Neural Network Inference of Molar Mass Distributions of Peptides during Tailor-Made Enzymatic Hydrolysis of Cheese Whey: Effects of pH and Temperature

The fine-tuning of the enzymatic hydrolysis of proteins may provide a pool of peptides with predefined molar mass distributions. However, the complex mixture of molecules (peptides and amino acids) that results after the proteolysis of cheese whey turns unfeasible the assessment of individual species. In this work, a hybrid kinetic model for the proteolysis of whey by alcalase, multipoint-immobilized on agarose, is presented, which takes into account the influence of pH (8.0-10.4) and temperature (40-55 degrees C) on the activity of the enzyme. Five ranges of peptides' molar mass have their reaction rates predicted by neural networks (NNs). The output of NNs trained for constant pH and temperatures was interpolated, instead of including these variables in the input vector of a larger NN. Thus, the model complexity was reduced. Coupled to differential mass balances, this hybrid model can be employed for the online inference of peptides' molar mass distributions. Experimental kinetic assays were carried out using a pH-stat, in a laboratory-scale (0.03 L) batch reactor. The neural-kinetic model was integrated to a supervisory system of a bench-scale continually stirred tank reactor (0.5 L), providing accurate predictions during validation tests.     

Nonparametric estimation for censored lifetimes suffering from unknown selection bias

In a population of individuals, where the random variable (r.v.) σ denotes the birth time and X the lifetime, we consider the case, where an individual can be observed only if its life-line (σ, X) = {(σ + y, y), 0 ≤ y ≤ X} intersects a given Borel set S in ℝ × ℝ₊. Denoting by σ _S and X _S the birth time and lifetime for the observed individuals, we point out that the distribution function (d.f.) F _S of the r.v. X _S suffers from a selection bias in the sense that F _S = ∝ w d F/μ _S, where w and μ _S depend only on the distribution of σ and on F, the d.f. of X. Assuming in addition that the r.v. X _S is randomly right-censored as soon as the individual is selected, we construct a productlimit estimator for the d.f. F _S and a nonparametric estimator ŵ for the weight function w. We prove a consistency result for ŵ and a weak convergence result for . We establish in addition an exponential bound for .      

On normal approximation for maximum likelihood estimation from single server queues

This paper is concerned with the rate of convergence of the distribution of the maximum likelihood estimators of the arrival and the service rates in a GI/G/1 queueing system. This revised version was published online in June 2006 with corrections to the Cover Date.     

Parallel optical fuzzy logic inference using a SLM-based architecture

A new optoelectronic fuzzy inference system is proposed for processing a large number of fuzzy rules in parallel. The proposed system using spatial light modulator implements various membership functions as well as max–min inference. It has the features of easy implementation and large data processing capability. The membership function decomposition method is used to save space bandwidth and accommodate multiple-input fuzzy inference.     

高中生如何解元素推断题

研究高中生如何解元素推断题能加深对化学问题解决的认识。用整群随机抽样法,以海南省某中学高二和高三年级各一个班的学生为被试,以改编的高考元素推断题为工具,用NVivo分析学生解题的书面报告,发现元素的解法和顺序有多种类型。这种多样性由不同的问题表征方式和解决策略引起。对课程与教学的启示:采用科学表征,并促进学生科学表征建构;重视问题解决的算法,矫正启发法造成的偏差。     

Cumulative Higher‐Order Logic as a Foundation for Set Theory

The systems K_α of transfinite cumulative types up to α are extended to systems K^∞_α that include a natural infinitary inference rule, the so‐called limit rule. For countable α a semantic completeness theorem for K^∞_α is proved by the method of reduction trees, and it is shown that every model of K^∞_α is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic first‐order set theories can be interpreted in K^∞_α, for suitable α.     

Sampling the Variational Posterior with Local Refinement

Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models. A key challenge of variational inference is to approximate the posterior with a distribution that is computationally tractable yet sufficiently expressive. We propose a novel method for generating samples from a highly flexible variational approximation. The method starts with a coarse initial approximation and generates samples by refining it in selected, local regions. This allows the samples to capture dependencies and multi-modality in the posterior, even when these are absent from the initial approximation. We demonstrate theoretically that our method always improves the quality of the approximation (as measured by the evidence lower bound). In experiments, our method consistently outperforms recent variational inference methods in terms of log-likelihood and ELBO across three example tasks: the Eight-Schools example (an inference task in a hierarchical model), training a ResNet-20 (Bayesian inference in a large neural network), and the Mushroom task (posterior sampling in a contextual bandit problem).     

Equality and Freedom as Uncertainty in Groups

In this paper, I investigate a connection between a common characterisation of freedom and how uncertainty is managed in a Bayesian hierarchical model. To do this, I consider a distributed factorization of a group’s optimization of free energy, in which each agent is attempting to align with the group and with its own model. I show how this can lead to equilibria for groups, defined by the capacity of the model being used, essentially how many different datasets it can handle. In particular, I show that there is a “sweet spot” in the capacity of a normal model in each agent’s decentralized optimization, and that this “sweet spot” corresponds to minimal free energy for the group. At the sweet spot, an agent can predict what the group will do and the group is not surprised by the agent. However, there is an asymmetry. A higher capacity model for an agent makes it harder for the individual to learn, as there are more parameters. Simultaneously, a higher capacity model for the group, implemented as a higher capacity model for each member agent, makes it easier for a group to integrate a new member. To optimize for a group of agents then requires one to make a trade-off in capacity, as each individual agent seeks to decrease capacity, but there is pressure from the group to increase capacity of all members. This pressure exists because as individual agent’s capacities are reduced, so too are their abilities to model other agents, and thereby to establish pro-social behavioural patterns. I then consider a basic two-level (dual process) Bayesian model of social reasoning and a set of three parameters of capacity that are required to implement such a model. Considering these three capacities as dependent elements in a free energy minimization for a group leads to a “sweet surface” in a three-dimensional space defining the triplet of parameters that each agent must use should they hope to minimize free energy as a group. Finally, I relate these three parameters to three notions of freedom and equality in human social organization, and postulate a correspondence between freedom and model capacity. That is, models with higher capacity, have more freedom as they can interact with more datasets.     

Entropic Dynamics: Quantum Mechanics from Entropy and Information Geometry

Entropic Dynamics (ED) is a framework in which Quantum Mechanics (QM) is derived as an application of entropic methods of inference. The magnitude of the wave function is manifestly epistemic: its square is a probability distribution. The epistemic nature of the phase of the wave function is also clear: it controls the flow of probability. The dynamics is driven by entropy subject to constraints that capture the relevant physical information. The central concern is to identify those constraints and how they are updated. After reviewing previous work I describe how considerations from information geometry allow us to derive a phase space geometry that combines Riemannian, symplectic, and complex structures. The ED that preserves these structures is QM. The full equivalence between ED and QM is achieved by taking account of how gauge symmetry and charge quantization are intimately related to quantum phases and the single‐valuedness of wave functions.