Number Of Possible States Research Articles

Synchronizing Complex Networks by an Adaptive AdjustmentMechanism

We propose an adaptive adjustment mechanism for synchronizingcomplex networks, in particular for sociological or/and biologicalsystems. We do not take it for granted that a dynamical system is puton isolated nodes and they are coupled with each other by one (or more)variable(s), as employed in most previous models. As a replacement, wesuppose that each node may have any finite number of possible states,and their evolutions with time are determined by theirnearest-neighbouring (or even second-nearest-neighbouring, etc) nodes inan adaptive adjustment mechanism. It is found that synchronization canbe achieved for almost all connected networks and that the scale-freeproperty can evidently improve the synchronizing speed.

Keyframe animation of virtual humans via motion data learning

AbstractThis paper proposes a method for creating human animations by utilizing motion capture data in traditional keyframe‐based motion editing. This automatically generates complicated sequential movements of the whole body from multiple constraints of end‐effectors. Different types of motion learning are introduced to optimize postures at each keyframe and motion curves for interpolating them, separately. Postures at every keyframe are determined by using hierarchical reinforcement learning so as to have similar features to motion samples with a data‐centric objective function. Plausible postures are efficiently sought among the huge number of possible states because a skeletal structure is hierarchically decomposed and postures are efficiently quantized to narrow down the configuration space. Optimized postures are then interpolated using motion curves that are learned with acceleration templates from referential motion segments. This new technique of reusing motion data is well suited to design motions by manipulating end‐effectors at each keyframe. © 2006 Wiley Periodicals, Inc. Syst Comp Jpn, 37(5): 25–33, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20443

A Reinforcement Learning Scheme for a Partially-Observable Multi-Agent Game

We formulate an automatic strategy acquisition problem for the multi-agent card game as a reinforcement learning problem. The problem can approximately be dealt with in the framework of a partially observable Markov decision process (POMDP) for a single-agent system. Hearts is an example of imperfect information games, which are more difficult to deal with than perfect information games. A POMDP is a decision problem that includes a process for estimating unobservable state variables. By regarding missing information as unobservable state variables, an imperfect information game can be formulated as a POMDP. However, the game of Hearts is a realistic problem that has a huge number of possible states, even when it is approximated as a single-agent system. Therefore, further approximation is necessary to make the strategy acquisition problem tractable. This article presents an approximation method based on estimating unobservable state variables and predicting the actions of the other agents. Simulation results show that our reinforcement learning method is applicable to such a difficult multi-agent problem.

A computational algebra approach to the reverse engineering of gene regulatory networks

This paper proposes a new method to reverse engineer gene regulatory networks from experimental data. The modeling framework used is time-discrete deterministic dynamical systems, with a finite set of states for each of the variables. The simplest examples of such models are Boolean networks, in which variables have only two possible states. The use of a larger number of possible states allows a finer discretization of experimental data and more than one possible mode of action for the variables, depending on threshold values. Furthermore, with a suitable choice of state set, one can employ powerful tools from computational algebra, that underlie the reverse-engineering algorithm, avoiding costly enumeration strategies. To perform well, the algorithm requires wildtype together with perturbation time courses. This makes it suitable for small to meso-scale networks rather than networks on a genome-wide scale. An analysis of the complexity of the algorithm is performed. The algorithm is validated on a recently published Boolean network model of segment polarity development in Drosophila melanogaster.

Reliability of power stations: Stochastic versus derated power approach

Consideration of the eventual forced outage of individual power stations leads to a large number of possible states of the power generating system, all with their own probability. It is possible to design a stochastic method to properly take into account all of these possibilities and to weigh them accordingly. In broader energy models, instead of these stochastic techniques that require a considerable amount of calculation time, mostly approximative static simplified methods are applied. Up till now, these simplified techniques have not been validated. The scope of this paper is to check their validity. Therefore, two approaches are compared: a complete stochastic approach and a method based on the derated power (which is the nominal power multiplied with the average availability) of the individual plants. The conclusion of this comparison is that derated power may be used in energy modelling instead of the complicated stochastic approach. The error made is very small and the correlation between the unserved load probability functions obtained by both methods is excellent. Copyright © 2004 John Wiley & Sons, Ltd.

Protein stability induced by ligand binding correlates with changes in protein flexibility.

The interaction between ligands and proteins usually induces changes in protein thermal stability with modifications in the midpoint denaturation temperature, enthalpy of unfolding, and heat capacity. These modifications are due to the coupling of unfolding with binding equilibrium. Furthermore, they can be attained by changes in protein structure and conformational flexibility induced by ligand interaction. To study these effects we have used bovine serum albumin (BSA) interacting with three different anilinonaphthalene sulfonate derivatives (ANS). These ligands have different effects on protein stability, conformation, and dynamics. Protein stability was studied by differential scanning calorimetry and fluorescence spectroscopy, whereas conformational changes were detected by circular dichroism and infrared spectroscopy including kinetics of hydrogen/deuterium exchange. The order of calorimetric midpoint of denaturation was: 1,8-ANS-BSA > 2,6-ANS-BSA > free BSA >> (nondetected) bis-ANS-BSA. Both 1,8-ANS and 2,6-ANS did not substantially modify the secondary structure of BSA, whereas bis-ANS induced a distorted alpha-helix conformation with an increase of disordered structure. Protein flexibility followed the order: 1,8-ANS-BSA < 2,6-ANS-BSA < free BSA << bis-ANS-BSA, indicating a clear correlation between stability and conformational flexibility. The structure induced by an excess of bis-ANS to BSA is compatible with a molten globule-like state. Within the context of the binding landscape model, we have distinguished five conformers (identified by subscript): BSA(1,8-ANS), BSA(2,6-ANS), BSA(free), BSA(bis-ANS), and BSA(unfolded) among the large number of possible states of the conformational dynamic ensemble. The relative population of each distinguishable conformer depends on the type and concentration of ligand and the temperature of the system.

Bacterial chemotaxis

Bacterial chemotaxis

THERMODYNAMIC REASONS OF AGGLOMERATION OF DUST PARTICLES IN THE THERMAL DUSTY PLASMA

The thermodynamic equilibrium of thermal dusty plasmas consisting of ionized gas (plasma) and solid particles (dust grains), which interact with each other, is studied. The tendency of grains in dusty plasmas to agglomerate corresponds to the tendency of dusty plasmas to balanced states. When grains agglomerate, electrical perturbations generated by each grain concentrate inside the agglomerate. The plasma is perturbed only by the agglomerate’s exterior surface. The greater number of possible states for electrons and ions in plasma depends on the volume of perturbation of grains. The fewer are the perturbations the greater is the amount of possible states for electrons and ions in plasma. If the grains collected from a distance smaller than 8 Debye lengths, the total volume of perturbations is minimized; the free energy of the plasma is also minimized.

Feedback generation and linguistic knowledge in ‘SLIM’ automatic tutor

SLIM is a prototype interactive multimedia self-learning linguistic software for foreign language students at beginner-false beginner level. It allows students to work both in an autonomous self-directed mode or in a way of programmed learning in which the process of self-instruction is pre-programmed and monitored. In this latter mode it incorporates assessment and evaluation tools in order to behave as an automatic tutor. It is organized into three basic components: audiovisual materials; a linguistic database recording all language material in text format; the supervisor. Audiovisual materials are partially taken from commercially available courses; the linguistic database is a highly sophisticated classification of all words and utterances of the course, both in written and spoken form, from all possible linguistic aspects. The supervisor is both an attractive, enjoyable and strongly pedagogically based software that allows the user to work on language materials. The most outstanding feature of SLIM is the use of speech analysis and recognition which is a fundamental aspect of all second language learning programmes. We also assume that a learning model can be represented by a finite state automaton made up by a fixed number of possible states – corresponding to the macro and microlevels at which the student's competence may be modelled – each one being internally constituted by the actual linguistic objects of knowledge of the language that make it up.

COMPUTATIONAL COMPLEXITY OF ARBITRAGE IN FRICTIONAL SECURITY MARKET

We are interested in computation of arbitrage condition in financial market with friction. We consider a deterministic model with a finite number of financial assets and a finite number of possible states of nature. The future return of each asset under each possible state of nature is given in the model. We derive a negative result on computational complexity of arbitrage in the case when assets are traded in integer numbers of shares and with a maximum amount of shares that can be bought for a fixed price.

Monte Carlo simulations for a model of amphiphiles aggregation

In this work we employed Monte Carlo simulations to study a spin-like lattice model that resembles some properties observed in micellar systems. This simple model for molecular aggregation was studied in dimensions d=1,2 and 3. The interaction energy favors the formation of a well-defined optimal aggregate of size n, where n is the number of possible states of the amphiphiles. In this model, both the amphiphiles and the water molecules (we treated aqueous solutions) occupy only a single site in the lattice. The simulations and numerical calculations in one dimension agree with the exact ones obtained in previous works. The minimum and the maximum in the aggregate-size distribution curve and the critical micellar concentration, which are the fingerprints of micellar aggregation, are obtained. The two- and three-dimensional cases also exhibit these features. We calculated the exponent γ that measures the dependence of the difference in height between the maximum and the minimum in the aggregate-size distribution curve on temperature. We found γ≅1, for all values of n we considered, independently of d.

Deep Teleology in Artificial Systems

Teleological variations of non-deterministic processes are defined. The immediate past of a system defines the state from which the ordinary (non-teleological) dynamical law governing the system derives different possible present states. For every possible present state, again a number of possible states for the next time step can be defined, and so on. After k time steps, a selection criterion is applied. The present state leading to the selected state after k time steps is taken to be the effective present state. Hence, the present state of a system is defined by its past in the sense that the past determines the possible states that are to be considered, and by its future in the sense that the selection of a possible future state determines the effective present state. A system that obeys this type of teleological dynamics may have significantly better performance than its non-teleological counterpart. The basic reason is that evolutions that are less optimal for the present time step, but which lead to a higher optimality after k time steps, may be preferred. This abstract concept of teleology is implemented for two concrete systems. First, it is applied to a general method for function approximation and classification problems. The method at issue treats all problems handled by conventional connectionism, and is suited for information with inner structure also. Second, it is applied to a dynamics in which forms of maximal homogeneity have to be produced. The relevance of the latter dynamics for generative art is illustrated. The teleology is `deep' in the sense that it is situated at the cellular level, in contradistinction with the teleology that is usually met in cognitive contexts, and which refers to macroscopic processes such as making plans. It is conjectured that deep level teleology is useful for machines, even though the issue if natural systems use this teleology is left open.

Complexity reduction of the MLSD/MLSDE receiver using the adaptive state allocation algorithm

The idea of adaptive state allocation (ASA) algorithm is used in this paper to substantially reduce the computational complexity of the maximum-likelihood sequence detection and estimation (MLSD/MLSDE) receiver without a significant degradation in its performance. In the ASA algorithm, the total number of states assigned to the trellis and the number of states selected from the entire set are changed adaptively based on the short-term power of the channel impulse response (CIR) or its estimate. The ASA algorithm is a combination of two methods: adaptive threshold (AT) and adaptive state partitioning (AP). In the AT method, a threshold value is formulated based on the probability of removing the correct state in the trellis diagram. At each time, only the paths whose costs are less than the minimum cost (corresponding to the best survivor path) plus the threshold value are retained and are extended to the next trellis stage. The AT method significantly reduces the computational complexity of the regular MLSDE mostly at high signal-to-noise ratio (SNR) with a negligible loss in performance. Simulation results for fading channels show that the AT method typically selects one trellis state (the minimum possible number of states) at high SNRs. In the AP method, the branch metrics are fused and diffused adaptively by using the Kullback-Leibler (KL) distance metric invoked for quantifying the differences between the probability density functions of the correct and incorrect branch metrics in the trellis. The adaptation is done such that the channel coefficients with short-term power less than a threshold are assumed to be zero in computing the branch metrics. The AP method decreases the computational complexity of the regular MLSDE at low SNRs.

Macroeconomic Fluctuations and Bargaining

I study the limit rule for bilateral bargaining when agents recognize that the aggregate economy (influencing the match surplus) follows a dynamic process that randomly switches back and forth between a finite number of possible states. The rule derived in this paper is of special importance for decentralized exchange economies with bargaining. Two simple applications are presented to illustrate this fact. The first example is a model of wage bargaining and trade externalities. I show that in those situations sophisticated bargaining tends to increase the volatility (due to extrinsic uncertainty) of the wage bill. The second example is based on the Kiyotaki-Wright model of money. I explain how equilibrium prices depend in a fundamental way on the dynamic bargaining solution.

Successive Minimization of the State Complexity of the Self-dual Lattices Using Korkin-Zolotarev Reduced Basis

This work presents a systematic method to successively minimize the state complexity of the self-dual lattices (in the sense that each section of the trellis has the minimum possible number of states fixing its preceding co-ordinates). This is based on representing the lattice on an orthogonal co-ordinate system corresponding to the Gram-Schmidt (GS) vectors of a Korkin-Zolotarev (KZ) reduced basis. As part of the computations, we give expressions for the GS vectors of a KZ basis of the K_{12}, \Lambda_{24}, and BW_n lattices. It is also shown that for the complex representation of the \Lambda_{24} and the BW_n lattices over the set of the Gaussian integers, we have: (i) the corresponding GS vectors are along the standard co-ordinate system, and (ii) the branch complexity at each section of the resulting trellis meets a certain lower bound. This results in a very efficient trellis representation for these lattices over the standard co-ordinate system.

Talking helps: evolving communicating agents for the predator-prey pursuit problem.

We analyze a general model of multi-agent communication in which all agents communicate simultaneously to a message board. A genetic algorithm is used to evolve multi-agent languages for the predator agents in a version of the predator-prey pursuit problem. We show that the resulting behavior of the communicating multi-agent system is equivalent to that of a Mealy finite state machine whose states are determined by the agents' usage of the evolved language. Simulations show that the evolution of a communication language improves the performance of the predators. Increasing the language size (and thus increasing the number of possible states in the Mealy machine) improves the performance even further. Furthermore, the evolved communicating predators perform significantly better than all previous work on similar prey. We introduce a method for incrementally increasing the language size, which results in an effective coarse-to-fine search that significantly reduces the evolution time required to find a solution. We present some observations on the effects of language size, experimental setup, and prey difficulty on the evolved Mealy machines. In particular, we observe that the start state is often revisited, and incrementally increasing the language size results in smaller Mealy machines. Finally, a simple rule is derived that provides a pessimistic estimate on the minimum language size that should be used for any multi-agent problem.

Uncertain destination dynamics.

Certain dynamical systems exhibit a sensitivity to initial conditions in which the asymptotic state is selected from an infinite number of possible states. The phase space of such systems is foliated with "attractors," each of which is associated with a particular set of initial conditions. The associated uncertain destination dynamics can be analyzed by an appropriate reduction of the full system to a subsystem that explicitly yields the dynamics.

Network optimizations for large-vocabulary speech recognition

The redundancy and the size of networks in large-vocabulary speech recognition systems can have a critical effect on their overall performance. We describe the use of two new algorithms: weighted determinization and minimization (Mohri, 1997a). These algorithms transform recognition labeled networks into equivalent ones that require much less time and space in large-vocabulary speech recognition. They are both optimal: weighted determinization eliminates the number of alternatives at each state to the minimum, and weighted minimization reduces the size of deterministic networks to the smallest possible number of states and transitions. These algorithms generalize classical automata determinization and minimization to deal properly with the probabilities of alternative hypotheses and with the relationships between units (distributions, phones, words) at different levels in the recognition system. We illustrate their use in several applications, and report the results of our experiments.

Nonequilibrium phase transitions induced by external noise in distributed systems

A formalism is proposed to describe nonequilibrium phase transitions induced by external multiplicative noise in distributed systems. This approach can reduce the problem to an investigation of a regular differential equation whose roots correspond to possible phase states in the system. By means of this theory the relative probability of the existence of one state can be compared with another and the number of possible states identified, and the genesis of the system under the action of fluctuations of the external medium can be traced.

Dynamic facility location when the total number of facilities is uncertain: A decision analysis approach

Models developed to analyze facility location decisions have typically optimized one or more objectives, subject to physical, structural, and policy constraints, in a static or deterministic setting. Because of the large capital outlays that are involved, however, facility location decisions are frequently long-term in nature. Consequently, there may be considerable uncertainty regarding the way in which relevant parameters in the location decision will change over time. In this paper, we propose two approaches for analyzing these types of dynamic location problems, focussing on situations where the total number of facilities to be located in uncertain. We term this type of location problem NOFUN (Number Of Facilities Uncertain). We analyze the NOFUN problem using two well-established decision criteria: the minimization of expected opportunity loss (EOL), and the minimization of maximum regret. In general, these criteria assume that there are a finite number of decision options and a finite number of possible states of nature. The minisum EOL criterion assumes that one can assign probabilities for the occurrence of the various states of nature and, therefore, find the initial set of facility locations that minimize the sum of expected losses across all future states. The minimax regret criteria finds the pattern of initial facility locations whose maximum loss is minimized over all possible future states.