The structure of the infinite models in integer programming

The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our results have implications for corner polyhedra. One consequence is that nonnegative, continuous valid functions suffice to describe corner polyhedra (with or without rational data)

Software for cut-generating functions in the Gomory--Johnson model and beyond

We present software for investigations with cut generating functions in the Gomory-Johnson model and extensions, implemented in the computer algebra system SageMath.Comment: 8 pages, 3 figures; to appear in Proc. International Congress on Mathematical Software 201

Chain Reduction for Binary and Zero-Suppressed Decision Diagrams

Chain reduction enables reduced ordered binary decision diagrams (BDDs) and zero-suppressed binary decision diagrams (ZDDs) to each take advantage of the others' ability to symbolically represent Boolean functions in compact form. For any Boolean function, its chain-reduced ZDD (CZDD) representation will be no larger than its ZDD representation, and at most twice the size of its BDD representation. The chain-reduced BDD (CBDD) of a function will be no larger than its BDD representation, and at most three times the size of its CZDD representation. Extensions to the standard algorithms for operating on BDDs and ZDDs enable them to operate on the chain-reduced versions. Experimental evaluations on representative benchmarks for encoding word lists, solving combinatorial problems, and operating on digital circuits indicate that chain reduction can provide significant benefits in terms of both memory and execution time

A consistent model for leptogenesis, dark matter and the IceCube signal

We discuss a left-right symmetric extension of the Standard Model in which the three additional right-handed neutrinos play a central role in explaining the baryon asymmetry of the Universe, the dark matter abundance and the ultra energetic signal detected by the IceCube experiment. The energy spectrum and neutrino flux measured by IceCube are ascribed to the decays of the lightest right-handed neutrino $N_1$, thus fixing its mass and lifetime, while the production of $N_1$ in the primordial thermal bath occurs via a freeze-in mechanism driven by the additional $SU(2)_R$ interactions. The constraints imposed by IceCube and the dark matter abundance allow nonetheless the heavier right-handed neutrinos to realize a standard type-I seesaw leptogenesis, with the $B-L$ asymmetry dominantly produced by the next-to-lightest neutrino $N_2$. Further consequences and predictions of the model are that: the $N_1$ production implies a specific power-law relation between the reheating temperature of the Universe and the vacuum expectation value of the $SU(2)_R$ triplet; leptogenesis imposes a lower bound on the reheating temperature of the Universe at 7\times10^9\,\mbox{GeV}. Additionally, the model requires a vanishing absolute neutrino mass scale $m_1\simeq0$.Comment: 19 pages, 4 figures. Constraints from cosmic-ray antiprotons and gamma rays added, with hadrophobic assignment of the matter multiplets to satisfy bounds. References added. Matches version published in JHE

Ontogeny influences sensitivity to climate change stressors in an endangered fish.

Coastal ecosystems are among the most human-impacted habitats globally, and their management is often critically linked to recovery of declining native species. In the San Francisco Estuary, the Delta Smelt (Hypomesus transpacificus) is an endemic, endangered fish strongly tied to Californian conservation planning. The complex life history of Delta Smelt combined with dynamic seasonal and spatial abiotic conditions result in dissimilar environments experienced among ontogenetic stages, which may yield stage-specific susceptibility to abiotic stressors. Climate change is forecasted to increase San Francisco Estuary water temperature and salinity; therefore, understanding the influences of ontogeny and phenotypic plasticity on tolerance to these critical environmental parameters is particularly important for Delta Smelt and other San Francisco Estuary fishes. We assessed thermal and salinity limits in several ontogenetic stages and acclimation states of Delta Smelt, and paired these data with environmental data to evaluate sensitivity to climate-change stressors. Thermal tolerance decreased among successive stages, with larval fish exhibiting the highest tolerance and post-spawning adults having the lowest. Delta Smelt had limited capacity to increase tolerance through thermal acclimation, and comparisons with field temperature data revealed that juvenile tolerance limits are the closest to current environmental conditions, which may make this stage especially susceptible to future climate warming. Maximal water temperatures observed in situ exceeded tolerance limits of juveniles and adults. Although these temperature events are currently rare, if they increase in frequency as predicted, it could result in habitat loss at these locations despite other favourable conditions for Delta Smelt. In contrast, Delta Smelt tolerated salinities spanning the range of expected environmental conditions for each ontogenetic stage, but salinity did impact survival in juvenile and adult stages in exposures over acute time scales. Our results underscore the importance of considering ontogeny and phenotypic plasticity in assessing the impacts of climate change, particularly for species adapted to spatially and temporally heterogeneous environments

On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson infinite group problem

We investigate three competing notions that generalize the notion of a facet of finite-dimensional polyhedra to the infinite-dimensional Gomory-Johnson model. These notions were known to coincide for continuous piecewise linear functions with rational breakpoints. We show that two of the notions, extreme functions and facets, coincide for the case of continuous piecewise linear functions, removing the hypothesis regarding rational breakpoints. We then separate the three notions using discontinuous examples.Comment: 18 pages, 2 figure

Infrared Photometry and Dust Absorption in Highly Inclined Spiral Galaxies

We present JHK surface photometry of 15 highly inclined, late-type (Sab-Sc) spirals and investigate the quantitative effects of dust extinction. Using the (J - H, H - K) two-color diagram, we compare the color changes along the minor axis of each galaxy to the predictions from different models of radiative transfer. Models in which scattering effects are significant and those with more than a small fraction of the light sources located near the edge of the dust distribution do not produce enough extinction to explain the observed color gradients across disk absorption features. The optical depth in dust near the plane as deduced from the color excess depends sensitively on the adopted dust geometry, ranging from tau = 4 to 15 in the visual band. This suggests that a realistic model of the dust distribution is required, even for infrared photometry, to correct for dust extinction in the bulges of nearly edge-on systems.Comment: Accepted for publication in the March 1996 AJ. LaTex source which generates 27 pages of text and tables (no figures). Complete (text + figs) compressed Postscript preprint is also available at ftp://bessel.mps.ohio-state.edu/pub/terndrup/inclined.ps.Z (854 Mbyte

Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result