Higher Dimensional Bases Research Articles

Early detection of abiotic stress in plants through SNARE proteins using hybrid feature fusion model.

Agriculture is the main source of livelihood for most of the population across the globe. Plants are often considered life savers for humanity, having evolved complex adaptations to cope with adverse environmental conditions. Protecting agricultural produce from devastating conditions such as stress is essential for the sustainable development of the nation. Plants respond to various environmental stressors such as drought, salinity, heat, cold, etc. Abiotic stress can significantly impact crop yield and development posing a major threat to agriculture. SNARE proteins play a major role in pathological processes as they are vital proteins in the life sciences. These proteins act as key players in stress responses. Feature extraction is essential for visualizing the underlying structure of the SNARE proteins in analyzing the root cause of abiotic stress in plants. To address this issue, we developed a hybrid model to capture the hidden structures of the SNAREs. A feature fusion technique has been devised by combining the potential strengths of convolutional neural networks (CNN) with a high dimensional radial basis function (RBF) network. Additionally, we employ a bi-directional long short-term memory (Bi-LSTM) network to classify the presence of SNARE proteins. Our feature fusion model successfully identified abiotic stress in plants with an accuracy of 74.6%. When compared with various existing frameworks, our model demonstrates superior classification results.

Massey products and Fujita decomposition over higher dimensional base

Let $$f:X\rightarrow Y$$ be a semistable fibration between smooth complex varieties of dimension n and m. This paper contains an analysis of the local systems of de Rham closed relative one forms and top forms on the fibers. In particular the latter recovers the local system of the second Fujita decomposition of $$f_*\omega _{X/Y}$$ over higher dimensional base. The so called theory of Massey products allows, under natural Castelnuovo-type hypothesis, to study the finiteness of the associated monodromy representations. Motivated by this result, we also make precise the close relation between Massey products and Castelnuovo-de Franchis type theorems.

A Mutual Information Measure of Phase-Amplitude Coupling using High Dimensional Sparse Models.

Cross frequency coupling (CFC) between electrophysiological signals in the brain has been observed and it's abnormalities have been observed in conditions such as Parkinson's disease and epilepsy. More recently, CFC has been observed in stomach-brain electrophysiologic studies and thus becomes an enticing possible target for diseases involving aberrations of the gut-brain axis. However, current methods of detecting coupling do not attempt to capture the underlying statistical relationships that give rise to this coupling. In this paper, we demonstrate a new method of calculating phase amplitude coupling by estimating the mutual information between phase and amplitude, using a flexible parametric modeling approach. Specifically, we develop an exponential generalized linear model (GLM) to model amplitude given phase, using a high dimensional basis of von-Mises function regressors and l1 regularized model selection. Using synthetically generated gut-brain coupled signals, we demonstrate that our method outperforms the existing gold-standard methods for detectable low-levels of phase amplitude coupling through receiver operating characteristic (ROC) curve analysis.

A Néron model of the universal jacobian

Jacobians of degenerating families of curves are well-understood over 1-dimensional bases due to work of Néron and Raynaud; the fundamental tool is the Néron model and its description via the Picard functor. Over higher-dimensional bases Néron models typically do not exist, but in this paper we construct a universal base change ℳ ˜ g,n →ℳ ¯ g,n after which a Néron model N g,n /ℳ ˜ g,n of the universal jacobian does exist. This yields a new partial compactification of the moduli space of curves, and of the universal jacobian over it. The map ℳ ˜ g,n →ℳ ¯ g,n is separated and relatively representable. The Néron model N g,n /ℳ ˜ g,n is separated and has a group law extending that on the jacobian. We show that Caporaso’s balanced Picard stack acquires a torsor structure after pullback to a certain open substack of ℳ ˜ g,n .

On the Dimension of the Bergman Space of Some Hartogs Domains with Higher Dimensional Bases

Let D be a Hartogs domain of the form $$D=D_{\varphi }(G)=\{(z,w)\in G\times \mathbb {C}^{N}\,:\,\Vert w\Vert <e^{-\varphi (z)}\}$$ , where $$\varphi $$ is a plurisubharmonic function on G and $$G\subseteq \mathbb {C}^{M}$$ is a pseudoconvex domain. We expand on the results of Jucha (J Geom Anal 22(1):23–37, 2012) and prove the infinite-dimensionality or triviality of the space of square integrable holomorphic functions on $$D_{\varphi }(G)$$ for various choices of $$\varphi $$ and G.

High-dimensional cryptography with spatial modes of light: tutorial

Fast and secure sharing of information is among the prime concerns of almost any communication system. While commonly used cryptographic algorithms cannot provide unconditional security, high-dimensional (HD) quantum key distribution (QKD) offers an exceptional means to this end. Here, we provide a tutorial to demonstrate that HD QKD protocols can be implemented in an effective way using optical elements that are known to most optics labs. We use spatial modes of light as our HD basis and show how to simulate QKD experiments with bright classical light, fostering its easy implementation for a more general audience including industry laboratories or laboratory classes in university teaching and in advanced laboratories for validation purposes. In particular, we use orbital angular momentum Bessel–Gaussian modes for our HD QKD demonstration to illustrate and highlight the benefits of using spatial modes as their natural Schmidt basis and self-healing feature.

Asymptotic expansions of fiber integrals over higher-dimensional bases

Abstract We give a formula of an asymptotic expansion of a function, provided in the form of a fiber integral around a critical value of a holomorphic map of toric type.

Moduli of Tango Structures and Dormant Miura Opers

The purpose of the present paper is to develop the theory of (pre-)Tango structures and (dormant generic) Miura $\mathfrak{g}$-opers (for a semisimple Lie algebra $\mathfrak{g}$) defined on pointed stable curves in positive characteristic. A (pre-)Tango structure is a certain line bundle of an algebraic curve in positive characteristic, which gives some pathological (relative to zero characteristic) phenomena. In the present paper, we construct the moduli spaces of (pre-)Tango structures and (dormant generic) Miura $\mathfrak{g}$-opers respectively, and prove certain properties of them. One of the main results of the present paper states that there exists a bijective correspondence between the (pre-)Tango structures (of prescribed monodromy) and the dormant generic Miura $\mathfrak{s} \mathfrak{l}_2$-opers (of prescribed exponent). By means of this correspondence, we achieve a detailed understanding of the moduli stack of (pre-)Tango structures. As an application, we construct a family of algebraic surfaces in positive characteristic parametrized by a higher dimensional base space whose fibers are pairwise non-isomorphic and violate the Kodaira vanishing theorem.

On the integral Hodge conjecture for real varieties, II

We establish the real integral Hodge conjecture for 1-cycles on various classes of uniruled threefolds (conic bundles, Fano threefolds with no real point, some del Pezzo fibrations) and on conic bundles over higher-dimensional bases which themselves satisfy the real integral Hodge conjecture for 1-cycles. In addition, we show that rationally connected threefolds over non-archimedean real closed fields do not satisfy the real integral Hodge conjecture in general and that over such fields, Br\"ocker's EPT theorem remains true for simply connected surfaces of geometric genus zero but fails for some K3 surfaces.

On an Analogue of the Conjecture of Birch and Swinnerton-Dyer for Abelian Schemes over Higher Dimensional Bases over Finite Fields

We formulate an analogue of the conjecture of Birch and Swinnerton-Dyer for Abelian schemes with everywhere good reduction over higher dimensional bases over finite fields of characteristic p . We prove the prime-to- p part conditionally on the finiteness of the p -primary part of the Tate-Shafarevich group or the equality of the analytic and the algebraic rank. If the base is a product of curves, Abelian varieties and K3 surfaces, we prove the prime-to- p part of the conjecture for constant or isoconstant Abelian schemes, in particular the prime-to- p part for (1) relative elliptic curves with good reduction or (2) Abelian schemes with constant isomorphism type of \mathscr{A}[p] or (3) Abelian schemes with supersingular generic fibre, and the full conjecture for relative elliptic curves with good reduction over curves and for constant Abelian schemes over arbitrary bases. We also reduce the conjecture to the case of surfaces as the basis.

Fujita decomposition over higher dimensional base

We generalize a result of Fujita, on the decomposition of Hodge bundles over curves, to the case of a higher dimensional base.

Birational geometry of algebraic varieties fibred into Fano double spaces

We develop a quadratic technique for proving the birational rigidity of Fano–Mori fibre spaces over a higher-dimensional base. As an application, we prove the birational rigidity of generic fibrations into Fano double spaces of dimension and index over a rationally connected base of dimension at most . We obtain a near-optimal estimate for the codimension of the set of hypersurfaces of a given degree in projective space that have positive-dimensional singular sets.

Global sensitivity analysis using support vector regression

• An orthogonal polynomial kernel function is proposed for SVR model. • An iteration scheme is introduced to optimize the proposed kernel function. • Sobol’ indices are obtained by post-processing the coefficients of the SVR model. • The proposed method is efficient for complex problems. Global sensitivity analysis (GSA) plays an important role in exploring the respective effects of input variables on response variables. In this paper, a new kernel function derived from orthogonal polynomials is proposed for support vector regression (SVR). Based on this new kernel function, the Sobol’ global sensitivity indices can be computed analytically by the coefficients of the surrogate model built by SVR. In order to improve the performance of the SVR model, a kernel function iteration scheme is introduced further. Due to the excellent generalization performance and structural risk minimization principle, the SVR possesses the advantages of solving non-linear prediction problems with small samples. Thus, the proposed method is capable of computing the Sobol’ indices with a relatively limited number of model evaluations. The proposed method is examined by several examples, and the sensitivity analysis results are compared with the sparse polynomial chaos expansion (PCE), high dimensional model representation (HDMR) and Gaussian radial basis (RBF) SVR model. The examined examples show that the proposed method is an efficient approach for GSA of complex models.

Spatial Bayesian latent factor regression modeling of coordinate-based meta-analysis data.

Now over 20 years old, functional MRI (fMRI) has a large and growing literature that is best synthesised with meta-analytic tools. As most authors do not share image data, only the peak activation coordinates (foci) reported in the article are available for Coordinate-Based Meta-Analysis (CBMA). Neuroimaging meta-analysis is used to (i) identify areas of consistent activation; and (ii) build a predictive model of task type or cognitive process for new studies (reverse inference). To simultaneously address these aims, we propose a Bayesian point process hierarchical model for CBMA. We model the foci from each study as a doubly stochastic Poisson process, where the study-specific log intensity function is characterized as a linear combination of a high-dimensional basis set. A sparse representation of the intensities is guaranteed through latent factor modeling of the basis coefficients. Within our framework, it is also possible to account for the effect of study-level covariates (meta-regression), significantly expanding the capabilities of the current neuroimaging meta-analysis methods available. We apply our methodology to synthetic data and neuroimaging meta-analysis datasets.

Compact moduli spaces for slope-semistable sheaves

We resolve pathological wall-crossing phenomena for moduli spaces of sheaves on higher-dimensional base manifolds. This is achieved by considering slope-semistability with respect to movable curves rather than divisors. Moreover, given a projective n-fold and a curve C that arises as the complete intersection of n-1 very ample divisors, we construct a modular compactification of the moduli space of vector bundles that are slope-stable with respect to C. Our construction generalises the algebro-geometric construction of the Donaldson-Uhlenbeck compactification by Joseph Le Potier and Jun Li. Furthermore, we describe the geometry of the newly construced moduli spaces by relating them to moduli spaces of simple sheaves and to Gieseker-Maruyama moduli spaces.

Bounded isotonic regression

Isotonic regression offers a flexible modeling approach under monotonicity assumptions, which are natural in many applications. Despite this attractive setting and extensive theoretical research, isotonic regression has enjoyed limited interest in practical modeling primarily due to its tendency to suffer significant overfitting, even in moderate dimension, as the monotonicity constraints do not offer sufficient complexity control. Here we propose to regularize isotonic regression by penalizing or constraining the range of the fitted model (i.e., the difference between the maximal and minimal predictions). We show that the optimal solution to this problem is obtained by constraining the non-penalized isotonic regression model to lie in the required range, and hence can be found easily given this non-penalized solution. This makes our approach applicable to large datasets and to generalized loss functions such as Huber’s loss or exponential family log-likelihoods. We also show how the problem can be reformulated as a Lasso problem in a very high dimensional basis of upper sets. Hence, range regularization inherits some of the statistical properties of Lasso, notably its degrees of freedom estimation. We demonstrate the favorable empirical performance of our approach compared to various relevant alternatives.

Moduli of vector bundles on higher-dimensional base manifolds — Construction and variation

We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson–Uhlenbeck compactification and explain how to use moduli spaces of quiver representations to show that Gieseker–Maruyama moduli spaces with respect to two different chosen polarizations are related via Thaddeus-flips through other “multi-Gieseker”-moduli spaces of sheaves. Moreover, as a new result, we show the existence of a natural morphism from a multi-Gieseker moduli space to the corresponding Donaldson–Uhlenbeck moduli space.

Moduli of vector bundles on higher-dimensional base manifolds: Construction and variation

This article should be in the special issue but was published as a normal issue. Please contact ijm@wspc.com

Balanced metrics on twisted Higgs bundles

A twisted Higgs bundle on a Kähler manifold X is a pair $$(E,\phi )$$ consisting of a holomorphic vector bundle E and a holomorphic bundle morphism $$\phi :M \otimes E \rightarrow E$$ for some holomorphic vector bundle M. Such objects were first considered by Hitchin when X is a curve and M is the tangent bundle of X, and also by Simpson for higher dimensional base. The Hitchin–Kobayashi correspondence for such pairs states that $$(E,\phi )$$ is polystable if and only if E admits a hermitian metric solving the Hitchin equation. This correspondence is a powerful tool to decide whether there exists a solution of the equation, but it provides little information as to the actual solution. In this paper we study a quantization of this problem that is expressed in terms of finite dimensional data and balanced metrics that give approximate solutions to the Hitchin equation. Motivation for this study comes from work of Donagi–Wijnholt (JHEP 05:068, 2013) concerning balanced metrics for the Vafa–Witten equations.

Quantum Dynamics with Gaussian Bases Defined by the Quantum Trajectories.

Development of a general approach to construction of efficient high-dimensional bases is an outstanding challenge in quantum dynamics describing large amplitude motion of molecules and fragments. A number of approaches, proposed over the years, utilize Gaussian bases whose parameters are somehow-usually by propagating classical trajectories or by solving coupled variational equations-tailored to the shape of a wave function evolving in time. In this paper we define the time-dependent Gaussian bases through an ensemble of quantum or Bohmian trajectories, known to provide a very compact representation of a wave function due to conservation of the probability density associated with each trajectory. Though the exact numerical implementation of the quantum trajectory dynamics itself is, generally, impractical, the quantum trajectories can be obtained from the wave function expanded in a basis. The resulting trajectories are used to guide compact Gaussian bases, as illustrated on several model problems.