On the reconstruction of planar lattice-convex sets from the covariogram

A finite subset $K$ of $\mathbb{Z}^d$ is said to be lattice-convex if $K$ is the intersection of $\mathbb{Z}^d$ with a convex set. The covariogram $g_K$ of $K\subseteq \mathbb{Z}^d$ is the function associating to each u \in \integer^d the cardinality of $K\cap (K+u)$. Daurat, G\'erard, and Nivat and independently Gardner, Gronchi, and Zong raised the problem on the reconstruction of lattice-convex sets $K$ from $g_K$. We provide a partial positive answer to this problem by showing that for $d=2$ and under mild extra assumptions, $g_K$ determines $K$ up to translations and reflections. As a complement to the theorem on reconstruction we also extend the known counterexamples (i.e., planar lattice-convex sets which are not reconstructible, up to translations and reflections) to an infinite family of counterexamples.Comment: accepted in Discrete and Computational Geometr

The structure of quantum Lie algebras for the classical series B_l, C_l and D_l

The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at $q=1$. We explain the relationship between the structure constants of quantum Lie algebras and quantum Clebsch-Gordan coefficients for adjoint x adjoint ---> adjoint. We present a practical method for the determination of these quantum Clebsch-Gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum Lie algebras associated to the classical Lie algebras B_l, C_l and D_l. In the quantum case also the structure constants of the Cartan subalgebra are non-zero and we observe that they are determined in terms of the simple quantum roots. We introduce an invariant Killing form on the quantum Lie algebras and find that it takes values which are simple q-deformations of the classical ones.Comment: 25 pages, amslatex, eepic. Final version for publication in J. Phys. A. Minor misprints in eqs. 5.11 and 5.12 correcte

Bronze Wheat

The years following the severe losses in yield of winter wheat due to stem rust in 1962 and 1963 have seen the release for production of many varieties that resist stem rust. The South Dakota Agricultural Experiment Station released Hume and Winoka and also joined in testing and release of rust resistant varieties developed in neighboring states. The breeding objective in the South Dakota program has been to select early, especially hardy, medium to short strawed lines having resistance to both stem and leaf rust, of good milling and baking qualities and of good yield and test weight. The success of such a program should enable growers to use fall sown wheat ever farther northward and eastward in this state. That such an objective is especially difficult is apparent from the fact that no one has yet developed a variety having to a significant degree all of those qualities. The ability to tiller heavily to fill out a stand depleted by winter losses also is an important trait

Correlations between hidden units in multilayer neural networks and replica symmetry breaking

We consider feed-forward neural networks with one hidden layer, tree architecture and a fixed hidden-to-output Boolean function. Focusing on the saturation limit of the storage problem the influence of replica symmetry breaking on the distribution of local fields at the hidden units is investigated. These field distributions determine the probability for finding a specific activation pattern of the hidden units as well as the corresponding correlation coefficients and therefore quantify the division of labor among the hidden units. We find that although modifying the storage capacity and the distribution of local fields markedly replica symmetry breaking has only a minor effect on the correlation coefficients. Detailed numerical results are provided for the PARITY, COMMITTEE and AND machines with K=3 hidden units and nonoverlapping receptive fields.Comment: 9 pages, 3 figures, RevTex, accepted for publication in Phys. Rev.

Intraoral Microbial Metabolism and Association with Host Taste Perception

Metabolomics has been identified as a means of functionally assessing the net biological activity of a particular microbial community. Considering the oral microbiome, such an approach remains largely underused. While the current knowledge of the oral microbiome is constantly expanding, there are several deficits in knowledge particularly relating to their interactions with their host. This work uses nuclear magnetic resonance spectroscopy to investigate metabolic differences between oral microbial metabolism of endogenous (i.e., salivary protein) and exogenous (i.e., dietary carbohydrates) substrates. It also investigated whether microbial generation of different metabolites may be associated with host taste perception. This work found that in the absence of exogenous substrate, oral bacteria readily catabolize salivary protein and generate metabolic profiles similar to those seen in vivo. Important metabolites such as acetate, butyrate, and propionate are generated at relatively high concentrations. Higher concentrations of metabolites were generated by tongue biofilm compared to planktonic salivary bacteria. Thus, as has been postulated, metabolite production in proximity to taste receptors could reach relatively high concentrations. In the presence of 0.25 M exogenous sucrose, increased catabolism was observed with increased concentrations of a range of metabolites relating to glycolysis (lactate, pyruvate, succinate). Additional pyruvate-derived molecules such as acetoin and alanine were also increased. Furthermore, there was evidence that individual taste sensitivity to sucrose was related to differences in the metabolic fate of sucrose in the mouth. High-sensitivity perceivers appeared more inclined toward continual citric acid cycle activity postsucrose, whereas low-sensitivity perceivers had a more efficient conversion of pyruvate to lactate. This work collectively indicates that the oral microbiome exists in a complex balance with the host, with fluctuating metabolic activity depending on nutrient availability. There is preliminary evidence of an association between host behavior (sweet taste perception) and oral catabolism of sugar.</p

Statistical mechanics of the multi-constraint continuous knapsack problem

We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem,which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large problem size, we analyse the space of solution and its volume, and estimate the optimal number of items to go into the knapsack as a function of the number of constraints. We study the stability of the replica symmetric (RS) solution and find that the RS calculation cannot estimate the optimal number of items in knapsack correctly if many constraints are required.In order to obtain a consistent solution in the RS region,we try the zero entropy approximation for this continuous solution space and get a stable solution within the RS ansatz.On the other hand, in replica symmetry breaking (RSB) region, the one step RSB solution is found by Parisi's scheme. It turns out that this problem is closely related to the problem of optimal storage capacity and of generalization by maximum stability rule of a spherical perceptron.Comment: Latex 13 pages using IOP style file, 5 figure

Analytical and Numerical Study of Internal Representations in Multilayer Neural Networks with Binary Weights

We study the weight space structure of the parity machine with binary weights by deriving the distribution of volumes associated to the internal representations of the learning examples. The learning behaviour and the symmetry breaking transition are analyzed and the results are found to be in very good agreement with extended numerical simulations.Comment: revtex, 20 pages + 9 figures, to appear in Phys. Rev.

Correlated patterns in non-monotonic graded-response perceptrons

The optimal capacity of graded-response perceptrons storing biased and spatially correlated patterns with non-monotonic input-output relations is studied. It is shown that only the structure of the output patterns is important for the overall performance of the perceptrons.Comment: 4 pages, 4 figure

Absence of anomalous negative lattice-expansion for polycrystalline sample of Tb2Ti2O7

High resolution X-ray powder-diffraction experiments on a well-characterized polycrystalline sample of the spin liquid Tb2Ti2O7 reveal that it shows normal positive thermal-expansion above 4 K, which does not agree with the intriguing anomalous negative thermal-expansion due to a magneto-elastic coupling reported for a single crystal sample below 20 K. We also performed a Rietveld profile refinement of a powder-diffraction pattern taken at a room temperature, and confirmed that it is consistent with the fully ordered cubic pyrochlore structure.Comment: 2 pages, 3 figure