Fractional dimensional Fock space and Haldane's exclusion statistics. q/p case

The discussion of Fractional dimensional Hilbert spaces in the context of Haldane exclusion statistics is extended from the case \cite{IG} of $g=1/p$ for the statistical parameter to the case of rational $g=q/p$ with $q,p$-coprime positive integers. The corresponding statistical mechanics for a gas of such particles is constructed. This procedure is used to define the statistical mechanics for particles with irrational $g$. Applications to strongly correlated systems such as the Hubbard and $t-J$ models are discussed.Comment: 11 pages, latex, no figure

The Effects of Post-Thermal Annealing on the Emission Spectra of GaAs/AlGaAs Quantum Dots grown by Droplet Epitaxy

We fabricated GaAs/AlGaAs quantum dots by droplet epitaxy method, and obtained the geometries of the dots from scanning transmission electron microscopy data. Post-thermal annealing is essential for the optical activation of quantum dots grown by droplet epitaxy. We investigated the emission energy shifts of the dots and underlying superlattice by post-thermal annealing with photoluminescence and cathodoluminescence measurements, and specified the emissions from the dots by selectively etching the structure down to a lower layer of quantum dots. We studied the influences of the degree of annealing on the optical properties of the dots from the peak shifts of the superlattice, which has the same composition as the dots, since the superlattice has uniform and well-defined geometry. Theoretical analysis provided the diffusion length dependence of the peak shifts of the emission spectra

Contextual Sequence Modeling for Recommendation with Recurrent Neural Networks

Recommendations can greatly benefit from good representations of the user state at recommendation time. Recent approaches that leverage Recurrent Neural Networks (RNNs) for session-based recommendations have shown that Deep Learning models can provide useful user representations for recommendation. However, current RNN modeling approaches summarize the user state by only taking into account the sequence of items that the user has interacted with in the past, without taking into account other essential types of context information such as the associated types of user-item interactions, the time gaps between events and the time of day for each interaction. To address this, we propose a new class of Contextual Recurrent Neural Networks for Recommendation (CRNNs) that can take into account the contextual information both in the input and output layers and modifying the behavior of the RNN by combining the context embedding with the item embedding and more explicitly, in the model dynamics, by parametrizing the hidden unit transitions as a function of context information. We compare our CRNNs approach with RNNs and non-sequential baselines and show good improvements on the next event prediction task

From Query-By-Keyword to Query-By-Example: LinkedIn Talent Search Approach

One key challenge in talent search is to translate complex criteria of a hiring position into a search query, while it is relatively easy for a searcher to list examples of suitable candidates for a given position. To improve search efficiency, we propose the next generation of talent search at LinkedIn, also referred to as Search By Ideal Candidates. In this system, a searcher provides one or several ideal candidates as the input to hire for a given position. The system then generates a query based on the ideal candidates and uses it to retrieve and rank results. Shifting from the traditional Query-By-Keyword to this new Query-By-Example system poses a number of challenges: How to generate a query that best describes the candidates? When moving to a completely different paradigm, how does one leverage previous product logs to learn ranking models and/or evaluate the new system with no existing usage logs? Finally, given the different nature between the two search paradigms, the ranking features typically used for Query-By-Keyword systems might not be optimal for Query-By-Example. This paper describes our approach to solving these challenges. We present experimental results confirming the effectiveness of the proposed solution, particularly on query building and search ranking tasks. As of writing this paper, the new system has been available to all LinkedIn members

Characterization of One-Dimensional Luttinger Liquids in Terms of Fractional Exclusion Statistics

We develop a bosonization approach to study the low temperature properties of one-dimensional gas of particles obeying fractional exclusion statistics (FES). It is shown that such ideal gas reproduces the low-energy excitations and asymptotic exponents of a one-component Luttinger liquid (with no internal degrees of freedom). The bosonized effective theory at low energy (or temperature) is identified to a $c=1$ conformal field theory (CFT) with compactified radius determined by the statistics parameter $\lambda$. Moreover, this CFT can be put into a form of the harmonic fluid description for Luttinger liquids, with the Haldane controlling parameter identified with the statistics parameter (of quasi-particle excitations). Thus we propose to use the latter to characterize the fixed points of 1-d Luttinger liquids. Such a characterization is further shown to be valid for generalized ideal gas of particles with mutual statistics in momentum space and for non-ideal gas with Luttinger-type interactions: In either case, the low temperature behavior is controlled by an effective statistics varying in a fixed-point line.Comment: 16 pages, a reference adde

Combinatorial interpretation of Haldane-Wu fractional exclusion statistics

Assuming that the maximal allowed number of identical particles in state is an integer parameter, q, we derive the statistical weight and analyze the associated equation which defines the statistical distribution. The derived distribution covers Fermi-Dirac and Bose-Einstein ones in the particular cases q = 1 and q -> infinity (n_i/q -> 1), respectively. We show that the derived statistical weight provides a natural combinatorial interpretation of Haldane-Wu fractional exclusion statistics, and present exact solutions of the distribution equation.Comment: 8 pages, 2 eps-figure