Petri Nets for Concurrent Programming

Concurrent programming is used in all large and complex computer systems. However, concurrency errors and system failures (ex: crashes and deadlocks) are common. We find that Petri nets can be used to model concurrent systems and find and remove errors ahead of time. We introduce a novel generalization of Petri nets with nondeterministic transition nodes to match real systems. These allow for a compact way to construct, optimize, and prove computer programs at the concurrency level. Petri net programs can also be optimized by automatically solving for maximal concurrency, where the maximum number of valid threads is determined by the structure of the Petri net prior to execution. We discuss an algorithm to compute the state graph of a given Petri net start state pair. We introduce our open source software framework which implements this theory as a general purpose concurrency focused middle-ware

The synthesis and reactivity of some 1,2,3,5 - and 1,3,2,4-dithiadiazolium salts

The reaction of N(SCI)2(^+) salts with SnCl(_2) provided a new route to the SNS(^+) synthon; an important reagent in the synthesis of inorganic sulphur-nitrogen containing heterocycles. The reactions of C(_6)H(_5)CN and C(_6)H(_5)CN with a variety of SNS(^+) salts (AsF(_6)-, SbCl(_6)" and AICI(_4)-) were examined. Both [SNS]AsF(_6)] and [SNS][SbCI(_6)] reacted in high yield to give the 1,3,2,4-dithiadiazolium salts (Ar.CNSNS(^+)) whereas [SNS][AICI(_4)] did not readily provide the analagous heterocycle. Reduction of these 1,3,2,4-dithiadiazolium cations provided the isostructural 1,3,2,4-dithiadiazole radicals which then underwent rearrangement to the 1,2,3,5-dithiadiazole. This isomerisation process was monitored by e.s.r. spectroscopy. Reaction of two or three equivalents of[SNS][AsF(_6)] with dicyanoaromatics (o,m and p- C(_6)H(_4)(CN)(_2), NC.C(_6)H(_4).C(_6)H(_4).CN and p-C(_6)F(_4)(CN)(_2)) or 1,3,5-tricyanobenzene yielded the novel bis- and tris-(dithiadiazolium) cations respectively. 1,4-phenylene bis(1-,3,2,4-dithiadiazolium) hexafluoroarsenate(V) was readily converted to a variety of other salts by anion metathesis and its reduction yielded the neutral bis(dithiadiazole) which was characterised by a single crystal X-ray structure determination. Reaction of 4-phenyl-1,2,3,5-dithiadiazolium hexafluoroarsenate(V) with [Et(_4)N][Pt(mnt)(_2)] and [Et(_4)N](_2)[Pt(mnt)(_2)] produced [PhCN(_2)S(_2)][Pt(mnt)(_2)] and [PhCN(_2)S(_2)](_2)[Pt(mnt)(_2)] respectively; the latter compound was characterised by an X- ray structure. The reaction of [PhCN(_2)S(_2)]CI with [Et(_4N][Pt(mnt)(_2)] in the presence of excess [PhCN(_2)S(_2)]CI yielded [(PhCN(_2)S(_2))(_2)CI][Pt(mnt)(_2)] . Crystals of the analogous compound, [(p-Cl.C(_6)H(_4).CNSSN)(_2)CI][Pt(mnt)(_2)] , were large enough for an X-ray structure determination and this provided the second example of the planar cation, [(ArCN(_2)S(_2))(_2)CI](^+).In comparison the reaction of phenyldithiadlazole, (PhCN2S2)2. with Pd(PPh(_3))(_4) led to the formation of Pd(_3)(PhCN(_2)S(_2))(_2)(PPh(_3))(_3); the solid state structure of which shows three square planar Pd centres held together by two bridging PhCN(_2)S(_2) ligands

Reproducing Kernel Hilbert Space Pruning for Sparse Hyperspectral Abundance Prediction

Hyperspectral measurements from long range sensors can give a detailed picture of the items, materials, and chemicals in a scene but analysis can be difficult, slow, and expensive due to high spatial and spectral resolutions of state-of-the-art sensors. As such, sparsity is important to enable the future of spectral compression and analytics. It has been observed that environmental and atmospheric effects, including scattering, can produce nonlinear effects posing challenges for existing source separation and compression methods. We present a novel transformation into Hilbert spaces for pruning and constructing sparse representations via non-negative least squares minimization. Then we introduce max likelihood compression vectors to decrease information loss. Our approach is benchmarked against standard pruning and least squares as well as deep learning methods. Our methods are evaluated in terms of overall spectral reconstruction error and compression rate using real and synthetic data. We find that pruning least squares methods converge quickly unlike matching pursuit methods. We find that Hilbert space pruning can reduce error by as much as 40% of the error of standard pruning and also outperform neural network autoencoders

Lemmas: Generation, Selection, Application

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates useful lemmas for automated theorem provers, demonstrating improvement for several representative systems and solving a hard problem not solved by any system for twenty years. By focusing on condensed detachment problems we simplify the setting considerably, allowing us to get at the essence of lemmas and their role in proof search

Formal Concept Lattice Representations and Algorithms for Hypergraphs

There is increasing focus on analyzing data represented as hypergraphs, which are better able to express complex relationships amongst entities than are graphs. Much of the critical information about hypergraph structure is available only in the intersection relationships of the hyperedges, and so forming the "intersection complex" of a hypergraph is quite valuable. This identifies a valuable isomorphism between the intersection complex and the "concept lattice" formed from taking the hypergraph's incidence matrix as a "formal context": hypergraphs also generalize graphs in that their incidence matrices are arbitrary Boolean matrices. This isomorphism allows connecting discrete algorithms for lattices and hypergraphs, in particular s-walks or s-paths on hypergraphs can be mapped to order theoretical operations on the concept lattice. We give new algorithms for formal concept lattices and hypergraph s-walks on concept lattices. We apply this to a large real-world dataset and find deep lattices implying high interconnectivity and complex geometry of hyperedges

The influence of high school calculus on student success in calculus at Kansas State University

Call number: LD2668 .R4 1967 R3

A new approach to the chronology of caves 268/272/275 in the Dunhuang Mogao Grottoes: combining radiocarbon dates and archaeological information within a Bayesian statistical framework

The construction chronology of three of the earliest Dunhuang Mogao Grottoes (Caves 268, 272, and 275) has been the subject of ongoing debate for over half a century. This chronology is a crucial topic in terms of further understanding of the establishment of the Dunhuang Mogao Grottoes, early Buddhism in the Gansu corridor, and its relationship with Buddhism developed in the Central Plains. Building upon archaeological, art historical and radiocarbon (14C) dating studies, we integrate new 14C data with these previously published findings utilizing Bayesian statistical modeling to improve the chronological resolution of this issue. Thus, we determine that all three of these caves were constructed around AD 410–440, suggesting coeval rather than sequential construction