Lattice Construction Research Articles

Phoneme lattice construction and its application to speech recognition and keyword spotting

An arrangement is provided for using a phoneme lattice for speech recognition and/or keyword spotting. The phoneme lattice may be constructed for an input speech signal and searched to produce a textual representation for the input speech signal and/or to determine if the input speech signal contains targeted keywords. An expectation maximization (EM) trained phoneme confusion matrix may be used when searching the phoneme lattice. The phoneme lattice may be constructed in a client and sent to a server, which may search the phoneme lattice to produce a result.

Interval-Valued Fuzzy Galois Connections: Algebraic Requirements and Concept Lattice Construction

Fuzzy formal concept analysis is concernedwith formal contexts expressing scalar-valued fuzzy relationships between objects and their properties. Existing fuzzy approaches assume that the relationship between given and given property is matter of degree in scale L (generally [0,1]). However, the extent to which object o has property a may be sometimes hard to assess precisely. Then it is convenient to use sub-interval from the scale L rather than precise value. Such formal contexts naturally lead to interval-valued fuzzy formal concepts. The aim of the paper is twofold. We provide sound minimal set of algebraic requirements for interval-valued implications in order to fulfill the fuzzy closure properties of the resulting Galois connection. Secondly, new approach based on generalization of Godel implication is proposed for building the complete lattice of all interval-valued fuzzy formal concepts.

Lattice construction of logarithmic modules for certain vertex algebras

A general method for constructing logarithmic modules in vertex operator algebra theory is presented. By utilizing this approach, we give explicit vertex operator construction of certain indecomposable and logarithmic modules for the triplet vertex algebra $${\mathcal{W}(p)}$$ and for other subalgebras of lattice vertex algebras and their N = 1 super extensions. We analyze in detail indecomposable modules obtained in this way, giving further evidence for the conjectural equivalence between the category of $${\mathcal{W}(p)}$$ -modules and the category of modules for the restricted quantum group $${\overline{\mathcal{U}}_q(sl_2)}$$ , q = e π i/p . We also construct logarithmic representations for a certain affine vertex operator algebra at admissible level realized in Adamović (J. Pure Appl. Algebra 196:119–134, 2005). In this way we prove the existence of the logarithmic representations predicted in Gaberdiel (Int. J. Modern Phys. A 18, 4593–4638, 2003). Our approach enlightens related logarithmic intertwining operators among indecomposable modules, which we also construct in the paper.

On the Horizon From the ORS

On the Horizon From the ORS

AN UPPER BOUND ON THE NUMBER OF PARITY CHECKS FOR BURST ERROR DETECTION AND CORRECTION IN EUCLIDEAN CODES

There are three standard weight functions on a linear code viz. Hamming weight, Lee weight, and Euclidean weight. Euclidean weight function is useful in connection with the lattice constructions (2) where the minimum norm of vectors in the lattice is related to the min- imum Euclidean weight of the code. In this paper, we obtain an upper bound over the number of parity check digits for Euclidean weight codes detecting and correcting burst errors.

Construction of pseudorandom binary lattices based on multiplicative characters

In this paper a large family of pseudorandom binary lattices is constructed by using the multiplicative characters of finite fields. This construction generalizes several one-dimensional constructions to arbitrary dimensions.

Optimality and scalability in lattice histogram construction

The Lattice Histogram is a recently proposed data summarization technique that achieves approximation quality preferable to that of an optimal plain histogram. Like other hierarchical synopsis methods, a lattice histogram (LH) aims to approximate data using a hierarchical structure. Still, this structure is not defined a priori; it consists an unknown , not a given, of the problem. Past work has defined the properties that an LH needs to obey and developed general-purpose approximation algorithms for the construction thereof. Still, two major issues remain unaddressed: First, the construction of an optimal LH for a given error metric is a problem unsolved to date. Second, the proposed algorithms suffer from too high space and time complexities that render their application in real-world settings problematic. In this paper, we address both these questions, focusing on the case that the target error metric is a maximum error metric. Our algorithms treat both the error-bounded LH construction problem, in which the space occupied by an LH is minimized under an error constraint, as well as the classic space-bounded problem. First, we develop a dynamic-programming scheme that detects an optimal LH under a given maximum-error bound. Second, we propose an efficient, practical, greedy algorithm that solves the same problem with much lower time and space requirements. Then, we show how both our algorithms can be applied to the classic space-bounded problem, aiming at minimizing error under a bound on space. Our experimental study with real-world data sets shows the effectiveness of our methods compared to competing summarization techniques. Moreover, our findings show that our greedy heuristic performs almost as well as the optimal solution in terms of accuracy.

Human Embryonic Stem Cell–Derived Mesoderm-like Epithelium Transitions to Mesenchymal Progenitor Cells

Human embryonic stem cells (hESC) have the potential to produce all of the cells in the body. They are able to self-renew indefinitely, potentially making them a source for large-scale production of therapeutic cell lines. Here, we developed a monolayer differentiation culture that induces hESC (WA09 and BG01) to form epithelial sheets with mesodermal gene expression patterns (BMP4, RUNX1, and GATA4). These E-cadherin+ CD90low cells then undergo apparent epithelial-mesenchymal transition for the derivation of mesenchymal progenitor cells (hESC-derived mesenchymal cells [hES-MC]) that by flow cytometry are negative for hematopoietic (CD34, CD45, and CD133) and endothelial (CD31 and CD146) markers, but positive for markers associated with mesenchymal stem cells (CD73, CD90, CD105, and CD166). To determine their functionality, we tested their capacity to produce the three lineages associated with mesenchymal stem cells and found they could form osteogenic and chondrogenic, but not adipogenic lineages. The derived hES-MC were able to remodel and contract collagen I lattice constructs to an equivalent degree as keloid fibroblasts and were induced to express alpha-smooth muscle actin when exposed to transforming growth factor (TGF)-beta1, but not platelet derived growth factor-B (PDGF-B). These data suggest that the derived hES-MC are multipotent cells with potential uses in tissue engineering and regenerative medicine and for providing a highly reproducible cell source for adult-like progenitor cells.

Exact solution of the Bose-Hubbard model on the Bethe lattice

The exact solution of a quantum Bethe lattice model in the thermodynamic limit amounts to solve a functional self-consistent equation. In this paper we obtain this equation for the Bose-Hubbard model on the Bethe lattice, under two equivalent forms. The first one, based on a coherent state path integral, leads in the large connectivity limit to the mean field treatment of Fisher et al. [Phys. Rev. B {\bf 40}, 546 (1989)] at the leading order, and to the bosonic Dynamical Mean Field Theory as a first correction, as recently derived by Byczuk and Vollhardt [Phys. Rev. B {\bf 77}, 235106 (2008)]. We obtain an alternative form of the equation using the occupation number representation, which can be easily solved with an arbitrary numerical precision, for any finite connectivity. We thus compute the transition line between the superfluid and Mott insulator phases of the model, along with thermodynamic observables and the space and imaginary time dependence of correlation functions. The finite connectivity of the Bethe lattice induces a richer physical content with respect to its infinitely connected counterpart: a notion of distance between sites of the lattice is preserved, and the bosons are still weakly mobile in the Mott insulator phase. The Bethe lattice construction can be viewed as an approximation to the finite dimensional version of the model. We show indeed a quantitatively reasonable agreement between our predictions and the results of Quantum Monte Carlo simulations in two and three dimensions.

Distributed algorithm for constructing concept lattice based on index

The presented concept lattice parallel/distributed algorithm needs to search plenty of non-related concepts when dealing with a large scale data,which reduces the performance of the algorithm.A distributed concept lattice construction algorithm based on index named LCBI was put forward.When inserting a new concept,it quickly found all the greatest correlative concepts of the new concept using index,then found out cross-sub-concepts of child nodes of all greatest correlative concepts using parallel and top-down search,which decreased the search area.Theoretical analysis and experimental results show that LCBI outperforms the other distributed algorithms when dealing with dense context.

Cross-section optimization of tower crane lattice boom

This paper discusses the problem of cross-section optimization of tower crane lattice boom. The trapezoid cross section has been analyzed. The triangular and rectangular cross sections have also been analyzed as special cases. Total mass of the construction has been selected as the objective function. Optimization parameters have been determined by Lagrange’s multipliers method. Criterion of stress is used as the constraint function. Numerical examples are performed by usage of the obtained theoretical solutions. Those results were than compared with ones obtained by usage of finite element method based computer program. On the base of the analysis that was carried out, the recommendations are given regarding the application of trapezoid, triangular and rectangular cross sections of the lattice constructions.

On a generalization of Littlewood's conjecture

We present a class of lattices in $\R^d$ ($d\ge 2$) which we call grid-Littlewood lattices and conjecture that any lattice is such. This conjecture is referred to as GLC. Littlewood's conjecture amounts to saying that $\Z^2$ is grid-Littlewood. We then prove the existence of grid-Littlewood lattices by first establishing a dimension bound for the set of possible exceptions. The existence of vectors (grid-Littlewood-vectors) in $\R^d$ with special Diophantine properties is proved by similar methods. Applications toDiophantine approximations are given. For dimension $d\ge 3$, we give explicit constructions of grid-Littlewood lattices (and in fact lattices satisfying a much stronger property). We also show that GLC is implied by a conjecture of G. A. Margulis concerning bounded orbits of the diagonal group. The unifying theme of the methods is to exploit rigidity results in dynamics ([4, 1, 5]), and derive results in Diophantine approximations or the geometry of numbers.

Transform Analysis for Pricing American Options Under Low-Dimensional Stochastic Volatility Models

This paper presents a new transform-based approach for path-independent lattice construction for pricing American options under low-dimensional stochastic volatility models. We derive multidimensional transforms which allow us to construct efficient path-independent lattices for virtually all low-dimensional stochastic volatility models given in the literature including one volatility factor-based stochastic volatility (SV) models, two volatility factors-based SV models, stochastic volatility jump (SVJ) models with one and two jump factors in the asset returns, and SVJ models with jumps in both asset returns and volatility. The lattice-based approximations of the prices of European options converge rapidly to their true prices obtained using quasi-analytical solutions.

Buildings: Interactions with Algebra and Geometry

The focus of the conference was on buildings and their applications. Buildings are combinatorial structures (metric cell complexes) which may be viewed as simultaneous generalizations of trees and projective spaces. There is a rich class of groups acting on buildings; the action can often be used to obtain structural results about the group itself. On the other hand, buildings and related metric spaces – such as Riemannian symmetric spaces, p -adic symmetric spaces, metric \operatorname{CAT}(0) -complexes – form an interesting class of geometric structures with a high degree of symmetry. In the last years, there were several new developments in the applications of buildings in arithmetic geometry, Riemannian geometry, representation theory, and geometric group theory. The workshop brought together experts from these areas whose work is related to buildings. This mixture worked out quite well and led to many discussions and interactions between people coming from different areas. A somewhat similar workshop Buildings and Curvature took place in 2004 in Oberwolfach. Then, the focus was more on Riemannian and metric geometry. The present workshop Buildings: Interactions with Algebra and Geometry took a more algebraic turn. There were 50 participants and 25 lectures. We had a substantial group of young participants, some of which could present their work at the conference. Both the young and the senior speakers succeeded remarkably well in presenting their work in a way which was accessible to people working in neighboring, but different areas. There were several talks reporting on essential progress in abstract building theory: R. Weiss presented his revision of the classification for locally finite affine buildings and A. Thuillier reported on a new approach to compactifications of Bruhat–Tits buildings and Berkovich spaces. For spherical buildings, C. Parker presented recent results on convex subsets, and K. Brown on displacement lengths of automorphisms in non-spherical buildings. However, most of the talks concerned applications in various areas. P. Littelmann gave a survey on applications of buildings in representation theory of algebraic groups. The talks by B. Rémy and G. Willis underlined the increasing importance of locally finite buildings in the new structure theory of locally compact totally disconnected groups. There were talks on constructions of lattices using buildings by A. Thomas and R. Gramlich. K.-U. Bux and K. Wortman presented strong and recent results on finiteness properties of arithmetic groups. U. Görtz reported on affine Deligne–Lusztig varieties and the reduction of Shimura varieties, which leads to interesting (and hard) combinatorial questions about folded galleries. The organizers had the clear impression that the workshop worked very well, that it led to new scientific collaboration, to new ideas and that it brought new geometric insights. We would like to thank the institute and its friendly and helpful staff. The additional support by the NSF for young researches from the US is gratefully acknowledged.

An incremental algorithm to construct a lattice of set intersections

An incremental algorithm to construct a lattice from a collection of sets is derived, refined, analyzed, and related to a similar previously published algorithm for constructing concept lattices. The lattice constructed by the algorithm is the one obtained by closing the collection of sets with respect to set intersection. The analysis explains the empirical efficiency of the related concept lattice construction algorithm that had been observed in previous studies. The derivation highlights the effectiveness of a correctness-by-construction approach to algorithm development.

Square means and geometric means in lattice-ordered groups and vector lattices

The geometric mean and the square mean of two positive real numbers are determined by the order in the sense that they can be written as (respectively) an infinite meet and an infinite join. We use this observation to define the geometric mean and the square mean on the positive elements of an Abelian lattice-ordered group. For certain totally ordered fields and vector lattices, the square mean can be used to define a new compatible addition. The resulting structure lives inside the complexification of the original structure and is constructed by using a general method for extending commutative lattice-ordered monoids to Abelian lattice-ordered groups. We describe this method and use it as the starting point for similar constructions of lattice-ordered rings and vector lattices.

Implementation of the Least-Squares Lattice with Order and Forgetting Factor Estimation for FPGA

A high performance RLS lattice filter with the estimation of an unknown order and forgetting factor of identified system was developed and implemented as a PCORE coprocessor for Xilinx EDK. The coprocessor implemented in FPGA hardware can fully exploit parallelisms in the algorithm and remove load from a microprocessor. The EDK integration allows effective programming and debugging of hardware accelerated DSP applications. The RLS lattice core extended by the order and forgetting factor estimation was implemented using the logarithmic numbers system (LNS) arithmetic. An optimal mapping of the RLS lattice onto the LNS arithmetic units found by the cyclic scheduling was used. The schedule allows us to run four independent filters in parallel on one arithmetic macro set. The coprocessor containing the RLS lattice core is highly configurable. It allows to exploit the modular structure of the RLS lattice filter and construct the pipelined serial connection of filters for even higher performance. It also allows to run independent parallel filters on the same input with different forgetting factors in order to estimate which order and exponential forgetting factor better describe the observed data. The FPGA coprocessor implementation presented in the paper is able to evaluate the RLS lattice filter of order 504 at 12 kHz input data sampling rate. For the filter of order up to 20, the probability of order and forgetting factor hypotheses can be continually estimated. It has been demonstrated that the implemented coprocessor accelerates the Microblaze solution up to 20 times. It has also been shown that the coprocessor performs up to 2.5 times faster than highly optimized solution using 50 MIPS SHARC DSP processor, while the Microblaze is capable of performing another tasks concurrently.

Mechanism of local amorphization of a heavily doped Ti1 − x V x CoSb intermetallic semiconductor

Structural and electron transport characteristics of a TiCoSb intermetallic semiconductor heavily doped with the V donor impurity (dopant concentration ∼9.5 × 1019 − 1.9 × 1021 cm−3, temperatures 80–380 K) have been investigated and the distribution of the electron density of states in this material has been calculated. Different occupancies have been established for Co and (Ti, V) atomic positions in the Ti1 − x V x CoSb lattice; this difference is equivalent to introduction of two types of acceptors into the semiconductor. Suppression of the metallic conductivity in the n-type semiconductor with an increase in the donor concentration has been found, which is explained by simultaneous generation of acceptors. It is shown that the methods of numerical calculation adequately describe the physical processes if the occupancy of unit-cell positions is taken into account in construction of the Wigner-Seitz lattice. The results obtained are discussed within the model of a heavily doped and compensated Shklovskii-Efros semiconductor.

The construction of good extensible rank-1 lattices

It has been shown by Hickernell and Niederreiter that there exist generating vectors for integration lattices which yield small integration errors for n = p, p 2 ,... for all integers p ≥ 2. This paper provides algorithms for the construction of generating vectors which are finitely extensible for n = p, p 2 ,... for all integers p ≥ 2. The proofs which show that our algorithms yield good extensible rank-1 lattices are based on a sieve principle. Particularly fast algorithms are obtained by using the fast component-by-component construction of Nuyens and Cools. Analogous results are presented for generating vectors with small weighted star discrepancy.

Characterizing positive and negative selection and their phylogenetic effects

Total evidence and the use of large datasets to overcome uncertainty are the state of the art in systematic analysis. This assumes that the only true phylogenetic signal is ancestry and that functional, structural, and other factors will not add an alternative signal. Using gene families, where individual codon positions were sorted into bins based upon average-pairwise dN/dS ratio, we show that standard, common phylogenetic methods that were designed for stochastic, neutral, site-independent processes, generate less robust phylogenetic signal for bins with strong negative or positive selection. This was true for phylogenetic reconstruction with parsimony, distance, and likelihood methods. Further, we present a case for the potential existence of systematic functional or structural signal that competes with ancestral signal. For the example of positive selection, we simulate the evolution of sequences through three dimensional lattice constructs with folding constraint and changing binding functionality and show that total evidence for these lattice genes presents trees with functional signal, but that the neutral synonymous sites in these genes show the true ancestral signal. In this case, sequence convergence is promoted by functional convergence.