The Wavelet Trie: Maintaining an Indexed Sequence of Strings in Compressed Space

An indexed sequence of strings is a data structure for storing a string sequence that supports random access, searching, range counting and analytics operations, both for exact matches and prefix search. String sequences lie at the core of column-oriented databases, log processing, and other storage and query tasks. In these applications each string can appear several times and the order of the strings in the sequence is relevant. The prefix structure of the strings is relevant as well: common prefixes are sought in strings to extract interesting features from the sequence. Moreover, space-efficiency is highly desirable as it translates directly into higher performance, since more data can fit in fast memory. We introduce and study the problem of compressed indexed sequence of strings, representing indexed sequences of strings in nearly-optimal compressed space, both in the static and dynamic settings, while preserving provably good performance for the supported operations. We present a new data structure for this problem, the Wavelet Trie, which combines the classical Patricia Trie with the Wavelet Tree, a succinct data structure for storing a compressed sequence. The resulting Wavelet Trie smoothly adapts to a sequence of strings that changes over time. It improves on the state-of-the-art compressed data structures by supporting a dynamic alphabet (i.e. the set of distinct strings) and prefix queries, both crucial requirements in the aforementioned applications, and on traditional indexes by reducing space occupancy to close to the entropy of the sequence

Type IIA/M-theory Moduli fixing in a Class of Orientifold Models

We present the study of type II A flux vacua and their M-theory duals for compactification on a class of Calabi-Yau orientifolds. The Kaehler potential is derived from toroidal compactifications and the superpotential contains a contribution from non-Abelian gauge degrees of freedoms. We obtain complete stabilisation of the moduli. We found one supersymmetric minimum and several non supersymmetric ones. Consistency of the analysis constrains the parameters of the models in a finite region containing a finite, although very large, number of flux vacua. From the M-theory side, we found some differences in the distributions of the physical quantities with respect to the M-theory ensemble studied by Acharya et al. In particular, it is easier to find small supersymmetry breaking scale.Comment: 37 pages, 4 figures, LaTeX. Extended one Section, added reference

Linear models for thin plates of polymer gels

Within the linearized three-dimensional theory of polymer gels, we consider a sequence of problems formulated on a family of cylindrical domains whose height tends to zero. We assume that the fluid pressure is controlled at the top and bottom faces of the cylinder, and we consider two different scaling regimes for the diffusivity tensor. Through asymptotic-analysis techniques we obtain two plate models where the transverse displacement is governed by a plate equation with an extra contribution from the fluid pressure. In the limit obtained within the first scaling regime the fluid pressure is affine across the thickness and hence it is determined by its instantaneous trace on the top and bottom faces. In the second model, instead, the value of the fluid pressure is governed by a three-dimensional diffusion equation

Predictive brains: forethought and the levels of explanation

Is any unified theory of brain function possible? Following a line of thought dat- ing back to the early cybernetics (see, e.g., Cordeschi, 2002), Clark (in press) has proposed the action-oriented Hierarchical Predictive Coding (HPC) as the account to be pursued in the effort of gain- ing the “Grand Unified Theory of the Mind”—or “painting the big picture,” as Edelman (2012) put it. Such line of thought is indeed appealing, but to be effectively pursued it should be confronted with experimental findings and explana- tory capabilities (Edelman, 2012). The point we are making in this note is that a brain with predictive capa- bilities is certainly necessary to endow the agent situated in the environment with forethought or foresight, a crucial issue to outline the unified account advocated by Clark. But the capacity for fore- thought is deeply entangled with the capacity for emotions and when emotions are brought into the game, cogni- tive functions become part of a large-scale functional brain network. However, for such complex networks a consistent view of hierarchical organization in large-scale functional networks has yet to emerge (Bressler and Menon, 2010), whilst heterarchical organization is likely to play a strategic role (Berntson et al., 2012). This raises the necessity of a multilevel approach that embraces causal relations across levels of explanation in either direc- tion (bottom–up or top–down), endorsing mutual calibration of constructs across levels (Berntson et al., 2012). Which, in turn, calls for a revised perspective on Marr’s levels of analysis framework (Marr, 1982). In the following we highlight some drawbacks of Clark’s proposal in address- ing the above issues

Exact Gravitational Dual of a Plasma Ball

We present an exact solution for a black hole localized near an infrared wall in four-dimensional anti-deSitter space. By computing the holographic stress tensor we show that the CFT dual of the black hole is a 2+1-dimensional ball (i.e., a disk) of plasma at finite temperature, surrounded by vacuum. This confirms some earlier conjectures about plasma balls in AdS/CFT. We also estimate the value of the surface tension for the ball. The solution displays a number of peculiarities, most notably a non-trivial curvature of the boundary geometry, as well as other properties associated to the vanishing deconfinement temperature of the set up. We discuss how these features are related to specific physics at the infrared and ultraviolet boundaries for this solution, and should not be generic properties of plasma balls.Comment: 23 pages, 3 figure

Heat kernel for Newton-Cartan trace anomalies

We compute the leading part of the trace anomaly for a free non-relativistic scalar in 2+1 dimensions coupled to a background Newton-Cartan metric. The anomaly is proportional to 1/m, where m is the mass of the scalar. We comment on the implications of a conjectured a-theorem for non-relativistic theories with boost invariance.Comment: 18 page

A numerical method to calculate the muon relaxation function in the presence of diffusion

We present an accurate and efficient method to calculate the effect of random fluctuations of the local field at the muon, for instance in the case muon diffusion, within the framework of the strong collision approximation. The method is based on a reformulation of the Markovian process over a discretized time base, leading to a summation equation for the muon polarization function which is solved by discrete Fourier transform. The latter is formally analogous, though not identical, to the integral equation of the original continuous-time model, solved by Laplace transform. With real-case parameter values, the solution of the discrete-time strong collision model is found to approximate the continuous-time solution with excellent accuracy even with a coarse-grained time sampling. Its calculation by the fast Fourier transform algorithm is very efficient and suitable for real time fitting of experimental data even on a slow computer.Comment: 7 pages, 3 figures. Submitted to Journal of Physics: Condensed Matte