Structural invertibility of transfer functions

In this note, we study certain properties of a transfer function in terms of the structure of the state-space representation (A, B, C). Specifically, the rank of the transfer function and the degree of a decoupled system (which can be obtained by applying a left decoupler) are characterized in terms of the structure of (A, B, C).     

On the invertibility of linear systems

Sain and Massey [1] have obtained necessary and sufficient conditions for the invertibility of continuous and discrete time linear systems and have also found bounds for what they termed the "inherent integration" (continuous time) or the "inherent delay" (discrete time) of an invertible linear system. In this note, we tighten these bounds by modifying an argument used to prove the Sain-Massey result.     

On the invertibility of linear multivariable systems

Some results concerning invertibility of a class of linear, time-invariant systems are presented. It is shown that by an appropriate factorization of the transfer matrix of such a system, the problem of cheeking its invertibility can be reduced to that of checking the invertibility of a lower-order system. A sufficient condition for invertibility is also obtained.     

The steady-state invertibility and feedforward control of linear time-invariant systems

The notion of steady-state invertibility of a system is introduced, which is concerned about the problem of being able to find an input so that the output of a stable system is asymptotically equal to a specified output of a certain class of functions. Necessary and sufficient conditions are found for a linear time-invariant system to be steady-state invertible. Application of these results is then made to find necessary and sufficient conditions for a feedforward controller to exist for a general linear time-invariant system, so that asymptotic tracking, in the presence of a general class of measurable disturbances occurs. Explicit feedforward controllers which will accomplish this are obtained. Properties of the steady-state invertibility condition are then obtained; in particular, it is shown that a system is "almost always" steady-state invertible if the number of plant inputs is not less than the number of outputs; if the number of plant inputs is less than the number of outputs, then a system is "almost never" steady-state invertible. It is then shown that a system which is minimum phase and which has at least the same number of inputs as outputs is always steady-state invertible.     

Action-Based Causal Reasoning

In this paper we present a causal theory based on aninterventionist conception of causality, i.e., a preference toselect causes among a set of actions which an agent has the abilityto perform or not to perform (free will). The most interestingproposals encountered in the literature, in nonmonotonic reasoning,all revolve around the ordered notion of similarity, abnormality,preference etc... but do not provide a full-fledgedsolution to the problem of the concrete definition of this order. Inour approach we relate the notion of action to norms (what isnormally the case when an action is undertaken, what is normally theoutcome of that action) and considering reasonable assumptions, weshow the existence and uniqueness of the set of voluntary causes foran observed effect (explanation problem). Moreover, the approach advocated in this paper handles ramifications correctly.     

Temporal Causal Abduction

The paper is devoted to presentation of the idea of Temporal Causal Networks (TCN). Temporal Causal Networks constitute a tool for representing and dealing with causal dependencies propagation over time. A temporal causal network is a causal network incorporating explicit representation of time during which its symptoms/nodes are valid, not valid, or unknown. The atemporal causal structure is basically an AND/OR/NOT causal graph, i.e. a causal graph incorporating basic logical connectives for the representation of different types of causal dependencies. The presented approach uses a specific time constraints propagation algorithm to determine possible system behavior in time. The main application includes simulation, monitoring and elements of diagnostic reasoning for dynamic systems with explicit time representation.     

Causal dynamic inference

We suggest a general logical framework for causal dynamic reasoning. As a first step, we introduce a uniform structural formalism and assign it two kinds of semantics, abstract dynamic models and relational models. The corresponding completeness results are proved. As a second step, we extend the structural formalism to a two-sorted state-transition calculus, and prove its completeness with respect to the associated relational semantics.     

Animating Causal Overlays

Most approaches to representing causality, such as the common causal graph, require a separate and static view, but in many cases it is useful to add the dimension of causality to the context of an existing visualization. Building on research from perceptual psychology that shows the perception of causality is a low‐level visual event derived from certain types of motion, we are investigating how to add animated causal representations, called visual causal vectors, onto other visualizations. We refer to these as causal overlays. Our initial experimental results show this approach has great potential but that extra cues are needed to elicit the perception of causality when the motions are overlaid on other graphical objects. In this paper we describe the approach and report on a study that examined two issues of this technique: how to accurately convey the causal flow and how to represent the strength of the causal effect.     

The invertibility of the XOR of rotations of a binary word

We prove the following result regarding operations on a binary word whose length is a power of two: computing the exclusive-or of a number of rotated versions of the word is an invertible (one-to-one) operation if and only if the number of versions combined is odd. (This result is not new; there is at least one earlier proof, due to Thomsen [Cryptographic hash functions, PhD thesis, Technical University of Denmark, 28 November 2008]. Our proof may be new.)     

Computational versus Causal Complexity

The main claim of this paper is that notions of implementation based on an isomorphic correspondence between physical and computational states are not tenable. Rather, ``implementation' has to be based on the notion of ``bisimulation' in order to be able to block unwanted implementation results and incorporate intuitions from computational practice. A formal definition of implementation is suggested, which satisfies theoretical and practical requirements and may also be used to make the functionalist notion of ``physical realization' precise. The upshot of this new definition of implementation is that implementation cannot distinguish isomorphic bisimilar from non-isomporphic bisimilar systems anymore, thus driving a wedge between the notions of causal and computational complexity. While computationalism does not seem to be affected by this result, the consequences for functionalism are not clear and need further investigations.     

Causal Message Sequence Charts

Scenario languages based on Message Sequence Charts (MSCs) have been widely studied in the last decade. The high expressive power of MSCs renders many basic problems concerning these languages undecidable. However, several of these problems are decidable for languages that possess a behavioral property called “existentially bounded”. Unfortunately, collections of scenarios outside this class are frequently exhibited by systems such as sliding window protocols. We propose here an extension of MSCs called causal Message Sequence Charts and a natural mechanism for defining languages of causal MSCs called causal HMSCs (CaHMSCs). These languages preserve decidable properties without requiring existential bounds. Further, they can model collections of scenarios generated by sliding window protocols. We establish here the basic theory of CaHMSCs as well as the expressive power and complexity of decision procedures for various subclasses of CaHMSCs. We also illustrate the modeling power of our formalism with the help of a realistic example based on the TCP sliding window feature.     

混合局部因果结构学习

局部因果结构学习是发现和学习给定一个目标变量的直接原因和直接结果而无需学习一个完整因果网络的过程.目前已有算法通常由两个步骤完成:步骤1使用约束类算法利用独立性测试学习目标变量的马尔科夫毯(MB)或父子节点集(PC),但是该步骤由于受到有限的数据样本量等因素影响使得独立性测试存在一定的错误性,而导致该步骤精度通常不是很...     

Left invertibility of discrete-time output-quantized systems: the linear case with finite inputs

This paper studies left invertibility of discrete-time linear output-quantized systems. Quantized outputs are generated according to a given partition of the state-space, while inputs are sequences on a finite alphabet. Left invertibility, i.e. injectivity of I/O map is reduced to left D-invertibility, under suitable conditions. While left invertibility takes into account membership to sets of a given partition, left D-invertibility considers only membership to a single set and is much easier to detect. The condition under which left invertibility and left D-invertibility are equivalent is that the elements of the dynamic matrix of the system form an algebraically independent set. Our main result is a method to compute left D-invertibility for all linear systems with no eigenvalue of modulus one. Therefore, we are able to check left invertibility of output-quantized linear systems for a full measure set of matrices. Some examples are presented to show the application of the proposed method.     

Scalable Techniques for Mining Causal Structures

Mining for association rules in market basket data has proved a fruitful area of research. Measures such as conditional probability (confidence) and correlation have been used to infer rules of the form “the existence of item A implies the existence of item B.” However, such rules indicate only a statistical relationship between A and B. They do not specify the nature of the relationship: whether the presence of A causes the presence of B, or the converse, or some other attribute or phenomenon causes both to appear together. In applications, knowing such causal relationships is extremely useful for enhancing understanding and effecting change. While distinguishing causality from correlation is a truly difficult problem, recent work in statistics and Bayesian learning provide some avenues of attack. In these fields, the goal has generally been to learn complete causal models, which are essentially impossible to learn in large-scale data mining applications with a large number of variables. In this paper, we consider the problem of determining casual relationships, instead of mere associations, when mining market basket data. We identify some problems with the direct application of Bayesian learning ideas to mining large databases, concerning both the scalability of algorithms and the appropriateness of the statistical techniques, and introduce some initial ideas for dealing with these problems. We present experimental results from applying our algorithms on several large, real-world data sets. The results indicate that the approach proposed here is both computationally feasible and successful in identifying interesting causal structures. An interesting outcome is that it is perhaps easier to infer the lack of causality than to infer causality, information that is useful in preventing erroneous decision making.     

动态因果模型的研究综述

功能磁共振成像技术的发展为揭示脑区间的有效连接机制奠定了基础,而动态因果模型的研究将更有利于连接机制的研究,为揭示脑的奥秘提供了有效、直接的方法。阐述了动态因果模型的基本概念和原理,论述了不同类别的动态因果模型连接方式、方法;分析了不同类别模型间的区别,并通过贝叶斯模型选择进行模型辨识。通过总结前人所做的工作,得出动态因果模型在使用过程中应该遵循的规则,概括了存在的问题。结合已有的动态因果模型研究成果,展望了未来的研究方向和亟待解决的关键问题。