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In the context of subscription-based services, many technologies improve over time and service providers can provide increasingly powerful service upgrades to their customers, but at a launching cost, and the expense of the sales of existing products. We propose a model of technology upgrades and characterize the optimal pricing and timing of technology introductions for a service provider who price-discriminates among customers based on their upgrade experience, in the face of customers who are averse to switching to improved offerings. We first characterize optimal discriminatory pricing for the infinite horizon pricing problem with fixed introduction times. We reduce the optimal pricing problem to a tractable optimization problem and propose an efficient algorithm for solving it. Our algorithm computes optimal discriminatory prices within a fraction of a second, even for large problem instances. We then show that periodic introduction times, combined with optimal pricing, enjoy optimality guarantees. In particular, we first show that as long as the introduction intervals are constrained to be non-increasing, it is optimal to have periodic introductions after an initial warm-up phase. When allowing general introduction intervals, we show that periodic introduction intervals after some time are optimal in a more restricted sense. Numerical experiments suggest that it is generally optimal to have periodic introductions after an initial warm-up phase. Finally, we focus on a setting in which the firm does not price-discriminate based on customers' experience. We show both analytically and numerically that in the non-discriminatory setting, a simple policy of Myerson (i.e., myopic) pricing and periodic introductions enjoys good performance guarantees.

We consider a generalization of the recently proposed gradient coding framework where a large dataset is divided across $n$ workers and each worker transmits to a master node one or more linear combinations of the gradients over the data subsets assigned to it. Unlike the conventional framework which requires the master node to recover the sum of the gradients over all the data subsets in the presence of $s$ straggler workers, we relax the goal of the master node to computing the sum of at least some α fraction of the gradients. The broad goal of our work is to study the optimal computation and communication load per worker for this approximate gradient coding framework. We begin by deriving a lower bound on the computation load of any feasible scheme and also propose a strategy which achieves this lower bound, albeit at the cost of high communication load and a number of data partitions which can be polynomial in the number of workers n. We then restrict attention to schemes which utilize a number of data partitions equal to $n$ and propose schemes based on cyclic assignment which have a lower communication load. When each worker transmits a single linear combination, we also prove lower bounds on the computation load of any scheme using $n$ data partitions. A full version of this paper is accessible at: https://arxiv.org/abs/2102.10163

This paper studies the optimality of matched-pair designs in randomized controlled trials (RCTs). Matched-pair designs are examples of stratified randomization, in which the researcher partitions a set of units into strata based on their observed covariates and assign a fraction of units in each stratum to treatment. A matched-pair design is such a procedure with two units per stratum. Despite the prevalence of stratified randomization in RCTs, implementations differ vastly. We provide an econometric framework in which, among all stratified randomization procedures, the optimal one in terms of the mean-squared error of the difference-in-means estimator is a matched-pair design that orders units according to a scalar function of their covariates and matches adjacent units. Our framework captures a leading motivation for stratifying in the sense that it shows that the proposed matched-pair design additionally minimizes the magnitude of the ex-post bias, i.e., the bias of the estimator conditional on realized treatment status. We then consider empirical counterparts to the optimal stratification using data from pilot experiments and provide two different procedures depending on whether the sample size of the pilot is large or small. For each procedure, we develop methods for testing the null hypothesis that the average treatment effect equals a prespecified value. Each test we provide is asymptotically exact in the sense that the limiting rejection probability under the null equals the nominal level. We run an experiment on the Amazon Mechanical Turk using one of the proposed procedures, replicating one of the treatment arms in Dellavigna and Pope (2018), and find the standard error decreases by 29%, so that only half of the sample size is required to attain the same standard error.

Crowdsourcing services provide a fast, efficient, and cost-effective way to obtain large labeled data for supervised learning. Unfortunately, the quality of crowdsourced labels cannot satisfy the standards of practical applications. Ground-truth inference, simply called label integration, designs proper aggregation methods to infer the unknown true label of each instance (sample) from the multiple noisy label set provided by ordinary crowd labelers (workers). However, nearly all existing label integration methods focus solely on the multiple noisy label set per individual instance while totally ignoring the intercorrelation among multiple noisy label sets of different instances. To solve this problem, a multiple noisy label distribution propagation (MNLDP) method is proposed in this article. MNLDP at first estimates the multiple noisy label distribution of each instance from its multiple noisy label set and then propagates its multiple noisy label distribution to its nearest neighbors. Consequently, each instance absorbs a fraction of the multiple noisy label distributions from its nearest neighbors and yet simultaneously maintains a fraction of its own original multiple noisy label distribution. Empirical studies on a collection of an artificial dataset, six simulated UCI datasets, and three real-world crowdsourced datasets show that MNLDP outperforms all other existing state-of-the-art label integration methods in terms of the integration accuracy and classification accuracy.

We consider some types of complex continued fraction expansions and their associated maps of the Euclidean fields Q ( − d ) , d = 1 , 2 , 3 , 7 and 11 introduced by Hurwitz (1887) [7] , Lakein (1973) [10] and Shiokawa et al. (1975) [20] . We show that there exists the Legendre constant for every type of continued fraction expansions introduced by them improving the proof by Ei et al. (2019) [4] in the case of the one by A. Hurwitz with Q ( − 1 ) .

We consider a population composed of a continuum of agents that seek to maximize a payoff function by moving on a network. The nodes in the network may represent physical locations or abstract choices. The population is stratified, i.e., agents opting for the same choice may not get the same payoff. In particular, we assume payoff functions with diminishing returns, i.e., agents in newer strata of a node receive a smaller payoff compared to older strata. In this first part of two-part work, we model the population dynamics under three choice revision policies, having varying levels of coordination i. no coordination and the agents are selfish, ii. coordination among agents in each node and iii. coordination across the entire population. For the case with selfish agents, we generalize the Smith dynamics to our setting, where we have a stratified population and network constraints. To model nodal coordination, we allow the fraction of population in a node, as a whole, to take the best response to the state of the population in the nodes neighborhood. For the case of population-wide coordination, we explore a dynamics where the population evolves according to centralized gra

In this paper we revisit the basic variant of the classical secretary problem. We propose a new approach in which we separate between an agent that evaluates the secretary performance and one that has to make the hiring decision. The evaluating agent (the sender) signals the quality of the candidate to the hiring agent (the receiver) who must make a decision. Whenever the two agents' interests are not fully aligned, this induces an information transmission (signaling) challenge for the sender. We study the sender's optimization problem subject to persuasiveness constraints of the receiver for several variants of the problem. Our results quantify the loss in performance for the sender due to online arrival. We provide optimal and near-optimal persuasive mechanisms that recover at least a constant fraction of a natural utility benchmark for the sender. The separation of evaluation and decision making can have a substantial impact on the approximation results. While in some scenarios, techniques and results closely mirror the conditions in the standard secretary problem, we also explore conditions that lead to very different characteristics., 35 pages, 2 figures

In intermodal transportation, it is essential to balance the trade-off between the cost and duration of a route. The duration of a path is inherently stochastic because of delays and the possibility of overbooking. We study a problem faced by a company that supports shippers with advice for the route selection. The challenge is to find Pareto-optimal solutions regarding the route's costs and the probability of arriving before a specific deadline. We show how this probability can be calculated in a network with scheduled departure times and the possibility of overbookings. To solve this problem, we give an optimal algorithm, but as its running time becomes too long for larger networks, we also develop a heuristic. The idea of this heuristic is to replace the stochastic variables by deterministic risk measures and solve the resulting deterministic optimization problem. The heuristic produces, in a fraction of the optimal algorithm's running time, solutions of which the costs are only a few percent higher than the optimal costs.

Designing feasible control strategies for opinion dynamics in complex social systems has never been an easy task. It requires a control protocol which 1) is not enforced on all individuals in the society, and 2) does not exclusively rely on specific opinion values shared by the social system. Thanks to the recent studies on noise-induced consensus in opinion dynamics, the noise-based intervention strategy has emerged as the only one meeting both of the above requirements, yet its underlying general theory is still lacking. In this paper, we perform rigorous theoretical analysis and simulations of a noise-based control strategy for opinion formation in which only a fraction of individuals is affected by randomly generated noise. We found that irrespective of the number of noise-driven individuals, including the case of only one single noise-affected individual, the system can attain a quasi-consensus in finite time, and the critical noise strength can be obtained. Our results highlight the efficiency of noise-driven mechanisms for the control of complex social dynamics., arXiv admin note: text overlap with arXiv:1711.01432

This paper investigates the prescribed finite-time control for the nonlinear system with uncertain nonlinearity and unknown control directions. Different from the existing finite/fixed-time control methods on the basis of the fraction order state feedback, the proposed prescribed finite-time control in this paper only employs regular state feedback. The key is that a novel prescribed finite-time performance function is introduced such that the controllers design is under standard Lyapunov stability theoretical framework. A lemma is developed as a tool for coping with the coexistence of multiple Nussbaum gains for the stochastic system with unknown control directions. Fuzzy logic systems are applied to approximate uncertain nonlinear functions. Applying the backstepping structure, an adaptive fuzzy control scheme is developed. The salient characteristic of the proposed control is that the finite convergence time and the accuracy of the tracking error are independent of the initial states and design parameters, and that can be assigned in a prior. A numerical example is given to demonstrate the feasibility and effectiveness of the proposed control scheme.

We consider the *adaptive influence maximization problem*: given a network and a budget $k$, iteratively select $k$ seeds in the network to maximize the expected number of adopters. In the *full-adoption feedback model*, after selecting each seed, the seed-picker observes all the resulting adoptions. In the *myopic feedback model*, the seed-picker only observes whether each neighbor of the chosen seed adopts. Motivated by the extreme success of greedy-based algorithms/heuristics for influence maximization, we propose the concept of *greedy adaptivity gap*, which compares the performance of the adaptive greedy algorithm to its non-adaptive counterpart. Our first result shows that, for submodular influence maximization, the adaptive greedy algorithm can perform up to a $(1-1/e)$-fraction worse than the non-adaptive greedy algorithm, and that this ratio is tight. More specifically, on one side we provide examples where the performance of the adaptive greedy algorithm is only a $(1-1/e)$ fraction of the performance of the non-adaptive greedy algorithm in four settings: for both feedback models and both the *independent cascade model* and the *linear threshold model*. On the other side, we prove that in any submodular cascade, the adaptive greedy algorithm always outputs a $(1-1/e)$-approximation to the expected number of adoptions in the optimal non-adaptive seed choice. Our second result shows that, for the general submodular diffusion model with full-adoption feedback, the adaptive greedy algorithm can outperform the non-adaptive greedy algorithm by an unbounded factor. Finally, we propose a risk-free variant of the adaptive greedy algorithm that always performs no worse than the non-adaptive greedy algorithm., Comment: 26 pages, 0 figure, accepted at JAIR'22: Journal of Artificial Intelligence Research 74 (2022) 303-351; A short version of this paper was accepted at AAAI'20: Thirty-Fourth AAAI Conference on Artificial Intelligence

Satellite-based remotely sensed observations of snow cover fraction (SCF) can have data gaps in spatially distributed coverage from sensor and orbital limitations. We mitigate these limitations in the example fine-resolution Moderate Resolution Imaging Spectroradiometer (MODIS) data by gap-filling using auxiliary 1-km datasets that either aid in downscaling from coarser-resolution (5 km) MODIS SCF wherever not fully covered by clouds, or else by themselves via regression wherever fully cloud covered. This study’s prototype predicts a 1-km version of the 500-m MOD10A1 SCF target. Due to noncollocatedness of spatial gaps even across input and auxiliary datasets, we consider a recent gap-agnostic advancement of partial convolution in computer vision for both training and predictive gap-filling. Partial convolution accommodates spatially consistent gaps across the input images, effectively implementing a two-dimensional masking. To overcome reduced usable data from noncollocated spatial gaps across inputs, we innovate a fully generalized three-dimensional masking in this partial convolution. This enables a valid output value at a pixel even if only a single valid input variable and its value exist in the neighborhood covered by the convolutional filter zone centered around that pixel. Thus, our gap-agnostic technique can use significantly more examples for training (∼67%) and prediction (∼100%), instead of only less than 10% for the previous partial convolution. We train an example simple three-layer legacy super-resolution convolutional neural network (SRCNN) to obtain downscaling and regression component performances that are better than baseline values of either climatology or MOD10C1 SCF as relevant. Our generalized partial convolution can enable multiple Earth science applications like downscaling, regression, classification, and segmentation that were hindered by data gaps.

Fuzzing is a technique of finding bugs by executing a target program recurrently with a large number of abnormal inputs. Most of the coverage-based fuzzers consider all parts of a program equally and pay too much attention to how to improve the code coverage. It is inefficient as the vulnerable code only takes a tiny fraction of the entire code. In this article, we design and implement an evolutionary fuzzing framework called V-Fuzz, which aims to find bugs efficiently and quickly in limited time for binary programs. V-Fuzz consists of two main components: 1) a vulnerability prediction model and 2) a vulnerability-oriented evolutionary fuzzer. Given a binary program to V-Fuzz, the vulnerability prediction model will give a prior estimation on which parts of a program are more likely to be vulnerable. Then, the fuzzer leverages an evolutionary algorithm to generate inputs which are more likely to arrive at the vulnerable locations, guided by the vulnerability prediction result. The experimental results demonstrate that V-Fuzz can find bugs efficiently with the assistance of vulnerability prediction. Moreover, V-Fuzz has discovered ten common vulnerabilities and exposures (CVEs), and three of them are newly discovered.

Spatial databases store objects with their locations and certain types of attached items. A variety of modern applications have been developed by leveraging the utilization of locations and items in spatial objects, such as searching points of interest, hot topics, or users' attitude in specified spatial regions. In many scenarios, the high and low-frequency items in a spatial region are worth noticing, considering they represent the majority's interest or eccentric users' opinion. However, existing works have yet to identify such items in an interactive manner, despite the significance of the endeavor in decision-making systems. This study recognizes a novel type of analytical query, called top/bottom-k fraction query, to discover such items in spatial databases. To achieve fast query response, we propose a multilayered data summary that is spread out across the main memory and external memory. A memory-based estimation method for top/bottom-k fraction queries is proposed. To maximize the use of the main memory space, we design a data summary tuning method to dynamically allocate memory space among different spatial partitions. The proposed approach is evaluated with real-life datasets and synthetic datasets in terms of estimation accuracy. Evaluation results demonstrate the effectiveness of the proposed data summary and corresponding estimation and tuning algorithms.

This paper studies the infinite-horizon optimal consumption with a path-dependent reference under exponential utility. The performance is measured by the difference between the nonnegative consumption rate and a fraction of the historical consumption maximum. The consumption running maximum process is chosen as an auxiliary state process, and hence the value function depends on two state variables. The Hamilton-Jacobi-Bellman (HJB) equation can be heuristically expressed in a piecewise manner across different regions to take into account all constraints. By employing the dual transform and smooth-fit principle, some thresholds of the wealth variable are derived such that a classical solution to the HJB equation and the feedback optimal investment and consumption strategies can be obtained in closed form in each region. A complete proof of the verification theorem is provided, and numerical examples are presented to illustrate some financial implications., Comment: Final version, forthcoming in Finance and Stochastics

We present a gentle approach to the justification of effective media approximations, for PDE's set outside the union of $n \gg 1$ spheres with low volume fraction. To illustrate our approach, we consider three classical examples: the derivation of the so-called strange term, made popular by Cioranescu and Murat, the derivation of the Brinkman term in the Stokes equation, and a scalar analogue of the effective viscosity problem. Under some separation assumption on the spheres, valid for periodic and random distributions of the centers, we recover effective models as $n$ goes to infinity by simple arguments., 20 pages. Final version, to appear in Asympt. Anal

This study aims to develop a valid and reliable measuring instrument that can measure the level of mathematical language used by students and their teachers during the teaching of fractions to fourth-grade primary school students. This study is a methodological validity and reliability study. In total, 999 students from fourteen different secondary schools were separated into two other sampling groups, where they participated in the sample of the survey for Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA). These stages are identified as the item pool stage, the testing validity of scope stage (expert opinion stage), the factor analysis stage (construct validity), and the reliability stage. Mathematical language scale in the teaching of fractions consists of the student approach, the use of fraction language and the use of symbols, and the written expressions of sub-dimensions. The exploratory factor analysis method (EFA) shows that the instrument can be built on three factors. It is also confirmed by the confirmatory factor analysis (CFA). It can be accepted according to NFI indexes. As a result, the mathematical language scale is found to be valid and reliable in fraction teaching. To this end, it can be stated that the MLSFT scale can be used in fraction teaching for elementary school students to reveal their abilities and the skills of teachers in terms of mathematical language used.

Free-to-play has become one of the most popular monetization models, and as a consequence game developers need to get the players to purchase in the game instead of getting players to buy the game. Game analytics and player monetization prediction are important parts in estimating the profitability of a free-to-play game. In this paper, we concentrate on predicting the fraction of monetizing players among all players. Our method is based on a survival analysis mixture cure model, and can be applied to unlabeled data collected from any free-to-play game. We formulate a statistical model and use the Expectation Maximization algorithm to solve the latent monetization percentage and the monetization rate. The original method is modified by using Bayesian inference, and the results of the versions are compared. The method can be applied as a preliminary profitability study in situations where there is no extensive historical game data available, such as game and business development scenarios that need to utilize real time analytics.

Using the market for initial coin offerings (ICOs) as a laboratory, we provide evidence that entrepreneurs use retention to alleviate information asymmetry. The underlying technology and the absence of regulation make the ICO market well suited to study this question empirically. Using a hand-collected data set, we show that ICO issuers that retain a larger fraction of their tokens are more successful in their funding efforts and are more likely to develop a working product. Moreover, we find that retention is a stronger signal when markets are crowded, and investors do not have as much time to conduct due diligence. This paper was accepted by Will Cong, Special Issue of Management Science: Blockchains and crypto economics. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.4631 .

Caching systems have long been crucial for improving the performance of a wide variety of network and web based online applications. In such systems, end-to-end application performance heavily depends on the fraction of objects transferred from the cache, also known as the cache hit probability. Many caching policies have been proposed and implemented to improve the hit probability. In this work, we propose a new method to compute an upper bound on hit probability for all non-anticipative caching policies, i.e., for policies that have no knowledge of future requests. Our key insight is to order the objects according to the ratio of their Hazard Rate (HR) function values to their sizes and place in the cache the objects with the largest ratios till the cache capacity is exhausted. Under some statistical assumptions, we prove that our proposed HR to size ratio based ordering model computes the maximum achievable hit probability and serves as an upper bound for all non-anticipative caching policies. We derive closed form expressions for the upper bound under some specific object request arrival processes. We also provide simulation results to validate its correctness and to compare it to the state-of-the-art upper bounds. We find it to be tighter than state-of-the-art upper bounds for a variety of object request arrival processes., IFIP WG 7.3 Performance

The large-scale protein-protein interaction (PPI) data has the potential to play a significant role in the endeavor of understanding cellular processes. However, the presence of a considerable fraction of false positives is a bottleneck in realizing this potential. There have been continuous efforts to utilize complementary resources for scoring confidence of PPIs in a manner that false positive interactions get a low confidence score. Gene Ontology (GO), a taxonomy of biological terms to represent the properties of gene products and their relations, has been widely used for this purpose. We utilize GO to introduce a new set of specificity measures: Relative Depth Specificity (RDS), Relative Node-based Specificity (RNS), and Relative Edge-based Specificity (RES), leading to a new family of similarity measures. We use these similarity measures to obtain a confidence score for each PPI. We evaluate the new measures using four different benchmarks. We show that all the three measures are quite effective. Notably, RNS and RES more effectively distinguish true PPIs from false positives than the existing alternatives. RES also shows a robust set-discriminating power and can be useful for protein functional clustering as well.

Online monitoring user cardinalities in graph streams is fundamental for many applications such as anomaly detection. These graph streams may contain edge duplicates and have a large number of user-item pairs, which makes it infeasible to exactly compute user cardinalities due to limited computational and memory resources. Existing methods are designed to approximately estimate user cardinalities, but their accuracy highly depends on complex parameters and they cannot provide anytime-available estimation. To address these problems, we develop novel bit/register sharing algorithms, which use a bit/register array to build a compact sketch of all users' connected items. Our algorithms exploit the dynamic properties of the bit/register arrays (e.g., the fraction of zero bits in the bit array) to significantly improve the estimation accuracy, and have low time complexity O(1) to update the estimations for a new user-item pair. In addition, our algorithms are simple and easy to use, without requirements to tune any parameter. Furthermore, we extend our methods to detect super spreaders with large cardinalities in real-time. We evaluate the performance of our methods on real-world datasets. The experimental results demonstrate that our methods are several times more accurate and faster than state-of-the-art methods using the same amount of memory.

This paper examines the average age minimization problem where only a fraction of the network users can transmit simultaneously over unreliable channels. Finding the optimal scheduling scheme, in this case, is known to be challenging. Accordingly, the Whittle’s index policy was proposed in the literature as a low-complexity heuristic to the problem. Although simple to implement, characterizing this policy’s performance is recognized to be a notoriously tricky task. In the sequel, we provide a new mathematical approach to establish its optimality in the many-users regime for specific network settings. Contrary to previous works in the literature that use restrictive mathematical assumptions, which can be challenging to verify, our novel approach is based on intricate techniques and it is free of any strong mathematical assumptions. These findings showcase that the Whittle’s index policy has analytically provable asymptotic optimality for the AoI minimization problem. Finally, we lay out numerical results that corroborate our theoretical findings and demonstrate the policy’s notable performance in the many-users regime.

Highlights • The MR-Linac provides the tools to deliver online MR-guided Adaptive Radiotherapy • Adapt-to-Shape-Lite is a novel radiotherapy planning workflow on the Elekta Unity MR-Linac • Adapt-to-Shape-Lite generated plans that fulfilled 99.9% of mandatory dose constraints • Adapt-to-Shape-Lite workflow can generate plans in relatively short durations • Therefore, we prefer Adapt-To-Shape-Lite as the primary workflow to treat Head-and-Neck cancers, Introduction The Elekta Unity MR-Linac (MRL) has enabled adaptive radiotherapy (ART) for patients with head and neck cancers (HNC). Adapt-To-Shape-Lite (ATS-Lite) is a novel Adapt-to-Shape strategy that provides ART without requiring daily clinician presence to perform online target and organ at risk (OAR) delineation. In this study we compared the performance of our clinically-delivered ATS-Lite strategy against three Adapt-To-Position (ATP) variants: Adapt Segments (ATP-AS), Optimise Weights (ATP-OW), and Optimise Shapes (ATP-OS). Methods Two patients with HNC received radical-dose radiotherapy on the MRL. For each fraction, an ATS-Lite plan was generated online and delivered and additional plans were generated offline for each ATP variant. To assess the clinical acceptability of a plan for every fraction, twenty clinical goals for targets and OARs were assessed for all four plans. Results 53 fractions were analysed. ATS-Lite passed 99.9% of mandatory dose constraints. ATP-AS and ATP-OW each failed 7.6% of mandatory dose constraints. The Planning Target Volumes for 54 Gy (D95% and D98%) were the most frequently failing dose constraint targets for ATP. ATS-Lite median fraction times for Patient 1 and 2 were 40 mins 9 s (range 28 mins 16 s – 47 mins 20 s) and 32 mins 14 s (range 25 mins 33 s – 44 mins 27 s), respectively. Conclusions Our early data show that the novel ATS-Lite strategy produced plans that fulfilled 99.9% of clinical dose constraints in a time frame that is tolerable for patients and comparable to ATP workflows. Therefore, ATS-Lite, which bridges the gap between ATP and full ATS, will be further utilised and developed within our institute and it is a workflow that should be considered for treating patients with HNC on the MRL.

Neural networks have dominated the research of hyperspectral image classification, attributing to the feature learning capacity of convolution operations. However, the fixed geometric structure of convolution kernels hinders long-range interaction between features from distant locations. In this article, we propose a novel spectral-spatial transformer network (SSTN), which consists of spatial attention and spectral association modules, to overcome the constraints of convolution kernels. Also, we design a factorized architecture search (FAS) framework that involves two independent subprocedures to determine the layer-level operation choices and block-level orders of SSTN. Unlike conventional neural architecture search (NAS) that requires a bilevel optimization of both network parameters and architecture settings, the FAS focuses only on finding out optimal architecture settings to enable a stable and fast architecture search. Extensive experiments conducted on five popular HSI benchmarks demonstrate the versatility of SSTNs over other state-of-the-art (SOTA) methods and justify the FAS strategy. On the University of Houston dataset, SSTN obtains comparable overall accuracy to SOTA methods with a small fraction (1.2%) of multiply-and-accumulate operations compared to a strong baseline spectral-spatial residual network (SSRN). Most importantly, SSTNs outperform other SOTA networks using only 1.2% or fewer MACs of SSRNs on the Indian Pines, the Kennedy Space Center, the University of Pavia, and the Pavia Center datasets.

A graph where each vertex $v$ has a list $L(v)$ of available colors is $L$-colorable if there is a proper coloring such that the color of $v$ is in $L(v)$ for each $v$. A graph is $k$-choosable if every assignment $L$ of at least $k$ colors to each vertex guarantees an $L$-coloring. Given a list assignment $L$, an $L$-request for a vertex $v$ is a color $c\in L(v)$. In this paper, we look at a variant of the widely studied class of precoloring extension problems from [Z. Dvo\v{r}\'ak, S. Norin, and L. Postle: List coloring with requests. J. Graph Theory 2019], wherein one must satisfy "enough", as opposed to all, of the requested set of precolors. A graph $G$ is $\varepsilon$-flexible for list size $k$ if for any $k$-list assignment $L$, and any set $S$ of $L$-requests, there is an $L$-coloring of $G$ satisfying an $\varepsilon$-fraction of the requests in $S$. It is conjectured that planar graphs are $\varepsilon$-flexible for list size $5$, yet it is proved only for list size $6$ and for certain subclasses of planar graphs. We give a stronger version of the main tool used in the proofs of the aforementioned results. By doing so, we improve upon a result by Masa\v{r}\'ik and show that planar graphs without $K_4^-$ are $\varepsilon$-flexible for list size $5$. We also prove that planar graphs without $4$-cycles and $3$-cycle distance at least 2 are $\varepsilon$-flexible for list size $4$. Finally, we introduce a new (slightly weaker) form of $\varepsilon$-flexibility where each vertex has exactly one request. In that setting, we provide a stronger tool and we demonstrate its usefulness to further extend the class of graphs that are $\varepsilon$-flexible for list size $5$., Comment: 18 pages, 4 figures

Superresolution mapping (SRM) is a commonly used method to cope with the problem of mixed pixels when predicting the spatial distribution within low-resolution pixels. Central to the popular SRM method is the spatial pattern model, which is utilized to represent the land cover spatial distribution within mixed pixels. The use of an inappropriate spatial pattern model limits such SRM analyses. Alternative approaches, such as deep-learning-based algorithms, which learn the spatial pattern from training data through a convolutional neural network, have been shown to have considerable potential. Deep learning methods, however, are limited by issues such as the way the fraction images are utilized. Here, a novel SRM model based on a generative adversarial network (GAN), GAN-SRM, is proposed that uses an end-to-end network to address the main limitations of existing SRM methods. The potential of the proposed GAN-SRM model was assessed using four land cover subsets and compared to hard classification and several popular SRM methods. The experimental results show that of the set of methods explored, the GAN-SRM model was able to generate the most accurate high-resolution land cover maps.

Although supercomputers are becoming increasingly powerful, their components have thus far not scaled proportionately. Compute power is growing enormously and is enabling finely resolved simulations that produce never-before-seen features. However, I/O capabilities lag by orders of magnitude, which means only a fraction of the simulation data can be stored for post hoc analysis. Prespecified plans for saving features and quantities of interest do not work for features that have not been seen before. Data-driven intelligent sampling schemes are needed to detect and save important parts of the simulation while it is running. Here, we propose a novel sampling scheme that reduces the size of the data by orders-of-magnitude while still preserving important regions. The approach we develop selects points with unusual data values and high gradients. We demonstrate that our approach outperforms traditional sampling schemes on a number of tasks.

For x irrational, we study the convergence of series of the form ∑ n − s f ( n x ) where f is a real-valued, 1-periodic function which is continuous, except for singularities at the integers with a potential growth. We show that it is possible to fully characterize the convergence set and to approximate the series in terms of the continued fraction of x. This improves and generalizes recent results by Rivoal who studied the examples f ( t ) = cot ⁡ ( π t ) and f ( t ) = sin − 2 ⁡ ( π t ) .

This paper considers “ $\delta $ -almost Reed–Muller codes”, i.e., linear codes spanned by evaluations of all but a $\delta $ fraction of monomials of degree at most $d$ . It is shown that for any $\delta > 0$ and any $\varepsilon >0$ , there exists a family of $\delta $ -almost Reed–Muller codes of constant rate that correct $1/2- \varepsilon $ fraction of random errors with high probability. For exact Reed–Muller codes, the analogous result is not known and represents a weaker version of the longstanding conjecture that Reed–Muller codes achieve capacity for random errors (Abbe-Shpilka-Wigderson STOC ’15). Our proof is based on the recent polarization result for Reed–Muller codes, combined with a combinatorial approach to establishing inequalities between the Reed–Muller code entropies.

Causal classification concerns the estimation of the net effect of a treatment on an outcome of interest at the instance level, i.e., of the individual treatment effect (ITE). For binary treatment and outcome variables, causal classification models produce ITE estimates that essentially allow one to rank instances from a large positive effect to a large negative effect. Often, as in uplift modeling (UM), one is merely interested in this ranking, rather than in the ITE estimates themselves. In this regard, we investigate the potential of learning to rank (L2R) techniques to learn a ranking of the instances directly. We propose a unified formalization of different binary causal classification performance measures from the UM literature and explore how these can be integrated into the L2R framework. Additionally, we introduce a new metric for UM with L2R called the promoted cumulative gain (PCG). We employ the L2R technique LambdaMART to optimize the ranking according to PCG and show improved results over the use of standard L2R metrics and equal to improved results when compared with state-of-the-art UM. Finally, we show how L2R techniques can be used to specifically optimize for the top-k fraction of the ranking in a UM context, however, these results do not generalize to the test set. ispartof: IEEE Transactions on Knowledge and Data Engineering vol:34 issue:10 pages:4888-4904 status: published

The partial potential impact fraction describes the proportion of disease cases that can be prevented if the distribution of modifiable continuous exposures is shifted in a population, while other risk factors are not modified. It is a useful quantity for evaluating the burden of disease in epidemiologic and public health studies. When exposures are measured with error, the partial potential impact fraction estimates may be biased, which necessitates methods to correct for the exposure measurement error. Motivated by the health professionals follow-up study, we develop a Bayesian approach to adjust for exposure measurement error when estimating the partial potential impact fraction under the main study/internal validation study design. We adopt the reclassification approach that leverages the strength of the main study/internal validation study design and clarifies transportability assumptions for valid inference. We assess the finite-sample performance of both the point and credible interval estimators via extensive simulations and apply the proposed approach in the health professionals follow-up study to estimate the partial potential impact fraction for colorectal cancer incidence under interventions exploring shifting the distributions of red meat, alcohol, and/or folate intake.

The learning difficulties of the mathematical concept of fraction is a topic that has been studied by different mathematical educators, but still is a relevant topic today, because despite the proposals that have been made to improve learning, they have not been used for all teachers besides those few that are involved in the use of the technology. Besides that there is little educational software that is based on research and is validated to be taken to the classroom. This article shows a virtual system that has been created for the student to interact with it in order to connect his knowledge with his play skills, skills of discovery, reasoning, communication among others and may have a significant learning of fraction

Morris (Rev Econ Stud 67:57–78, 2000) defines the $$p$$ -cohesion by a connected subgraph in which every vertex has at least a fraction p of its neighbors in the subgraph, i.e., at most a fraction ( $$1-p$$ ) of its neighbors outside. We can find that a $$p$$ -cohesion ensures not only inner-cohesiveness but also outer-sparseness. The textbook on networks by Easley and Kleinberg (Networks, Crowds, and Markets - Reasoning About a Highly Connected World, Cambridge University Press, 2010) shows that $$p$$ -cohesions are fortress-like cohesive subgraphs which can hamper the entry of the cascade, following the contagion model. Despite the elegant definition and promising properties, to our best knowledge, there is no existing study on $$p$$ -cohesion regarding problem complexity and efficient computing algorithms. In this paper, we fill this gap by conducting a comprehensive theoretical analysis on the complexity of the problem and developing efficient computing algorithms. We focus on the minimal $$p$$ -cohesion because they are elementary units of $$p$$ -cohesions and the combination of multiple minimal $$p$$ -cohesions is a larger $$p$$ -cohesion. We demonstrate that the discovered minimal $$p$$ -cohesions can be utilized to solve the MinSeed problem: finding a smallest set of initial adopters (seeds) such that all the network users are eventually influenced. Extensive experiments on 8 real-life social networks verify the effectiveness of this model and the efficiency of our algorithms.

BACKGROUND People report negative attitudes towards fractions and percentages relative to whole numbers (WNs, Sidney, Thompson, Fitzsimmons, & Taber, 2021), and these attitudes may relate to an individual's interpretation of what experiences with these number types signify. Because fractions are challenging, individual differences related to beliefs about challenge, such as endorsement of a growth versus fixed mindset (Dweck, 2006) and interpretations of easy or difficult experiences (Fisher & Oyserman, 2017), could relate to attitudes towards fractions relative to other number types. AIMS Two studies tested whether gender, math skills, mindset beliefs, and perceptions of difficulty relate to negative math attitudes towards specific number types. SAMPLES Two samples of college students (Study 1: N = 491; Study 2: N = 415), approximately 19 years of age (17% male, 51% first year students) participated. METHODS Participants rated attitudes pertaining to WNs, fractions, and percentages, endorsement of a growth mindset, and perceptions of ease and difficulty. RESULTS Replicating prior work (Sidney, Thompson, Fitzsimmons, & Taber, 2021), college students endorsed more negative attitudes about fractions than WNs and percentages. Self-reported ACT scores related to all number-type attitudes, endorsement of the belief that 'difficult tasks/goals are important' related to fraction attitudes, and endorsement of the belief that 'easy tasks/goals are possible' related to whole number attitudes. Endorsement of a growth mindset did not relate to specific math attitudes. CONCLUSIONS People struggle to integrate their whole number and rational number representations, and one reason people hold negative attitudes about fractions may be that they view them as difficult and even impossible.

It has been known that the Hosoya index of caterpillar graph can be calculated as the numerator of the simple continued fraction. Recently in [MATCH Commun. Math. Comput. Chem. 2020, 84 (2), 399-428], the author introduces a more general graph called caterpillar-bond graph and shows that its Hosoya index can be calculated as the numerator of the general continued fraction. In this paper, we show how the Hosoya index of the graph with non-uniform ring structure can be calculated from the negative continued fraction. We also give the relation between some radial graphs and multidimensional continued fractions in the sense of the Hosoya index.

Background In the case of dynamic radiotherapy plans, the fractionation schemes can have dosimetric effects. Our goal was to define the effect of the fraction dose on the plan quality and the beam delivery. Materials and methods Treatment plans were created for 5 early-stage lung cancer patients with different dose schedules. The planned total dose was 60 Gy, fraction dose was 2 Gy, 3 Gy, 5 Gy, 12 Gy and 20 Gy. Additionally renormalized plans were created by changing the prescribed fraction dose after optimization. The dosimetric parameters and the beam delivery parameters were collected to define the plan quality and the complexity of the treatment plans. The accuracy of dose delivery was verified with dose measurements using electronic portal imaging device (EPID). Results The plan quality was independent from the used fractionation scheme. The fraction dose could be changed safely after the optimization, the delivery accuracy of the treatment plans with changed prescribed dose was not lower. According to EPID based measurements, the high fraction dose and dose rate caused the saturation of the detector, which lowered the gamma passing rate. The aperture complexity score, the gantry speed and the dose rate changes were not predicting factors for the gamma passing rate values. Conclusions The plan quality and the delivery accuracy are independent from the fraction dose, moreover the fraction dose can be changed safely after the dose optimization. The saturation effect of the EPID has to be considered when the action limits of the quality assurance system are defined.

In the paper, an integral rational interpolant on a continual set of nodes, which is the ratio of a functional polynomial of degree $L$ to a functional polynomial of degree $M$, is constructed and investigated. The resulting interpolant is one that preserves any rational functional of the resulting form.

To explore the application value of quantitative susceptibility mapping (QSM) based on Laplace algorithm in the diagnosis of Parkinson’s disease, 48 Parkinson’s disease patients admitted to our hospital were included as the research objects. They were randomly divided into control group (24 cases) and experimental group (24 cases). All patients underwent quantitative magnetic susceptibility imaging scan. In the experimental group, the improved Laplace algorithm was used for QSM diagnosis, while in the control group, conventional QSM diagnosis was used. Through calculations of precision, recall, dice similarity coefficient, intersection-over-union (IoU), and area under the curve (AUC), the quality improvement effect of the improved Laplace algorithm for QSM image was assessed. Then, the diagnostic accuracy of the algorithm was verified by comparing with the results of QSM image diagnosis in Parkinson’s patients without algorithm processing. The results showed that compared with the traditional Laplace algorithm, the improved Laplace algorithm can considerably reduce the image noise level ( P < 0.05 ). The dice, IoU, precision, and recall rate of image quality evaluation indicator were considerably improved ( P < 0.05 ), and the AUC reached 0.896. There were no significant differences in fraction anisotropy (FA) and mean diffusivity (MD) between the two groups ( P > 0.05 ) and no significant differences in magnetic susceptibility of brain nuclei between the two groups ( P > 0.05 ). However, they all showed high magnetic susceptibility in the substantia nigra region of the brain. Compared with the control group, the diagnostic accuracy of the experimental group was 97.5 ± 1.23%, which was considerably higher than that of the control group (86.5 ± 3.56%) ( P < 0.05 ). In short, the image quality of QSM based on Laplace improved algorithm was greatly improved, and the diagnostic accuracy of PD was also greatly improved, which was worthy of promotion in the field of clinical QSM imaging diagnosis of PD.

An effective fraction of data with missing values from various physiochemical sensors in the Internet of Things is still emerging owing to unreliable links and accidental damage. This phenomenon will limit the predicative ability and performance for supporting data analyses by IoT-based platforms. Therefore, it is necessary to exploit a way to reconstruct these lost data with high accuracy. A new data reconstruction method based on spectral k-support norm minimization (DR-SKSNM) is proposed for NB-IoT data, and a relative density-based clustering algorithm is embedded into model processing for improving the accuracy of reconstruction. First, sensors are grouped by similar patterns of measurement. A relative density-based clustering, which can effectively identify clusters in data sets with different densities, is applied to separate sensors into different groups. Second, based on the correlations of sensor data and its joint low rank, an algorithm based on the matrix spectral k-support norm minimization with automatic weight is developed. Moreover, the alternating direction method of multipliers (ADMM) is used to obtain its optimal solution. Finally, the proposed method is evaluated by using two simulated and real sensor data sources from Panzhihua environmental monitoring station with random missing patterns and consecutive missing patterns. From the simulation results, it is proved that our algorithm performs well, and it can propagate through low-rank characteristics to estimate a large missing region’s value.

In this paper, we look at a family of Renyi-like continued fraction expansions and the associated conformal iterated function systems. We show that for every k ≥ 2 , every such associated system has full Hausdorff dimension spectrum. We construct two examples of iterated function systems that do not have full Hausdorff dimension spectrum. One is a subsystem of any given Renyi-like system, while the second consists of similarities.

The standard agency model assumes that the agent does not care how his decisions influence others. This is a strong assumption, which we relax. We find that, although monetary incentives are also effective with socially attentive agents, the principal may optimally set none. This could explain the puzzle why empirically only a fraction of employees experiences monetary incentives. Furthermore, in case the agent's type is private information, the principal optimally offers a single pooling contract, i.e., never screens for different types, no matter how rich the set of possible attentiveness levels is and what shape the underlying distribution function has.

Several vaccines with different efficacies and effectivenesses are currently being distributed across the world to control the COVID-19 pandemic. Having enough doses from the most efficient vaccines in a short time is not possible for all countries. Hence, policymakers may propose using various combinations of available vaccines to control the pandemic with vaccine-induced herd immunity by vaccinating a fraction of the population. The classic vaccine-induced herd-immunity threshold suggests that we can stop spreading the disease by vaccinating a fraction of the population. However, that classic threshold is defined only for a single vaccine and may be invalid and biased when we have multi-vaccine strategies for a disease or multiple variants, potentially leading policymakers to suboptimal vaccine-allocation policies. Here, we determine which combination of multiple vaccines may lead to herd immunity. We show that simplifying the problem and considering the vaccination of the population as a single-vaccine strategy whose effectiveness is the sample mean of all effectivenesses would not be ideal, because many multi-vaccine strategies with a smaller herd-immunity threshold can be proposed. We show that the herd-immunity threshold may vary due to changes in vaccine-uptake proportions. Moreover, we propose methods to determine the optimal combination of multiple vaccines in order to achieve herd immunity and apply our results to the issue of multiple variants. In addition, we determine a condition for reaching herd immunity in the presence of new emerging variants of concern. We show by example that new variants could influence our estimation of the vaccination reproduction number. It follows that the herd-immunity threshold must be updated not only when multi-vaccine strategies are used but also when multiple variants coexist in the population.

Ordinary Least Squares (OLS) estimation of monetary policy rules produces potentially inconsistent estimates of policy parameters. The reason is that central banks react to variables, such as inflation and the output gap, that are endogenous to monetary policy shocks. Endogeneity implies a correlation between regressors and the error term -- hence, an asymptotic bias. In principle, Instrumental Variables (IV) estimation can solve this endogeneity problem. In practice, however, IV estimation poses challenges, as the validity of potential instruments depends on various unobserved features of the economic environment. We argue in favor of OLS estimation of monetary policy rules. To that end, we show analytically in the three-equation New Keynesian model that the asymptotic OLS bias is proportional to the fraction of the variance of regressors due to monetary policy shocks. Using Monte Carlo simulations, we then show that this relationship also holds in a quantitative model of the U.S. economy. Since monetary policy shocks explain only a small fraction of the variance of regressors typically included in monetary policy rules, the endogeneity bias tends to be small. For realistic sample sizes, OLS outperforms IV. Finally, we estimate a standard Taylor rule on different subsamples of U.S. data and find that OLS and IV estimates are quite similar.

In many computing applications, there is a need to estimate different features of large data sets, such as the number of distinct elements or the similarity with other data sets. This can be efficiently implemented using probabilistic data structures known as sketches; for example, Hyperloglog is widely used for cardinality estimate and Minhash for similarity estimate. Many of these sketches rely on computing hash functions on the elements and counting the number of consecutive leading zeros (or ones) to identify the minimum (or maximum) hash value for data updating. This functionality usually accounts for the most demanding part of the sketch implementation; an efficient and low power hash computation and leading zero counting are therefore required for high performance. A novel but important observation is exploited in this paper; namely the trailing hash bits are rarely used in these sketches (e.g., the leading zeros counting stops once the first one is found, which usually occurs after a few bits). Based on this feature, a so-called Two-Step Hashing (TSH) scheme is proposed in this paper to significantly reduce the power consumption. Therefore rather than computing all hash bits (as in the traditional scheme), TSH computes a few leading hash bits in a first step and the trailing hash bits in the second step, that is only required when the leading bits are all zeros (or ones). Hence, in most cases only a fraction of the hash bits is computed, so significantly reducing the power dissipation of hash computations when they are used to check the number of consecutive leading zeros, or the minimum value. The use of TSH for sketches with both single and multiple pipeline implementations are considered; evaluation results based on HyperLogLog (HLL) as a sketch with a Cyclic Redundancy Check hash function show that TSH saves up to 75.9 % (78.7 %) power dissipation in a single (multiple) pipeline implementation.

Neural networks have achieved state of the art performance across a wide variety of machine learning tasks, often with large and computation-heavy models. Inducing sparseness as a way to reduce the memory and computation footprint of these models has seen significant research attention in recent years. In this paper, we present a new method for dynamic sparseness, whereby part of the computations are omitted dynamically, based on the input. For efficiency, we combined the idea of dynamic sparseness with block-wise matrix-vector multiplications. In contrast to static sparseness, which permanently zeroes out selected positions in weight matrices, our method preserves the full network capabilities by potentially accessing any trained weights. Yet, matrix vector multiplications are accelerated by omitting a pre-defined fraction of weight blocks from the matrix, based on the input. Experimental results on the task of language modeling, using recurrent and quasi-recurrent models, show that the proposed method can outperform static sparseness baselines. In addition, our method can reach similar language modeling perplexities as the dense baseline, at half the computational cost at inference time.

This paper provides a mathematical model to show that the incorrect estimation of r, the fraction of asymptomatic COVID-19 carriers in the general population, can account for much of the world's failure to contain the pandemic in its early phases. The SE(A+O)R model with infectives separated into asymptomatic and ordinary carriers, supplemented by a model of the data generation process, is calibrated to standard datasets for several countries. It is shown that certain fundamental parameters, notably r, are unidentifiable with this data. A number of potential types of policy intervention are analyzed. It is found that the lack of parameter identifiability implies that only some, but not all, potential policy interventions can be correctly predicted. In an example representing Italy in March 2020, a hypothetical optimal policy of isolating confirmed cases that aims to reduce the basic reproduction number of the outbreak to R0 = 0.8 assuming r = 10%, only achieves R0 = 1.4 if it turns out that r = 40%., 15 pages, 10 figures

We review the optimal booking limit in the two-class static revenue management model with customers’ buy-up behavior. This is when a deterministic fraction of the low-fare customer class that cannot book early are willing to book the higher fare later. This simple model with dependent demands is difficult to analyze. Some well-known publications, such as Talluri and van Ryzin ( 2004 ) and Phillips ( 2005 ), treat this model incorrectly. In this note, we correct an erroneous formula for the modified fare ratio with the proper probabilistic interpretation. The correction was established previously by Brumelle et al. ( 1990 ). Numerical examples reveal that the corrected modified fare ratio provides a lower optimal booking limit, resulting in a higher expected revenue than those obtained by using the incorrect modified fare ratio.

The partial reuse algebraic multigrid (AMG) setup cost amortization strategy is presented for the solution of non-steady state problems. The transfer operators are reused from the previous time steps, and the system matrices and the smoother operators are rebuilt on each of the AMG hierarchy levels. It is shown on the example of modelling a two-fluid dam break scenario that the strategy may decrease the AMG preconditioner setup cost by 40 $$\%$$ to 200 $$\%$$ . The total compute time is decreased by up to 20 $$\%$$ , but the specific outcome depends on the fraction of time that the setup step initially takes.