Distil the informative essence of loop detector data set: Is network-level traffic forecasting hungry for more data?

Network-level traffic condition forecasting has been intensively studied for decades. Although prediction accuracy has been continuously improved with emerging deep learning models and ever-expanding traffic data, traffic forecasting still faces many challenges in practice. These challenges include the robustness of data-driven models, the inherent unpredictability of traffic dynamics, and whether further improvement of traffic forecasting requires more sensor data. In this paper, we focus on this latter question and particularly on data from loop detectors. To answer this, we propose an uncertainty-aware traffic forecasting framework to explore how many samples of loop data are truly effective for training forecasting models. Firstly, the model design combines traffic flow theory with graph neural networks, ensuring the robustness of prediction and uncertainty quantification. Secondly, evidential learning is employed to quantify different sources of uncertainty in a single pass. The estimated uncertainty is used to "distil" the essence of the dataset that sufficiently covers the information content. Results from a case study of a highway network around Amsterdam show that, from 2018 to 2021, more than 80\% of the data during daytime can be removed. The remaining 20\% samples have equal prediction power for training models. This result suggests that indeed large traffic datasets can be subdivided into significantly smaller but equally informative datasets. From these findings, we conclude that the proposed methodology proves valuable in evaluating large traffic datasets' true information content. Further extensions, such as extracting smaller, spatially non-redundant datasets, are possible with this method.Comment: 13 pages, 5 figure

On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

Large Car-following Data Based on Lyft level-5 Open Dataset: Following Autonomous Vehicles vs. Human-driven Vehicles

Car-Following (CF), as a fundamental driving behaviour, has significant influences on the safety and efficiency of traffic flow. Investigating how human drivers react differently when following autonomous vs. human-driven vehicles (HV) is thus critical for mixed traffic flow. Research in this field can be expedited with trajectory datasets collected by Autonomous Vehicles (AVs). However, trajectories collected by AVs are noisy and not readily applicable for studying CF behaviour. This paper extracts and enhances two categories of CF data, HV-following-AV (H-A) and HV-following-HV (H-H), from the open Lyft level-5 dataset. First, CF pairs are selected based on specific rules. Next, the quality of raw data is assessed by anomaly analysis. Then, the raw CF data is corrected and enhanced via motion planning, Kalman filtering, and wavelet denoising. As a result, 29k+ H-A and 42k+ H-H car-following segments are obtained, with a total driving distance of 150k+ km. A diversity assessment shows that the processed data cover complete CF regimes for calibrating CF models. This open and ready-to-use dataset provides the opportunity to investigate the CF behaviours of following AVs vs. HVs from real-world data. It can further facilitate studies on exploring the impact of AVs on mixed urban traffic.Comment: 6 pages, 9 figure

A unified approach to combinatorial key predistribution schemes for sensor networks

There have been numerous recent proposals for key predistribution schemes for wireless sensor networks based on various types of combinatorial structures such as designs and codes. Many of these schemes have very similar properties and are analysed in a similar manner. We seek to provide a unified framework to study these kinds of schemes. To do so, we define a new, general class of designs, termed “partially balanced t-designs”, that is sufficiently general that it encompasses almost all of the designs that have been proposed for combinatorial key predistribution schemes. However, this new class of designs still has sufficient structure that we are able to derive general formulas for the metrics of the resulting key predistribution schemes. These metrics can be evaluated for a particular scheme simply by substituting appropriate parameters of the underlying combinatorial structure into our general formulas. We also compare various classes of schemes based on different designs, and point out that some existing proposed schemes are in fact identical, even though their descriptions may seem different. We believe that our general framework should facilitate the analysis of proposals for combinatorial key predistribution schemes and their comparison with existing schemes, and also allow researchers to easily evaluate which scheme or schemes present the best combination of performance metrics for a given application scenario

Maximum principle and mutation thresholds for four-letter sequence evolution

A four-state mutation-selection model for the evolution of populations of DNA-sequences is investigated with particular interest in the phenomenon of error thresholds. The mutation model considered is the Kimura 3ST mutation scheme, fitness functions, which determine the selection process, come from the permutation-invariant class. Error thresholds can be found for various fitness functions, the phase diagrams are more interesting than for equivalent two-state models. Results for (small) finite sequence lengths are compared with those for infinite sequence length, obtained via a maximum principle that is equivalent to the principle of minimal free energy in physics.Comment: 25 pages, 16 figure

Signal and noise of Diamond Pixel Detectors at High Radiation Fluences

CVD diamond is an attractive material option for LHC vertex detectors because of its strong radiation-hardness causal to its large band gap and strong lattice. In particular, pixel detectors operating close to the interaction point profit from tiny leakage currents and small pixel capacitances of diamond resulting in low noise figures when compared to silicon. On the other hand, the charge signal from traversing high energy particles is smaller in diamond than in silicon by a factor of about 2.2. Therefore, a quantitative determination of the signal-to-noise ratio (S/N) of diamond in comparison with silicon at fluences in excess of 10$^{15}$ n$_{eq}$ cm$^{-2}$, which are expected for the LHC upgrade, is important. Based on measurements of irradiated diamond sensors and the FE-I4 pixel readout chip design, we determine the signal and the noise of diamond pixel detectors irradiated with high particle fluences. To characterize the effect of the radiation damage on the materials and the signal decrease, the change of the mean free path $\lambda_{e/h}$ of the charge carriers is determined as a function of irradiation fluence. We make use of the FE-I4 pixel chip developed for ATLAS upgrades to realistically estimate the expected noise figures: the expected leakage current at a given fluence is taken from calibrated calculations and the pixel capacitance is measured using a purposely developed chip (PixCap). We compare the resulting S/N figures with those for planar silicon pixel detectors using published charge loss measurements and the same extrapolation methods as for diamond. It is shown that the expected S/N of a diamond pixel detector with pixel pitches typical for LHC, exceeds that of planar silicon pixels at fluences beyond 10$^{15}$ particles cm$^{-2}$, the exact value only depending on the maximum operation voltage assumed for irradiated silicon pixel detectors

Information-theoretic interpretation of quantum error-correcting codes

Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while clarifying the differences between classical and quantum codes. More specifically, it is shown how quantum information theory accounts for the fact that "redundant" information can be distributed over quantum bits even though this does not violate the quantum "no-cloning" theorem. Such a remarkable feature, which has no counterpart for classical codes, is related to the property that the ternary mutual entropy vanishes for a tripartite system in a pure state. This information-theoretic description of quantum coding is used to derive the quantum analogue of the Singleton bound on the number of logical bits that can be preserved by a code of fixed length which can recover a given number of errors.Comment: 14 pages RevTeX, 8 Postscript figures. Added appendix. To appear in Phys. Rev.

The propagator for the step potential and delta function potential using the path decomposition expansion

We present a derivation of the propagator for a particle in the presence of the step and delta function potentials. These propagators are known, but we present a direct path integral derivation, based on the path decomposition expansion and the Brownian motion definition of the path integral. The derivation exploits properties of the Catalan numbers, which enumerate certain classes of lattice paths.Comment: 11 pages, 3 figure

Efficient implementation of selective recoupling in heteronuclear spin systems using Hadamard matrices

We present an efficient scheme which couples any designated pair of spins in heteronuclear spin systems. The scheme is based on the existence of Hadamard matrices. For a system of $n$ spins with pairwise coupling, the scheme concatenates $cn$ intervals of system evolution and uses at most $c n^2$ pulses where $c \approx 1$. Our results demonstrate that, in many systems, selective recoupling is possible with linear overhead, contrary to common speculation that exponential effort is always required.Comment: 7 pages, 4 figures, mypsfig2, revtex, submitted April 27, 199