A subgroup of coeliac disease patients continues to experience symptoms even on a gluten-free diet (GFD). We attempted to determine whether these symptoms could be due to either cross-contamination with gluten-containing foods or cross-reactivity between α-gliadin and non-gluten foods consumed on a GFD. We measured the reactivity of affinity-purified polyclonal and monoclonal α-gliadin 33-mer peptide antibodies against gliadin and additional food antigens commonly consumed by patients on a GFD using ELISA and dot-blot. We also examined the immune reactivity of these antibodies with various tissue antigens. We observed significant immune reactivity when these antibodies were applied to cow’s milk, milk chocolate, milk butyrophilin, whey protein, casein, yeast, oats, corn, millet, instant coffee and rice. To investigate whether there was cross-reactivity between α-gliadin antibody and different tissue antigens, we measured the degree to which this antibody bound to these antigens. The most significant binding occurred with asialoganglioside, hepatocyte, glutamic acid decarboxylase 65, adrenal 21-hydroxylase, and various neural antigens. The specificity of anti-α-gliadin binding to different food and tissue antigens was demonstrated by absorption and inhibition studies. We also observed significant cross-reactivity between α-gliadin 33-mer and various food antigens, but some of these reactions were associated with the contamination of non-gluten foods with traces of gluten. The consumption of cross-reactive foods as well as gluten-contaminated foods may be responsible for the continuing symptoms presented by a subgroup of patients with coeliac disease. The lack of response of some CD patients may also be due to antibody cross-reactivity with non-gliadin foods. These should then be treated as gluten-like peptides and should also be excluded from the diet when the GFD seems to fail.

Abstract:
Matrix elements of a two-body interaction between states of the jn configutation (n identical nucleons in the j-orbit) are functions of two-body energies. In some cases, diagonal matrix elements are linear combinations of two-body energies. The coefficients of these linear combinations are rational and non-negative numbers, independent of the two-body interaction. It is shown that if in the jn configuration there is only one state with given spin J, its eigenvalue (the diagonal matrix element) is equal to a linear combination of two-body energies with rational and non-negative coefficients. These coefficients have the same values for any two-body interaction (solvable eigenvalues). If there are several J-states in the jn configuration, they define a sub-matrix of the interaction which should be diagonalized to yield eigenvalues and eigenstates. Bases of these states are constructed from which the sub-matrix characterized by J may be obtained for any two-body interaction. The diagonal elements are linear combinations of two-body energies whose coefficients are independent of the two-body interaction and the non-vanishing ones are rational and positive. Aslo in the non-diagonal elements the coefficients have a simple form. States in the seniority scheme are shown to form such bases. If one of them is an eigenstate of any two-body interaciton its eigenvalue is shown to be solvable.

Abstract:
Eigenvalues of eigenstates in jn configurations (n identical nucle- ons in the j -orbit) are functions of two-body energies. In some cases they are linear combinations of two-body energies whose coe+/-cients are independent of the interaction and are rational non-negative num- bers. It is shown here that a state which is an eigenstate of any two-body interaction has this solvability property. This includes, in particular, any state with spin J if there are no other states with this J in the jn configuration. It is also shown that eigenstates with solvable eigenvalues have definite seniority v and thus, exhibit partial dynamical symmetry.

Abstract:
This paper is focused on the derivation of some universal properties of capacity-approaching low-density parity-check (LDPC) code ensembles whose transmission takes place over memoryless binary-input output-symmetric (MBIOS) channels. Properties of the degree distributions, graphical complexity and the number of fundamental cycles in the bipartite graphs are considered via the derivation of information-theoretic bounds. These bounds are expressed in terms of the target block/ bit error probability and the gap (in rate) to capacity. Most of the bounds are general for any decoding algorithm, and some others are proved under belief propagation (BP) decoding. Proving these bounds under a certain decoding algorithm, validates them automatically also under any sub-optimal decoding algorithm. A proper modification of these bounds makes them universal for the set of all MBIOS channels which exhibit a given capacity. Bounds on the degree distributions and graphical complexity apply to finite-length LDPC codes and to the asymptotic case of an infinite block length. The bounds are compared with capacity-approaching LDPC code ensembles under BP decoding, and they are shown to be informative and are easy to calculate. Finally, some interesting open problems are considered.

Abstract:
This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random variable with the same mean are derived. The derivation of these bounds combines elements of information theory with the Chen-Stein method for Poisson approximation. The resulting bounds are easy to compute, and their applicability is exemplified. This conference paper presents in part the first half of the paper entitled "An information-theoretic perspective of the Poisson approximation via the Chen-Stein method" (see:arxiv:1206.6811). A generalization of the bounds that considers the accuracy of the Poisson approximation for the entropy of a sum of non-negative, integer-valued and bounded random variables is introduced in the full paper. It also derives lower bounds on the total variation distance, relative entropy and other measures that are not considered in this conference paper.

Abstract:
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal coupling, and they apply to discrete random variables which are defined over finite or countably infinite alphabets. Loosened versions of these bounds are demonstrated to reproduce some previously reported results. The use of the new bounds is exemplified for the Poisson approximation, where bounds on the local and total variation distances follow from Stein's method.

Abstract:
New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.

Abstract:
This is a survey paper with some original results of the author on refined versions of the Azuma-Hoeffding inequality with some examples that are related to information theory. This work has evolved to the joint paper with Maxim Raginsky in arXiv:1212.4663v3.

Abstract:
This paper is focused on the moderate-deviations analysis of binary hypothesis testing. The analysis relies on a concentration inequality for discrete-parameter martingales with bounded jumps, where this inequality forms a refinement to the Azuma-Hoeffding inequality. Relations of the analysis to the moderate deviations principle for i.i.d. random variables and to the relative entropy are considered.