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We present a hypothetical argument against finite-state processes in statistical language modeling that is based on semantics rather than syntax. In this theoretical model, we suppose that the semantic properties of texts in a natural language could be approximately captured by a recently introduced concept of a perigraphic process. Perigraphic processes are a class of stochastic processes that satisfy a Zipf-law accumulation of a subset of factual knowledge, which is time-independent, compressed, and effectively inferrable from the process. We show that the classes of finite-state processes and of perigraphic processes are disjoint, and we present a new simple example of perigraphic processes over a finite alphabet called Oracle processes. The disjointness result makes use of the Hilberg condition, i.e., the almost sure power-law growth of algorithmic mutual information. Using a strongly consistent estimator of the number of hidden states, we show that finite-state processes do not satisfy the Hilberg condition whereas Oracle processes satisfy the Hilberg condition via the data-processing inequality. We discuss the relevance of these mathematical results for theoretical and computational linguistics.

Deep reinforcement learning (DRL) has attracted strong interest since AlphaGo beat human professionals, and its applications in stock trading are widespread. In this paper, an enhanced stock trading strategy called Dual Action and Dual Environment Deep Q-Network (DADE-DQN) for profit and risk reduction is proposed. Our approach incorporates several key highlights. First, to achieve a better balance between exploration and exploitation, a dual-action selection and dual-environment mechanism are incorporated into our DQN framework. Second, our approach optimizes the utilization of storage transitions by utilizing independent replay memories and performing dual mini-batch updates, leading to faster convergence and more efficient learning. Third, a novel deep network structure that incorporates Long Short-Term Memory (LSTM) and attention mechanisms is introduced, thereby improving the network’s ability to capture essential features and patterns. In addition, an innovative feature selection method is presented to efficiently enhance the input data by utilizing mutual information to identify and eliminate irrelevant features. Evaluation on six datasets shows that our DADE-DQN algorithm outperforms multiple DRL-based strategies (TDQN, DQN-Pattern, DQN-Vanilla) and traditional strategies (B&H, S&H, MR, TF). For example, on the KS11 dataset, the DADE-DQN strategy has achieved an impressive cumulative return of 79.43% and a Sharpe ratio of 2.21, outperforming all other methods. These experimental results demonstrate the performance of our approach in enhancing stock trading strategies.

As we discuss, a stationary stochastic process is nonergodic when a random persistent topic can be detected in the infinite random text sampled from the process, whereas we call the process strongly nonergodic when an infinite sequence of independent random bits, called probabilistic facts, is needed to describe this topic completely. Replacing probabilistic facts with an algorithmically random sequence of bits, called algorithmic facts, we adapt this property back to ergodic processes. Subsequently, we call a process perigraphic if the number of algorithmic facts which can be inferred from a finite text sampled from the process grows like a power of the text length. We present a simple example of such a process. Moreover, we demonstrate an assertion which we call the theorem about facts and words. This proposition states that the number of probabilistic or algorithmic facts which can be inferred from a text drawn from a process must be roughly smaller than the number of distinct word-like strings detected in this text by means of the Prediction by Partial Matching (PPM) compression algorithm. We also observe that the number of the word-like strings for a sample of plays by Shakespeare follows an empirical stepwise power law, in a stark contrast to Markov processes. Hence, we suppose that natural language considered as a process is not only non-Markov but also perigraphic.

This paper presents an approach to obtain a deformation which matches two images acquired from different medical imaging modalities. This problem arises in the investigation of human brains. Two distance functionals for the images are proposed with different pros and cons. These functionals are to be minimized. We add a smoothing term to the minimization problem which retains certain desired elastic features in the solution. At each minimization step an approximate solution for the linearized problem is computed with a multigrid method as an inner iteration. Furthermore, we use a multiresolution minimization approach to obtain a suitable initial guess. Finally, we present some experimental results for registration problems of synthetic images and for a real computer tomography (CT)--magnetic resonance imaging (MRI) registration.

A coterie under an underlying set U is a family of subsets of U such that every pair of subsets has at least one element in common, but neither is a subset of the other. A coterie C under U is said to be nondominated (ND) if there is no other coterie D under U such that, for every $Q \\in C$, there exists $Q' \\in D$ satisfying $Q' \\subseteq Q$. We introduce the operation $\\sigma$ which transforms a ND coterie to another ND coterie. A regular coterie is a natural generalization of a vote-assignable coterie. We show that any regular ND coterie C can be transformed to any other regular ND coterie D by judiciously applying the $\\sigma$ operation to C at most |C|+|D|-2 times. As another application of the $\\sigma$ operation, we present an incrementally polynomial-time algorithm for generating all regular ND coteries. We then introduce the concept of a g-regular functional as a generalization of availability. We show how to construct an optimum coterie C with respect to a g-regular functional in O(n3|C|) time, where n =|U|. Finally, we discuss the structures of optimum coteries with respect to a g-regular functional.