Parameter Estimation in the Age of Degeneracy and Unidentifiability

Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one’s ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the notion of degeneracy where multiple parameter sets produce the same pattern. Therefore, the inverse function of determining the model parameters from the data is not well defined. Degeneracy is not only a mathematical property of models, but it has also been reported in biological experiments. Classical studies on structural unidentifiability focused on the notion that one can at most identify combinations of unidentifiable model parameters. We have identified a different type of structural degeneracy/unidentifiability present in a family of models, which we refer to as the Lambda-Omega (Λ-Ω) models. These are an extension of the classical lambda-omega (λ-ω) models that have been used to model biological systems, and display a richer dynamic behavior and waveforms that range from sinusoidal to square wave to spike like. We show that the Λ-Ω models feature infinitely many parameter sets that produce identical stable oscillations, except possible for a phase shift (reflecting the initial phase). These degenerate parameters are not identifiable combinations of unidentifiable parameters as is the case in structural degeneracy. In fact, reducing the number of model parameters in the Λ-Ω models is minimal in the sense that each one controls a different aspect of the model dynamics and the dynamic complexity of the system would be reduced by reducing the number of parameters. We argue that the family of Λ-Ω models serves as a framework for the systematic investigation of degeneracy and identifiability in dynamic models and for the investigation of the interplay between structural and other forms of unidentifiability resulting on the lack of information from the experimental/observational data.

Active inference unifies intentional and conflict-resolution imperatives of motor control

The field of motor control has long focused on the achievement of external goals through action (e.g., reaching and grasping objects). However, recent studies in conditions of multisensory conflict, such as when a subject experiences the rubber hand illusion or embodies an avatar in virtual reality, reveal the presence of unconscious movements that are not goal-directed, but rather aim at resolving multisensory conflicts; for example, by aligning the position of a person’s arm with that of an embodied avatar. This second, conflict-resolution imperative of movement control did not emerge in classical studies of motor adaptation and online corrections, which did not allow movements to reduce the conflicts; and has been largely ignored so far in formal theories. Here, we propose a model of movement control grounded in the theory of active inference that integrates intentional and conflict-resolution imperatives. We present three simulations showing that the active inference model is able to characterize movements guided by the intention to achieve an external goal, by the necessity to resolve multisensory conflict, or both. Furthermore, our simulations reveal a fundamental difference between the (active) inference underlying intentional and conflict-resolution imperatives, respectively, by showing that it is driven by two different (model and sensory) kinds of prediction errors. Finally, our simulations show that when movement is only guided by conflict-resolution, the model incorrectly infers that is velocity is zero, as if it was not moving. This result suggests a novel speculative explanation for the fact that people are unaware of their subtle compensatory movements to avoid multisensory conflict. Furthermore, it can potentially help shed light on deficits of motor awareness that arise in psychopathological conditions.

Molecular Segmentation of the Spinal Trigeminal Nucleus in the Adult Mouse Brain

The trigeminal column is a hindbrain structure formed by second order sensory neurons that receive afferences from trigeminal primary (ganglionic) nerve fibers. Classical studies subdivide it into the principal sensory trigeminal nucleus located next to the pontine nerve root, and the spinal trigeminal nucleus which in turn consists of oral, interpolar and caudal subnuclei. On the other hand, according to the prosomeric model, this column would be subdivided into segmental units derived from respective rhombomeres. Experimental studies have mapped the principal sensory trigeminal nucleus to pontine rhombomeres (r) r2-r3 in the mouse. The spinal trigeminal nucleus emerges as a plurisegmental formation covering several rhombomeres (r4 to r11 in mice) across pontine, retropontine and medullary hindbrain regions. In the present work we reexamined the issue of rhombomeric vs. classical subdivisions of this column. To this end, we analyzed its subdivisions in an AZIN2-lacZ transgenic mouse, known as a reference model for hindbrain topography, together with transgenic reporter lines for trigeminal fibers. We screened as well for genes differentially expressed along the axial dimension of this structure in the adult and juvenile mouse brain. This analysis yielded genes from multiple functional families that display transverse domains fitting the mentioned rhombomeric map. The spinal trigeminal nucleus thus represents a plurisegmental structure with a series of distinct neuromeric units having unique combinatorial molecular profiles.

A REVIEW ON THE CLASSICAL CONCEPT OF TOURISM ATTRACTION

In most countries, tourism is seen as one of the important sectors that help in improving economic stability. There was a variety of tourism destinations that could be promoted. It is believed that each tourism destination has its attractions. Numerous studies on tourism attractions have been published since the 1970s. However, different authors have their perspectives on tourism attractions. Therefore, this article explores the relationship between the early study on tourism attraction with the current studies. This article's main objective is to explore the classical concept of tourism attraction and review the current trend in tourism study. Previous literature published in various sources of the database will be reviewed. The result shows that different concepts on tourism attractions have been outlined among the leading authors. The integration of classical studies on tourism attraction concept demonstrated that it covers four main components; Management, Human, Place, and Experience. The concepts published from the 1970s to the 1990s proved relevant to be used in recent studies. This study attempts to provide an overview of the significant influence of previous literature on the current studies.

Parameter estimation in the age of degeneracy and unidentifiability

Parameter estimation from observable or experimental data is a crucial stage in any modeling study. Identifiability refers to one's ability to uniquely estimate the model parameters from the available data. Structural unidentifiability in dynamic models, the opposite of identifiability, is associated with the notion of degeneracy where multiple parameter sets produce the same pattern. Therefore, the inverse function of determining the model parameters from the data is not well defined. Degeneracy is not only a mathematical property of models, but it has also been reported in biological experiments. Classical studies on structural unidentifiability focused on the notion that one can at most identify combinations of unidentifiable model parameters. We have identified a different type of structural degeneracy/unidentifiability present in a family of models, which we refer to as the Lambda-Omega (\Ldaomega) models. These are an extension of the classical lambda-omega (\ldaomega) models that have been used to model biological systems, and display a richer dynamic behavior and waveforms that range from sinusoidal to square-wave to spike-like. We show that the \Ldaomega\, models feature infinitely many parameter sets that produce identical stable oscillations, except possible for a phase-shift (reflecting the initial phase). These degenerate parameters are not identifiable combinations of unidentifiable parameters as is the case in structural degeneracy. In fact, reducing the number of model parameters in the \Ldaomega\, models is minimal in the sense that each one controls a different aspect of the model dynamics and the dynamic complexity of the system would be reduced by reducing the number of parameters. We argue that the family of \Ldaomega\, models serves as a framework for the systematic investigation of degeneracy and identifiability in dynamic models and for the investigation of the interplay between structural and other forms of unidentifiability resulting on the lack of information from the experimental/observational data.

Internal Instability in Soils: A Critical Review of the Fundamentals and Ramifications

Seepage-induced fine-particle migration that leads to a change in the conductivity of a soil matrix is referred to as internal instability. This could jeopardize the structural integrity of the soil matrix by initiating suffusion (or suffosion), a form of internal erosion. Susceptibility to suffusion has been studied mostly under extreme laboratory conditions to develop empirical design criteria, which are typically based on the particle size distribution. The physics governing the process have not been comprehensively uncovered in the classical studies because of experimental limitations. Mainstream evaluation methods often over-idealize the suffusion process, holding a probabilistic perspective for estimating constriction sizes and fines migration. Prospective studies on constitutive modeling techniques and modern computational techniques have allowed a more representative evaluation and deeper insight into the problem. Recent advances in sensing technologies, visualization, and tracking techniques have equally enriched the quality of the data on suffusion. This paper sets out to present the long-standing knowledge on the internal instability phenomenon in soils. An attempt is made to pinpoint ambiguities and underscore research gaps. The classical empirical studies and modern visualizing techniques are integrated with particle-based numerical simulations to strengthen the theoretical understanding of the phenomenon.

The Cellular and Molecular Basis of Sour Taste

Sour taste, the taste of acids, is one of the most enigmatic of the five basic taste qualities; its function is unclear and its receptor was until recently unknown. Sour tastes are transduced in taste buds on the tongue and palate epithelium by a subset of taste receptor cells, known as type III cells. Type III cells express a number of unique markers, including the PKD2L1 gene, which allow for their identification and manipulation. These cells respond to acid stimuli with action potentials and release neurotransmitters onto afferent nerve fibers, with cell bodies in geniculate and petrosal ganglia. Here, we review classical studies of sour taste leading up to the identification of the sour receptor as the proton channel, OTOP1. Expected final online publication date for the Annual Review of Physiology, Volume 84 is February 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

The Divided Liang Dynasty Literary World Seen through the Liu-Dao Dispute

The tension between the literary styles of Liu Xiaochuo 劉孝綽 (481–539) and Dao Qia 到洽 (490–527) can be understood as a debate between poetic genius and a more scholarly focus, signaling a confrontation between the capital's literary camps in the Putong reign 普通 (520–527) of the Liang Dynasty 梁 (502–557). The major difference between the literary camps lies in the consideration given to natural poetic talent versus erudition in writings. When Xiao Gang 蕭綱 (503–551), Liu Xiaochuo's supporter, became crown prince in 531, his own conflict with the scholarly group including Dao Gai 到溉 (477–548) and Zhu Yi 朱异 (483–540) probably prompted his “Letter to the Prince of Xiangdong” 與湘東王書 (Yu Xiangdong Wang shu). In this letter Xiao Gang displays his literary view deemphasizing scholarly learning and erudition in poetry. By comparison Xiao Yan 蕭衍 (464–549) and Xiao Yi 蕭繹 (508–555) valued scholarly learning still more and regarded literature as a relatively insignificant talent or minor accomplishment. Xiao Gang represents a departure—by placing literary talent above scholarship, he catered to the fashion among the Liang Dynasty's nobility for reciting poetry and writing fu 賦 (rhapsody) while “rarely taking classical studies as their profession” 罕以經朮為業 and thus elevated the social status of belles lettres.