Topological aspects of DNA function and protein folding.

The Topological Aspects of DNA Function and Protein Folding international meeting provided an interdisciplinary forum for biological scientists, physicists and mathematicians to discuss recent developments in the application of topology to the study of DNA and protein structure. It had 111 invited participants, 48 talks and 21 posters. The present article discusses the importance of topology and introduces the articles from the meeting's speakers.

On the q=1/2 non-extensive maximum entropy distribution

A detailed mathematical analysis on the q = 1/2 non-extensive maximum entropydistribution of Tsallis' is undertaken. The analysis is based upon the splitting of such adistribution into two orthogonal components. One of the components corresponds to theminimum norm solution of the problem posed by the fulfillment of the a priori conditionson the given expectation values. The remaining component takes care of the normalizationconstraint and is the projection of a constant onto the Null space of the "expectation-values-transformation"

A non-extensive maximum entropy based regulations method for bad conditioned inverse problems

A regularization method based on the non-extensive maximum entropy principle is devised. Special emphasis is given to the q=1/2 case. We show that, when the residual principle is considered as constraint, the q=1/2 generalized distribution of Tsallis yields a regularized solution for bad-conditioned problems. The so devised regularized distribution is endowed with a component which corresponds to the well known regularized solution of Tikhonov (1977).

Frames: a maximum entropy statistical estimate of the inverse problem

A maximum entropy statistical treatment of an inverse problem concerning frame theory is presented. The problem arises from the fact that a frame is an overcomplete set of vectors that defines a mapping with no unique inverse. Although any vector in the concomitant space can be expressed as a linear combination of frame elements, the coefficients of the expansion are not unique. Frame theory guarantees the existence of a set of coefficients which is “optimal” in a minimum norm sense. We show here that these coefficients are also “optimal” from a maximum entropy viewpoint.

A Topological Approach to Fuzzy Sets

This thesis presents a topological approach to studying fuzzy setsby means of modifier operators. Modifier operators are mathematical models, e.g., for hedges, and we present briefly different approaches to studying modifier operators. We are interested in compositional modifier operators, modifiers for short, and these modifiers depend on binary relations. We show that if a modifier depends on a reflexive and transitive binary relation on U, then there exists a unique topology on U such that this modifier is the closure operator in that topology. Also, if U is finite then there exists a lattice isomorphism between the class of all reflexive and transitive relations and the class of all topologies on U. We define topological similarity relation "≈" between L-fuzzy sets in an universe U, and show that the class LU/ ≈ is isomorphic with the class of all topologies on U, if U is finite and L is suitable. We consider finite bitopological spaces as approximation spaces, and we show that lower and upper approximations can be computed by means of α-level sets also in the case of equivalence relations. This means that approximations in the sense of Rough Set Theory can be computed by means of α-level sets. Finally, we present and application to data analysis: we study an approach to detecting dependencies of attributes in data base-like systems, called information systems.

Transfer entropy reconstruction and labeling of neuronal connections from simulated calcium imaging

Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous approach based on information theory, the Generalized Transfer Entropy, to the reconstruction of connectivity of simulated neuronal networks of both excitatory and inhibitory neurons. We show that, due to the model-free nature of the developed measure, both kinds of connections can be reliably inferred if the average firing rate between synchronous burst events exceeds a small minimum frequency. Furthermore, we suggest, based on systematic simulations, that even lower spontaneous inter-burst rates could be raised to meet the requirements of our reconstruction algorithm by applying a weak spatially homogeneous stimulation to the entire network. By combining multiple recordings of the same in silico network before and after pharmacologically blocking inhibitory synaptic transmission, we show then how it becomes possible to infer with high confidence the excitatory or inhibitory nature of each individual neuron.

An Analysis of Eye Scanpath Entropy in a Progressively Forming Virtual Environment

A sign of presence in virtual environments is that people respond to situations and events as if they were real, where response may be considered at many different levels, ranging from unconscious physiological responses through to overt behavior,emotions, and thoughts. In this paper we consider two responses that gave different indications of the onset of presence in a gradually forming environment. Two aspects of the response of people to an immersive virtual environment were recorded: their eye scanpath, and their skin conductance response (SCR). The scenario was formed over a period of 2 min, by introducing an increasing number of its polygons in random order in a head-tracked head-mounted display. For one group of experimental participants (n 8) the environment formed into one in which they found themselves standing on top of a 3 m high column. For a second group of participants (n 6) the environment was otherwise the same except that the column was only 1 cm high, so that they would be standing at normal ground level. For a third group of participants (n 14) the polygons never formed into a meaningful environment. The participants who stood on top of the tall column exhibited a significant decrease in entropy of the eye scanpath and an increase in the number of SCR by 99 s into the scenario, at a time when only 65% of the polygons had been displayed. The ground level participants exhibited a similar decrease in scanpath entropy, but not the increase in SCR. The random scenario grouping did not exhibit this decrease in eye scanpath entropy. A drop in scanpath entropy indicates that the environment had cohered into a meaningful perception. An increase in the rate of SCR indicates the perception of an aversive stimulus. These results suggest that on these two dimensions (scanpath entropy and rate of SCR) participants were responding realistically to the scenario shown in the virtual environment. In addition, the response occurred well before the entire scenario had been displayed, suggesting that once a set of minimal cues exists within a scenario,it is enough to form a meaningful perception. Moreover, at the level of the sympathetic nervous system, the participants who were standing on top of the column exhibited arousal as if their experience might be real. This is an important practical aspect of the concept of presence.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

Fuzzy subgroups, algebraic and topological points of view and complex analysis

Fuzzy subsets and fuzzy subgroups are basic concepts in fuzzy mathematics. We shall concentrate on fuzzy subgroups dealing with some of their algebraic, topological and complex analytical properties. Explorations are theoretical belonging to pure mathematics. One of our ideas is to show how widely fuzzy subgroups can be used in mathematics, which brings out the wealth of this concept. In complex analysis we focus on Möbius transformations, combining them with fuzzy subgroups in the algebraic and topological sense. We also survey MV spaces with or without a link to fuzzy subgroups. Spectral space is known in MV algebra. We are interested in its topological properties in MV-semilinear space. Later on, we shall study MV algebras in connection with Riemann surfaces. In fact, the Riemann surface as a concept belongs to complex analysis. On the other hand, Möbius transformations form a part of the theory of Riemann surfaces. In general, this work gives a good understanding how it is possible to fit together different fields of mathematics.

On Topological Solitons in The Faddeev-Skyrme Model and its Extensions

The topological solitons of two classical field theories, the Faddeev-Skyrme model and the Ginzburg-Landau model are studied numerically and analytically in this work. The aim is to gain information on the existence and properties of these topological solitons, their structure and behaviour under relaxation. First, the conditions and mechanisms leading to the possibility of topological solitons are explored from the field theoretical point of view. This leads one to consider continuous deformations of the solutions of the equations of motion. The results of algebraic topology necessary for the systematic treatment of such deformations are reviewed and methods of determining the homotopy classes of topological solitons are presented. The Faddeev-Skyrme and Ginzburg-Landau models are presented, some earlier results reviewed and the numerical methods used in this work are described. The topological solitons of the Faddeev-Skyrme model, Hopfions, are found to follow the same mechanisms of relaxation in three different domains with three different topological classifications. For two of the domains, the necessary but unusual topological classification is presented. Finite size topological solitons are not found in the Ginzburg-Landau model and a scaling argument is used to suggest that there are indeed none unless a certain modification to the model, due to R. S. Ward, is made. In that case, the Hopfions of the Faddeev-Skyrme model are seen to be present for some parameter values. A boundary in the parameter space separating the region where the Hopfions exist and the area where they do not exist is found and the behaviour of the Hopfion energy on this boundary is studied.

Feature selection using Fuzzy Entropy measures with Yu's Similarity measure

In this study, feature selection in classification based problems is highlighted. The role of feature selection methods is to select important features by discarding redundant and irrelevant features in the data set, we investigated this case by using fuzzy entropy measures. We developed fuzzy entropy based feature selection method using Yu's similarity and test this using similarity classifier. As the similarity classifier we used Yu's similarity, we tested our similarity on the real world data set which is dermatological data set. By performing feature selection based on fuzzy entropy measures before classification on our data set the empirical results were very promising, the highest classification accuracy of 98.83% was achieved when testing our similarity measure to the data set. The achieved results were then compared with some other results previously obtained using different similarity classifiers, the obtained results show better accuracy than the one achieved before. The used methods helped to reduce the dimensionality of the used data set, to speed up the computation time of a learning algorithm and therefore have simplified the classification task

The Effects of Anesthetic Induced Loss of Consciousness on Quantitative Electroen Cephalogram, and Bispectral and Spectral Entropy Indices. Studies on Healthy Male

Changes in the electroencephalography (EEG) signal have been used to study the effects of anesthetic agents on the brain function. Several commercial EEG based anesthesia depth monitors have been developed to measure the level of the hypnotic component of anesthesia. Specific anesthetic related changes can be seen in the EEG, but still it remains difficult to determine whether the subject is consciousness or not during anesthesia. EEG reactivity to external stimuli may be seen in unconsciousness subjects, in anesthesia or even in coma. Changes in regional cerebral blood flow, which can be measured with positron emission tomography (PET), can be used as a surrogate for changes in neuronal activity. The aim of this study was to investigate the effects of dexmedetomidine, propofol, sevoflurane and xenon on the EEG and the behavior of two commercial anesthesia depth monitors, Bispectral Index (BIS) and Entropy. Slowly escalating drug concentrations were used with dexmedetomidine, propofol and sevoflurane. EEG reactivity at clinically determined similar level of consciousness was studied and the performance of BIS and Entropy in differentiating consciousness form unconsciousness was evaluated. Changes in brain activity during emergence from dexmedetomidine and propofol induced unconsciousness were studied using PET imaging. Additionally, the effects of normobaric hyperoxia, induced during denitrogenation prior to xenon anesthesia induction, on the EEG were studied. Dexmedetomidine and propofol caused increases in the low frequency, high amplitude (delta 0.5-4 Hz and theta 4.1-8 Hz) EEG activity during stepwise increased drug concentrations from the awake state to unconsciousness. With sevoflurane, an increase in delta activity was also seen, and an increase in alpha- slow beta (8.1-15 Hz) band power was seen in both propofol and sevoflurane. EEG reactivity to a verbal command in the unconsciousness state was best retained with propofol, and almost disappeared with sevoflurane. The ability of BIS and Entropy to differentiate consciousness from unconsciousness was poor. At the emergence from dexmedetomidine and propofol induced unconsciousness, activation was detected in deep brain structures, but not within the cortex. In xenon anesthesia, EEG band powers increased in delta, theta and alpha (8-12Hz) frequencies. In steady state xenon anesthesia, BIS and Entropy indices were low and these monitors seemed to work well in xenon anesthesia. Normobaric hyperoxia alone did not cause changes in the EEG. All of these results are based on studies in healthy volunteers and their application to clinical practice should be considered carefully.

The European Union and Assembling Biofuel Development – topological investigations concerning the associations between law, policy and space

Biofuels for transport are a renewable source of energy that were once heralded as a solution to multiple problems associated with poor urban air quality, the overproduction of agricultural commodities, the energy security of the European Union (EU) and climate change. It was only after the Union had implemented an incentivizing framework of legal and political instruments for the production, trade and consumption of biofuels that the problems of weakening food security, environmental degradation and increasing greenhouse gases through land-use changes began to unfold. In other words, the difference between political aims for why biofuels are promoted and their consequences has grown – which is also recognized by the EU policy-makers. Therefore, the global networks of producing, trading and consuming biofuels may face a complete restructure if the European Commission accomplishes its pursuit to sideline crop-based biofuels after 2020. My aim with this dissertation is not only to trace the manifold evolutions of the instruments used by the Union to govern biofuels but also to reveal how this evolution has influenced the dynamics of biofuel development. Therefore, I study the ways the EU’s legal and political instruments of steering biofuels are coconstitutive with the globalized spaces of biofuel development. My analytical strategy can be outlined through three concepts. I use the term ‘assemblage’ to approach the operations of the loose entity of actors and non-human elements that are the constituents of multi-scalar and -sectorial biofuel development. ‘Topology’ refers to the spatiality of this European biofuel assemblage and its parts whose evolving relations are treated as the active constituents of space, instead of simply being located in space. I apply the concept of ‘nomosphere’ to characterize the framework of policies, laws and other instruments that the EU applies and construes while attempting to govern biofuels. Even though both the materials and methods vary in the independent articles, these three concepts characterize my analytical strategy that allows me to study law, policy and space associated with each other. The results of my examinations underscore the importance of the instruments of governance of the EU constituting and stabilizing the spaces of producing and, on the other hand, how topological ruptures in biofuel development have enforced the need to reform policies. This analysis maps the vast scope of actors that are influenced by the mechanism of EU biofuel governance and, what is more, shows how they are actively engaging in the Union’s institutional policy formulation. By examining the consequences of fast biofuel development that are spatially dislocated from the established spaces of producing, trading and consuming biofuels such as indirect land use changes, I unfold the processes not tackled by the instruments of the EU. Indeed, it is these spatially dislocated processes that have pushed the Commission construing a new type of governing biofuels: transferring the instruments of climate change mitigation to land-use policies. Although efficient in mitigating these dislocated consequences, these instruments have also created peculiar ontological scaffolding for governing biofuels. According to this mode of governance, the spatiality of biofuel development appears to be already determined and the agency that could dampen the negative consequences originating from land-use practices is treated as irrelevant.

Brain tissue segmentation using q-entropy in multiple sclerosis magnetic resonance images

The loss of brain volume has been used as a marker of tissue destruction and can be used as an index of the progression of neurodegenerative diseases, such as multiple sclerosis. In the present study, we tested a new method for tissue segmentation based on pixel intensity threshold using generalized Tsallis entropy to determine a statistical segmentation parameter for each single class of brain tissue. We compared the performance of this method using a range of different q parameters and found a different optimal q parameter for white matter, gray matter, and cerebrospinal fluid. Our results support the conclusion that the differences in structural correlations and scale invariant similarities present in each tissue class can be accessed by generalized Tsallis entropy, obtaining the intensity limits for these tissue class separations. In order to test this method, we used it for analysis of brain magnetic resonance images of 43 patients and 10 healthy controls matched for gender and age. The values found for the entropic q index were 0.2 for cerebrospinal fluid, 0.1 for white matter and 1.5 for gray matter. With this algorithm, we could detect an annual loss of 0.98% for the patients, in agreement with literature data. Thus, we can conclude that the entropy of Tsallis adds advantages to the process of automatic target segmentation of tissue classes, which had not been demonstrated previously.

Enthalpy-entropy compensation based on isotherms of mango

Moisture equilibrium data of mango pulp were determined using the static gravimetric method. Adsorption and desorption isotherms were obtained in the range of 30-70 ºC, to water activities (a w) from 0.02 to 0.97. The application of the GAB model to the experimental results, using direct nonlinear regression analysis, provided agreement between experimental and calculated values. The net isosteric heat of sorption was estimated from equilibrium sorption data, using the Clausius-Clapeyron equation. Isosteric heats of sorption were found to increase with increasing temperature and could be well adjusted by an exponential relationship. The enthalpy-entropy compensation theory was applied to sorption isotherms and plots of deltaH versus deltaS provided the isokinetic temperatures, indicating an enthalpy controlled sorption process.