Limitations of Algebraic Approaches to Graph Isomorphism Testing

We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and only if if the graphs are isomorphic, and then to (try to) decide satisfiability of the system using, for example, the Gr\"obner basis algorithm. In some cases this can be done in polynomial time, in particular, if the equations admit a bounded degree refutation in an algebraic proof systems such as Nullstellensatz or polynomial calculus. We prove linear lower bounds on the polynomial calculus degree over all fields of characteristic different from 2 and also linear lower bounds for the degree of Positivstellensatz calculus derivations. We compare this approach to recently studied linear and semidefinite programming approaches to isomorphism testing, which are known to be related to the combinatorial Weisfeiler-Lehman algorithm. We exactly characterise the power of the Weisfeiler-Lehman algorithm in terms of an algebraic proof system that lies between degree-k Nullstellensatz and degree-k polynomial calculus

Graphs Identified by Logics with Counting

We classify graphs and, more generally, finite relational structures that are identified by C2, that is, two-variable first-order logic with counting. Using this classification, we show that it can be decided in almost linear time whether a structure is identified by C2. Our classification implies that for every graph identified by this logic, all vertex-colored versions of it are also identified. A similar statement is true for finite relational structures. We provide constructions that solve the inversion problem for finite structures in linear time. This problem has previously been shown to be polynomial time solvable by Martin Otto. For graphs, we conclude that every C2-equivalence class contains a graph whose orbits are exactly the classes of the C2-partition of its vertex set and which has a single automorphism witnessing this fact. For general k, we show that such statements are not true by providing examples of graphs of size linear in k which are identified by C3 but for which the orbit partition is strictly finer than the Ck-partition. We also provide identified graphs which have vertex-colored versions that are not identified by Ck.Comment: 33 pages, 8 Figure

Dependence Logic with Generalized Quantifiers: Axiomatizations

We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result considers the extension of dependence logic where Q is interpreted as "there exists uncountable many." Both of the axiomatizations are shown to be sound and complete for FO(Q) consequences.Comment: 17 page

Lithologic and Structural Interpretation of Gravity Data, Northeastern Iowa

A gravity survey was conducted over approximately 4600 square km of northeast Iowa. It was undertaken to provide detailed gravity coverage at approximately 1.6 km intervals and to model the source of several significant gravity and magnetic anomalies. 1,460 gravity stations were occupied in the survey area. Bouguer gravity and residual gravity anomaly maps were prepared, the latter using band-pass filter and trend-surface analysis techniques. The residual maps reveal that the large oval Bouguer gravity anomaly centered beneath Decorah can be traced to the southern border of the survey. Profiles crossing this feature were prepared from the Bouguer map and a total intensity magnetic anomaly map. These profiles, combined with drill hole information, support the interpretation of a mafic (troctolite) intrusive extending over 90 km from the northwest corner of Winneshiek County to near the southern boundary of Fayette County. The western portion is dominated by a shallow elastic basin while the eastern portion appears to be dominantly felsic in nature. The gravity interpretation did not provide conclusive evidence for faulting near Decorah although faulting cannot be ruled out

Counter Machines and Distributed Automata: A Story about Exchanging Space and Time

We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of counters. The two classes differ in the extra features they offer: one allows to copy counter values, whereas the other allows to compute copyless sums of counters. Our distributed automata, on the other hand, operate on directed path graphs that represent words. All nodes of a path synchronously execute the same finite-state machine, whose state diagram must be acyclic except for self-loops, and each node receives as input the state of its direct predecessor. These devices form a subclass of linear-time one-way cellular automata.Comment: 15 pages (+ 13 pages of appendices), 5 figures; To appear in the proceedings of AUTOMATA 2018

Parametrised Complexity of Model Checking and Satisfiability in Propositional Dependence Logic

In this paper, we initiate a systematic study of the parametrised complexity in the field of Dependence Logics which finds its origin in the Dependence Logic of V\"a\"an\"anen from 2007. We study a propositional variant of this logic (PDL) and investigate a variety of parametrisations with respect to the central decision problems. The model checking problem (MC) of PDL is NP-complete. The subject of this research is to identify a list of parametrisations (formula-size, treewidth, treedepth, team-size, number of variables) under which MC becomes fixed-parameter tractable. Furthermore, we show that the number of disjunctions or the arity of dependence atoms (dep-arity) as a parameter both yield a paraNP-completeness result. Then, we consider the satisfiability problem (SAT) showing a different picture: under team-size, or dep-arity SAT is paraNP-complete whereas under all other mentioned parameters the problem is in FPT. Finally, we introduce a variant of the satisfiability problem, asking for teams of a given size, and show for this problem an almost complete picture.Comment: Update includes refined result

POLG2 deficiency causes adult-onset syndromic sensory neuropathy, ataxia and parkinsonism

Objective: Mitochondrial dysfunction plays a key role in the pathophysiology of neurodegenerative disorders such as ataxia and Parkinson's disease. We describe an extended Belgian pedigree where seven individuals presented with adult-onset cerebellar ataxia, axonal peripheral ataxic neuropathy, and tremor, in variable combination with parkinsonism, seizures, cognitive decline, and ophthalmoplegia. We sought to identify the underlying molecular etiology and characterize the mitochondrial pathophysiology of this neurological syndrome. Methods: Clinical, neurophysiological, and neuroradiological evaluations were conducted. Patient muscle and cultured fibroblasts underwent extensive analyses to assess mitochondrial function. Genetic studies including genome-wide sequencing were conducted. Results: Hallmarks of mitochondrial dysfunction were present in patients' tissues including ultrastructural anomalies of mitochondria, mosaic cytochrome c oxidase deficiency, and multiple mtDNA deletions. We identified a splice acceptor variant in POLG2, c.970-1G>C, segregating with disease in this family and associated with a concomitant decrease in levels of POLG2 protein in patient cells. Interpretation: This work extends the clinical spectrum of POLG2 deficiency to include an overwhelming, adult-onset neurological syndrome that includes cerebellar syndrome, peripheral neuropathy, tremor, and parkinsonism. We therefore suggest to include POLG2 sequencing in the evaluation of ataxia and sensory neuropathy in adults, especially when it is accompanied by tremor or parkinsonism with white matter disease. The demonstration that deletions of mtDNA resulting from autosomal-dominant POLG2 variant lead to a monogenic neurodegenerative multicomponent syndrome provides further evidence for a major role of mitochondrial dysfunction in the pathomechanism of nonsyndromic forms of the component neurodegenerative disorders

High burden of tuberculosis infection and disease among people receiving medication-assisted treatment for substance use disorder in Tanzania

OBJECTIVE: To determine the prevalence of tuberculosis (TB) disease and infection as well as incident TB disease among people who use drugs (PWUD) attending Medication Assisted Treatment (MAT) clinics in Dar-es-Salaam, Tanzania. METHODS: In this prospective cohort study, a total of 901 consenting participants were enrolled from November 2016 to February 2017 and a structured questionnaire administered to them through the open data kit application on android tablets. Twenty-two months later, we revisited the MAT clinics and reviewed 823 of the 901 enrolled participant's medical records in search for documentation on TB disease diagnosis and treatment. Medical records reviewed included those of participants whom at enrolment were asymptomatic, not on TB disease treatment, not on TB preventive therapy and those who had a documented tuberculin skin test (TST) result. RESULTS: Of the 823 medical records reviewed 22 months after enrolment, 42 had documentation of being diagnosed with TB disease and initiated on TB treatment. This is equivalent to a TB disease incidence rate of 2,925.2 patients per 100,000 person years with a total follow up time of 1,440 person-years. At enrolment the prevalence of TB disease and TB infection was 2.6% and 54% respectively and the HIV prevalence was 44% and 16% among females and males respectively. CONCLUSION: PWUD attending MAT clinics bear an extremely high burden of TB and HIV and are known to have driven TB epidemics in a number of countries. Our reported TB disease incidence is 12 times that of the general Tanzanian incidence of 237 per 100,000 further emphasizing that this group should be prioritized for TB screening, testing and treatment. Gender specific approaches should also be developed as female PWUDs are markedly more affected with HIV and TB disease than male PWUDs

Ross River virus antibody prevalence in the Fiji Islands, 2013-2015

A unique outbreak of Ross River virus (RRV) infection was reported in Fiji in 1979. In 2013, 29 RRV seroprevalence among residents was 46.5%. Of those born after 1982, 37.4% had anti-RRV 30 antibodies. Between 2013-2015, 10.9% of residents had seroconverted to RRV suggesting 31 ongoing endemic circulation of RRV in Fiji