Communication: Transition State Theory for dissipative systems without a dividing surface

Transition state theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when the reactive system is coupled to an environment. The calculations made in this way then overestimate the reaction rate and the results depend critically on the choice of the dividing surface. In this Communication, we study the phase space of a stochastically driven system close to an energetic barrier in order to identify the geometric structure unambiguously determining the reactive trajectories, which is then incorporated in a simple rate formula for reactions in condensed phase that is both independent of the dividing surface and exact.

Some past decision theory models for euro construction model codes and for road drainage in Spain, and modest hints with multi-criteria methods for agro and environmental assurance

The authors are from UPM and are relatively grouped, and all have intervened in different academic or real cases on the subject, at different times as being of different age. With precedent from E. Torroja and A. Páez in Madrid Spain Safety Probabilistic models for concrete about 1957, now in ICOSSAR conferences, author J.M. Antón involved since autumn 1967 for euro-steel construction in CECM produced a math model for independent load superposition reductions, and using it a load coefficient pattern for codes in Rome Feb. 1969, practically adopted for European constructions, giving in JCSS Lisbon Feb. 1974 suggestion of union for concrete-steel-al.. That model uses model for loads like Gumbel type I, for 50 years for one type of load, reduced to 1 year to be added to other independent loads, the sum set in Gumbel theories to 50 years return period, there are parallel models. A complete reliability system was produced, including non linear effects as from buckling, phenomena considered somehow in actual Construction Eurocodes produced from Model Codes. The system was considered by author in CEB in presence of Hydraulic effects from rivers, floods, sea, in reference with actual practice. When redacting a Road Drainage Norm in MOPU Spain an optimization model was realized by authors giving a way to determine the figure of Return Period, 10 to 50 years, for the cases of hydraulic flows to be considered in road drainage. Satisfactory examples were a stream in SE of Spain with Gumbel Type I model and a paper of Ven Te Chow with Mississippi in Keokuk using Gumbel type II, and the model can be modernized with more varied extreme laws. In fact in the MOPU drainage norm the redacting commission acted also as expert to set a table of return periods for elements of road drainage, in fact as a multi-criteria complex decision system. These precedent ideas were used e.g. in wide Codes, indicated in symposia or meetings, but not published in journals in English, and a condensate of contributions of authors is presented. The authors are somehow involved in optimization for hydraulic and agro planning, and give modest hints of intended applications in presence of agro and environment planning as a selection of the criteria and utility functions involved in bayesian, multi-criteria or mixed decision systems. Modest consideration is made of changing in climate, and on the production and commercial systems, and on others as social and financial.

Reply to Comment on ``Towards a large deviation theory for strongly correlated systems''

The computational study commented by Touchette opens the door to a desirable generalization of standard large deviation theory for special, though ubiquitous, correlations. We focus on three interrelated aspects: (i) numerical results strongly suggest that the standard exponential probability law is asymptotically replaced by a power-law dominant term; (ii) a subdominant term appears to reinforce the thermodynamically extensive entropic nature of q-generalized rate function; (iii) the correlations we discussed, correspond to Q -Gaussian distributions, differing from Lévy?s, except in the case of Cauchy?Lorentz distributions. Touchette has agreeably discussed point (i), but, unfortunately, points (ii) and (iii) escaped to his analysis. Claiming the absence of connection with q-exponentials is unjustified.

A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

A general stability criterion for switched linear systems having stable and unstable subsystems

We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those having stable subsystems and mixtures of stable and unstable subsystems.

Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems

Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a "heuristic argument" that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages"). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods.

Agreement Abstractions in Anonymous and Homonymous Distributed Systems Prone to Failures

The distributed computing models typically assume every process in the system has a distinct identifier (ID) or each process is programmed differently, which is named as eponymous system. In such kind of distributed systems, the unique ID is helpful to solve problems: it can be incorporated into messages to make them trackable (i.e., to or from which process they are sent) to facilitate the message transmission; several problems (leader election, consensus, etc.) can be solved without the information of network property in priori if processes have unique IDs; messages in the register of one process will not be overwritten by others process if this process announces; it is useful to break the symmetry. Hence, eponymous systems have influenced the distributed computing community significantly either in theory or in practice. However, every thing in the world has its own two sides. The unique ID also has disadvantages: it can leak information of the network(size); processes in the system have no privacy; assign unique ID is costly in bulk-production(e.g, sensors). Hence, homonymous system is appeared. If some processes share the same ID and programmed identically is called homonymous system. Furthermore, if all processes shared the same ID or have no ID is named as anonymous system. In homonymous or anonymous distributed systems, the symmetry problem (i.e., how to distinguish messages sent from which process) is the main obstacle in the design of algorithms. This thesis is aimed to propose different symmetry break methods (e.g., random function, counting technique, etc.) to solve agreement problem. Agreement is a fundamental problem in distributed computing including a family of abstractions. In this thesis, we mainly focus on the design of consensus, set agreement, broadcast algorithms in anonymous and homonymous distributed systems. Firstly, the fault-tolerant broadcast abstraction is studied in anonymous systems with reliable or fair lossy communication channels separately. Two classes of anonymous failure detectors AΘ and AP∗ are proposed, and both of them together with a already proposed failure detector ψ are implemented and used to enrich the system model to implement broadcast abstraction. Then, in the study of the consensus abstraction, it is proved the AΩ′ failure detector class is strictly weaker than AΩ and AΩ′ is implementable. The first implementation of consensus in anonymous asynchronous distributed systems augmented with AΩ′ and where a majority of processes does not crash. Finally, a general consensus problem– k-set agreement is researched and the weakest failure detector L used to solve it, in asynchronous message passing systems where processes may crash and recover, with homonyms (i.e., processes may have equal identities), and without a complete initial knowledge of the membership.

Engineering Computational Emotion - A Reference Model for Emotion in Artificial Systems

Emotion is generally argued to be an influence on the behavior of life systems, largely concerning flexibility and adaptivity. The way in which life systems acts in response to a particular situations of the environment, has revealed the decisive and crucial importance of this feature in the success of behaviors. And this source of inspiration has influenced the way of thinking artificial systems. During the last decades, artificial systems have undergone such an evolution that each day more are integrated in our daily life. They have become greater in complexity, and the subsequent effects are related to an increased demand of systems that ensure resilience, robustness, availability, security or safety among others. All of them questions that raise quite a fundamental challenges in control design. This thesis has been developed under the framework of the Autonomous System project, a.k.a the ASys-Project. Short-term objectives of immediate application are focused on to design improved systems, and the approaching of intelligence in control strategies. Besides this, long-term objectives underlying ASys-Project concentrate on high order capabilities such as cognition, awareness and autonomy. This thesis is placed within the general fields of Engineery and Emotion science, and provides a theoretical foundation for engineering and designing computational emotion for artificial systems. The starting question that has grounded this thesis aims the problem of emotion--based autonomy. And how to feedback systems with valuable meaning has conformed the general objective. Both the starting question and the general objective, have underlaid the study of emotion, the influence on systems behavior, the key foundations that justify this feature in life systems, how emotion is integrated within the normal operation, and how this entire problem of emotion can be explained in artificial systems. By assuming essential differences concerning structure, purpose and operation between life and artificial systems, the essential motivation has been the exploration of what emotion solves in nature to afterwards analyze analogies for man--made systems. This work provides a reference model in which a collection of entities, relationships, models, functions and informational artifacts, are all interacting to provide the system with non-explicit knowledge under the form of emotion-like relevances. This solution aims to provide a reference model under which to design solutions for emotional operation, but related to the real needs of artificial systems. The proposal consists of a multi-purpose architecture that implement two broad modules in order to attend: (a) the range of processes related to the environment affectation, and (b) the range or processes related to the emotion perception-like and the higher levels of reasoning. This has required an intense and critical analysis beyond the state of the art around the most relevant theories of emotion and technical systems, in order to obtain the required support for those foundations that sustain each model. The problem has been interpreted and is described on the basis of AGSys, an agent assumed with the minimum rationality as to provide the capability to perform emotional assessment. AGSys is a conceptualization of a Model-based Cognitive agent that embodies an inner agent ESys, the responsible of performing the emotional operation inside of AGSys. The solution consists of multiple computational modules working federated, and aimed at conforming a mutual feedback loop between AGSys and ESys. Throughout this solution, the environment and the effects that might influence over the system are described as different problems. While AGSys operates as a common system within the external environment, ESys is designed to operate within a conceptualized inner environment. And this inner environment is built on the basis of those relevances that might occur inside of AGSys in the interaction with the external environment. This allows for a high-quality separate reasoning concerning mission goals defined in AGSys, and emotional goals defined in ESys. This way, it is provided a possible path for high-level reasoning under the influence of goals congruence. High-level reasoning model uses knowledge about emotional goals stability, letting this way new directions in which mission goals might be assessed under the situational state of this stability. This high-level reasoning is grounded by the work of MEP, a model of emotion perception that is thought as an analogy of a well-known theory in emotion science. The work of this model is described under the operation of a recursive-like process labeled as R-Loop, together with a system of emotional goals that are assumed as individual agents. This way, AGSys integrates knowledge that concerns the relation between a perceived object, and the effect which this perception induces on the situational state of the emotional goals. This knowledge enables a high-order system of information that provides the sustain for a high-level reasoning. The extent to which this reasoning might be approached is just delineated and assumed as future work. This thesis has been studied beyond a long range of fields of knowledge. This knowledge can be structured into two main objectives: (a) the fields of psychology, cognitive science, neurology and biological sciences in order to obtain understanding concerning the problem of the emotional phenomena, and (b) a large amount of computer science branches such as Autonomic Computing (AC), Self-adaptive software, Self-X systems, Model Integrated Computing (MIC) or the paradigm of models@runtime among others, in order to obtain knowledge about tools for designing each part of the solution. The final approach has been mainly performed on the basis of the entire acquired knowledge, and described under the fields of Artificial Intelligence, Model-Based Systems (MBS), and additional mathematical formalizations to provide punctual understanding in those cases that it has been required. This approach describes a reference model to feedback systems with valuable meaning, allowing for reasoning with regard to (a) the relationship between the environment and the relevance of the effects on the system, and (b) dynamical evaluations concerning the inner situational state of the system as a result of those effects. And this reasoning provides a framework of distinguishable states of AGSys derived from its own circumstances, that can be assumed as artificial emotion.

Agreement Abstractions in Anonymous and Homonymous Distributed Systems Prone to Failures

The distributed computing models typically assume every process in the system has a distinct identifier (ID) or each process is programmed differently, which is named as eponymous system. In such kind of distributed systems, the unique ID is helpful to solve problems: it can be incorporated into messages to make them trackable (i.e., to or from which process they are sent) to facilitate the message transmission; several problems (leader election, consensus, etc.) can be solved without the information of network property in priori if processes have unique IDs; messages in the register of one process will not be overwritten by others process if this process announces; it is useful to break the symmetry. Hence, eponymous systems have influenced the distributed computing community significantly either in theory or in practice. However, every thing in the world has its own two sides. The unique ID also has disadvantages: it can leak information of the network(size); processes in the system have no privacy; assign unique ID is costly in bulk-production(e.g, sensors). Hence, homonymous system is appeared. If some processes share the same ID and programmed identically is called homonymous system. Furthermore, if all processes shared the same ID or have no ID is named as anonymous system. In homonymous or anonymous distributed systems, the symmetry problem (i.e., how to distinguish messages sent from which process) is the main obstacle in the design of algorithms. This thesis is aimed to propose different symmetry break methods (e.g., random function, counting technique, etc.) to solve agreement problem. Agreement is a fundamental problem in distributed computing including a family of abstractions. In this thesis, we mainly focus on the design of consensus, set agreement, broadcast algorithms in anonymous and homonymous distributed systems. Firstly, the fault-tolerant broadcast abstraction is studied in anonymous systems with reliable or fair lossy communication channels separately. Two classes of anonymous failure detectors AΘ and AP∗ are proposed, and both of them together with a already proposed failure detector ψ are implemented and used to enrich the system model to implement broadcast abstraction. Then, in the study of the consensus abstraction, it is proved the AΩ′ failure detector class is strictly weaker than AΩ and AΩ′ is implementable. The first implementation of consensus in anonymous asynchronous distributed systems augmented with AΩ′ and where a majority of processes does not crash. Finally, a general consensus problem– k-set agreement is researched and the weakest failure detector L used to solve it, in asynchronous message passing systems where processes may crash and recover, with homonyms (i.e., processes may have equal identities), and without a complete initial knowledge of the membership.