Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07305
Li, Zhiqiang, Zheng, Hanyun
In this paper, we prove that for a metric coarse expanding conformal system $f:(mathfrak{X}_1,X)rightarrow (mathfrak{X}_0,X)$ with repellor $X$, the map $f|_X:Xrightarrow X$ is asymptotically $h$-expansive. Moreover, we show that $f|_X$ is not $h$-expansive if there exists at least one branch point in the repellor. As a consequence of asymptotic $h$-expansiveness, for $f|_X$ and each real-valued continuous potential on $X$, there exists at least one equilibrium state. For such maps, if some additional assumptions are satisfied, we can furthermore establish a level-2 large deviation principle for iterated preimages, followed by an equidistribution result.
{"title":"Weak expansion properties and a large deviation principle for coarse\u0000 expanding conformal systems","authors":"Li, Zhiqiang, Zheng, Hanyun","doi":"10.48550/arxiv.2311.07305","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07305","url":null,"abstract":"In this paper, we prove that for a metric coarse expanding conformal system $f:(mathfrak{X}_1,X)rightarrow (mathfrak{X}_0,X)$ with repellor $X$, the map $f|_X:Xrightarrow X$ is asymptotically $h$-expansive. Moreover, we show that $f|_X$ is not $h$-expansive if there exists at least one branch point in the repellor. As a consequence of asymptotic $h$-expansiveness, for $f|_X$ and each real-valued continuous potential on $X$, there exists at least one equilibrium state. For such maps, if some additional assumptions are satisfied, we can furthermore establish a level-2 large deviation principle for iterated preimages, followed by an equidistribution result.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07481
Boxi, Sovan, Gupta, Nayantara
The very high energy gamma-ray source HESS J1809-193 has been detected by the LHAASO and HAWC observatory beyond 100 TeV energy. It is an interesting candidate for exploring the underlying mechanisms of gamma-ray production due to the presence of supernova remnants, pulsar and molecular clouds close to it. We have considered the injection of the energetic cosmic rays from a past explosion, whose reminiscent may be SNR G011.0-00.0, which is located within the extended gamma-ray source HESS J1809-193. We explain the multi-wavelength data from the region of HESS J1809-193 with synchrotron, inverse Compton, bremsstrahlung emission of cosmic ray electrons and secondary gamma-ray production in interactions of cosmic ray protons with the cold protons in the local molecular clouds within a time-dependent framework including the diffusion loss of cosmic rays. The observational data has been modelled with the secondary photons produced by the time-evolved cosmic ray spectrum, assuming the age of the explosion is 4500 years.
{"title":"HESS J1809-193: Gamma-Ray Emission by Cosmic Rays from Past Explosion","authors":"Boxi, Sovan, Gupta, Nayantara","doi":"10.48550/arxiv.2311.07481","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07481","url":null,"abstract":"The very high energy gamma-ray source HESS J1809-193 has been detected by the LHAASO and HAWC observatory beyond 100 TeV energy. It is an interesting candidate for exploring the underlying mechanisms of gamma-ray production due to the presence of supernova remnants, pulsar and molecular clouds close to it. We have considered the injection of the energetic cosmic rays from a past explosion, whose reminiscent may be SNR G011.0-00.0, which is located within the extended gamma-ray source HESS J1809-193. We explain the multi-wavelength data from the region of HESS J1809-193 with synchrotron, inverse Compton, bremsstrahlung emission of cosmic ray electrons and secondary gamma-ray production in interactions of cosmic ray protons with the cold protons in the local molecular clouds within a time-dependent framework including the diffusion loss of cosmic rays. The observational data has been modelled with the secondary photons produced by the time-evolved cosmic ray spectrum, assuming the age of the explosion is 4500 years.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07477
Fieback, Laura, Dash, Bidya, Spiegelberg, Jakob, Gottschalk, Hanno
Quantifying predictive uncertainty of deep semantic segmentation networks is essential in safety-critical tasks. In applications like autonomous driving, where video data is available, convolutional long short-term memory networks are capable of not only providing semantic segmentations but also predicting the segmentations of the next timesteps. These models use cell states to broadcast information from previous data by taking a time series of inputs to predict one or even further steps into the future. We present a temporal postprocessing method which estimates the prediction performance of convolutional long short-term memory networks by either predicting the intersection over union of predicted and ground truth segments or classifying between intersection over union being equal to zero or greater than zero. To this end, we create temporal cell state-based input metrics per segment and investigate different models for the estimation of the predictive quality based on these metrics. We further study the influence of the number of considered cell states for the proposed metrics.
{"title":"Temporal Performance Prediction for Deep Convolutional Long Short-Term\u0000 Memory Networks","authors":"Fieback, Laura, Dash, Bidya, Spiegelberg, Jakob, Gottschalk, Hanno","doi":"10.48550/arxiv.2311.07477","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07477","url":null,"abstract":"Quantifying predictive uncertainty of deep semantic segmentation networks is essential in safety-critical tasks. In applications like autonomous driving, where video data is available, convolutional long short-term memory networks are capable of not only providing semantic segmentations but also predicting the segmentations of the next timesteps. These models use cell states to broadcast information from previous data by taking a time series of inputs to predict one or even further steps into the future. We present a temporal postprocessing method which estimates the prediction performance of convolutional long short-term memory networks by either predicting the intersection over union of predicted and ground truth segments or classifying between intersection over union being equal to zero or greater than zero. To this end, we create temporal cell state-based input metrics per segment and investigate different models for the estimation of the predictive quality based on these metrics. We further study the influence of the number of considered cell states for the proposed metrics.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recent studies have highlighted a phenomenon in large language models (LLMs) known as "the reversal curse," in which the order of knowledge entities in the training data biases the models' comprehension. For example, if a model is trained on sentences where entity A consistently appears before entity B, it can respond to queries about A by providing B. However, it may encounter confusion when presented with questions concerning B. We contend that the reversal curse is partially a result of specific model training objectives, particularly evident in the prevalent use of the next-token prediction within most causal language models. For the next-token prediction, models solely focus on a token's preceding context, resulting in a restricted comprehension of the input. In contrast, we illustrate that the GLM, trained using the autoregressive blank infilling objective where tokens to be predicted have access to the entire context, exhibits better resilience against the reversal curse. We propose a novel training method, BIdirectional Casual language modeling Optimization (BICO), designed to mitigate the reversal curse when fine-tuning pretrained causal language models on new data. BICO modifies the causal attention mechanism to function bidirectionally and employs a mask denoising optimization. In the task designed to assess the reversal curse, our approach improves Llama's accuracy from the original 0% to around 70%. We hope that more attention can be focused on exploring and addressing these inherent weaknesses of the current LLMs, in order to achieve a higher level of intelligence.
{"title":"Are We Falling in a Middle-Intelligence Trap? An Analysis and Mitigation\u0000 of the Reversal Curse","authors":"Lv, Ang, Zhang, Kaiyi, Xie, Shufang, Tu, Quan, Chen, Yuhan, Wen, Ji-Rong, Yan, Rui","doi":"10.48550/arxiv.2311.07468","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07468","url":null,"abstract":"Recent studies have highlighted a phenomenon in large language models (LLMs) known as \"the reversal curse,\" in which the order of knowledge entities in the training data biases the models' comprehension. For example, if a model is trained on sentences where entity A consistently appears before entity B, it can respond to queries about A by providing B. However, it may encounter confusion when presented with questions concerning B. We contend that the reversal curse is partially a result of specific model training objectives, particularly evident in the prevalent use of the next-token prediction within most causal language models. For the next-token prediction, models solely focus on a token's preceding context, resulting in a restricted comprehension of the input. In contrast, we illustrate that the GLM, trained using the autoregressive blank infilling objective where tokens to be predicted have access to the entire context, exhibits better resilience against the reversal curse. We propose a novel training method, BIdirectional Casual language modeling Optimization (BICO), designed to mitigate the reversal curse when fine-tuning pretrained causal language models on new data. BICO modifies the causal attention mechanism to function bidirectionally and employs a mask denoising optimization. In the task designed to assess the reversal curse, our approach improves Llama's accuracy from the original 0% to around 70%. We hope that more attention can be focused on exploring and addressing these inherent weaknesses of the current LLMs, in order to achieve a higher level of intelligence.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07470
Pan, Haowen, Cao, Yixin, Wang, Xiaozhi, Yang, Xun
Multi-modal large language models (LLM) have achieved powerful capabilities for visual semantic understanding in recent years. However, little is known about how LLMs comprehend visual information and interpret different modalities of features. In this paper, we propose a new method for identifying multi-modal neurons in transformer-based multi-modal LLMs. Through a series of experiments, We highlight three critical properties of multi-modal neurons by four well-designed quantitative evaluation metrics. Furthermore, we introduce a knowledge editing method based on the identified multi-modal neurons, for modifying a specific token to another designative token. We hope our findings can inspire further explanatory researches on understanding mechanisms of multi-modal LLMs.
{"title":"Finding and Editing Multi-Modal Neurons in Pre-Trained Transformer","authors":"Pan, Haowen, Cao, Yixin, Wang, Xiaozhi, Yang, Xun","doi":"10.48550/arxiv.2311.07470","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07470","url":null,"abstract":"Multi-modal large language models (LLM) have achieved powerful capabilities for visual semantic understanding in recent years. However, little is known about how LLMs comprehend visual information and interpret different modalities of features. In this paper, we propose a new method for identifying multi-modal neurons in transformer-based multi-modal LLMs. Through a series of experiments, We highlight three critical properties of multi-modal neurons by four well-designed quantitative evaluation metrics. Furthermore, we introduce a knowledge editing method based on the identified multi-modal neurons, for modifying a specific token to another designative token. We hope our findings can inspire further explanatory researches on understanding mechanisms of multi-modal LLMs.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07471
Bertilsson, Magnus, Leupold, Stefan
The leading-order chiral Lagrangian for the baryon octet and decuplet states coupled to Goldstone bosons and external sources contains six low-energy constants. Five of them are fairly well known from phenomenology, but the sixth one is practically unknown. This coupling constant provides the strength of the (p-wave) coupling of Goldstone bosons to decuplet states. Its size and even sign are under debate. Quark model and QCD for a large number of colors provide predictions, but some recent phenomenological analyses suggest even an opposite sign for the Delta-pion coupling. The Goldberger-Treiman relation connects this coupling constant to the axial charge of the Delta baryon. This suggests a Wu-type experiment to determine the unknown low-energy constant. While this is not feasible in the Delta sector because of the large hadronic width of the Delta, there is a flavor symmetry related process that is accessible: the weak semileptonic decay of the Omega baryon to a spin 3/2 cascade baryon. A broad research program is suggested that can pin down at least the rough size and the sign of the last unknown low-energy constant of the leading-order Lagrangian. It encompasses experimental measurements, in particular the forward-backward asymmetry of the semileptonic decay, together with a determination of the quark-mass dependences using lattice QCD for the narrow decuplet states and chiral perturbation theory to extrapolate to the Delta sector. Besides discussing the strategy of the research program, the present work provides a feasibility check based on a simple leading-order calculation.
{"title":"Goldberger-Treiman relation and Wu-type experiment in the decuplet\u0000 sector","authors":"Bertilsson, Magnus, Leupold, Stefan","doi":"10.48550/arxiv.2311.07471","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07471","url":null,"abstract":"The leading-order chiral Lagrangian for the baryon octet and decuplet states coupled to Goldstone bosons and external sources contains six low-energy constants. Five of them are fairly well known from phenomenology, but the sixth one is practically unknown. This coupling constant provides the strength of the (p-wave) coupling of Goldstone bosons to decuplet states. Its size and even sign are under debate. Quark model and QCD for a large number of colors provide predictions, but some recent phenomenological analyses suggest even an opposite sign for the Delta-pion coupling. The Goldberger-Treiman relation connects this coupling constant to the axial charge of the Delta baryon. This suggests a Wu-type experiment to determine the unknown low-energy constant. While this is not feasible in the Delta sector because of the large hadronic width of the Delta, there is a flavor symmetry related process that is accessible: the weak semileptonic decay of the Omega baryon to a spin 3/2 cascade baryon. A broad research program is suggested that can pin down at least the rough size and the sign of the last unknown low-energy constant of the leading-order Lagrangian. It encompasses experimental measurements, in particular the forward-backward asymmetry of the semileptonic decay, together with a determination of the quark-mass dependences using lattice QCD for the narrow decuplet states and chiral perturbation theory to extrapolate to the Delta sector. Besides discussing the strategy of the research program, the present work provides a feasibility check based on a simple leading-order calculation.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07098
Harre, Jan-Vincent, Smith, Alexis M. S.
Tidal orbital decay plays a vital role in the evolution of hot Jupiter systems. As of now, this was only observationally confirmed for the WASP-12 system. There are a few other candidates, including WASP-4 b, but no conclusive result could be obtained for these systems as of yet. In this study, we present an analysis of new TESS data of WASP-4 b together with archival data, taking the light-time effect (LTE), induced by the second planetary companion, into account as well. We make use of three different Markov-Chain-Monte-Carlo models; a circular orbit with a constant orbital period, a circular orbit with a decaying orbit, and an elliptical orbit with apsidal precession. This analysis is repeated for four cases. The first case features no LTE correction, with the remaining three cases featuring three different timing correction approaches. Comparison of these models yields no conclusive answer to the cause of WASP-4,b's apparent transit timing variations. A broad range of values of the orbital decay and apsidal precession parameters are possible, depending on the LTE correction. This work highlights the importance of continued photometric and spectroscopic monitoring of hot Jupiters.
{"title":"The apparent tidal decay of WASP-4 b can be explained by the R{o}mer\u0000 effect","authors":"Harre, Jan-Vincent, Smith, Alexis M. S.","doi":"10.48550/arxiv.2311.07098","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07098","url":null,"abstract":"Tidal orbital decay plays a vital role in the evolution of hot Jupiter systems. As of now, this was only observationally confirmed for the WASP-12 system. There are a few other candidates, including WASP-4 b, but no conclusive result could be obtained for these systems as of yet. In this study, we present an analysis of new TESS data of WASP-4 b together with archival data, taking the light-time effect (LTE), induced by the second planetary companion, into account as well. We make use of three different Markov-Chain-Monte-Carlo models; a circular orbit with a constant orbital period, a circular orbit with a decaying orbit, and an elliptical orbit with apsidal precession. This analysis is repeated for four cases. The first case features no LTE correction, with the remaining three cases featuring three different timing correction approaches. Comparison of these models yields no conclusive answer to the cause of WASP-4,b's apparent transit timing variations. A broad range of values of the orbital decay and apsidal precession parameters are possible, depending on the LTE correction. This work highlights the importance of continued photometric and spectroscopic monitoring of hot Jupiters.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07105
Lin, Qingquan, Lu, Weining
Multi-robot systems are widely used in spatially distributed tasks, and their collaborative path planning is of great significance for working efficiency. Currently, different multi-robot collaborative path planning methods have been proposed, but how to process the sensory information of neighboring robots at different locations from a local perception perspective in real environment to make better decisions is still a major difficulty. To address this problem, this paper proposes a multi-robot collaborative path planning method based on geometric graph neural network (GeoGNN). GeoGNN introduces the relative position information of neighboring robots into each interaction layer of the graph neural network to better integrate neighbor sensing information. An expert data generation method is designed for the robot to advance in a single step, by which expert data are generated in ROS to train the network. Experimental results show that the accuracy of the proposed method is improved by about 5% compared to the model based only on CNN on the expert data set. In ROS simulation environment path planning test, the success rate is improved by about 4% compared to CNN and flowtime increase is reduced about 8%, which outperforms other graph neural network models.
{"title":"Collaborative Goal Tracking of Multiple Mobile Robots Based on Geometric\u0000 Graph Neural Network","authors":"Lin, Qingquan, Lu, Weining","doi":"10.48550/arxiv.2311.07105","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07105","url":null,"abstract":"Multi-robot systems are widely used in spatially distributed tasks, and their collaborative path planning is of great significance for working efficiency. Currently, different multi-robot collaborative path planning methods have been proposed, but how to process the sensory information of neighboring robots at different locations from a local perception perspective in real environment to make better decisions is still a major difficulty. To address this problem, this paper proposes a multi-robot collaborative path planning method based on geometric graph neural network (GeoGNN). GeoGNN introduces the relative position information of neighboring robots into each interaction layer of the graph neural network to better integrate neighbor sensing information. An expert data generation method is designed for the robot to advance in a single step, by which expert data are generated in ROS to train the network. Experimental results show that the accuracy of the proposed method is improved by about 5% compared to the model based only on CNN on the expert data set. In ROS simulation environment path planning test, the success rate is improved by about 4% compared to CNN and flowtime increase is reduced about 8%, which outperforms other graph neural network models.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Movable antenna (MA) array is a novel technology recently developed where positions of transmit/receive antennas can be flexibly adjusted in the specified region to reconfigure the wireless channel and achieve a higher capacity. In this letter, we, for the first time, investigate the MA array-assisted physical-layer security where the confidential information is transmitted from a MA array-enabled Alice to a single-antenna Bob, in the presence of multiple single-antenna and colluding eavesdroppers. We aim to maximize the achievable secrecy rate by jointly designing the transmit beamforming and positions of all antennas at Alice subject to the transmit power budget and specified regions for positions of all transmit antennas. The resulting problem is highly non-convex, for which the projected gradient ascent (PGA) and the alternating optimization methods are utilized to obtain a high-quality suboptimal solution. Simulation results demonstrate that since the additional spatial degree of freedom (DoF) can be fully exploited, the MA array significantly enhances the secrecy rate compared to the conventional fixed-position antenna (FPA) array.
{"title":"Secure Wireless Communication via Movable-Antenna Array","authors":"Hu, Guojie, Wu, Qingqing, Xu, Kui, Si, Jiangbo, Al-Dhahir, Naofal","doi":"10.48550/arxiv.2311.07104","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07104","url":null,"abstract":"Movable antenna (MA) array is a novel technology recently developed where positions of transmit/receive antennas can be flexibly adjusted in the specified region to reconfigure the wireless channel and achieve a higher capacity. In this letter, we, for the first time, investigate the MA array-assisted physical-layer security where the confidential information is transmitted from a MA array-enabled Alice to a single-antenna Bob, in the presence of multiple single-antenna and colluding eavesdroppers. We aim to maximize the achievable secrecy rate by jointly designing the transmit beamforming and positions of all antennas at Alice subject to the transmit power budget and specified regions for positions of all transmit antennas. The resulting problem is highly non-convex, for which the projected gradient ascent (PGA) and the alternating optimization methods are utilized to obtain a high-quality suboptimal solution. Simulation results demonstrate that since the additional spatial degree of freedom (DoF) can be fully exploited, the MA array significantly enhances the secrecy rate compared to the conventional fixed-position antenna (FPA) array.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-13DOI: 10.48550/arxiv.2311.07108
Xu, Tao, He, Jianping
It is critical and challenging to design robust predictors for stochastic dynamical systems (SDSs) with uncertainty quantification (UQ) in the prediction. Specifically, robustness guarantees the worst-case performance when the predictor's information set of the system is inadequate, and UQ characterizes how confident the predictor is about the predictions. However, it is difficult for traditional robust predictors to provide robust UQ because they were designed to robustify the performance of point predictions. In this paper, we investigate how to robustify the probabilistic prediction for SDS, which can inherently provide robust distributional UQ. To characterize the performance of probabilistic predictors, we generalize the concept of likelihood function to likelihood functional, and prove that this metric is a proper scoring rule. Based on this metric, we propose a framework to quantify when the predictor is robust and analyze how the information set affects the robustness. Our framework makes it possible to design robust probabilistic predictors by solving functional optimization problems concerning different information sets. In particular, we design a class of moment-based optimal robust probabilistic predictors and provide a practical Kalman-filter-based algorithm for implementation. Extensive numerical simulations are provided to elaborate on our results.
{"title":"Robust Probabilistic Prediction for Stochastic Dynamical Systems","authors":"Xu, Tao, He, Jianping","doi":"10.48550/arxiv.2311.07108","DOIUrl":"https://doi.org/10.48550/arxiv.2311.07108","url":null,"abstract":"It is critical and challenging to design robust predictors for stochastic dynamical systems (SDSs) with uncertainty quantification (UQ) in the prediction. Specifically, robustness guarantees the worst-case performance when the predictor's information set of the system is inadequate, and UQ characterizes how confident the predictor is about the predictions. However, it is difficult for traditional robust predictors to provide robust UQ because they were designed to robustify the performance of point predictions. In this paper, we investigate how to robustify the probabilistic prediction for SDS, which can inherently provide robust distributional UQ. To characterize the performance of probabilistic predictors, we generalize the concept of likelihood function to likelihood functional, and prove that this metric is a proper scoring rule. Based on this metric, we propose a framework to quantify when the predictor is robust and analyze how the information set affects the robustness. Our framework makes it possible to design robust probabilistic predictors by solving functional optimization problems concerning different information sets. In particular, we design a class of moment-based optimal robust probabilistic predictors and provide a practical Kalman-filter-based algorithm for implementation. Extensive numerical simulations are provided to elaborate on our results.","PeriodicalId":496270,"journal":{"name":"arXiv (Cornell University)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136352643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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