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Seismic data often contain gaps due to various obstacles in the investigated area and recording instrument failures. Deep learning techniques offer promising solutions for reconstructing missing data parts by leveraging existing information. However, self-supervised methods frequently struggle with capturing under-represented features such as weaker events, crossing dips, and higher frequencies. To address these challenges, we propose a novel ensemble deep model along with a tailored self-supervised training approach for reconstructing seismic data with consecutive missing traces. Our model comprises two branches of U-nets, each fed from distinct data transformation modules aimed at amplifying under-represented features and promoting diversity among learners. Our loss function minimizes relative errors at the outputs of individual branches and the entire model, ensuring accurate reconstruction of various features while maintaining overall data integrity. Additionally, we employ masking while training to enhance sample diversity and memory efficiency. Application on two benchmark synthetic datasets and two real datasets demonstrates improved accuracy compared to a conventional U-net, successfully reconstructing weak events, diffractions, higher frequencies, and reflections obscured by groundroll. However, our method requires a threefold of training time compared to a simple U-net. An implementation of our method with TensorFlow is also made available.

Trace-wise noise is a type of noise often seen in seismic data, which is characterized by vertical coherency and horizontal incoherency. Using self-supervised deep learning to attenuate this type of noise, the conventional blind-trace deep learning trains a network to blindly reconstruct each trace in the data from its surrounding traces; it attenuates isolated trace-wise noise but causes signal leakage in clean and noisy traces and reconstruction errors next to each noisy trace. To reduce signal leakage and improve denoising, we propose a new loss function and masking procedure in semi-blind-trace deep learning. Our hybrid loss function has weighted active zones that cover masked and non-masked traces. Therefore, the network is not blinded to clean traces during their reconstruction. During training, we dynamically change the masks' characteristics. The goal is to train the network to learn the characteristics of the signal instead of noise. The proposed algorithm enables the designed U-net to detect and attenuate trace-wise noise without having prior information about the noise. A new hyperparameter of our method is the relative weight between the masked and non-masked traces' contribution to the loss function. Numerical experiments show that selecting a small value for this parameter is enough to significantly decrease signal leakage. The proposed algorithm is tested on synthetic and real off-shore and land datasets with different noises. The results show the superb ability of the method to attenuate trace-wise noise while preserving other events. An implementation of the proposed algorithm as a Python code is also made available.

In this paper, we propose a novel joint intelligent trajectory design and resource allocation algorithm based on user's mobility and their requested services for unmanned aerial vehicles (UAVs) assisted networks, where UAVs act as nodes of a network function virtualization (NFV) enabled network. Our objective is to maximize energy efficiency and minimize the average delay on all services by allocating the limited radio and NFV resources. In addition, due to the traffic conditions and mobility of users, we let some Virtual Network Functions (VNFs) to migrate from their current locations to other locations to satisfy the Quality of Service requirements. We formulate our problem to find near-optimal locations of UAVs, transmit power, subcarrier assignment, placement, and scheduling the requested service's functions over the UAVs and perform suitable VNF migration. Then we propose a novel Hierarchical Hybrid Continuous and Discrete Action (HHCDA) deep reinforcement learning method to solve our problem. Finally, the convergence and computational complexity of the proposed algorithm and its performance analyzed for different parameters. Simulation results show that our proposed HHCDA method decreases the request reject rate and average delay by 31.5% and 20% and increases the energy efficiency by 40% compared to DDPG method.

In delay-sensitive industrial internet of things (IIoT) applications, the age of information (AoI) is employed to characterize the freshness of information. Meanwhile, the emerging network function virtualization provides flexibility and agility for service providers to deliver a given network service using a sequence of virtual network functions (VNFs). However, suitable VNF placement and scheduling in these schemes is NP-hard and finding a globally optimal solution by traditional approaches is complex. Recently, deep reinforcement learning (DRL) has appeared as a viable way to solve such problems. In this paper, we first utilize single agent low-complex compound action actor-critic RL to cover both discrete and continuous actions and jointly minimize VNF cost and AoI in terms of network resources under end-to end Quality of Service constraints. To surmount the single-agent capacity limitation for learning, we then extend our solution to a multi-agent DRL scheme in which agents collaborate with each other. Simulation results demonstrate that single-agent schemes significantly outperform the greedy algorithm in terms of average network cost and AoI. Moreover, multi-agent solution decreases the average cost by dividing the tasks between the agents. However, it needs more iterations to be learned due to the requirement on the agents collaboration.

In this paper, we devise a novel radio resource block (RB) structure named dynamic resource block structure (D-RBS) which can handle low latency traffics and large fluctuations in data rates by exploiting smart time and frequency duplexing. In our framework, the main resource block with a predefined bandwidth and time duration is divided into several small blocks with the same bandwidth and time duration. Depending on the service requirements, e.g., data rate and latency, the users are assigned to some these small blocks which could be noncontiguous both in frequency and time. This is in contrast to the previously introduced static resource block structure (S-RBS) where the size of each RB is predetermined and fixed. We provide resource allocation frameworks for this RB structure and formulate the optimization problems whose solutions are obtained by alternate search method (ASM) based on successive convex approximation approach (SCA). We provide a global optimal solution by exploiting the monotonic optimization method. By simulation we study the performance of our proposed scheme with S-RBS scheme and show it has 26% gain compared to the S-RBS scheme.

We develop an entropic framework to model the dynamics of stocks and European Options. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. The objective of the paper is to lay down an alternative framework for modeling dynamics. An important information about the dynamics of a stock's price is scale invariance. By imposing the scale invariant symmetry, we arrive at choosing the logarithm of the stock's price as the proper variable to model. The dynamics of stock log price is derived using two pieces of information, the continuity of motion and the directionality constraint. The resulting model is the same as the Geometric Brownian Motion, GBM, of the stock price which is manifestly scale invariant. Furthermore, we come up with the dynamics of probability density function, which is a Fokker--Planck equation. Next, we extend the model to value the European Options on a stock. Derivative securities ought to be prices such that there is no arbitrage. To ensure the no-arbitrage pricing, we derive the risk-neutral measure by incorporating the risk-neutral information. Consequently, the Black--Scholes model and the Black--Scholes-Merton differential equation are derived.

An Entropic Dynamics of exchange rates is laid down to model the dynamics of foreign exchange rates, FX, and European Options on FX. The main objective is to represent an alternative framework to model dynamics. Entropic inference is an inductive inference framework equipped with proper tools to handle situations where incomplete information is available. Entropic Dynamics is an application of entropic inference, which is equipped with the entropic notion of time to model dynamics. The scale invariance is a symmetry of the dynamics of exchange rates, which is manifested in our formalism. To make the formalism manifestly invariant under this symmetry, we arrive at choosing the logarithm of the exchange rate as the proper variable to model. By taking into account the relevant information about the exchange rates, we derive the Geometric Brownian Motion, GBM, of the exchange rate, which is manifestly invariant under the scale transformation. Securities should be valued such that there is no arbitrage opportunity. To this end, we derive a risk-neutral measure to value European Options on FX. The resulting model is the celebrated Garman-Kohlhagen model.

The Entropic Dynamics reconstruction of quantum mechanics is extended to quantum field theory in curved space-time. The Entropic Dynamics framework, which derives quantum theory as an application of the method of maximum entropy, is combined with the covariant methods of Dirac, Hojman, Kucha\v{r}, and Teitelboim, which they used to develop a framework for classical covariant Hamiltonian theories. The goal is to formulate an information-based alternative to current approaches based on algebraic quantum field theory. One key ingredient is the adoption of a local notion of entropic time in which instants are defined on curved three-dimensional surfaces and time evolution consists of the accumulation of changes induced by local deformations of these surfaces. The resulting dynamics is a non-dissipative diffusion that is constrained by the requirements of foliation invariance and incorporates the necessary local quantum potentials. As applications of the formalism we derive the Ehrenfest relations for fields in curved-spacetime and briefly discuss the nature of divergences in quantum field theory., Comment: V2 contains added comments on reconstructing QFT, on QFT divergences, various improvements in style, and corrects some typos. V3 contains new section containing applications, including a derivation of the Ehrenfest relations for a quantum scalar field in curved space-time

Entropic Dynamics (ED) is a framework for constructing dynamical theories of inference using the tools of inductive reasoning. A central feature of the ED framework is the special focus placed on time. In previous work a global entropic time was used to derive a quantum theory of relativistic scalar fields. This theory, however, suffered from a lack of explicit or manifest Lorentz symmetry. In this paper we explore an alternative formulation in which the relativistic aspects of the theory are manifest. The approach we pursue here is inspired by the works of Dirac, Kuchar, and Teitelboim in their development of covariant Hamiltonian methods. The key ingredient here is the adoption of a local notion of time, which we call entropic time. This construction allows the expression of arbitrary notion of simultaneity, in accord with relativity. In order to ensure, however, that this local time dynamics is compatible with the background spacetime we must impose a set of Poisson bracket constraints; these constraints themselves result from requiring the dynamcics to be path independent, in the sense of Teitelboim and Kuchar., Comment: An extended version of work presented at MaxEnt 2016, the 36th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering; July 10-15 2016, Ghent, Belgium

This paper addresses the four enabling technologies, namely multi-user sparse code multiple access (SCMA), content caching, energy harvesting, and physical layer security for proposing an energy and spectral efficient resource allocation algorithm for the access and backhaul links in heterogeneous cellular networks. Although each of the above mentioned issues could be a topic of research, in a real situation, we would face a complicated scenario where they should be considered jointly, and hence, our target is to consider these technologies jointly in a unified framework. Moreover, we propose two novel content delivery scenarios: 1) single frame content delivery (SFCD), and 2) multiple frames content delivery (MFCD), where the time duration of serving user requests is divided into several frames. In the first scenario, the requested content by each user is served over one frame. However, in the second scenario, the requested content by each user can be delivered over several frames. We formulate the resource allocation for the proposed scenarios as optimization problems where our main aim is to maximize the energy efficiency of access links subject to the transmit power and rate constraints of access and backhaul links, caching and energy harvesting constraints, and SCMA codebook allocation limitations. Due to the practical limitations, we assume that the channel state information values between eavesdroppers and base stations are uncertain and design the network for the worst case scenario. Since the corresponding optimization problems are mixed integer non-linear and nonconvex programming, NP-hard, and intractable, we propose an iterative algorithm based on the well-known alternate and successive convex approximation methods.

Entropic dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. Entropic dynamics on flat spaces has been extensively studied. The objective of this paper is to extend the entropic dynamics of $N$ particles to curved spaces. The important new feature is that the displacement of a particle does not transform like a vector because fluctuations can be large enough to feel the effects of curvature. The final result is a modified Schr\"odinger equation in which the usual Laplacian is replaced by the Laplace-Beltrami operator., Comment: Presented at MaxEnt 2015, the 35th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 19--24, 2015, Potsdam NY, USA)