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

We prove an upper bound on the free energy of a two-dimensional homogeneous Bose gas in the thermodynamic limit. We show that for $a^2 \rho \ll 1$ and $\beta \rho \gtrsim 1$ the free energy per unit volume differs from the one of the non-interacting system by at most $4 \pi \rho^2 |\ln a^2 \rho|^{-1} (2 - [1 - \beta_{\mathrm{c}}/\beta]_+^2)$ to leading order, where $a$ is the scattering length of the two-body interaction potential, $\rho$ is the density, $\beta$ the inverse temperature and $\beta_{\mathrm{c}}$ 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

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

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

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

Quorum sensing architecture network in Escherichia coli virulence and pathogenesis

Escherichia coli is a Gram-negative commensal bacterium of the normal microbiota of humans and animals. However, several E. coli strains are opportunistic pathogens responsible for severe bacterial infections, including gastrointestinal and urinary tract infections. Due to the emergence of multidrug-resistant serotypes that can cause a wide spectrum of diseases, E. coli is considered one of the most troublesome human pathogens worldwide. Therefore, a more thorough understanding of its virulence control mechanisms is essential for the development of new anti-pathogenic strategies. Numerous bacteria rely on a cell density-dependent communication system known as quorum sensing (QS) to regulate several bacterial functions, including the expression of virulence factors. The QS systems described for E. coli include the orphan SdiA regulator, an autoinducer-2 (AI-2), an autoinducer-3 (AI-3) system, and indole, which allow E. coli to establish different communication processes to sense and respond to the surrounding environment. This review aims to summarise the current knowledge of the global QS network in E. coli and its influence on virulence and pathogenesis. This understanding will help to improve anti-virulence strategies with the E. coli QS network in focus. This review highlights the latest findings in the field of cell-to-cell communication systems in Escherichia coli and discusses the relevance of this complicated signalling network for the virulence and pathogenesis of this bacterium