In this paper we consider the question what is the scientific and career performance of principal investigators (PIs) of publicly funded research projects compared to scientific performance of all researchers. Our study is based on high quality data about (i) research projects awarded in Slovenia in the period 1994–2016 (7508 projects with 2725 PIs in total) and (ii) about scientific productivity of all researchers in Slovenia that were active in the period 1970-2016 – there are 19598 such researchers in total, including the PIs. We compare average productivity, collaboration, internationality and interdisciplinarity of PIs and of all active researchers. Our analysis shows that for all four indicators the average performance of PIs is much higher compared to average performance of all active researchers. Additionally, we analyze careers of both groups of researchers. The results show that the PIs have on average longer and more fruitful career compared to all active researchers, with regards to all career indicators.

A fundamental problem in technological studies is how to measure the evolution of technology. The literature has suggested several approaches to measuring the level of technology (or state-of-the-art) and changes in technology. However, the measurement of technological advances and technological evolution is often a complex and elusive topic in science. The study here starts by establishing a conceptual framework of technological evolution based on the theory of technological parasitism, in broad analogy with biology. Then, the measurement of the evolution of technology is modelled in terms of morphological changes within complex systems considering the interaction between a host technology and its subsystems of technology. The coefficient of evolutionary growth of the model here indicates the grade and type of the evolutionary route of a technology.

In the last years complex networks tools contributed to provide insights on the structure of research, through the study of collaboration, citation and co-occurrence networks. The network approach focuses on pairwise relationships, often compressing multidimensional data structures and inevitably losing information. In this paper we propose for the first time a simplicial complex approach to word co-occurrences, providing a natural framework for the study of higher-order relations in the space of scientific knowledge. Using topological methods we explore the conceptual landscape of mathematical research, focusing on homological holes, regions with low connectivity in the simplicial structure. We find that homological holes are ubiquitous, which suggests that they capture some essential feature of research practice in mathematics.

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. Since a finite volume of space can’t contain more than a finite amount of information, I argue that the mathematical real numbers are not physically real. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics that uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic.

We propose four axiomatic systems for intuitionistic linear temporal logic and show that each of these systems is sound for a class of structures based either on Kripke frames or on dynamic topological systems. Our topological semantics features a new interpretation for the `henceforth’ modality that is a natural intuitionistic variant of the classical one. Using the soundness results, we show that the four logics obtained from the axiomatic systems are distinct. Finally, we show that when the language is restricted to the `henceforth’-free fragment, the set of valid formulas for the relational and topological semantics coincide.

There is one, and only one way, consistent with fundamental physics, that the efficiency of general digital computation can continue increasing indefinitely, and that is to apply the principles of reversible computing. We need to begin intensive development work on this technology soon if we want to maintain advances in computing and the attendant economic growth. NOTE: This paper is an extended author’s preprint of the feature article titled “Throwing Computing Into Reverse” (print) or “The Future of Computing Depends on Making it Reversible” (online), published by IEEE Spectrum in Aug.-Sep. 2017. This preprint is based on the original draft manuscript that the author submitted to Spectrum, prior to IEEE edits and feedback from external readers.

We revisit the old work of de Paiva on the models of the Lambek Calculus in dialectica models making sure that the syntactic details that were sketchy on the first version got completed and verified. We extend the Lambek Calculus with a kappa modality, inspired by Yetter’s work, which makes the calculus commutative. Then we add the of-course modality !, as Girard did, to re-introduce weakening and contraction for all formulas and get back the full power of intuitionistic and classical logic. We also present the categorical semantics, proved sound and complete. Finally we show the traditional properties of type systems, like subject reduction, the Church-Rosser theorem and normalization for the calculi of extended modalities, which we did not have before.

The paper utilizes some fundamental results obtained in the context of topological quantum field theory, hyper finite sub-factors, Turaev-Viro machine and four dimensional fusion algebra to shed mathematical, physical and philosophical light on the major problem of cold fusion reactors. In particular, we develop a picture model for the quantum vacuum by using modern transfinite quantum field theory but also guided by philosophical ideas about the picture of the space of logic and reality.

Thermodynamics is a physical branch of science that governs the thermal behavior of dynamical systems from those as simple as refrigerators to those as complex as our expanding universe. The laws of thermodynamics involving conservation of energy and nonconservation of entropy are, without a doubt, two of the most useful and general laws in all sciences. The first law of thermodynamics, according to which energy cannot be created or destroyed, merely transformed from one form to another, and the second law of thermodynamics, according to which the usable energy in an adiabatically isolated dynamical system is always diminishing in spite of the fact that energy is conserved, have had an impact far beyond science and engineering. In this paper, we trace the history of thermodynamics from its classical to its postmodern forms, and present a tutorial and didactic exposition of thermodynamics as it pertains to some of the deepest secrets of the universe

This is a very brief introduction to quantum computing and quantum information theory, primarily aimed at geometers. Beyond basic definitions and examples, I emphasize aspects of interest to geometers, especially connections with asymptotic representation theory. Proofs of most statements can be found in standard references.