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2022 ◽  
Author(s):  
Abraham Nunes ◽  
Selena Singh ◽  
Jared Allman ◽  
Suzanna Becker ◽  
Abigail Ortiz ◽  
...  

Bipolar disorder (BD) is a mood disorder involving recurring (hypo)manic and depressive episodes. The inherently temporal nature of BD has inspired its conceptualization using dynamical systems theory, which is a mathematical framework for understanding systems that evolve over time. In this paper we provide a critical review of dynamical systems models of BD. Owing to heterogeneity of methodologies and experimental designs in computational modeling, we designed a structured approach to guide our review in a fashion that parallels the appraisal of animal models by their Face, Predictive, and Construct Validity. This tool, the Validity Appraisal Guide for Computational Models (VAG-CM) is not an absolute estimate of validity, but rather a guide for more objective appraisal of models in this review. We identified 26 studies published before November 18, 2021 that proposed generative dynamical systems models of time-varying signals in BD. Two raters independently applied the VAG-CM to included studies, obtaining a mean Cohen's kappa of 0.55 (95% CI [0.45, 0.64]) prior to establishing consensus ratings. Consensus VAG-CM ratings revealed three model/study clusters: data-driven models with face validity, theory-driven models with predictive validity, and theory-driven models lacking all forms of validity. We conclude that future models should be developed using a hybrid approach that first operationalizes BD features of interest using empirical data (a data-driven approach), followed by explanations of those features using generative models with components that are homologous to physiological or psychological systems involved in BD (a theory-driven approach).


PLoS ONE ◽  
2022 ◽  
Vol 17 (1) ◽  
pp. e0262080
Author(s):  
Geoffrey C. Poole ◽  
S. Kathleen Fogg ◽  
Scott J. O’Daniel ◽  
Byron E. Amerson ◽  
Ann Marie Reinhold ◽  
...  

Hyporheic exchange is now widely acknowledged as a key driver of ecosystem processes in many streams. Yet stream ecologists have been slow to adopt nuanced hydrologic frameworks developed and applied by engineers and hydrologists to describe the relationship between water storage, water age, and water balance in finite hydrosystems such as hyporheic zones. Here, in the context of hyporheic hydrology, we summarize a well-established mathematical framework useful for describing hyporheic hydrology, while also applying the framework heuristically to visualize the relationships between water age, rates of hyporheic exchange, and water volume within hyporheic zones. Building on this heuristic application, we discuss how improved accuracy in the conceptualization of hyporheic exchange can yield a deeper understanding of the role of the hyporheic zone in stream ecosystems. Although the equations presented here have been well-described for decades, our aim is to make the mathematical basis as accessible as possible and to encourage broader understanding among aquatic ecologists of the implications of tailed age distributions commonly observed in water discharged from and stored within hyporheic zones. Our quantitative description of “hyporheic hydraulic geometry,” associated visualizations, and discussion offer a nuanced and realistic understanding of hyporheic hydrology to aid in considering hyporheic exchange in the context of river and stream ecosystem science and management.


2022 ◽  
Vol 4 ◽  
Author(s):  
David Orrell ◽  
Monireh Houshmand

This paper describes an approach to economics that is inspired by quantum computing, and is motivated by the need to develop a consistent quantum mathematical framework for economics. The traditional neoclassical approach assumes that rational utility-optimisers drive market prices to a stable equilibrium, subject to external perturbations or market failures. While this approach has been highly influential, it has come under increasing criticism following the financial crisis of 2007/8. The quantum approach, in contrast, is inherently probabilistic and dynamic. Decision-makers are described, not by a utility function, but by a propensity function which specifies the probability of transacting. We show how a number of cognitive phenomena such as preference reversal and the disjunction effect can be modelled by using a simple quantum circuit to generate an appropriate propensity function. Conversely, a general propensity function can be quantized, via an entropic force, to incorporate effects such as interference and entanglement that characterise human decision-making. Applications to some common problems and topics in economics and finance, including the use of quantum artificial intelligence, are discussed.


2022 ◽  
Author(s):  
Eyke Hüllermeier ◽  
Marcel Wever ◽  
Eneldo Loza Mencia ◽  
Johannes Fürnkranz ◽  
Michael Rapp

AbstractThe idea to exploit label dependencies for better prediction is at the core of methods for multi-label classification (MLC), and performance improvements are normally explained in this way. Surprisingly, however, there is no established methodology that allows to analyze the dependence-awareness of MLC algorithms. With that goal in mind, we introduce a class of loss functions that are able to capture the important aspect of label dependence. To this end, we leverage the mathematical framework of non-additive measures and integrals. Roughly speaking, a non-additive measure allows for modeling the importance of correct predictions of label subsets (instead of single labels), and thereby their impact on the overall evaluation, in a flexible way. The well-known Hamming and subset 0/1 losses are rather extreme special cases of this function class, which give full importance to single label sets or the entire label set, respectively. We present concrete instantiations of this class, which appear to be especially appealing from a modeling perspective. The assessment of multi-label classifiers in terms of these losses is illustrated in an empirical study, clearly showing their aptness at capturing label dependencies. Finally, while not being the main goal of this study, we also show some preliminary results on the minimization of this parametrized family of losses.


2022 ◽  
pp. 1-20
Author(s):  
Noah Stemeroff

Abstract Perspectival realists often appeal to the methodology of science to secure a realist account of the retention and continued success of scientific claims through the progress of science (e.g. Massimi, 2016). However, in the context of modern physics, the retention and continued success of scientific claims is typically only definable within a mathematical framework. In this paper, I argue that this concern leaves the perspectivist open to Cassirer’s (1910) neo-Kantian critique of the applicability of mathematics in the natural sciences. To support this criticism, I present a case study on the conservation of energy in modern physics.


Author(s):  
Firoz Ahmad ◽  
Ahmad Yusuf Adhami ◽  
Boby John ◽  
Amit Reza

Many decision-making problems can solve successfully by traditional optimization methods with a well-defined configuration.  The formulation of such optimization problems depends on crisply objective functions and a specific system of constraints.  Nevertheless, in reality, in any decision-making process, it is often observed that due to some doubt or hesitation, it is pretty tricky for decision-maker(s) to specify the precise/crisp value of any parameters and compelled to take opinions from different experts which leads towards a set of conflicting values regarding satisfaction level of decision-maker(s). Therefore the real decision-making problem cannot always be deterministic. Various types of uncertainties in parameters make it fuzzy.  This paper presents a practical mathematical framework to reflect the reality involved in any decision-making process. The proposed method has taken advantage of the hesitant fuzzy aggregation operator and presents a particular way to emerge in a decision-making process. For this purpose,  we have discussed a couple of different hesitant fuzzy aggregation operators and developed linear and hyperbolic membership functions under hesitant fuzziness, which contains the concept of hesitant degrees for different objectives.  Finally, an example based on a multiobjective optimization problem is presented to illustrate the validity and applicability of our proposed models.


2022 ◽  
Vol 32 (2) ◽  
Author(s):  
O. E. Omel’chenko

AbstractAbout two decades ago it was discovered that systems of nonlocally coupled oscillators can exhibit unusual symmetry-breaking patterns composed of coherent and incoherent regions. Since then such patterns, called chimera states, have been the subject of intensive study but mostly in the stationary case when the coarse-grained system dynamics remains unchanged over time. Nonstationary coherence–incoherence patterns, in particular periodically breathing chimera states, were also reported, however not investigated systematically because of their complexity. In this paper we suggest a semi-analytic solution to the above problem providing a mathematical framework for the analysis of breathing chimera states in a ring of nonlocally coupled phase oscillators. Our approach relies on the consideration of an integro-differential equation describing the long-term coarse-grained dynamics of the oscillator system. For this equation we specify a class of solutions relevant to breathing chimera states. We derive a self-consistency equation for these solutions and carry out their stability analysis. We show that our approach correctly predicts macroscopic features of breathing chimera states. Moreover, we point out its potential application to other models which can be studied using the Ott–Antonsen reduction technique.


Author(s):  
Hanna Kurniawati

Planning under uncertainty is critical to robotics. The partially observable Markov decision process (POMDP) is a mathematical framework for such planning problems. POMDPs are powerful because of their careful quantification of the nondeterministic effects of actions and the partial observability of the states. But for the same reason, they are notorious for their high computational complexity and have been deemed impractical for robotics. However, over the past two decades, the development of sampling-based approximate solvers has led to tremendous advances in POMDP-solving capabilities. Although these solvers do not generate the optimal solution, they can compute good POMDP solutions that significantly improve the robustness of robotics systems within reasonable computational resources, thereby making POMDPs practical for many realistic robotics problems. This article presents a review of POMDPs, emphasizing computational issues that have hindered their practicality in robotics and ideas in sampling-based solvers that have alleviated such difficulties, together with lessons learned from applying POMDPs to physical robots. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.


2022 ◽  
Author(s):  
Katherine M Steele ◽  
Michael H Schwartz

Background Altered motor control is common in cerebral palsy (CP). Understanding how altered motor control effects movement and treatment outcomes is important, but challenging due to complex interactions between impairments. While regression can be used to examine associations between impairments and gait, causal modeling provides a mathematical framework to specify assumed causal relationships, identify covariates that may introduce bias, and test model plausibility. The goal of this research was to quantify the causal effects of altered motor control and other impairments on gait, before and after single-event multi-level orthopedic surgery (SEMLS). Methods We evaluated the impact of SEMLS on change in Gait Deviation Index (GDI) between gait analyses. We constructed our causal model with a Directed Acyclic Graph that included the assumed causal relationships between SEMLS, change in GDI, baseline GDI (GDIpre), baseline neurologic and orthopedic impairments (Imppre), age, and surgical history. We identified the adjustment set to evaluate the causal effect of SEMLS on change in GDI and the impact of Imppre on change in GDI and GDIpre. We used Bayesian Additive Regression Trees (BART) and accumulated local effects to assess relative effects. Results We prospectively recruited a cohort of children with bilateral CP undergoing SEMLS (N=54, 35 males, age: 10.5+/-3.1 years) and identified a control cohort with bilateral CP who did not undergo SEMLS (N=55, 30 males, age: 10.0+/-3.4 years). There was a small positive causal effect of SEMLS on change in GDI (1.68 GDI points). Altered motor control (i.e., dynamic and static motor control) and strength had strong effects on GDIpre, but minimal effects on change in GDI. Spasticity and orthopedic impairments had minimal effects on GDIpre or change in GDI. Conclusions Altered motor control and other baseline impairments did have a strong effect on GDIpre, indicating that these impairments do have a causal effect on a child's gait pattern but minimal effect on expected changes in GDI after SEMLS. Heterogeneity in outcomes suggests there are other factors contributing to changes in gait. Identifying these factors and employing causal methods to examine the complex relationships between impairments and movement will be required to advance our understanding and care of children with CP.


2022 ◽  
Vol 19 (186) ◽  
Author(s):  
Jietuo Wang ◽  
Federico Dalla Barba ◽  
Alessio Roccon ◽  
Gaetano Sardina ◽  
Alfredo Soldati ◽  
...  

The outbreak of the COVID-19 pandemic highlighted the importance of accurately modelling the pathogen transmission via droplets and aerosols emitted while speaking, coughing and sneezing. In this work, we present an effective model for assessing the direct contagion risk associated with these pathogen-laden droplets. In particular, using the most recent studies on multi-phase flow physics, we develop an effective yet simple framework capable of predicting the infection risk associated with different respiratory activities in different ambient conditions. We start by describing the mathematical framework and benchmarking the model predictions against well-assessed literature results. Then, we provide a systematic assessment of the effects of physical distancing and face coverings on the direct infection risk. The present results indicate that the risk of infection is vastly impacted by the ambient conditions and the type of respiratory activity, suggesting the non-existence of a universal safe distance. Meanwhile, wearing face masks provides excellent protection, effectively limiting the transmission of pathogens even at short physical distances, i.e. 1 m.


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