Balázs Gerencsér

Bio: Balázs Gerencsér is an academic researcher from Alfréd Rényi Institute of Mathematics. The author has contributed to research in topics: Markov chain & Upper and lower bounds. The author has an hindex of 9, co-authored 59 publications receiving 311 citations. Previous affiliations of Balázs Gerencsér include Université catholique de Louvain & Eötvös Loránd University.

Invariant Gaussian processes and independent sets on regular graphs of large girth

Abstract: We prove that every 3-regular, n-vertex simple graph with sufficiently large girth contains an independent set of size at least 0.4361n. The best known bound is 0.4352n. In fact, computer simulation suggests that the bound our method provides is about 0.438n.

Risk and protective factors in the origin of conotruncal defects of heart-a population-based case-control study

Abstract: Congenital heart defect (CHD) cases have been evaluated together as a group in some previous epidemiological studies. However, different CHD entities have different etiologies, and the underlying causes are unclear in the vast majority of patients. Thus the aim of this study was to analyze the possible association of different maternal diseases with the risk of four types of conotruncal defects (CTD), that is, truncus arteriosus, d-transposition of the great arteries, tetralogy of Fallot, and double-outlet right ventricle based on autopsy or surgical report diagnosis. Acute and chronic diseases with related drug treatments and peri-conceptual folic acid or multivitamin supplementations were compared in mothers of 598 CTD cases, of 902 matched controls, and 38,151 population controls without any defects, and with 20,896 malformed controls with other isolated non-cardiac defects in the population-based large dataset of the Hungarian Case-Control Surveillance of Congenital Abnormalities. Mothers who had medically recorded influenza and the common cold with secondary complications in the prenatal maternity logbook during the second and/or third gestational months were associated with a higher risk of CTD (OR with 95% CI: 2.22, 1.19-3.88). The common denominator of these maternal diseases may be high fever, which could be prevented by antifever therapies. On the other hand, high doses of medically recorded folic acid in early pregnancy were able to reduce the birth prevalence of CTD (OR with 95% CI: 0.54, 0.39-0.73), and this reduction was significant in transposition of the great arteries (0.46, 0.29-0.71) as well. In conclusion, high fever related maternal diseases may have a role in the origin of CTD, while high doses of folic acid in early pregnancy were able to reduce of CTD, particularly transposition of great vessels.

Primitive sets of nonnegative matrices and synchronizing automata

Abstract: A set of nonnegative matrices $\mathcal{M}=\{M_1, M_2, \ldots, M_k\}$ is called primitive if there exist indices $i_1, i_2, \ldots, i_m$ such that $M_{i_1} M_{i_2} \ldots M_{i_m}$ is positive (i.e. has all its entries $>0$). The length of the shortest such product is called the exponent of $\mathcal{M}$. The concept of primitive sets of matrices comes up in a number of problems within control theory, non-homogeneous Markov chains, automata theory etc. Recently, connections between synchronizing automata and primitive sets of matrices were established. In the present paper, we significantly strengthen these links by providing equivalence results, both in terms of combinatorial characterization, and computational aspects. We study the maximal exponent among all primitive sets of $n \times n$ matrices, which we denote by $\exp(n)$. We prove that $\lim_{n\rightarrow\infty} \tfrac{\log \exp(n)}{n} = \tfrac{\log 3}{3}$, and moreover, we establish that this bound leads to a resolution of the Cerný problem for carefully synchronizing automata. We also study the set of matrices with no zero rows and columns, denoted by $\mathcal{NZ}$, due to its intriguing connections to the Cerný conjecture and the recent generalization of Perron-Frobenius theory for this class. We characterize computational complexity of different problems related to the exponent of $\mathcal{NZ}$ matrix sets, and present a quadratic bound on the exponents of sets belonging to a special subclass. Namely, we show that the exponent of a set of matrices having total support is bounded by $2n^2 -5n +5$.

Optimal One-Dimensional Coverage by Unreliable Sensors

Abstract: This paper regards the problem of optimally placing unreliable sensors in a one- dimensional environment. We assume that sensors can fail with a certain probability and we minimize the expected maximum distance between any point in the environment and the closest active sensor. We provide a computational method to find the optimal placement and we estimate the costs of the equispaced placement and of the uniform random placement. When the number of sensors goes to infinity, the equispaced placement is asymptotically equivalent to the optimal placement (that is, the ratio between their costs converges to one), whereas the cost of the random placement remains strictly larger.

Primitive Sets of Nonnegative Matrices and Synchronizing Automata

Abstract: A set of nonnegative matrices $\mathcal{M}=\{M_1, M_2, \ldots, M_k\}$ is called primitive if there exist possibly equal indices $i_1, i_2, \ldots, i_m$ such that $M_{i_1} M_{i_2} \cdots M_{i_m}$ is entrywise positive. The length of the shortest such product is called the exponent of $\mathcal{M}$. Recently, connections between synchronizing automata and primitive sets of matrices were established. In the present paper, we strengthen these links by providing equivalence results, both in terms of combinatorial characterization and computational complexity. We pay special attention to the set of matrices without zero rows and columns, denoted by $\mathscr{NZ}$, due to its intriguing connections to the Cerný conjecture. We rely on synchronizing automata theory to derive a number of results about primitive sets of matrices. Making use of an asymptotic estimate by Rystsov [Cybernetics, 16 (1980), pp. 194--198], we show that the maximal exponent $\exp(n)$ of primitive sets of $n \times n$ matrices satisfy $\lim_...

Coverage control for mobile sensing networks

Abstract: This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Clinical risk factors for pre-eclampsia determined in early pregnancy: systematic review and meta-analysis of large cohort studies

Abstract: Objective To develop a practical evidence based list of clinical risk factors that can be assessed by a clinician at ≤16 weeks’ gestation to estimate a woman’s risk of pre-eclampsia. Design Systematic review and meta-analysis of cohort studies. Data sources PubMed and Embase databases, 2000-15. Eligibility criteria for selecting studies Cohort studies with ≥1000 participants that evaluated the risk of pre-eclampsia in relation to a common and generally accepted clinical risk factor assessed at ≤16 weeks’ gestation. Data extraction Two independent reviewers extracted data from included studies. A pooled event rate and pooled relative risk for pre-eclampsia were calculated for each of 14 risk factors. Results There were 25 356 688 pregnancies among 92 studies. The pooled relative risk for each risk factor significantly exceeded 1.0, except for prior intrauterine growth restriction. Women with antiphospholipid antibody syndrome had the highest pooled rate of pre-eclampsia (17.3%, 95% confidence interval 6.8% to 31.4%). Those with prior pre-eclampsia had the greatest pooled relative risk (8.4, 7.1 to 9.9). Chronic hypertension ranked second, both in terms of its pooled rate (16.0%, 12.6% to 19.7%) and pooled relative risk (5.1, 4.0 to 6.5) of pre-eclampsia. Pregestational diabetes (pooled rate 11.0%, 8.4% to 13.8%; pooled relative risk 3.7, 3.1 to 4.3), prepregnancy body mass index (BMI) >30 (7.1%, 6.1% to 8.2%; 2.8, 2.6 to 3.1), and use of assisted reproductive technology (6.2%, 4.7% to 7.9%; 1.8, 1.6 to 2.1) were other prominent risk factors. Conclusions There are several practical clinical risk factors that, either alone or in combination, might identify women in early pregnancy who are at “high risk” of pre-eclampsia. These data can inform the generation of a clinical prediction model for pre-eclampsia and the use of aspirin prophylaxis in pregnancy.

Analysis of Recursive Stochastic Algorithms

Abstract: Recursive algorithms where random observations enter are studied in a fairly general framework. An important feature is that the observations may depend on previous ?outputs? of the algorithm. The considered class of algorithms contains, e.g., stochastic approximation algorithms, recursive identification algorithms, and algorithms for adaptive control of linear systems. It is shown how a deterministic differential equation can be associated with the algorithm. Problems like convergence with probality one, possible convergence points and asymptotic behavior of the algorithm can all be studied in terms of this differential equation. Theorems stating the precise relationships between the differential equation and the algorithm are given as well as examples of applications of the results to problems in identification and adaptive control.

Prevalence of congenital heart disease

Abstract: Background Today most patients with congenital heart disease survive childhood to be cared for by adult cardiologists. The number of physicians that should be trained to manage these lesions is unknown because we do not know the number of patients. Methods To answer this question, the expected numbers of infants with each major type of congenital heart defect born in each 5-year period since 1940 were estimated from birth rates and incidence. The numbers expected to survive with or without treatment were estimated from data on natural history and the results of treatment. Finally, lesions were categorized as simple, moderate, or complex, based on the amount of expertise in management needed for optimal patient care. Results From 1940 to 2002, about 1 million patients with simple lesions, and half that number each with moderate and complex lesions, were born in the United States. If all were treated, there would be 750,000 survivors with simple lesions, 400,000 with moderate lesions, and 180,000 with complex lesions; in addition, there would be 3,000,000 subjects alive with bicuspid aortic valves. Without treatment, the survival in each group would be 400,000, 220,000, and 30,000, respectively. The actual numbers surviving will be between these 2 sets of estimates. Conclusions Survival of patients with congenital heart disease, treated or untreated, is expected to produce large numbers of adults with congenital disease, and it is likely that many more adult cardiologists will need to be trained to manage moderate and complex congenital lesions.