Finite Number Of Ways Research Articles

Data assimilation with agent-based models using Markov chain sampling

Every day, weather forecasting centres around the world make use of noisy, incomplete observations of the atmosphere to update their weather forecasts. This process is known as data assimilation, data fusion or state estimation and is best expressed as Bayesian inference: given a set of observations, some prior beliefs and a model of the target system, what is the probability distribution of some set of unobserved quantities or latent variables at some time, possibly in the future? While data assimilation has developed rapidly in some areas, relatively little progress has been made in performing data assimilation with agent-based models. This has hampered the use of agent-based models to make quantitative claims about real-world systems. Here we present an algorithm that uses Markov-Chain-Monte-Carlo (MCMC) methods to generate samples of the parameters and trajectories of an agent-based model over a window of time given a set of possibly noisy, aggregated and incomplete observations of the system. This can be used as-is, or as part of a data assimilation cycle or sequential-MCMC algorithm. Our algorithm is applicable to time-stepping, agent-based models whose agents have a finite set of states and a finite number of ways of acting on the world. As presented, the algorithm is only practical for agents with a few bytes of internal state although we discuss ways of removing this restriction. We demonstrate the algorithm by performing data assimilation with an agent-based, spatial predator-prey model.

On quartic double fivefolds and the matrix factorizations of exceptional quaternionic representations

On étudie les quartiques doubles de dimension cinq du point de vue des variétés Fano de type Calabi–Yau et des représentations quaternioniques exceptionnelles. On démontre tout d’abord qu’une quartique double de dimension cinq générique peut être représentée comme un recouvrement double de ℙ 5 ramifié le long d’une section linéaire de la quartique Spin 12 -invariante dans ℙ 31 . Le nombre de telles représentations est fini. Ensuite, en utilisant la géométrie des décompositions de Vinberg de type II de certaines représentations quaternioniques exceptionnelles et en se basant sur des calculs effectués grâce au logiciel Macaulay2, on démontre l’existence d’un fibré vectoriel sphérique de rang 6 sur de telles quartiques doubles. On déduit finalement de l’existence de ces fibrés que l’unité homologique des catégories Calabi–Yau de dimension trois associées par Kuznetsov aux quartiques doubles de dimension cinq est ℂ⊕ℂ[3].

Network structure effects in reservoir computers.

A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition, or control of robotic systems. Typically, a reservoir computer is constructed by connecting a large number of nonlinear nodes in a network, driving the nodes with an input signal and using the node outputs to fit a training signal. In this work, we set up reservoirs where the edges (or connections) between all the network nodes are either +1 or 0 and proceed to alter the network structure by flipping some of these edges from +1 to -1. We use this simple network because it turns out to be easy to characterize; we may use the fraction of edges flipped as a measure of how much we have altered the network. In some cases, the network can be rearranged in a finite number of ways without changing its structure; these rearrangements are symmetries of the network, and the number of symmetries is also useful for characterizing the network. We find that changing the number of edges flipped in the network changes the rank of the covariance of a matrix consisting of the time series from the different nodes in the network and speculate that this rank is important for understanding the reservoir computer performance.

High-Fugacity Expansion, Lee–Yang Zeros, and Order–Disorder Transitions in Hard-Core Lattice Systems

We establish existence of order-disorder phase transitions for a class of "non-sliding" hard-core lattice particle systems on a lattice in two or more dimensions. All particles have the same shape and can be made to cover the lattice perfectly in a finite number of ways. We also show that the pressure and correlation functions have a convergent expansion in powers of the inverse of the fugacity. This implies that the Lee-Yang zeros lie in an annulus with finite positive radii.

Discovering temporal regularities in retail customers\u2019 shopping behavior

In this paper we investigate the regularities characterizing the temporal purchasing behavior of the customers of a retail market chain. Most of the literature studying purchasing behavior focuses on what customers buy while giving few importance to the temporal dimension. As a consequence, the state of the art does not allow capturing which are the temporal purchasing patterns of each customers. These patterns should describe the customer’s temporal habits highlighting when she typically makes a purchase in correlation with information about the amount of expenditure, number of purchased items and other similar aggregates. This knowledge could be exploited for different scopes: set temporal discounts for making the purchases of customers more regular with respect the time, set personalized discounts in the day and time window preferred by the customer, provide recommendations for shopping time schedule, etc. To this aim, we introduce a framework for extracting from personal retail data a temporal purchasing profile able to summarize whether and when a customer makes her distinctive purchases. The individual profile describes a set of regular and characterizing shopping behavioral patterns, and the sequences in which these patterns take place. We show how to compare different customers by providing a collective perspective to their individual profiles, and how to group the customers with respect to these comparable profiles. By analyzing real datasets containing millions of shopping sessions we found that there is a limited number of patterns summarizing the temporal purchasing behavior of all the customers, and that they are sequentially followed in a finite number of ways. Moreover, we recognized regular customers characterized by a small number of temporal purchasing behaviors, and changing customers characterized by various types of temporal purchasing behaviors. Finally, we discuss on how the profiles can be exploited both by customers to enable personalized services, and by the retail market chain for providing tailored discounts based on temporal purchasing regularity.

The experience of teaching using a game based approach: Teachers as learners, collaborators and catalysts

This study focuses on the analysis of collective meaning associated with secondary physical education teachers’ ( n = 12) experiences of teaching games using a game based approach (GBA). Participants taught in one of two different international contexts, southeast Australia or southeast England, and all had some experience of using a GBA to teach games. A phenomenographic research framework was utilised to uncover the qualitatively finite number of ways that GBA-related teaching was/can be experienced. As guided by use of a phenomenographic analysis framework, three conceptions of awareness were identified that detail the collective meaning associated with participants’ experiences of teaching using a GBA, namely that of a Learner, a Collaborator and/or a Catalyst. An analysis of findings is presented with discussion focusing on what can be learnt from the different ways GBA teaching is experienced and implications for GBA teaching practice.

Raising the bar in analysis: Wimmer's Ethnic Boundary Making

Most books on ethnicity and race purport to relate specifically to one country, for instance, the USA. So Wimmer's new book is highly ambitious in presenting a comparative analytical framework for understanding ethnic boundary making, which transcends the particularities of any one country. While stressing the many ways in which actors are strategic in their practices, assertions and affiliations, in Ethnic Boundary Making, Andreas Wimmer insists on avoiding the tiresome binaries of instrumentalism versus primordialism. Wimmer's comparative framework centres on a search for recurring processual patterns. The search for such patterns means that there are only a finite number of ways in which ethnic boundaries are made, redefined, demolished, and so on – even across quite disparate societies around the world. It is this dogged determination to be precise and comprehensive that marks this book from others.

The Taxation Paradox: It’s Global, Not Local

Conventional wisdom suggests that taxation is a jurisdictionally specific discipline. For those advising private clients, the economic implications of taxation are a critical foundation for incorporating taxes in wealth management. Understanding the intricacies of a specific country’s tax code, however, provides little insight into the economic implications of taxes and how they impact risk, return, and investment strategy. Therefore, tax-efficient asset management is a global rather than local discipline. At its most basic level, tax on investment and capital is imposed by governments in a finite number of ways. Rather than becoming experts in local tax codes, wealth managers should understand the economic principles of taxation that apply globally to avoid making decisions that may be tax wise but pound foolish. <b>TOPICS:</b>Wealth management, legal/regulatory/public policy, global

Mortgaging the Future of Medical Research

Mortgaging the Future of Medical Research

Diastolic and Systolic Heart Failure Are Distinct Phenotypes Within the Heart Failure Spectrum

Heart failure (HF) is a major worldwide public health problem. One in 5 people aged 40 years in the United States will develop HF during his or her lifetime,1 and HF remains the leading cause for hospitalization among the elderly.2 Although age- and sex-specific HF incidence is not increasing,3 overall HF survival has improved, and the number of people aged >65 years is increasing rapidly. Thus, the absolute number of patients with HF will continue to increase. Half of the patients with HF have a preserved ejection fraction (HFpEF), and the remainder display reduced ejection fraction (HFrEF).4,–,6 The proportion of patients with normal ejection fraction (EF) is increasing steadily because of increased incidence and/or increasing physician recognition of the syndrome.4 Resource utilization associated with HF is high in both the inpatient and outpatient settings, regardless of EF. Response by De Keulenaer and Brutsaert on p 2014 Heart failure is a syndrome that can be defined clinically by a collection of symptoms (dyspnea, fatigue, exertional intolerance) and signs (edema, gallop, rales) that are attributable to a cardiac disorder.2 Heart failure may also be defined hemodynamically by an inability to provide adequate cardiac output to the body at rest or with exertion, or to do so only in the setting of elevated cardiac filling pressures. The cardiovascular system responds to a wide variety of insults (eg, myocardial disease, ischemia, valvular or pericardial disease) in a finite number of ways, both hemodynamically (elevated filling pressures, depressed output) and symptomatically (dyspnea, fatigue, angina). However, these similarities in clinical expression do not indicate that the underlying mechanisms of disease are the same or that treatment will be similar. For example, a headache may be noted with a migraine or brain tumor; dyspnea may be reported …

Topology of some tiling spaces without finite local complexity

A basic assumption of tiling theory is that adjacent tiles can meet in only a finite number of ways, up to rigid motions. However, there are many interesting tiling spaces that do not have this property. They have 'fault lines', along which tiles can slide past one another. We investigate the topology of a certain class of tiling spaces of this type. We show that they can be written as inverse limits of CW complexes, and their Čech cohomology is related to properties of the fault lines.

The number of planar central configurations for the 4–body problem is finite when 3 mass positions are fixed

In the n n –body problem a central configuration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 n=3 and for n &gt; 4 n&gt;4 that if n − 1 n-1 masses are located at fixed points in the plane, then there are only a finite number of ways to position the remaining n n th mass in such a way that they define a central configuration. Lindstrom leaves open the case n = 4 n=4 . In this paper we prove the case n = 4 n=4 using as variables the mutual distances between the particles.

On beyond LTP. Long-term potentiation.

In a challenging and insightful commentary, Sanes and Lichtman (1999) courageously point out in print what has often been discussed at recent meetings: LTP seems to have lost its usefulness as a paradigm for studying synaptic plasticity, much less learning and memory. The authors then offer two broad explanations for the current profusion (and confusion) of potential molecular mechanisms for LTP. The first is the simple suggestion that “Many molecules are required to mediate the process.” The second is that a variety of historical, experimental, and biological “factors have thwarted attempts to pinpoint a minimal cadre of essential molecules among a larger group of candidates.” Sanes and Lichtman favor this second, less optimistic explanation. I will argue that the truth lies somewhere in between. Sanes and Lichtman suggest that one reason we have a clear molecular explanation for, say, the action potential but not for LTP is that “the molecular biologists and biochemists studying action potentials knew what they were trying to explain.” In contrast, they correctly point out that it has “remained a challenge to supply a clear definition, description or function” for LTP. I agree that the inability to measure with a microelectrode alone the subtle mechanistic differences between one form of long-lasting synaptic potentiation and another has prevented a clear definition of LTP. The problem is magnified because the Nature of modern Science of the Cell biology of the Neuron has been to equate function with what is measured by a microelectrode. Thus, the trend has been to accept almost any manipulation that alters the tetanus-induced increase in EPSP slope as a legitimate functional study of LTP. It seems evident that a new paradigm is needed. In fact, many investigators have been quietly forging new ways of investigating synaptic regulation in the CNS, despite the frustration of having their work often relegated to non-functional status. In theory, there are a finite number of ways to change the strength of synaptic transmission. For example, the probability that a presynaptic action potential causes release of a vesicle of transmitter can be altered. An able group of molecular biologists and biochemists have made great strides in understanding this facet of synaptic regulation by investigating the molecular mechanisms of vesicular transmitter release. These studies, starting with descriptions of the proteins in synaptic vesicles (Reichardt and Kelly 1983) and interacting proteins in the plasma membrane (Bennett and Scheller 1994), have lead inevitably to exciting insights into the mechanisms of controlled synaptic vesicle fusion (Sutton et al. 1998; Chen et al. 1999). The next step will be to clarify the sites of regulation by calcium and by protein phosphorylation (Bennett 1997; Bajjalieh 1999). Another way that synaptic strength can be altered is to change the magnitude of the current-through-activated postsynaptic glutamate receptors. Here again, molecular biologists and biochemists have defined COMMENTARY

Use of catastrophe theory to obtain a fundamental understanding of elementary particle stability

Using Arnold's Classification Theorem applied to a four-dimensional manifold, it is shown that there is only a finite number of ways in which energy can discontinuously change state. It is demonstrated that each of these energy flow pathways can be associated with a distinct elementary particle. The theory not only shows how the formation of particles from the stress-energy present in the space-time manifold can be predicted from first principles, but also that there must exist five fundamental forces in a universe in which discontinuous energy transitions are possible. Finally, the existence of a new, as yet undiscovered particle is predicted, which is associated with this new fifth force.

Generation of representative members of an RrSst weighted median filer class

The weighted median filter (WMF) is a generalisation of the median filter. The WMF has been described elsewhere, where it was shown that a given WMF class operates in a finite number of ways. An expression for the number of modes of operation of any WMF class, in a given group of classes, has recently been derived. Here, an algorithm is described for constructing a complete set of representative members of any class in such a group. This algorithm, expressed as a Pascal program, is used to generate results for two useful classes of WMFs.

A method for modelling and evaluating integrated energy systems in agriculture

The successful integration of energy conservation or production processes requires detailed information on how the technology will interact with other processes in the system. This information must be organized into a working model of the production system if it is to be used effectively. Like any large-scale industrial or environmental system, agricultural production systems can be modelled as a collection of discrete physical processes interconnected in a finite number of ways. The modelling of these processes and their interconnection are explored in this paper. In addition to model development, process integration as a concept is explored. Starting with the traditional definition of process integration, the author refines and expands this concept. This expanded concept, called system integration, is coupled with the modelling method to investigate some of the issues associated with the design and evaluation of integrated energy systems in agriculture.

RESEARCH NOTE / THE MAP AS INFORMATION CHANNEL: IGNORANCE BEFORE AND AFTER LOOKING AT A CHOROPLETH MAP

In this note, elementary concepts of information theory are applied to develop a measure of the information conveyed to a map reader by a map. For concreteness, a choropleth map is discussed though the framework is applicable to any map with a finite number of symbols colored in a finite number of ways. The measure takes account of prior and posterior ignorance of the map reader, summarized in a set of discrete subjective probability distributions. The framework presented permits empirical estimation of information content and map-reading performance. More important, from the viewpoint of cartographic design, is the potential for incorporating psychophysical relationships between subjective probabilities and map symbolism in order to maximize information conveyed. Cette étude démontre les concepts élémentaires de la théorie de l'information utilisés dans le but d'en arriver à connaître le degré de renseignements transmis au lecteur de la carte. Afin de donner un exemple concret, une carte établie selon la méthode statistique a été utilisée, bien que la méthode d'approche de cette étude peut s'appliquer à toute carte qui présente un nombre limité de symboles colorés d'un nombre limité de manières. Ce degré de renseignements tient compte des connaissances du lecteur avant et après son étude de la carte; le tout réparti suivant des probabilités admises. La méthode d'approche présentée permet une évaluation empirique des renseignements fournis et des résultats obtenus par la lecture de la carte. Plus important encore, considéré au point de vue de la représentation cartographique, est la possibilité d'établir des rapports psychophysiques entre les probabilités admises et le symbolisme cartographique en vue de porter l'information transmise au maximum.

A generalized k-nearest neighbor rule

A family of supervised, nonparametric decision rules, based on tolerance regions, is described which includes the k -Nearest Neighbor decision rules when there are two classes. There are two practical reasons for doing so: first, a family of decision rules similar to the k -Nearest Neighbor rules can be specified which applies to a broader collection of pattern recognition problems. This is because in the general class of rules constraints are weakened between the number of training samples required in each training sample set and the respective a priori class probabilities; and, a discrete loss function weighting the importance of the finite number of ways to make a decision error can be introduced. Second, within the family of decision rules based on tolerance regions, there are decision rules which have a property allowing for preprocessing of the training set data resulting in significant data reduction. Theoretical performance for a special case is presented.

The Computer as a Tool for Legal Research

For example, the telegraphic abstract prepared for section 2-313 of the Uniform Commercial Code17 can be translated loosely from its machineable form into English as follows: Goods were processed by selling from a seller to a buyer; an express warranty was defined or created in that a bargain occurred from a buyer to a seller conditional upon an affirmation, a promise, a description, and a sample. In this rough paraphrase, the italicized words are those taken from the original text, and the connectives are an approximation of the meaning of the role indicator codes that were used to tag the underlined words. The analysis described up to this point is performed by individuals skilled in the literature of the field. A further analysis of the underlined words takes place via machine: the English words are looked up in the WRU Semantic Code Dictionary, and a set of codes representing various generic aspects of the original English word is substituted for the original, so that the finally coded form consists of role indicators (three-letter codes), punctuation (commas, periods, and the like), and semantic (four-letter codes). The telegraphic abstracts for all of the documents in a given file finally are maintained in coded form serially on magnetic tape, in readiness for computer search. At search time, a question is prepared, which resembles very much the form of a coded telegraphic abstract, and the file is searched for references that match (in the logical sense) the question. Some comment should be made about the facilities delivered by this unique indexing method. Although the analysis is complex by comparison with other methods, the human effort required is minimized by the restrictions imposed in the format and structure. (Only a small set of role indicators actually are used, and there is a finite number of ways in which they combine naturally; this makes it easy for the indexer to make the necessary decisions.) The format also increases the resolution of searches; that is, it decreases the possibility of false drops. On the other hand, the generic coding of the key words selected from the source document increases the system's ability to find references characterized by synonyms or terms of broader or narrower significance, and this facility of course increases the probability that all relevant documents will be found. In summary, the WRU coding system embodies a considerable refinement in analysis over most indexing systems, and its indexing depth probability is greater than that of most conventional systems. These would be desirable attributes to incorporate into an automatic indexing system. Melton & Bensing, supra note I6, at 240-43. This content downloaded from 157.55.39.255 on Mon, 01 Aug 2016 06:10:17 UTC All use subject to http://about.jstor.org/terms LAW AND CONTEMPORARY PROBLEMS E. Searching of Conventionally Indexed Documents, with Search Augmented by Statistically Associated Index Terms John C. Lyons, of the Graduate School of Public Law, George Washington University, with the participation of the Datatrol Corporation, has adapted Dr. Edmund Stiles' factor8 to the searching of files of documents dealing with antitrust problems.'9 The technique consists essentially of the following steps: i. Preparation of the File to Be Searched a) Choose (via human analysis) index terms to represent each document in the file. b) Prepare a Term Profile tape using the following procedure: Compute association factors relating each unique index in the entire file with each of the other terms with which it ever co-occurs in a document, using Stiles' modified chi-square formula, (IfN-ABjN1 In 2v/ = ASSOCIATION FACTOR AB(N-A)(N-B) J where A is the number of documents indexed by one term, B is the number of documents indexed by a second term, f is the number of documents indexed by both terms, and N is the total number of documents in the collection. Then, for each index prepare a list (the term profile) of the other terms with which the given exhibits significant association. For example, Lyons reports20 that the Clayton Act Section iI was found in this manner to be associated with the following