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\mathbb{E}(|\xi|^{2}|1-\xi|^{2})\leq 0\ ,| blackboard_E ( italic_ξ | 1 - italic_ξ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT - blackboard_E ( | italic_ξ | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) blackboard_E ( | 1 - italic_ξ | start_POSTSUPERSCRIPT 2 end_POSTSUPE... | the cost per iteration is fixed (or bounded). The downside is that the convergence rate is not guaranteed to improve by increasing | The main contribution of this article is to show that Orthomin(k𝑘kitalic_k) does not perform better in general (that is, for matrices A𝐴Aitalic_A | We should point out that in the case when ξ𝜉\xiitalic_ξ is real valued (which is not the case here), | Figure 5: The case when −ρ𝜌-\rho- italic_ρ does not belong to Hull(ζ1,…,ζd)Hullsubscript𝜁1…subscript𝜁𝑑\operatorname{Hull}(\zeta_{1},\dots,\zeta_{d})roman_Hull ( italic_ζ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_ζ start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT ): ρ=0.9,d=15formulae-sequence𝜌0.9𝑑15\rho... | C |
𝒫𝒫\mathcal{P}caligraphic_P is a function from δ𝛿\deltaitalic_δ to [0,1]01[0,1][ 0 , 1 ] which to each rule (p,X)→(q,α)→𝑝𝑋𝑞𝛼(p,X)\rightarrow(q,\alpha)( italic_p , italic_X ) → ( italic_q , italic_α ) in δ𝛿\deltaitalic_δ assigns its probability 𝒫((p,X)→(q,α))∈[0,1]𝒫→𝑝𝑋𝑞𝛼01\mathcal{P}((p,X)\rightarrow(q,\al... | The model-checking of stateless probabilistic pushdown system (pBPA) against probabilistic computational tree logic PCTL is generally undecidable. | The model-checking of probabilistic pushdown systems (pPDS) against probabilistic computational tree logic PCTL is generally undecidable. | Among the probabilistic infinite-state systems, one is the probabilistic pushdown systems, which were dubbed “probabilistic pushdown automata” in [4, 3, 6], the input alphabet of which contains only one symbol. Throughout the paper, such a limited version of probabilistic pushdown automata will be dubbed “probabilistic... | The stateless probabilistic pushdown system (pPBA) is a probabilistic pushdown system (pPDS) whose state set Q𝑄Qitalic_Q is a singleton (or, we can just omit Q𝑄Qitalic_Q without any influence). | D |
Another important issue is the selection of the design points used to construct the Gaussian process emulator, also known as experimental design. In applications where the posterior distribution concentrates with respect to the prior, it might be more efficient to choose design points that are somehow adapted to the po... | The main focus of this work is to analyse the error introduced in the posterior distribution by using a Gaussian process emulator as a surrogate model. The error is measured in the Hellinger distance, which is shown in [41, 15] to be a suitable metric for evaluation of perturbations to the posterior measure in Bayesian... | The convergence results on Gaussian process regression presented in section 3 are mainly known results from the theory of scattered data interpolation [43, 37, 28]. The error bounds are given in terms of the fill distance of the design points used to construct the Gaussian process emulator, and depend in several ways o... | Gaussian process emulators are frequently used as surrogate models. In this work, we analysed the error that is introduced in the Bayesian posterior distribution when a Gaussian process emulator is used to approximate the forward model, either in terms of the parameter-to-observation map or the negative log-likelihood.... | In practical applications of Gaussian process emulators, such as in [19], the derivation of the emulator is often more involved than the simple approach presented in section 3. The hyper-parameters in the covariance kernel of the emulator are often unknown, and there is often a discrepancy between the mathematical mode... | D |
Taking τ≈OPT/logn𝜏𝑂𝑃𝑇𝑛\tau\approx OPT/\log nitalic_τ ≈ italic_O italic_P italic_T / roman_log italic_n gives the promised competitive ratio. | We let OPT𝑂𝑃𝑇OPTitalic_O italic_P italic_T denote the expected (offline) optimum. W𝑊Witalic_W is the set | For any set T𝑇Titalic_T, we let V(ℱ;T)𝑉ℱ𝑇V\left({\cal F};T\right)italic_V ( caligraphic_F ; italic_T ) denote the value | for intermediate values, we let Wjsubscript𝑊𝑗W_{j}italic_W start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT denote the set W𝑊Witalic_W before | Let ℱℱ{\cal F}caligraphic_F denote the family of all feasible sets. For any T⊆[n]𝑇delimited-[]𝑛T\subseteq\left[n\right]italic_T ⊆ [ italic_n ], | B |
}[\deg(\circ)]-1}=2.lim inf start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT 2 square-root start_ARG italic_d start_POSTSUBSCRIPT roman_av end_POSTSUBSCRIPT ( italic_G start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ) - 1 end_ARG ≤ 2 square-root start_ARG blackboard_E start_POSTSUBSCRIPT ( italic_G , ∘ ) end_POSTSUBSCRIPT... | This implies the required claim for the sequence Hnsubscript𝐻𝑛H_{n}italic_H start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT and completes the | We now prove part II of the theorem. Let Gnisubscript𝐺subscript𝑛𝑖G_{n_{i}}italic_G start_POSTSUBSCRIPT italic_n start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT end_POSTSUBSCRIPT be a subsequence | proof of the theorem when the sequence Gnsubscript𝐺𝑛G_{n}italic_G start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT has no leaves. | These bounds imply the required inequality in (4.2) and completes the proof of part II of the theorem. | D |
Each random variable among the n𝑛nitalic_n numbers of random variables has the same probability of being an abnormal random variable. Thus, possible locations of the k𝑘kitalic_k different random variables out of n𝑛nitalic_n follow uniform prior distribution; namely, every hypothesis has the same prior probability to... | In Algorithm 6, for two different hypotheses Hvsubscript𝐻𝑣H_{v}italic_H start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT and Hwsubscript𝐻𝑤H_{w}italic_H start_POSTSUBSCRIPT italic_w end_POSTSUBSCRIPT, we choose the probability likelihood ratio threshold of the Neyman-Pearson testing in a way, such that the hypothesis ... | We first consider an upper bound on the error probability of hypothesis testing. Without loss of generality, let us assume H1subscript𝐻1H_{1}italic_H start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT is the true hypothesis. The error probability ℙerrsubscriptℙ𝑒𝑟𝑟{\mathbb{P}}_{err}blackboard_P start_POSTSUBSCRIPT italic_e i... | We also remark that the error exponent (Chernoff information) for the Neyman-Person test is tight, in the sense that a lower bound on the error probability for pairwise Neyman-Person test scales with the same exponent. | Without loss of generality, we assume that p1subscript𝑝1p_{1}italic_p start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT is the true probability distribution for the observation data 𝒀=𝒚𝒀𝒚{\boldsymbol{Y}}={\boldsymbol{y}}bold_italic_Y = bold_italic_y. Since the error probability ℙerrsubscriptℙ𝑒𝑟𝑟{\mathbb{P}}_{err}blackb... | C |
Based on above, there is a method to estimate drivers’ posture by subtracting acceleration of vehicle from the one of wearable sensor. Method 1: Subtracting acceleration of smart phone from the one of hitoe. This method subtracts acceleration of smart phone which a driver holds from acceleration of hitoe which a driver... | For drivers’ posture estimation in vehicles, we need to consider two things. The first is that acceleration data of wearable sensor includes acceleration of vehicle. The second is that considering safety management of vehicles, specific dangerous posture such as picking up things during driving needs to be detected. | For method 2 verification, hitoe wearer got on a regular bus and changed posture while seating like picking up things to confirm feasibility of posture detection analysis from hitoe acceleration data. Figure 3 shows acceleration data on a regular bus. From Fig.3, acceleration change from bus is mainly slight changes of... | Then, there is a method to detect acceleration patterns of specific posture such as picking up things by analyzing hitoe acceleration data. Method 2: Detecting specific posture patterns from hitoe acceleration data. Because drivers of bus and taxi are instructed to avoid sudden departure, acceleration of X-axis and Y-a... | This paper studied methods to estimate postures of drivers on vehicles using wearable acceleration sensor hitoe and conducted field tests. The method to subtract vehicle acceleration using hitoe and smart phone has problems of accuracy differences between them. On the other hand, posture changes such as picking things ... | C |
Step 2: Stream data of security camera movie is sent to a small computer in a shop. A small computer is a computer which has a certain degree of computation power, memory size and communication capability. For example, Rasbpberry Pi can be used for this to analyze images. | Step 3: A small computer cuts off each image from movie and extracts feature values from the image data. To extract feature values, libraries of dlib, OpenCV can be used. | We confirmed a precision ratio of security camera movie analysis by Jubatus stream processing. To estimate shoplifting actions, firstly we checked to judge users’ posture. We implemented Jubatus plug-in which extracts feature values from an image and Python client which judges users’ posture from one image of security ... | To extract feature values, we used dlib library which extracts 68 coordinate points of eyes, nose, mouth, shape of the face from face images. From 68 coordinate points, we separate to X and Y axis and we obtain 136 feature values. For obtained feature values, we normalize relative coordinate in each face image by deduc... | Step 4: A small computer detects customer’s suspicious behavior from feature values. To analyze stream data of feature values, we use online machine learning Jubatus[6]. Jubatus can detect not only shoplifting behavior based on pre-defined rules but also suspicious behavior based on machine learning. | A |
In the recent years, there has been incessant avidity in studying multi-user quantum communication because it offers opportunity to construct quantum networks. With quantum networks, quantum information between physically separate quantum systems can be transmitted. In fact, it forms a salient component of quantum comp... | In the recent years, there has been incessant avidity in studying multi-user quantum communication because it offers opportunity to construct quantum networks. With quantum networks, quantum information between physically separate quantum systems can be transmitted. In fact, it forms a salient component of quantum comp... | To sum it up, in this paper, we propose a quantum routing protocol with multihop teleportation for wireless mesh backbone networks. The quantum channel that linked the intermediate nodes has been realized through entanglement swapping based on four-qubit cluster state. After quantum entanglement swapping, quantum link ... | 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 are removable. In WMN, there exist quantum wireless cha... | Recently, a scheme for faithful quantum communication in quantum wireless multihop networks, by performing quantum teleportation between two distant nodes which do not initially share entanglement with each other, was proposed by Wang et al. MA2 . Xiong et al. MA3 proposed a quantum communication network model where a... | D |
As a processing of tracking cameras, Tacit Computing discovers the camera in which the child appears, and delivers movies of the camera to the parents’ mobile terminals when the parents request movies. And for watching, image analyzing functions such as OpenCV library are arranged on gateways or network edge SSE (Subsc... | We have proposed Tacit Computing technology [10] to utilize shared use of devices from various services for Open IoT era. Tacit Computing can discover devices with necessary data for users on demand based on live data of each device, and can use them. We have also implemented elemental technologies of Tacit Computing. | Tacit Computing enables ad-hoc devices using for users by live data discovering technology and device virtualization technology. However, we think discovering and using the device based on the situation at that time by previous Tacit Computing only answers the user’s needs only one time. | For example of Tacit Computing, let us consider tracking cameras. Tracking cameras are usage that movies of small children in schools or roads are taken by security cameras near the children and parents can see the movies by their mobile terminals. Tracking cameras can satisfy parents’ needs to confirm children’s safet... | Tracking cameras can be achieved by not only Tacit Computing but also solution services using security cameras and machine learning techniques. Therefore, we set a problem to be solved as ”providing continuous services that use devices discovered by Tacit Computing at reasonable prices”. | D |
Let Ui(k)subscript𝑈𝑖𝑘U_{i}(k)italic_U start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_k ) be the k𝑘kitalic_kth bit in the binary expansion of Xisubscript𝑋𝑖X_{i}italic_X start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT, thus X1=U1(1)/2+U1(2)/22+…subscript𝑋1subscript𝑈112subscript𝑈12superscript22…X_{1}=U... | We note that NLP is equivalent to finding an optimum partition (Voronoi partition) of ℝnsuperscriptℝ𝑛\mathbb{R}^{n}blackboard_R start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT, where each cell of the partition is associated with a unique lattice point and is the set of vectors which are closest to that lattice poin... | The partition of the Babai cell after two rounds of communication is shown in Fig. 10 along with a tree representation of the protocol. | Figure 2: The Babai partition (rectangular partition with solid lines) and the Voronoi partition (hexagonal partition with dotted lines) for a lattice in ℝ2superscriptℝ2\mathbb{R}^{2}blackboard_R start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT. The first stage of the algorithm determines the cell of the Babai partition whi... | Figure 10: Partition created by the infinite round protocol (a) after one round (b) after two rounds. (c) Protocol tree for the infinite-round protocol. | B |
The main limitation of this approach is that its formulation is based on the hypothesis that the human body’s mechanical impedance mainly determines the task dynamics. | Thus, they only apply to tasks where the environmental dynamics are negligible compared to the body impedance, which is not the case when there is contact with the ground. | We proposed a structure of a semi-autonomous controller organised in a hierarchical architecture that has a parallelism in the biological motor control Figure 6. At the apex of the hierarchy is the TS planner, which acts on the input of walking towards a target. The TS planning appears to be based on stereotyped optimi... | vCoRR𝑣𝐶𝑜subscript𝑅𝑅vCoR_{R}italic_v italic_C italic_o italic_R start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT and vCoRL𝑣𝐶𝑜subscript𝑅𝐿vCoR_{L}italic_v italic_C italic_o italic_R start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT are the projections ON THE GROUND OR ON THE FOOTSOLE? of the CoRs that are used ... | The dynamic motion primitives theory was developed as an extension of the motor primitives and, until now, it is unclear how they are connected[5]. Our theory is based on the integration of our task-space planner with the joint-space planner λ0−PMPsubscript𝜆0𝑃𝑀𝑃\lambda_{0}-PMPitalic_λ start_POSTSUBSCRIPT 0 end_PO... | A |
E𝐸Eitalic_E is partitioned into p𝑝pitalic_p disjoint sets E1,…,Epsubscript𝐸1…subscript𝐸𝑝E_{1},\ldots,E_{p}italic_E start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_E start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT, where |Ei|=risubscript𝐸𝑖subscript𝑟𝑖|E_{i}|=r_{i}| italic_E start_POSTSUBSCRIPT italic_i end_P... | Let C∗superscript𝐶C^{*}italic_C start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT denote the smallest value of the parameter C𝐶Citalic_C, | Hence, and from |X|=LP𝑋subscript𝐿𝑃|X|=L_{P}| italic_X | = italic_L start_POSTSUBSCRIPT italic_P end_POSTSUBSCRIPT, we get that the number of connected components is reduced by LPsubscript𝐿𝑃L_{P}italic_L start_POSTSUBSCRIPT italic_P end_POSTSUBSCRIPT. Then, | We will denote by k^^𝑘\hat{k}over^ start_ARG italic_k end_ARG the number of rounds performed by the algorithm (Steps 1-1). | We will denote by [p]delimited-[]𝑝[p][ italic_p ] the set {1,2,…,p}12…𝑝\{1,2,\ldots,p\}{ 1 , 2 , … , italic_p }. | D |
In order to assess running times of the algorithm we have performed tests on from 1 up to 8 GPUs on datasets with varying number of rows and columns. The GEO accession numbers of the datasets as well as run times of the algorithm are presented in Table 1. | Figure 1: Speedups obtained using multiple GPUs (GeForce GTX 1080 Ti) for the datasets from Table 1. | In order to assess running times of the algorithm we have performed tests on from 1 up to 8 GPUs on datasets with varying number of rows and columns. The GEO accession numbers of the datasets as well as run times of the algorithm are presented in Table 1. | Handling missing values. We introduce a very important feature which allows to remove the impact of missing values on the results of the method. As EBIC search is driven by counting of rows, a greater or equal relation between the values in columns used to capture missing values, instead of the real trends in the data.... | Table 1: Datasets used in the experiment as well as an average running time (in minutes) using a cluster of 8 GeForce GTX 1080 Ti GPUs. | D |
For the issue of preference evolution with unobservable preferences, see also Ely and Yilankaya (2001) and Güth and Peleg (2001). | Next, we show that if a pure-strategy profile is not a Nash equilibrium of the objective game, then it is not stable when preferences are almost unobservable. | a pure-strategy outcome can be stable if it is a strict Nash equilibrium or the unique Nash equilibrium of the objective game. | each of the three equilibrium outcomes can be stable supported by a materialist configuration with no observability. | We show that a Nash equilibrium of an objective game can be supported by stable materialist preferences if it is | D |
G⊢Σi⇒⋀rCirproves𝐺⇒subscriptΣ𝑖subscript𝑟subscript𝐶𝑖𝑟G\vdash\Sigma_{i}\Rightarrow\bigwedge\limits_{r}C_{ir}italic_G ⊢ roman_Σ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ⇒ ⋀ start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT italic_C start_POSTSUBSCRIPT italic_i italic_r end_POSTSUBSCRIPT. | Substituting the left sequents for each i,r𝑖𝑟i,ritalic_i , italic_r in the rule (‡)‡(\ddagger)( ‡ ) and then applying (L∗)(L*)( italic_L ∗ ), we obtain | Applying (R∧)limit-from𝑅(R\wedge)( italic_R ∧ ) on the left sequents and (L∧)limit-from𝐿(L\wedge)( italic_L ∧ ) on the right ones, we get for each i,j,r,s𝑖𝑗𝑟𝑠i,j,r,sitalic_i , italic_j , italic_r , italic_s: | Now, by the rules (R∗)(R*)( italic_R ∗ ) and (L→)(L\to)( italic_L → ) on the sequents (8), (9), and (10), we get | C_{ir},\Thetaitalic_G ⊢ roman_Γ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT , italic_φ ⇒ + start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ⋁ start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT italic_C start_POSTSUBSCRIPT italic_i italic_r end_POSTSUBSCRIPT , roman_Θ. Moreover, applying (L+)limit-from𝐿(L+)( italic_L + ) on ... | A |
Using this notation our main question becomes to calculate 𝔼[Xn]𝔼delimited-[]subscript𝑋𝑛\mathbb{E}\left[X_{n}\right]blackboard_E [ italic_X start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ] and 𝔼[Yn]𝔼delimited-[]subscript𝑌𝑛\mathbb{E}\left[Y_{n}\right]blackboard_E [ italic_Y start_POSTSUBSCRIPT italic_n end_POS... | We briefly describe the non-recursive part of the edge elimination procedures of Hougardy and Schroeder [3] and Jonker and Volgenant [4]. For both edge elimination precedures we fix an optimal tour and assume that an edge pq𝑝𝑞pqitalic_p italic_q is in the optimal tour. | For the probabilistic analysis of Hougardy and Schroeder, we first develop a new criterion for detecting useless edges. The new criterion detects fewer useless edges than the original, but it makes the analysis easier. The crucial property is that all edges that will be deleted by the new criterion will be deleted by t... | In this section we outline the key ideas of the previous edge elimination procedures and the probabilistic analysis of Hougardy and Schroeder. | After we first describe our model and notation for this paper, we give an outline of the key ideas of the edge elimination procedures from [3] and [4] and our results. | C |
ζ3(x,y)subscript𝜁3𝑥𝑦\displaystyle\zeta_{3}(x,y)italic_ζ start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ( italic_x , italic_y ) | ζ3(x,y)subscript𝜁3𝑥𝑦\displaystyle\zeta_{3}(x,y)italic_ζ start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT ( italic_x , italic_y ) | =sin(x)+cos(y).absent𝑥𝑦\displaystyle=\sin(x)+\cos(y).= roman_sin ( italic_x ) + roman_cos ( italic_y ) . | ζ1(x,y)subscript𝜁1𝑥𝑦\displaystyle\zeta_{1}(x,y)italic_ζ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ( italic_x , italic_y ) | ζ2(x,y)subscript𝜁2𝑥𝑦\displaystyle\zeta_{2}(x,y)italic_ζ start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ( italic_x , italic_y ) | B |
Utilization of contextual semantics which is significant for distinguishing objects of varying sizes. | We use FCN [7], SegNet [9], Stacked Hourglass Network (SHG) [12] and EncNet [13] as our baseline models. FCN is the generally used framework for semantic segmentation, and SegNet is an adaptation of FCN by replacing the decoder with a series of pooling and convolution layers. SHG and EncNet are compared with our CxtHGN... | We develop a novel Contextual Hourglass Network (CxtHGNet) for semantic segmentation of high-resolution aerial imagery. Our CxtHGNet can extract rich multi-scale features of the image and learn the contextual semantics in scenes, due to the incorporation of bottom-up, top-down inference across various scales, attention... | Besides the pixel-level information, how to utilize contextual information is a key point for semantic labeling. Contextual relationships provide valuable information from neighborhood objects. Recently, channel-wise [13], point-wise [14] attention mechanisms or their combination [15] have been utilized for exploiting ... | Recently, various deep neural networks structures have been utilized for semantic segmentation in aerial and medical imagery. In [2, 3, 4, 5, 6], Fully Convolutional Networks (FCN) [7] have been used as the backbone of their networks. Audebert et al. [8] further utilizes SegNet [9] for the segmentation task which is an... | D |
Denardo et al. (2013) Cowan and Katehakis (2015) Pike-Burke et al. (2018), Lattimore and Szepesvári (2018), Pike-Burke and Grunewalder (2017). | In the sequel we first establish in Theorem 5, a necessary asymptotic lower bound for the rate of increase of the regret function of f-UF policies. We then construct a class of “block f-UF” policies and provide conditions under which they are asymptotically optimal within the class of f-UF policies, achieving this asym... | Similar action constrained optimization problems also arise in MDPs cf. Feinberg (1994), Borkar and Jain (2014), queueing Hordijk and Spieksma (1989), | search-based and targeted advertising online learning, cf. Rusmevichientong and Williamson (2006), Agarwal et al. (2014) and references therein. | The updates for Φl(B^,θ¯¯^l)superscriptsubscriptΦ𝑙^𝐵superscript^¯¯𝜃𝑙\Phi_{l}^{(\hat{B},\hat{\underline{\underline{\theta}}}^{l})}roman_Φ start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT start_POSTSUPERSCRIPT ( over^ start_ARG italic_B end_ARG , over^ start_ARG under¯ start_ARG under¯ start_ARG italic_θ end_ARG end_AR... | B |
}_{g}(S_{r},v),\operatorname{dis}_{g}(S_{r},v)\neq+\infty\}.{ italic_g ∈ caligraphic_G | roman_dis start_POSTSUBSCRIPT italic_g end_POSTSUBSCRIPT ( italic_S , italic_v ) < roman_dis start_POSTSUBSCRIPT italic_g end_POSTSUBSCRIPT ( italic_S start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT , italic_v ) , roman_dis start_PO... | 1}(1+\epsilon)f^{*}(S_{\operatorname{opt}}).italic_f start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( italic_S start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ) ≥ over¯ start_ARG italic_x end_ARG ( caligraphic_R start_POSTSUBSCRIPT italic_l end_POSTSUBSCRIPT , italic_S start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ) - italic_ϵ ... | Now our objective function f∗(S)superscript𝑓𝑆f^{*}(S)italic_f start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( italic_S ) can be expressed as | It has been shown in [2] that the MP problem is monotone nondecreasing and submodular, and therefore the greedy algorithm provides a good approximation [17]. However, the greedy algorithm demands an efficient oracle of the objective function f∗(S)superscript𝑓𝑆f^{*}(S)italic_f start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCR... | should be an accurate estimate of f∗(S)superscript𝑓𝑆f^{*}(S)italic_f start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( italic_S ) when l𝑙litalic_l is sufficiently large. As a result, the subset S⊆V𝑆𝑉S\subseteq Vitalic_S ⊆ italic_V that can maximize x¯(ℛl,S)¯𝑥subscriptℛ𝑙𝑆\overline{x}(\operatorname{\mathcal{R}}_{l}... | B |
MobileNets are neural networks that perform efficiently. It can also be used on mobile devices and reach a fairly high accuracy [54, 55, 56, 57]. SSD [58, 59, 60] uses VGG16 [61] to extract feature maps. SSD classifies and locates objects in a single forward pass. MobileNet-SSD combines SSD and MobileNets which perform... | Figure 2: illustrates the trade-off between speed (FPS) and accuracy (MOTA) using different confidence thresholds.100% Threshold: Require detection for each frame, considered as baseline. 0% Threshold: Same as fixed frame skipping, never triggers detection based on confidence score but triggers when reaching the maximu... | MobileNets are neural networks that perform efficiently. It can also be used on mobile devices and reach a fairly high accuracy [54, 55, 56, 57]. SSD [58, 59, 60] uses VGG16 [61] to extract feature maps. SSD classifies and locates objects in a single forward pass. MobileNet-SSD combines SSD and MobileNets which perform... | SqueezeNet uses a squeeze layer and an expanded layer to reach a really fast performance. The paper on SqueezeNet provides a quantitative analysis to show that SqueezeNet can be 510 times fewer parameters to reach the same accuracy as AlexNet [62]. Using SqueezeNet, the system reaches the lowest MOTA (9.4%) but perform... | Deep learning-based lightweight detectors are designed to have a smaller number of parameters or require fewer computational passes compared to their heavier counterparts. While this translates to faster processing speeds, it typically comes at the expense of accuracy. In this paper, we utilize the YOLOv3 Tiny, MobileN... | C |
Robust Stability: The robotic system in Fig. 3 is robust and stable against the external disturbances, parameters uncertainties, and noises. | By inspecting the matrix Aesubscript𝐴𝑒A_{e}italic_A start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT and based on the boundedness of both e˙v,esubscript˙𝑒𝑣𝑒\dot{e}_{v,e}over˙ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_v , italic_e end_POSTSUBSCRIPT and F^esubscript^𝐹𝑒\hat{F}_{e}over^ start_ARG italic_F ... | 6666-DOF Impedance Control: In the presence of the applied force/desired impedance at the end-effector, the end-effector tracking error tends to zero as time tends to ∞\infty∞. | Force Estimation: The end-effector contact force has to be estimated with fast response and the estimation error tends to zero as the time tends to ∞\infty∞. | Fig. 7 shows the response of the system in the task space (the actual end-effector position and orientation can be found from the forward kinematics). From this figure, it is possible to recognize that the controller has good tracking of the desired trajectories of the end-effector (i.e., the tracking error tends to ze... | C |
Permutations are formed in a very similar fashion where we take our vectors visubscript𝑣𝑖v_{i}italic_v start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT and find their symbolic representation based on their ordinal ranking as explained in Section 1.1. The different permutation types can be viewed as an inequality-based ... | If the delay τ𝜏\tauitalic_τ is too small (e.g. τ=1𝜏1\tau=1italic_τ = 1 for a continuous dynamical system with a high sampling rate) the delay embedded reconstructed attractor will be clustered around the hyper-diagonal in ℝnsuperscriptℝ𝑛\mathbb{R}^{n}blackboard_R start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT. A... | Takens’ embedding theorem explains that, theoretically, any delay τ𝜏\tauitalic_τ would be suitable for reconstructing the original topology of the attractor; however, this has the requirement of unrestricted signal length with no additive noise in the signal [15]. Since this is rarely a condition found in real-world s... | In Fig. 14 we see that all of the methods reach a larger value of τ𝜏\tauitalic_τ, in comparison to the expert suggested τ=9𝜏9\tau=9italic_τ = 9 when the time series contains at least 300 data points. However, we see that the time domain method seems to be more robust to signal length compared to mutual information an... | We can now find the maximum significant frequency fmaxsubscript𝑓maxf_{\rm max}italic_f start_POSTSUBSCRIPT roman_max end_POSTSUBSCRIPT as the highest frequency in the Fourier spectrum with an amplitude greater than the specified cutoff. For this method to accurately function, it is required that there is some additive... | B |
Ekerå furthermore uses the simulator to estimate the number of runs n𝑛nitalic_n with tradeoff factor s≥1𝑠1s\geq 1italic_s ≥ 1 that are needed to solve for r𝑟ritalic_r with at least 99%percent9999\%99 % success probability when using lattice-based post-processing. | Shor originally introduced the order-finding algorithm for the purpose of factoring general integers N𝑁Nitalic_N via a classical reduction that follows from the work of Miller [16]: | In 1994, in a seminal work with profound cryptologic implications, Shor [29, 30] introduced polynomial-time quantum algorithms for factoring integers — via a reduction to order finding in cyclic subgroups of ℤN∗superscriptsubscriptℤ𝑁\mathbb{Z}_{N}^{*}blackboard_Z start_POSTSUBSCRIPT italic_N end_POSTSUBSCRIPT start_PO... | We have implemented the simulator for the purpose of heuristically evaluating the efficiency of the two classical post-processing algorithms described in Sect. 6. | Furthermore, Ekerå gives lower bounds on the probability of successfully recovering r𝑟ritalic_r from j𝑗jitalic_j in a single run of the quantum part of the order-finding algorithm, as a function of the search space in the classical post-processing part of the algorithm, and of the length of the control register in th... | A |
xi←ShardTransactions(Shard)←subscript𝑥𝑖𝑆ℎ𝑎𝑟𝑑𝑇𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛𝑠𝑆ℎ𝑎𝑟𝑑x_{i}\leftarrow ShardTransactions(Shard)italic_x start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ← italic_S italic_h italic_a italic_r italic_d italic_T italic_r italic_a italic_n italic_s italic_a italic_c italic_... | srsuperscript𝑠𝑟s^{r}italic_s start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT= AcknowledgeTransmission() | }^{s},t\right)\right]italic_W start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT ( italic_M start_POSTSUBSCRIPT italic_t - 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT ) = start_UNDERACCENT ( italic_x start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_s end_POSTSUPERSC... | Collect lists of srsuperscript𝑠𝑟s^{r}italic_s start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT for every Pisubscript𝑃𝑖P_{i}italic_P start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT | Verify cooperation of Pi∈CLsubscript𝑃𝑖superscript𝐶𝐿P_{i}\in C^{L}italic_P start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∈ italic_C start_POSTSUPERSCRIPT italic_L end_POSTSUPERSCRIPT using lists of srsuperscript𝑠𝑟s^{r}italic_s start_POSTSUPERSCRIPT italic_r end_POSTSUPERSCRIPT | A |
{\omega})\in\mathsf{dom}(f)italic_π start_POSTSUBSCRIPT roman_Σ end_POSTSUBSCRIPT ( italic_u start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ( italic_v start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT italic_ω end_POSTSUPERSC... | We define the notion of critical pattern for the 2DBT T~~𝑇\widetilde{T}over~ start_ARG italic_T end_ARG. We say that T~~𝑇\widetilde{T}over~ start_ARG italic_T end_ARG admits | We have established that f𝑓fitalic_f is continuous if and only if 𝒯~~𝒯\widetilde{\mathcal{T}}over~ start_ARG caligraphic_T end_ARG | continuous if and only if 𝒯𝒯\mathcal{T}caligraphic_T admits a strong critical pattern. If 𝒯𝒯\mathcal{T}caligraphic_T | Conversely, if f𝑓fitalic_f is continuous, 𝒯~~𝒯\widetilde{\mathcal{T}}over~ start_ARG caligraphic_T end_ARG admits a | D |
In Appendix A we give an example that shows that the number of transitions can be quadratic in |Q|𝑄|Q|| italic_Q |, even for UBAs with a strongly connected state space. We assume |Q|≤|δ|𝑄𝛿|Q|\leq|\delta|| italic_Q | ≤ | italic_δ |, as states without outgoing transitions can be removed. | In this paper we obtain a faster algorithm (recall that E𝐸Eitalic_E is the set of transitions in the Markov chain): | We define |δ|:=|{(q,r)∣∃a∈Σ:r∈δ(q,a)}|assign𝛿conditional-set𝑞𝑟:𝑎Σ𝑟𝛿𝑞𝑎|\delta|:=|\{(q,r)\mid\exists\,a\in\Sigma:r\in\delta(q,a)\}|| italic_δ | := | { ( italic_q , italic_r ) ∣ ∃ italic_a ∈ roman_Σ : italic_r ∈ italic_δ ( italic_q , italic_a ) } |, i.e., |δ|≤|Q|2𝛿superscript𝑄2|\delta|\leq|Q|^{2}| italic_δ | ≤ ... | There is a natural notion of an infinite random word over ΣΣ\Sigmaroman_Σ: in each step sample a letter from ΣΣ\Sigmaroman_Σ uniformly at random, e.g., if Σ={a,b}Σ𝑎𝑏\Sigma=\{a,b\}roman_Σ = { italic_a , italic_b } then choose a𝑎aitalic_a and b𝑏bitalic_b with probability 1/2121/21 / 2 each. | In this paper, ΣΣ\Sigmaroman_Σ may be a large set (of states in a Markov chain), so it is imperative to allow for multiple labels per transition. | D |
Name of game, plus citation which gives to name and rules we use (but is not necessarily the inventor of the game). | We use the word ‘instance’ of a game to refer a particular arrangement of cards for that game, usually after random shuffling. Most games are won by rearranging cards so as to place them in order on a set of ‘foundations’, typically from A to K within each suit: in some cases the player is given some cards already plac... | Number of cards initially placed in foundations, ∙∙\bullet∙ for hole being used, or S for Spider-type elimination of suits. Symbols Used: | We do automate the use of the dominance of Section 5.4.1 but only under strict conditions. First, it is disabled completely for games of more than one deck, for games with Spider-type building rules, or games like Gaps without either foundations or a hole. | A game is played with a number of complete ‘decks’ of cards, normally the standard deck with 13 cards of each of 4 suits. The rules of a game specify how the cards are placed before play starts: in the initial position some cards may be ‘hidden’ from the player, for example by being placed ‘face-down’. | B |
This manuscript introduces hyppo, a hypothesis package that provides various tests with high finite-sample statistical power on multivariate and nonlinear relationships. hyppo is a well-tested, multi-platform, Python 3 compatible library that allows users to conduct hypothesis tests on their data, and is also extensibl... | This manuscript introduces hyppo, a hypothesis package that provides various tests with high finite-sample statistical power on multivariate and nonlinear relationships. hyppo is a well-tested, multi-platform, Python 3 compatible library that allows users to conduct hypothesis tests on their data, and is also extensibl... | Inspired by the desire to allow for convenient use of these independence tests, hyppo has been developed as a hypothesis testing package. The package structure is modeled on the scikit-learn and energy R packages’ API. | The evaluation uses a spiral simulation with 1000 samples and 2 dimensions for each test and compares test statistics over 20 repetitions. Figure 1b shows the difference between the hyppo implementation of the independence test and the respective R package implementation of the independence test. | hyppo is an extensive and extensible open-source Python package for multivariate hypothesis testing. | B |
More recently, VRPSR value function approximations are made via neural networks. Joe and Lau (2020) show that neural nets can outperform the scenario-based method of Bent and Van Hentenryck (2004) as well as an approximate value iteration procedure. In the context of same-day delivery, Chen et al. (2022) use neural net... | The first set of experiments highlights the benefit of a Vehicle View. Figures 5 and 6 depict the results. Figure 5 displays the performance of each agent and of the benchmarks while Figure 6 shows the performance of each agent as a function of the number of training epochs. The expected number of serviced requests by ... | The state of a VRPSR game is the player’s view of the game world at an epoch. A view consists of the time bar plus the player’s field of vision. The player’s field of vision is the visible portion of the playable area. We consider four views, each of which is depicted in Figure 3. In the World View, the field of vision... | The performance disparity between the World Agent and the Vehicle Agent points to a Vehicle View as an important factor in modeling the VRPSR as a game. Vehicle Views allow agents to associate each pixel in the view with specific actions, e.g., pixels in the top half of the view require upward movement and pixels on th... | The vehicle routing problem with stochastic requests (VRPSR) dispatches a single vehicle to meet customer requests arriving at random times across a given operating horizon and at random locations across a known service area. The objective is to design a dynamic routing policy, beginning and ending at a depot, that max... | D |
Shin (2002) and, in the context of social learning, Dasaratha, Golub, and Hak (2023)). In these models, Bayesian agents’ beliefs are ranked by their precisions. The analogous number of signals aggregated is simply proportional to precision and so a signal-counting interpretation does not provide obvious additional insi... | Welch (1992)), however, the existence of such a ranking is not obvious and the signal-counting interpretation gives a distinct measure that considerably simplifies our analysis. | models on this dimension. A key contribution of our model is ranking networks where agents learn in the long run based on the rate of this learning, and this section concludes by defining a measure that will provide such a ranking for a class of generation networks. | number of independent private signals. This signal-counting interpretation gives a simple measure of accuracy in the binary-state setting studied in Banerjee (1992), Bikhchandani, Hirshleifer, and | networks. In our environment, rational actions are a log-linear function of observations and admit a signal-counting interpretation. Thus, we can measure the efficiency of learning in terms of the fraction of available signals incorporated | A |
Graph Kernels (GK): GK methods map graphs into a Hilbert space, which can be fed to downstream classifiers (e.g., Support Vector Machine (SVM)) to perform graph classification [10]. | The designs of kernels include neighborhood aggregation (e.g., Weisfeiler-Lehman [30]), extraction of subgraph patterns (e.g., Graphlet [31], and walks/paths (e.g., shortest-path [1] and random walk [14]). | DNN, graph kernel (Shortest Path (SP)) with SVM, and several state-of-the-art graph learning frameworks (i.e., graph2vec [26] and DGCNN [35], and GCN [18]) as baselines for comparisons. | 10.9%percent10.910.9\%10.9 % in accuracy, 9.1%percent9.19.1\%9.1 % in precision, 14.6%percent14.614.6\%14.6 % in recall, and 14.0%percent14.014.0\%14.0 % in F1-score. | thresholds on edges [13], we use a dual space and smooth kernels that can be described by the theory of traditional wavelet transform. | A |
We show for our selected species’ reference genomes, human (large), C. elegans (medium), yeast (small) the average execution time to remap a single read depending on the AirLift case. The execution time is shown for different versions of each reference genome (row) and is shown for the four remapping cases: 1) reads th... | Figure S1: Percentage of different annotations missed when remapping reads from an old reference (x-axis) to the latest reference (hg38), using a remapping tool that solely relies on existing chain files (e.g., UCSC LiftOver [27]) | Table S1: Annotations in the new reference not covered by reads when remapping reads across reference genomes with a remapping tool that solely relies on chain files (e.g., UCSC LiftOver). | Figure 1: Limitations of Existing Remapping Tools. Existing remapping tools correctly remap reads that mapped completely within a region indicated by the chain file (e.g., Read 2). However, these tools 1) cannot remap reads that mapped within a region in the old reference that does not appear in the new reference (e.g.... | Figure 5: AirLift execution time results. We show the execution time (log-scale y-axis) of running three remapping tools, CrossMap (blue), AirLift (orange), and LiftOver (green) on a read set to a new reference genome against the baseline (red) of fully mapping a read set to the new reference genome. We plot the execut... | A |
Abolghasemi, P. Et al. “Pay Attention! - Robustifying a Deep Visuomotor Policy Through Task-Focused Visual Attention” The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2019, pp. 4254-4262 | Visualizing what a neural network has learned poses many challenges. Multiple techniques for evaluating support features have recently been developed to provide insight into otherwise black box classifiers. Salience maps may be computed by simply observing output sensitivity to localized input perturbations (Zeiler and... | Bach et al. On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer-Wise Relevance Propagation,, PLoS ONE 2015 | Deep neural networks (DNNs) have transformed computational analysis across a variety of domains from robotic control devices (Abolghasemi 2019) to genomics (Zou et al. 2019) to neuroimaging (Douglas et al. 2013). Despite their success, DNNs can be susceptible to adversarial examples, or examples that are only slightly ... | Bach, S. Et al. “Controlling Explanatory Heatmap Resolution and Semantics via Decomposition Depth,” ICIP (2016) | D |
𝚒𝚗𝚒𝚝𝚒𝚗𝚒𝚝\mathtt{init}typewriter_init(T)𝑇(T)( italic_T ): Initializes the iterator and sets height h=0ℎ0h=0italic_h = 0. | 𝚑𝚊𝚜𝙽𝚎𝚡𝚝𝚑𝚊𝚜𝙽𝚎𝚡𝚝\mathtt{hasNext}typewriter_hasNext: Returns true exactly if nodes of height hℎhitalic_h | For any call of 𝚑𝚊𝚜𝙽𝚎𝚡𝚝𝚑𝚊𝚜𝙽𝚎𝚡𝚝\mathtt{hasNext}typewriter_hasNext, return (n′<n)superscript𝑛′𝑛(n^{\prime}<n)( italic_n start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT < italic_n ). If 𝚗𝚎𝚡𝚝𝚗𝚎𝚡𝚝\mathtt{next}typewriter_next is called with | 𝚗𝚎𝚡𝚝𝚗𝚎𝚡𝚝\mathtt{next}typewriter_next: Returns a choice dictionary containing nodes of height hℎhitalic_h | 𝚑𝚊𝚜𝙽𝚎𝚡𝚝()𝚑𝚊𝚜𝙽𝚎𝚡𝚝\mathtt{hasNext}()typewriter_hasNext ( ): Output 𝚝𝚛𝚞𝚎𝚝𝚛𝚞𝚎\mathtt{true}typewriter_true exactly if the | A |
Starting from t=15𝑡15t=15italic_t = 15 s, all drones start to change formation, and the arrow drawn in the figure becomes the direction of the next formation change. | This is the first fully autonomous, onboard fast and accurate relative localization scheme implemented on a team of 13 lightweight and resource-constrained aerial vehicles | Fig. 13 shows how a 5 robots team achieves a formation flight based on the proposed initialization method, relative localization and distributed control. | Fig. 15 demonstrates more experiments which all rely on the onboard relative localization, e.g., outdoor autonomous formation flight of three Crazyflies with wind disturbances, and autonomous leader-follower flight through a window based on the visual object detection on the leader and non-visual relative localization ... | Figure 15: More flight experiments based on the relative localization. Left: outdoor formation flights of three Crazyflies. Right: leader-follower flight. | C |
We first validate the two hypotheses by measuring the performance change between the sequential questions for each patient case using the following statistics: | Confidence: frequency of participants choosing “Definitely YES/NO” as oppose to “Rather YES/NO” or “I don’t know”. | These three combinations of evidence were shown sequentially so that the participant could change their answer to the pivotal question of class prediction correctness. For answers, we chose a 5 point Likert scale consisting of “Definitely/Rather YES/NO” and “I don’t know”. On purpose, half of the presented observations... | To analyze the results in detail, we deliver the following visualizations. Figure 13 presents specific answers given by the participants at each step of the questionnaire. Participants are clustered based on their answers with hierarchical clustering using the Manhattan distance with complete linkage, which is the best... | Accuracy: frequency of participants choosing “Definitely/Rather YES” when the prediction was accurate and “Definitely/Rather NO” when the prediction was wrong. | D |
The levels of activity of the many pump and dump groups in the Internet differ considerably. The most active ones perform roughly one pump and dump operation a day. Less active groups perform one operation a week. Other groups perform operations only when they believe the market conditions are good. The steps during th... | The announce is repeated several times, more frequently as the starting time of the operation gets closer. | A few days or hours before the operation the admins announce that the pump and dump will happen and communicate which is the exchange that will be used, the exact starting time of the operation, and whether the operation will be FFA (Free for All—everybody gets the message at the same time) or Ranked (VIPs and members ... | Pump and dumps groups have leaders (or admins) that administrate the group, and a hierarchy of members. If a member is higher in the hierarchy, he gets the message that starts the pump by revealing the target cryptocurrency a few moments earlier than lower ranked members. This way, the member has higher probability to ... | When the pump starts, the target cryptocurrency is revealed to the members of the group. The exact time depends on the position in the hierarchy. Usually, the name of the cryptocurrency is contained in an image that is obfuscated in a way that only humans can read it quickly. Fig. 2 shows an example, a message that ins... | B |
The code C𝐶Citalic_C is convex if the Uνsubscript𝑈𝜈U_{\nu}italic_U start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT are convex. | A finite information structure (S,M)𝑆𝑀(S,M)( italic_S , italic_M ) is a pair of a thin category S𝑆Sitalic_S, as in Definition 12 | The probability space PCsubscript𝑃𝐶P_{C}italic_P start_POSTSUBSCRIPT italic_C end_POSTSUBSCRIPT associated to a binary code C𝐶Citalic_C is given by | The code C𝐶Citalic_C is convex if the Uνsubscript𝑈𝜈U_{\nu}italic_U start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT are convex. | Given a binary convex code C𝐶Citalic_C, there is a finite information structure (S,M)𝑆𝑀(S,M)( italic_S , italic_M ) and a | D |
Neurotechnology not only has the potential to impact human rights, but is can also impact autonomy, confidentiality and protection. Note that it is possible to obtain information through BCIs that can be extracted to reveal security breaches [26]. Neurotechnology such as BCI relies on multiple types of probabilistic in... | While neurotechnology has the can help achieve human augmentation, it also has the potential to impact human rights [22]. Three of the areas which neurotechnology is said to impact is the right to mental integrity, freedom of thought, and freedom from discrimination. The right to mental integrity is a concern with neur... | Whether it is data hostage situation of the data from a TMS or malicious brain-hacking of a neuroprosthetic, given the risks associated with physicians and surgeons using neurotechnology for augmentations along with the impact that augmentation has on people in general, there is no doubt that there is a chance that the... | The other way in which physicians or surgeons can be discriminated is in an instance where either malicious brain-hacking or a data hostage leading, with either of them leading to data sharing occurs. What makes doctors neural data valuable is that the doctors are known for being very well off financially. With proper ... | Given the value of neural information, these motivate malicious agents, companies and corporations to perform malicious brain-hacking, or retrieve, aggregate disseminate and use the information of the neurotechnology users without their informed consent. In the case of malicious brain-hacking, after a malicious agent h... | D |
The algorithm is called the Wiedemann XL algorithm and is used for the direct attack against Rainbow in [25]. | For a target degree d∈ℤ≥0𝑑subscriptℤabsent0d\in\mathbb{Z}_{\geq 0}italic_d ∈ blackboard_Z start_POSTSUBSCRIPT ≥ 0 end_POSTSUBSCRIPT, the XL (eXtended Linearization) algorithm generates a new system of degree d𝑑ditalic_d by multiplying the system f1,…,fmsubscript𝑓1…subscript𝑓𝑚f_{1},\dots,f_{m}italic_f start_POSTSUB... | The XL algorithm with respect to a target degree d𝑑ditalic_d generates the Macaulay matrix of a degree d𝑑ditalic_d whose columns correspond to the monomials of degree d𝑑ditalic_d. | For a multi-graded polynomial system, we can naturally consider the XL algorithm that generates the Macaulay matrix whose columns correspond to the monomials of degree 𝐝∈ℤ≥0s𝐝superscriptsubscriptℤabsent0𝑠{\bf d}\in\mathbb{Z}_{\geq 0}^{s}bold_d ∈ blackboard_Z start_POSTSUBSCRIPT ≥ 0 end_POSTSUBSCRIPT start_POSTSUPERS... | As mentioned in Subsection 2.2, the XL algorithm generates the Macaulay matrix of degree d𝑑ditalic_d and its complexity is estimated as (4). | B |
Liu, D., Yang, L.T., Wang, P., Zhao, R., Zhang, Q.: Tt-tsvd: A multi-modal tensor train decomposition with its application in convolutional neural networks for smart healthcare. | ACM Transactions on Multimedia Computing, Communications, and Applications (TOMM) 18(1s), 1–17 (2022) | In: Proceedings of International Conference on Computer Graphics and Interactive Techniques’ ACM, pp. 689–694 (2004) | ACM Transactions on Multimedia Computing, Communications, and Applications (TOMM) 18(1s), 1–17 (2022) | ACM Transactions on Multimedia Computing, Communications, and Applications (TOMM) 18(1s), 1–17 (2022) | A |
We prove this result for a general class of games, in which the receiver has two actions (denoted A and R for consistency). Moreover, sender and receiver can have utilities us,ur:{A,R}×Θ→ℝ:subscript𝑢𝑠subscript𝑢𝑟→𝐴𝑅Θℝu_{s},u_{r}:\{A,R\}\times\Theta\to\mathbb{R}italic_u start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIP... | We conjecture that our results can be strengthened to the refined concept of sequential equilibrium (which was studied in [16, 31, 32]) using suitable sequences of belief systems. For simplicity, we here stick to the more straightforward notion of Bayes-Nash equilibrium. | Rubinstein [16] introduce the problem of constrained delegation. They show, among other things, that the optimal decision scheme in constrained delegation is deterministic. Furthermore, they prove that there is always a Bayes-Nash equilibrium where the receiver plays the optimal decision scheme from constrained delegat... | For the constrained equilibrium problem, we show that a Bayes-Nash equilibrium can always be computed in polynomial time by repeatedly solving a maximum flow problem. We compare the utility obtained in an equilibrium with the one achievable with commitment power, for the sender and the receiver, respectively. Formally,... | More formally, for the price of anarchy we bound the ratio of the optimal utility achievable with commitment over the worst utility in any Bayes-Nash equilibrium. For the price of stability we bound the ratio of the optimal utility achievable with commitment over the best utility in any Bayes-Nash equilibrium. | A |
Here, {hk}subscriptℎ𝑘\{h_{k}\}{ italic_h start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT } are the hidden/latent states and its evolution is governed by a recursive application of a feed-forward layer with activation σ𝜎\sigmaitalic_σ, and y^ksubscript^𝑦𝑘\hat{y}_{k}over^ start_ARG italic_y end_ARG start_POSTSUBSCRIPT... | In this paper, we make a step in this direction by studying the approximation and optimization properties of RNNs. Compared with the static feed-forward setting, the key distinguishing feature here is the presence of temporal dynamics in terms of both the recurrent architectures in the model and the dynamical structure... | Here, we adopt a continuous-time approach in order gain access to more quantitative tools, including classical results in approximation theory and stochastic analysis, which help us derive precise results in approximation rates and optimization dynamics. The extension of these results to discrete time may be performed ... | The model (2) is not easy to analyze due to its discrete iterative nature. Hence, here we employ a continuous-time idealization that replaces the time-step index k𝑘kitalic_k by a continuous time parameter t𝑡titalic_t. This allows us to employ a large variety of continuum analysis tools to gain insights to the learnin... | Correspondingly, we define a continuous version of (2) as a hypothesis space to model continuous-time functionals | C |
Finally, it would be interesting to see if some of the ideas introduced in this paper can be used to decide whether there is a 7878\frac{7}{8}divide start_ARG 7 end_ARG start_ARG 8 end_ARG-approximation algorithm for MAX SAT. What makes MAX SAT potentially easier than MAX NAE-SAT is that we can take advantage of indivi... | We thank Ryan O’Donnell for sharing the code used to generate the experimental results in [29]. We also thank the anonymous reviewers for numerous useful comments. Some plots in this paper were made using Numpy [17] and Matplotlib [20]. | All the previous experimental results (including the previous state of the art results of Avidor et al. [7]) only considered monotone rounding functions f:ℝ→[−1,1]:𝑓→ℝ11f:\mathbb{R}\to[-1,1]italic_f : blackboard_R → [ - 1 , 1 ]. This was for good reason, as for MAX CUT, and our new results for MAX NAE-{3}3\{3\}{ 3 }-... | To help illustrate our techniques, we also perform this analysis for the simpler case of MAX-CUT, giving an alternative description for the optimal rounding function found by O’Donnell and Wu [29]. | Using MATLAB, we implemented a search to find the optimal 𝐟^^𝐟\hat{\mathbf{f}}over^ start_ARG bold_f end_ARG, for various choices of α∈[0,1]𝛼01\alpha\in[0,1]italic_α ∈ [ 0 , 1 ], ρ∈[−1,0]𝜌10\rho\in[-1,0]italic_ρ ∈ [ - 1 , 0 ], and (for MAX NAE-{3}3\{3\}{ 3 }-SAT) ρ0∈{max(−13,ρ),0}subscript𝜌013𝜌0\rho_{0}\in\{\max... | A |
(2nnlognm)≤2O(Nlog2Nm).binomial2𝑛𝑛𝑛𝑚superscript2𝑂𝑁superscript2𝑁𝑚\binom{2n}{\frac{n\log n}{\sqrt{m}}}\leq 2^{O(\frac{N\log^{2}N}{\sqrt{m}})}.( FRACOP start_ARG 2 italic_n end_ARG start_ARG divide start_ARG italic_n roman_log italic_n end_ARG start_ARG square-root start_ARG italic_m end_ARG end_ARG end_ARG ... | Thus the probability that all of those sets I𝐼Iitalic_I are covered by a triple in S𝑆Sitalic_S is overwhelming. | We get that for the remaining S𝑆Sitalic_S, |S|≤O(mn)𝑆𝑂𝑚𝑛|S|\leq O(mn)| italic_S | ≤ italic_O ( italic_m italic_n ), and with high probability, all subsets of U𝑈Uitalic_U of size (n/m)log(n)𝑛𝑚𝑛(n/\sqrt{m})\log(n)( italic_n / square-root start_ARG italic_m end_ARG ) roman_log ( italic_n ) are covered by S𝑆S... | For any three fixed elements i,j,k∈I𝑖𝑗𝑘𝐼i,j,k\in Iitalic_i , italic_j , italic_k ∈ italic_I which are pairwise distinct, the probability that {i,j,k}𝑖𝑗𝑘\{i,j,k\}{ italic_i , italic_j , italic_k } is not in S𝑆Sitalic_S is 1−Nm3|T|≤1−2mN21𝑁𝑚3𝑇12𝑚superscript𝑁21-\frac{Nm}{3|T|}\leq 1-\frac{2m}{N^{2}}1 - div... | The remaining subsets I𝐼Iitalic_I of U𝑈Uitalic_U of size n(logn)/m𝑛𝑛𝑚n(\log n)/\sqrt{m}italic_n ( roman_log italic_n ) / square-root start_ARG italic_m end_ARG are still covered by the remaining triples of S𝑆Sitalic_S as long as they were before we shrank U𝑈Uitalic_U. | A |
Recursive functions, more specifically referred to as μ𝜇\muitalic_μ-recursive functions, form a special subset of the set ⋃n=0∞{f:ℕn↪ℕ}superscriptsubscript𝑛0conditional-set𝑓↪superscriptℕ𝑛ℕ\bigcup_{n=0}^{\infty}\big{\{}f:\mathbb{N}^{n}\hookrightarrow\mathbb{N}\big{\}}⋃ start_POSTSUBSCRIPT italic_n = 0 end_POSTSUBSCR... | In order to investigate Fekete’s lemma in view of computability, we apply the theory of Turing machines [37, 39] and recursive functions [24]. For brevity, we restrict ourselves to an informal description. A comprehensive formal introduction on the topic may be found in [31, 41, 34, 29]. | An essential component in proving uncomputability of some kind is the notion of recursive and recursively enumerable sets, which we will introduce in the following. | In the following, we will introduce some definitions from computable analysis [41, 34, 29], which we will apply subsequently. | Subsequently, we will make use of a generalized version of Lemma 16: the established characterization of Σ1subscriptΣ1\Sigma_{1}roman_Σ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT and Π1subscriptΠ1\Pi_{1}roman_Π start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT extends to the suprema and infima of computable sequences of computable ... | C |
With the optimality of parallel privatization established, the original problem of finding the optimal privacy-utility tradeoff can be decomposed into multiple privacy funnel problems, each of which is associated with a different weighting. Each privacy funnel problem only involves a single component of the raw data ve... | Note that in the above definition, L∗superscript𝐿L^{*}italic_L start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT is not a function of the released rate R𝑅Ritalic_R. Instead, it is the minimum leakage with arbitrarily large released rate. The impact of the released rate and the sufficient condition to achieve the optimal pr... | In addition to the privacy and utility, the released rate, which represents the necessary number of bits per letter to transmit the privatized data, is also an important metric of a privatization mechanism as mentioned in Section II-A. We have studied the optimal tradeoff between privacy and utility. The next interesti... | When the utility requirement is below the threshold, there exists a zero-leakage privatization. When the utility requirement is above the threshold, the minimum privacy leakage is shown to be linearly proportional to the utility requirement. With the closed-form solution to each privacy funnel problem, it remains to fi... | Due to the lack of information of which task to be carried out, a robust privatization based on a given set of possible tasks is considered. We first derive the single-letter characterization of the optimal privacy-utility tradeoff. By applying log-loss distortion as the utility metric, the minimum privacy leakage prob... | C |
{{Unit}}}}}}}= ( ( italic_Unit ⊎ italic_Unit ) ⊎ ( ( ( sansserif_BtT start_POSTSUPERSCRIPT sansserif_fE end_POSTSUPERSCRIPT start_POSTSUBSCRIPT sansserif_1 ; italic_Bool end_POSTSUBSCRIPT ) × sansserif_BtT start_POSTSUPERSCRIPT sansserif_fE end_POSTSUPERSCRIPT start_POSTSUBSCRIPT sansserif_1 ; italic_List start_POSTSUB... | =((𝑈𝑛𝑖𝑡⊎𝑈𝑛𝑖𝑡)⊎(((𝐵𝑜𝑜𝑙⊎𝑈𝑛𝑖𝑡)×𝑈𝑛𝑖𝑡)⊎𝑈𝑛𝑖𝑡))⊎𝑈𝑛𝑖𝑡absent⊎⊎⊎𝑈𝑛𝑖𝑡𝑈𝑛𝑖𝑡⊎⊎𝐵𝑜𝑜𝑙𝑈𝑛𝑖𝑡𝑈𝑛𝑖𝑡𝑈𝑛𝑖𝑡𝑈𝑛𝑖𝑡\displaystyle=\mathit{{\color[rgb]{1,0.37,1}\definecolor[named]{pgfstrokecolor% | =((𝑈𝑛𝑖𝑡⊎𝑈𝑛𝑖𝑡)⊎(((𝐵𝑜𝑜𝑙⊎𝑈𝑛𝑖𝑡)×𝖡𝗍𝖳𝟢;𝐿𝑖𝑠𝑡B1𝖿𝖤)⊎𝑈𝑛𝑖𝑡))⊎𝑈𝑛𝑖𝑡absent⊎⊎⊎𝑈𝑛𝑖𝑡𝑈𝑛𝑖𝑡⊎⊎𝐵𝑜𝑜𝑙𝑈𝑛𝑖𝑡subscriptsuperscript𝖡𝗍𝖳𝖿𝖤0superscriptsubscript𝐿𝑖𝑠𝑡𝐵1𝑈𝑛𝑖𝑡𝑈𝑛𝑖𝑡\displaystyle=\mathit{{\color[rgb]{1,0.37,1}\definecolor[named]{pgfstrokecolor% | =𝖡𝗍𝖳𝟥;𝑈𝑛𝑖𝑡⊎(𝐵𝑜𝑜𝑙×𝐿𝑖𝑠𝑡B)𝖿𝖤absentsubscriptsuperscript𝖡𝗍𝖳𝖿𝖤3⊎𝑈𝑛𝑖𝑡𝐵𝑜𝑜𝑙subscript𝐿𝑖𝑠𝑡𝐵\displaystyle=\mathsf{{\color[rgb]{0,0.5,1}\definecolor[named]{pgfstrokecolor}% | =((𝑈𝑛𝑖𝑡⊎𝑈𝑛𝑖𝑡)⊎(((𝖡𝗍𝖳𝟣;𝐵𝑜𝑜𝑙𝖿𝖤)×𝖡𝗍𝖳𝟣;𝐿𝑖𝑠𝑡B𝖿𝖤)⊎𝑈𝑛𝑖𝑡))⊎𝑈𝑛𝑖𝑡absent⊎⊎⊎𝑈𝑛𝑖𝑡𝑈𝑛𝑖𝑡⊎subscriptsuperscript𝖡𝗍𝖳𝖿𝖤1𝐵𝑜𝑜𝑙subscriptsuperscript𝖡𝗍𝖳𝖿𝖤1subscript𝐿𝑖𝑠𝑡𝐵𝑈𝑛𝑖𝑡𝑈𝑛𝑖𝑡\displaystyle=\mathit{{\color[rgb]{1,0.37,1}\definecolor[named]{pgfstrokecolor% | B |
Our contributions. To identify the most fundamental factors causing OoD failure, our strategy is to (a) study tasks that are “easy” to succeed at, and (b) to demonstrate that ERM relies on spurious features despite how easy the tasks are. More concretely: | a class of easy-to-learn tasks, we enumerate a set of constraints that the tasks must satisfy; notably, this class of tasks will encompass the empirical example described above. | In particular, we empirically and theoretically demonstrate how ERM can rely on the spurious feature even in much easier tasks where these explanations would fall apart: these are tasks where unlike in the first model (a) the invariant feature is fully predictive and unlike in the second model, (b) the invariant featur... | Our contributions. To identify the most fundamental factors causing OoD failure, our strategy is to (a) study tasks that are “easy” to succeed at, and (b) to demonstrate that ERM relies on spurious features despite how easy the tasks are. More concretely: | We formulate a set of constraints on how our tasks must be designed so that they are easy to succeed at (e.g., the invariant feature must be fully predictive of the label). Notably, this class of easy-to-learn tasks | D |
In the proof of our structure theorem (Theorem 3.3), we may assume without loss of generality that r⩾128d𝑟128𝑑r\geqslant 128ditalic_r ⩾ 128 italic_d, as otherwise the claim can be satisfied by any known constant-approximation. We will call π𝜋\piitalic_π a tour; the proof is analogous when π𝜋\piitalic_π is a Steine... | To construct the patched tour π′superscript𝜋′\pi^{\prime}italic_π start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT, apply the above patching on π𝜋\piitalic_π in each | Step 5 on π′superscript𝜋′\pi^{\prime}italic_π start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT can only decrease the total weight of π′superscript𝜋′\pi^{\prime}italic_π start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT. This concludes | We construct the tour π′superscript𝜋′\pi^{\prime}italic_π start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT by iteratively processing all crossings per grid | 3.3 Constructing the patched tour π′superscript𝜋′\pi^{\prime}italic_π start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT and analyzing its crossings | C |
},\theta_{v})italic_η start_POSTSUBSCRIPT italic_c end_POSTSUBSCRIPT + italic_γ italic_V start_POSTSUPERSCRIPT italic_π start_POSTSUBSCRIPT italic_θ end_POSTSUBSCRIPT end_POSTSUPERSCRIPT ( italic_s start_POSTSUBSCRIPT italic_c + 1 , italic_t end_POSTSUBSCRIPT , italic_θ start_POSTSUBSCRIPT italic_v end_POSTSUBSCRIPT ) ... | Policy gradient method [29] is used to train the actor-critic policy. Here, we describe the main steps of the algorithm. | Finally, we note that the critic is only used at the training phase to help the actor converge to the optimal policy. | where α𝛼\alphaitalic_α is the learning rate. To compute the advantage A(sc,t,ac,t)𝐴subscript𝑠𝑐𝑡subscript𝑎𝑐𝑡A(s_{c,t},a_{c,t})italic_A ( italic_s start_POSTSUBSCRIPT italic_c , italic_t end_POSTSUBSCRIPT , italic_a start_POSTSUBSCRIPT italic_c , italic_t end_POSTSUBSCRIPT ) for a given action, we need to estima... | The formulated problem is then decoupled into two subproblems which are solved online per chunk. The first is the physical layer subproblem whose objective is to maximize the download rates for each user while ensuring fairness. The second is the application layer subproblem whose objective is to use the achievable dow... | B |
\right)-\left(\frac{a}{a+1}\right)^{2}q_{i}^{2}.( divide start_ARG italic_a end_ARG start_ARG italic_a + 1 end_ARG ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ( divide start_ARG italic_c italic_q start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT + italic_q start_POSTSUBSCRIPT ... | Now we centre our attention on the score parameter for the beta-CoRM and the score parameters for the generalised versions, since as detailed throughout the paper these parameters play a vital role in the feature selection step. In Table 8 we first present the median and credible interval of the score parameter for the... | By doing so, the set of jumps pisubscript𝑝𝑖p_{i}italic_p start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT can be thought as the probability that an observation regardless of the class has the corresponding n𝑛nitalic_n-gram, and for each of the d𝑑ditalic_d correlated groups these weights are perturbed by the scores mj... | Now that the discrete beta-CoRM approach for grouped binary matrices has been fully described, in this section we present a generalisation of the model that yields a natural feature selection procedure which will be particularly useful if the feature space is a high-dimensional object and our goal is discrimination abo... | Working with hierarchies of discrete nonparametric priors has become quite popular since it allows the so-called effect of sharing of information. In this paper, we centre our attention on the class of compound random measures (Griffin and Leisen, , 2017, 2018) as the discrete nonparametric prior. We believe that compo... | C |
(2) The AutoCluster system. AutoCluster enables the auto-optimisation of risk clustering adapted onto data. Various notions of clustering algorithms and similarity measures are tested. A loss function is designed that considers the clustering performance in terms of internal quality, inter-cluster variation, and model ... | (3) Strategies to improve imbalanced clustering. Firstly, an internal quality metric for imbalanced clustering is proposed, namely bSI𝑏𝑆𝐼bSIitalic_b italic_S italic_I, which is demonstrated to be more appropriate than existing CVIs. Secondly, an unsupervised feature selection method, namely EMRI, is proposed to id... | A rectifier function f(x)𝑓𝑥f(x)italic_f ( italic_x ) is designed to inhibit information of sufficient safety x∈S𝑥𝑆x\in Sitalic_x ∈ italic_S, by a weight ϕ∈[0,1)italic-ϕ01\phi\in[0,1)italic_ϕ ∈ [ 0 , 1 ), thus the learning attentions are pushed onto the risk domain, which can be regarded as a cost-sensitive strateg... | Features play a key role in improving the quality of machine learning, which serves to bridge the gap between raw data and algorithm inputs [28]. For risk clustering, feature extraction is expected to derive and construct information that is effective to distinguish between risk and safety. High interpretability is als... | A way of risk detection is by finding patterns that do not directly conform to expected safety [11]. Clustering has an advantage in discovering data patterns from multiple dimensions, which is promising to detect outliers as the risk and anomaly instances, under the premise that majority instances are safe and normal. ... | A |
Among signal processing, the time-domain finite-impulse response filter performs processing in a finite time on the output when an impulse function is input to a system. When considering applications that transfer signal data from devices over the network, to reduce network costs, it is assumed that signal processing s... | The proposed method behaves as follows (Figure 1). When the code is input, the syntax is analyzed and the loop statement is determined. By adding #pragma omp parallel for to the loop statement, OpenMP code that specifies parallel processing is created. Here, the gene pattern is set to 1 when parallel processing is perf... | Based on these situations, I propose the order of verification with six offloads is as follows; many core CPU function block offload, GPU function block offload, FPGA function block offload, many core CPU loop statement offload, GPU loop statement offload, FPGA loop sentence offload. Offload verifications are performed... | In this experiment, the implementation receives codes, it parses by Clang [45] and verifies offloading of function block and loop statements for three offloading destinations of GPU, FPGA and many core CPU. Based on six verifications, the implementation selects or creates a high performance pattern and measures the per... | For 3 applications, Figure 4 shows the processing time by a single core of CPU, which device and which method was used for offloading, the offload processing time, the degree of performance improvement, and the results of offloading to another device. The degree of performance improvement shows how much improve process... | C |
A schematic representation of the response mechanism to the two quantities of explosive is shown in Figure 16. | Assuming a planar shock wave impinging the front surfaces at the same time, we study the response of a multi-drum column with a circular cross-section. Figure 22 and 23 display the displacement and velocity, at several monitoring points, of a column with circular cross-section under 200200200200 kg and 400400400400 kg ... | The loading force is characterized by its maximum specific thrust 𝒫𝒫\mathcal{P}caligraphic_P and the maximum specific impulse ℐℐ\mathcal{I}caligraphic_I. For targets small enough to assume that the blast wave acts simultaneously and uniformly on the impinged surfaces, the maximum specific thrust and impulse can be co... | By relying on the simplified approach of considering a planar shock wave impinging only the front surface of the structure, we investigate the dynamic response and the validity of the proposed scaling laws for deformable multi-block masonry structures. | The more detailed characterization of blast loads is here adopted and the scaling laws are tested. In particular, we consider the spatial and temporal effects of an hemispherical shock wave. More complex phenomena than those considered in deriving the similarity laws are thus accounted for. In particular, the shock wav... | C |
Ecsuperscript𝐸𝑐{E^{c}}italic_E start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT representation dimension | Etsuperscript𝐸𝑡E^{t}italic_E start_POSTSUPERSCRIPT italic_t end_POSTSUPERSCRIPT representation dimension | Ecbtsuperscript𝐸𝑐𝑏𝑡{E^{cbt}}italic_E start_POSTSUPERSCRIPT italic_c italic_b italic_t end_POSTSUPERSCRIPT representation dimension | Ebsuperscript𝐸𝑏E^{b}italic_E start_POSTSUPERSCRIPT italic_b end_POSTSUPERSCRIPT representation dimension | Ecsuperscript𝐸𝑐{E^{c}}italic_E start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT representation dimension | C |
\mathcal{P}).italic_h ( over¯ start_ARG caligraphic_P end_ARG ) = italic_C + divide start_ARG 1 end_ARG start_ARG italic_p start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG ( italic_u start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT - italic_l start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ) start_POSTSUPERSCRIPT 2 end... | for all j∈{1,2,…,p}𝑗12…𝑝j\in\{1,2,\dots,p\}italic_j ∈ { 1 , 2 , … , italic_p }. It holds that 𝒫¯¯𝒫\bar{\mathcal{P}}over¯ start_ARG caligraphic_P end_ARG is a solution to (35). | Since 𝒫𝒫\mathcal{P}caligraphic_P was an arbitrary feasible point for the optimization, this implies that 𝒫¯¯𝒫\bar{\mathcal{P}}over¯ start_ARG caligraphic_P end_ARG is a solution to the optimization. | To prove the result, we show that the proposed 𝒫¯¯𝒫\bar{\mathcal{P}}over¯ start_ARG caligraphic_P end_ARG is feasible for the optimization, and that h(𝒫¯)≤h(𝒫)ℎ¯𝒫ℎ𝒫h(\bar{\mathcal{P}})\leq h(\mathcal{P})italic_h ( over¯ start_ARG caligraphic_P end_ARG ) ≤ italic_h ( caligraphic_P ) for all feasible 𝒫𝒫\mathcal... | i\neq k\end{subarray}}^{n_{x}}(u_{i}-l_{i})^{2}italic_C ≔ ∑ start_POSTSUBSCRIPT start_ARG start_ROW start_CELL italic_i = 1 end_CELL end_ROW start_ROW start_CELL italic_i ≠ italic_k end_CELL end_ROW end_ARG end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_n start_POSTSUBSCRIPT italic_x end_POSTSUBSCRIPT end_POSTSUPERSCRI... | B |
TLS 1.3 handshake involves multiple steps, including Client_Hello, Server_Hello, certificate exchanges, and verifications. Client_Hello and Server_Hello contain nonce and (EC)DHE𝐸𝐶𝐷𝐻𝐸(EC)DHE( italic_E italic_C ) italic_D italic_H italic_E parameters to generate a handshake secret. Subsequent messages are encry... | Blockchain uses consensus mechanisms and linked blocks to maintain data integrity [15]. BE-RAN introduces a global blockchain address (BC ADD) as a universal identifier for UEs and RAN elements, enabling user-centric identity management and mutual authentication. This approach builds upon previous work in blockchain-en... | The computational overhead is measured by the execution time of protocols, conducted on Ubuntu 20.04.1 4GB RAM, with 4 Cores at 4.2 GHz virtualized on a PC with Windows 10 installed. With the same physical environment, the computational overhead is measurable by comparing the execution time on the same platform, listed... | Based on TLS 1.3, IKEv2, and NIST standards, we assume 256-bit nonces and hash outputs, 3072-bit public keys for finite-field cryptography, 256-bit private keys, and 256-bit keys for ECC. BC ADD length is assumed to be 272 bits. X.509 v3 certificates are 699 bytes, and IPv6 addresses (128 bits) replace IKEv2 IDs. | BeMutual requires only 2 signals, compared to 4 for IKEv2 and 9 for TLS 1.3. Environment overhead, particularly for BE-RAN, depends on the underlying blockchain platform and consensus mechanism. For static BE-RAN deployment, user BC ADD synchronization is assumed, minimizing additional costs. | D |
In [9], HS present an easy-to-understand algorithm to calculate a minimum planar linear arrangement for any free tree in linear time. The idea behind the algorithm was presented in Section 2. The implementation has two procedures, embed and embed_branch, that perform a series of actions in the following order: | The second algorithm for the projective case is based on a different approach based on intervals (Algorithms 4.4 and 4.6). Although the pseudocode given can be regarded as a formal interpretation of GT’s sketch [5] its correctness stems largely from the theorems and lemmas given by HS [9] (summarized in Section 2). In ... | In Section 4, we give an even simpler algorithm that can be seen as a different interpretation of HS’s algorithm as it uses the same idea for ordering the subtrees but instead of calculating displacements for nodes it only uses the interval of positions where a subtree must be arranged. | Procedure embed puts immediate subtrees with an even index in one side of the arrangement and immediate subtrees with odd index in the other side (the bigger the subtree, the farther away from the centroidal vertex), calling procedure embed_branch for every subtree. | Procedure embed gets one centroidal vertex, c𝑐citalic_c, uses it as a root and orders its immediate subtrees by size. | D |
Next, we show how to improve the above results and achieve near-optimal excess risk by adding a smoothness assumption. | While β𝛽\betaitalic_β-smoothness does not improve the sensitivity estimates in Proposition 2.2 (as the sensitivity estimates are tight by Appendix F), it can be used to yield stronger excess risk bounds, which are nearly optimal in the ERM setting. Consider the smooth, strongly convex, Lipschitz function class | Plugging the sensitivity estimates from Proposition 2.2 into Proposition 2.3 yields excess risk upper bounds for the class ℱμ,L,RERM::superscriptsubscriptℱ𝜇𝐿𝑅𝐸𝑅𝑀absent\mathcal{F}_{\mu,L,R}^{ERM}:caligraphic_F start_POSTSUBSCRIPT italic_μ , italic_L , italic_R end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_E ita... | Since the smooth, strongly convex, Lipschitz loss function class is a subset of the strongly convex, Lipschitz loss function class, we obtain by Proposition 4.1 the following upper bounds on the expected excess population loss of smooth, strongly convex, Lipschitz functions: 𝔼X∼𝒟n,𝒜F(w𝒜(X),𝒟)−F(w∗(𝒟),𝒟)≲L2μ... | By the results in Section 2.3 and Section 2.3.1, we can obtain excess adversarial risk bounds for strongly convex-concave, Lipschitz F𝐹Fitalic_F with or without the β𝛽\betaitalic_β-smoothness (in w𝑤witalic_w) assumption. Here we state the results for β𝛽\betaitalic_β-smooth F,𝐹F,italic_F , which is a simple consequ... | A |
ESE-Seg (Xu et al., 2019) estimated the shape of the detected objects by using an explicit shape encoding and decoding framework. It is based on Inner-center Radius (IR) and fits it using Chebyshev polynomial fitting, and YOLOv3 is the object detector. ESE-Seg archives mAP of 21.6% on the COCO dataset. | FourierNet (Benbarka et al., 2020) uses polygon representation to represent each mask. It is a fully convolutional method with no anchor boxes, a shape vector is predicted and then converted into contour points using Fourier transform. The predicted boundaries are smoother than PolarMask. FourierNet achieves 24.3% mAP ... | YOLO (Redmon et al., 2016), SSD (Liu et al., 2016) and RetinaNet (Lin et al., 2017) are the most common one-stage object detectors. YOLO divides the image into S x S grid cells, which are responsible for detecting N objects whose centers fall within. Each grid cell predicts N boxes, every box is represented using x,y,w... | PolarMask (Xie et al., 2020) was published concurrently with ESE-Seg but conducted independently. PolarMask proposed an additional polar IoU loss. Also, it does not require box detection, but it is necessary for ESE-Seg. PolarMask outperforms ESE-Seg by mAP of 7.5% on the COCO dataset. | ESE-Seg (Xu et al., 2019) estimated the shape of the detected objects by using an explicit shape encoding and decoding framework. It is based on Inner-center Radius (IR) and fits it using Chebyshev polynomial fitting, and YOLOv3 is the object detector. ESE-Seg archives mAP of 21.6% on the COCO dataset. | C |
{L}}^{T})^{-1}\bm{\mu}_{\mathcal{L}}( bold_Σ start_POSTSUBSCRIPT bold_italic_μ start_POSTSUBSCRIPT caligraphic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT - bold_italic_μ start_POSTSUBSCRIPT caligraphic_L end_POSTSUBSCRIPT bold_italic_μ start_POSTSUBSCRIPT caligraphic_L end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_T end_PO... | 3. A powerful and robust BEAST from a regularized resampling approximation of the oracle. Motivated by the form of the BEAST with oracle, we construct the practical BEAST to approximate the optimal power by approximating the oracle weights in testing uniformity. The proposed BEAST combines the ideas of resampling and r... | 2. A benchmark of feasible power from the BEAST with oracle. We begin by considering the test of uniformity. By utilizing the properties of the binary expansion filtration, we show in a heuristic asymptotic study of the BEAST a surprising fact that for any given alternative, the Neyman-Pearson test for testing uniformi... | 1. A unification of important nonparamatric tests of independence. In Section 3, we show that many important tests of independence in literature can be approximated by some quadratic forms of symmetry statistics, which are shown to be complete sufficient statistics for dependence in Zhang (2019). In particular, each of... | In this section, we study how to construct a powerful robust nonparametric test of uniformity based on what we learned in Sections 3 and 4.1. As discussed in Section 3, the deterministic weights of symmetry statistics in existing tests create an issue on the uniformity and robustness: They make the test powerful for so... | D |
A special kind of graph, the trees (e.g., Kd-tree and Octree), works on 3D shapes with different representations and can support various CNN architectures. Kd-Net [80] uses a kd-tree data structure to represent point cloud connectivity. However, the networks have high computational costs. O-CNN [177] designs an Octree ... | Scene-level segmentation: involves segmenting entire scenes or environments to understand the spatial context and layout of cultural heritage sites, capturing relationships between objects and features. Matrone et al. [120] make a comparative analysis of machine learning and deep learning methods for semantic segmentat... | Likewise, Hung et al. [17] back-project 2D multi-view image features onto the 3D point cloud space and use a unified network to extract local details and global context from sub-volumes and the global scene, respectively. Liu et al. [115] argue that voxel-based and point-based NN are computationally inefficient in high... | Basic framework: is one of the main driving forces behind the development of 3D segmentation. Generally, two main basic frameworks exist, including PointNet and PointNet++. The PointNet framework utilizes shared MLPs to capture point-wise features and employs max-pooling to aggregate these features into a global repres... | SO-Net [97] sets up a self-organization map (SOM) from point clouds and hierarchically learns node-wise features on this map using the PointNet architecture. However, it fails to exploit local features fully. PartNet [221] decomposes 3D shapes top-down and proposes a Recursive Neural Network (RvNN) for learning the hie... | D |
=2e−|x|.absent2superscript𝑒𝑥\displaystyle=2e^{-|x|}.= 2 italic_e start_POSTSUPERSCRIPT - | italic_x | end_POSTSUPERSCRIPT . | The factor of 2222 appears because Theorem 10 applies to one-sided error, but the absolute value forces us to consider two-sided error. | Note that f𝑓fitalic_f is well-defined because of the extreme value theorem. Define fψ:𝕌(D)→ℝ:subscript𝑓𝜓→𝕌𝐷ℝf_{\psi}:\mathbb{U}(D)\to\mathbb{R}italic_f start_POSTSUBSCRIPT italic_ψ end_POSTSUBSCRIPT : blackboard_U ( italic_D ) → blackboard_R by: | where Re(λi)Resubscript𝜆𝑖\mathrm{Re}(\lambda_{i})roman_Re ( italic_λ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ) denotes the real part of λisubscript𝜆𝑖\lambda_{i}italic_λ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT. The last line holds because the eigenvalues of a unitary matrix have absolute value 1111. | where the first line applies the phase-invariance of the design, the second line holds for the algorithm ℬℬ\mathcal{B}caligraphic_B defined in Lemma 23, the third line holds by the definition of σU,tsubscript𝜎𝑈𝑡\sigma_{U,t}italic_σ start_POSTSUBSCRIPT italic_U , italic_t end_POSTSUBSCRIPT, the fourth line applies Le... | A |
It should be pointed out that both MOH and CirCut are originally designed for the maxcut problem (1.3) and we have to modify them to produce approximate reference solutions for the anti-Cheeger cut problem (1.2) in this work. The interested readers may find more details on MOH and CirCut for the anti-Cheeger cut in App... | Figure 2: The flowchart of CIA2 — a continuous iterative algorithm for the anti-Cheeger cut equipped with breaking out of local optima by the maxcut. Fanti(𝒙)subscript𝐹anti𝒙F_{\text{anti}}(\mbox{\boldmath$x$})italic_F start_POSTSUBSCRIPT anti end_POSTSUBSCRIPT ( bold_italic_x ) denotes the objective function | Based on an equivalent continuous formulation, we proposed three continuous iterative algorithms (CIAs) for the anti-Cheeger cut problem, in which the objective function values are monotonically updated and all the subproblems have explicit analytic solutions. With a careful subgradient selection, we were able to prove... | That is, the anti-Cheeger cut problem (1.5) and the maxcut problem (1.6) are fully treated on equal terms by CIA2. | Table 1: Numerical results for the anti-Cheeger problem by continuous iterative algorithms on G-set. | D |
We cannot immediately use an oracle for Problem A> with z=e+y𝑧𝑒𝑦z=e+yitalic_z = italic_e + italic_y because | distribution μ=(1,0,…,0)𝜇10…0\mu=(1,0,\dots,0)italic_μ = ( 1 , 0 , … , 0 ), and a vector z∈{0,1,2}n𝑧superscript012𝑛z\in\{0,1,2\}^{n}italic_z ∈ { 0 , 1 , 2 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT, decide whether | Problem A> requires z∈{0,1,2}n𝑧superscript012𝑛z\in\{0,1,2\}^{n}italic_z ∈ { 0 , 1 , 2 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT. However, we can obtain a valid | }+z^{\intercal}-M\cdot z^{\intercal}( italic_z - italic_e ) start_POSTSUPERSCRIPT ⊺ end_POSTSUPERSCRIPT = italic_M ⋅ italic_z start_POSTSUPERSCRIPT ⊺ end_POSTSUPERSCRIPT - italic_e start_POSTSUPERSCRIPT ⊺ end_POSTSUPERSCRIPT - italic_x start_POSTSUPERSCRIPT ⊺ end_POSTSUPERSCRIPT + italic_z start_POSTSUPERSCRIPT ⊺ end_P... | an initial distribution μ=(1,0,…,0)𝜇10…0\mu=(1,0,\dots,0)italic_μ = ( 1 , 0 , … , 0 ), and a vector z∈{0,1,2}n𝑧superscript012𝑛z\in\{0,1,2\}^{n}italic_z ∈ { 0 , 1 , 2 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT, decide whether | B |
Similar results are shown in Table 3 on City100 dataset. The competing methods include RCAN and RCAN* [39], where RCAN* is trained with real low-resolution and high-resolution pairs; CinCGAN [35]; CamSR-SRGAN [3] and CamSR-VDSR [3] which are two variants of CameraSR model based on SRGAN and VDSR. | Starting from the backbone model EDSR in model #1, we add KANS to build model #2, which improves PSNR from 27.494 to 27.718; SSIM from 0.813 to 0.823; LPIPS from 0.157 to 0.151. By introducing HFSO and IS, the performance of the model can be further boosted to our best model #4 with 27.850 on PSNR, 0.824 on SSIM and 0.... | Our model improves the PSNR value from 30.260 to 30.714, compared to the second best model CamSR-VDSR. When compared with CamSR-based models, the proposed model improves the LPIPS measure by a large margin. | From Table 8, the model trained with HFSO shows better results across the three evaluation measures when compared to HF-loss only. In particular, compared with the HF-only, HFSO increases PSNR from 27.734 to 27.850 and LPIPS from 0.153 to 0.148. | On the RealSR results from Tables 1 and 2, our model outperforms competing approaches by a large margin for all three measures, especially on LPIPS evaluations. The DASR model and Noise-injection model have better perceptual results than other competing models, but they are still not as good as our model. On ×4absent4\... | B |
To unleash the full potential of FEEL, recent works exploited cooperation among multiple edge servers for model training. In [12], a client-edge-cloud hierarchical FL system along with a training algorithm, namely HierFAVG, was developed, which takes advantages of the Cloud and edge servers to accelerate model training... | In this paper, we investigated a novel FL architecture, namely semi-decentralized federated edge learning (SD-FEEL), to realize low-latency distributed learning on non-IID data. Convergence analysis was conducted for the training algorithm of SD-FEEL, from which, various insights were drawn for system implementation. S... | Attributed to the emergence of mobile edge computing (MEC) [6], federated edge learning (FEEL), where an edge server located in close proximity to the client nodes (e.g., a base station) is deployed as the PS, was proposed as a promising alternative to Cloud-based FL [7]. Despite its great promise in reducing model upl... | We extend SD-FEEL to the case with non-IID data. To investigate impacts of the network topology on learning performance, the edge servers are allowed to share and aggregate models multiple times in each round of inter-cluster model aggregation. | In this paper, we investigate a novel FL architecture, namely semi-decentralized federated edge learning (SD-FEEL), to improve the training efficiency. This architecture is motivated by the low communication latency between edge servers so that efficient model exchanges can be realized. Specifically, we consider multip... | D |
This is a simple consequence of Proposition 2 and the fact that the axiom lbda1 (resp. lbda2, lbda3) is sound in the class of models of time(sc)timesc{\textsf{time}}({\textsf{sc}})time ( sc ) with the constraint C1 (resp. C2, C3). | We say that ϕitalic-ϕ\phiitalic_ϕ is true in a model of deemed ability M=⟨T,<,g⟩𝑀𝑇𝑔M=\langle T,<,g\rangleitalic_M = ⟨ italic_T , < , italic_g ⟩, when for every instant t∈T𝑡𝑇t\in Titalic_t ∈ italic_T, we have that M,t⊧time(sc)ϕsubscriptmodelstimesc𝑀𝑡italic-ϕM,t\models_{{\textsf{time}}({\textsf{sc}})}\phiitalic_M... | The interpretation of Ltime(sc)subscript𝐿timescL_{{\textsf{time}}({\textsf{sc}})}italic_L start_POSTSUBSCRIPT time ( sc ) end_POSTSUBSCRIPT in a model Mtime(sc)=⟨T,<,g⟩subscript𝑀timesc𝑇𝑔M_{{\textsf{time}}({\textsf{sc}})}=\langle T,<,g\rangleitalic_M start_POSTSUBSCRIPT time ( sc ) end_POSTSUBSCRIPT = ⟨ italic_T ,... | Moreover, lbdar1 preserves validity: if ϕitalic-ϕ\phiitalic_ϕ is true in every model of time(sc)timesc{\textsf{time}}({\textsf{sc}})time ( sc ) then it is true in every model of lbda. | If ϕ∈Ltime(sc)italic-ϕsubscript𝐿timesc\phi\in L_{{\textsf{time}}({\textsf{sc}})}italic_ϕ ∈ italic_L start_POSTSUBSCRIPT time ( sc ) end_POSTSUBSCRIPT, ⊢time(sc)ϕ\vdash_{{\textsf{time}}({\textsf{sc}})}\phi⊢ start_POSTSUBSCRIPT time ( sc ) end_POSTSUBSCRIPT italic_ϕ iff ⊧time(sc)ϕsubscriptmodelstimescabsentitalic-ϕ\m... | C |
The algorithm is not just based on the detection of the abrupt rise of the price. The fundamental idea is to leverage the abnormal growth of so-called market buy orders, buy orders that are used when the investor wants to buy extremely quickly and whatever is the price. Just like the colluding members of a pump and dum... | Moreover, we describe a new kind of pump operation—that we refer to as crowd pump to distinguish it from the standard pump and dump, discussing the differences in the organization and aim between the standard pump and dump and the crowd pump. | Now, we focus on a new kind of pump operation. We will call it crowd pump—a pump and dump event that results from the non-directly organized actions of a crowd of people. We analyze how these operations happen, and we illustrate the differences from standard pump and dumps. Lastly, we offer that it is possible to lever... | Although there are some key differences between the crowd pump and standard pump and dump, our intuition is that the rush orders are a very relevant feature also in this kind of operation. | At the end of our analysis, we find the following main differences between crowd pump and pump and dump operations: | A |
\Longrightarrow M^{\prime}\notin\mathcal{T}(o)\right\}\,.caligraphic_T start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( italic_o ) = { italic_M ∈ caligraphic_T ( italic_o ) | italic_M start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ⊂ italic_M ⟹ italic_M start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ∉ caligraphic_T ( italic_o ) ... | the core collections 𝒯∗(o)superscript𝒯𝑜\mathcal{T}^{*}(o)caligraphic_T start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( italic_o ), | M∗∈𝒯∗(o)⊆𝒯(o)superscript𝑀superscript𝒯𝑜𝒯𝑜M^{*}\in\mathcal{T}^{*}(o)\subseteq\mathcal{T}(o)italic_M start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ∈ caligraphic_T start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( italic_o ) ⊆ caligraphic_T ( italic_o ) | We note that 𝒯∗(o)superscript𝒯𝑜\mathcal{T}^{*}(o)caligraphic_T start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT ( italic_o ) is a (non-empty) antichain of the partially ordered | (𝒯(o),⊆)𝒯𝑜(\mathcal{T}(o),\subseteq)( caligraphic_T ( italic_o ) , ⊆ ).101010An antichain of a partially ordered set is a subset of mutually incomparable | C |
Wireless technologies have recently undergone tremendous growth in terms of supporting more users and providing higher spectral efficiency, with the next generation of cellular networks planning to support massive machine-to-machine communication [1], large IoT networks [2], and unprecedented data rates [3]. The number... | Figure 9: BER comparison of MMSE and RI-MIMO-512 for massive MIMO systems with very large number of antennas at the base station. | Instead, Massive MIMO systems [14, 15], where the number of base station antennas is much larger than the number of users, have emerged as the dominant solution to the poor bit error performance of practically-feasible MIMO detectors. Such systems have extremely well-conditioned channels, and hence even linear detector... | In this section, we will address the need and performance of RI-MIMO/TRIM for massive MIMO systems. Massive MIMO systems tend to have a much higher number of antennas at the receiver than at the transmitter. Due to this, the channel is extremely well-conditioned, and even linear detectors such as MMSE or iterative algo... | Figure 12: Spectral Efficiency: Comparison between throughput of MMSE and RI-MIMO for massive MIMO scenarios with large number of antennas at the base station. | B |
The main advantage of the proposed online deep learning (ODL) algorithm is its ability to adapt to different environments, different channel types, and different scenario conditions that BS cannot measure directly, e.g., UE speed. | This paper proposes a novel online deep learning solution for adaptive modulation and coding for massive MIMO systems. It learns to predict the probability of transmission success for different MCS values and selects the MCS with the highest expected throughput. Simulation results show that the proposed approach outper... | Due to the channel aging effect, user speed is an important hidden factor for the optimal choice of MCS, and it is hard to catch it with an offline pre-trained AI-based model. In the proposed approach, the model is able to adaptively learn the behavior of the UE and implicitly take into account its speed. In the state ... | Following New Radio (5G) downlink AMC procedure [2], user equipment (UE) has to suggest to the serving base station (BS) an appropriate modulation and coding scheme (MCS) to be used in the next transmission. The proposed MCS is provided by UE using a channel quality indicator (CQI). However, this indication is not enou... | The novelty of our work is in the proposed scheme of online deep learning with a new optimization target. On the one hand, it is simpler and more effective than the existing Q-learning approach ([10, 11]) to the AMC problem. On the one hand, it outperforms the basic OLLA approach because of the better utilization of th... | B |
For instance, the proposed iteration scheme can then be made more implementable via the Poisson thinning (Theorem 3.7). | We begin Section 3 with the construction of approximate solutions and their convergence towards the true solution as a sequence (Theorem 3.1). | In addition, the modes of convergence of the sequences of approximate solutions and associated hard bounding functions can be strengthened (Theorem 3.8). | In this section, we provide numerical examples to justify our theoretical findings, namely the recursive formula (Theorem 3.5), hard bounding functions (Theorem 3.6), thinning (Theorem 3.7) and the convergence (Theorem 3.8). | We close the main section by developing the Poisson thinning (Theorem 3.7) and strengthening the modes of convergence (Theorem 3.8), provided that the jump rate is uniformly bounded. | B |
By Proposition 6, we see that there exists an optimal solution to (3) in {0,1}V(G)superscript01𝑉𝐺\{0,1\}^{V(G)}{ 0 , 1 } start_POSTSUPERSCRIPT italic_V ( italic_G ) end_POSTSUPERSCRIPT. | In what follows, we will show that by fixing and translating some variables, we may restrict all variables to only attain values in {0,1}01\{0,1\}{ 0 , 1 }, in which case we end up with a stable set problem over a subgraph of G𝐺Gitalic_G. | If β=0𝛽0\beta=0italic_β = 0, then the constraint can be replaced by fixing the respective variables to 00, and we remove the edge from G𝐺Gitalic_G. | If one of these submatrices is all-zero, we remove the respective set Jtsubscript𝐽𝑡J_{t}italic_J start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT. | If β>1𝛽1\beta>1italic_β > 1, then the constraint is redundant, and so we also remove the edge from G𝐺Gitalic_G. | B |
^{1+\nu}\ln\frac{4N}{\beta}}{N}\right\}.roman_max { divide start_ARG 8 italic_C start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT italic_M start_POSTSUBSCRIPT italic_ν end_POSTSUBSCRIPT start_POSTSUPERSCRIPT divide start_ARG 2 end_ARG start_ARG 1 + italic_ν end_ARG end_POSTSUPERSCRIPT italic_R start_POSTSUBSCRIPT 0 end_POSTS... | The final, third step of the proof consists of providing explicit formulas and bounds for the parameters of the method and derivation of the desired result using induction and Bernstein’s inequality. Below, we provide the complete statement of Theorem 2.1. | Next, if the minimum in (81) is attained on any of the first three terms, then applying the derivations from the end of the proof of Theorem 5.1, we get that the method requires | That is, with the choice of the stepsize parameter a𝑎aitalic_a as in (52), the method uses unit batch sizes at each iteration. Therefore, iteration and oracle complexities coincide in this case. Next, we consider two possible situations. | Next, we estimate the iteration and oracle complexities of the method and consider 3333 possible situations. | D |
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