standard deviations. If an unconventional theoretical concept is to play a role in meeting the foundational challenges of quantum theory, then it seems important to bring it into contact with experiment as much as possible. Our experiment does this for the quantum measure., Comment: 24 pages, 3 figures

Thomason [$\textit{Trans. Amer. Math. Soc.}$ 296.1 (1986)] proved that every sufficiently large tournament contains Hamilton paths and cycles with all possible orientations, except possibly the consistently oriented Hamilton cycle. This paper establishes $\textit{transversal}$ generalizations of these classical results. For a collection $\mathbf{T}=\{T_1,\dots,T_m\}$ of not-necessarily distinct tournaments on the common vertex set $V$, an $m$-edge directed subgraph $\mathcal{D}$ with the vertices in $V$ is called a transversal if there exists an bijection $\varphi\colon E(\mathcal{D})\to [m]$ such that $e\in E(T_{\varphi(e)})$ for all $e\in E(\mathcal{D})$. We prove that for sufficiently large $n$, there exist transversal Hamilton cycles of all possible orientations possibly except the consistently oriented one. We also obtain a similar result for the transversal Hamilton paths of all possible orientations. These results generalize the classical theorem of Thomason, and our approach provides another proof of this theorem.

In this work, we demonstrate that the modulation of carrier density can alter the superconducting transition temperature by up to $204$ mK in epitaxial Indium Nitride on Gallium Nitride, accounting for the $10$% of the transition temperature in ungated conditions. Our samples are likely free from strong localization effects and significant granularity, as indicated by $( k_{f l} \gg 1 )$, suggesting that the primary determinant of the transition temperature in InN is carrier density, rather than disorder scattering. The observed behavior is consistent with BCS s-wave superconductivity, corroborated by the superconducting parameters we measured. Furthermore, we observed a $60$% bipolar suppression of the supercurrent in our experiments., Comment: 6 pages, 5 figures, supplementary material attached. Comments are welcome

In this paper, we have explored the charge transfer mechanism in transition metal dichalcogenide (TMDC) quantum dots (QDs) of molybdenum disulfide ($\rm{MoS_2}$) and tungsten disulfide ($\rm{WS_2}$). Rhodamine 6G (R6G), a dye from the rhodamine family, has been employed as the fluorescent molecule, with MoS$_2$ and WS$_2$ QDs acting as electron acceptors in the photo-induced charge transfer process. The TMDC QDs were synthesized using a top-down approach and characterized through transmission electron microscopy (TEM), UV-Vis spectrophotometry, and fluorimetry. TEM images revealed well-dispersed particles measuring 2 nm in size. These QDs exhibit strong fluorescence emission when excited with light at wavelengths below 350 nm. Under light exposure, photons generate charges in the fluorescent dye molecules, and the TMDC QDs facilitate the charge transfer process. The charge transfer phenomenon was investigated using time-correlated single photon counting (TCSPC), a time-resolved fluorescence spectroscopic technique. The time-resolved fluorescence study indicated a change in the fluorescence (FL) lifetime of R6G molecules in the presence of QDs. The FL lifetime of R6G molecules without QDs was found to be 4.0 ns, which decreased to 1.9 ns and 3.8 ns in the presence of MoS$_2$ and WS$_2$ QDs, respectively. This reduction in FL lifetime suggests that the MoS$_2$ and WS$_2$ QDs provide an additional pathway for photo-generated electrons in the excited state of R6G molecules. This research can be extended to optoelectronic devices, where charge transfer is crucial for device efficiency and performance., Comment: 7 pages, 10 figures

In this article, we review the interdisciplinary techniques (borrowed from physics, mathematics, statistics, machine-learning, etc.) and methodological framework that we have used to understand climate systems, which serve as examples of "complex systems". We believe that this would offer valuable insights to comprehend the complexity of climate variability and pave the way for drafting policies for action against climate change, etc. Our basic aim is to analyse time-series data structures across diverse climate parameters, extract Fourier-transformed features to recognize and model the trends/seasonalities in the climate variables using standard methods like detrended residual series analyses, correlation structures among climate parameters, Granger causal models, and other statistical machine-learning techniques. We cite and briefly explain two case studies: (i) the relationship between the Standardised Precipitation Index (SPI) and specific climate variables including Sea Surface Temperature (SST), El Ni\~no Southern Oscillation (ENSO), and Indian Ocean Dipole (IOD), uncovering temporal shifts in correlations between SPI and these variables, and reveal complex patterns that drive drought and wet climate conditions in South-West Australia; (ii) the complex interactions of North Atlantic Oscillation (NAO) index, with SST and sea ice extent (SIE), potentially arising from positive feedback loops., Comment: 21 pages, 12 figures. Accepted in the Indian Journal of Theoretical Physics (Institute of Theoretical Physics, Calcutta, 1953)

Deep neural networks (DNNs) are powerful tools for approximating the distribution of complex data. It is known that data passing through a trained DNN classifier undergoes a series of geometric and topological simplifications. While some progress has been made toward understanding these transformations in neural networks with smooth activation functions, an understanding in the more general setting of non-smooth activation functions, such as the rectified linear unit (ReLU), which tend to perform better, is required. Here we propose that the geometric transformations performed by DNNs during classification tasks have parallels to those expected under Hamilton's Ricci flow - a tool from differential geometry that evolves a manifold by smoothing its curvature, in order to identify its topology. To illustrate this idea, we present a computational framework to quantify the geometric changes that occur as data passes through successive layers of a DNN, and use this framework to motivate a notion of `global Ricci network flow' that can be used to assess a DNN's ability to disentangle complex data geometries to solve classification problems. By training more than $1,500$ DNN classifiers of different widths and depths on synthetic and real-world data, we show that the strength of global Ricci network flow-like behaviour correlates with accuracy for well-trained DNNs, independently of depth, width and data set. Our findings motivate the use of tools from differential and discrete geometry to the problem of explainability in deep learning.

In 1975, Erd\H{o}s asked for the maximum number of edges that an $n$-vertex graph can have if it does not contain two edge-disjoint cycles on the same vertex set. It is known that Tur\'an-type results can be used to prove an upper bound of $n^{3/2+o(1)}$. However, this approach cannot give an upper bound better than $\Omega(n^{3/2})$. We show that, for any $k\geq 2$, every $n$-vertex graph with at least $n \cdot \mathrm{polylog}(n)$ edges contains $k$ pairwise edge-disjoint cycles with the same vertex set, resolving this old problem in a strong form up to a polylogarithmic factor. The well-known construction of Pyber, R\"odl and Szemer\'edi of graphs without $4$-regular subgraphs shows that there are $n$-vertex graphs with $\Omega(n\log \log n)$ edges which do not contain two cycles with the same vertex set, so the polylogarithmic term in our result cannot be completely removed. Our proof combines a variety of techniques including sublinear expanders, absorption and a novel tool for regularisation, which is of independent interest. Among other applications, this tool can be used to regularise an expander while still preserving certain key expansion properties., Comment: 34 pages, 2 figures

In this work, we have demonstrated the acquisition of pulsed ODMR data with the help of a high speed oscilloscope. We show how the on-system data averaging and the memory of the oscilloscope can be utilized to obtain high SNR data at high speeds. The problem of experimental drift and the strategy for eliminating the same is discussed. Two distinct methods of data acquisition and processing are discussed, and their applicability to different pulsed protocols is investigated. Rabi Oscillations, Ramsey Interferometry, T1 measurement, and spin echo are demonstrated.

Formal rules and policies are fundamental in formally specifying a social system: its operation, boundaries, processes, and even ontology. Recent scholarship has highlighted the role of formal policy in collective knowledge creation, game communities, the production of digital public goods, and national social media governance. Researchers have shown interest in how online communities convene tenable self-governance mechanisms to regulate member activities and distribute rights and privileges by designating responsibilities, roles, and hierarchies. We present NLP4Gov, an interactive kit to train and aid scholars and practitioners alike in computational policy analysis. The library explores and integrates methods and capabilities from computational linguistics and NLP to generate semantic and symbolic representations of community policies from text records. Versatile, documented, and accessible, NLP4Gov provides granular and comparative views into institutional structures and interactions, along with other information extraction capabilities for downstream analysis.

The quest for supersymmetric (SUSY) particles is among the main search channels currently pursued at the LHC. Particularly, electroweak (EW) particles with masses as low as a few hundred GeV are still viable. Recent searches for the ``golden channel'', $pp \to \tilde \chi_2^{\rm 0} \tilde \chi_1^{\rm \pm} \to \tilde \chi_1^{\rm 0} Z^{(*)} \, \tilde \chi_1^{\rm 0} W^{\pm (*)}$ show consistent excesses between ATLAS and CMS in the 2~lepton, 3-lepton and mono-jet searches, assuming $m_{\tilde \chi_2^{\rm 0}} \approx m_{\tilde \chi_1^{\rm \pm}} \gtrsim 200$ GeV and $\Delta m := m_{\tilde \chi_2^{\rm 0}} - m_{\tilde \chi_1^{\rm 0}} \approx 20$ GeV. This mass configuration arises naturally in SUSY scenarios with wino/bino Dark Matter (DM) or higgsino DM. In these scenarios the lightest supersymmetric particle (LSP), assumed to be the lightest neutralino, as a DM candidate, is in good agreement with the observed limits on the DM content of the universe, as well as with negative results from Direct Detection (DD) experiments. We analyze these two scenarios with respect to the observed excesses, taking into account all relevant experimental constraints. We show that in particular wino/bino DM with different signs of the $SU(2)$ and $U(1)$ soft SUSY-breaking parameters can describe well the experimental excesses, while being in agreement with all other constraints., Comment: 29 pages, 10 figures

A system in equilibrium keeps ``exploring" nearby states in the phase space and consequently, fluctuations can contain information, that the mean value does not. However, such measurements involve a fairly complex interplay of effects arising in the device and measurement electronics, that are non-trivial to disentangle. In this paper, we briefly analyse some of these issues and show the relevance of a two-amplifier cross-correlation technique for semiconductors and thin films commonly encountered. We show that by using home-built amplifiers costing less than $10$ USD/piece one can measure spectral densities as low as $\sim 10^{-18}-10^{-19}~ {\rm {V^2}{Hz^{-1}}}$. We apply this method to an ionic liquid gated Ga:ZnO channel and show that the glass transition of the ionic liquid brings about a change in the exponent of the low frequency resistance fluctuations. Our analysis suggests that a log-normal distribution of the Debye relaxation times of the fluctuations and an increased weight of the long timescale relaxations can give a semi-quantitative explanation of the observed change in the exponent., Comment: 6 pages, 5 figures, supplementary material attached. Comments are welcome

The recent results reported by the CMS collaboration, indicating "bumps" in the $\gamma\gamma$ and $\tau\tau$ channels at $m_\phi\approx 95$ GeV, provide interesting hints for new physics. We find that the lightest Higgs state of the general 2HDM (2HDM Type-III) can perfectly and simultaneously accommodate the two excesses alongside with the LEP long-standing anomaly observed in the $b\bar{b}$ channel while meeting all theoretical and experimental requirements. Furthermore, the study predicts an enhanced production process for the SM-like Higgs in $pp\to t\bar t H_{\rm SM}$, offering a testable hypothesis for future experiments., Comment: Contribution to: LHCP 2023, 299

Consider a multipartite graph $G$ with maximum degree at most $n-o(n)$, parts $V_1,\ldots,V_k$ have size $|V_i|=n$, and every vertex has at most $o(n)$ neighbors in any part $V_i$. Loh and Sudakov proved that any such $G$ has an independent transversal. They further conjectured that the vertex set of $G$ can be decomposed into pairwise disjoint independent transversals. In the present paper, we resolve this conjecture approximately by showing that $G$ contains $n-o(n)$ pairwise disjoint independent transversals. As applications, we give approximate answers to questions of Yuster, and of Fischer, K\"uhn, and Osthus.

In the last decade, graphene has become an exciting platform for electron optical experiments, in many aspects superior to conventional two-dimensional electron gases (2DEGs). A major advantage, besides the ultra-large mobilities, is the fine control over the electrostatics, which gives the possibility of realising gap-less and compact p-n interfaces with high precision. The latter host non-trivial states, \eg, snake states in moderate magnetic fields, and serve as building blocks of complex electron interferometers. Thanks to the Dirac spectrum and its non-trivial Berry phase, the internal (valley and sublattice) degrees of freedom, and the possibility to tailor the band structure using proximity effects, such interferometers open up a completely new playground based on novel device architectures. In this review, we introduce the theoretical background of graphene electron optics, fabrication methods used to realise electron-optical devices, and techniques for corresponding numerical simulations. Based on this, we give a comprehensive review of ballistic transport experiments and simple building blocks of electron optical devices both in single and bilayer graphene, highlighting the novel physics that is brought in compared to conventional 2DEGs. After describing the different magnetic field regimes in graphene p-n junctions and nanostructures, we conclude by discussing the state of the art in graphene-based Mach-Zender and Fabry-Perot interferometers., Comment: The authors welcome any comments regarding the content of the review

We consider a light scalar dark matter candidate with mass in the GeV range whose $p$-wave annihilation is enhanced through a Breit-Wigner resonance. The annihilation actually proceeds in the $s$-channel via a dark photon mediator whose mass is nearly equal to the masses of the incoming particles. We compute the temperature at which kinetic decoupling between dark matter and the primordial plasma occurs and show that including the effect of kinetic decoupling can reduce the dark matter relic density by orders of magnitude. For typical scalar masses ranging from 200 MeV to 5 GeV, we determine the range of values allowed for the dark photon couplings to the scalar and to the standard model particles after requiring the relic density to be in agreement with the value extracted from cosmological observations. We then show that $\mu$ and $y$-distortions of the CMB spectrum and X-ray data from XMM-Newton strongly constrain the model and rule out the region where the dark matter annihilation cross-section is strongly enhanced at small dispersion velocities. Constraints from direct detection searches and from accelerator searches for dark photons offer complementary probes of the model., Comment: 33 pages, 9 captioned figures

micrOMEGAs is a numerical code to compute dark matter (DM) observables in generic extensions of the Standard Model of particle physics. We present a new version of micrOMEGAs that includes a generalization of the Boltzmann equations governing the DM cosmic abundance evolution which can be solved to compute the relic density of N-component DM. The direct and indirect detection rates in such scenarios take into account the relative contribution of each component such that constraints on the combined signal of all DM components can be imposed. The co-scattering mechanism for DM production is also included, whereas the routines used to compute the relic density of feebly interacting particles have been improved in order to take into account the effect of thermal masses of t-channel particles. Finally, the tables for the DM self-annihilation - induced photon spectra have been extended down to DM masses of 110 MeV, and they now include annihilation channels into light mesons., Comment: 39 pages, 1 figure

Chatbots have become one of the main pathways for the delivery of business automation tools. Multi-agent systems offer a framework for designing chatbots at scale, making it easier to support complex conversations that span across multiple domains as well as enabling developers to maintain and expand their capabilities incrementally over time. However, multi-agent systems complicate the natural language understanding (NLU) of user intents, especially when they rely on decentralized NLU models: some utterances (termed single intent) may invoke a single agent while others (termed multi-intent) may explicitly invoke multiple agents. Without correctly parsing multi-intent inputs, decentralized NLU approaches will not achieve high prediction accuracy. In this paper, we propose an efficient parsing and orchestration pipeline algorithm to service multi-intent utterances from the user in the context of a multi-agent system. Our proposed approach achieved comparable performance to competitive deep learning models on three different datasets while being up to 48 times faster., Comment: 16 pages

This is the first work to look at the application of large language models (LLMs) for the purpose of model space edits in automated planning tasks. To set the stage for this union, we explore two different flavors of model space problems that have been studied in the AI planning literature and explore the effect of an LLM on those tasks. We empirically demonstrate how the performance of an LLM contrasts with combinatorial search (CS) -- an approach that has been traditionally used to solve model space tasks in planning, both with the LLM in the role of a standalone model space reasoner as well as in the role of a statistical signal in concert with the CS approach as part of a two-stage process. Our experiments show promising results suggesting further forays of LLMs into the exciting world of model space reasoning for planning tasks in the future., Comment: 24 pages