Bad semidefinite programs: they all look the same

Conic linear programs, among them semidefinite programs, often behave pathologically: the optimal values of the primal and dual programs may differ, and may not be attained. We present a novel analysis of these pathological behaviors. We call a conic linear system $Ax <= b$ {\em badly behaved} if the value of $\sup { | A x <= b }$ is finite but the dual program has no solution with the same value for {\em some} $c.$ We describe simple and intuitive geometric characterizations of badly behaved conic linear systems. Our main motivation is the striking similarity of badly behaved semidefinite systems in the literature; we characterize such systems by certain {\em excluded matrices}, which are easy to spot in all published examples. We show how to transform semidefinite systems into a canonical form, which allows us to easily verify whether they are badly behaved. We prove several other structural results about badly behaved semidefinite systems; for example, we show that they are in $NP \cap co-NP$ in the real number model of computing. As a byproduct, we prove that all linear maps that act on symmetric matrices can be brought into a canonical form; this canonical form allows us to easily check whether the image of the semidefinite cone under the given linear map is closed.Comment: For some reason, the intended changes between versions 4 and 5 did not take effect, so versions 4 and 5 are the same. So version 6 is the final version. The only difference between version 4 and version 6 is that 2 typos were fixed: in the last displayed formula on page 6, "7" was replaced by "1"; and in the 4th displayed formula on page 12 "A_1 - A_2 - A_3" was replaced by "A_3 - A_2 - A_1

Assessing Alternatives for Directional Detection of a WIMP Halo

The future of direct terrestrial WIMP detection lies on two fronts: new, much larger low background detectors sensitive to energy deposition, and detectors with directional sensitivity. The former can large range of WIMP parameter space using well tested technology while the latter may be necessary if one is to disentangle particle physics parameters from astrophysical halo parameters. Because directional detectors will be quite difficult to construct it is worthwhile exploring in advance generally which experimental features will yield the greatest benefits at the lowest costs. We examine the sensitivity of directional detectors with varying angular tracking resolution with and without the ability to distinguish forward versus backward recoils, and compare these to the sensitivity of a detector where the track is projected onto a two-dimensional plane. The latter detector regardless of where it is placed on the Earth, can be oriented to produce a significantly better discrimination signal than a 3D detector without this capability, and with sensitivity within a factor of 2 of a full 3D tracking detector. Required event rates to distinguish signals from backgrounds for a simple isothermal halo range from the low teens in the best case to many thousands in the worst.Comment: 4 pages, including 2 figues and 2 tables, submitted to PR

The occurrence of the extinct shark genus Sphenodus in the Jurassic of Sicily

During the systematic revision of some historical collections containing Mesozoic ammonites, housed at the "G.G. Gemmellaro" Geological Museum of the Palermo University, a fossil shark’s tooth has been discovered. This specimen, indicated as Lamna in the original catalogue, can be attributed to the genus Sphenodus, an extinct cosmopolitan shark ranging from Lower Jurassic rocks to the Paleocene. The specimen is part of the Mariano Gemmellaro Collection which mainly consists of Middle-Upper Jurassic ammonites coming from Tardàra Mountain, between Menfi and Sambuca di Sicilia (Agrigento Province, Southwestern Sicily). Some of the ammonite specimens were listed, but not illustrated, by M. Gemmellaro in a note of 1919. The succession described in this area consists (from bottom to the top) of Lower Jurassic shallow-water carbonates followed by condensed ammonitic limestones of “Rosso ammonitico-type” (Middle-Late Jurassic in age), Calpionellid limestones (Upper Jurassic-Lower Cretaceous) and cherty calcilutites of Scaglia-type (Upper Cretaceous-Eocene). Since the exact stratigraphic level from which the shark tooth comes is not recorded, a thin section was made of the rock matrix surrounding the tooth. The sedimentological and paleontological analysis of the thin section has highlighted the presence of a microfacies characteristic of the Upper Jurassic condensed deposits of Rosso ammonitico-type, data that fits very well with the geology of the Tardàra area. The study of the Tardàra shark’s tooth has provided both the stimulus and opportunity to undertake a taxonomic review of the Jurassic specimens of Sphenodus collected from a range of Sicilian localities (Gemmellaro G.G., 1871; Seguenza G., 1887; Di Stefano & Cortese, 1891; Seguenza L., 1900; De Gregorio A., 1922) that, to date, have not been re-examined in the light of more recent scholarship. In particular, the specimens described and illustrated by G.G. Gemmellaro (1871), and stored in his eponymous museum, have been revised with the aim of providing a contribution to our knowledge of the genus Sphenodus in the Sicilian Mesozoic successions

Discrete complex analysis on planar quad-graphs

We develop a linear theory of discrete complex analysis on general quad-graphs, continuing and extending previous work of Duffin, Mercat, Kenyon, Chelkak and Smirnov on discrete complex analysis on rhombic quad-graphs. Our approach based on the medial graph yields more instructive proofs of discrete analogs of several classical theorems and even new results. We provide discrete counterparts of fundamental concepts in complex analysis such as holomorphic functions, derivatives, the Laplacian, and exterior calculus. Also, we discuss discrete versions of important basic theorems such as Green's identities and Cauchy's integral formulae. For the first time, we discretize Green's first identity and Cauchy's integral formula for the derivative of a holomorphic function. In this paper, we focus on planar quad-graphs, but we would like to mention that many notions and theorems can be adapted to discrete Riemann surfaces in a straightforward way. In the case of planar parallelogram-graphs with bounded interior angles and bounded ratio of side lengths, we construct a discrete Green's function and discrete Cauchy's kernels with asymptotics comparable to the smooth case. Further restricting to the integer lattice of a two-dimensional skew coordinate system yields appropriate discrete Cauchy's integral formulae for higher order derivatives.Comment: 49 pages, 8 figure

Functional Maps Representation on Product Manifolds

We consider the tasks of representing, analyzing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace--Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.Comment: Accepted to Computer Graphics Foru

AltitudeOmics : Resetting of Cerebrovascular CO2 Reactivity Following Acclimatization to High Altitude.

Previous studies reported enhanced cerebrovascular CO2 reactivity upon ascent to high altitude using linear models. However, there is evidence that this response may be sigmoidal in nature. Moreover, it was speculated that these changes at high altitude are mediated by alterations in acid-base buffering. Accordingly, we reanalyzed previously published data to assess middle cerebral blood flow velocity (MCAv) responses to modified rebreathing at sea level (SL), upon ascent (ALT1) and following 16 days of acclimatization (ALT16) to 5260 m in 21 lowlanders. Using sigmoid curve fitting of the MCAv responses to CO2, we found the amplitude (95 vs. 129%, SL vs. ALT1, 95% confidence intervals (CI) [77, 112], [111, 145], respectively, P = 0.024) and the slope of the sigmoid response (4.5 vs. 7.5%/mmHg, SL vs. ALT1, 95% CIs [3.1, 5.9], [6.0, 9.0], respectively, P = 0.026) to be enhanced at ALT1, which persisted with acclimatization at ALT16 (amplitude: 177, 95% CI [139, 215], P &lt; 0.001; slope: 10.3%/mmHg, 95% CI [8.2, 12.5], P = 0.003) compared to SL. Meanwhile, the sigmoidal response midpoint was unchanged at ALT1 (SL: 36.5 mmHg; ALT1: 35.4 mmHg, 95% CIs [34.0, 39.0], [33.1, 37.7], respectively, P = 0.982), while it was reduced by ~7 mmHg at ALT16 (28.6 mmHg, 95% CI [26.4, 30.8], P = 0.001 vs. SL), indicating leftward shift of the cerebrovascular CO2 response to a lower arterial partial pressure of CO2 (PaCO2) following acclimatization to altitude. Sigmoid fitting revealed a leftward shift in the midpoint of the cerebrovascular response curve which could not be observed with linear fitting. These findings demonstrate that there is resetting of the cerebrovascular CO2 reactivity operating point to a lower PaCO2 following acclimatization to high altitude. This cerebrovascular resetting is likely the result of an altered acid-base buffer status resulting from prolonged exposure to the severe hypocapnia associated with ventilatory acclimatization to high altitude

Late Viséan pelagic chondrichthyans from northern Europe

The relatively rich assemblages of shark teeth from pelagic limestone (Mississippian, late Viséan, late Asbian–middle Brigantian) of three northern European regions: the Rhenish Mountains (Westenfeld Quarry, Germany), the Holy Cross Mountains (Todowa Grz ą ba at the edge of Ostrówka Quarry, Poland), and Derbyshire (Cawdor Quarry, Matlock, England, UK) display certain similarities, with the absolute predominance of the teeth of Falcatidae (small Symmoriiformes) and the constant presence of Thrinacodus spp. The largest and most diverse assemblage from Todowa Grz ą ba contains at least three species of a falcatid Denaea , a xenacanthimorph Bransonella nebraskensis , a newly described phoebodontid Thrinacodus dziki sp. nov., a few ctenacanthiform and euselachian teeth, and two abraded euchondrocephalan dental elements. Anachronistidae, common in the most of late Viséan pelagic faunas, are absent from Todowa Grz ą ba and Westenfeld. The material under study differs from the shallow-water chondrichthyan fauna, hitherto described from the Mississippian carbonate platform facies, by its taxonomic content (particularly almost total absence of Euchondro- cephali), generally lower diversity, and higher frequency of small teet