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Ocean circulation redistributes heat, freshwater, carbon, and nutrients all around the globe. Because of their importance in regulating climate, weather, extreme events, sea level, fisheries, and ecosystems, large-scale ocean currents should be monitored continuously. The Atlantic is unique as the only ocean basin where heat is, on average, transported northward in both hemispheres as part of the Atlantic Meridional Overturning Circulation (AMOC). The largely unrestricted connection with the Arctic and Southern Oceans allows ocean currents to exchange heat, freshwater, and other properties with polar latitudes.

Postprint (published version)

We ask for feasibly constructive proofs of known circuit lower bounds for explicit functions on bit strings of length n. In 1995 Razborov showed that many can be proved in PV1, a bounded arithmetic formalizing polynomial time reasoning. He formalized circuit lower bound statements for small n of doubly logarithmic order. It is open whether PV1 proves known lower bounds in succinct formalizations for n of logarithmic order. We give such proofs in APC1, an extension of PV1 formalizing probabilistic polynomial time reasoning: for parity and AC0, for mod q and AC0[p] (only for n slightly smaller than logarithmic), and for k-clique and monotone circuits. We also formalize Razborov and Rudich’s natural proof barrier. We ask for short propositional proofs of circuit lower bounds expressed succinctly by propositional formulas of size nO(1) or at least much smaller than the 2O(n) size of the common “truth table” formula. We discuss two such expressions: one via feasible functions witnessing errors of circuits, and one via the anticheckers of Lipton and Young 1994. Our APC1 formalizations yield conditional upper bounds for the succinct formulas obtained by witnessing: we get short Extended Frege proofs from general circuit lower bounds expressed by the common “truth-table” formulas. We also show how to construct in quasipolynomial time propositional proofs of quasipolynomial size tautologies expressing AC0[p] quasipolynomial size lower bounds; these proofs are in Jerábek’s system WF., Peer Reviewed, Postprint (author's final draft)

A polynomial time ultrapower is a structure given by the set of polynomial time computable functions modulo some ultrafilter. They model the universal theory ∀PV of all polynomial time functions. Generalizing a theorem of Hirschfeld (Israel J Math 20(2):111–126, 1975), we show that every countable model of ∀PV is isomorphic to an existentially closed substructure of a polynomial time ultrapower. Moreover, one can take a substructure of a special form, namely a limit polynomial time ultrapower in the classical sense of Keisler (in: Bergelson, V., Blass, A., Di Nasso, M., Jin, R. (eds.) Ultrafilters across mathematics, contemporary mathematics vol 530, pp 163–179. AMS, New York, 1963). Using a polynomial time ultrapower over a nonstandard Herbrand saturated model of ∀PV we show that ∀PV is consistent with a formal statement of a polynomial size circuit lower bound for a polynomial time computable function. This improves upon a recent result of Krajíček and Oliveira (Logical methods in computer science 13 (1:4), 2017)., Peer Reviewed, Postprint (author's final draft)

We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatable unless P = NP. Indeed, we show that it is NP-hard to distinguish between formulas that have Resolution refutations of polynomial length and those that do not have subexponential length refutations. This also implies that Resolution is not automatable in subexponential time or quasi-polynomial time unless NP is included in SUBEXP or QP, respectively., Both authors were partially funded by European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant agreement ERC-2014-CoG 648276 (AUTAR). First author partially funded by MICCIN grant TIN2016-76573-C2-1P (TASSAT3)., Peer Reviewed, Postprint (author's final draft)

In this project we do an algorithmic study of problems from computational geometry with countably infinite input, especially countable sets in R^n. To do so, we use the infinite time Blum-Shub-Smale (ITBSS) machine, which is capable to extend computations to infinite time. We present this framework, explained with several algorithms, some results on the ITBSS Machine, and a storage system capable of encoding, editing and extracting sequences of real numbers. We study different geometric problems, giving algorithmic solutions to several of them. The accumulation points problem in R^2 is presented and solved for countable sets with finitely many accumulation points. Also, the convex hull problem is studied. We show how to compute the closure of the convex hull of countable bounded sets in R^n. The non-crossing perfect matching problem with infinite input is addressed as well.

Purpose. Drawing on the concept of dynamic managerial capabilities, to propose a model that incorporates managerial human and social capital, and managerial cognition in the dynamic capabilities framework. Design/Method/Approach. The study is an empirical in the context of the current conflict in the eastern Ukraine and is an analysis a non-profit field with an extremely high dynamic environment. The data was collected using a quantitative survey with 70 private corps, non-commissioned officers, and higher-ranked officers. Findings. The model provides a direct relationship between dynamic capabilities and dynamic managerial capabilities, whereby the latter is constituted by the perceived manager’s competence (manager’s human capital), manager’s team (manager’s social capital), and manager’s goal congruence towards the goals of the organization (managerial cognition). Theoretical implications. This paper expanded the body of research on dynamic managerial capabilities by developing the following arguments: (1) dynamic managerial capabilities directly influence organizational dynamic capabilities; (2) managerial social capital mediates relationships between managerial human capital and organizational dynamic capabilities; (3) managerial social capital mediates relationships between managerial cognition and organizational dynamic capabilities. Originality/value. This research not only shows how a non-profit organization can act efficiently, it is also an example of an application of strategic management theory to a practical field with life or death consequences. Research limitations/Future research. This research opens avenues for future research on dynamic capabilities in non-profit organizations. Paper type - empirical.

We show that the problem of finding a Resolution refutation that is at most polynomially longer than a shortest one is NP-hard. In the parlance of proof complexity, Resolution is not automatizable unless P = NP. Indeed, we show that it is NP-hard to distinguish between formulas that have Resolution refutations of polynomial length and those that do not have subexponential length refutations. This also implies that Resolution is not automatizable in subexponential time or quasi-polynomial time unless~NP is included in SUBEXP or QP, respectively., Peer Reviewed, Postprint (author's final draft)

The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the sentence. We study the parameterized space complexity of the model-checking problem for queries with a bounded number of variables. For each bound on the quantifier alternation rank the problem becomes complete for the corresponding level of what we call the tree hierarchy, a hierarchy of parameterized complexity classes defined via space bounded alternating machines between parameterized logarithmic space and fixed-parameter tractable time. We observe that a parameterized logarithmic space model-checker for existential bounded variable queries would allow to improve Savitch's classical simulation of nondeterministic logarithmic space in deterministic space O(log2n). Further, we define a highly space efficient model-checker for queries with a bounded number of variables and bounded quantifier alternation rank. We study its optimality under the assumption that Savitch's Theorem is optimal., Peer Reviewed, Postprint (published version)

The complexity of the parameterized halting problem for nondeterministic Turing machines p-Halt is known to be related to the question of whether there are logics capturing various complexity classes [10]. Among others, if p-Halt is in para-AC0, the parameterized version of the circuit complexity class AC0, then AC0, or equivalently, (+, x)-invariant FO, has a logic. Although it is widely believed that p-Halt ∉. para-AC0, we show that the problem is hard to settle by establishing a connection to the question in classical complexity of whether NE ⊈ LINH. Here, LINH denotes the linear time hierarchy. On the other hand, we suggest an approach toward proving NE ⊈ LINH using bounded arithmetic. More specifically, we demonstrate that if the much celebrated MRDP (for Matiyasevich-Robinson-Davis-Putnam) theorem can be proved in a certain fragment of arithmetic, then NE ⊈ LINH. Interestingly, central to this result is a para-AC0 lower bound for the parameterized model-checking problem for FO on arithmetical structures., Peer Reviewed, Postprint (author's final draft)

We link two concepts from the literature, namely hard sequences for the satisfiability problem sat and so-called pseudo proof systems proposed for study by Krajícek. Pseudo proof systems are elements of a particular nonstandard model constructed by forcing with random variables. We show that the existence of mad pseudo proof systems is equivalent to the existence of a randomized polynomial time procedure with a highly restrictive use of randomness which produces satisfiable formulas whose satisfying assignments are probably hard to find., Peer Reviewed, Postprint (published version)

Die vorliegende Arbeit widmet sich der Untersuchung endogener Pfadbrüche in der organisationalen Pfadabhängigkeit, wobei ein besonderer Schwerpunkt auf die Einflüsse der Sinnstiftung, Sinngebung und der Handlungsfähigkeit innerhalb einer Organisation gelegt wird. Am Beispiel einer Station eines Klinikums, die einen Übergang von traditionell hierarchischen zu selbstorganisierten Arbeitsweisen vollzieht, wird untersucht, inwiefern Handelnde innerhalb ihrer Organisationen existierende Strukturen aktiv überwinden können. Die methodologische Basis dieser Arbeit bildet ein qualitativer Ansatz, der halbstrukturierte Interviews, teilnehmende Beobachtung sowie die Analyse von Sekundärdaten umfasst. Die empirischen Befunde illustrieren, dass die Kombination aus Sinnstiftungs- und Sinngebungsprozessen sowie die Übertragung von Handlungsfähigkeit kritische Faktoren für die endogene Überwindung von Pfadabhängigkeiten darstellen. Diese Arbeit bietet umfassende theoretische und praktische Implikationen. Sie erweitert das Verständnis der Möglichkeiten, wie Organisationen Pfadabhängigkeiten endogen überwinden können und betont die Bedeutung von aktiver Einflussnahme durch Handelnde, kollaborativer Sinnstiftung und der Führungspraktiken im Kontext des organisationalen Wandels. Zudem liefert sie praxisnahe Erkenntnisse für das Management von Organisationen, insbesondere hinsichtlich der Förderung von Reflexivität, der Stärkung der Handlungsfähigkeit der Mitarbeiter sowie der Rolle von Führungskräften bei der Initiierung und Umsetzung der Überwindung einer Pfadabhängigkeit.