Variable Lambda Research Articles

Duality in elliptic Ruijsenaars system and elliptic symmetric functions

We demonstrate that the symmetric elliptic polynomials E_lambda (x) originally discovered in the study of generalized Noumi–Shiraishi functions are eigenfunctions of the elliptic Ruijsenaars–Schneider (eRS) Hamiltonians that act on the mother function variable y_i (substitute of the Young-diagram variable lambda ). This means they are eigenfunctions of the dual eRS system. At the same time, their orthogonal complements in the Schur scalar product, P_lambda (x) are eigenfunctions of the elliptic reduction of the Koroteev–Shakirov (KS) Hamiltonians. This means that these latter are related to the dual eRS Hamiltonians by a somewhat mysterious orthogonality transformation, which is well defined only on the full space of time variables, while the coordinates x_i appear only after the Miwa transform. This observation explains the difficulties with getting the apparently self-dual Hamiltonians from the double elliptic version of the KS Hamiltonians.

Improvement of Catastrophic Forgetting using variable Lambda value in EWC

Improvement of Catastrophic Forgetting using variable Lambda value in EWC

Should the Equilibrium Point Hypothesis (EPH) be Considered a Scientific Theory?

The purpose of this commentary is to discuss factors that limit consideration of the equilibrium point hypothesis as a scientific theory. The EPH describes control of motor neuron threshold through the variable lambda, which corresponds to a unique referent configuration for a muscle, joint, or combination of joints. One of the most compelling features of the equilibrium point hypothesis is the integration of posture and movement control into a single mechanism. While the essential core of the hypothesis is based upon spinal circuitry interacting with peripheral mechanics, the proponents have extended the theory to include the higher-level processes that generate lambda, and in doing so, imposed an injunction against the supraspinal nervous system modeling, computing, or predicting dynamics. This limitation contradicts evidence that humans take account of body and environmental dynamics in motor selection, motor control, and motor adaptation processes. A number of unresolved limitations to the EPH have been debated in the literature for many years, including whether muscle resistance to displacement, measured during movement, is adequate to support this form of control, violations in equifinality predictions, spinal circuits that alter the proposed invariant characteristic for muscles, and limitations in the description of how the complexity of spinal circuitry might be integrated to yield a unique and stable equilibrium position for a given motor neuron threshold. In addition, an important empirical limitation of EPH is the measurement of the invariant characteristic, which needs to be done under a constant central state. While there is no question that the EPH is an elegant and generative hypothesis for motor control research, the claim that this hypothesis has reached the status of a scientific theory is premature.

RP-HPLC Analysis and Antidiabetic Activity of Swertia paniculata

1,2,6,8-Tetrahydroxyxanthone (SR1) and 2,8-dihydroxy-1,6-dimethoxyxanthone (SR2) have been qualitatively and quantitatively determined in leaves and rhizomes of Swertia paniculata. The methanol extracts were analyzed on a C18 column using MeOH and H20 as mobile phase at a flow rate of 1 mL/min. Identification was achieved using an UV variable lambda detector set at 260 nm. Variation in the bioactive compounds with respect to season and altitude was determined, along with the examination of the antidiabetic activity of the plant. The maximum concentration of SR1 and SR2 was found in leaves collected from Tungnath (3600 m), Uttarakhand, India, in October. The blood sugar level in alloxan induced rats was decreased by 51.0% by the methanol extract of the leaves. Overall, results showed that the concentration of bioactive compounds increased with altitude. October was the period of prime potency and should be the time of harvest for S. paniculata.

Reducing the bias and uncertainty of free energy estimates by using regression to fit thermodynamic integration data

This report presents the application of polynomial regression for estimating free energy differences using thermodynamic integration data, i.e., slope of free energy with respect to the switching variable lambda. We employ linear regression to construct a polynomial that optimally fits the thermodynamic integration data, and thus reduces the bias and uncertainty of the resulting free energy estimate. Two test systems with analytical solutions were used to verify the accuracy and precision of the approach. Our results suggest that use of regression with high degree of polynomials provides the most accurate free energy difference estimates, but often with slightly larger uncertainty, compared to commonly used quadrature techniques. High degree polynomials possess the flexibility to closely fit the thermodynamic integration data but are often sensitive to small changes in the data points. Thus, we also used Chebyshev nodes to guide in the selection of nonequidistant lambda values for use in thermodynamic integration. We conclude that polynomial regression with nonequidistant lambda values delivers the most accurate and precise free energy estimates for thermodynamic integration data for the systems considered here. Software and documentation is available at http://www.phys.uidaho.edu/ytreberg/software.

Bos taurus genome sequence reveals the assortment of immunoglobulin and surrogate light chain genes in domestic cattle

BackgroundThe assortment of cattle immunoglobulin and surrogate light chain genes has been extracted from the version 3.1 of Bos taurus genome sequence as a part of an international effort to sequence and annotate the bovine genome.Results63 variable lambda chain and 22 variable kappa chain genes were identified and phylogenetically assigned to 8 and 4 subgroups, respectively. The specified phylogenetic relationships are compatible with the established ruminant light chain variable gene families or subgroups. Because of gaps and uncertainties in the assembled genome sequence, the number of genes might change in the future versions of the genome sequence. In addition, three bovine surrogate light chain genes were identified. The corresponding cDNAs were cloned and the expression of the surrogate light chain genes was demonstrated from fetal material.ConclusionThe bovine kappa gene locus is compact and simple which may reflect the preferential use of the lambda chain in cattle. The relative orientation of variable and joining genes in both loci are consistent with a deletion mechanism in VJ joining. The orientation of some variable genes cannot be determined from the data available. The number of functional variable genes is moderate when compared to man or mouse. Thus, post-recombinatorial mechanisms might contribute to the generation of the bovine pre-immune antibody repertoire. The heavy chains probably contribute more to recombinational immunoglobulin repertoire diversity than the light chains but the heavy chain locus could not be annotated from the version 3.1 of Bos taurus genome.

Numerical Techniques to Optimize Free Energy Estimation Using Thermodynamic Integration

Free energy estimation using thermodynamic integration (TI) involves numerically approximating an integral based on a limited set of discrete data points. These discrete data points represent the free energy slope as a function of the switching variable lambda for TI simulations. We present several numerical techniques for generating optimal free energy estimates utilizing polynomials, instead of the often-used quadrature, to fit the data and thus reduce the bias and uncertainty of the resulting estimates. The specific techniques utilized in our current study are Lagrange and Newton interpolation, cubic spline, and polynomial regression. To further improve the overall accuracy of free energy estimates using these techniques, we also investigated the use of non-equidistant lambda values (based on Chebyshev nodes) for thermodynamic integration simulations. Our results demonstrate that the use of non-equidistant lambda values and high degrees of polynomials gives the more accurate and precise free energy estimates compared to that of trapezoidal quadrature. Regression, in particular, offers the greatest flexibility that permits the degree of polynomial to vary for any desired accuracy without imposing any limitations on the number of lambda values.

A New Integration Method Proposed for Hyperbolic Sine Constitutive Equation Used in Semi-Solid Forming

This paper describes a new integration algorithm for hyperbolic sine constitutive equation (HSCE) used in semi-solid forming. An intermediate variable Lambda ranged from zero to one is introduced to replace the inelastic strain rate in HSCE so that the inelastic strain rate can be solved indirectly from the Lambda. The proposed integration algorithm is based on the stress update concept and the effect of normal stress updating on the material compression is also discussed thoroughly in this paper. The investigation results show that the new algorithm can integrate the HSCE efficiently and the normal stress should keep constant as the deviatoric stress updating. An example of semi-solid extruding was given in the paper at last to illustrate the implementation of new algorithm and effect of normal stress updating on the compression of material.

Finite size scaling for the atomic Shannon-information entropy.

We have developed the finite size scaling method to treat the criticality of Shannon-information entropy for any given quantum Hamiltonian. This approach gives very accurate results for the critical parameters by using a systematic expansion in a finite basis set. To illustrate this approach we present a study to estimate the critical exponents of the Shannon-information entropy S approximately (lambda-lambda(c))(alpha(S) ), the electronic energy E approximately (lambda-lambda(c))(alpha(E) ), and the correlation length xi approximately mid R:lambda-lambda(c)mid R:(-nu) for atoms with the variable lambda=1/Z, which is the inverse of the nuclear charge Z. This was realized by approximating the multielectron atomic Hamiltonian with a one-electron model Hamiltonian. This model is very accurate for describing the electronic structure of the atoms near their critical points. For several atoms in their ground electronic states, we have found that the critical exponents (alpha(E),nu,alpha(S)) for He (Z=2), C (Z=6), N (Z=7), F (Z=9), and Ne (Z=10), respectively, are (1, 0, 0). At the critical points lambda(c)=1/Z(c), the bound state energies become absorbed or degenerate with continuum states and the entropies reach their maximum values, indicating a maximal delocalization of the electronic wave function.

Global nature of dilute-to-dense transition of granular flows in a 2D channel.

The dilute-to-dense transition of granular flow of particle size d(0) is studied experimentally in a two-dimensional channel (width D) with confined exit (width d). Our results show that with fixed d and D there is a maximum inflow rate Q(c) above which the flow changes from dilute to dense and the outflow rate <Q(t)> drops abruptly from Q(c) to a dense rate Q(d). A rescaled critical rate q(c) is found to be a function of a scaling variable lambda only: q(c) approximately F(lambda), where lambda identical with d/d(0) d/D-d. This form of lambda suggests that the dilute-to-dense transition is a global property of the flow, unlike the jamming transition which depends only on d/d(0). Furthermore, the transition is found to occur when the area fraction of particles near the exit exceeds a critical value which is close to 0.65+/-0.03.

Analysis of immunoglobulin light chain rearrangements in the salivary gland and blood of a patient with Sjögren's syndrome

Patients with Sjögren's syndrome (SS) have characteristic lymphocytic infiltrates of the salivary glands. To determine whether the B cells accumulating in the salivary glands of SS patients represent a distinct population and to delineate their potential immunopathologic impact, individual B cells obtained from the parotid gland and from the peripheral blood were analyzed for immunglobulin light chain gene rearrangements by PCR amplification of genomic DNA. The productive immunglobulin light chain repertoire in the parotid gland of the SS patient was found to be restricted, showing a preferential usage of particular variable lambda chain genes (Vλ2E) and variable kappa chain genes (VκA27). Moreover, clonally related VL chain rearrangements were identified; namely, VκA27–Jκ5 and VκA19–Jκ2 in the parotid gland, and Vλ1C–Jλ3 in the parotid gland and the peripheral blood. Vκ and Vλ rearrangements from the parotid gland exhibited a significantly elevated mutational frequency compared with those from the peripheral blood (P < 0.001). Mutational analysis revealed a pattern of somatic hypermutation similar to that found in normal donors, and a comparable impact of selection of mutated rearrangements in both the peripheral blood and the parotid gland. These data indicate that there is biased usage of VL chain genes caused by selection and clonal expansion of B cells expressing particular VL genes. In addition, the data document an accumulation of B cells bearing mutated VL gene rearrangements within the parotid gland of the SS patient. These results suggest a role of antigen-activated and selected B cells in the local autoimmune process in SS.

Twisted Traces of Quantum Intertwiners¶and Quantum Dynamical R-Matrices¶Corresponding to Generalized Belavin–Drinfeld Triples

This paper is a continuation of math.QA/9907181 and math.QA/9908115. We consider traces of intertwiners between certain representations of the quantized enveloping algebra associated to a semisimple complex Lie algebra g, which are twisted by a ``generalized Belavin-Drinfeld triple'', i.e a triple consisting of two subdiagrams of the Dynkin diagram of g together with an isomorphism between them. The generating functions F(lambda,mu) for such traces depend on two weights lambda and mu. We show that F(lambda,mu) satisfy two sets of difference equations in the variable lambda: the Macdonald-Ruijsenaars (MR) equations and the quantum Knizhnik-Zamolodchikov (qKZB) equations. These equations involve as a main ingredient the quantum dynamical R-matrices constructed in math.QA/9912009. When the generalized Belavin-Drinfeld triple is an automorphism, we show that F(lambda,mu) satisfy another two sets of difference equations with respect to the weight mu. These dual MR and dual qKZB equations involve the usual Felder's dynamical R-matrix. These results were first obtained by the first author and A. Varchenko in the special case of the trivial Belavin-Drinfeld triple. However, the symmetry between lambda and mu which exists in that case is destroyed in the twisted setting. At the end, we brielfly treat the (simialr) case of Kac-Moody algebras g and derive the classical limits of all the previous results.

The human immunoglobulin variable lambda locus IGLV9 gene is a monomorphic marker in the urban Brazilian population

The physical map of the human immunoglobulin variable lambda locus (IGLV) located on chromosome 22q11.1-q11.2 shows the existence of 52 functional V-lambda genes distributed among three V-clusters. The IGLV9S1 gene, located in the V–B cluster, is a sequence tagged site and is a useful marker for restriction fragment length polymorphism (RFLP) population studies. The V-lambda genes are associated in the genome with EcoRI fragments detectable in Southern blots of genomic DNA samples. We have analysed DNA samples of an urban Brazilian population by Southern- EcoRI-RFLP using an IGLV9 gene segment. Among 75 unrelated individuals analysed, we detected a single 6.0 kb EcoRI fragment containing the IGLV9 gene at 100% frequency. Reverse transcription followed by polymerase chain reaction (RT-PCR) of peripheral blood leukocyte total RNA from unrelated individuals showed that IGLV9S1 is a functional gene contributing to the B lymphocyte repertoire. These data represent evidence for monomorphism of the IGVL9S1 gene in this urban population. We demonstrate that IGLV9S1 is a functional single copy gene and is an important marker in the IGLV locus.

AN ANALYSIS OF EXPERIENCE REPLAY IN TEMPORAL DIFFERENCE LEARNING

Temporal difference TD methods are used by reinforcement learning algorithms for predicting future rewards. This article analyzes theoretically and illustrates experimentally the effects of performing TD lambda prediction udpates backwards for a number of past experiences. More exactly, two related techniques described in the literature are examined, referred to as replayed TD and backwards TD. The former is essentially an online learning method which performs at each time step a regular TD 0 update, and then replays updates backwards for a number of previous states. The latter operates in offline mode, after the end of a trial updating backwards the predictions for all visited states. They are both shown to be approximately equivalent to TD lambda with variable lambda values selected in a particular way. This is true even if they perform only TD 0 updates. The experimental results show that replayed TD 0 is competitive to TD lambda with regard to learning speed and quality.

A 37-kb restriction map of the human immunoglobulin lambda variable locus, VB cluster, harboring four functional genes and two non-coding V&lt;FONT FACE=Symbol&gt;l&lt;/font&gt; sequences

The human immunoglobulin lambda variable locus (IGLV) is mapped at chromosome 22 band q11.1-q11.2. The 30 functional germline v-lambda genes sequenced untill now have been subgrouped into 10 families (V&lt;FONT FACE="Symbol"&gt;l&lt;/font&gt;1 to V&lt;FONT FACE="Symbol"&gt;l&lt;/font&gt;10). The number of V&lt;FONT FACE="Symbol"&gt;l&lt;/font&gt; genes has been estimated at approximately 70. This locus is formed by three gene clusters (VA, VB and VC) that encompass the variable coding genes (V) responsible for the synthesis of lambda-type Ig light chains, and the J&lt;FONT FACE="Symbol"&gt;l&lt;/font&gt;-C&lt;FONT FACE="Symbol"&gt;l&lt;/font&gt; cluster with the joining segments and the constant genes. Recently the entire variable lambda gene locus was mapped by contig methodology and its one- megabase DNA totally sequenced. All the known functional V-lambda genes and pseudogenes were located. We screened a human genomic DNA cosmid library and isolated a clone with an insert of 37 kb (cosmid 8.3) encompassing four functional genes (IGLV7S1, IGLV1S1, IGLV1S2 and IGLV5a), a pseudogene (V&lt;FONT FACE="Symbol"&gt;l&lt;/font&gt;A) and a vestigial sequence (vg1) to study in detail the positions of the restriction sites surrounding the V&lt;FONT FACE="Symbol"&gt;l&lt;/font&gt; genes. We generated a high resolution restriction map, locating 31 restriction sites in 37 kb of the VB cluster, a region rich in functional V&lt;FONT FACE="Symbol"&gt;l&lt;/font&gt; genes. This mapping information opens the perspective for further RFLP studies and sequencing

EcoRI Restriction Fragment-Length Polymorphism of the Human Immunoglobulin Variable Lambda 8 (IGLV8) Subgroup Reveals a Gene Family

The human immunoglobulin lambda locus (IGL) maps on chromosome 22q11.1–q11.2 and directs the synthesis of lambda-type Ig light chains. This locus is formed by three gene clusters (VA, VB and VC) that encompass the variable coding genes and the J-C cluster plus the joining segments and the constant genes. Recently the variable lambda gene clusters were mapped by the contig methodology which located all the known functional v-lambda genes and pseudogenes. The 30 functional v-lambda genes described so far were subgrouped into ten families (VλI to VλX), but RFLP studies have estimated that the germline repertoire contains about 70 genes. Based on sequence comparisons, we defined specific oligonucleotide primers for the unique IGLV8S1 genedescribed. The cloned 244 bp product obtained from genomic DNA with these primers was sequenced and used as probe in Southern hybridization EcoRI RFLP analysis of Brazilian people. We detected the IGLV8S1 gene in a 3.7 kb EcoRI restriction fragment present in all the individuals analyzed, in agreement with the physical map of the IGL locus. Moreover, we detected an 8.0 kb EcoRI monomorphic fragment and a 6.0 kb EcoRI polymorphic fragment. These data suggest that the IGLV8 subgroup is a gene family.

Genomic organisation of 34 kb of the human immunoglobulin lambda locus (IGLV): Restriction map and sequences of new Vλ III genes

In order to improve our knowledge of the human immunoglobulin variable lambda locus (IGLV), we mapped one cosmid clone (designated as C40.2) isolated by screening a Colo320HSR genomic library. The 34 kb insert of the C40.2 clone was shown to contain six genes. One gene, IGLV2S1, belongs to the VλII subgroup. Four genes belong to the VλIII subgroup. Two of them, IGLV3S1 and IGLV3S2, are potentially functional whereas the two others are pseudogenes. The size of the IGLV3S2 leader intron is four times longer than the classical intron size of 110 bp. The cosmid also contains a vestigial sequence λvg2. All these genes share the same orientation of transcription. Pulsed field gel electrophoresis analysis of the IGLV locus shows that most of the Vλ I subgroup genes are located at the 5' end of the locus.

Rapid detection of antigen binding by antibody fragments expressed in the periplasm of Escherichia coli

Bacterial expression systems can greatly facilitate protein engineering of antibodies. We have developed a system for high-level expression of antibodies, antibody fragments, or hybrid antibodies with novel effector functions in the periplasm of Escherichia coli. From 5 ml of cells, a simple extraction yields sufficient material for SDS-gel electrophoresis, detection and characterization of hapten binding. To demonstrate our system, heavy-chain variable regions and lambda 1 light chains of a mouse anti-NP antibody were synthesized as hybrid proteins with a bacterial signal peptide (Omp F). Each chain is secreted into the periplasm where processing (cleavage of the signal peptide), folding and heterodimer association take place. Periplasmic proteins are released by cold osmotic shock, and hapten-binding activity is easily detected without further manipulation. The ease of genetic engineering in this system will facilitate the production of immunoglobulin derivatives designed for specific applications, and expression of these molecules in a native state will allow the rapid screening of combinatorial libraries and the results of mutagenesis.

Definition of the human immunoglobulin variable lambda (IGLV) gene subgroups

Comparison of 60 human immunoglobulin variable lambda (IGLV) sequences allowed us to define seven subgroups designated V lambda I to V lambda VII. We demonstrate that all lambda proteins sequenced so far fall into the subgroups I, II, III and VI, and that the lambda regions previously assigned to subgroups IV and V belong, in fact, to subgroups III and II, respectively. Four sequences not belonging to any of the subgroups I, II, III and VI define the new subgroups IV, V and VII. Interestingly, these subgroups show a higher homology to rabbit or mouse V lambda genes than to the other human V lambda subgroups. By comparison of the proteins either with the sequences deduced from the germ-line genes or with the consensus sequences, the rate of amino acid changes due to somatic mutations or allelic variations was evaluated in several lambda proteins. Framework and complementarity-determining regions of the human IGLV genes and proteins were delineated. Alignment of the lambda sequences shows that functional V-J rearrangement occurs, with or without deletion of nucleotides encoding one or two amino acids at the 3' end of the V gene. Diversity of the third complementarity-determining region is due to somatic mutations and to flexible V-J junction, but there is no evidence of N-diversity in the human lambda locus.

First genomic sequence of a human lg variable lambda gene belonging to subgroup III

First genomic sequence of a human lg variable lambda gene belonging to subgroup III