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Results for “Problem Formulation”

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At least 325 records · Page 18Linked to original sources

PubMed1997

Computerized tumor boundary detection using a Hopfield neural network.

In this paper, we present a new approach for detection of brain tumor boundaries in medical images using a Hopfield neural network. The boundary detection problem is formulated as an optimization process that seeks the boundary points to minimize an energy functional based on an active contour model. A modified Hopfield network is constructed to solve the optimization problem. Taking advantage of the collective computational ability and energy convergence capability of the Hopfield network, our method produces the results comparable to those of standard "snakes"-based algorithms, but it requires less computing time. With the parallel processing potential of the Hopfield network, the proposed boundary detection can be implemented for real time processing. Experiments on different magnetic resonance imaging (MRI) data sets show the effectiveness of our approach.

Algorithms↗

PubMed2005

Information geometry of interspike intervals in spiking neurons.

An information geometrical method is developed for characterizing or classifying neurons in cortical areas, whose spike rates fluctuate in time. Under the assumption that the interspike intervals of a spike sequence of a neuron obey a gamma process with a time-variant spike rate and a fixed shape parameter, we formulate the problem of characterization as a semiparametric statistical estimation, where the spike rate is a nuisance parameter. We derive optimal criteria from the information geometrical viewpoint when certain assumptions are added to the formulation, and we show that some existing measures, such as the coefficient of variation and the local variation, are expressed as estimators of certain functions under the same assumptions.

Action Potentials↗

PubMed1976

Problem-solving in science.

Problem-solving is a characteristic activity of scientists, Theoretical problems are formulated as a consequence of scientists' thirst for knowledge, and their solutions take the form of general propositions, termed hypotheses, which are consistent with, and provide provisionally satisfactory explanations of, empirical observations. Practical problems appear as the result of feedback from the extra-scientific world of everyday life, industry and professional practice. Their solutions provide an improved basis for decision-making in terms of existing options or increase the number of options from which a choice may be made. The categories theoretical and practical are not mutually exclusive: practical problems often generate interesting theoretical problems, and the solution of a theoretical problem may entrain the solution of a host of practical problems. All hypotheses are provisional because it is impossible to establish the truth of a generalization by rigorous deduction from any number of particular instances, though a single instance may suffice to refute it. This asymmetry forms the basis of Popper's analysis of scientific methodology. This analysis, though acceptable in the main, is open to criticism in the following respects; (1) it ignores the contribution to scientific progress made by unplanned perceptions; (2) it ignores the contribution of hypotheses which do not generate testable predictions; (3) it does not do justice to the extra-logical component in knowing (Polanyi's tacit dimension); and (4) its treatment of practical problems in inadequate.

Decision Making↗

PubMedDate not supplied

Potentialities of passive thermoacoustic tomography in hyperthermia.

The potentiality of passive thermoacoustic tomography (PTT) is considered theoretically. The problem is formulated to reconstruct the distribution of the thermodynamic temperature at a depth from the acoustic radiation generated by thermal noise and measured by a set of piezotransducers on the body surface. The 2-D inverse problem has been studied. Three mathematical methods of reconstruction were investigated: (1) the least squares method; (2) Tikhonov's regularization method; and (3) the method of elimination of non-physical solutions. The reconstruction in square as well as in rectangular areas was studied. If one uses the least squares method the square area can be separated into 5 x 5 subareas, the typical dimension of every one is 0.5-2 cm for measurements conducted in the frequency range 2-0.5 MHz. The precision deltaT in temperature reconstruction in different layers is about 0.1-0.2 K for smooth distributions of the thermodynamic temperature and 0.1-0.4 K for abrupt distributions, if the number of different scans is about 10(2) and the time of data collecting is about 1 min.

Acoustics↗

PubMed1994

Understanding the pressure cost of ventilation: why does high-frequency ventilation work?

OBJECTIVES: To understand when the use of high-frequency ventilation would be advantageous, we formulated the problem of achieving adequate alveolar ventilation at minimal pressure cost by dividing it into two simpler problems: a) the pressure cost per unit of convective oscillatory flow; and b) the convective flow cost necessary to achieve a unit of alveolar ventilation. METHODS: Simple solutions for each of these cost functions were formulated using established models of gas exchange and lung mechanics, including the effects of lung inflation tidal volume and respiratory frequency in alveolar ventilation, nonlinear lung tissue compliance, and alveolar recruitment and derecruitment. Solutions to these models were combined to assess the total pressure cost of high-frequency ventilation as a function of the ventilatory settings and the pathophysiologic variables of the patient. MAIN RESULTS: The model predicted that for variables applicable to an infant with respiratory distress syndrome, the selection of positive end-expiratory pressure (PEEP) becomes critical because the penalties in pressure cost are amplified for both high and low values of PEEP. The selection of frequency is not as critical for frequencies > 10 Hz, although it is more important than in the normal neonatal lung. CONCLUSIONS: This analysis illustrates the importance of using high-frequency ventilation in infant respiratory distress syndrome and of optimizing the amount of PEEP. It also points out the danger of barotrauma in the derecruited lung. When the lungs are in a derecruited state, the combinations of frequency, PEEP, and tidal volume that yield adequate ventilation with safe distention of recruited alveoli are severely limited.

Animals↗

PubMedDate not supplied

Joint classification and pairing of human chromosomes.

We reexamine the problems of computer-aided classification and pairing of human chromosomes, and propose to jointly optimize the solutions of these two related problems. The combined problem is formulated into one of optimal three-dimensional assignment with an objective function of maximum likelihood. This formulation poses two technical challenges: 1) estimation of the posterior probability that two chromosomes form a pair and the pair belongs to a class and 2) good heuristic algorithms to solve the three-dimensional assignment problem which is NP-hard. We present various techniques to solve these problems. We also generalize our algorithms to cases where the cell data are incomplete as often encountered in practice.

Algorithms↗

PubMed1977

The female hysterical personality disorder.

It is not uncommon in family practice for the family physician to encounter the female patient with a hysterical personality disorder. A case presentation and interview are provided to help the family physician recognize the problem. A formulation of this case stresses psychosexual development, which will provide the reader with insight that can be generalized to other patients. Major emphasis is given to practical guidelines for the clinician for management of this frequently difficult problem in a medical setting.

Adult↗

PubMed2004

Quantum adiabatic optimization and combinatorial landscapes.

In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of the satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma=M/N . We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (instead of only energy) is used, and are able to show the existence of a dynamic threshold gamma= gamma(d) starting with some value of K -the number of variables in each clause. Beyond the dynamic threshold, the algorithm should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz. We have been able to map the ensemble of random graphs onto another ensemble with fluctuations significantly reduced. This enabled us to obtain tight upper bounds on the satisfiability transition and to recompute the dynamical transition using the extended set of landscapes.

Journal Article↗

PubMed2000

Partitive Formulation of Information in Probabilistic Problems: Beyond Heuristics and Frequency Format Explanations.

I propose a simple theory on the use of base rate according to which neither heuristic nor frequentist factors underlie demonstrations of the occurrence or the elimination of the base-rate fallacy. According to this view, what is crucial for the occurrence or elimination of the base-rate fallacy is the absence or presence, respectively, of what can be called a partitive formulation (Macchi, 1995) of the conditional likelihood datum. A partitive formulation defines the set of which the numerical datum is a part (in terms of percentages or frequencies) by referring to the likelihood datum relative to the base rate information. The predictive power of this hypothesis is shown by comparing responses to different versions of problems containing the same implied natural heuristic principles and supplied data, but which differ in the way the information is presented (partitive vs nonpartitive). Whether probabilistic or frequentist, the partitive versions lead to an almost complete elimination of the bias which remains when nonpartitive versions are used. On the basis of these experimental results, the paper includes a critical discussion of heuristic, frequentist, and mental models theories. Copyright 2000 Academic Press.

Journal Article↗

PubMed2006

Fibertract segmentation in position orientation space from high angular resolution diffusion MRI.

In diffusion MRI, standard approaches for fibertract identification are based on algorithms that generate lines of coherent diffusion, currently known as tractography. A tract is then identified as a set of such lines selected on some criteria. In the present study, we investigate whether fibertract identification can be formulated as a segmentation task that recognizes a fibertract as a region where diffusion is intense and coherent. Indeed, we show that it is possible to segment efficiently well-known fibertracts with classical image processing methods provided that the problem is formulated in a five-dimensional space of position and orientation. As an example, we choose to adapt to this newly defined high-dimensional non-Euclidean space, called position orientation space, an algorithm based on the hidden Markov random field framework. Structures such as the cerebellar peduncles, corticospinal tract, association bundles can be identified and represented in three dimensions by a back projection technique similar to maximum intensity projection. Potential advantages and drawbacks as compared to classical tractography are discussed; for example, it appears that our formulation handles naturally crossing tracts and is not biased by human intervention.

Algorithms↗

PubMed1996

Structural analysis of social behavior as a common metric for programmatic psychopathology and psychotherapy research.

This article describes the use of Structural Analysis of Social Behavior (SASB; L. Benjamin, 1974) as applied to programmatic psychodynamic-interpersonal psychotherapy research. SASB fosters cumulative, theory-driven research by permitting problem-treatment-outcome (PTO) congruence--the conceptualization and measurement of patients' problems, treatment processes, and outcome in a common metric. In this explanation of the principle of PTO congruence, the following are discussed: a general model of interpersonal psychopathology and etiology, SASB-based assessment devices for measuring early history and formulating presenting problems, empirical studies of interpersonal process in therapy, the relationship between manual-guided training and interpersonal process, and the assessment of outcome. A generic interpersonal model of psychotherapy is proposed that theoretically links all of these elements. Finally, the use of these SASB-based models for cross-theory integrative research from a common-factors approach is discussed.

Humans↗

PubMed2003

Symmetric BEM formulation for the M/EEG forward problem.

The forward M/EEG problem consists in simulating the electric potential and the magnetic field produced outside the head by currents in the brain related to neural activity. All previously proposed solutions using the Boundary Element Method (BEM) were based on a double-layer integral formulation. We have developed an alternative symmetric BEM formulation, achieving a significantly higher accuracy for sources close to tissue interfaces, namely in the cortex. Numerical experiments using a spherical semi-realistic multilayer head model with a known analytical solution are presented, showing that the new BEM performs better than the formulations used in our earlier comparisons, and in most cases outperforms the Finite Element Method (FEM) as far as accuracy is concerned, thus making the BEM a viable choice.

Algorithms↗

PubMed1997

Self-organizing Internal Representation in Learning of Navigation: A Physical Experiment by the Mobile Robot YAMABICO.

This paper discusses a novel scheme for sensory-based navigation of a mobile robot. In our previous work ([Tani and Fukumura, 1994], Neural Networks, 7(3), 553-563), we formulated the problem of goal-directed navigation as an embedding problem of dynamical systems: desired trajectories in a task space should be embedded in an adequate sensory-based internal state space so that a unique mapping from the internal state space to the motor command could be established. In the current formulation a recurrent neural network is employed, which shows that an adequate internal state space can be self-organized, through supervised training with sensorimotor sequences. The experiment was conducted using a real mobile robot equipped with a laser range sensor, demonstrating the validity of the presented scheme by working in a noisy real-world environment. Copyright 1996 Elsevier Science Ltd.

Journal Article↗

PubMed2005

Diffusive transport in networks built of containers and tubes.

We have developed analytical and numerical methods to study the transport of noninteracting particles in large networks consisting of M d -dimensional containers C1,...,C(M) with radii R(i) linked together by tubes of length l(ij) and radii a(ij) where i,j = 1,2,...,M. Tubes may join directly with each other, forming junctions. It is possible that some links are absent. Instead of solving the diffusion equation for the full problem we formulated an approach that is computationally more efficient. We derived a set of rate equations that govern the time dependence of the number of particles in each container, N1(t), N2(t),...,N(M)(t). In such a way the complicated transport problem is reduced to a set of M first-order integro-differential equations in time, which can be solved efficiently by the algorithm presented here. The workings of the method have been demonstrated on a couple of examples: networks involving three, four, and seven containers and one network with a three-point junction. Already simple networks with relatively few containers exhibit interesting transport behavior. For example, we showed that it is possible to adjust the geometry of the networks so that the particle concentration varies in time in a wave-like manner. Such behavior deviates from simple exponential growth and decay occurring in the two-container system.

Journal Article↗

PubMed2005

Paediatric formulations--getting to the heart of the problem.

Many medicines prescribed for children are unlicensed. Solid dosage forms present problems as children have difficulty swallowing whole tablets or capsules. When medicines are not licensed for children, it is unlikely that there will be a suitable, licensed liquid formulation and so extemporaneous liquid preparations (prepared at the dispensary or by GMP 'special' manufacturers) are often used. This study looked at a list of medicines commonly prescribed for children with cardiovascular conditions in an English specialist paediatric hospital and classified them according to licensed status and available formulations. As expected, most medicines used for children with cardiovascular problems were unlicensed and where this was the case, usually only 'special' liquids or extemporaneous preparations were available. Problems linked with formulations highlighted in this therapeutic category were: problems in dosing accuracy and unknown bioavailability of extemporaneous products, the use of potentially toxic excipients, and lack of access to modified release preparations for children. These problems are likely to extend to other paediatric therapeutic areas. There is currently a large, unmet need to improve formulations of commonly used paediatric medicines, both through licensing and standardising the production of extemporaneous and 'special' formulations. It is expected that the awaited European regulation will help to meet some of those needs.

Cardiovascular Agents↗

PubMed2002

On the problem in model selection of neural network regression in overrealizable scenario.

In considering a statistical model selection of neural networks and radial basis functions under an overrealizable case, the problem of unidentifiability emerges. Because the model selection criterion is an unbiased estimator of the generalization error based on the training error, this article analyzes the expected training error and the expected generalization error of neural networks and radial basis functions in overrealizable cases and clarifies the difference from regular models, for which identifiability holds. As a special case of an overrealizable scenario, we assumed a gaussian noise sequence as training data. In the least-squares estimation under this assumption, we first formulated the problem, in which the calculation of the expected errors of unidentifiable networks is reduced to the calculation of the expectation of the supremum of the chi2 process. Under this formulation, we gave an upper bound of the expected training error and a lower bound of the expected generalization error, where the generalization is measured at a set of training inputs. Furthermore, we gave stochastic bounds on the training error and the generalization error. The obtained upper bound of the expected training error is smaller than in regular models, and the lower bound of the expected generalization error is larger than in regular models. The result tells us that the degree of overfitting in neural networks and radial basis functions is higher than in regular models. Correspondingly, it also tells us that the generalization capability is worse than in the case of regular models. The article may be enough to show a difference between neural networks and regular models in the context of the least-squares estimation in a simple situation. This is a first step in constructing a model selection criterion in an overrealizable case. Further important problems in this direction are also included in this article.

Journal Article↗

PubMed1999

Do we all mean the same thing by "problem-based learning"? A review of the concepts and a formulation of the ground rules.

Problem-based learning (PBL) has emerged as a useful tool of epistemological reform in higher education, particularly in medical schools. Indeed, PBL has spent most of its career inducing revolutionary undergraduate medical reform. Nevertheless, obtaining informed agreement on the characteristics of the PBL "genus" is a challenge when the label is vulnerable to being borrowed for prestige or subversion. Many "PBL" single-subject courses within traditional curricula do not use PBL at all. Such semantic uncertainty compromises the evidence-base on the added value of problem-based versus traditional approaches and the main messages for good practice. This literature review explores what is meant by the term PBL by aiming to answer the following questions: What difficulties are inherent in the "problem-based" tag? What does the term "problem-based curriculum" imply? How has PBL been characterized and validated by focusing on its purpose? How else has PBL been characterized? How does PBL relate to problem solving? How does PBL relate to epistemological reform? In conclusion, what ground rules can be formulated for PBL? Despite much conceptual fog lingering over the PBL literature, useful ground rules can be formulated.

Curriculum↗

PubMed2005

New simple tests for age-at-onset anticipation: application to panic disorder.

Recently, testing for anticipation has received renewed interest. It is well known that standard statistical methods are inappropriate for this purpose due to problems of sampling bias. Few statistical tests have been proposed for comparing mean age of onset in affected parents with mean age of onset in affected children. All of them are difficult to compute and lack software to perform the tests. In this report, we formulate the problem in terms of symmetry tests. We propose a simple generalized paired t-test and a Wilcoxon signed rank test to adjust for the bias caused by the right truncation of both the parent's and child's ages at onset. We also extend the generalized paired t-test to a random effects model that enables analysis of correlated data from nuclear families, and could be further extended to larger family structures. We illustrate the approaches with an example of panic disorder.

Age of Onset↗