Point interactions in one dimension and holonomic quantum fields

We introduce and study a family of quantum fields, associated to delta-interactions in one dimension. These fields are analogous to holonomic quantum fields of M. Sato, T. Miwa and M. Jimbo. Corresponding field operators belong to an infinite-dimensional representation of the group SL(2,\Rb) in the Fock space of ordinary harmonic oscillator. We compute form factors of such fields and their correlation functions, which are related to the determinants of Schroedinger operators with a finite number of point interactions. It is also shown that these determinants coincide with tau functions, obtained through the trivialization of the $\mathrm{det}^*$-bundle over a Grassmannian associated to a family of Schroedinger operators.Comment: 17 page

Diagonalization of the XXZ Hamiltonian by Vertex Operators

We diagonalize the anti-ferroelectric XXZ-Hamiltonian directly in the thermodynamic limit, where the model becomes invariant under the action of affine U_q( sl(2) ). Our method is based on the representation theory of quantum affine algebras, the related vertex operators and KZ equation, and thereby bypasses the usual process of starting from a finite lattice, taking the thermodynamic limit and filling the Dirac sea. From recent results on the algebraic structure of the corner transfer matrix of the model, we obtain the vacuum vector of the Hamiltonian. The rest of the eigenvectors are obtained by applying the vertex operators, which act as particle creation operators in the space of eigenvectors. We check the agreement of our results with those obtained using the Bethe Ansatz in a number of cases, and with others obtained in the scaling limit --- the $su(2)$-invariant Thirring model.Comment: 65 page

Non Abelian Vortices as Instantons on Noncommutative Discrete Space

There seems to be close relationship between the moduli space of vortices and the moduli space of instantons, which is not yet clearly understood from a standpoint of the field theory. We clarify the reasons why many similarities are found in the methods for constructing the moduli of instanton and vortex, viewed in the light of the notion of the self-duality. We show that the non-Abelian vortex is nothing but the instanton in $R^{2} \times Z_{2}$ from a viewpoint of the noncommutative differential geometry and the gauge theory in discrete space. The action for pure Yang-Mills theory in $R^{2} \times Z_{2}$ is equivalent to that for Yang-Mills-Higgs theory in $R^{2}$.Comment: 19 pages, various arguments are added, the exposition is improve

Relativistic Hydrodynamic Evolutions with Black Hole Excision

We present a numerical code designed to study astrophysical phenomena involving dynamical spacetimes containing black holes in the presence of relativistic hydrodynamic matter. We present evolutions of the collapse of a fluid star from the onset of collapse to the settling of the resulting black hole to a final stationary state. In order to evolve stably after the black hole forms, we excise a region inside the hole before a singularity is encountered. This excision region is introduced after the appearance of an apparent horizon, but while a significant amount of matter remains outside the hole. We test our code by evolving accurately a vacuum Schwarzschild black hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder dust collapse, and the collapse of nonrotating and rotating stars. These systems are tracked reliably for hundreds of M following excision, where M is the mass of the black hole. We perform these tests both in axisymmetry and in full 3+1 dimensions. We then apply our code to study the effect of the stellar spin parameter J/M^2 on the final outcome of gravitational collapse of rapidly rotating n = 1 polytropes. We find that a black hole forms only if J/M^2<1, in agreement with previous simulations. When J/M^2>1, the collapsing star forms a torus which fragments into nonaxisymmetric clumps, capable of generating appreciable ``splash'' gravitational radiation.Comment: 17 pages, 14 figures, submitted to PR

Higher-Order Assembly of BRCC36-KIAA0157 Is Required for DUB Activity and Biological Function

BRCC36 is a Zn²⁺-dependent deubiquitinating enzyme (DUB) that hydrolyzes lysine-63-linked ubiquitin chains as part of distinct macromolecular complexes that participate in either interferon signaling or DNA-damage recognition. The MPN⁺ domain protein BRCC36 associates with pseudo DUB MPN⁻ proteins KIAA0157 or Abraxas, which are essential for BRCC36 enzymatic activity. To understand the basis for BRCC36 regulation, we have solved the structure of an active BRCC36-KIAA0157 heterodimer and an inactive BRCC36 homodimer. Structural and functional characterizations show how BRCC36 is switched to an active conformation by contacts with KIAA0157. Higher-order association of BRCC36 and KIAA0157 into a dimer of heterodimers (super dimers) was required for DUB activity and interaction with targeting proteins SHMT2 and RAP80. These data provide an explanation of how an inactive pseudo DUB allosterically activates a cognate DUB partner and implicates super dimerization as a new regulatory mechanism underlying BRCC36 DUB activity, subcellular localization, and biological function

Parametric POMDPs for planning in continuous state spaces

This thesis is concerned with planning and acting under uncertainty in partially-observable continuous domains. In particular, it focusses on the problem of mobile robot navigation given a known map. The dominant paradigm for robot localisation is to use Bayesian estimation to maintain a probability distribution over possible robot poses. In contrast, control algorithms often base their decisions on the assumption that a single state, such as the mode of this distribution, is correct. In scenarios involving significant uncertainty, this can lead to serious control errors. It is generally agreed that the reliability of navigation in uncertain environments would be greatly improved by the ability to consider the entire distribution when acting, rather than the single most likely state. The framework adopted in this thesis for modelling navigation problems mathematically is the Partially Observable Markov Decision Process (POMDP). An exact solution to a POMDP problem provides the optimal balance between reward-seeking behaviour and information-seeking behaviour, in the presence of sensor and actuation noise. Unfortunately, previous exact and approximate solution methods have had difficulty scaling to real applications. The contribution of this thesis is the formulation of an approach to planning in the space of continuous parameterised approximations to probability distributions. Theoretical and practical results are presented which show that, when compared with similar methods from the literature, this approach is capable of scaling to larger and more realistic problems. In order to apply the solution algorithm to real-world problems, a number of novel improvements are proposed. Specifically, Monte Carlo methods are employed to estimate distributions over future parameterised beliefs, improving planning accuracy without a loss of efficiency. Conditional independence assumptions are exploited to simplify the problem, reducing computational requirements. Scalability is further increased by focussing computation on likely beliefs, using metric indexing structures for efficient function approximation. Local online planning is incorporated to assist global offline planning, allowing the precision of the latter to be decreased without adversely affecting solution quality. Finally, the algorithm is implemented and demonstrated during real-time control of a mobile robot in a challenging navigation task. We argue that this task is substantially more challenging and realistic than previous problems to which POMDP solution methods have been applied. Results show that POMDP planning, which considers the evolution of the entire probability distribution over robot poses, produces significantly more robust behaviour when compared with a heuristic planner which considers only the most likely states and outcomes

Personalized peptide-based vaccination for treatment of colorectal cancer: rational and progress

Colorectal cancer (CRC) is one of the most common cancers globally and is associated with a high rate of morbidity and mortality. A large proportion of patients with early stage CRC who undergo conventional treatments develop local recurrence or distant metastasis and in this group of advanced disease, the survival rate is low. Furthermore there is often a poor response and/or toxicity associated with chemotherapy and chemo-resistance may limit continuing conventional treatment alone. Choosing novel and targeted therapeutic approaches based on clinicopathological and molecular features of tumors in combination with conventional therapeutic approach could be used to eradicate residual micrometastasis and therefore improve patient prognosis and also be used preventively. Peptide-based vaccination therapy is one class of cancer treatment that could be used to induce tumor-specific immune responses, through the recognition of specific antigen-derived peptides in tumor cells, and this has emerged as a promising anti-cancer therapeutic strategy. The aim of this review was to summarize the main findings of recent studies in exciting field of peptide-based vaccination therapy in CRC patients as a novel therapeutic approach in treatment of CRC