Recognition of human activities using wearable sensors is essential for applications related to health and well-being. However, the complex data captured by inertial sensors poses challenges in accurately identifying ...
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We introduce a new conjecture on the computational hardness of detecting random lifts of graphs: we claim that there is no polynomial-time algorithm that can distinguish between a large random $d$ -regular graph and...
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ISBN:
(数字)9798331516741
ISBN:
(纸本)9798331516758
We introduce a new conjecture on the computational hardness of detecting random lifts of graphs: we claim that there is no polynomial-time algorithm that can distinguish between a large random
$d$
-regular graph and a large random lift of a Ramanujan
$d$
-regular base graph (provided the lift is corrupted by a small amount of extra noise), and likewise for bipartite random graphs and lifts of bipartite Ramanujan graphs. We give evidence for this conjecture by proving lower bounds against the local statistics hierarchy of hypothesis testing semidefinite programs. We then explore the consequences of the conjecture for the hardness of certifying bounds on numerous functions of random regular graphs, expanding on a direction initiated by Bandeira, Banks, Kunisky, Moore, and Wein (2021). Conditional on this conjecture, we show that no polynomial-time algorithm can certify tight bounds on the maximum cut or maximum independent set of random 3- or 4-regular graphs, or on the chromatic number of random 7-regular graphs. Asymptotically for large degree for the maximum independent set and for any degree for the minimum dominating set, we show similar gaps, finding that naive spectral and combinatorial bounds are optimal among efficiently computable ones. Likewise, for small set vertex and edge expansion in the limit of very small sets, we show that the spectral bounds due to Kahale (1995) are optimal efficient certificates.
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical app...
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This work aims to numerically investigate the performance of the multiquadric (MQ) radial basis function in more general formats for image reconstruction applications. Desired features, i.e., accuracy and shape parame...
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The complexity and heterogeneity of data in many real-world applications pose significant challenges for traditional machine learning and signal processing techniques. For instance, in medicine, effective analysis of ...
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This study explores the potential of utilizing the energy flexibility of heat customers to reduce peak loads and improve the efficiency of district heating systems. Using Modelica and compiled in Dymola, a rule-based ...
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In the early 21st century, Internet of Drones (IoD) ushered in a rapid growth period and is gradually expanded from military field to civilian field. Currently, there are more and more scenarios where multiple drones ...
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Any serious heart ailment is referred to as coronary heart disease. Researchers are concentrating on developing smart systems to identify heart disease precisely based on electronic health data, with the use of machin...
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In the past decade, the demand for high-volume production of high-precision products with complex shapes has led to the development of new manufacturing processes. Among these processes, the Selective Thermoplastic El...
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