Moist-entropic vertical adiabatic lapse rates: the standard cases and some lead towards inhomogeneous conditions

This note is a companion of Marquet and Geleyn (2013, {arXiv:1401.2379 [ao-ph]}), where adiabatic lapse rates $\Gamma_{ns}$ and $\Gamma_{sw}$ are derived for non-saturated ($\Gamma_{ns}$) or saturated ($\Gamma_{sw}$) parcel of moist-air. They are computed in terms of the vertical derivative of the moist-air entropy potential temperature $\theta_s$ defined in Marquet (2011, {arXiv:1401.1097 [ao-ph]}). The saturated value $\Gamma_{sw}$ is rewritten in this note so that a more compact formulation is obtained. The new formulation for $\Gamma_{sw}$ is expressed in term of a weighting factor $C$. This factor may represent the proportion of an air parcel being in saturated conditions.Comment: Based on a note published in the WGNE Blue-Book in 2012 (3 pages, 0 Figures). V2: add arXiv links to Marquet (2011) and Marquet and Geleyn (2013

Formulations of moist thermodynamics for atmospheric modelling

Internal energy, enthalpy and entropy are the key quantities to study thermodynamic properties of the moist atmosphere, because they correspond to the First (internal energy and enthalpy) and Second (entropy) Laws of thermodynamics. The aim of this chapter is to search for analytical formulas for the specific values of enthalpy and entropy and for the moist-air mixture composing the atmosphere. The Third Law of thermodynamics leads to the definition of absolute reference values for thermal enthalpies and entropies of all atmospheric species. It is shown in this Chapter 22 that it is possible to define and compute a general moist-air entropy potential temperature, which is really an equivalent of the moist-air specific entropy in all circumstances (saturated, or not saturated). Similarly, it is shown that it is possible to define and compute the moist-air specific enthalpy, which is different from the thermal part of what is called Moist-Static-Energy in atmospheric studies.Comment: 44 pages, 8 figures, URL:http://www.worldscientific.com/doi/abs/10.1142/9781783266913_002

On a general definition of the squared Brunt-V\"{a}is\"{a}l\"{a} Frequency associated with the specific moist entropy potential temperature

The squared Brunt-V\"{a}is\"{a}l\"{a} Frequency (BVF) is computed in terms of the moist entropy potential temperature recently defined in Marquet (2011). Both homogeneously saturated and non-saturated versions of $N^2$ (the squared BVF) are derived. The method employed for computing these special homogeneous cases relies on the expression of density written as a function of pressure, total water content and specific moist entropy only. The associated conservative variable diagrams are discussed and compared with existing ones. Despite being obtained without any simplification, the formulations for $N^2$ remain nicely compact and are clearly linked with the squared BVF expressed in terms of the adiabatic non-saturated and saturated lapse rates. As in previous similar expressions, the extreme homogeneous solutions for $N^2$ are of course different, but they are not analytically discontinuous. This allows us to define a simple bridging expression for a single general shape of $N^2$, depending only on the basic mean atmospheric quantities and on a transition parameter, to be defined (or parameterized) in connection with the type of application sought. This integrated result remains a linear combination (with complex but purely local weights) of two terms only, namely the environmental gradient of the moist entropy potential temperature and the environmental gradient of the total water content. Simplified versions of the various equations are also proposed for the case in which the moist entropy potential temperature is approximated by a function of both so-called moist-conservative variables of Betts (1973).Comment: Paper submitted in July 2011 to the Quarterly Journal of the Royal Meteorological Society. Published: Volume 139, Issue 670, pages 85-100, January 2013 Part A. http://onlinelibrary.wiley.com/doi/10.1002/qj.1957/abstract (27 pages / 10 black and white Figures). V2: add arXiv link to Marquet (2011

A Portfolio Approach to Venture Capital Financing

This paper studies the contracting choices between an entrepreneur and venture capital investors in a portfolio context. We rely on the mean-variance framework and derive the optimal choices for an entrepreneur with and without the presence of different kinds of venture capitalists. In particular, we show that the entrepreneur always has the incentive to share the risk and benefits of the venture whenever possible. On the basis of their objectives and characteristics, we distinguish the situations of the corporate, independent, and bank-sponsored venture capital funds. Our framework enables us to derive the optimal contract design for the entrepreneur, featuring the choice of investor, the entrepreneur’s investment in the venture, and her dilution in the project’s equity as a function of her bargaining power. This result allows us to characterize the choice of the investor depending on her cost of equity and debt capital. In addition to project size and risk, entrepreneur’s risk aversion turns out to be a critical determinant of VC investor choice –a finding which is strongly supported by a panel analysis of VC fund flows for 5 European countries over the 2002-2009 period.Venture capital, Portfolio choice, Entrepreneur, Risk aversion

Incompressible states of a two-component Fermi gas in a double-well optical lattice

We propose a scheme to investigate the effect of frustration on the magnetic phase transitions of cold atoms confined in an optical lattice. We also demonstrate how to get two-leg spin ladders with frustrated spin-exchange coupling which display a phase transition from a spin liquid to a fully incompressible state. Various experimental quantities are further analyzed for describing this phase.Comment: 10 pages, 7 figures. Published in Phys. Rev.

Deep Occlusion Reasoning for Multi-Camera Multi-Target Detection

People detection in single 2D images has improved greatly in recent years. However, comparatively little of this progress has percolated into multi-camera multi-people tracking algorithms, whose performance still degrades severely when scenes become very crowded. In this work, we introduce a new architecture that combines Convolutional Neural Nets and Conditional Random Fields to explicitly model those ambiguities. One of its key ingredients are high-order CRF terms that model potential occlusions and give our approach its robustness even when many people are present. Our model is trained end-to-end and we show that it outperforms several state-of-art algorithms on challenging scenes

Multi-Modal Mean-Fields via Cardinality-Based Clamping

Mean Field inference is central to statistical physics. It has attracted much interest in the Computer Vision community to efficiently solve problems expressible in terms of large Conditional Random Fields. However, since it models the posterior probability distribution as a product of marginal probabilities, it may fail to properly account for important dependencies between variables. We therefore replace the fully factorized distribution of Mean Field by a weighted mixture of such distributions, that similarly minimizes the KL-Divergence to the true posterior. By introducing two new ideas, namely, conditioning on groups of variables instead of single ones and using a parameter of the conditional random field potentials, that we identify to the temperature in the sense of statistical physics to select such groups, we can perform this minimization efficiently. Our extension of the clamping method proposed in previous works allows us to both produce a more descriptive approximation of the true posterior and, inspired by the diverse MAP paradigms, fit a mixture of Mean Field approximations. We demonstrate that this positively impacts real-world algorithms that initially relied on mean fields.Comment: Submitted for review to CVPR 201

Start-ups Defined as Portfolios of Embedded Options

In this paper we show the advantages of staged investments for venture capitalists. We develop an option-pricing model that enables to evaluate the flexibility acquired by a venture capitalist when he stages his investment process. Instead of investing a fixed amount at the beginning of the investment, the venture capitalist proceeds to a staged investment (one first investment and a second investment). The second investment will be triggered by a successful achievement of the first investment. Should the first investment be unsuccessful, the second investment will not be executed. Staging the investment in two phases enables the investor to reduce its uncertainty at the beginning of the project. As it will be demonstrated in the paper, the decision to proceed to the second investment can be modelled as a portfolio of a call option and a binary option.real options, staged investments, structured products, embedded options