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We settle a long-standing problem in the theory of Hecke algebras of complex reflection groups by constructing many (graded) integral cellular bases of these algebras. As applications, we explicitly construct the simple modules of Ariki's…
We propose a method for computing approximations to the Hecke eigenvalues of a classical modular eigenform $f$, based on the analytic evaluation of $f$ at points in the upper half plane. Our approach works with arbitrary precision, allows…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
We categorify the Hecke algebra with parameters 1 and v using a variation of the category of Soergel bimodules.
This article analyzes the periodic orbits of Syracuse dynamical systems in a novel algebraic setting: the commutative ring of graded $n$-adic integers. Within this context, this article introduces a dual-radix modular division algorithm for…
In spatial regression models, spatial heterogeneity may be considered with either continuous or discrete specifications. The latter is related to delineation of spatially connected regions with homogeneous relationships between variables…
Bayesian inference via standard Markov Chain Monte Carlo (MCMC) methods is too computationally intensive to handle large datasets, since the cost per step usually scales like $\Theta(n)$ in the number of data points $n$. We propose the…
Complex networks can be used for modeling street meshes and urban agglomerates. With such a model, many aspects of a city can be investigated to promote a better quality of life to its citizens. Along these lines, this paper proposes a set…
We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.
We prove a strong induction theorem for graded Hecke algebras and we classify the tempered and square integrable representations of such algebras using methods of equivariant homology.
We develop lagged Metropolis-Hastings walk for sampling from simple undirected graphs according to given stationary sampling probabilities. We explain how to apply the technique together with designed graphs for sampling of units-in-space.…
Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admits unfoldings to skew-symmetric matrices. We develop an combinatorial algorithm that…
We explore a natural action of Hecke operators acting on formal sums of optimal embeddings of real quadratic orders into Eichler orders. By associating an optimal embedding to its root geodesic on the corresponding Shimura curve, we can…
We are going to analyze local algorithms over sparse random graphs. These algorithms are based on local information where local regards to a decision made by the exploration of a small neighbourhood of a certain vertex plus a believe of the…
We derive a numerical algorithm for evaluating the Riemannian logarithm on the Stiefel manifold with respect to the canonical metric. In contrast to the existing optimization-based approach, we work from a purely matrix-algebraic…
Distributed Computation has been a recent trend in engineering research. Parallel Computation is widely used in different areas of Data Mining, Image Processing, Simulating Models, Aerodynamics and so forth. One of the major usage of…
Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They…
In this paper, we present, evaluate and analyse the performance of parallel synchronous Jacobi algorithms by different partitioned procedures including band-row splitting, band-row sparsity pattern splitting and substructuring splitting,…
Recently, the influence of potentially present symmetries has begun to be studied in complex networks. A typical way of studying symmetries is via the automorphism group of the corresponding graph. Since complex networks are often subject…
We propose a categorification of the cyclotomic Hecke algebra in terms of the equivariant K-theory of the framed matrix factorizations. The construction generalizes the earlier construction of the authors for a categorification of the…