arXiv subjects

Xiao Xiao

Publications and source records attributed to Xiao Xiao.

At least 91 records · Page 5Linked to original sources

arXiv2017

Failure to replicate long-range tunable attractions in colloidal system

Recently, a temperature-sensitive long-range attraction colloidal system exhibiting melting and pre-melting of colloidal crystals has been reported by Li et al.[1]. If it is true, it would be an ideal system to simulate a board range of phase transitions happening in atomic systems. We have reanalyzed their data in [1] and have discovered great inconsistency in their radial distribution functions g(r) and pair potentials u(r). We have tried to reproduce their experimental results but failed to find the temperature-sensitive long rang attraction as reported by Li et al. Based on our experimental observations, We conclude that the melting and premelting reported in their paper are non-equilibrium phenomena caused by non-uniform temperature in the samples of Li et al..

cond-mat.soft↗

arXiv2017

Odd-integer quantum Hall states and giant spin susceptibility in p-type few-layer WSe2

We fabricate high-mobility p-type few-layer WSe2 field-effect transistors and surprisingly observe a series of quantum Hall (QH) states following an unconventional sequence predominated by odd-integer states under a moderate strength magnetic field. By tilting the magnetic field, we discover Landau level (LL) crossing effects at ultra-low coincident angles, revealing that the Zeeman energy is about three times as large as the cyclotron energy near the valence band top at Γ valley. This result implies the significant roles played by the exchange interactions in p-type few-layer WSe2, in which itinerant or QH ferromagnetism likely occurs. Evidently, the Γ valley of few-layer WSe2 offers a unique platform with unusually heavy hole-carriers and a substantially enhanced g-factor for exploring strongly correlated phenomena.

cond-mat.mes-hall↗

arXiv2016

Minimal $F$-crystals and isomorphism numbers of isosimple $F$-crystals

In this paper we generalize minimal $p$-divisible groups defined by Oort to $F$-crystal over an algebraically closed field of positive characteristic. We prove a structural theorem and give an explicit formula of the Frobenius endomorphism of the isosimple minimal $F$-crystals that are the building blocks of minimal $F$-crystals. We then define an invariant called the minimal height for $F$-crystals using minimal $F$-crystals and give an upper bound of the isomorphism numbers of isosimple $F$-crystals in terms of their ranks, Hodge slopes and Newton slopes.

math.NT↗

arXiv2015

Comparing process-based and constraint-based approaches for modeling macroecological patterns

Ecological patterns arise from the interplay of many different processes, and yet the emergence of consistent phenomena across a diverse range of ecological systems suggests that many patterns may in part be determined by statistical or numerical constraints. Differentiating the extent to which patterns in a given system are determined statistically, and where it requires explicit ecological processes, has been difficult. We tackled this challenge by directly comparing models from a constraint-based theory, the Maximum Entropy Theory of Ecology (METE) and models from a process-based theory, the size-structured neutral theory (SSNT). Models from both theories were capable of characterizing the distribution of individuals among species and the distribution of body size among individuals across 76 forest communities. However, the SSNT models consistently yielded higher overall likelihood, as well as more realistic characterizations of the relationship between species abundance and average body size of conspecific individuals. This suggests that the details of the biological processes contain additional information for understanding community structure that are not fully captured by the METE constraints in these systems. Our approach provides a first step towards differentiating between process- and constraint-based models of ecological systems and a general methodology for comparing ecological models that make predictions for multiple patterns.

q-bio.PE↗

arXiv2015

Holographic Representation of Higher Spin Gauge Fields

Extending the results of \cite{Heem}, \cite{KLRS} on the holographic representation of local gauge field operators in anti de Sitter space, here we construct the bulk operators for higher spin gauge fields in the leading order of $\frac{1}{N}$ expansion. Working in holographic gauge for higher spin gauge fields, we show that gauge field operators with integer spin $s>1$ can be represented by an integration over a ball region, which is the interior region of the spacelike bulk lightcone on the boundary. The construction is shown to be AdS-covariant up to gauge transformations, and the two-point function between higher spin gauge fields and boundary higher spin current exhibit singularities on both bulk and boundary lightcones. We also comment on possible extension to the level of three-point functions and carry out a causal construction for higher spin fields in de Sitter spacetime.

hep-th↗

arXiv2015

Lagrangian space consistency relation for large scale structure

Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present. The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.

hep-th↗

arXiv2015

A process-independent explanation for the general form of Taylor's Law

Taylors Law (TL) describes the scaling relationship between the mean and variance of populations as a power-law. TL is widely observed in ecological systems across space and time with exponents varying largely between 1 and 2. Many ecological explanations have been proposed for TL but it is also commonly observed outside ecology. We propose that TL arises from the constraining influence of two primary variables: the number of individuals and the number of censuses or sites. We show that most possible configurations of individuals among censuses or sites produce the power-law form of TL with exponents between 1 and 2. This feasible set approach suggests that TL is a statistical pattern driven by two constraints, providing an a priori explanation for this ubiquitous pattern. However, the exact form of any specific mean-variance relationship cannot be predicted in this way, i.e., this approach does a poor job of predicting variation in the exponent, suggesting that TL may still contain ecological information.

q-bio.PE↗

arXiv2014

Subtle Invariants of $F$-crystals

Vasiu proved that the level torsion $\ell_{\mathcal{M}}$ of an $F$-crystal $\mathcal{M}$ over an algebraically closed field of characteristic $p>0$ is a non-negative integer that is an effectively computable upper bound of the isomorphism number $n_{\mathcal{M}}$ of $\mathcal{M}$ and expected that in fact one always has $n_{\mathcal{M}} = \ell_{\mathcal{M}}$. In this paper, we prove that this equality holds.

math.NT↗

arXiv2014

The effect of surface buoyancy gradients on oceanic Rossby wave propagation

Motivated by the discrepancy between satellite observations of coherent westward propagating surface features and Rossby wave theory, this paper revisits the planetary wave propagation problem, taking into account the effects of lateral buoyancy gradients at the ocean's surface. The standard theory for long baroclinic Rossby waves is based on an expansion of the quasigeostrophic stretching operator in normal modes, $ϕ_n(z)$, satisfying a Neumann boundary condition at the surface, $ϕ_n'(0) = 0$. Buoyancy gradients are, by thermal wind balance, proportional to the vertical derivative of the streamfunction, thus such modes are unable to represent ubiquitous lateral buoyancy gradients in the ocean's mixed layer. Here, we re-derive the wave propagation problem in terms of an expansion in a recently-developed "surface-aware" (SA) basis that can account for buoyancy anomalies at the ocean's surface. The problem is studied in the context of an idealized Charney-like baroclinic wave problem set in an oceanic context, where a surface mean buoyancy gradient interacts with a constant interior potential vorticity gradient that results from both $β$ and the curvature of the mean shear. The wave frequencies, growth rates and phases are systematically compared to those computed from a two-layer model, a truncated expansion in standard baroclinic modes and to a high-vertical resolution calculation that represents the true solution. The full solution generally shows faster wave propagation when lateral surface gradients are present. Moreover, the wave problem in the SA basis best captures the full solution, even with just a two or three modes.

physics.ao-ph↗

arXiv2014

Note on Adiabatic Modes and Ward Identities In A Closed Universe

As statements regarding the soft limit of cosmological correlation functions, consistency relations are known to exist in any flat FRW universe. In this letter we explore the possibility of finding such relations in a spatially closed universe, where the soft limit $\textbf{q}\rightarrow 0$ does not exist in any rigorous sense. Despite the absence of spatial infinity of the spatial slices, we find the adiabatic modes and their associated consistency relations in a toy universe with background topology $R\times S^2$. Flat FRW universe adiabatic modes are recovered via taking the large radius limit $R\gg \mathcal{H}^{-1}$, for which we are living in a small local patch of Hubble size on the sphere. It is shown that both dilation and translation adiabatic modes in the local patch are recovered by a global dilation on the sphere, acting at different places.

hep-th↗

arXiv2014

Holographic Representation of Local Operators In De Sitter Space

Assuming the existence of the dS/CFT correspondence, we construct local scalar fields with $m^2>\left( \frac{d}{2} \right)^2$ in de Sitter space by smearing over conformal field theory operators on the future/past boundary. To maintain bulk micro-causality and recover the bulk Wightman function in the Euclidean vacuum, the smearing prescription must involve two sets of single--trace operators with dimensions $Δ$ and $d-Δ$. Thus the local operator prescription in de Sitter space differs from the analytic continuation from the prescription in anti--de Sitter space. Pushing a local operator in the global patch to future/past infinity is shown to lead to an operator relation between single--trace operators in conformal field theories at $\mathcal{I}^\pm$, which can be interpreted as a basis transformation, also identified as the relation between an operator in CFT and its shadow operator. Construction of spin$-s$ gauge field operators is discussed, it is shown that the construction of higher spin gauge fields in de Sitter space is equivalent to constructing scalar fields with specific values of mass parameter $m^2<\left( \frac{d}{2} \right)^2$. An acausal higher spin bulk operator which matches onto boundary higher spin current is constructed. Implementation of the scalar operator constructions in AdS and dS with embedding formalism is briefly described.

hep-th↗

arXiv2014

Multiplicative Iteration for Nonnegative Quadratic Programming

In many applications, it makes sense to solve the least square problems with nonnegative constraints. In this article, we present a new multiplicative iteration that monotonically decreases the value of the nonnegative quadratic programming (NNQP) objective function. This new algorithm has a simple closed form and is easily implemented on a parallel machine. We prove the global convergence of the new algorithm and apply it to solving image super-resolution and color image labelling problems. The experimental results demonstrate the effectiveness and broad applicability of the new algorithm.

math.NA↗

arXiv2014

Soft-Pion Theorems for Large Scale Structure

Consistency relations -- which relate an N-point function to a squeezed (N+1)-point function -- are useful in large scale structure (LSS) because of their non-perturbative nature: they hold even if the N-point function is deep in the nonlinear regime, and even if they involve astrophysically messy galaxy observables. The non-perturbative nature of the consistency relations is guaranteed by the fact that they are symmetry statements, in which the velocity plays the role of the soft pion. In this paper, we address two issues: (1) how to derive the relations systematically using the residual coordinate freedom in the Newtonian gauge, and relate them to known results in $ζ$-gauge (often used in studies of inflation); (2) under what conditions the consistency relations are violated. In the non-relativistic limit, our derivation reproduces the Newtonian consistency relation discovered by Kehagias \& Riotto and Peloso & Pietroni. More generally, there is an infinite set of consistency relations, as is known in $ζ$-gauge. There is a one-to-one correspondence between symmetries in the two gauges; in particular, the Newtonian consistency relation follows from the dilation and special conformal symmetries in $ζ$-gauge. We probe the robustness of the consistency relations by studying models of galaxy dynamics and biasing. We give a systematic list of conditions under which the consistency relations are violated; violations occur if the galaxy bias is non-local in an infrared divergent way. We emphasize the relevance of the adiabatic mode condition, as distinct from symmetry considerations. As a by-product of our investigation, we discuss a simple fluid Lagrangian for LSS.

hep-th↗

arXiv2013

A strong test of the Maximum Entropy Theory of Ecology

The Maximum Entropy Theory of Ecology (METE) is a unified theory of biodiversity that predicts a large number of macroecological patterns using only information on the species richness, total abundance, and total metabolic rate of the community. We evaluated four major predictions of METE simultaneously at an unprecedented scale using data from 60 globally distributed forest communities including over 300,000 individuals and nearly 2000 species. METE successfully captured 96% and 89% of the variation in the species abundance distribution and the individual size distribution, but performed poorly when characterizing the size-density relationship and intraspecific distribution of individual size. Specifically, METE predicted a negative correlation between size and species abundance, which is weak in natural communities. By evaluating multiple predictions with large quantities of data, our study not only identifies a mismatch between abundance and body size in METE, but also demonstrates the importance of conducting strong tests of ecological theories.

q-bio.PE↗

arXiv2013

An empirical evaluation of four variants of a universal species-area relationship

The Maximum Entropy Theory of Ecology (METE) predicts a universal species-area relationship (SAR) that can be fully characterized using only the total abundance (N) and species richness (S) at a single spatial scale. This theory has shown promise for characterizing scale dependence in the SAR. However, there are currently four different approaches to applying METE to predict the SAR and it is unclear which approach should be used due to a lack of empirical evaluation. Specifically, METE can be applied recursively or a non-recursively and can use either a theoretical or observed species-abundance distribution (SAD). We compared the four different combinations of approaches using empirical data from 16 datasets containing over 1000 species and 300,000 individual trees and herbs. In general, METE accurately downscaled the SAR (R^2> 0.94), but the recursive approach consistently under-predicted richness, and METEs accuracy did not depend strongly on using the observed or predicted SAD. This suggests that best approach to scaling diversity using METE is to use a combination of non-recursive scaling and the theoretical abundance distribution, which allows predictions to be made across a broad range of spatial scales with only knowledge of the species richness and total abundance at a single scale.

q-bio.QM↗

arXiv2013

Tumbling through a landscape: Evidence of instabilities in high-dimensional moduli spaces

We argue that a generic instability afflicts vacua that arise in theories whose moduli space has large dimension. Specifically, by studying theories with multiple scalar fields we provide numerical evidence that for a generic local minimum of the potential the usual semiclassical bubble nucleation rate, Gamma = A e^{-B}, increases rapidly as function of the number of fields in the theory. As a consequence, the fraction of vacua with tunneling rates low enough to maintain metastability appears to fall exponentially as a function of the moduli space dimension. We discuss possible implications for the landscape of string theory. Notably, if our results prove applicable to string theory, the landscape of metastable vacua may not contain sufficient diversity to offer a natural explanation of dark energy.

hep-th↗

arXiv2012

Bubble Nucleation of Spatial Vector Fields

We study domain-walls and bubble nucleation in a non-relativistic vector field theory with different longitudinal and transverse speeds of sound. We describe analytical and numerical methods to calculate the orientation dependent domain-wall tension, $σ(θ)$. We then use this tension to calculate the critical bubble shape. The longitudinally oriented domain-wall tends to be the heaviest, and sometime suffers an instability. It can spontaneously break into zigzag segments. In this case, the critical bubble develops kinks, and its energy, and therefore the tunneling rate, scales with the sound speeds very differently than what would be expected for a smooth bubble.

hep-th↗

arXiv2012

Computing isomorphism numbers of F-crystals by using level torsions

The isomorphism number of an $F$-crystal $(M, ϕ)$ over an algebraically closed field of positive characteristic is the smallest non-negative integer $n_M$ such that the $n_M$-th level truncation of $(M, ϕ)$ determines the isomorphism class of $(M, ϕ)$. When $(M, ϕ)$ is isoclinic, namely it has a unique Newton slopes $λ$, we provide an efficiently computable upper bound of $n_M$ in terms of the Hodge slopes of $(M, ϕ)$ and $λ$. This is achieved by providing an upper bound of the level torsion of $(M, ϕ)$ introduced by Vasiu. We also check that this upper bound is optimal for many families of isoclinic $F$-crystals that are of special interests (such as isoclinic $F$-crystals of K3 type).

math.NT↗