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In this work, we study an inverse problem of recovering information about the weight distribution in a distributed-order time-fractional diffusion model from the observation at one single point on the domain boundary. In the absence of an explicit knowledge of the involved problem data, we prove that the one-point observation can uniquely determine the support of the weight distribution. The proof is based on asymptotic behavior of the measurement as well as analytic continuation and Titchmarch convolution theorem. In addition, when the problem data are fully known, we give an alternative proof of an existing result, which states that the over-posed one-point boundary observation can uniquely determine the weight. Several numerical experiments are presented to complement the theoretical analysis.

Regression modeling is the workhorse of statistics and there is a vast literature on estimation of the regression function. It is realized in recent years that in regression analysis the ultimate aim may be the estimation of a level set of the regression function, instead of the estimation of the regression function itself. The published work on estimation of the level set has thus far focused mainly on nonparametric regression, especially on point estimation. In this paper, the construction of confidence sets for the level set of linear regression is considered. In particular, $1-\alpha$ level upper, lower and two-sided confidence sets are constructed for the normal-error linear regression. It is shown that these confidence sets can be easily constructed from the corresponding $1-\alpha$ level simultaneous confidence bands. It is also pointed out that the construction method is readily applicable to other parametric regression models where the mean response depends on a linear predictor through a monotonic link function, which include generalized linear models, linear mixed models and generalized linear mixed models. Therefore the method proposed in this paper is widely applicable. Examples are given to illustrate the method.

Unit testing is one of the most established quality-assurance techniques for software development. One major advantage of unit testing is the adjustable trade-off between efficiency (i.e., testing effort) and effectiveness (i.e., fault-detection probability). To this end, various strategies have been proposed to exploit this trade-off. In particular, test-suite reduction (TSR) reduces the number of (presumably redundant) test cases while testing a single program version. Regression-test selection (RTS) selects test cases for testing consecutive program revisions. However, both TSR and RTS may influence -- or even obstruct -- each others' performance when used in combination. For instance, test cases discarded during TSR for a particular program version may become relevant again for RTS. However, finding a combination of both strategies leading to a reasonable trade-off throughout the version history of a program is an open question. The goal of this paper is to gain a better understanding of the interactions between TSR and RTS with respect to efficiency and effectiveness. To this end, we present a configurable framework called RegreTS for automated unit-testing of C programs. The framework comprises different strategies for TSR and RTS and possible combinations thereof. We apply this framework to a collection of subject systems, delivering several crucial insights. First, TSR has almost always a negative impact on the effectiveness of RTS, yet a positive impact on efficiency. Second, test cases revealing to testers the effect of program modifications between consecutive program versions are far more effective than test cases simply covering modified code parts, yet causing much more testing effort.

In this study we approach the complexity of the vaccine debate from a new and comprehensive perspective. Focusing on the Italian context, we examine almost all the online information produced in the 2016-2021 timeframe by both sources that have a reputation for misinformation and those that do not. Although reliable sources can rely on larger newsrooms and cover more news than misinformation ones, the transfer entropy analysis of the corresponding time series reveals that the former have not always informationally dominated the latter on the vaccine subject. Indeed, the pre-pandemic period sees misinformation establish itself as leader of the process, even in causal terms, and gain dramatically more user engagement than news from reliable sources. Despite this information gap was filled during the Covid-19 outbreak, the newfound leading role of reliable sources as drivers of the information ecosystem has only partially had a beneficial effect in reducing user engagement with misinformation on vaccines. Our results indeed show that, except for effectiveness of vaccination, reliable sources have never adequately countered the anti-vax narrative, specially in the pre-pandemic period, thus contributing to exacerbate science denial and belief in conspiracy theories. At the same time, however, they confirm the efficacy of assiduously proposing a convincing counter-narrative to misinformation spread. Indeed, effectiveness of vaccination turns out to be the least engaging topic discussed by misinformation during the pandemic period, when compared to other polarising arguments such as safety concerns, legal issues and vaccine business. By highlighting the strengths and weaknesses of institutional and mainstream communication, our findings can be a valuable asset for improving and better targeting campaigns against misinformation on vaccines.

The {\em insertion-deletion channel} takes as input a binary string $x \in\{0, 1\}^n$, and outputs a string $\widetilde{x}$ where some of the bits have been deleted and others inserted independently at random. In the {\em trace reconstruction problem}, one is given many outputs (called {\em traces}) of the insertion-deletion channel on the same input message $x$, and asked to recover the input message. Nazarov and Peres (STOC 2017), and De, Odonnell and Servido (STOC 2017) showed that any string $x$ can be reconstructed from $\exp(O(n^{1/3}))$ traces. Holden, Pemantle, Peres and Zhai (COLT 2018) adapt the techniques used to prove this upper bound, to an algorithm for the average-case trace reconstruction with a sample complexity of $\exp(O(\log^{1/3} n))$. However, it is not clear how to apply their techniques more generally and in particular for the recent worst-case upper bound of $\exp(\widetilde{O}(n^{1/5}))$ shown by Chase (STOC 2021) for the deletion-channel. We prove a general reduction from the average-case to smaller instances of a problem similar to worst-case. Using this reduction and a generalization of Chase's bound, we construct an improved average-case algorithm with a sample complexity of $\exp(\widetilde{O}(\log^{1/5} n))$. Additionally, we show that Chase's upper-bound holds for the insertion-deletion channel as well.

Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea of variational inference is to trade statistical accuracy for computational efficiency. It aims to approximate the posterior, reducing computation costs but potentially compromising its statistical accuracy. In this work, we study this statistical and computational trade-off in variational inference via a case study in inferential model selection. Focusing on Gaussian inferential models (a.k.a. variational approximating families) with diagonal plus low-rank precision matrices, we initiate a theoretical study of the trade-offs in two aspects, Bayesian posterior inference error and frequentist uncertainty quantification error. From the Bayesian posterior inference perspective, we characterize the error of the variational posterior relative to the exact posterior. We prove that, given a fixed computation budget, a lower-rank inferential model produces variational posteriors with a higher statistical approximation error, but a lower computational error; it reduces variances in stochastic optimization and, in turn, accelerates convergence. From the frequentist uncertainty quantification perspective, we consider the precision matrix of the variational posterior as an uncertainty estimate. We find that, relative to the true asymptotic precision, the variational approximation suffers from an additional statistical error originating from the sampling uncertainty of the data. Moreover, this statistical error becomes the dominant factor as the computation budget increases. As a consequence, for small datasets, the inferential model need not be full-rank to achieve optimal estimation error. We finally demonstrate these statistical and computational trade-offs inference across empirical studies, corroborating the theoretical findings.

Object detection problem solving has developed greatly within the past few years. There is a need for lighter models in instances where hardware limitations exist, as well as a demand for models to be tailored to mobile devices. In this article, we will assess the methods used when creating algorithms that address these issues. The main goal of this article is to increase accuracy in state-of-the-art algorithms while maintaining speed and real-time efficiency. The most significant issues in one-stage object detection pertains to small objects and inaccurate localization. As a solution, we created a new network by the name of MobileDenseNet suitable for embedded systems. We also developed a light neck FCPNLite for mobile devices that will aid with the detection of small objects. Our research revealed that very few papers cited necks in embedded systems. What differentiates our network from others is our use of concatenation features. A small yet significant change to the head of the network amplified accuracy without increasing speed or limiting parameters. In short, our focus on the challenging CoCo and Pascal VOC datasets were 24.8 and 76.8 in percentage terms respectively - a rate higher than that recorded by other state-of-the-art systems thus far. Our network is able to increase accuracy while maintaining real-time efficiency on mobile devices. We calculated operational speed on Pixel 3 (Snapdragon 845) to 22.8 fps. The source code of this research is available on //github.com/hajizadeh/MobileDenseNet.

The hypergraph Moore bound is an elegant statement that characterizes the extremal trade-off between the girth - the number of hyperedges in the smallest cycle or even cover (a subhypergraph with all degrees even) and size - the number of hyperedges in a hypergraph. For graphs (i.e., $2$-uniform hypergraphs), a bound tight up to the leading constant was proven in a classical work of Alon, Hoory and Linial [AHL02]. For hypergraphs of uniformity $k>2$, an appropriate generalization was conjectured by Feige [Fei08]. The conjecture was settled up to an additional $\log^{4k+1} n$ factor in the size in a recent work of Guruswami, Kothari and Manohar [GKM21]. Their argument relies on a connection between the existence of short even covers and the spectrum of a certain randomly signed Kikuchi matrix. Their analysis, especially for the case of odd $k$, is significantly complicated. In this work, we present a substantially simpler and shorter proof of the hypergraph Moore bound. Our key idea is the use of a new reweighted Kikuchi matrix and an edge deletion step that allows us to drop several involved steps in [GKM21]'s analysis such as combinatorial bucketing of rows of the Kikuchi matrix and the use of the Schudy-Sviridenko polynomial concentration. Our simpler proof also obtains tighter parameters: in particular, the argument gives a new proof of the classical Moore bound of [AHL02] with no loss (the proof in [GKM21] loses a $\log^3 n$ factor), and loses only a single logarithmic factor for all $k>2$-uniform hypergraphs. As in [GKM21], our ideas naturally extend to yield a simpler proof of the full trade-off for strongly refuting smoothed instances of constraint satisfaction problems with similarly improved parameters.

High-end vehicles have been furnished with a number of electronic control units (ECUs), which provide upgrading functions to enhance the driving experience. The controller area network (CAN) is a well-known protocol that connects these ECUs because of its modesty and efficiency. However, the CAN bus is vulnerable to various types of attacks. Although the intrusion detection system (IDS) is proposed to address the security problem of the CAN bus, most previous studies only provide alerts when attacks occur without knowing the specific type of attack. Moreover, an IDS is designed for a specific car model due to diverse car manufacturers. In this study, we proposed a novel deep learning model called supervised contrastive (SupCon) ResNet, which can handle multiple attack identification on the CAN bus. Furthermore, the model can be used to improve the performance of a limited-size dataset using a transfer learning technique. The capability of the proposed model is evaluated on two real car datasets. When tested with the car hacking dataset, the experiment results show that the SupCon ResNet model improves the overall false-negative rates of four types of attack by four times on average, compared to other models. In addition, the model achieves the highest F1 score at 0.9994 on the survival dataset by utilizing transfer learning. Finally, the model can adapt to hardware constraints in terms of memory size and running time.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.