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This study introduces a robust solution for the detection of Distributed Denial of Service (DDoS) attacks in Internet of Things (IoT) systems, leveraging the capabilities of Graph Convolutional Networks (GCN). By conceptualizing IoT devices as nodes within a graph structure, we present a detection mechanism capable of operating efficiently even in lossy network environments. We introduce various graph topologies for modeling IoT networks and evaluate them for detecting tunable futuristic DDoS attacks. By studying different levels of network connection loss and various attack situations, we demonstrate that the correlation-based hybrid graph structure is effective in spotting DDoS attacks, substantiating its good performance even in lossy network scenarios. The results indicate a remarkable performance of the GCN-based DDoS detection model with an F1 score of up to 91%. Furthermore, we observe at most a 2% drop in F1-score in environments with up to 50% connection loss. The findings from this study highlight the advantages of utilizing GCN for the security of IoT systems which benefit from high detection accuracy while being resilient to connection disruption., Comment: 11 pages, 13 figures

We study equivariant Seiberg-Witten Floer theory of rational homology $3$-spheres in the special case where the group action is given by an involution. The case of involutions deserves special attention because we can couple the involution to the charge conjugation symmetry of Seiberg-Witten theory. This leads to new Floer-theoretic invariants which we study and apply in a variety of applications. In particular, we construct a series of delta-invariants $\delta^E_*, \delta^R_*, \delta^S_*$ which are the equivariant equivalents of the Ozsv\'ath-Szab\'o $d$-invariant. The delta-invariants come in three types: equivariant, Real and spin depending on the type of the spin$^c$-structure involved. The delta-invariants satisfy many useful properties, including a Froyshov-type inequality for equivariant cobordisms. We compute the delta-invariants in a wide range of examples including: equivariant plumbings, branched double covers of knots and equivariant Dehn surgery. We also consider various applications including obstructions to extending involutions over bounding $4$-manifolds, non-smoothable involutions on $4$-manifolds with boundary, equivariant embeddings of $3$-manifolds in $4$-manifolds and non-orientable surfaces bounding knots., Comment: 53 pages

Advancements in Generative AI hold immense promise to push Internet of Things (IoT) to the next level. In this article, we share our vision on IoT in the era of Generative AI. We discuss some of the most important applications of Generative AI in IoT-related domains. We also identify some of the most critical challenges and discuss current gaps as well as promising opportunities on enabling Generative AI for IoT. We hope this article can inspire new research on IoT in the era of Generative AI., Comment: 8 pages, 3 figures, 1 table

We compute the equivariant index of the twisted horizontal Dolbeault operator on compact toric contact manifolds of Reeb type. The operator is elliptic transverse to the Reeb foliation and its equivariant index defines a distribution on the torus. Using the good cone condition, we show that the symbol localises to the closed Reeb orbits corresponding to the edges of the moment cone and obtain an Atiyah-Bott-Lefschetz type formula for the index. For the horizontal Dolbeault operator, we obtain an expression for the index as a sum over the lattice points of the moment cone, by applying an adaptation of the Lawrence-Varchenko polytope decomposition to rational polyhedral cones., Comment: 31 pages; Minor corrections

We present a comprehensive study on applying machine learning to detect distributed Denial of service (DDoS) attacks using large-scale Internet of Things (IoT) systems. While prior works and existing DDoS attacks have largely focused on individual nodes transmitting packets at a high volume, we investigate more sophisticated futuristic attacks that use large numbers of IoT devices and camouflage their attack by having each node transmit at a volume typical of benign traffic. We introduce new correlation-aware architectures that take into account the correlation of traffic across IoT nodes, and we also compare the effectiveness of centralized and distributed detection models. We extensively analyze the proposed architectures by evaluating five different neural network models trained on a dataset derived from a 4060-node real-world IoT system. We observe that long short-term memory (LSTM) and a transformer-based model, in conjunction with the architectures that use correlation information of the IoT nodes, provide higher performance (in terms of F1 score and binary accuracy) than the other models and architectures, especially when the attacker camouflages itself by following benign traffic distribution on each transmitting node. For instance, by using the LSTM model, the distributed correlation-aware architecture gives 81% F1 score for the attacker that camouflages their attack with benign traffic as compared to 35% for the architecture that does not use correlation information. We also investigate the performance of heuristics for selecting a subset of nodes to share their data for correlation-aware architectures to meet resource constraints., Comment: 16 pages, 17 figures, journal

Coupling light from a point source to a propagating mode is an important problem in nano-photonics and is essential for many applications in quantum optics. Circular "bullseye" cavities, consisting of concentric rings of alternating refractive index, are a promising technology that can achieve near-unity coupling into a first lens. Here we design a bullseye structure suitable for enhancing the emission from dye molecules, 2D materials and nano-diamonds positioned on the surface of these cavities. A periodic design of cavity, meeting the Bragg scattering condition, achieves a Purcell factor of 22.5 and collection efficiency of 80 %. We also tackle the more challenging task of designing a cavity for coupling to a low numerical aperture fibre in the near field. Using an iterative procedure, we show that apodized (non-periodic) rings can achieve a collection efficiency that exceeds the periodic Bragg cavity., Comment: 9 pages, 6 figures

In this paper we further develop the theory of equivariant Seiberg-Witten-Floer cohomology of the two authors, with an emphasis on Brieskorn homology spheres. We obtain the following applications. First, we show that the knot concordance invariants $\theta^{(c)}$ defined by the first author satisfy $\theta^{(c)}(T_{a,b}) = (a-1)(b-1)/2$ for torus knots, whenever $c$ is a prime not dividing $ab$. Since $\theta^{(c)}$ is a lower bound for the slice genus, this gives a new proof of the Milnor conjecture of a similar flavour to the proofs using the Ozsv\'ath-Szab\'o $\tau$-invariant or Rasmussen $s$-invariant. Second, we prove that a free cyclic group action on a Brieskorn homology $3$-sphere $Y = \Sigma(a_1 , \dots , a_r)$ does not extend smoothly to any contractible smooth $4$-manifold bounding $Y$. This generalises to arbitrary $r$ the result of Anvari-Hambleton in the case $r=3$. Third, given a finite subgroup of the Seifert circle action on $Y = \Sigma(a_1 , \dots , a_r)$ of prime order $p$ acting non-freely on $Y$, we prove that if the rank of $HF_{red}^+(Y)$ is greater than $p$ times the rank of $HF_{red}^+(Y/\mathbb{Z}_p)$, then the $\mathbb{Z}_p$-action on $Y$ does not extend smoothly to any contractible smooth $4$-manifold bounding $Y$. We also prove a similar non-extension result for equivariant connected sums of Brieskorn homology spheres., Comment: 38 pages, accepted version. To appear in J. Topol

A device that is able to produce single photons is a fundamental building block for a number of quantum technologies. Significant progress has been made in engineering quantum emission in the solid state, for instance, using semiconductor quantum dots as well as defect sites in bulk and two-dimensional materials. Here we report the discovery of a room-temperature quantum emitter embedded deep within the band gap of aluminum nitride. Using spectral, polarization, and photon-counting time-resolved measurements we demonstrate bright ($>10^5$ counts per second), pure ($g^{(2)}(0) < 0.2$), and polarized room-temperature quantum light emission from color centers in this commercially important semiconductor.

Spin defects in foils of hexagonal boron nitride are an attractive platform for magnetic field imaging, since the probe can be placed in close proximity to the target. However, as a III-V material the electron spin coherence is limited by the nuclear spin environment, with spin echo coherence time of $\sim100~\mathrm{ns}$ at room temperature accessible magnetic fields. We use a strong continuous microwave drive with a modulation in order to stabilize a Rabi oscillation, extending the coherence time up to $\sim4~\mathrm{\mu s}$, which is close to the 10-$\mathrm{\mu s}$ electron spin lifetime in our sample. We then define a protected qubit basis, and show full control of the protected qubit. The coherence times of a superposition of the protected qubit can be as high as $0.8~\mathrm{\mu s}$. This work establishes that boron vacancies in hexagonal boron nitride can have electron spin coherence times that are competitive with typical NV-centers in small nanodiamonds under ambient conditions.

Among the wide-bandgap compound semiconductors, gallium nitride is the most widely available material due to its prevalence in the solid state lighting and high-speed/high-power electronics industries. It is now known that GaN is one of only a handful of materials to host color centers that emit quantum light at room temperature. In this paper, we report on a bright color center in a semi-polar gallium nitride substrate, emitting at room temperature in the near-infrared. We show that a hemispherical solid immersion lens, near index matched to the semiconductor, can be used to enhance the photon collection efficiency by a factor of $4.3\pm0.1$, whilst improving the lateral resolution by a factor equal to the refractive index of the lens.

As IoT deployments grow in scale for applications such as smart cities, they face increasing cyber-security threats. In particular, as evidenced by the famous Mirai incident and other ongoing threats, large-scale IoT device networks are particularly susceptible to being hijacked and used as botnets to launch distributed denial of service (DDoS) attacks. Real large-scale datasets are needed to train and evaluate the use of machine learning algorithms such as deep neural networks to detect and defend against such DDoS attacks. We present a dataset from an urban IoT deployment of 4060 nodes describing their spatio-temporal activity under benign conditions. We also provide a synthetic DDoS attack generator that injects attack activity into the dataset based on tunable parameters such as number of nodes attacked and duration of attack. We discuss some of the features of the dataset. We also demonstrate the utility of the dataset as well as our synthetic DDoS attack generator by using them for the training and evaluation of a simple multi-label feed-forward neural network that aims to identify which nodes are under attack and when., Comment: 5 pages, 8 figures

We develop an equivariant version of Seiberg-Witten-Floer cohomology for finite group actions on rational homology $3$-spheres. Our construction is based on an equivariant version of the Seiberg-Witten-Floer stable homotopy type, as constructed by Manolescu. We use these equivariant cohomology groups to define a series of $d$-invariants $d_{G,c}(Y,\mathfrak{s})$ which are indexed by the group cohomology of $G$. These invariants satisfy a Froyshov-type inequality under equivariant cobordisms. Lastly we consider a variety of applications of these $d$-invariants: concordance invariants of knots via branched covers, obstructions to extending group actions over bounding $4$-manifolds, Nielsen realisation problems for $4$-manifolds with boundary and obstructions to equivariant embeddings of $3$-manifolds in $4$-manifolds., Comment: 58 pages, minor corrections

Airborne transmission is now believed to be the primary way that COVID-19 spreads. We study the airborne transmission risk associated with holding in-person classes on university campuses. We utilize a model for airborne transmission risk in an enclosed room that considers the air change rate for the room, mask efficiency, initial infection probability of the occupants, and also the activity level of the occupants. We introduce, and use for our evaluations, a metric $R_0^{eff}$ that represents the ratio of new infections that occur over a week due to classroom interactions to the number of infected individuals at the beginning of the week. This can be seen as a surrogate for the well-known $R_0$ reproductive number metric, but limited in scope to classroom interactions and calculated on a weekly basis. The simulations take into account the possibility of repeated in-classroom interactions between students throughout the week. We presented model predictions were generated using Fall 2019 and Fall 2020 course registration data at a large US university, allowing us to evaluate the difference in transmission risk between in-person and hybrid programs. We quantify the impact of parameters such as reduced occupancy levels and mask efficacy. Our simulations indicate that universal mask usage results in an approximately $3.6\times$ reduction in new infections through classroom interactions. Moving 90% of the classes online leads to about $18\times$ reduction in new cases. Reducing class occupancy to 20%, by having hybrid classes, results in an approximately $2.15-2.3\times$ further reduction in new infections., Comment: 6 pages, typos corrected, picture of figure 1(f) corrected, added acknowledgments, added funding support

Pandemic and epidemic diseases such as CoVID-19, SARS-CoV2, and Ebola have spread to multiple countries and infected thousands of people. Such diseases spread mainly through person-to-person contacts. Health care authorities recommend contact tracing procedures to prevent the spread to a vast population. Although several mobile applications have been developed to trace contacts, they typically require collection of privacy-intrusive information such as GPS locations, and the logging of privacy-sensitive data on a third party server, or require additional infrastructure such as WiFi APs with known locations. In this paper, we introduce CONTAIN, a privacy-oriented mobile contact tracing application that does not rely on GPS or any other form of infrastructure-based location sensing, nor the continuous logging of any other personally identifiable information on a server. The goal of CONTAIN is to allow users to determine with complete privacy if they have been within a short distance, specifically, Bluetooth wireless range, of someone that is infected, and potentially also when. We identify and prove the privacy guarantees provided by our approach. Our simulation study utilizing an empirical trace dataset (Asturies) involving 100 mobile devices and around 60000 records shows that users can maximize their possibility of identifying if they were near an infected user by turning on the app during active times.

We analyse the problem of assigning sign choices to O-planes in orientifolds of type II string theory. We show that there exists a sequence of invariant $p$-gerbes with $p\geq-1$, which give rise to sign choices and are related by coboundary maps. We prove that the sign choice homomorphisms stabilise with the dimension of the orientifold and we derive topological constraints on the possible sign configurations. Concrete calculations for spherical and toroidal orientifolds are carried out, and in particular we exhibit a four-dimensional orientifold where not every sign choice is geometrically attainable. We elucidate how the $K$-theory groups associated with invariant $p$-gerbes for $p=-1,0,1$ interact with the coboundary maps. This allows us to interpret a notion of $K$-theory due to Gao and Hori as a special case of twisted $KR$-theory, which consequently implies the homotopy invariance and Fredholm module description of their construction., Comment: 29 pages; v2: minor corrections and comments added; Final version to appear in Communications in Mathematical Physics

By computerized analysis of cortical activity recorded via fMRI for pediatric epilepsy patients, we implement algorithmic localization of epileptic seizure focus within one of eight cortical lobes. Our innovative machine learning techniques involve intensive analysis of large matrices of mutual information coefficients between pairs of anatomically identified cortical regions. Drastic selection of pairs of regions with significant inter-connectivity provide efficient inputs for our Multi-Layer Perceptron (MLP) classifier. By imposing rigorous parameter parsimony to avoid over fitting we construct a small size MLP with very good percentages of successful classification., Comment: 25 pages,5 figures

In order to compare and benchmark the mathematical software, the performance profiles have been introduced [1]. However, it has been proved that the algorithm is not flawless. The main issue with the performance profile is that it may rank the solvers with respect to the best solver, by excluding the best one and running the algorithm on the remaining set of the solvers, the method may rank the solvers in a different way. We characterize such systems of problems-solvers and propose an efficient and reliable algorithm to overcome this negative side effect. The proposed method is unbiased in comparing the solvers and is successful in detecting the top ones, Comment: 9 pages, 3 figures

We prove an analogue of the Hitchin-Kobayashi correspondence for compact, oriented, taut Riemannian foliated manifolds with transverse Hermitian structure. In particular, our Hitchin-Kobayashi theorem holds on any compact Sasakian manifold. We define the notion of stability for foliated Hermitian vector bundles with transverse holomorphic structure and prove that such bundles admit a basic Hermitian-Einstein connection if and only if they are polystable. Our proof is obtained by adapting the proof by Uhlenbeck and Yau to the foliated setting. We relate the transverse Hermitian-Einstein equations to higher dimensional instanton equations and in particular we look at the relation to higher contact instantons on Sasaki manifolds. For foliations of complex codimension 1, we obtain a transverse Narasimhan-Seshadri theorem. We also demonstrate that the weak Uhlenbeck compactness theorem fails in general for basic connections on a foliated bundle. This shows that not every result in gauge theory carries over to the foliated setting., Comment: 42 pages

We consider Real bundle gerbes on manifolds equipped with an involution and prove that they are classified by their Real Dixmier-Douady class in Grothendieck's equivariant sheaf cohomology. We show that the Grothendieck group of Real bundle gerbe modules is isomorphic to twisted KR-theory for a torsion Real Dixmier-Douady class. Using these modules as building blocks, we introduce geometric cycles for twisted KR-homology and prove that they generate a real-oriented generalised homology theory dual to twisted KR-theory for Real closed manifolds, and more generally for Real finite CW-complexes, for any Real Dixmier-Douady class. This is achieved by defining an explicit natural transformation to analytic twisted KR-homology and proving that it is an isomorphism. Our model both refines and extends previous results by Wang and Baum-Carey-Wang to the Real setting. Our constructions further provide a new framework for the classification of orientifolds in string theory, providing precise conditions for orientifold lifts of H-fluxes and for orientifold projections of open string states., Comment: 44 pages; v2: minor changes, citations added; v3: technical corrections throughout, main results unchanged, some clarifying comments and reference added; v4: exposition improved, proof of Theorem 6.10 corrected, references added; v5: Final version to appear in Advances in Theoretical and Mathematical Physics; v6: published version with minor corrections, references updated

We calculate the $E$-polynomials of the $SL_3(\mathbb{C})$ and $GL_3(\mathbb{C})$-character varieties of compact oriented surfaces of any genus and the $E$-polynomials of the $SL_2(\mathbb{C})$ and $GL_2(\mathbb{C})$-character varieties of compact non-orientable surfaces of any Euler characteristic. Our methods also give a new and significantly simpler computation of the $E$-polynomials of the $SL_2(\mathbb{C})$-character varieties of compact orientable surfaces, which were computed by Logares, Mu\~noz and Newstead for genus $g=1,2$ and by Martinez and Mu\~noz for $g \ge 3$. Our technique is based on the arithmetic of character varieties over finite fields. More specifically, we show how to extend the approach of Hausel and Rodriguez-Villegas used for non-singular (twisted) character varieties to the singular (untwisted) case., Comment: 41 pages