4,385 research outputs found

    IST Austria Thesis

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    We study the interacting homogeneous Bose gas in two spatial dimensions in the thermodynamic limit at fixed density. We shall be concerned with some mathematical aspects of this complicated problem in many-body quantum mechanics. More specifically, we consider the dilute limit where the scattering length of the interaction potential, which is a measure for the effective range of the potential, is small compared to the average distance between the particles. We are interested in a setting with positive (i.e., non-zero) temperature. After giving a survey of the relevant literature in the field, we provide some facts and examples to set expectations for the two-dimensional system. The crucial difference to the three-dimensional system is that there is no Bose–Einstein condensate at positive temperature due to the Hohenberg–Mermin–Wagner theorem. However, it turns out that an asymptotic formula for the free energy holds similarly to the three-dimensional case. We motivate this formula by considering a toy model with δ interaction potential. By restricting this model Hamiltonian to certain trial states with a quasi-condensate we obtain an upper bound for the free energy that still has the quasi-condensate fraction as a free parameter. When minimizing over the quasi-condensate fraction, we obtain the Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity, which plays an important role in our rigorous contribution. The mathematically rigorous result that we prove concerns the specific free energy in the dilute limit. We give upper and lower bounds on the free energy in terms of the free energy of the non-interacting system and a correction term coming from the interaction. Both bounds match and thus we obtain the leading term of an asymptotic approximation in the dilute limit, provided the thermal wavelength of the particles is of the same order (or larger) than the average distance between the particles. The remarkable feature of this result is its generality: the correction term depends on the interaction potential only through its scattering length and it holds for all nonnegative interaction potentials with finite scattering length that are measurable. In particular, this allows to model an interaction of hard disks

    The free energy of the two-dimensional dilute Bose gas. II. Upper bound

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    We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for a2ρ1a^2 \rho \ll 1 and βρ1\beta \rho \gtrsim 1 the free energy per unit volume differs from the one of the non-interacting system by at most 4πρ2lna2ρ1(2[1βc/β]+2)4 \pi \rho^2 |\ln a^2 \rho|^{-1} (2 - [1 - \beta_{\mathrm{c}}/\beta]_+^2) to leading order, where aa is the scattering length of the two-body interaction potential, ρ\rho is the density, β\beta the inverse temperature and βc\beta_{\mathrm{c}} is the inverse Berezinskii--Kosterlitz--Thouless critical temperature for superfluidity. In combination with the corresponding matching lower bound proved in \cite{DMS19} this shows equality in the asymptotic expansion.Comment: LaTeX, 24 pages; final version, to appear in J. Math. Phy

    The Role of Internationalization Strategy in Fostering Innovation: An Empirical Study Using Machine Learning Technique

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    In today’s highly dynamic global market, firms increasingly conduct R&D internationally to enhance their innovation and competitiveness. We analyze the relationship between firm internationalization strategy and innovation performance. We argue that the relationship is inverse U-shaped, due to concave returns and convex costs of firm internationalization regarding innovation performance. We test our hypothesis using a novel machine-learning technique and develop a dictionary on internationalization, based on the most-cited papers on firm internationalization. We then apply this dictionary to firms’ 10-K annual reports to obtain a unique score of each firm’s internationalization strategy and use panel data econometrics to analyze the relationship with innovation performance. The results support the hypothesis of an inverted U-shape relationship between firms’ internationalization strategy and innovation performance. Further tests substantiate the findings. Our study contributes to the literature on firm internationalization and firm innovation by identifying a trade-off in benefits and costs of firm internationalization

    The free energy of the two-dimensional dilute Bose gas. I. Lower bound

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    We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density and inverse temperature differs from the one of the noninteracting system by the correction term . Here, is the scattering length of the interaction potential, and is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit and if

    Investigating prostate cancer tumour-stroma interactions - clinical and biological insights from an evolutionary game

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    BACKGROUND: Tumours are made up of a mixed population of different types of cells that include normal structures as well as ones associated with the malignancy, and there are multiple interactions between the malignant cells and the local microenvironment. These intercellular interactions, modulated by the microenvironment, effect tumour progression and represent a largely under appreciated therapeutic target. We use observations of primary tumor biology from prostate cancer to extrapolate a mathematical model: specifically; it has been observed that in prostate cancer three disparate cellular outcomes predominate: (i) the tumour remains well differentiated and clinically indolent - in this case the local stromal cells may act to restrain the growth of the cancer; (ii) early in its genesis the tumour acquires a highly malignant phenotype, growing rapidly and displacing the original stromal population (often referred to as small cell prostate cancer) - these less common aggressive tumours are relatively independent of the local microenvironment; and, (iii) the tumour co-opts the local stroma - taking on a classic stromagenic phenotype where interactions with the local microenvironment are critical to the cancer growth. METHODS: We present an evolutionary game theoretical construct that models the influence of tumour-stroma interactions in driving these outcomes. We consider three characteristic and distinct cellular populations: stromal cells, tumour cells that are self-reliant in terms of microenvironmental factors and tumour cells that depend on the environment for resources but can also co-opt stroma. 
RESULTS: Using evolutionary game theory we explore a number of different scenarios that elucidate the impact of tumour-stromal interactions on the dynamics of prostate cancer growth and progression and how different treatments in the metastatic setting can affect different types of tumors.
CONCLUSIONS: The tumour microenvironment plays a crucial role selecting the traits of the tumour cells that will determine prostate cancer progression. Equally important, treatments like hormone therapy affect the selection of these cancer phenotypes making it very important to understand how they impact prostate cancer’s somatic evolution

    Signifiers as a First-class Abstraction in Hypermedia Multi-Agent Systems

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    Hypermedia APIs enable the design of reusable hypermedia clients that discover and exploit affordances on the Web. However, the reusability of such clients remains limited since they cannot plan and reason about interaction. This paper provides a conceptual bridge between hypermedia-driven affordance exploitation on the Web and methods for representing and reasoning about actions that have been extensively explored for Multi-Agent Systems (MAS) and, more broadly, Artificial Intelligence. We build on concepts and methods from Affordance Theory and Human-Computer Interaction that support interaction efficiency in open and evolvable environments to introduce signifiers as a first-class abstraction in Web-based MAS: Signifiers are designed with respect to the agent-environment context of their usage and enable agents with heterogeneous abilities to act and to reason about action. We define a formal model for the contextual exposure of signifiers in hypermedia environments that aims to drive affordance exploitation. We demonstrate our approach with a prototypical Web-based MAS where two agents with different reasoning abilities proactively discover how to interact with their environment by perceiving only the signifiers that fit their abilities. We show that signifier exposure can be inherently managed based on the dynamic agent-environment context towards facilitating effective and efficient interactions on the Web

    Dynamics of reactive and inert gases in soil air and groundwater in the context of noble gases as environmental tracers

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    Applications of inert gases in groundwater hydrology require a profound understanding of underlying biogeochemical processes. Some of these processes are, however, not well understood and therefore require further investigation. This is the first study simultaneously investigating soil air and groundwater in the context of noble gas tracer applications, accounting for seasonal effects in different climate regions. The sampled data confirm a general reliability of common assumptions proposed in the literature. In particular, a solubility-controlled description of excess air formation and of groundwater degassing can be confirmed. This study identifies certain effects which need to be taken into account to reliably evaluate noble gas patterns. First, long-term samplings suggest a permanent temperature-driven equilibration of shallow groundwater with entrapped air bubbles, even some years after recharge. Second, minor groundwater degassing is found to challenge existing excess air model approaches, depending on the amount and the fractionation of excess air. Third, soil air composition data of this study imply a potential bias of noble gas temperatures by up to about 2°C due to microbial oxygen depletion and a reduced sum value of O2+CO2. This effect causes systematically lower noble gas temperatures in tropical groundwater samples and in shallow mid-latitude groundwater samples after strong recharge during the warm season. However, a general bias of noble gas temperatures in mid-latitudes is probably prevented by a predominant recharge during the cold season, accompanied by nearly atmospheric noble gas mixing ratios in the soil air. Findings of this study provide a remarkable contribution to the reliability of noble gas tracer applications in hydrology, in particular with regard to paleoclimate reconstructions and an understanding of subsurface gas dynamics

    Analyse der Versorgungssituation autistischer Kinder und Jugendlicher im Regierungsbezirk Schwaben

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    Analyse der Versorgungssituation autistischer Kinder und Jugendlicher im Regierungsbezirk Schwaben

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