Aligator.jl - A Julia Package for Loop Invariant Generation

We describe the Aligator.jl software package for automatically generating all polynomial invariants of the rich class of extended P-solvable loops with nested conditionals. Aligator.jl is written in the programming language Julia and is open-source. Aligator.jl transforms program loops into a system of algebraic recurrences and implements techniques from symbolic computation to solve recurrences, derive closed form solutions of loop variables and infer the ideal of polynomial invariants by variable elimination based on Gr\"obner basis computation

Generating all polynomial invariants in simple loops

AbstractThis paper presents a method for automatically generating all polynomial invariants in simple loops. It is first shown that the set of polynomials serving as loop invariants has the algebraic structure of an ideal. Based on this connection, a fixpoint procedure using operations on ideals and Gröbner basis constructions is proposed for finding all polynomial invariants. Most importantly, it is proved that the procedure terminates in at most m+1 iterations, where m is the number of program variables. The proof relies on showing that the irreducible components of the varieties associated with the ideals generated by the procedure either remain the same or increase their dimension at every iteration of the fixpoint procedure. This yields a correct and complete algorithm for inferring conjunctions of polynomial equalities as invariants. The method has been implemented in Maple using the Groebner package. The implementation has been used to automatically discover non-trivial invariants for several examples to illustrate the power of the technique

Synthesis for Polynomial Lasso Programs

We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities). Central to this approach is the discovery of non-linear (algebraic) loop invariants. We extend Sankaranarayanan, Sipma, and Manna's template-based approach and prove a completeness criterion. We perform program synthesis by generating a constraint whose solution is a synthesized program together with a loop invariant that proves the program's correctness. This constraint is non-linear and is passed to an SMT solver. Moreover, we can enforce the termination of the synthesized program with the support of test cases.Comment: Paper at VMCAI'14, including appendi

Finding polynomial loop invariants for probabilistic programs

Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle's Positivstellensatz and a transformation to a sum-of-squares problem, we find sufficient conditions on the coefficients. Then, we solve a semidefinite programming feasibility problem to synthesize the loop invariants. If the semidefinite program is unfeasible, we backtrack after increasing the degree of the template. Our approach is semi-complete in the sense that it will always lead us to a feasible solution if one exists and numerical errors are small. Experimental results show the efficiency of our approach.Comment: accompanies an ATVA 2017 submissio

The first hominin of Europe

The earliest hominin occupation of Europe is one of the most debated topics in palaeoanthropology. However, the purportedly oldest of the Early Pleistocene sites in Eurasia lack precise age control and contain stone tools rather than human fossil remains(1-5). Here we report the discovery of a human mandible associated with an assemblage of Mode 1 lithic tools and faunal remains bearing traces of hominin processing, in stratigraphic level TE9 at the site of the Sima del Elefante, Atapuerca, Spain(6-8). Level TE9 has been dated to the Early Pleistocene ( approximately 1.2 - 1.1 Myr), based on a combination of palaeomagnetism, cosmogenic nuclides and biostratigraphy. The Sima del Elefante site thus emerges as the oldest, most accurately dated record of human occupation in Europe, to our knowledge. The study of the human mandible suggests that the first settlement of Western Europe could be related to an early demographic expansion out of Africa. The new evidence, with previous findings in other Atapuerca sites ( level TD6 from Gran Dolina(9-13)), also suggests that a speciation event occurred in this extreme area of the Eurasian continent during the Early Pleistocene, initiating the hominin lineage represented by the TE9 and TD6 hominins.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62855/1/nature06815.pd

Four millennia of Iberian biomolecular prehistory illustrate the impact of prehistoric migrations at the far end of Eurasia

Population genomic studies of ancient human remains have shown how modern-day European population structure has been shaped by a number of prehistoric migrations. The Neolithization of Europe has been associated with large-scale migrations from Anatolia, which was followed by migrations of herders from the Pontic steppe at the onset of the Bronze Age. Southwestern Europe was one of the last parts of the continent reached by these migrations, and modern-day populations from this region show intriguing similarities to the initial Neolithic migrants. Partly due to climatic conditions that are unfavorable for DNA preservation, regional studies on the Mediterranean remain challenging. Here, we present genome-wide sequence data from 13 individuals combined with stable isotope analysis from the north and south of Iberia covering a four-millennial temporal transect (7, 500–3, 500 BP). Early Iberian farmers and Early Central European farmers exhibit significant genetic differences, suggesting two independent fronts of the Neolithic expansion. The first Neolithic migrants that arrived in Iberia had low levels of genetic diversity, potentially reflecting a small number of individuals; this diversity gradually increased over time from mixing with local hunter-gatherers and potential population expansion. The impact of post-Neolithic migrations on Iberia was much smaller than for the rest of the continent, showing little external influence from the Neolithic to the Bronze Age. Paleodietary reconstruction shows that these populations have a remarkable degree of dietary homogeneity across space and time, suggesting a strong reliance on terrestrial food resources despite changing culture and genetic make-up

Impact of D-limonene synthase up- or down-regulation on sweet orange fruit and juice odor perception

[EN] Citrus fruits are characterized by a complex mixture of volatiles making up their characteristic aromas, being the D-limonene the most abundant one. However, its role on citrus fruit and juice odor is controversial. Transgenic oranges engineered for alterations in the presence or concentration of few related chemical groups enable asking precise questions about their contribution to overall odor, either positive or negative, as perceived by the human nose. Here, either down- or up-regulation of a D-limonene synthase allowed us to infer that a decrease of as much as 51 times in D-limonene and an increase of as much as 3.2 times in linalool in juice were neutral for odor perception while an increase of only 3 times in ethyl esters stimulated the preference of 66% of the judges. The ability to address these questions presents exciting opportunities to understand the basic principles of selection of food. (C) 2016 Elsevier Ltd. All rights reserved.We are grateful to Drs. Lorenzo Zacarias and M. Jesus Rodrigo (IATA-CSIC) for the GC-MS facilities and support. We would like to acknowledge also to Drs. Berta Alquezar and Elsa Pons for their critical review of the manuscript and to all the panelists that participated in the sensory panel. This research is being funded in part by Fundo de Defesa da Citricultura (Fundecitrus).Rodríguez-Baixauli, AM.; Peris-Rodrigo, JE.; Redondo, A.; Shimada, T.; Costell, E.; Carbonell, I.; Rojas, C.... (2017). Impact of D-limonene synthase up- or down-regulation on sweet orange fruit and juice odor perception. Food Chemistry. 217:139-150. doi:10.1016/j.foodchem.2016.08.076S13915021

SAT Modulo Linear Arithmetic for Solving Polynomial

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world

Global methylome scores correlate with histological subtypes of colorectal carcinoma and show different associations with common clinical and molecular features

Background. The typical methylation patterns associated with cancer are hypermethylation at gene promoters and global genome hypomethylation. Aberrant CpG island hypermethylation at promoter regions and global genome hypomethylation have not been associated with histological colorectal carcinomas (CRC) subsets. Using Illumina’s 450 k Infinium Human Methylation beadchip, the methylome of 82 CRCs were analyzed, comprising different histological subtypes: 40 serrated adenocarcinomas (SAC), 32 conventional carcinomas (CC) and 10 CRCs showing histological and molecular features of microsatellite instability (hmMSI‐H), and, additionally, 35 normal adjacent mucosae. Scores reflecting the overall methylation at 250 bp, 1 kb and 2 kb from the transcription starting site (TSS) were studied. Results. SAC has an intermediate methylation pattern between CC and hmMSI‐H for the three genome locations. In addition, the shift from promoter hypermethylation to genomic hypomethylation occurs at a small sequence between 250 bp and 1 Kb from the gene TSS, and an asymmetric distribution of methylation was observed between both sides of the CpG islands (N vs. S shores). Conclusion. These findings show that different histological subtypes of CRC have a particular global methylation pattern depending on sequence distance to TSS and highlight the so far underestimated importance of CpGs aberrantly hypomethylated in the clinical phenotype of CRCs.This work was supported by two grants from Instituto de Salud Carlos III, Ministerio de Sanidad, Spain and FEDER funds (refs: PI12-1232, PI18-0144) and another from the European Union’s Horizon 2020 research and innovation program (ref. 848098