Linear evasion differential game of one evader and several pursuers with integral constraints

AbstractAn evasion differential game of one evader and many pursuers is studied. The dynamics of state variables $$x_1,\ldots , x_m$$ x 1 , … , x m are described by linear differential equations. The control functions of players are subjected to integral constraints. If $$x_i(t) \ne 0$$ x i ( t ) ≠ 0 for all $$i \in \{1,\ldots ,m\}$$ i ∈ { 1 , … , m } and $$t \ge 0$$ t ≥ 0 , then we say that evasion is possible. It is assumed that the total energy of pursuers doesn't exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible

Importance of the pleckstrin homology domain of dynamin in clathrin-mediated endocytosis

AbstractThe GTPase dynamin plays an essential role in clathrin-mediated endocytosis [1–3]. Substantial evidence suggests that dynamin oligomerisation around the necks of endocytosing vesicles and subsequent dynamin-catalysed GTP hydrolysis is responsible for membrane fission [4,5]. The pleckstrin homology (PH) domain of dynamin has previously been shown to interact with phosphoinositides, but it has not been determined whether this interaction is essential for dynamin's function in endocytosis [6–9]. In this study, we address the in vivo function of the PH domain of dynamin by assaying the effects of deletions and point mutations in this region on transferrin uptake in COS-7 fibroblasts. Overexpression of a dynamin construct lacking its entire PH domain potently blocked transferrin uptake, as did overexpression of a dynamin construct containing a mutation in the first variable loop of the PH domain. Structural modelling of this latter mutant suggested that the lysine residue at position 535 (Lys535) may be critical in the coordination of phosphoinositides, and indeed, the purified mutant no longer interacted with lipid nanotubes. Interestingly, the inhibitory phenotype of cells expressing this dynamin mutant was partially relieved by a second mutation in the carboxy-terminal proline-rich domain (PRD), one that prevents dynamin from binding to the Src homology 3 (SH3) domain of amphiphysin. These data demonstrate that dynamin's interaction with phosphoinositides through its PH domain is essential for endocytosis. These findings also support our hypothesis that PRD–SH3 domain interactions are important in the recruitment of dynamin to sites of endocytosis

Constitucionalismo societal e regimes-privados autoconstitucionalizados: contribuições e visão crítica

Society has reached a degree of interdependence not seen in recent times. Technology and economics facilitated evolutionary processes of specialization of social systems. On the other hand, as an immediate effect,the national state started to experience the reflexes of globalization and the institutional weakening of a societal model that moves outside territorial domains. The rise of self-constitutionalized private regimes, replacing the previous state-constitutional regulations, presents itself as an object of study and interconnection between the theory of constitutional law and that of legal sociology. In this context, the emergence of a new theoretical current, called the "sociology of constitutions", emerges as a fertile theoretical field for debates about the weakening of the nation-state and the rise of models of normalization of life different from those associated with it. to the State-centrist model. The consequences in constitutional law are relevant, especially in the way in which new rights can be established and exercised. As a result of this, it is proposed, as objectives of this study, to promote the contextualization of the transnational phenomenon, associated with the issues of a democratic order that involve it and, finally, to demonstrate the main characteristics of the selfconstitutionalization of private regimes. Luhmann's Theory of Social Systems will be used as a method for describing differences and modes of observation of the theories worked on throughout the article. As a method of procedure, the indirect documentation search technique will be used, with a review of national and foreign bibliography.La sociedad ha alcanzado un grado de interdependencia no visto en los últimos tiempos. La tecnología y la economía han facilitado procesos evolutivos de especialización de los sistemas sociales. Por otro lado, como efecto inmediato, el Estado nacional pasó a experimentar los reflejos de la globalización y el debilitamiento institucional de un modelo de sociedad que se dirige fuera de los dominios territoriales. Se presenta como objeto de estudio y de interconexión entre la teoría del derecho constitucional y la de la sociología jurídica el surgimiento de los regímenes privados autoconstitucionales, en sustitución de las anteriores normas constitucionales estatales. En este contexto, el surgimiento de una nueva corriente teórica, denominada "sociología de las constituciones", se erige como un campo teórico fértil para llevar a cabo debates sobre el debilitamiento del Estado-nación y el surgimiento de modelos de normalización de vida distintos a los asociados a el Este modelo do-centrista. Las consecuencias en el derecho constitucional son relevantes, especialmente en la forma en que se pueden establecer y ejercer nuevos derechos. Como consecuencia de ello, se propone, como objetivos del presente estudio, promover la contextualización del fenómeno transnacional, asociado a las cuestiones democráticas que lo envuelven y, finalmente, evidenciar las principales características de la autoconstitucionalización de la vida privada. regímenes. Se utilizará la Teoría de los Sistemas Sociales de Luhmann como método para describir las diferencias y formas de observar las teorías trabajadas a lo largo del artículo. Como método de procedimiento se utilizará la técnica de investigación documental indirecta, con revisión de bibliografía nacional y extranjera.A sociedade atingiu um grau de interdependência não visto em tempos recentes. A tecnologia e a economia facilitaram processos evolutivos de especialização de sistemas sociais. Em contrapartida, como efeito imediato, o Estado nacional passou a experimentar os reflexos da globalização e do enfraquecimento institucional de um modelo societal que se direciona para fora dos domínios territoriais. A ascensão de regimes privados autoconstitucionalizados, substituindo as anteriores regulações estatais-constitucionais, apresenta-se como objeto de estudo e de interconexão entre a teoria do direito constitucional e a da sociologia jurídica. Neste contexto, o surgimento de uma nova corrente teórica, denominada de “sociologia das constituições”, eleva-se como campo teórico fértil para a realização de debates acerca da fragilização do Estado-nação e da ascensão de modelos de normatização da vida distintos daqueles associados ao modelo Estado-centrista. As consequências no direito constitucional são relevantes, especialmente na maneira em que novos direitos possam ser estabelecidos e exercidos. Em consequência disso, propõe-se, como objetivos do presente estudo, promover a contextualização do fenômeno transnacional, associado às questões de ordem democrática que o envolvem e, por fim, demonstrar as principais características da autoconstitucionalização de regimes privados. Será utilizada, como método para a descrição de diferenças e dos modos de observação das teorias trabalhadas ao longo do artigo, a Teoria dos Sistemas Sociais de Luhmann. Como método de procedimento, será empregada a técnica de pesquisa de documentação indireta, com revisão de bibliografia nacional e estrangeira

Mathematical Modelling of Optical Coherence Tomography

In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for different positions of the mirror. Different approaches are addressed depending on the different assumptions made about the optical properties of the sample. This procedure is applied to a full field OCT system and an extension to standard (time and frequency domain) OCT is briefly presented.Comment: 28 pages, 5 figures, book chapte

Instances and connectors : issues for a second generation process language

This work is supported by UK EPSRC grants GR/L34433 and GR/L32699Over the past decade a variety of process languages have been defined, used and evaluated. It is now possible to consider second generation languages based on this experience. Rather than develop a second generation wish list this position paper explores two issues: instances and connectors. Instances relate to the relationship between a process model as a description and the, possibly multiple, enacting instances which are created from it. Connectors refers to the issue of concurrency control and achieving a higher level of abstraction in how parts of a model interact. We believe that these issues are key to developing systems which can effectively support business processes, and that they have not received sufficient attention within the process modelling community. Through exploring these issues we also illustrate our approach to designing a second generation process language.Postprin

The role of 5f-orbital participation in unexpected inversion of the σ-bond metathesis reactivity trend of triamidoamine thorium(iv) and uranium(iv) alkyls

We report on the role of 5f-orbital participation in the unexpected inversion of the σ-bond metathesis reactivity trend of triamidoamine thorium(IV) and uranium(IV) alkyls. Reaction of KCH2Ph with [U(TrenTIPS)(I)] [2a, TrenTIPS = N(CH2CH2NSiPri3)33−] gave the cyclometallate [U{N(CH2CH2NSiPri3)2(CH2CH2NSiPri2C[H]MeCH2)}] (3a) with the intermediate benzyl complex not observable. In contrast, when [Th(TrenTIPS)(I)] (2b) was treated with KCH2Ph, [Th(TrenTIPS)(CH2Ph)] (4) was isolated; which is notable as Tren N-silylalkyl metal alkyls tend to spontaneously cyclometallate. Thermolysis of 4 results in the extrusion of toluene and formation of the cyclometallate [Th{N(CH2CH2NSiPri3)2(CH2CH2NSiPri2C[H]MeCH2)}] (3b). This reactivity is the reverse of what would be predicted. Since the bonding of thorium is mainly electrostatic it would be predicted to undergo facile cyclometallation, whereas the more covalent uranium system might be expected to form an isolable benzyl intermediate. The thermolysis of 4 follows well-defined first order kinetics with an activation energy of 22.3 ± 0.1 kcal mol−1, and Eyring analyses yields ΔH‡ = 21.7 ± 3.6 kcal mol−1 and ΔS‡ = −10.5 ± 3.1 cal K−1 mol−1, which is consistent with a σ-bond metathesis reaction. Computational examination of the reaction profile shows that the inversion of the reactivity trend can be attributed to the greater f-orbital participation of the bonding for uranium facilitating the σ-bond metathesis transition state whereas for thorium the transition state is more ionic resulting in an isolable benzyl complex. The activation barriers are computed to be 19.0 and 22.2 kcal mol−1 for the uranium and thorium cases, respectively, and the latter agrees excellently with the experimental value. Reductive decomposition of “[U(TrenTIPS)(CH2Ph)]” to [U(TrenTIPS)] and bibenzyl followed by cyclometallation to give 3a with elimination of dihydrogen was found to be endergonic by 4 kcal mol−1 which rules out a redox-based cyclometallation route for uranium

Whole breast and regional nodal irradiation in prone versus supine position in left sided breast cancer

Background: Prone whole breast irradiation (WBI) leads to reduced heart and lung doses in breast cancer patients receiving adjuvant radiotherapy. In this feasibility trial, we investigated the prone position for whole breast + lymph node irradiation (WB + LNI). Methods: A new support device was developed for optimal target coverage, on which patients are positioned in a position resembling a phase from the crawl swimming technique (prone crawl position). Five left sided breast cancer patients were included and simulated in supine and prone position. For each patient, a treatment plan was made in prone and supine position for WB + LNI to the whole axilla and the unoperated part of the axilla. Patients served as their own controls for comparing dosimetry of target volumes and organs at risk (OAR) in prone versus in supine position. Results: Target volume coverage differed only slightly between prone and supine position. Doses were significantly reduced (P < 0.05) in prone position for ipsilateral lung (Dmean, D2, V5, V10, V20, V30), contralateral lung (Dmean, D2), contralateral breast (Dmean, D2 and for total axillary WB + LNI also V5), thyroid (Dmean, D2, V5, V10, V20, V30), oesophagus (Dmean and for partial axillary WB + LNI also D2 and V5), skin (D2 and for partial axillary WB + LNI V105 and V107). There were no significant differences for heart and humeral head doses. Conclusions: Prone crawl position in WB + LNI allows for good breast and nodal target coverage with better sparing of ipsilateral lung, thyroid, contralateral breast, contralateral lung and oesophagus when compared to supine position. There is no difference in heart and humeral head doses

Nuclear Factor of Activated T Cells-dependent Down-regulation of the Transcription Factor Glioma-associated Protein 1 (GLI1) Underlies the Growth Inhibitory Properties of Arachidonic Acid

Numerous reports have demonstrated a tumor inhibitory effect of polyunsaturated fatty acids (PUFAs). However, the molecular mechanisms modulating this phenomenon are in part poorly understood. Here, we provide evidence of a novel antitumoral mechanism of the PUFA arachidonic acid (AA). In vivo and in vitro experiments showed that AA treatment decreased tumor growth and metastasis, and increased apoptosis. Molecular analysis of this effect showed significantly reduced expression of a subset of antiapoptotic proteins, including BCL2, BFL1/A1 and 4-1BB, in AA-treated cells. We demonstrated that downregulation of the transcription factor GLI1 in AA-treated cells is the underlying mechanism controlling BCL2, BFL1/A1 and 4-1BB expression. Using luciferase reporters, chromatin immunoprecipitation, and expression studies, we found that GLI1 binds to the promoter of these antiapoptotic molecules, and regulates their expression and promoter activity. We provide evidence that AA-induced apoptosis and downregulation of antiapoptotic genes can be inhibited by overexpressing GLI1 in AA-sensitive cells. Conversely, inhibition of GLI1 mimics AA treatments, leading to decreased tumor growth, cell viability and expression of antiapoptotic molecules. Further characterization showed that AA represses GLI1 expression by stimulating NFATc1 nuclear translocation, which then binds the GLI1 promoter and represses its transcription. AA was shown to increase reactive oxygen species. Treatment with antioxidants reduced the AA-induced apoptosis, downregulation of GLI1 and NFATc1 activation, indicating that NFATc1 activation and GLI1 repression require the generation of reactive oxygen species. Collectively, these results define a novel mechanism underlying AA antitumoral functions that may serve as a foundation for the future PUFA-based therapeutic approaches

Accurate Visuomotor Control below the Perceptual Threshold of Size Discrimination

Background: Human resolution for object size is typically determined by psychophysical methods that are based on conscious perception. In contrast, grasping of the same objects might be less conscious. It is suggested that grasping is mediated by mechanisms other than those mediating conscious perception. In this study, we compared the visual resolution for object size of the visuomotor and the perceptual system. Methodology/Principal Findings: In Experiment 1, participants discriminated the size of pairs of objects once through perceptual judgments and once by grasping movements toward the objects. Notably, the actual size differences were set below the Just Noticeable Difference (JND). We found that grasping trajectories reflected the actual size differences between the objects regardless of the JND. This pattern was observed even in trials in which the perceptual judgments were erroneous. The results of an additional control experiment showed that these findings were not confounded by task demands. Participants were not aware, therefore, that their size discrimination via grasp was veridical. Conclusions/Significance: We conclude that human resolution is not fully tapped by perceptually determined thresholds

No correlation between distorted body representations underlying tactile distance perception and position sense

Both tactile distance perception and position sense are believed to require that immediate afferent signals be referenced to a stored representation of body size and shape (the body model). For both of these abilities, recent studies have reported that the stored body representations involved are highly distorted, at least in the case of the hand, with the hand dorsum represented as wider and squatter than it actually is. Here, we investigated whether individual differences in the magnitude of these distortions are shared between tactile distance perception and position sense, as would be predicted by the hypothesis that a single distorted body model underlies both tasks. We used established tasks to measure distortions of the represented shape of the hand dorsum. Consistent with previous results, in both cases there were clear biases to overestimate distances oriented along the medio-lateral axis of the hand compared to the proximo- distal axis. Moreover, within each task there were clear split-half correlations, demonstrating that both tasks show consistent individual differences. Critically, however, there was no correlation between the magnitudes of distortion in the two tasks. This casts doubt on the proposal that a common body model underlies both tactile distance perception and position sense