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Published work

31 published item(s)

preprint2026arXiv

Evaluating Developmental Cognition Capabilities of LLMs

Conversational AI is increasingly personalized around users' preferences, histories, goals, and knowledge, but much less around how users interpret and take up model outputs to construct and understand their reality. We draw on Robert Kegan's constructive-developmental theory as a complementary lens on this dimension. Existing methods for assessing developmental stage in the Keganian tradition rely either on expert interviews that do not scale or on sentence-completion instruments that are proprietary, lengthy, or invasive. To make this perspective tractable for LLM evaluation, we introduce the Developmental Sentence Completion Test (DSCT), a 20-item instrument designed to elicit developmental signal in self-administered text. Throughout, we treat the resulting labels as characterizations of stage-like structure in elicited responses, not as validated person-level developmental stage. We then ask how much of that signal can be recovered by LLMs across three elicited response regimes: simulated personas, real human respondents, and default model-generated answers. On simulated personas, top frontier models recover simulator-intended labels with high accuracy. On real human DSCT responses, human-LLM agreement is fair, with much stronger within-neighborhood than exact agreement. Finally, when LLMs answer DSCT prompts without persona-conditioning, their responses exhibit stable stage-like differences across model families, with larger and newer models tending to generate higher-rated text. These results suggest that stage-conditioned signal is cleaner in synthetic responses than in human-written DSCT text, and that the core constraint for stage-aware conversational AI is not classifier accuracy alone, but the availability of developmental signal from elicited text.

preprint2024arXiv

CodeFuse-Query: A Data-Centric Static Code Analysis System for Large-Scale Organizations

In the domain of large-scale software development, the demands for dynamic and multifaceted static code analysis exceed the capabilities of traditional tools. To bridge this gap, we present CodeFuse-Query, a system that redefines static code analysis through the fusion of Domain Optimized System Design and Logic Oriented Computation Design. CodeFuse-Query reimagines code analysis as a data computation task, support scanning over 10 billion lines of code daily and more than 300 different tasks. It optimizes resource utilization, prioritizes data reusability, applies incremental code extraction, and introduces tasks types specially for Code Change, underscoring its domain-optimized design. The system's logic-oriented facet employs Datalog, utilizing a unique two-tiered schema, COREF, to convert source code into data facts. Through Godel, a distinctive language, CodeFuse-Query enables formulation of complex tasks as logical expressions, harnessing Datalog's declarative prowess. This paper provides empirical evidence of CodeFuse-Query's transformative approach, demonstrating its robustness, scalability, and efficiency. We also highlight its real-world impact and diverse applications, emphasizing its potential to reshape the landscape of static code analysis in the context of large-scale software development.Furthermore, in the spirit of collaboration and advancing the field, our project is open-sourced and the repository is available for public access

preprint2022arXiv

A Miniature 3-DoF Flexible Parallel Robotic Wrist Using NiTi Wires for Gastrointestinal Endoscopic Surgery

Gastrointestinal endoscopic surgery (GES) has high requirements for instruments' size and distal dexterity, because of the narrow endoscopic channel and long, tortuous human gastrointestinal tract. This paper utilized Nickel-Titanium (NiTi) wires to develop a miniature 3-DoF (pitch-yaw-translation) flexible parallel robotic wrist (FPRW). Additionally, we assembled an electric knife on the wrist's connection interface and then teleoperated it to perform an endoscopic submucosal dissection (ESD) on porcine stomachs. The effective performance in each ESD workflow proves that the designed FPRW has sufficient workspace, high distal dexterity, and high positioning accuracy.

preprint2022arXiv

An Embedding-Based Grocery Search Model at Instacart

The key to e-commerce search is how to best utilize the large yet noisy log data. In this paper, we present our embedding-based model for grocery search at Instacart. The system learns query and product representations with a two-tower transformer-based encoder architecture. To tackle the cold-start problem, we focus on content-based features. To train the model efficiently on noisy data, we propose a self-adversarial learning method and a cascade training method. AccOn an offline human evaluation dataset, we achieve 10% relative improvement in RECALL@20, and for online A/B testing, we achieve 4.1% cart-adds per search (CAPS) and 1.5% gross merchandise value (GMV) improvement. We describe how we train and deploy the embedding based search model and give a detailed analysis of the effectiveness of our method.

preprint2022arXiv

Fast Quantum Calibration using Bayesian Optimization with State Parameter Estimator for Non-Markovian Environment

As quantum systems expand in size and complexity, manual qubit characterization and gate optimization will be a non-scalable and time-consuming venture. Physical qubits have to be carefully calibrated because quantum processors are very sensitive to the external environment, with control hardware parameters slowly drifting during operation, affecting gate fidelity. Currently, existing calibration techniques require complex and lengthy measurements to independently control the different parameters of each gate and are unscalable to large quantum systems. Therefore, fully automated protocols with the desired functionalities are required to speed up the calibration process. This paper aims to propose single-qubit calibration of superconducting qubits under continuous weak measurements from a real physical experimental settings point of view. We propose a real-time optimal estimator of qubit states, which utilizes weak measurements and Bayesian optimization to find the optimal control pulses for gate design. Our numerical results demonstrate a significant reduction in the calibration process, obtaining a high gate fidelity. Using the proposed estimator we estimated the qubit state with and without measurement noise and the estimation error between the qubit state and the estimator state is less than 0.02. With this setup, we drive an approximated pi pulse with final fidelity of 0.9928. This shows that our proposed strategy is robust against the presence of measurement and environmental noise and can also be applicable for the calibration of many other quantum computation technologies.

preprint2022arXiv

Long-term Spatio-temporal Forecasting via Dynamic Multiple-Graph Attention

Many real-world ubiquitous applications, such as parking recommendations and air pollution monitoring, benefit significantly from accurate long-term spatio-temporal forecasting (LSTF). LSTF makes use of long-term dependency between spatial and temporal domains, contextual information, and inherent pattern in the data. Recent studies have revealed the potential of multi-graph neural networks (MGNNs) to improve prediction performance. However, existing MGNN methods cannot be directly applied to LSTF due to several issues: the low level of generality, insufficient use of contextual information, and the imbalanced graph fusion approach. To address these issues, we construct new graph models to represent the contextual information of each node and the long-term spatio-temporal data dependency structure. To fuse the information across multiple graphs, we propose a new dynamic multi-graph fusion module to characterize the correlations of nodes within a graph and the nodes across graphs via the spatial attention and graph attention mechanisms. Furthermore, we introduce a trainable weight tensor to indicate the importance of each node in different graphs. Extensive experiments on two large-scale datasets demonstrate that our proposed approaches significantly improve the performance of existing graph neural network models in LSTF prediction tasks.

preprint2022arXiv

The Arithmetic Partial Derivative

The arithmetic partial derivative (with respect to a prime $p$) is a function from the set of integers that sends $p$ to 1 and satisfies the Leibniz rule. In this paper, we prove that the $p$-adic valuation of the sequence of higher order partial derivatives is eventually periodic. We also prove a criterion to determine when an integer has integral anti-partial derivatives. As an application, we show that there are infinitely many integers with exactly $n$ integral anti-partial derivatives for any nonnegative integer $n$.

preprint2021arXiv

Computational modelling and data-driven homogenisation of knitted membranes

Knitting is an effective technique for producing complex three-dimensional surfaces owing to the inherent flexibility of interlooped yarns and recent advances in manufacturing providing better control of local stitch patterns. Fully yarn-level modelling of large-scale knitted membranes is not feasible. Therefore, we use a two-scale homogenisation approach and model the membrane as a Kirchhoff-Love shell on the macroscale and as Euler-Bernoulli rods on the microscale. The governing equations for both the shell and the rod are discretised with cubic B-spline basis functions. For homogenisation we consider only the in-plane response of the membrane. The solution of the nonlinear microscale problem requires a significant amount of time due to the large deformations and the enforcement of contact constraints, rendering conventional online computational homogenisation approaches infeasible. To sidestep this problem, we use a pre-trained statistical Gaussian Process Regression (GPR) model to map the macroscale deformations to macroscale stresses. During the offline learning phase, the GPR model is trained by solving the microscale problem for a sufficiently rich set of deformation states obtained by either uniform or Sobol sampling. The trained GPR model encodes the nonlinearities and anisotropies present in the microscale and serves as a material model for the membrane response of the macroscale shell. The bending response can be chosen in dependence of the mesh size to penalise the fine out-of-plane wrinkling of the membrane. After verifying and validating the different components of the proposed approach, we introduce several examples involving membranes subjected to tension and shear to demonstrate its versatility and good performance.

preprint2021arXiv

Infill topology and shape optimisation of lattice-skin structures

Lattice-skin structures composed of a thin-shell skin and a lattice infill are widespread in nature and large-scale engineering due to their efficiency and exceptional mechanical properties. Recent advances in additive manufacturing, or 3D printing, make it possible to create lattice-skin structures of almost any size with arbitrary shape and geometric complexity. We propose a novel gradient-based approach to optimising both the shape and infill of lattice-skin structures to improve their efficiency further. The respective gradients are computed by fully considering the lattice-skin coupling while the lattice topology and shape optimisation problems are solved in a sequential manner. The shell is modelled as a Kirchhoff-Love shell and analysed using isogeometric subdivision surfaces, whereas the lattice is modelled as a pin-jointed truss. The lattice consists of many cells, possibly of different sizes, with each containing a small number of struts. We propose a penalisation approach akin to the SIMP (solid isotropic material with penalisation) method for topology optimisation of the lattice. Furthermore, a corresponding sensitivity filter and a lattice extraction technique are introduced to ensure the stability of the optimisation process and to eliminate scattered struts of small cross-sectional areas. The developed topology optimisation technique is suitable for non-periodic, non-uniform lattices. For shape optimisation of both the shell and the lattice, the geometry of the lattice-skin structure is parameterised using the free-form deformation technique. The topology and shape optimisation problems are solved in an iterative, sequential manner. The effectiveness of the proposed approach and the influence of different algorithmic parameters are demonstrated with several numerical examples.

preprint2020arXiv

Many Body Thermodynamics on Quantum Computers via Partition Function Zeros

Interacting quantum systems illustrate complex phenomena including phase transitions to novel ordered phases. The universal nature of critical phenomena reduces their description to determining only the transition temperature and the critical exponents. Numerically calculating these results for systems in new universality classes is complicated due to critical slowing down, requiring increasing resources near the critical point. An alternative approach analytically continues the calculation onto the complex plane and determines the partition function via its zeros. Here we show how to robustly perform this analysis on noisy intermediate scale trapped ion quantum computers in a scalable manner, using the XXZ model as a prototype. We illustrate the transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the determination of critical phenomena for systems that cannot be solved otherwise.

preprint2020arXiv

MSDU-net: A Multi-Scale Dilated U-net for Blur Detection

Blur detection is the separation of blurred and clear regions of an image, which is an important and challenging task in computer vision. In this work, we regard blur detection as an image segmentation problem. Inspired by the success of the U-net architecture for image segmentation, we design a Multi-Scale Dilated convolutional neural network based on U-net, which we call MSDU-net. The MSDU-net uses a group of multi-scale feature extractors with dilated convolutions to extract texture information at different scales. The U-shape architecture of the MSDU-net fuses the different-scale texture features and generates a semantic feature which allows us to achieve better results on the blur detection task. We show that using the MSDU-net we are able to outperform other state of the art blur detection methods on two publicly available benchmarks.

preprint2020arXiv

Topologically robust CAD model generation for structural optimisation

Computer-aided design (CAD) models play a crucial role in the design, manufacturing and maintenance of products. Therefore, the mesh-based finite element descriptions common in structural optimisation must be first translated into CAD models. Currently, this can at best be performed semi-manually. We propose a fully automated and topologically accurate approach to synthesise a structurally-sound parametric CAD model from topology optimised finite element models. Our solution is to first convert the topology optimised structure into a spatial frame structure and then to regenerate it in a CAD system using standard constructive solid geometry (CSG) operations. The obtained parametric CAD models are compact, that is, have as few as possible geometric parameters, which makes them ideal for editing and further processing within a CAD system. The critical task of converting the topology optimised structure into an optimal spatial frame structure is accomplished in several steps. We first generate from the topology optimised voxel model a one-voxel-wide voxel chain model using a topology-preserving skeletonisation algorithm from digital topology. The weighted undirected graph defined by the voxel chain model yields a spatial frame structure after processing it with standard graph algorithms. Subsequently, we optimise the cross-sections and layout of the frame members to recover its optimality, which may have been compromised during the conversion process. At last, we generate the obtained frame structure in a CAD system by repeatedly combining primitive solids, like cylinders and spheres, using boolean operations. The resulting solid model is a boundary representation (B-Rep) consisting of trimmed non-uniform rational B-spline (NURBS) curves and surfaces.

preprint2016arXiv

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.

preprint2015arXiv

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.

preprint2015arXiv

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.

preprint2015arXiv

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.

preprint2015arXiv

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.

preprint2014arXiv

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.

preprint2014arXiv

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.

preprint2014arXiv

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.

preprint2014arXiv

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.

preprint2014arXiv

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.

preprint2014arXiv

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.

preprint2013arXiv

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.

preprint2013arXiv

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.

preprint2013arXiv

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.

preprint2012arXiv

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.

preprint2012arXiv

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).

preprint2012arXiv

Moving Stable Solitons in Galileon Theory

Despite the no-go theorem [5] which rules out static stable solitons in Galileon theory, we propose a family of solitons that evade the theorem by traveling at the speed of light. These domain-wall-like solitons are stable under small fluctuations-analysis of perturbation shows neither ghost-like nor tachyon-like instabilities, and perturbative collision of these solitons suggests that they pass through each other asymptotically, which maybe an indication of the integrability of the theory itself.

preprint2011arXiv

Observation of backscattering-immune chiral electromagnetic modes without time reversal breaking

A strategy is proposed to realize robust transport in time reversal invariant photonic system. Using numerical simulation and microwave experiment, we demonstrate that a chiral guided mode in the channel of a three-dimensional dielectric woodpile photonic crystal is immune to the scattering of a square patch of metal or dielectric inserted to block the channel. The chirality based robust transport can be realized in nonmagnetic dielectric materials without any external field.

preprint2010arXiv

Geometric-arithmetic averaging of dyadic weights

The theory of (Muckenhoupt) weights arises in many areas of analysis, for example in connection with bounds for singular integrals and maximal functions on weighted spaces. We prove that a certain averaging process gives a method for constructing A_p weights from a measurably varying family of dyadic A_p weights. This averaging process is suggested by the relationship between the A_p weight class and the space of functions of bounded mean oscillation. The same averaging process also constructs weights satisfying reverse Holder (RH_p) conditions from families of dyadic RH_p weights, and extends to the polydisc as well.