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Let the theorem be true $\forall v_i \in V$ such that $\level(v_i) < m$. Let $\level(v_k) = m$. Let $v_i, v_j, i < j$ be predecessors of $v_k$ in $G$. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> | **A**: From Equation \ref{Eq_2}, $\ell^1_k = f^1_k(\ell^0_k \bigwedge \ell^1_j) = g_{\odot}((\nu(v_i), 1) \bigwedge (1, \nu(v_j))) = g_{\odot}(\nu(v_i), \nu(v_j)) = (1, \nu(v_i) \odot \nu(v_j)) = (1, \nu(v_k))$ is uniquely defined.
The case $\tau(v_k) = +$ is proved similarly.
\end{itemize}.
**B**: By induction hypo... | BAC | CBA | CBA | CBA | Selection 3 |
<|MaskedSetence|> (1776). An Inquiry into the Nature and Causes
of the Wealth of Nations, London: Muethen \& Co., Ltd, 5th edition, 1904.
\bibitem {Bannerjee-Maskin(1996)}Bannerjee, A.V. <|MaskedSetence|> <|MaskedSetence|> A
Walrasian theory of money and barter, \textit{Quarterly Journal of Economics,. | **A**: \begin{thebibliography}{99} %
\bibitem {Adam Smith}Smith, A.
**B**: Maskin (1996).
**C**: and E.
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{\em AMS 2010 subject classifications}: 60G15, 62G08, 65D05, 65D30, 65J22
\section{Introduction}
{Given a} {mathematical model} of a physical process, we are interested in the inverse problem of determining the inputs to the model given some noisy observations related to the model outputs. <|MaskedSetence|> <|Masked... | **A**:
Since the posterior distribution is generally intractable, sampling methods such as Markov chain Monte Carlo (MCMC) \cite{hastings70,mrrtt53,robert_casella,cmps14,gc11,crsw13} are typically used {to explore it}.
**B**: .
**C**: Adopting a Bayesian {approach
\cite{kaipio2005statistical,stuart10}}, we incorpor... | CAB | CAB | CAB | BAC | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> Let $(T,x) \in \G$ be
a tree. Let $w \in W_{2k}(T,x)$ and let the sequence of vertices visited by $w$ be denoted
$w_0 = x, w_1, \ldots, w_{2k} = x$. Let $e_j = (w_{j-1},w_j)$. <|MaskedSetence|> | **A**: In order to prove Theorem \ref{thm:cover} we will consider unimodular networks with
edge weights and bound the expectation of weighted closed walks.
**B**: By choosing appropriate
weights we will deduce both statements in Theorem \ref{thm:cover}.
**C**: The \emph{height profile} of $w$.
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<|MaskedSetence|> <|MaskedSetence|> Compared with conventional compressed sensing problems, in our setting, each random variable may take dramatically different realizations in different observations. Therefore, the compressed hypothesis testing problem considered in this paper is quite different from the conventiona... | **A**: \section{Conclusion}\label{sec:conclusion}
In this paper, we studied the compressed hypothesis testing problem, which is finding $k$ anomalous random variables following a different probability distribution among $n$ random variables by using mixed observations of these $n$ random variables.
**B**: Our analysis... | ABC | ABC | ABC | ABC | Selection 2 |
<|MaskedSetence|> 453-512], among others) to formulate a higher-dimensional linear
program (LP) model of the Assignment Problem (AP; Burkhard [2009]; Bazaraa et
al. [2010; pp. <|MaskedSetence|> Our modeling variables respectively involve
multiple arcs of its underlying graph (i.e., the MAPG). <|MaskedSetence|> | **A**: [2010; pp.
**B**: Our \textit{Kirchhoff
Equations} (KEs)/\textquotedblleft flow-balance\textquotedblright%
/\textquotedblleft mass-conservation\textquotedblright\ constraints are.
**C**: 535-550]) polytope.
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It is observed that for equal (free space) propagation conditions for Bob and Eve, the angular proximity does not depend on the absolute distances. <|MaskedSetence|> This fact is illustrated in Figure 1, where for $r=2$ the same minimum angular proximity holds for the three considered types of satellite. <|MaskedSete... | **A**: This means that the same condition holds for any type of satellite orbit.
**B**:
\begin{figure}[tbh]
\includegraphics[scale=0.23]{Fig2}
\protect\caption{Illustration of the influence of wiretap system parameters on Eve's amplitude signal degradation for different values of system parameters.}
\end{figure}.
**... | ACB | ACB | ACB | CBA | Selection 1 |
\section{Wireless mesh network and routing protocol}
A wireless mesh network (WMN) can be described as a mesh network established through the connection of wireless access points which have been installed at the location of each network users. It consists of mesh routers, which are stationary, and mesh client, which ar... | **A**: Quantum information can be transmitted from node-to-node only when quantum route and classical route co-exist.
**B**: Classical information is transmitted along classical route while quantum information is via the quantum route.
\begin{widetext}
\begin{figure*}[!t]
\centering \includegraphics[height=60mm, width... | ABC | CAB | CAB | CAB | Selection 2 |
\begin{remaAu}\label{rema-ibvp}
Note that balance of linear momentum in the form of Definition~\ref{def-fem-02}(ii) implies conservation of mass \cite{Mar1994,Aub2013a}. Conservation of mass (i) can thus be solved independently, i.e., it serves merely as an evolution equation for the mass density. <|MaskedSetence|... | **A**: Moreover, balance of angular momentum (iii) boiled down to the symmetry of the Cauchy stress, a condition which can be incorporated into (ii).
**B**: The weak form of the mechanical IBVP, by Remark~\ref{rema-ibvp}, mainly consists of the
the weak form of the balance of linear momentum, which is equivalent to t... | ACB | ACB | CAB | ACB | Selection 1 |
<|MaskedSetence|>
Random variables and vectors and their realizations, are denoted by upper and lower case versions of the same letter, respectively. <|MaskedSetence|> <|MaskedSetence|> We will consider the two-node case, and lattices of dimension two. . | **A**: Vectors and matrices are written in boldface.
\section{Lattice Basis and Source Model}
\label{sec:sourcemodel}
We now describe the family of lattices and the statistical model for the information source used in this work.
**B**: For a differentiable function $f~:~\mathbb{R} \to\mathbb{R}$, $\dot{f}(x)$ will d... | BCA | BCA | BCA | CBA | Selection 3 |
<|MaskedSetence|> The description of gait as a set of "six determinants" as proposed in the classic paper from Inman and Eberhart in 1953 \cite{inman1953major} led the clinical evaluation of gait to focus on pelvic tilt and rotation, knee and hip flexion, knee and ankle interaction, and lateral pelvic displacement. Mo... | **A**:
Multiple proposed models aim to capture biological locomotion and its motor control, but they can only partially capture the locomotion dynamics \cite{Torricelli2016, Kuo2007}.
**B**: .
**C**: \end{frontmatter}
\section{\textit{Introduction}}
Human locomotion has been studied for decades due to its relevance ... | CAB | CAB | CAB | CAB | Selection 4 |
The model of the HPC system we used for our experiment is Lenovo NeXtScale nx360 M5. It is a distributed system; the models of the processors in this HPC are Xeon Haswell E5-2695 Dual 14-core and Xeon Broadwell E5-2695 Dual 14-core. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|> The operating system is CentOS... | **A**: There are 400 nodes each having 28 cores.
**B**: The speed of a processor is 2.3 GHz.
**C**: Each node has 192 GB memory.
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<|MaskedSetence|> Though we have the complete characterizations of LLLs, new ideas are still needed to quantify the critical thresholds and their gaps, because the mathematical characterizations, such as Shearer's inequality system and the programm for VLLL, are usually hard to solve ~\cite{Harvey2017Computing,he2017v... | **A**: % of the relative power of quantum.
**B**: Precisely, we show that in contrast to QLLL, the interior of CLLL goes beyond Shearer's bound generally.
**C**: Specifically, we show that Shearer's bound is tight for QLLL.
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<|MaskedSetence|>
The intermediate relay node $R$ assists the communication between the two nodes. <|MaskedSetence|> \ref{FF1}.
Transmissions are assumed perfectly synchronised and the communication in the MAC and broadcasts phases are orthogonal. <|MaskedSetence|> | **A**: The two-way relay network model is a cooperative communication network that consists of two nodes $1$ and $2$ that want to communicate to each other but there is no direct link between them \cite{ZLWL,RW}.
**B**:
The relay node decodes the sum of the messages from the two nodes in the uplink,
and broadcasts it... | ACB | ACB | ACB | ACB | Selection 1 |
It is based on an appropriate rounding of a solution to the flow LP relaxation of \textsc{Min-Max~SP}. We will show that the approximation ratio obtained is very close to an integrality gap of this LP relaxation, which is at least $\Omega(\sqrt{n})$,
even for arc series-parallel graphs.
This paper is organized as fol... | **A**: .
**B**: We also recall a formulation of the min-max version of the
\emph{representatives selection problem}~\cite{DW13,DK12}.
**C**: Our approximation algorithm, constructed in
Section~\ref{sdsp} will use the flow LP relaxation and some known approximation results on this selection problem.
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\section{Methods}
The new version of EBIC provides a comprehensive open source framework for performing biclustering analysis. The major improvements over the original release of the method include:
\begin{itemize}
\item \textbf{Support for Big Data}. In the previous version of EBIC only a very limited number of rows c... | **A**: This remains a large number, as for the majority of genomic datasets the algorithm converged using a population size of 1,600 or less individuals.
\item \textbf{Handling missing values}.
**B**: This greatly enhances the flexibility and applicability of the method to almost any type of data.
**C**: Thus, at lea... | CBA | CBA | CBA | CBA | Selection 1 |
To prove the lemma, by Definition \ref{CalculusExtension}, we need to show that each instance of the axioms of $G_L$ and each rule of $G_L$ is provable and admissible in $G$, respectively. If $S$ is an instance of an axiom in $G_L$, by Definition \ref{CalculusForLogic}, $I(S)$ is in $L$ and hence in $M$. <|MaskedSeten... | **A**: Then:
\item[$\bullet$] Let $R$ be an instance of the conjunction or disjunction rules.
**B**: Thus, $G \vdash S$.
**C**: Let $R=$ \AxiomC{$S_1, \ldots, S_n$}
\UnaryInfC{$S$}
\DisplayProof
be an instance of a rule in $G_L$.
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To valid the performance of CxtHGNet, we test our model on the open benchmark of aerial image labeling, namely Potsdam dataset~\cite{Rottensteiner_2012_ISPRS}. <|MaskedSetence|> <|MaskedSetence|> Each image has the size of 6,000 $\times$ 6,000 and contains 5 channels, namely near-infrared (NIR), red (R), green (G), b... | **A**: The Potsdam dataset includes 38 high-resolution aerial images, where 24 images are used for training.
**B**: The Vaihingen dataset consists of 33 high-resolution aerial images, 16 of which are given labels for training.
**C**:
\end{comment}
In this section, we first briefly describe the dataset, then provide ... | CAB | CAB | CAB | ABC | Selection 2 |
What remains to define is which operation, BST or pass-through, to apply to which index, and to determine the various medial sets. <|MaskedSetence|> The medial indices are split into $\medsetMinusBrace{i}$ and $\medsetPlusBrace{i}$. These sets will be defined as part of the recursion. <|MaskedSetence|> These two subs... | **A**: At stage $i$ of the cascade, each index is either medial or lateral.
**B**: Important subsets of these sets are $\numedsetMinus{i}$ and $\numedsetPlus{i}$, respectively.
**C**:
When moving from stage $i<t$ to stage $i+1$, define the ``active set'' $\sigma_i$ as
\begin{equation} \label{eq_def of active set}
\s... | ABC | CBA | ABC | ABC | Selection 3 |
<|MaskedSetence|> Furthermore, the resource constraints must be satisfied at each period in the sense that for each resource its total budget utilization during the first $n$ periods cannot exceed the total
$n$-period budget available for all $n$. <|MaskedSetence|> In this way the bandit activation problem... | **A**: For example, if a particular bandit consumes a large amount of some resource at each activation, then after one activation the controller may have to wait for several subsequent periods until the budget of this resource is sufficiently replenished so that the bandit may be activated again.
**B**: Thus, for eac... | CBA | CBA | CBA | CBA | Selection 1 |
\end{center}
\end{table}
As seen in the table \ref{attention}, mean attentiveness never dropped below 50\% so we were unable to validate the improvement due to pitch and volume modulation. We argue that a potential reason for this anomaly might be the anticipation towards Nao humanoid among the audience. Becaus... | **A**: The feedback uses attention tracking, Openface library had been used.
**B**: .
**C**: The data set is created from real life speeches of TED speakers.
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Interestingly, methods based on density have allowed to overcome these limitations. Arbitrary shapes are reconstructed according with a local density-connectivity criterion. For example, DBSCAN\cite{DBSCAN} considers a point belonging to a cluster, if sufficiently many points in a neighborhood are common (density reach... | **A**: Density peaks are considered as points surrounded by a sufficiently many points with lower density.
**B**: Due to the simplicity of this rule CDP can be applied whenever density can be measured which hold in a wide range of applications.\\
Once peaks are identified, each one is assigned to a different cluster w... | BCA | CAB | CAB | CAB | Selection 4 |
\label{fig: example}
\vspace{-5mm}
\end{figure}
\textbf{Contribution.} Our work is driven by considering the difference between the IM problem and the MP problem. <|MaskedSetence|> <|MaskedSetence|> Consider an illustrative example shown in Fig. \ref{fig: example} where there is one seed node of the misinformation. ... | **A**: If we uniformly select a node and do the reverse sampling, we may select the nodes that are far distant from the misinformation and they actually do not require much effort to be protected (e.g., the safe nodes in the graph).
**B**: However, in the MP problem, the ultimate goal is to protect the nodes from bein... | ACB | CBA | CBA | CBA | Selection 2 |
\label{sec_metric}
The performance of TSDB is evaluated by a set of metrics. First, a set of statistical metrics is needed to evaluate the performance of each type of operations, including minimum, maximum, average, middle-average, 1st, 5th, 50th, 90th, 95th and 99th percentile of \textbf{cost-time}. <|MaskedSetence|>... | **A**: We took the maximum difference between the start space consumption and used disk space during the test process as the \textbf{space consumption} of the TSDB.
**B**: Cost-time is used as the performance measurement and it means the elapse time between sending a request or statement to the TSDB and receiving the ... | BAC | BAC | ACB | BAC | Selection 1 |
<|MaskedSetence|> This article is such an attempt.
Our goal is to enable computers to yield data which approximates internal human representations of perceived objects. <|MaskedSetence|>
The objects are given to us in some modality, usually visual or textual. <|MaskedSetence|> . | **A**:
These representation are the flows of thoughts \cite{thought} and
emotions \cite{feeling} related to an object, or groups of objects.
**B**: For example, the object depicted in Fig.~\ref{fig:FIG_THOUGHTS_PERCEPT} (A) is visual.
**C**: However, to the best of our knowledge, to this day there have been no attem... | ABC | CAB | CAB | CAB | Selection 3 |
Fig. \ref{fig:Fe} shows the response of the proposed algorithm to estimate the environment effect/end-effector contact force. From this figure, it is possible to recognize that the norm of the end-effector generalized force has maximum value of $1$ N/N.m at the beginning of operation due to the time taken by the DOb to... | **A**: Consequently, one can contend that the second control objective is achieved.
\begin{figure}[!t]
\centering
\includegraphics[width=0.95\columnwidth]{Fnorm_TS_Inv_Kin.pdf}
\caption{Error norm of estimation of the environment dynamics/contact force}.
**B**: This initial time is about $3$ s.
**C**: The norm of ... | BCA | CBA | BCA | BCA | Selection 1 |
We built a Naïve Bayes model as a base model with traditional preprocessing methods to compare it with the models built trained on word and sentence vectors. These models are completely trained on text, none of the non-word tokens or symbols were considered. A complete section is dedicated to preprocessing later in the... | **A**: To over some this the CBOW model was proposed where the words are activated according to their occurrence in the sentence.
**B**: Moreover, these vectors contain only once activated row and the rest are zeros..
**C**: In ‘A review on Feature Selection and Feature Extraction for Text Classification’ by Foram P.... | CAB | CBA | CAB | CAB | Selection 4 |
<|MaskedSetence|> A threshold for separating noise in the persistence domain is discussed in the following paragraph.
\paragraph{Threshold and Cutoff Analysis}\label{persAnalysis}
To determine the noise floor in the normalized Fast Fourier Transform (FFT) spectrum, we compute the $0$-dimensional persistence of the FFT... | **A**: We can now use the modified $z$-score $z_m$ for evaluating the ``significance" of each point in the sublevel set persistence diagram of the Fourier spectrum.
**B**: However, we apply both the FFT and 0-D sublevel set persistence to the original signal so we need to determine if this cutoff is also suitable for ... | ABC | ACB | ABC | ABC | Selection 4 |
<|MaskedSetence|> Selecting the optimum value of $K$ is a classical bias-variance tradeoff. Large values of $k$ ($>$50) lead to poor generalization on test data. Table~\ref{tab:tab1} shows the weight assigned to each feature input given to neural network in descending order. Here the features are prediction made by HM... | **A**: The predictions of these HMMs are combined by a neural network containing 60 units with ReLU activation.
**B**: For our dataset, much of the reduction appears after 20-25 classifiers.
**C**: The table clearly indicates temporal feature count has the highest importance in determining the next state taken by att... | BCA | ACB | ACB | ACB | Selection 3 |
If $\mwlet$ is smooth and $a_{\mathrm d}, 1/B$ are small enough, then the results in~\cite{balazs2011theory} imply that the DCWT is invertible. <|MaskedSetence|> This can be done either directly using dual filters $\widetilde{\mwlet}_{k}$, or iteratively~\cite{gr93,necciari2018audlet} using conjugate
gradient iterat... | **A**: Nonetheless, the dual filter bank shares the number of channels $K+1$ and the decimation factor $a$ of the wavelet analysis.
**B**:
Inversion can be achieved by interpreting the wavelet transform as a filter bank analysis and invoking the frame theory of uniform filter banks~\cite{bofehl98,cvetkovic1998oversam... | BCA | CAB | BCA | BCA | Selection 3 |
<|MaskedSetence|> MFG are apropos since they can cope with a massive number of interacting agents in a dynamic environment. Yet, the existing mean-field approaches \cite{meanfielddens1,meanfielddens2} are not specifically designed for millimeter wave networks, and, consequently, they do not consider the characteristi... | **A**: We formulate the uplink power control as a mean-field game that takes into account the characteristics of millimeter wave networks.
**B**: Further, we model the randomness of the deployment of BSs as well as MUs using stochastic geometry \cite{mmwavecoverage}.
**C**: A centralized approach is proposed in \ci... | CAB | BCA | CAB | CAB | Selection 1 |
Concretely, with this advanced release, when a task ends, it immediately releases the dependencies that are not currently used by any of its child tasks.
Furthermore, as soon as child tasks finish, they release the dependencies that are not currently used by any of their sibling tasks.
To further clarify this, we rem... | **A**: Using weak dependencies, more tasks can be thus instantiated earlier and in parallel,.
**B**: This is possible because operands marked as weak can only be read or written by child tasks.
**C**: Although this rule guarantees the correctness of the execution, it usually introduces artificial coarse-grained depen... | CBA | BAC | CBA | CBA | Selection 4 |
Despite their ubiquity, open multi-agent systems have received surprisingly little attention in either control or in contiguous fields. Notions of ``open" systems can be found in the computer science literature \cite{Huynh2006,Pinyol2013} when referring to software agents and the problem of evaluating reputation in ope... | **A**:
The contribution of this paper is twofold, as it covers both theoretical results and concrete examples.
**B**: As a theoretical contribution, we introduce an abstract framework for discrete-time open multi-agent systems: this framework is based upon proper definitions of state evolutions, equilibria, and stabi... | ABC | ABC | ABC | ABC | Selection 3 |
\bibliography{files/refs}
%\newpag
\begin{IEEEbiography}[{\includegraphics[width=1in,height=1.25in,clip,keepaspectratio]{figs/tyler2.jpg}}]{Dr. <|MaskedSetence|> R. Reid}
is a Research Engineer on the Controls and Automated Systems team at Ford Motor Company working in the area of localization and mapping. <|Maske... | **A**: Tyler G.
**B**: ('12) in Aeronautics and Astronautics from Stanford where he worked in the GPS Research Lab.
**C**: He is also a lecturer at Stanford University in Aeronautics and Astronautics.
| ACB | ABC | ACB | ACB | Selection 4 |
<|MaskedSetence|> Motivated by data from human brain functional networks, in this technical note, we analytically show that partial synchronization can be induced by strong regional connections in coupled subnetworks of Kuramoto oscillators. To quantify the required strength of regional connections, we first obtai... | **A**: \begin{abstract}
Partial, instead of complete, synchronization has been widely observed in various networks including, in particular, brain networks.
**B**: Our result based on the incremental $\infty$-norm is the first known criterion that is applicable to non-complete graphs.
**C**:
\end{abstract}
\beg... | ABC | ABC | ABC | CAB | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> This endows the aggregator the power to negotiate on $q$: the aggregator offers $x$ units of options, only if the LSE buys $l'-x$ units of energy in the day-ahead market. For the moment, we treat $l'$ as given. <|MaskedSetence|> There is no trade of load reduction if the offer is ... | **A**: The aggregator chooses $l'>0$ and dictates that $x+q=l'$.
**B**: \noindent B.1 {\em Symmetric Decision Making}
Consider the following modification to the options market: before time $t_0$, the aggregator proposes a demand response offer to the LSE.
**C**:
Upon receiving the demand response offer, the LSE deci... | BAC | BAC | BAC | BAC | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> We consider a homogeneous perturbation cost function for all state perturbations, that is $\forall s, a': c_{adv}(s, a') = c_{adv}$. For both the resilience and robustness measurements, we set $c_{adv} = 1$ (i.e., each perturbation incurs a cost of $1$ to the adversary). <|MaskedS... | **A**: The training process is terminated when the adversarial regret is maximized and the 100-episode average of the number of adversarial perturbations is quasi-stable for 200 episodes.
**B**: Total Reward & 500 \\ \hline
\end{tabular}
\end{table}
\textbf{Adversarial Agent:} In these ... | CBA | CBA | CBA | CAB | Selection 1 |
\label{fig:DPresult:fuelbar}
\end{figure}
\section{CONCLUSIONS}\label{ACC2019:section:conclusion}\vspace{-0.15cm}
This paper presents the integrated power and thermal management for a power split HEV during cold winter days in congested city driving scenario. The objective is to optimize the fuel efficiency while acco... | **A**: Extending the i-PTM to enhance aftertreatment performance in cold start phase will be also considered in the future works
\addtolength{\textheight}{-12cm} % This command serves to balance the column lengths
% on the last page of .
**B**: The simulation results of a real-worl... | CBA | CBA | CBA | CBA | Selection 1 |
In this paper we propose and analyse an algorithm that computes a symmetric or skew-symmetric low-rank approximation to large symmetric or skew-symmetric time-depen\-dent matrices that are either given explicitly or are the unknown solution to a matrix differential equation. A related algorithm is given for the approxi... | **A**: For tensors, our main motivation comes from the quantum dynamics of bosonic or fermionic systems, where the symmetric or anti-symmetric wave function is approximated by low-rank symmetric or anti-symmetric Tucker tensors in the
MCTDHB and MCTDHF methods for bosons and fermions, respectively \cite{AlonSC08,Caill... | ABC | ABC | CAB | ABC | Selection 2 |
\label{sec:positive}
%\input{positive}
In this section, for a large class of nonconvex minmax problems, we prove a general positive result that gives an upper bound on the a priori probability of the bad set \eqref{eq: bad set def} for finite samples of the scenario approach. In other words, we establish a finite ... | **A**: The class of nonconvex functions is vast, and it appears that very little can be said about a priori estimates under the scenario method at this level of generality; indeed, it is natural to expect, at least in principle, that the greater the regularity of the functions under consideration, tighter the bounds th... | ABC | CAB | CAB | CAB | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> "Long Time Stability and Convergence Rate of MacCormack Rapid Solver Method for Nonstationary Stokes-Darcy Problem", Comput. <|MaskedSetence|> Appl., Vol $75$, $(2018)$, $3663$-$3684,$ $22$ pages.
\bibitem{en1ts}
E. Ngondiep. "An efficient three-level explicit time-split... | **A**: Math.
**B**: E.
**C**: Ngondiep.
| CBA | BCA | BCA | BCA | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> The agents interact with each other through their utilities. Assuming those agents optimize their utilities in a non-cooperative way, they form a \emph{differential game}.
Exact Nash equilibria to the differential game are generally hard to solve when $N$ is large. <|MaskedSetence... | **A**: Alternatively, MFG considers the continuum problem as $N\to\infty$.
**B**:
In the MFG framework, a population of $N$ rational utility-optimizing agents are modeled by a dynamic system.
**C**: Mean field game (MFG) is a game-theoretic framework to model complex multi-agent dynamic systems \cite{lasry2007mean}.... | CBA | CBA | CAB | CBA | Selection 4 |
In this paper, a non-linear acceleration method (the NL) and its modification (the MNL) are introduced in order to accelerate and improve iterative algorithms. Besides, a complete analysis on convergence is given. <|MaskedSetence|> The proposed method is also capable of stabilizing diverging algorithms. <|MaskedSete... | **A**: It is stated that the proposed method can improve a wide variety of {\color{black} linearly convergent algorithms} including optimization methods, band-limited signal recovery methods and sparse recovery algorithms.
**B**: It is shown that the MNL method improves iterative sparse recovery algorithms such as th... | ABC | ABC | ABC | ABC | Selection 2 |
Boundary Layers, Mathematical Proceedings of the Royal Irish Academy 98 (A) (1998) 173–190.
\bibitem{14} P. W.Hemker, G. I. <|MaskedSetence|> P. <|MaskedSetence|> R. <|MaskedSetence|> F.Hegarty, Numerical solution of a convection diffusion problem with Robin boundary conditions,. | **A**: Shishkin, L.
**B**: Shishkina, High-order time-accurate schemes for singularly perturbed
parabolic convection-diffusion problems with Robin boundary conditions, Computational Methods in Applied
Mathematics 2 (1) (2002) 3–25.
\bibitem{15} A.
**C**: Ansari, A.
| BCA | ABC | ABC | ABC | Selection 2 |
<|MaskedSetence|> They can be interpreted, to some extent, as measures of the degree of observability of the system. <|MaskedSetence|> This is consistent with the well-known fact that the more observable a system is, the more robustly its state can be estimated from output measurements.
Finally, an interesting prope... | **A**: These two parameters (i.e., $p_r$ and $D$) reflect properties of the system whose state is being estimated.
**B**: In conclusion, the estimator inherits partially its resilience property from characteristics of the system being observed.
**C**: If $p_r<1/2$, and if $w_t=0$ for all $t$, then the estimator defi... | ABC | ABC | ABC | BAC | Selection 2 |
<|MaskedSetence|> <|MaskedSetence|> At the first sight, this condition seems to be strict but it has proved to be successful in many engineering applications and real-world problems so far. In fact, most of the existing works use only one RVE for the two-scale computation process.
While a two-scale computational c... | **A**: In doing so, we have plenty of possibilities of solving the microscopic BVP \eqref{microscopic-boundary-value-problem}, one of which is associated to one way of computing macroscopic energy density.
**B**:
When the heterogeneous materials under consideration can be, up to the first-order approximation, chara... | BCA | BCA | BCA | CAB | Selection 3 |
<|MaskedSetence|> Engquist and A. Majda, Absorbing boundary conditions for
the numerical simulation of waves, \emph{\ Math. Comp.}, 31, 629-651, 1977.
\bibitem{Jiang1} B. <|MaskedSetence|> <|MaskedSetence|> | **A**: Jiang, \emph{ The Least-Squares Finite Element Method.
**B**: Theory and Applications in Computational Fluid Dynamics and Electromagnetics}, Springer-Verlag, Heidelberg, 1998.
\bibitem{Jiang2} B.~Jiang, J.~Wu and L.~A.~Povinelli, The origin of spurious solutions in computational electromagnetics, \emph{Jo... | BAC | CAB | CAB | CAB | Selection 4 |
\subsection{Reinforcement Learning Overview}\label{RL}
In the RL framework, an agent learns through episodic interaction with an environment how to successfully complete a task by learning a \textit{policy} that maps observations to actions. The environment initializes an episode by randomly generating a ground truth s... | **A**: Typically, trajectories from some fixed number of episodes (referred to as rollouts) are collected during interaction between the agent and environment, and used to update the policy and value functions.
**B**: \ref{fig:Agent_env_detail}.
\begin{figure}[h]
\begin{center}
\includegraphics[width=.75\linewidth]{F... | CAB | CAB | BAC | CAB | Selection 4 |
<|MaskedSetence|> This framework is inherently secure and resilient by design. First, the games-in-games framework anticipates the attack behavior and designs a control policy that would prepare to defend against the anticipated attacks. The framework provides a clean-slate design and provides a built-in security for... | **A**: The developed games-in-games framework can be adopted to address the mosaic control design as the composability of the framework provides agility required by the mosaic control objective.
**B**: Each agent can respond to events that inflict damages on the agent and go through a self-healing process that can rec... | ABC | ABC | BAC | ABC | Selection 1 |
\skipnoindent{\em Restful Web Service:}
LabVIEW allows VIs to be equipped with restful web services which manipulates the data via HTTP methods like GET, POST etc. <|MaskedSetence|> %Modbus is a serial communication protocol published by Modicon in 1979 for use with it’s PLCs. <|MaskedSetence|> <|MaskedSetence|>
... | **A**: These services don't require any authentication by default.
\skipnoindent{\em Modbus Serial And TCP:}
RTUs P2A and P2B run Modbus TCP while the analyzers installed in P1 and P3 are connected via Modbus serial.
**B**: Since then the protocol has been open sourced and due to it’s simplicity it’s very popular in... | ACB | ACB | ACB | BCA | Selection 2 |
\subsection{Simulation results}
We consider the following scenario: at $t=1$s, there is a step change of $(3.5, 3.5, 3.5, 3.5, 3.5, 7)$p.u. <|MaskedSetence|> Neither the original load demand nor its change is known. <|MaskedSetence|>
At first, we do not set limits to the tie-line power. In this subsection, we analyz... | **A**: The load estimate method in Remark \ref{load_estimate} is utilized.
**B**: load demand at buses 4, 8, 20, 37, 42, and 52 respectively.
**C**: They also have similar frequency nadir.
| BAC | BAC | BAC | ABC | Selection 3 |
<|MaskedSetence|> Most of those were detected by the machine and only rarely caused machine stops by ripped cardboards when trying to package the product. In some cases the detracting of the cardboard failed. <|MaskedSetence|> Another reasons for down times were stops at the machine following in the packaging line. ... | **A**: This has to occur multiple times as the machine is programmed to retry on missed detraction.
**B**: The most common defect observed in production was products not positioned correctly in the bucket chain.
**C**: A list of observed states is shown in table \ref{Tab:ObservedDefects}.
\begin{table}[h]
\caption{O... | BAC | CAB | BAC | BAC | Selection 1 |
<|MaskedSetence|> <|MaskedSetence|> ``Plain'' means the plain block solver proposed in Section 3. ``Overlapping'' means overlapping blocks method with $\iota
= 1$ in Section 4.1. ``Shifting'' means the shifting blocks method in
Section 4.2. <|MaskedSetence|> | **A**: We shift blocks twice by $1/3$ and $2/3$, and feed the.
**B**: In Table \ref{cputime}, ``Sampling'' means the Monte Carlo sampling time
(including a burn-in time, which is the waiting time before collecting
samples).
**C**: \ref{cputime}.
| CBA | BCA | CBA | CBA | Selection 1 |
\label{sec:combined}
As stated in Section \ref{sec:intro}, for a given system, there are many works studying event-triggered control using Lyapunov functions to reach the goal of maintaining the stability of the system, while increasing the efficiency of the system. <|MaskedSetence|> Recently, some works began establi... | **A**: In particular, there are not yet established ways to compare the performance of an event-triggered algorithm with another.
Consequently, many different algorithms can be proposed to ultimately solve the same problem, while each algorithm is slightly different and produces different trajectories.
**B**: To the b... | CAB | CAB | CAB | BCA | Selection 3 |
\end{proof}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Surface regularity and properties of the distance function} \label{S:d_for_C1}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
In the previous two sections we have seen that when $... | **A**: On the other hand, some applications may require solving PDE on surfaces that are less regular than $C^2$.
**B**: We shall see below that the closest point projection plays a pivotal role in analyzing finite element methods on $C^2$ surfaces.
**C**: Thus it is natural to ask which properties of the distance... | BAC | BAC | ABC | BAC | Selection 1 |
\begin{keyword}
Invertible hybrid automaton, strong connectedness and differential flatness, explicit system inversion
\end{keyword}
\begin{abstract} % Abstract of not more than 200 words.
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can ex... | **A**: The results constitute a generalisation of control of invertible hybrid systems which is very useful if, e.g., fast reaction for stabilisation or transitions is relevant.
**B**: Relevant system properties are derived, an approach for construction and for trajectory calculation is proposed and two demonstrative... | BAC | BAC | ACB | BAC | Selection 4 |
Computer Sciences, University of California, Berkeley, CA 94720, USA}
\begin{keyword} % Five to ten keywords,
Smart grid; Demand response; Market implementation; Competitive equilibrium; Tractable integer programming. <|MaskedSetence|> We have proposed Multiple-Arrival Multiple-Deadline~(MAM... | **A**: We also show the strengths of the MAMD services by simulation.
**B**: % chosen from the IFAC
\end{keyword} % keyword list or with the
\vspace{-20pt}
\begin{abstract} % Abstract of not more than 200 wor... | BCA | BCA | BCA | BCA | Selection 3 |
\bibitem{10}
Pyragas K. <|MaskedSetence|> Phys. <|MaskedSetence|> Lett. <|MaskedSetence|> C. Chaos and Time-Series Analysis, Oxford University Press, Oxford, Vol. 69 (2003)
\bibitem{S} Shalby L., Predictive feedback control method for stabilization of continuous time systems. Advances in Systems Science and Appli... | **A**: Rev.
**B**: Continuous control of chaos by self controlling feedback.
**C**: A 170, 421-428 (1992)
\bibitem{18}
Sprott, J.
| BAC | BAC | CAB | BAC | Selection 4 |
AC hardware controllers are torque steering motor, electronic brake booster, electronic throttle, gear shifter and parking brake. The vehicle states, such as wheel speed and steering angle, are sensed automatically and sent to the computer system via a Controller Area Network (CAN) bus. This enables either the HD or th... | **A**: The state-of-the-art perception technologies can be broken into two categories: computer vision-based and machine learning-based ones \cite{Apolloni2005}.
**B**: The former generally addresses visual perception problems by formulating them with explicit projective geometry models and finding the best solution ... | ABC | CAB | CAB | CAB | Selection 3 |
\bibitem{Acosta20171} Acosta, G., Bersetche, F.M., Borthagaray, J.P.: A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian. Comput. Math. <|MaskedSetence|> {\bf74}, 784--816 (2017).
\bibitem{Acosta20172}Acosta, G., Borthagaray, J.P.: A fractional Laplace equation: regularity of so... | **A**: Comp.
**B**: {\bf87}, 1821--1857 (2017).
\bibitem{Acosta20174} Acosta, G., Bersetche, F.M., Borthagaray, J.P.: Finite element approximations for fractional evolution problems.
**C**: Appl.
| CAB | CAB | CAB | BAC | Selection 1 |
<|MaskedSetence|> <|MaskedSetence|> Indeed, while ticketing data would represent the most natural source of such information, it does not generally provide destination information when a passenger enters the network, is often not available for processing in real-time, and in dense networks does not indicate which rou... | **A**: Efficient movement of people in increasingly dense cities is one of the key challenges towards sustainable growth of urban areas throughout the world.
**B**: Enabling effective response to incidents and unforeseen events requires real-time monitoring of the public transport network level of service, which in t... | CAB | ABC | ABC | ABC | Selection 3 |
<|MaskedSetence|> The measured state is communicated when a predefined error threshold is exceeded.
At each sampling instant, the receiving agent independently predicts the state, which is measured by the sender, based on previous estimations and a model. The sender performs the identical prediction and communicates ... | **A**: If the measured signal (e.g., a human foot angle) can be described by a cyclically excited system model, the model is shared with the receiver and the communication is reduced to those samples that cannot be predicted using the model and previously transmitted data.
**B**: Well known approaches are event-based ... | BCA | BCA | BCA | ACB | Selection 3 |
\end {align*}
Similar to the proof of Lemma \ref{lem2}, we complete the proof.
\end{proof}
The optimal strong convergence order of the numerical approximation which only use the increments of the Wiener process is known to be $1$ for SDEs with Lipschitz and regular coefficients driven by additive noises (see e.g. \cit... | **A**: .
**B**: However, for SDEs with non-globally monotone coefficients driven by additive noises, it seems that there exists a order barrier to achieve optimal strong rate (see e.g.
**C**: To this end, the following a priori estimate is needed to the proof of Theorem \ref{SC1}.
| BCA | BCA | BCA | BCA | Selection 3 |
\bibitem{5} Dennis, J. E. (Jr.), Schnabel, R. B.: Numerical methods for unconstrained optimization and nonlinear equations. SIAM, Philadelphia (1996)
\bibitem{6} Deuflhard, P. Newton methods for nonlinear problems. <|MaskedSetence|> Springer-Verlag, Berlin ( 2004)
\bibitem{7} Hern\'{a}ndez-Ver\'{o}n, M.A., Rubio,... | **A**: Affine invariance and adaptive algorithms.
**B**: Press, StateNew York etc.
**C**: Appl.
| ACB | ACB | ACB | ACB | Selection 3 |
\end{split}
\end{equation}
Similar discretizations hold for the Neumann conditions in other directions. <|MaskedSetence|> It is shown that the proposed scheme is uniquely solvable for sufficiently small $Kh$, where $K$ is the wave number and $h$ is the mesh step size. The bound on the error norms to the proposed schem... | **A**: Using the difference schemes at the boundary point $(x_0,y_j,z_k), j,k=0(1)N$, we can eliminate the values $u_{-1,j,k}$ at the ghost points.
\section{Convergence analysis}\label{sec:3}
In this section, the theoretical analysis for the proposed scheme is presented.
**B**: For the three dimensional case, the trea... | ACB | ACB | ACB | CBA | Selection 3 |
<|MaskedSetence|> Most existing works on estimating ROA rely on analytical Lyapunov functions, which are subject to two limitations: the analytic Lyapunov functions may not be always readily available, and the resulting ROA may be overly conservative. <|MaskedSetence|> In addition, a Gaussian Process Upper Confidence... | **A**: This work overcomes these two limitations by leveraging the converse Lyapunov theorem in control theory to eliminate the need for an analytic Lyapunov function and learning the unknown Lyapunov function with the Gaussian Process (GP) approach.
**B**: This paper introduces a novel framework to construct the regi... | BAC | BAC | BCA | BAC | Selection 4 |
\thanks{S. A. Alavi, K. <|MaskedSetence|> <|MaskedSetence|> Rahimian are with the School of Electronic Engineering and Computer Science, Queen Mary University of London, London E1 4NS, U.K. (e-mail: k.mehran@qmul.ac.uk).}
\thanks{H. <|MaskedSetence|> Vahidinasab is with the Department of Electrical Engineering, Abba... | **A**: Mehran, Y.
**B**: Hao, and A.
**C**: Mirsaeedi is with the School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran.}
\thanks{V.
| CBA | ABC | ABC | ABC | Selection 2 |
Section~\ref{sec:dynamics} presents the dynamic modeling of bias and drift in GPS receivers and showcases how TSA attacks can be modeled and designed to mislead standard state estimators. <|MaskedSetence|> <|MaskedSetence|> <|MaskedSetence|>
\section{Dynamic Modeling Under GPS Spoofing}~\label{sec:dynamics}
The... | **A**: Section~\ref{sec:numtests} concludes the paper with realistic numerical tests on real GPS data.
**B**: For reproducibility, the data used in the numerical tests and the results are all provided through a Github link.
**C**: Section~\ref{sec:RSE} presents a robust state estimator in addition to a state correcti... | CAB | CAB | ABC | CAB | Selection 2 |
<|MaskedSetence|> Each of panels (a)-(g) in this figure is
a graph of the efficiency $\eta$ as a function of one of the parameters in the optimization. Thus,
each point corresponds to a 7-dimensional vector of parameter values used by DEA. The optimal efficiency found is marked by a large red disk. <|MaskedSetence|... | **A**: \end{table}
Figure~\ref{FIG:DEAConv} summarizes the progression of the DEA towards an
optimal result.
**B**: In particular it shows the efficiency as a function of DEA step..
**C**: The remaining panel, Fig.~\ref{FIG:DEAConv}(h), shows the progress of optimization.
| ABC | ACB | ACB | ACB | Selection 3 |
\end{figure*}
One approach to dynamic federation is to impose some sort of hierarchy -- within co-located clusters, one node can serve as a leader to be responsible for in-cluster synchronization and global communication. <|MaskedSetence|> The leader gathers these frames and constructs a dynamic 3D model from which es... | **A**: While the pseudocode may seem simple, it highlights important opportunities and challenges that emerge from the very nature of programming a geographically-distributed aggregate of computing resources.
**B**: This leader could arrange for the other nodes to take pictures at specified times.
**C**: Testing is l... | BCA | BCA | CAB | BCA | Selection 4 |
<|MaskedSetence|> <|MaskedSetence|> Philadelphia: Series in Applied Mathematics,
Vol. 11. SIAM.
\bibitem{PeriodicPopulation} % 25
Zhao XQ. (2017) A Population Model with Periodic Delay. In: Dynamical Systems in Population Biology. <|MaskedSetence|> Springer, Cham
\bibitem{StochasticTrains} % 26
Annabell Berger, An... | **A**: \bibitem{powermethod} % 24
Trefethen, L.N., Bau, D., 1998.
**B**: CMS Books in Mathematics (Ouvrages de mathematiques de la SMC).
**C**: Numerical Linear Algebra.
| ACB | ACB | ABC | ACB | Selection 4 |
\begin{table}[!h]
\centering
\small
\caption{Local approximation of 3D models. <|MaskedSetence|> In bold, we highlight the errors with the lowest order of magnitude. The single asterisk highlights those cases where the maximum number of iterations, here set to $15$, is reached. <|MaskedSetence|> <|MaskedSetence|> | **A**: The labels A.1, A.2 and A.3 refer to the models in Figure \ref{figure:3Dmodels}.
**B**: Kriging runs in a single step and no number is displayed.
**C**: \label{table:3Dmodels}}
\scalebox{0.9}{.
| ACB | ABC | ABC | ABC | Selection 3 |
\paragraph{RL, Business-as-usual} penalizing violations with a suitably high cost lets the optimization procedure yield a policy which tends to not violate the constraints. Safety is typically not strictly guaranteed and only few results provide weak guarantees.
\paragraph{Safe RL MPC} In the approach we propose, a ro... | **A**: In particular, the introduction of a nominal (potentially inaccurate) linear model allows one to significantly reduce the amount of stored data.
**B**:
Safe RL-MPC is based on the approach first advocated in~\cite{Gros2018,Zanon2019}.
**C**: Similarly to (b), RL updates the parametrization of the robust MPC s... | CBA | CBA | ACB | CBA | Selection 1 |
\label{fig:Feedback2}
\end{figure}
\section{Conclusion}
This paper proposed a technique to deploy deterministic policy gradient methods using a constrained parametric optimization problem as a support for the optimal policy approximation. This approach allows one to impose strict safety constraints on the resulting po... | **A**: The proposed techniques are illustrated in simple simulations, showing their behavior.
**B**: In particular, robust Nonlinear Model Predictive Control, where safety requirements can be imposed explicitly, can be selected as a parametric optimization problem.
**C**: The specific case of robust Model Predictive ... | BCA | ABC | BCA | BCA | Selection 3 |
\end{equation}
where $x=2$ and $a$, $b$ are two parameters. Firstly, we verify the weak convergence of the BE method on a finite time interval $[0,T]$.
Let $T=6$ and we create 2000 discretized Brownian paths over $[0,T]$ with a small step-size $\bar{\delta}= 2^{-11}$. Since the exact solution can not be obtained, we us... | **A**: \ref{order of weak convergence multiple} plots.
**B**: And three sets of $a,b$ are tested.
**C**: Fig.
| BCA | BCA | BCA | BCA | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> the overview \cite{Nosratabadi17} and the references therein. <|MaskedSetence|>
Hence, scheduling of DERs is usually cast as a stochastic optimization problem.
The additional requirement of computational scalability---i.e. scheduling numerous devices at once---exacerbate the chal... | **A**:
In this context, the problem of scheduling the power exchange between a population of heterogenous DERs (or an aggregation thereof) and the corresponding upper-level system is a pivotal problem that has received considerable research attention, cf.
**B**:
A general key challenge is the uncertainty surrounding... | BAC | CAB | CAB | CAB | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> Several related decentralized control problems were shown to be intractable~\cite{blondel}.
Tractability is closely related to how information is shared between the different controllers. For LQG problems with \textit{partially nested} information, the optimal controller is linear ... | **A**: Numerical approaches include vectorization~\cite{rotkowitz_vectorization,vamsi_elia} and Galerkin-style finite-dimensional approximation~\cite{scherer02,voulgaris_stabilization}..
**B**: Our results are presented in continuous time with an infinite-horizon cost but can easily be generalized to discrete time and... | BCA | BCA | BCA | BAC | Selection 1 |
\end{exmp}
\section{Conclusion}
This paper addresses the disturbance rejection problem of nonlinear event-based systems. Assuming the existence of a pre-designed control law with desirable local $\mathcal{L}_2$ performance characteristics, we propose a triggering condition that preserves finite gain local $\mathcal{L}... | **A**: We show.
**B**: Our formulation is rather general; {\it i.e.} we consider a nonlinear plant and assume that disturbances are bounded by a Lipschitz-continuous function of the state.
**C**:
First we show that the inter-event time period is lower bounded by a nonzero constant and focus on enlarging this constan... | BCA | BCA | BCA | BCA | Selection 3 |
\noindent \textbf{Proof.} See Appendix \ref{Proof_T1}. <|MaskedSetence|> <|MaskedSetence|> The emphasis is placed in the effect of constraints and disturbances on closed-loop stability and performance. <|MaskedSetence|> The discussion is focused on the effect of $N_e$ and $N_c$ on the performance and computational t... | **A**: {\hfill$\square$} \vspace{0.1cm}
\section{Examples}
In this section, we discuss two examples to illustrate the results presented previously and compare the performance of the framework discussed formerly.
**B**: The second example discusses the simulations results for a van der Pol oscillator using the framewor... | ACB | ACB | CBA | ACB | Selection 4 |
\keywords {Data compression, Functional tensors, Tucker decomposition, Sparse approximations, Randomized least squares}
\section{Introduction}
Functional tensors are based on interpretation of high dimensional functions as tensors and their decomposition in several tensor formats as particular approximations. Consequen... | **A**: This functional tensor, stored as a surrogate at a fraction of cost of the original dataset, can be rapidly evaluated to recover accurate approximations of the data.
**B**: Examples of such methods include multivariate volume block data reduction by taking advantage of local multiway structure \cite{Fout:2005},... | ACB | ACB | CBA | ACB | Selection 1 |
\end{tabular}
\end{table}
For 10 of the 14 test matrices reported, setting $k=10$ always picks the optimal preconditioner for the problem across every one of the 1,000 trials. <|MaskedSetence|> Moreover, even when the accuracy parameter $k=10$, the returned preconditioner never needs more than 15\% iterations over... | **A**: If we take $k=50$, this happens for 11 of the 14 test matrices.
**B**: Increasing $k$ causes the preconditioner returned by Algorithm \ref{alg:pick} to concentrate further around the true minimal-stability preconditioner (see Theorem \ref{thm:pick},) and so this implies that the preconditioner stability criter... | ACB | ACB | ACB | ACB | Selection 2 |
\bibitem{Helal2} M. H. <|MaskedSetence|> <|MaskedSetence|> C. Berndt, R. J. Evans, and K. S. Williams, Gauss and Jacobi Sums, John Wiley and Sons Inc., A Wiley-Interscience Publication, New York, $(1998)$.
\bibitem{Berndt2} B. C. Berndt and R. J. Evans, Sums of Gauss, Jacobi and Jacobsthal, J. Number Theory, $\textbf... | **A**: Tanti, Computation of Jacobi sums and cyclotomic numbers with reduced complexity, Bulletin of Pure and Applied Sciences, $\textbf{38E (1)}$ $(2019)$, $306-310$.
\bibitem{Berndt1} B.
**B**: D.
**C**: Ahmed and J.
| CAB | CAB | BAC | CAB | Selection 4 |
<|MaskedSetence|> This signature acts as a key for the map, within which we store all cardIds that have an event matching that key. The bin of the map is an object itself, a reference to which is held by any card that has a corresponding event matching the event signature.
Each card's objects are instantiated with the... | **A**: \subsection{Determining Uniqueness}
For each event an event signature is created that consists of the time at the respective granularity and if appropriate the location string.
**B**: For each card we extract a list of event bins up to the set cardinality.
**C**: If not, those $n$ events are considered unique... | ABC | ABC | ACB | ABC | Selection 1 |
\end{table}
\subsection{Knowledge Engineering}
When the semantic network was modelled (ontology), and the communication between the FreeCiv client and the KB-RL agent was set up (Connector, and Action Handler), the next step was to engineer the knowledge. At first, we encoded the game's essential knowledge, such as sta... | **A**: Accordingly, the expert knowledge rules encoded such macro decisions.
**B**: We call them expert KI sets.
**C**: These knowledge rules did not contain any strategic decisions for playing the game, but rather the game basics.
| CBA | CBA | ACB | CBA | Selection 4 |
\paragraph{Future work}
Investigating the level of dependence between variables is still a thorny issue. Such an issue is usually tackled by investigating the properties of mutual information or multiinformation. We believe that considering multiinformation density instead of multiinformation (i.e., the random variable... | **A**: For instance, the asymptotic normality of this measure could be of interest.
**B**: A quick derivation (see Appendix~\ref{an:norm}) shows that, in the simple case of a homogeneous correlation matrix and a partitioning into 1-dimensional vectors, $i_d$ is not asymptotically normal.
**C**: Its generalization to ... | CAB | CBA | CAB | CAB | Selection 3 |
<|MaskedSetence|> The state $\ket{\varphi}$ can be created with a variation of quantum counting, followed by Grover's search algorithm, serving the dual purpose of estimating the normalization constant $Z$.
Another recent quantum k-means clustering method exists, developed by Kerenidis et al \cite{qmeans}, though the... | **A**:
\section{Time Complexity Analysis}.
**B**: Finally, a classical description of the final centroids is extracted by once again using vector state tomography.
**C**: |\textbf{X}^{i}-\textbf{X}^{j}|^2=Z(4P(0)-2).
\end{equation}
The state $\ket{\psi}$ can be easily constructed by simple Hadamard and CSWAP gates. ... | ABC | CBA | CBA | CBA | Selection 4 |
Figure \ref{scale0} helps to understand why the variety decreases with high Dropout rates: With medium Dropout rates in generation, the result images look slightly different but also start to get noisy. If the Dropout rate is increased even more, the image generation completely breaks and only results in random noise. ... | **A**: So, values should definitely be scaled if Dropout is used.
\begin{figure}[h]
\centering
\includegraphics[width=0.5\linewidth]{scale0.png}
\caption{Model trained with a Dropout rate of 0.8.
**B**: This is most certainly due to under-saturation in units: Dropout is applied, so the average signal value is decre... | BAC | CAB | BAC | BAC | Selection 3 |
<|MaskedSetence|> This is then followed by a max pooling layer. A dropout of rate 0.25 is applied to reduce overfitting. This is followed by a sequence of four convolutional layers. <|MaskedSetence|> A single max pooling layer follows these four layers with a dropout of rate 0.25. In order to convert the output into ... | **A**: The first two have a filter size of 128 each and the latter two have a filter size of 256 each.
**B**: \end{tabular}
\end{table}
The network consists of two convolutional layers with a filter size of 64 each.
**C**: Each model was set to run for 100 epochs.
| BAC | BAC | BAC | ACB | Selection 2 |
\caption{Information about the datasets used in our experiment with current benchmarking accuracy, trained on all features.}
\label{tab:information about the datasets used in our experiment}
\end{table}%
\subsection{Results}
We conduct our experiments in two steps. In the first step we train gumbel... | **A**: Cora, Citeseer, and Pubmed are evaluated by classification accuracy.
**B**: The listed methods use the same train/valid/test data split.
**C**: .
| ABC | ABC | ABC | CBA | Selection 3 |
The first set of experiments highlights the benefit of a Vehicle View. <|MaskedSetence|> <|MaskedSetence|> The expected number of serviced requests by the World Agent (3.4) is particularly low. The Vehicle (21.9), Zoom (21.8), and Survey Agents (22.3) each demonstrate substantial improvements over the World Agent and... | **A**: Of the 250 instances used to calculate the EVPI, nearly 25 percent solve to optimality within the allotted time.
**B**: Figures~\ref{fig:resultsall} and~\ref{fig:views_comparison} depict the results.
**C**: Figure~\ref{fig:resultsall} displays the performance of each agent and of the benchmarks while Figure~\r... | BCA | BCA | BCA | BAC | Selection 3 |
\label{figure:Markov}
\end{figure}
The state space S is the set of arms and has a cardinality $|S| = K$ and $P$ models the autonomy of the intermediate in pulling the arms. <|MaskedSetence|> For example a person who watches a “Horror” movie and likes it, is likely to pick the next movie they watch as a “Horror” m... | **A**: This variable is used to model the effect of recommendation systems.
**B**: Thus even if $P$ is initially unknown, it is easily estimated.
**C**: This Markovian structure shows the dependence of future choices of the intermediate based on the current choice.
| CBA | CBA | BCA | CBA | Selection 1 |
The rest of this paper is organized as follows. In section II, we mention some related work. In section III, we cover the RF energy harvesting ideas briefly. <|MaskedSetence|> Section V concludes this paper.
\section{Related Work}
There are several works related to energy harvesting for sensor nodes from previous auth... | **A**: They also mentioned that this sleep and awake state transformation would take additional energy which maybe more than if the node would have been alive.
**B**: Specific energy consumption model for the sensors were not mentioned in the paper though.
\textbf{Sinha} mentioned about \cite{sinha2001dynamic} improvi... | CBA | CBA | CBA | ACB | Selection 3 |
<|MaskedSetence|> <|MaskedSetence|> A consequence is that agents' beliefs, which \emph{a priori} are multi-dimensional objects, are in fact ranked in the standard Blackwell ordering: a higher value of $r_i$ implies a weakly higher expected utility for any decision problem.
Such comparisons are straightforward in a di... | **A**: The signal-counting interpretation gives a way to compare agents' accuracy and welfare across different networks or positions in a given network in a binary-state setting.
**B**: Rather than comparing the full distributions of beliefs, we can compare the summary statistics $r_i$.
**C**: In the binary-state mod... | ABC | ACB | ABC | ABC | Selection 1 |
\includegraphics[width=17cm]{figures/fig4.jpg}
\caption{Visual comparison of selected saliency detection.}
\label{fig:4}
\end{figure*}
We found that the saliency detection methods do not perform well in street view images. <|MaskedSetence|> <|MaskedSetence|> Also, the road regions are less salient than others, a... | **A**: So the saliency detection used in the previous works in street view image is not ideal.
**B**: Individuals tend to place labels onto uniform regions, and the sky region is obviously on the top of the list of positions we expect users to place the labels on.
**C**: For the contrast-based traditional methods lik... | ACB | CBA | CBA | CBA | Selection 2 |
The output of U-net model with pretrained weights of the ResNet is fast and accurate. This helps doctors to start the treatment at the earliest. U-net is consist of an encoder and decoder. Encoder narrow down the information of the image to a latent space. Then decoder taking input latent space regenerates the image. ... | **A**: We are using ResNet as encoder and we are going to use the weights from pretrained network.
**B**: The output mask is a black and white image.
**C**: As real world images are not of the same size and more sometime are corrupted.
| BCA | CBA | CBA | CBA | Selection 3 |
\includegraphics{teleport.png}
\caption{Informal description of Protocol}
\label{Figure: 3.8 }
\end{figure}
On the other hand, the protocol has been described informally in plain English. The revolutions of the previous century have simplified certain algebras. <|MaskedSetence|> In previous approaches, alg... | **A**: Several non-simple algebras still wait to be simplified such as Algebra for modelling Quantum Teleportation protocol.
**B**: Our research effort is to formalize the protocol in an easy to understand and simplified way.
**C**: This would also helps us in verifying the correctness of quantum teleportation protoc... | ABC | CBA | ABC | ABC | Selection 4 |
% Set height instead of width since both images are equally tall but the left one is wider (since it has a ylabel)
\caption{The rotation angle \emph{predicted} by the ST module for MNIST images as a function of the rotation \emph{applied} to the input image. <|MaskedSetence|> The reason for this is that a rotation ... | **A**: This is because a rotation of the feature map does not correspond to a rotation of the input.
**B**: .
**C**: STN-C1 has not learned to predict the image orientation (left).
| CAB | CAB | CAB | CBA | Selection 1 |
&= d∘π₀ \\ % By action of \T^∞
&= λ(y,e). d␣y \\
&= λ(y,e). <|MaskedSetence|> <|MaskedSetence|> \ssupⁿ␣(\T^∞d'␣(n_g␣(y,|(x,e)|))) \\ % By defining property of n_g
&= λ(y,e). <|MaskedSetence|> | **A**: d'(y,|(x,e)|) \\ % Since d' is a coalgebra hom
&= π₁␣\left(\desup␣(d␣x)\right) \qedhere
\end{align*}\end{proof}
\hypertarget{the-terminal-tux2070-coalgebra}{%
\section{\texorpdfstring{The terminal
\(\T⁰\)-coalgebra}{The terminal \textbackslash T⁰-coalgebra}}\label{the-terminal-tux2070-coalgebra}}.
**B... | CBA | CBA | CAB | CBA | Selection 1 |
<|MaskedSetence|> controls (14,-1.9) and (18,-1.9) .. <|MaskedSetence|> On the right: explicit cut between the same two graphs (the cut is shown below). <|MaskedSetence|> It is easily checked that there is a bijective correspondence between alternating paths on the left and alternating paths on the right.}\label{exe... | **A**: Both representations lead to the same result, as the cut-elimination is represented by \emph{execution}, an operation defined from alternating paths.
**B**: (17.95,-0.2) {};
\end{tikzpicture}
\end{tabular}
\caption{On the left: implicit cut between two graphs (one is plain, the other is dashed).
**C**: \draw[<... | CBA | CBA | BAC | CBA | Selection 4 |
<|MaskedSetence|> Previously, it was known that a greedy algorithm is 0.5--competitive against the clairvoyant benchmark that knows the entire sequence of requests in advance (Gong et al.\ (2021)).
We give a novel algorithm that is $(1-1/e)$--competitive for arbitrary usage distributions when the starting capacity ... | **A**: This is the best achievable competitive ratio guarantee for the problem, i.e., no online algorithm can have better competitive ratio.
**B**: Our technique generalizes the primal-dual analysis framework for online resource allocation and may be of broader interest.
**C**: \ABSTRACT{
We consider the problem of ... | CAB | CAB | CAB | CAB | Selection 3 |
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