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Digital memcomputing machines (DMMs) have been designed to solve complex combinatorial optimization problems. Since DMMs are fundamentally classical dynamical systems, their ordinary differential equations (ODEs) can be efficiently simulated on modern computers. This provides a unique platform to study their performance under various conditions. An aspect that has received little attention so far is how their performance is affected by the numerical errors in the solution of their ODEs and the physical noise they would be naturally subject to if built in hardware. Here, we analyze these two aspects in detail by varying the integration time step (numerical noise) and adding stochastic perturbations (physical noise) into the equations of DMMs. We are particularly interested in understanding how noise induces a chaotic transition that marks the shift from successful problem-solving to failure in these systems. Our study includes an analysis of power spectra and Lyapunov exponents depending on the noise strength. The results reveal a correlation between the instance solvability and the sign of the ensemble averaged mean largest Lyapunov exponent. Interestingly, we find a regime in which DMMs with positive mean largest Lyapunov exponents still exhibit solvability. Furthermore, the power spectra provide additional information about our system by distinguishing between regular behavior (peaks) and chaotic behavior (broadband spectrum). Therefore, power spectra could be utilized to control whether a DMM operates in the optimal dynamical regime. Overall, we find that the qualitative effects of numerical and physical noise are mostly similar, despite their fundamentally different origin. 

Recently, there has been an increasing interest in employing dynamical systems as solvers of NP-complete problems. In this paper, we present accurate implementations of two continuous-time dynamical solvers, known in the literature as analog SAT and digital memcomputing, using advanced numerical integration algorithms of SPICE circuit simulators. For this purpose, we have developed Python scripts that convert Boolean satisfiability (SAT) problems into electronic circuits representing the analog SAT and digital memcomputing dynamical systems. Our Python scripts process conjunctive normal form (CNF) files and create netlists that can be directly imported into LTspice. We explore the SPICE implementations of analog SAT and digital memcomputing solvers by applying these to a selected set of problems and present some interesting and potentially useful findings related to digital memcomputing and analog SAT. In this work, we also introduce networks of continuous-time solvers with potential applications extending beyond the solution of Boolean satisfiability problems. 

This paper addresses novel applications to practical modelling of the newly developed theory of necessary optimality conditions in controlled sweeping/Moreau processes with free time and pointwise control and state constraints. Problems of this type appear, in particular, in dynamical models dealing with unmanned surface vehicles (USVs) and nanoparticles. We formulate optimal control problems for a general class of such dynamical systems and show that the developed necessary optimality conditions for constrained free-time controlled sweeping processes lead us to designing efficient procedures to solve practical models of this class. Moreover, the paper contains numerical calculations of optimal solutions to marine USVs and nanoparticle models in specific situations. Overall, this study contributes to the advancement of optimal control theory for constrained sweeping processes and its practical applications in the fields of marine USVs and nanoparticle modelling. 

Anomaly analysis is an important component of any surveillance system. In recent years, it has drawn the attention of the computer vision and machine learning communities. In this article, our overarching goal is thus to provide a coherent and systematic review of state-of-the-art techniques and a comprehensive review of the research works in anomaly analysis. We will provide a broad vision of computational models, datasets, metrics, extensive experiments, and what anomaly analysis can do in images and videos. Intensively covering nearly 200 publications, we review (i) anomaly related surveys, (ii) taxonomy for anomaly problems, (iii) the computational models, (iv) the benchmark datasets for studying abnormalities in images and videos, and (v) the performance of state-of-the-art methods in this research problem. In addition, we provide insightful discussions and pave the way for future work. 

Nucleon structure functions, as measured in lepton-nucleon scattering, have historically provided a critical observable in the study of partonic dynamics within the nucleon. However, at very large parton momenta, it is both experimentally and theoretically challenging to extract parton distributions due to the probable onset of nonperturbative contributions and the unavailability of high-precision data at critical kinematics. Extraction of the neutron structure and the d quark distribution have been further challenging because of the necessity of applying nuclear corrections when utilizing scattering data from a deuteron target to extract the free neutron structure. However, a program of experiments has been carried out recently at the energy-upgraded Jefferson Lab electron accelerator aimed at significantly reducing the nuclear correction uncertainties on the d quark distribution function at large partonic momentum. This allows leveraging the vast body of deuterium data covering a large kinematic range to be utilized for d quark parton distribution function extraction. In this Letter, we present new data from experiment E12-10-002, carried out in Jefferson Lab Experimental Hall C, on the deuteron to proton cross section ratio at large Bjorken $x$. These results significantly improve the precision of existing data and provide a first look at the expected impact on quark distributions extracted from parton distribution function fits. 

NKX3.1’s downregulation is strongly associated with prostate cancer (PCa) initiation, progression, and CRPC development. Nevertheless, a clear disagreement exists between NKX3.1 protein and mRNA levels in PCa tissues, indicating that its regulation at a post-translational level plays a vital role. This study identified a strong negative relationship between NKX3.1 and LIMK2, which is critical in CRPC pathogenesis. We identified that NKX3.1 degradation by direct phosphorylation by LIMK2 is crucial for promoting oncogenicity in CRPC cells and in vivo. LIMK2 also downregulates NKX3.1 mRNA levels. In return, NKX3.1 promotes LIMK2’s ubiquitylation. Thus, the negative crosstalk between LIMK2-NKX3.1 regulates AR, ARv7, and AKT signaling, promoting aggressive phenotypes. We also provide a new link between NKX3.1 and PTEN, both of which are downregulated by LIMK2. PTEN loss is strongly linked with NKX3.1 downregulation. As NKX3.1 is a prostate-specific tumor suppressor, preserving its levels by LIMK2 inhibition provides a tremendous opportunity for developing targeted therapy in CRPC. Further, as NKX3.1 downregulates AR transcription and inhibits AKT signaling, restoring its levels by inhibiting LIMK2 is expected to be especially beneficial by co-targeting two driver pathways in tandem, a highly desirable requisite for developing effective PCa therapeutics.