Hamiltonian Monte Carlo is a prominent Markov Chain Monte Carlo algorithm, which employs symplectic integrators to sample from high dimensional target distributions in many applications, such as statistical mechanics, Bayesian statistics and generative models. However, such distributions tend to have thin high density regions, posing a significant challenge for symplectic integrators to maintain the small energy errors needed for a high acceptance probability. Instead, we propose a variant called Conservative Hamiltonian Monte Carlo, using $R$--reversible energy-preserving integrators to retain a high acceptance probability. We show our algorithm can achieve approximate stationarity with an error determined by the Jacobian approximation of the energy-preserving proposal map. Numerical evidence shows improved convergence and robustness over integration parameters on target distributions with thin high density regions and in high dimensions. Moreover, a version of our algorithm can also be applied to target distributions without gradient information.

Conservative symmetric second-order one-step schemes are derived for dynamical systems describing various many-body systems using the Discrete Multiplier Method. This includes conservative schemes for the $n$-species Lotka-Volterra system, the $n$-body problem with radially symmetric potential and the $n$-point vortex models in the plane and on the sphere. In particular, we recover Greenspan-Labudde's conservative schemes for the $n$-body problem. Numerical experiments are shown verifying the conservative property of the schemes and second-order accuracy.

In this paper, we introduce a three-component Gierer-Meinhardt model in the semi-strong interaction regime, characterized by an asymptotically large diffusivity ratio. A key feature of this model is that the interior spike can undergo Hopf bifurcations in both amplitude and position, leading to rich oscillatory dynamics not present in classical two-component systems. Using asymptotic analysis and numerical path-following, we construct localized spike equilibria and analyze spike nucleation that occurs through slow passage beyond a saddle-node bifurcation. Moreover, stability of spike equilibrium is analyzed by introducing time-scaling parameters, which reveal two distinct mechanisms: amplitude oscillations triggered by large-eigenvalue instabilities and oscillatory spike motion associated with small eigenvalues. Numerical simulations illustrate these dynamics and their transition regimes. This dual mechanism highlights richer spike behavior in three-component systems and suggests several open problems for future study.

In this paper, we present a novel hybrid deep learning model, named ConvLSTMTransNet, designed for time series prediction, with a specific application to internet traffic telemetry. This model integrates the strengths of Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM) networks, and Transformer encoders to capture complex spatial-temporal relationships inherent in time series data. The ConvLSTMTransNet model was evaluated against three baseline models: RNN, LSTM, and Gated Recurrent Unit (GRU), using real internet traffic data sampled from high-speed ports on a provider edge router. Performance metrics such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Weighted Absolute Percentage Error (WAPE) were used to assess each model's accuracy. Our findings demonstrate that ConvLSTMTransNet significantly outperforms the baseline models by approximately 10% in terms of prediction accuracy. ConvLSTMTransNet surpasses traditional models due to its innovative architectural features, which enhance its ability to capture temporal dependencies and extract spatial features from internet traffic data. Overall, these findings underscore the importance of employing advanced architectures tailored to the complexities of internet traffic data for achieving more precise predictions.

Delivering hands-on practice laboratories for introductory courses on operating systems is a difficult task. One of the main sources of the difficulty is the sheer size and complexity of the operating systems software. Consequently, some of the solutions adopted in the literature to teach operating systems laboratory consider smaller and simpler systems, generally referred to as instructional operating systems. This work continues in the same direction and is threefold. First, it considers a simpler hardware platform. Second, it argues that a minimal operating system is a viable option for delivering laboratories. Third, it presents a laboratory teaching platform, whereby students build a minimal operating system for an embedded hardware platform. The proposed platform is called MiniOS. An important aspect of MiniOS is that it is sufficiently supported with additional technical and pedagogic material. Finally, the effectiveness of the proposed approach to teach operating systems laboratories is illustrated through the experience of using it to deliver laboratory projects in the Operating Systems course at the University of Northern British Columbia. Finally, we discuss experimental research in computing education and considered the qualitative results of this work as part of a larger research endeavour.

The exponential growth of the Internet of Things (IoT) has significantly increased the complexity and volume of cybersecurity threats, necessitating the development of advanced, scalable, and interpretable security frameworks. This paper presents an innovative, comprehensive framework for real-time IoT attack detection and response that leverages Machine Learning (ML), Explainable AI (XAI), and Large Language Models (LLM). By integrating XAI techniques such as SHAP (SHapley Additive exPlanations) and LIME (Local Interpretable Model-agnostic Explanations) with a model-independent architecture, we ensure our framework's adaptability across various ML algorithms. Additionally, the incorporation of LLMs enhances the interpretability and accessibility of detection decisions, providing system administrators with actionable, human-understandable explanations of detected threats. Our end-to-end framework not only facilitates a seamless transition from model development to deployment but also represents a real-world application capability that is often lacking in existing research. Based on our experiments with the CIC-IOT-2023 dataset \cite{neto2023ciciot2023}, Gemini and OPENAI LLMS demonstrate unique strengths in attack mitigation: Gemini offers precise, focused strategies, while OPENAI provides extensive, in-depth security measures. Incorporating SHAP and LIME algorithms within XAI provides comprehensive insights into attack detection, emphasizing opportunities for model improvement through detailed feature analysis, fine-tuning, and the adaptation of misclassifications to enhance accuracy.

Rapid intensification (RI) of tropical cyclones (TCs) provides a great challenge in operational forecasting and contributes significantly to the development of major TCs. RI is commonly defined as an increase in the maximum sustained surface wind speed beyond a certain threshold within 24 h. The most widely used threshold is 30 kt (15.4 m/s), which was determined statistically. Here we propose a new definition for RI by objectively clustering TCs using the intensification rate, initial intensity, and radius of the maximum wind speed. A group of 770 samples is separated at a threshold of 45 kt (23.2 m/s). The threshold is 40 kt (20.6 m/s) for the western North Atlantic, where TC size measurements are more reliable. Monte Carlo experiments demonstrate that the proposed threshold is robust even considering the uncertainty in RMW of as high as 30 km. We show that, when a TC undergoes RI, its maximum wind speed is approximately 60+/-15 kt (30.9+/-7.7 m/s) and the radius of the maximum wind speed is 45+/-20 km. The new threshold outperforms the conventional threshold of 30 kt/24h in (1) describing the bimodal distribution of lifetime maximum intensity, and (2) explaining the annual count of Category 5 TCs. This new definition provides a more physically-based threshold and describes a more reliable representation to the extreme events. Although more comparisons are needed for operational application, it is likely to be desirable for process-based case studies, and could provide a more valuable metric for TC intensification classification and research.

We study the excitation spectrum of the one-dimensional spin-1/2 XXZ chain with antiferromagnetic Ising anisotropy across a magnetic quantum phase transition induced by the application of a site-dependent transverse magnetic field. Motivated by the chain antiferromagnet BaCo$_2$V$_2$O$_8$, we consider a situation where the transverse magnetic field has a strong uniform component and a weaker staggered part. To determine the nature of the excitations giving rise to the spin dynamical structure factor, we use a combination of analytical approaches and the numerically exact time-dependent matrix product state method. We identify below the quantum phase transition high-energy many-body two-magnon and three-magnon repulsively bound states which are clearly visible due to the staggered component of the magnetic field. At high magnetic fields and low temperature, single magnons dominate the dynamics. Our theory results are in very good agreement with terahertz spectroscopy experimental results presented in [Wang et al., Nature 631, 760 (2024)].

This is an ongoing list of problems that has resulted from the PIMS (Pacific Institute of Mathematical Sciences) Collaborative Research Group L-functions in Analytic Number Theory: 2022- 2025. The focus of this list is on Moments of $L$-functions and related topics.

Effective internet traffic prediction in smaller ISP networks is challenged by limited data availability. This paper explores this issue using transfer learning and data augmentation techniques with two LSTM-based models, LSTMSeq2Seq and LSTMSeq2SeqAtn, initially trained on a comprehensive dataset provided by Juniper Networks and subsequently applied to smaller datasets. The datasets represent real internet traffic telemetry, offering insights into diverse traffic patterns across different network domains. Our study revealed that while both models performed well in single-step predictions, multi-step forecasts were challenging, particularly in terms of long-term accuracy. In smaller datasets, LSTMSeq2Seq generally outperformed LSTMSeq2SeqAtn, indicating that higher model complexity does not necessarily translate to better performance. The models' effectiveness varied across different network domains, reflecting the influence of distinct traffic characteristics. To address data scarcity, Discrete Wavelet Transform was used for data augmentation, leading to significant improvements in model performance, especially in shorter-term forecasts. Our analysis showed that data augmentation is crucial in scenarios with limited data. Additionally, the study included an analysis of the models' variability and consistency, with attention mechanisms in LSTMSeq2SeqAtn providing better short-term forecasting consistency but greater variability in longer forecasts. The results highlight the benefits and limitations of different modeling approaches in traffic prediction. Overall, this research underscores the importance of transfer learning and data augmentation in enhancing the accuracy of traffic prediction models, particularly in smaller ISP networks with limited data availability.

Traffic routing is vital for the proper functioning of the Internet. As users and network traffic increase, researchers try to develop adaptive and intelligent routing algorithms that can fulfill various QoS requirements. Reinforcement Learning (RL) based routing algorithms have shown better performance than traditional approaches. We developed a QoS-aware, reusable RL routing algorithm, RLSR-Routing over SDN. During the learning process, our algorithm ensures loop-free path exploration. While finding the path for one traffic demand (a source destination pair with certain amount of traffic), RLSR-Routing learns the overall network QoS status, which can be used to speed up algorithm convergence when finding the path for other traffic demands. By adapting Segment Routing, our algorithm can achieve flow-based, source packet routing, and reduce communications required between SDN controller and network plane. Our algorithm shows better performance in terms of load balancing than the traditional approaches. It also has faster convergence than the non-reusable RL approach when finding paths for multiple traffic demands.

We prove that for any two projection operators $f,g$ on Hilbert space, their anticommutator norm is given by the formula \[\|fg + gf\| = \|fg\| + \|fg\|^2.\] The result demonstrates an interesting contrast between the commutator and anticommutator of two projection operators on Hilbert space. Specifically, the norm of the anticommutator $\|fg + gf\|$ is a simple quadratic function of the norm $\|fg\|$ while the commutator norm $\|fg - gf\|$ is not a function of $\|fg\|$. Nevertheless, the result gives the following bounds that are functions of $\|fg\|$ on the commutator norm: $\|fg\| - \|fg\|^2 \le \|fg - gf\| \le \|fg\|$.

We report the measurement of the parity-violating asymmetry in the N to $\Delta$ transition via the $e^- + p \rightarrow e^- + \Delta ^+$ reaction at two different kinematic points with low four-momentum transfer Q$^2$. Measurements were made with incident electron beam energies of 0.877 and 1.16 GeV, corresponding to $Q^2$ values of 0.0111 and 0.0208 (GeV/c)$^2$, respectively. These measurements put constraints on a low-energy constant in the weak Lagrangian, $d_\Delta$, corresponding to a parity-violating electric-dipole transition matrix element. This matrix element has been shown to be large in the strangeness-changing channel, via weak hyperon decays such as $\Sigma ^+ \rightarrow p\gamma$. The measurements reported here constrain $d_\Delta$ in the strangeness-conserving channel. The final asymmetries were -0.65 +- 1.00 (stat.) +- 1.02 (syst) ppm (parts per million) for 0.877 GeV and -3.59 +- 0.82 (stat.) +- 1.33 (syst.} ppm for 1.16 GeV. With these results we deduce a small value for $d_\Delta$, consistent with zero, in the strangeness-conserving channel, in contrast to the large value for $d_\Delta$ previously reported in the strangeness-changing channel.

We propose a new precision measurement of parity-violating electron scattering on the proton at very low Q^2 and forward angles to challenge predictions of the Standard Model and search for new physics. A unique opportunity exists to carry out the first precision measurement of the proton's weak charge, $Q_W =1 - 4\sin^2\theta_W$. A 2200 hour measurement of the parity violating asymmetry in elastic ep scattering at Q^2=0.03 (GeV/c)^2 employing 180 $\mu$A of 85% polarized beam on a 35 cm liquid Hydrogen target will determine the proton's weak charge with approximately 4% combined statistical and systematic errors. The Standard Model makes a firm prediction of $Q_W$, based on the running of the weak mixing angle from the Z0 pole down to low energies, corresponding to a 10 sigma effect in this experiment.

The Qweak experiment has measured the parity-violating asymmetry in polarized e-p elastic scattering at Q^2 = 0.025(GeV/c)^2, employing 145 microamps of 89% longitudinally polarized electrons on a 34.4cm long liquid hydrogen target at Jefferson Lab. The results of the experiment's commissioning run are reported here, constituting approximately 4% of the data collected in the experiment. From these initial results the measured asymmetry is Aep = -279 +- 35 (statistics) +- 31 (systematics) ppb, which is the smallest and most precise asymmetry ever measured in polarized e-p scattering. The small Q^2 of this experiment has made possible the first determination of the weak charge of the proton, QpW, by incorporating earlier parity-violating electron scattering (PVES) data at higher Q^2 to constrain hadronic corrections. The value of QpW obtained in this way is QpW(PVES) = 0.064 +- 0.012, in good agreement with the Standard Model prediction of QpW(SM) = 0.0710 +- 0.0007. When this result is further combined with the Cs atomic parity violation (APV) measurement, significant constraints on the weak charges of the up and down quarks can also be extracted. That PVES+APV analysis reveals the neutron's weak charge to be QnW(PVES+APV) = -0.975 +- 0.010.

The fields of particle and nuclear physics have undertaken extensive programs to search for evidence of physics beyond that explained by current theories. The observation of the Higgs boson at the Large Hadron Collider completed the set of particles predicted by the Standard Model (SM), currently the best description of fundamental particles and forces. However, the theory's limitations include a failure to predict fundamental parameters and the inability to account for dark matter/energy, gravity, and the matter-antimater asymmetry in the universe, among other phenomena. Given the lack of additional particles found so far through direct searches in the post-Higgs era, indirect searches utilizing precise measurements of well predicted SM observables allow highly targeted alternative tests for physics beyond the SM. Indirect searches have the potential to reach mass/energy scales beyond those directly accessible by today's high-energy accelerators. The value of the weak charge of the proton Q_W^p is an example of such an indirect search, as it sets the strength of the proton's interaction with particles via the well-predicted neutral electroweak force. Parity violation (invariance under spatial inversion (x,y,z) -> (-x,-y,-z)) is violated only in the weak interaction, thus providing a unique tool to isolate the weak interaction in order to measure the proton's weak charge. Here we report Q_W^p=0.0719+-0.0045, as extracted from our measured parity-violating (PV) polarized electron-proton scattering asymmetry, A_ep=-226.5+-9.3 ppb. Our value of Q_W^p is in excellent agreement with the SM, and sets multi-TeV-scale constraints on any semi-leptonic PV physics not described within the SM.

We investigate the response to radio-frequency driving of an ultracold gas of attractively interacting fermions in a one-dimensional optical lattice. We study the system dynamics by monitoring the driving-induced population transfer to a third state, and the evolution of the momentum density and pair distributions. Depending on the frequency of the radio-frequency field, two different dynamical regimes emerge when considering the evolution of the third level population. One regime exhibits (off)resonant many-body oscillations reminiscent of Rabi oscillations in a discrete two-level system, while the other displays a strong linear rise. Within this second regime, we connect, via linear response theory, the extracted transfer rate to the system single-particle spectral function, and infer the nature of the excitations from Bethe ansatz calculations. In addition, we show that this radio-frequency technique can be employed to gain insights into this many-body system coupling mechanism away from equilibrium. This is done by monitoring the momentum density redistributions and the evolution of the pair correlations during the drive. Capturing such non-equilibrium physics goes beyond a linear response treatment, and is achieved here by conducting time-dependent matrix product state simulations.

The response of a gravitational wave detector to scalar waves is analysed in the framework of the debate on the choice of conformal frames for scalar-tensor theories. A correction to the geodesic equation arising in the Einstein conformal frame modifies the geodesic deviation equation. This modification is due to the non-metricity of the theory in the Einstein frame, yielding a longitudinal mode that is absent in the Jordan conformal frame.

Diabetic Retinopathy (DR) is one of the major causes of visual impairment and blindness across the world. It is usually found in patients who suffer from diabetes for a long period. The major focus of this work is to derive optimal representation of retinal images that further helps to improve the performance of DR recognition models. To extract optimal representation, features extracted from multiple pre-trained ConvNet models are blended using proposed multi-modal fusion module. These final representations are used to train a Deep Neural Network (DNN) used for DR identification and severity level prediction. As each ConvNet extracts different features, fusing them using 1D pooling and cross pooling leads to better representation than using features extracted from a single ConvNet. Experimental studies on benchmark Kaggle APTOS 2019 contest dataset reveals that the model trained on proposed blended feature representations is superior to the existing methods. In addition, we notice that cross average pooling based fusion of features from Xception and VGG16 is the most appropriate for DR recognition. With the proposed model, we achieve an accuracy of 97.41%, and a kappa statistic of 94.82 for DR identification and an accuracy of 81.7% and a kappa statistic of 71.1% for severity level prediction. Another interesting observation is that DNN with dropout at input layer converges more quickly when trained using blended features, compared to the same model trained using uni-modal deep features.

Charged lepton flavor violating muon decay ${\mu}^+{\rightarrow}e^+X_H$, where $X_H$ is a massive neutral boson, was sought by searching for extra peaks in the muon decay ${\mu}^+{\rightarrow}e^+{\nu}\bar{\nu}$ energy spectrum in the $m_{X_H}$ mass region $47.8-95.1$ MeV/$c^2$. No signal was found and 90% confidence level upper limits were set on the branching ratio ${\Gamma}({\mu}^+{\rightarrow}e^+X_H)/{\Gamma}({\mu}^+{\rightarrow}e^+{\nu}\bar{\nu})$ at the level of $10^{-5}$ for this region.