Rationality of Euler-Chow series and finite generation of Cox rings

In this paper we work with a series whose coefficients are the Euler characteristic of Chow varieties of a given projective variety. For varieties where the Cox ring is defined, it is easy to see that in this case the ring associated to the series is the Cox ring. If this ring is noetherian then the series is rational. It is an open question whether the converse holds. In this paper we give an example showing the converse fails. However we conjecture that it holds when the variety is rationally connected. As an evidence of this conjecture, It is proved that the series is not rational, and in a sense defined, not algebraic, in the case of the blowup of the projective plane at nine or more points in general position. Furthermore, we also treat some other examples of varieties with infinitely generated Cox ring, studied by Mukai and Hassett-Tschinkel. These are the first examples known where the series is not rational. We also compute the series for Del Pezzo surfaces.Comment: 26 pages. In this last version we correct many typos and add a cite of a work of Artebani and Laface in Theorem 1.6 which was brought to our attention. More typo correction

Universal Properties of Fermi Gases in One-dimension

In this Rapid Communication, we investigate the universal properties of a spin-polarized two-component Fermi gas in one dimension (1D) using Bethe ansatz. We discuss the quantum phases and phase transitions by obtaining exact results for the equation of state, the contact, the magnetic susceptibility and the contact susceptibility, giving a precise understanding of the 1D analogue of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimension (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility $\chi \sim {1}/{\sqrt{T}}\exp(-\Delta/T)$ at low temperatures, where $\Delta$ is the energy gap and $T$ is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization $P$ and the contact $C$ for both repulsive and attractive Fermi gases. Our findings emphasize the role of the pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions.Comment: 4 figures, the main pape

The Effect of Social Crowdedness on Preference for Utilitarian Products

In a modern society with high population density, consumers usually face crowded consumption environment. Meanwhile, the choices they can make are more and more abundant. Is there any correlation between social crowdedness and the preference for different types of products? This research investigates whether social crowdedness, defined as the number of people in a given area—impacts consumers’ propensity to choose functional products rather than hedonic products. We propose that social crowdedness increases the likelihood of preference for functional products rather than hedonic products. This effect occurs because density settings make consumers experience a loss of perceived control, which in turn makes them engage in interpretive cognition, exhibit a desire for structured and meaningful products, and practical function of the product as a compensatory method to help them regain control. Two studies provide support for this hypothesis. Study 1 confirms the relationship between social crowdedness and the product type preference. Study 2 examined the mediating role of perceived control as the underlying mechanism, which is, social crowdedness gives rise to a feeling of loss of perceived control, to fill up this, consumers seek products with more practical and useful function feature rather than hedonic and pleasure-oriented products as compensation to fill the gap. This study expands the research in the fields of social crowdedness from consumer behavioral perspectives. Also, the research may contribute to the marketing planning of different types of commodities in various environments

Boolean function monotonicity testing requires (almost) n1/2n^{1/2} non-adaptive queries

We prove a lower bound of $\Omega(n^{1/2 - c})$, for all $c>0$, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an $n$-variable Boolean function is monotone versus constant-far from monotone. This improves a $\tilde{\Omega}(n^{1/5})$ lower bound for the same problem that was recently given in [CST14] and is very close to $\Omega(n^{1/2})$, which we conjecture is the optimal lower bound for this model

A Benchmarking Model for Household Water Consumption Based on Adaptive Logic Networks

Household water benchmarking is an important step in evaluating a household's water usage and comparing it with similar house- holds. It can provide an indicator if a household consumes more water than usual during a certain period of time or some households consume more than other similar households in a particular region. This paper proposes a benchmarking model for household water consumption based on Adaptive Logic Networks (ALNs). Real world data collected by a water consumption monitoring system installed in Sosnowiec, Poland and Skiathos, Greece is respectively used to build a model for each city. The results indicate that the developed models can successfully prediction for a particular use purpose