Affinity Class Research Articles

Anosov Diffeomorphisms and $${\gamma}$$ γ -Tilings

We consider a toral Anosov automorphism \({G_\gamma:{\mathbb{T}}_\gamma\to{\mathbb{T}}_\gamma}\) given by \({G_\gamma(x,y)=(ax+y,x)}\) in the \({ }\) base, where \({a\in\mathbb{N} \backslash\{1\}}\), \({\gamma=1/(a+1/(a+1/\ldots))}\), \({v=(\gamma,1)}\) and \({w=(-1,\gamma)}\) in the canonical base of \({{\mathbb{R}}^2}\) and \({{\mathbb{T}}_\gamma={\mathbb{R}}^2/(v{\mathbb{Z}} \times w{\mathbb{Z}})}\). We introduce the notion of \({\gamma}\)-tilings to prove the existence of a one-to-one correspondence between (i) marked smooth conjugacy classes of Anosov diffeomorphisms, with invariant measures absolutely continuous with respect to the Lebesgue measure, that are in the isotopy class of \({G_\gamma}\); (ii) affine classes of \({\gamma}\)-tilings; and (iii) \({\gamma}\)-solenoid functions. Solenoid functions provide a parametrization of the infinite dimensional space of the mathematical objects described in these equivalences.

DnaK-Dependent Accelerated Evolutionary Rate in Prokaryotes.

Many proteins depend on an interaction with molecular chaperones in order to fold into a functional tertiary structure. Previous studies showed that protein interaction with the GroEL/GroES chaperonine and Hsp90 chaperone can buffer the impact of slightly deleterious mutations in the protein sequence. This capacity of GroEL/GroES to prevent protein misfolding has been shown to accelerate the evolution of its client proteins. Whether other bacterial chaperones have a similar effect on their client proteins is currently unknown. Here, we study the impact of DnaK (Hsp70) chaperone on the evolution of its client proteins. Evolutionary parameters were derived from comparison of the Escherichia coli proteome to 1,808,565 orthologous proteins in 1,149 proteobacterial genomes. Our analysis reveals a significant positive correlation between protein binding frequency with DnaK and evolutionary rate. Proteins with high binding affinity to DnaK evolve on average 4.3-fold faster than proteins in the lowest binding affinity class at the genus resolution. Differences in evolutionary rates of DnaK interactor classes are still significant after adjusting for possible effects caused by protein expression level. Furthermore, we observe an additive effect of DnaK and GroEL chaperones on the evolutionary rates of their common interactors. Finally, we found pronounced similarities in the physicochemical profiles that characterize proteins belonging to DnaK and GroEL interactomes. Our results thus implicate DnaK-mediated folding as a major component in shaping protein evolutionary dynamics in bacteria and supply further evidence for the long-term manifestation of chaperone-mediated folding on genome evolution.

Data‐driven optimal tracking control for a class of affine non‐linear continuous‐time systems with completely unknown dynamics

In this study, the optimal tracking control problem (OTCP) for affine non-linear continuous-time systems with completely unknown dynamics is addressed based on data by introducing the reinforcement learning (RL) technique. Unlike existing methods to the OTCP, the proposed data-driven policy iteration (PI) method does not need to have or identify any knowledge of the system dynamics, including both drift dynamics and input dynamics. To carry out the proposed method, the original OTCP is pre-processed to construct an augmented system composed of the error system dynamics and the desired trajectory dynamics. Then, based on the augmented system, a data-driven PI, which introduces discount factor to solve the OTCP, is implemented on an actor–critic neural network (NN) structure by only using system data rather than the exact knowledge of system dynamics. Two NNs are used in the structure to generate the optimal cost and optimal control policy, respectively, and the weights are updated by a least-square approach which minimises the residual errors. The proposed method is an off-policy RL method, where the data can be arbitrarily sampled on the state and input domain. Finally, simulation results are provided to show the effectiveness of the proposed method.

Derivative Pricing for a Multi-Curve Extension of the Gaussian, Exponentially Quadratic Short Rate Model

The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are second order polynomials of Gaussian factor processes. This leads to an exponentially quadratic model class that is less well known than the exponentially affine class. In the latter class the factors enter linearly and for positivity one considers square root factor processes. While the square root factors in the affine class have more involved distributions, in the quadratic class the factors remain Gaussian and this leads to various advantages, in particular for derivative pricing. After some preliminaries on martingale modeling in the multi-curve setup, we concentrate on pricing of linear and optional derivatives. For linear derivatives, we exhibit an adjustment factor that allows one to pass from pre-crisis single curve values to the corresponding post-crisis multi-curve values.

Baire classes of affine vector-valued functions

We investigate Baire classes of strongly affine mappings with values in Fr\'echet spaces. We show, in particular, that the validity of the vector-valued Mokobodzki's result on affine functions of the first Baire class is related to the approximation property of the range space. We further extend several results known for scalar functions on Choquet simplices or on dual balls of $L_1$-preduals to the vector-valued case. This concerns, in particular, affine classes of strongly affine Baire mappings, the abstract Dirichlet problem and the weak Dirichlet problem for Baire mappings. Some of these results have weaker conclusions than their scalar versions. We also establish an affine version of the Jayne-Rogers selection theorem.

Optimal Sobolev norms in the affine class

Optimal Sobolev norms under volume preserving affine transformations are considered. It turns out that this minimal transform is equivalent to the (p,2) Fisher information matrix defined by Lutwak, Lv, Yang, and Zhang. Furthermore, some analytic inequalities regarding to the Lp affine and Lp sine energies for the optimal function are investigated.

The FOXO1 Transcription Factor Instructs the Germinal Center Dark Zone Program

The pathways regulating formation of the germinal center (GC) dark zone (DZ) and light zone (LZ) are unknown. In this study we show that FOXO1 transcription factor expression was restricted to the GC DZ and was required for DZ formation, since its absence in mice led to the loss of DZ gene programs and the formation of LZ-only GCs. FOXO1-negative GC B cells displayed normal somatic hypermutation but defective affinity maturation and class switch recombination. The function of FOXO1 in sustaining the DZ program involved the trans-activation of the chemokine receptor CXCR4, and cooperation with the BCL6 transcription factor in the trans-repression of genes involved in immune activation, DNA repair, and plasma cell differentiation. These results also have implications for the role of FOXO1 in lymphomagenesis because they suggest that constitutive FOXO1 activity might be required for the oncogenic activity of deregulated BCL6 expression.

Observer based minimum variance control of uncertain piecewise affine systems subject to additive noise

In this paper, a class of uncertain piecewise affine (PWA) systems, subject to system and measurement additive noises is studied. The additive noise signals considered here do not vanish at the equilibrium and the uncertainties are norm bounded. The problem of minimizing the bound on the variance of the steady response of uncertain PWA systems, by means of a hybrid observer–controller, is formulated as an optimization problem subject to a number of constraints in the form of matrix inequalities. The derived constraints are obtained by considering a piecewise quadratic Lyapunov function in combination with the general stability conditions regarding the existence of an upper stochastic bound on the steady state variance for a class of stochastic hybrid systems (SHS). Then the uncertain PWA approximation of a practical system with nonlinear dynamics is presented considering system and measurement noises. The uncertainties arise in the form of the difference between the actual nonlinear dynamics and the PWA approximation. Utilizing the introduced methods, a hybrid observer–controller is designed and implemented on the nonlinear system to demonstrate the effectiveness of the proposed controller design procedure.

On the class of infinite horizon optimal control problems affine, which are structurally stable

We prove in this article that there is in the set of all problems we consider a subset, which is residual. Every problem in this subset is shown to be structurally stable and defines a dynamical system, which looks like the graph of the figure given in Section 1, contrary to what happens for ordinary dynamical systems, that is, the ones associated with ODEs. There, the initial value problem (in the smooth case) is uniquely solvable; the structurally stable systems look like the figure given in Section 1, but sources are equilibria. Copyright © 2015 John Wiley & Sons, Ltd.

Maximizing concave piecewise affine functions on the unitary group

We show that a convex relaxation, introduced by Sridharan, McEneaney, Gu and James to approximate the value function of an optimal control problem arising from quantum gate synthesis, is exact. This relaxation applies to the maximization of a class of concave piecewise affine functions over the unitary group.

Option valuation with observable volatility and jump dynamics

Abstract Under very general conditions, the total quadratic variation of a jump-diffusion process can be decomposed into diffusive volatility and squared jump variation. We use this result to develop a new option valuation model in which the underlying asset price exhibits volatility and jump intensity dynamics. The volatility and jump intensity dynamics in the model are directly driven by model-free empirical measures of diffusive volatility and jump variation. Because the empirical measures are observed in discrete intervals, our option valuation model is cast in discrete time, allowing for straightforward filtering and estimation of the model. Our model belongs to the affine class enabling us to derive the conditional characteristic function so that option values can be computed rapidly without simulation. When estimated on S&P500 index options and returns the new model performs well compared with standard benchmarks.

Large-scale recognition of high-affinity protease–inhibitor complexes using topological autocorrelation and support vector machines

Several methods have been developed for the computer-aided discovery of new protease substrates and inhibitors. In this paper, we report a novel machine learning implementation to identify high-affinity protease–inhibitor complexes. The implemented proteochemometrics algorithm consists of creating topological autocorrelation descriptors for proteases and inhibitors, and then to develop support vector machine models to relate the feature vectors to the affinity class (high or low) of hypothetical protein–inhibitor complexes based on experimental inhibition constant (Ki) values. The approach based on the autocorrelation features surpassed an atom-centred (AC) approach using AC information of inhibitors. Unique to our approach is that our final classifier could recognise 80% of inhibition-complex of new ligands to be stable or unstable using only chemical connectivity of the ligands and sequence information of the targets. Moreover, the analysis of substructure classification showed a very homogenous behaviour of the model on the whole target–ligand space. The predictor is available online at: http://www.materialsinformatics.net/autoproti.html

CTLA-4-mediated suppressor effect by human T follicular regulatory cells (IRC11P.432)

Abstract T follicular helper (Tfh) cells, a subset of CD4 T cells, help B cells produce high affinity class switched antibodies and are essential for generation of germinal centers (GC). T follicular regulatory cells (Tfr) are a newly defined regulatory CD4 T cell subset that suppresses GC formation and B cell function through CTLA-4 dependent mechanisms in murine models. We will test the hypothesis in human systems that Tfr have significant regulatory effects on antibody production in a CTLA-4 dependent manner. Tfh and Tfr cells from human mesenteric lymph nodes were analyzed using flow cytometry. Tfr were defined as CXCR5+, PD-1bright, FoxP3+ cells that were also found to be Bcl6+, CD25+, CD127dim, ICOS+. Flow sorted Tfr and Tfh cells were used to determine the effect of Tfr on Tfh-mediated B cell production of IgG. Tfh cells with mitogen helped B cells produce high amounts of IgG whereas addition of Tfr to this co-culture decreased the IgG levels >90%. Tfh/Tfh ratio directly impacts levels of suppression. The mechanism of the suppressive effect of Tfr cells was investigated by neutralizing IL-10, TGF-β RII and CTLA-4 in the co-culture functional assay. Only anti-CTLA-4 affected IgG production. The present study in the human system suggests that Tfr cells suppressed Tfh-induced antibody production by B cells with CTLA-4 playing an important role in this suppression. These regulatory interactions may play a role in autoimmune diseases and humoral response to vaccines and pathogens.

MiR-148a promotes plasma cell differentiation and targets the germinal center transcription factors Mitf and Bach2.

Bcells undergo affinity maturation and class switch recombination of their immunoglobulin receptors during a germinal center (GC) reaction, before they differentiate into long-lived antibody-secreting plasma cells (PCs). Transcription factors such as Bach2 and Mitf are essential during this process, as they delay premature differentiation of GC Bcells by repressing Blimp-1 and IRF4, two transcription factors required for terminal PC differentiation. Therefore, Bach2 and Mitf expression must be attenuated in activated Bcells to allow terminal PC differentiation, but the precise mechanism remains enigmatic. Here, we provide evidence that miR-148a, a small noncoding microRNA, fosters PC differentiation and survival. Next-generation sequencing revealed that miR-148a is the most abundant microRNA in primary human and murine PCs, and its expression is upregulated in activated murine Bcells and coincides with Blimp-1 synthesis. miR-148a targets Bach2, Mitf and proapoptotic factors such as PTEN and Bim. When prematurely expressed, miR-148a promotes the differentiation and survival of plasmablasts and reduces frequencies of IgG1(+) cells in primary B-cell cultures. In summary, we propose that miR-148a is a new player in the regulatory network controlling terminal PC differentiation and could, therefore, be a therapeutic target for interfering with PC differentiation and survival.

In-vivo imaging of grey and white matter neuroinflammation in Alzheimer's disease: a positron emission tomography study with a novel radioligand, [18F]-FEPPA.

Our primary aim was to compare neuroinflammation in cognitively intact control subjects and patients with Alzheimer's disease (AD) by using positron emission tomography (PET) with translocator protein 18 kDa (TSPO)-specific radioligand [(18)F]-FEPPA. [(18)F]-FEPPA PET scans were acquired on a high-resolution research tomograph in 21 patients with AD (47- 81 years) and 21 control subjects (49-82 years). They were analyzed by using a 2-tissue compartment model with arterial plasma input function. Differences in neuroinflammation, indexed as [(18)F]-FEPPA binding were compared, adjusting for differences in binding affinity class as determined by a single polymorphism in the TSPO gene (rs6971). In grey matter areas, [(18)F]-FEPPA was significantly higher in AD compared with healthy control subjects. Large increases were seen in the hippocampus, prefrontal, temporal, parietal and occipital cortex (average Cohen's d= 0.89). Voxel-based analyses confirmed significant clusters of neuroinflammation in the frontal, temporal and parietal cortex in patients with AD. In white matter, [(18)F]-FEPPA binding was elevated in the posterior limb of the internal capsule, and the cingulum bundle. Higher neuroinflammation in the parietal cortex (r= -0.7, P= 0.005), and posterior limb of the internal capsule (r= -0.8, P=0.001) was associated with poorer visuospatial function. In addition, a higher [(18)F]-FEPPA binding in the posterior limb of the internal capsule was associated with a greater impairment in language ability (r= -0.7, P=0.004). Elevated neuroinflammation can be detected in AD patients throughout the brain grey and white matter by using [(18)F]-FEPPA PET. Our results also suggest that neuroinflammation is associated with some cognitive deficits.

Identifying Affinity Classes of Inorganic Materials Binding Sequences via a Graph-Based Model.

Rapid advances in bionanotechnology have recently generated growing interest in identifying peptides that bind to inorganic materials and classifying them based on their inorganic material affinities. However, there are some distinct characteristics of inorganic materials binding sequence data that limit the performance of many widely-used classification methods when applied to this problem. In this paper, we propose a novel framework to predict the affinity classes of peptide sequences with respect to an associated inorganic material. We first generate a large set of simulated peptide sequences based on an amino acid transition matrix tailored for the specific inorganic material. Then the probability of test sequences belonging to a specific affinity class is calculated by minimizing an objective function. In addition, the objective function is minimized through iterative propagation of probability estimates among sequences and sequence clusters. Results of computational experiments on two real inorganic material binding sequence data sets show that the proposed framework is highly effective for identifying the affinity classes of inorganic material binding sequences. Moreover, the experiments on the structural classification of proteins (SCOP) data set shows that the proposed framework is general and can be applied to traditional protein sequences.

An Arbitrage-Free Nelson-Siegel Term Structure Model with Stochastic Volatility for the Determination of Currency Risk Premia

This paper uses a risk-averse formulation of the uncovered interest rate parity to determine exchange rates through interest rate differentials, and ultimately extract currency risk premia. The method proposed consists of developing an affine Arbitrage-Free class of dynamic Nelson-Siegel term structure models with stochastic volatility to obtain the domestic and foreign discount rate variations, which in turn are used to derive a representation of exchange rate depreciations. No-arbitrage restrictions allow to endogenously capturing currency risk premia. Empirical findings suggest that estimated currency risk premia are able to account for the forward premium puzzle and their properties are examined.

Baire classes of strongly affine functions on simplices and on [formula omitted]-algebras

For each n∈ω, n≥2, we construct a metrizable simplex X and a strongly affine function of Baire class n on X that is not of affine class n. As a corollary we obtain a separable C⁎-algebra E such that, for each n∈ω, n≥2, the n-th Baire class of E⁎⁎ does not coincide with the n-th intrinsic Baire class of E⁎⁎.

Option Valuation with Observable Volatility and Jump Dynamics

Under very general conditions, the total quadratic variation of a jump-diffusion process can be decomposed into diffusive volatility and squared jump variation. We use this result to develop a new option valuation model in which the underlying asset price exhibits volatility and jump intensity dynamics. The volatility and jump intensity dynamics in the model are directly driven by model-free empirical measures of diffusive volatility and jump variation. Because the empirical measures are observed in discrete intervals, our option valuation model is cast in discrete time, allowing for straightforward filtering and estimation of the model. Our model belongs to the affine class enabling us to derive the conditional characteristic function so that option values can be computed rapidly without simulation. When estimated on S&P500 index options and returns the new model performs well compared with standard benchmarks.

The deterministic shift extension and the affine dynamic Nelson–Siegel model

The affine dynamic Nelson–Siegel model links the affine class of models with the Nelson–Siegel interpolation scheme of the yield curve. Its parameters are interpreted as the latent factors of the spot rate process driven by an affine diffusion. Using an appropriate specification of this diffusion, the yields become in form of the Nelson–Siegel model but an adjustment term is introduced. In this paper, the model is extended using a deterministic shift extension so as to perfectly fit the term structure and reduce the correction term. This enhancement allows to simulate the yield curve and the spot rate process consistently with the market data used for the calibration of the model. A numerical example discusses the calibration results of the original model and the proposed extension.