Arbitrary Terms Research Articles

Monoallelic Chromatin Conformation Flanking Long-Range Silenced Domains in Cancer-Derived and Normal Cells

Epigenetic inactivation of chromatin plays an important role in determining cell phenotype in both normal and cancer cells, but our knowledge is still incomplete with respect to any potential monoallelic nature of the phenomenon. We have genotyped DNA isolated from chromatin of two colorectal cancer-derived lines and a culture of normal human intestinal epithelial cells (HIEC), which was immunoprecipitated with antibodies to acetylated vs. methylated histone H3K9, and presented the data as B allele frequency differences over multiple single-nucleotide polymorphism (SNP) moving window averages. [B allele is an arbitrary term defined as one of the two alleles at any given SNP, named A and B]. Three different validation tests confirmed that peaks exhibiting differences represented monoallelic domains. These complementary tests confirmed the following: 1) genes in the regions of high B allele frequency difference were expressed monoallelically; 2) in normal cells all five imprinting control regions which carried heterozygous SNPs were characterized by B allele difference peaks; and 3) the haplotypes in the B allele difference peaks were faithfully maintained in the chromatin immunoprecipitated with the respective antibodies. In both samples most of the monoallelic domains were found at the boundaries between regions of open and closed chromatin. With respect to the cancer line, this supports the established concept of conformation spreading, but the results from the normal cells were unexpected. Since these cells were polyclonal, the monoallelic structures were probably not determined by random choice as occurs in X-inactivation, so we propose that epigenetic inactivation in some domains may be heritable and polymorphic in normal human cells.

One-loop Kähler potential in 5D gauged supergravity with generic prepotential

We calculate one-loop contributions to the Kähler potential in 4D effective theory of 5D gauged supergravity (SUGRA) on S1/Z2 with a generic form of the prepotential and arbitrary boundary terms. Our result is applicable to a wide class of 5D SUGRA models. The derivation is systematically performed by means of an N=1 superfield formalism based on the superconformal formulation of 5D SUGRA. As an illustrative example, we provide an explicit expression of the Kähler potential in the case of 5D flat spacetime.

External verification analysis: A code-independent verification technique for unsteady PDE codes

The External Verification Analysis (EVA) code verification technique is developed and presented. An extension of the Method of Manufactured Solutions (MMS), EVA provides a reference solution that can be used to verify both the spatial and temporal discretization schemes of an unsteady PDE solver, without the addition of arbitrary source terms. This feature of EVA allows the code to truly be treated as a “black box” during verification, simplifying the verification procedure. Currently, however, the EVA technique solves the interior equations of a PDE code only – thus the implementation of boundary conditions in the PDE code is not verified. The mathematical foundation of EVA is explained in detail, and the process used to verify a PDE code is discussed. The EVA technique is then demonstrated on a high-order, nonlinear Computational Aeroacoustics code.

Identities for the fundamental solution of thin plate bending problems and the nonuniqueness of the hypersingular BIE solution for multi-connected domains

Four integral identities for the fundamental solution of thin plate bending problems are presented in this paper. These identities can be derived by imposing rigid-body translation and rotation solutions to the two direct boundary integral equations (BIEs) for plate bending problems, or by integrating directly the governing equation for the fundamental solution. These integral identities can be used to develop weakly-singular and nonsingular forms of the BIEs for plate bending problems. They can also be employed to show the nonuniqueness of the solution of the hypersingular BIE for plates on multi-connected (or multiply-connected) domains. This nonuniqueness is shown for the first time in this paper. It is shown that the solution of the singular (deflection) BIE is unique, while the hypersingular (rotation) BIE can admit an arbitrary rigid-body translation term in the deflection solution, on the edge of a hole. However, since both the singular and hypersingular BIEs are required in solving a plate bending problem using the boundary element method (BEM), the BEM solution is always unique on edges of holes in plates on multi-connected domains. Numerical examples of plates with holes are presented to show the correctness and effectiveness of the BEM for multi-connected domain problems.

Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory

We find exact solutions of the Generalized Modified Boussinesq (GMB) equation, the Kuromoto-Sivashinsky (KS) equation the and, Camassa-Holm (CH) equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether’s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.

The generalized Bohl–Perron principle for the neutral type vector functional differential equations

We consider a vector homogeneous neutral type functional differential vector equation of a certain class. It is proved that, if the corresponding nonhomogeneous equation with the zero initial conditions and an arbitrary free term bounded on the positive half-line, has a bounded solution, then the considered homogeneous equation is exponentially stable.

CageR: Cage‐Based Reverse Engineering of Animated 3D Shapes

AbstractWe present CageR: A novel framework for converting animated 3D shape sequences into compact and stable cage‐based representations. Given a raw animated sequence with one‐to‐one point correspondences together with an initial cage embedding, our algorithm automatically generates smoothly varying cage embeddings which faithfully reconstruct the enclosed object deformation. Our technique is fast, automatic, oblivious to the cage coordinate system, provides controllable error and exploits a GPU implementation. At the core of our method, we introduce a new algebraic algorithm based on maximum volume sub‐matrices (maxvol) to speed up and stabilize the deformation inversion. We also present a new spectral regularization algorithm that can apply arbitrary regularization terms on selected subparts of the inversion spectrum. This step allows to enforce a highly localized cage regularization, guaranteeing its smooth variation along the sequence. We demonstrate the speed, accuracy and robustness of our framework on various synthetic and acquired data sets. The benefits of our approach are illustrated in applications such as animation compression and post‐editing.

On the spin separation of algebraic two-component relativistic Hamiltonians

The separation of the spin-free and spin-dependent terms of a given relativistic Hamiltonian is usually facilitated by the Dirac identity. However, this is no longer possible for the recently developed exact two-component relativistic Hamiltonians derived from the matrix representation of the Dirac equation in a kinetically balanced basis. This stems from the fact that the decoupling matrix does not have an explicit form. To resolve this formal difficulty, we first define the spin-dependent term as the difference between a two-component Hamiltonian corresponding to the full Dirac equation and its one-component counterpart corresponding to the spin-free Dirac equation. The series expansion of the spin-dependent term is then developed in two different ways. One is in the spirit of the Douglas-Kroll-Hess (DKH) transformation and the other is based on the perturbative expansion of a two-component Hamiltonian of fixed structure, either the two-step Barysz-Sadlej-Snijders (BSS) or the one-step exact two-component (X2C) form. The algorithms for constructing arbitrary order terms are proposed for both schemes and their convergence patterns are assessed numerically. Truncating the expansions to finite orders leads naturally to a sequence of novel spin-dependent Hamiltonians. In particular, the order-by-order distinctions among the DKH, BSS, and X2C approaches can nicely be revealed. The well-known Pauli, zeroth-order regular approximation, and DKH1 spin-dependent Hamiltonians can also be recovered naturally by appropriately approximating the decoupling and renormalization matrices. On the practical side, the sf-X2C+so-DKH3 Hamiltonian, together with appropriately constructed generally contracted basis sets, is most promising for accounting for relativistic effects in two steps, first spin-free and then spin-dependent, with the latter applied either perturbatively or variationally.

143 QUALITY OF LIFE AND AGING IN BRAZIL

Introduction: The number of elder people in the world is growing both in absolute and relative terms and India is not an exception. The greatest challenge over the coming years will be maintaining the health of this increasing number of older adult. Older people is a very arbitrary term here we mean is 60+years. Objective: To assess the food habit and food belief in eastern Rajasthan. Methods: Survey data collection: face to face interviews; food frequency questionnaire (dietary diaries); and follow-up interviews. 143 elderly people (aged 60+) randomly selected. Resuls: Elders of high income ate significantly (p<0.05) more than the recommended by the ICMR and more health conscious. Daily intake of lower income group is significantly low than the ICMR recommendation. Female of both income groups have less than recommendation and they are suffering from many diseases like overweight, arthritis, knee problem etc. Lower income group significantly (p<0.05) follow the traditional food whereas the high income group mix the global as well as traditional. Male live quality of life than female. Conclusions: Male is more calorie and health conscious and enjoys active aging than female.

A BOUNDARY-LAYER APPROACH TO STRESS ANALYSIS IN THE SIMPLE SHEARING OF RUBBER BLOCKS

Abstract Rubbers are usually modeled as being perfectly incompressible. In the simple shear of rubber blocks, the normal stress components, therefore, contain an arbitrary constant pressure term to be determined from the boundary conditions. There is therefore a fundamental ambiguity in the determination of this pressure because the normal stresses are expected to be identically zero on different faces of the sheared block. It is proposed here that the stress distribution near a face should be determined by the normal stress boundary condition at that face and that this distribution is valid only within a short distance from the face, giving rise to boundary layers at the faces of the sheared block. At the intersection of these boundary layers it will be assumed that the stress is additive. It is further assumed that the stresses within the bulk of the material should be determined by treating the perfectly incompressible material as equivalent to a slightly compressible material. The form of slight compressibility adopted here is that usually assumed in the finite element simulation of rubbers. These reasonable assumptions give rise to a complex stress pattern within the block. The results are qualitatively similar to results obtained by other authors on using a finite element approach for a neo-Hookean material. The possible occurrence of cavitation at the corners of the block is also examined.

The lightest scalar in theories with broken supersymmetry

We study the scalar mass matrix of general supersymmetric theories with local gauge symmetries, and derive an absolute upper bound on the lightest scalar mass. This bound can be saturated by suitably tuning the superpotential, and its positivity therefore represents a necessary and sufficient condition for the existence of metastable vacua. It is derived by looking at the subspace of all those directions in field space for which an arbitrary supersymmetric mass term is not allowed and scalar masses are controlled by supersymmetry-breaking splitting effects. This subspace includes not only the direction of supersymmetry breaking, but also the directions of gauge symmetry breaking and the lightest scalar is in general a linear combination of fields spanning all these directions. We present explicit results for the simplest case of theories with a single local gauge symmetry. For renormalizable gauge theories, the lightest scalar is a combination of the Goldstino partners and its square mass is always positive. For more general non-linear sigma models, on the other hand, the lightest scalar can involve also the Goldstone partner and its square mass is not always positive.

An equivalence-preserving CPS translation via multi-language semantics

Language-based security relies on the assumption that all potential attacks follow the rules of the language in question. When programs are compiled into a different language, this is true only if the translation process preserves observational equivalence. To prove that a translation preserves equivalence, one must show that if two program fragments cannot be distinguished by any source context, then their translations cannot be distinguished by any target context. Informally, target contexts must be no more powerful than source contexts, i.e., for every target context there exists a source context that "behaves the same." This seems to amount to being able to "back-translate" arbitrary target terms. However, that is simply not viable for practical compilers where the target language is lower-level and, thus, contains expressions that have no source equivalent. In this paper, we give a CPS translation from a less expressive source language (STLC) to a more expressive target language (System F) and prove that the translation preserves observational equivalence. The key to our equivalence-preserving compilation is the choice of the right type translation: a source type σ mandates a set of behaviors and we must ensure that its translation σ + mandates semantically equivalent behaviors at the target level. Based on this type translation, we demonstrate how to prove that for every target term of type σ + , there exists an equivalent source term of type σ- even when sub-terms of the target term are not necessarily "back-translatable" themselves. A key novelty of our proof, resulting in a pleasant proof structure, is that it leverages a multi-language semantics where source and target terms may interoperate.

Extending [formula omitted]-clauses with disequalities

The class H 1 has proven particularly useful for the analysis of term-manipulating programs such as cryptographic protocols. Here, we show that clauses from that class can be extended with disequalities between arbitrary terms while retaining decidability of satisfiability. The proof is based on a normalization procedure together with a procedure to decide whether a finite automaton with disequalities accepts less than k elements, and a subtle combinatorial argument to prove that only finitely many disequalities need to be considered.

Integrated symbol table, engine and heap memory management in multi-engine prolog

We describe an integrated solution to symbol, heap and logic engine memory management in a context where exchanges of arbitrary Prolog terms occur between multiple dynamically created engines, implemented in a new Java-based experimental Prolog system. As our symbols represent not just Prolog atoms, but also handles to Java objects (including arbitrary size integers and decimals), everything is centered around a symbol garbage collection algorithm ensuring that external objects are shared and exchanged between logic engines efficiently. Taking advantage of a tag-on-data heap representation of Prolog terms, our algorithm performs in-place updates of live symbol references directly on heap cells. With appropriate fine tuning of collection policies our algorithm provides an integrated memory management solution for Prolog systems, with amortized cost dominated by normally occurring heap garbage collection costs.

Remarks on gauge invariance and first-class constraints

Gauge symmetries lead to first-class constraints. This assertion is, of course, true only for non-trivial gauge symmetries, i.e., gauge symmetries that act non-trivially on-shell on the dynamical variables. We illustrate this well-appreciated fact for time reparametrization invariance in the context of modifications of gravity-suggested in a recent proposal by Hořava-in which the Hamiltonian constraint is deformed by arbitrary spatial diffeomorphism invariant terms, where some subtleties are found to arise.

Global attractivity in a rational delay difference equation with quadratic terms

For the following rational difference equation with arbitrary delay and quadratic terms: we determine sufficient conditions on the parameter values which guarantee that the unique non-negative fixed point attracts all positive solutions. When the fixed point is the origin (F = 0), we show that it attracts all non-negative solutions of the more general equation where . We also show that altering some of the above conditions on parameters causes the origin to not be globally attracting.

Testing two-field inflation

We derive accurate semianalytic formulas for the power spectra from two-field inflation assuming an arbitrary potential and arbitrary noncanonical kinetic terms, and we use them both to build phenomenological intuition and to constrain classes of two-field models using WMAP data. Using covariant formalism, we first develop a framework for understanding the background field kinematics and introduce a ``slow-turn'' approximation. Next, we find covariant expressions for the evolution of the adiabatic/curvature and entropy/isocurvature modes, and we discuss how the evolution of modes can be inferred mostly from the background kinematics and the geometry of the field manifold. From these expressions, we derive semianalytic formulas for the curvature, isocurvature, and cross spectra, and the standard spectral observables, all to second order in the slow-roll and slow-turn approximations. In tandem, we show how our covariant formalism provides useful intuition into how the general features of the inflationary Lagrangian translate into distinct features in the observable power spectra. In particular, we find that key features of the power spectra can be directly read off from the nature of the roll path, the curve the field vector rolls along with respect to the two-dimensional field manifold. For example, models whose roll path makes a sharp turn around 60 e-foldings before the end of inflation tend to be ruled out because they produce stronger departures from scale invariance than are allowed by the latest CMB observations. Finally, we apply our formalism to confront four classes of two-field models with WMAP data, including doubly quadratic and quartic potentials and nonstandard kinetic terms, showing how whether a model is ruled out or not depends not only on certain features of the inflationary Lagrangian, but also on the initial conditions. Ultimately, for a two-field model to be consistent with observations, we show that it must possess the right balance of certain kinematical and dynamical behaviors, which we reduce to a set of functions that represent the main characteristics of any two-field model of inflation.

Meso-GSHMC: A stochastic algorithm for meso-scale constant temperature simulations

Abstract We consider the problem of time-stepping/sampling for molecular and meso-scale particle dynamics. The aim of the work is to derive numerical time-stepping methods that generate samples exactly from the desired target temperature distribution. The numerical methods proposed in this paper rely on the well-known splitting of stochastic thermostat equations into conservative and fluctuation-dissipation parts. We propose a methodology to derive numerical approximation to the fluctuation-dissipation part that exactly samples from the underlying Boltzmann distribution. Our methodology applies to Langevin dynamics as well as Dissipative Particle Dynamics and, more generally, to arbitrary position dependent fluctuation-dissipation terms. A Metropolis criterion is introduced to correct for numerical inconsistency in the conservative dynamics part of the model. Shadow energies are used to increase the acceptance rate under the Metropolis criterion. We call the newly proposed method meso-GSHMC.

ON THE ZEROS OF SELF-RECIPROCAL POLYNOMIALS SATISFYING CERTAIN COEFFICIENT CONDITIONS

Kim and Park investigated the distribution of zeros around the unit circle of real self-reciprocal polynomials of even degrees with five terms, where the absolute value of middle coefficient equals the sum of all other coefficients. In this paper, we extend some of their results to the same kinds of polynomials with arbitrary many nonzero terms.

A NOTE ON THE NON-COMMUTATIVE LAPLACE–VARADHAN INTEGRAL LEMMA

We continue the study of the free energy of quantum lattice spin systems where to the local Hamiltonian H an arbitrary mean field term is added, a polynomial function of the arithmetic mean of some local observables X and Y that do not necessarily commute. By slightly extending a recent paper by Hiai, Mosonyi, Ohno and Petz [10], we prove in general that the free energy is given by a variational principle over the range of the operators X and Y. As in [10], the result is a non-commutative extension of the Laplace–Varadhan asymptotic formula.