OBDDs of a Monotone Function and Its Prime Implicants

Exact and truncated computations of prime implicants of coherent and non-coherent fault trees within Aralia

A comparison of fault trees and the Dynamic Flowgraph Methodology for the analysis of FPGA-based safety systems part 2: Theoretical investigations

Solving dynamic flowgraph methodology models using binary decision diagrams

We introduce a new hierarchy over monotone set functions, that we refer to as MPH (Maximum over Positive Hypergraphs). Levels of the hierarchy correspond to the degree of complementarity in a given function. The highest level of the hierarchy, MPH-m (where m is the total number of items) captures all monotone functions. The lowest level, MPH-1, captures all monotone submodular functions, and more generally, the class of functions known as XOS. Every monotone function that has a positive hypergraph representation of rank k (in the sense defined by Abraham, Babaioff, Dughmi and Roughgarden [EC 2012]) is in MPH-k. Every monotone function that has supermodular degree k (in the sense defined by Feige and Izsak [ITCS 2013]) is in MPH-(k+1). In both cases, the converse direction does not hold, even in an approximate sense. We present additional results that demonstrate the expressiveness power of MPH-k.One can obtain good approximation ratios for some natural optimization problems, provided that functions are required to lie in low levels of the MPH hierarchy. We present two such applications. One shows that the maximum welfare problem can be approximated within a ratio of k+1 if all players hold valuation functions in MPH-k. The other is an upper bound of 2k on the price of anarchy of simultaneous first price auctions.

Let I be a finite interval and r,s∈N. Given a set M, of functions defined on I, denote by Δ+sM the subset of all functions y∈M such that the s-difference Δτsy(⋅) is nonnegative on I, ∀τ>0. Further, denote by Δ+sWpr, the class of functions x on I with the seminorm ‖x(r)‖Lp≤1, such that Δτsx≥0, τ>0. Let Mn(hk):={∑i=1ncihk(wit−θi)∣ci,wi, θi∈R, be a single hidden layer perceptron univariate model with n units in the hidden layer, and activation functions hk(t)=t+k, t∈R, k∈N0. We give two-sided estimates both of the best unconstrained approximation E(Δ+sWpr,Mn(hk))Lq, k=r−1,r, s=0,1,...,r+1, and of the best s-monotonicity preserving approximation E(Δ+sWpr,Δ+sMn(hk))Lq, k=r−1,r, s=0,1,...,r+1. The most significant results are contained in theorem 2.2.

We consider exact learning of monotone Boolean functions by membership queries, in the case that only r of the n variables are relevant. The learner proceeds in a number of rounds. In each round he submits to the function oracle a set of queries which may be chosen depending on the results from previous rounds. In a STOC’98 paper we proved that O(2 r + r logn) queries in O(r) rounds are sufficient. While the query bound is optimal for trivial information-theoretic reasons, it was open whether parallelism can be improved without increasing the amount of queries. In the present paper we prove a negative answer:Θ(r) rounds are necessary in the worst case, even for learning a very special type of monotone function. The proof is an adversary argument, based on a distance inequality in binary codes. On the other hand, a Las Vegas strategy based on another STOC’98 result can learn monotone functions in 2log2 r + O(1) rounds, without using significantly more queries. We also study the constant factors in the deterministic case.

This article explores the algorithms for solving individual classes of discrete extremal problems to find the exact optimum. When obtaining algorithms, the procedures for decoding and finding the maximum upper zero of discrete monotonic functions are used. Formulations of the tasks of decoding and searching for the maximum upper zero of discrete monotonic functions are formulated. To solve the problems of decoding and searching for the maximum upper zero of individual classes of 3-digit monotonic functions, estimates are given for the complexity of deciphering monotonic functions in a class.

Partial functions of the k-valued logic monotone with respect to an arbitrary partially ordered set with the least and largest elements and distinct from a lattice are considered. It is shown that the set of closed classes of partial monotone functions containing a precomplete in Pk class of everywhere determined monotone function is infinite.

We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrangement-invariant class of functions; in the second one we find extremal values for the expectation of a random process with monotone trajectories at a random time. In both cases we reduce the continuous problems to their discrete counterparts. The obtained discrete problems are on the one hand interesting on their own, and on the other hand give a natural explanation of the structure of the extremal functions for the continuous problems.

New Erwinia carotovora‐specific and Erwinia carotovora ssp.carofovora‐specific primer sets were designed and thoroughly checked in order to estimate their usefulness in practical diagnostics of soft rot erwinias on different host plants. Both primer sets proved to be specific within Erwinia genus. They did not recognise any of bacterial isolates belonging to various taxonomical groups, including pectolytic Pseudomonas associated with soft‐rot. E.carotovora primer set gave positive results with all E.carotovota isolates and strains tested. Amplification of specific DNA fragment was observed also with E.rhapontici and E.cypripedii DNA but not with the DNA of E.chrysanthemi. PCR performed with Ecc primer set showed presence of specific DNA fragment in 86% of standard Ecc strains and 89% of biochemically typical Polish Ecc isolates. Specific band could also be detected with E.c.ssp.betavasculorum, E.c.ssp.wasabiae, E.c.ssp.odorifera, Exypripedii and E.rhapontici species. No amplification of DNA was observed with any of E.c.ssp.atroseptica strains and isolates tested nor with two E.chrysanthemi strains. About 50% of biochemically atypical E.carotovora isolates were identified by PCR to subspecies. The results show, that the specificity of our primers is very high (E.carotovora‐specific primer set) or comparatively high (Ecc‐specific primer set), therefore in polish environmental conditions, with Ecc and Eca as the main soft‐rot pathogens the PCR method based on these primers may be succesfully used for identification and differentiation of soft rot erwinias.

Genetic analysis of 111 samples from ceviche cocktails and fish fillets used for ceviche, obtained from fish markets and processing plants in the Pacific zone of Panama were conducted to determine species composition, trace origin (native, nonnative or imported frozen species) and CITES species status. A total of 21 species were detected (20 fishes and one invertebrate): Coryphaena hippurus (dolphin fish), Pangasianodon hypophthalmus (basa), Trachinotus falcatus (pompano), Cyclopsetta querna (toothed flounder), Atheresthes stomias (arrow-tooth flounder), Lobotes pacificus (Pacific tripletail), Bagre panamensis (Chihuil sea-catfish), B. bagre (Coco sea-catfish), Ariopsis seemanni (Tete sea-catfish), Aspistor luniscutis (yellow sea-catfish), Centropomus viridis (white snook), C. undecimalis (Union snook), Sphyrae naensis (Mexican barracuda), Oreochromis niloticus (Nile tilapia), O. mossambicus (Mozambique tilapia), Cynoscion praedatorius (Boccone weakfish), Protonibea diacanthus (blackspotted croaker), Gadus chalcogrammus (Alaska pollock), Sphyrna lewini (scalloped hammerhead shark), Makaira nigricans (blue marlin) and Dosidicus gigas (giant Humbolt squid). Native species found in ceviche samples were reduced in numbers compared with imported and cultivated ones. Thus, the most common detected fish species was basa, followed by the Nile tilapia and the dolphin fish. This is a positive result in terms of sustainability of local fisheries, since basa is imported as frozen fish meat from Asia. The same applies for Nile tilapia, a cultivated freshwater species not captured from local fisheries. For the dolphin fish, despite being common and exploited in Pacific waters, previous studies suggest its fishery is sustainable in Panama waters. In terms of conservation status, one species cataloged by IUCN as vulnerable (VU), the blue marlin (M. nigricans) and one as critically endangered (CR), the scalloped hammerhead shark (S. lewini) were detected. Sphyrae lewini is also catalog as CITES appendix II. The giant Humbolt squid (D. gigas), classified by IUCN as data deficient (DD), was the only invertebrate detected in samples obtained from a ceviche processing plant. Two sets of primers and dual labeled probes were designed for qPCR eDNA detection of the only CITES species, S. lewini. These represent the first qPCR markers for eDNA detection of S. lewini. Results from this project promote the sustainable use of fishery resources and might provide ceviche producers with a certificate from MarViva Foundation certifying that their ceviche is free of sharks or species threatened/protected by law, giving added value to their product. Molecular detection and molecular traceability are sensitive and species specific, what makes of this tool a reliable method to combat IUU (illegal, unreported and undocumented) fishing.

Translation among CNFs, characteristic models and ordered binary decision diagrams

: This paper introduces design methods for numeric function generators (NFGs) using decision diagrams. NFGs are hardware accelerators to compute values of numeric functions such as trigonometric, logarithmic, square root, and reciprocal functions. Most existing design methods for NFGs are intended only for a specific class of numeric functions. However, by using decision diagrams for discrete functions (i.e., word-level decision diagrams), we can systematically design fast and compact NFGs for a larger class of functions. This paper shows three design methods for NFGs using 1) multi-terminal binary decision diagrams (MTBDDs), 2) binary moment diagrams (BMDs), and 3) edge-valued binary decision diagrams (EVBDDs).

RT-LAMP assay combining multi-fluorescent probes for SARS-CoV-2 RNA detection and variant differentiation

Capture and RT-PCR of hepatitis C virus RNA with safety primers.