In this paper, we consider classes of decision tables with many-valued decisions closed relative to removal of attributes (columns) and changing sets of decisions assigned to rows. For tables from an arbitrary closed class, we study a function $\mathcal{H}^{\infty}_{\psi ,A}(n)$ that characterizes the dependence in the worst case of the minimum complexity of deterministic decision trees on the minimum complexity of nondeterministic decision trees. Note that nondeterministic decision trees for a decision table can be interpreted as a way to represent an arbitrary system of true decision rules for this table that cover all rows. We indicate the condition for the function $\mathcal{H}^{\infty}_{\psi ,A}(n)$ to be defined everywhere. If this function is everywhere defined, then it is either bounded from above by a constant or is greater than or equal to $n$ for infinitely many $n$. In particular, for any nondecreasing function $\varphi$ such that $\varphi (n)\geq n$ and $\varphi (0)=0$, the function $\mathcal{H}^{\infty}_{\psi ,A}(n)$ can grow between $\varphi (n)$ and $\varphi (n)+n$. We indicate also conditions for the function $\mathcal{H}^{\infty}_{\psi,A}(n)$ to be bounded from above by a polynomial on $n$.
相關內容
In this paper we tackle the problem of persistently covering a complex non-convex environment with a team of robots. We consider scenarios where the coverage quality of the environment deteriorates with time, requiring to constantly revisit every point. As a first step, our solution finds a partition of the environment where the amount of work for each robot, weighted by the importance of each point, is equal. This is achieved using a power diagram and finding an equitable partition through a provably correct distributed control law on the power weights. Compared to other existing partitioning methods, our solution considers a continuous environment formulation with non-convex obstacles. In the second step, each robot computes a graph that gathers sweep-like paths and covers its entire partition. At each planning time, the coverage error at the graph vertices is assigned as weights of the corresponding edges. Then, our solution is capable of efficiently finding the optimal open coverage path through the graph with respect to the coverage error per distance traversed. Simulation and experimental results are presented to support our proposal.
In this paper, we present a novel deep image clustering approach termed PICI, which enforces the partial information discrimination and the cross-level interaction in a joint learning framework. In particular, we leverage a Transformer encoder as the backbone, through which the masked image modeling with two paralleled augmented views is formulated. After deriving the class tokens from the masked images by the Transformer encoder, three partial information learning modules are further incorporated, including the PISD module for training the auto-encoder via masked image reconstruction, the PICD module for employing two levels of contrastive learning, and the CLI module for mutual interaction between the instance-level and cluster-level subspaces. Extensive experiments have been conducted on six real-world image datasets, which demononstrate the superior clustering performance of the proposed PICI approach over the state-of-the-art deep clustering approaches. The source code is available at //github.com/Regan-Zhang/PICI.
In this paper, we focus on numerical approximations of Piecewise Diffusion Markov Processes (PDifMPs), particularly when the explicit flow maps are unavailable. Our approach is based on the thinning method for modelling the jump mechanism and combines the Euler-Maruyama scheme to approximate the underlying flow dynamics. For the proposed approximation schemes, we study both the mean-square and weak convergence. Weak convergence of the algorithms is established by a martingale problem formulation. Moreover, we employ these results to simulate the migration patterns exhibited by moving glioma cells at the microscopic level. Further, we develop and implement a splitting method for this PDifMP model and employ both the Thinned Euler-Maruyama and the splitting scheme in our simulation example, allowing us to compare both methods.
In this paper, we leverage a multi-agent reinforcement learning (MARL) framework to jointly learn a computation offloading decision and multichannel access policy with corresponding signaling. Specifically, the base station and industrial Internet of Things mobile devices are reinforcement learning agents that need to cooperate to execute their computation tasks within a deadline constraint. We adopt an emergent communication protocol learning framework to solve this problem. The numerical results illustrate the effectiveness of emergent communication in improving the channel access success rate and the number of successfully computed tasks compared to contention-based, contention-free, and no-communication approaches. Moreover, the proposed task offloading policy outperforms remote and local computation baselines.
In this paper, we propose and study construction of confidence bands for shape-constrained regression functions when the predictor is multivariate. In particular, we consider the continuous multidimensional white noise model given by $d Y(\mathbf{t}) = n^{1/2} f(\mathbf{t}) \,d\mathbf{t} + d W(\mathbf{t})$, where $Y$ is the observed stochastic process on $[0,1]^d$ ($d\ge 1$), $W$ is the standard Brownian sheet on $[0,1]^d$, and $f$ is the unknown function of interest assumed to belong to a (shape-constrained) function class, e.g., coordinate-wise monotone functions or convex functions. The constructed confidence bands are based on local kernel averaging with bandwidth chosen automatically via a multivariate multiscale statistic. The confidence bands have guaranteed coverage for every $n$ and for every member of the underlying function class. Under monotonicity/convexity constraints on $f$, the proposed confidence bands automatically adapt (in terms of width) to the global and local (H\"{o}lder) smoothness and intrinsic dimensionality of the unknown $f$; the bands are also shown to be optimal in a certain sense. These bands have (almost) parametric ($n^{-1/2}$) widths when the underlying function has ``low-complexity'' (e.g., piecewise constant/affine).
In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the automated planning. The main benefit of using general constraint solvers for such purpose, instead of developing dedicated tools, is that we can rely on the efficient search that is already implemented within the solver, enabling us to focus on geometric aspects of the problem. We may also use the solver's built-in optimization capabilities to search for the shortest possible constructions. We evaluate our approach on 74 solvable problems from the Wernick's list, and compare it to the dedicated triangle construction solver ArgoTriCS. The results show that our approach is comparable to dedicated tools, while it requires much less effort to implement. Also, our model often finds shorter constructions, thanks to the optimization capabilities offered by the constraint solvers.
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron, defined by systems $A x \leq b$ or $Ax = b,\, x \geq 0$ with a sparse matrix $A$. We develop algorithms for these problems that outperform state of the art ILP and counting algorithms on sparse instances with bounded elements. We use known and new methods to develop new exponential algorithms for Edge/Vertex Multi-Packing/Multi-Cover Problems on graphs and hypergraphs. This framework consists of many different problems, such as the Stable Multi-set, Vertex Multi-cover, Dominating Multi-set, Set Multi-cover, Multi-set Multi-cover, and Hypergraph Multi-matching problems, which are natural generalizations of the standard Stable Set, Vertex Cover, Dominating Set, Set Cover, and Maximal Matching problems.
In this paper, we present conditions for identifying the generator of a linear stochastic differential equation (SDE) from the distribution of its solution process with a given fixed initial state. These identifiability conditions are crucial in causal inference using linear SDEs as they enable the identification of the post-intervention distributions from its observational distribution. Specifically, we derive a sufficient and necessary condition for identifying the generator of linear SDEs with additive noise, as well as a sufficient condition for identifying the generator of linear SDEs with multiplicative noise. We show that the conditions derived for both types of SDEs are generic. Moreover, we offer geometric interpretations of the derived identifiability conditions to enhance their understanding. To validate our theoretical results, we perform a series of simulations, which support and substantiate the established findings.
In this paper, we explore the concept of integrated sensing and communication (ISAC) within a downlink cell-free massive MIMO (multiple-input multiple-output) system featuring multi-static sensing and users requiring ultra-reliable low-latency communications (URLLC). Our focus involves the formulation of two non-convex algorithms that jointly solve power and blocklength allocation for end-to-end (E2E) minimization. The objectives are to jointly minimize sensing/communication processing and transmission energy consumption, while simultaneously meeting the requirements for sensing and URLLC. To address the inherent non-convexity of these optimization problems, we utilize techniques such as the Feasible Point Pursuit - Successive Convex Approximation (FPP-SCA), Concave-Convex Programming (CCP), and fractional programming. We conduct a comparative analysis of the performance of these algorithms in ISAC scenarios and against a URLLC-only scenario where sensing is not integrated. Our numerical results highlight the superior performance of the E2E energy minimization algorithm, especially in scenarios without sensing capability. Additionally, our study underscores the increasing prominence of energy consumption associated with sensing processing tasks as the number of sensing receive access points rises. Furthermore, the results emphasize that a higher sensing signal-to-interference-plus-noise ratio threshold is associated with an escalation in E2E energy consumption, thereby narrowing the performance gap between the two proposed algorithms.
In this paper, we introduce a new method for querying triadic concepts through partial or complete matching of triples using an inverted index, to retrieve already computed triadic concepts that contain a set of terms in their extent, intent, and/or modus. As opposed to the approximation approach described in Ananias, this method (i) does not need to keep the initial triadic context or its three dyadic counterparts, (ii) avoids the application of derivation operators on the triple components through context exploration, and (iii) eliminates the requirement for a factorization phase to get triadic concepts as the answer to one-dimensional queries. Additionally, our solution introduces a novel metric for ranking the retrieved triadic concepts based on their similarity to a given query. Lastly, an empirical study is primarily done to illustrate the effectiveness and scalability of our approach against the approximation one. Our solution not only showcases superior efficiency, but also highlights a better scalability, making it suitable for big data scenarios.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191