arXiv subjects

Jiajun Xu

Publications and source records attributed to Jiajun Xu.

35 records · Page 2Linked to original sources

arXiv2024

Weakly Supervised Object Detection for Automatic Tooth-marked Tongue Recognition

Tongue diagnosis in Traditional Chinese Medicine (TCM) is a crucial diagnostic method that can reflect an individual's health status. Traditional methods for identifying tooth-marked tongues are subjective and inconsistent because they rely on practitioner experience. We propose a novel fully automated Weakly Supervised method using Vision transformer and Multiple instance learning WSVM for tongue extraction and tooth-marked tongue recognition. Our approach first accurately detects and extracts the tongue region from clinical images, removing any irrelevant background information. Then, we implement an end-to-end weakly supervised object detection method. We utilize Vision Transformer (ViT) to process tongue images in patches and employ multiple instance loss to identify tooth-marked regions with only image-level annotations. WSVM achieves high accuracy in tooth-marked tongue classification, and visualization experiments demonstrate its effectiveness in pinpointing these regions. This automated approach enhances the objectivity and accuracy of tooth-marked tongue diagnosis. It provides significant clinical value by assisting TCM practitioners in making precise diagnoses and treatment recommendations. Code is available at https://github.com/yc-zh/WSVM.

cs.CV↗

arXiv2024

A General-Purpose Device for Interaction with LLMs

This paper investigates integrating large language models (LLMs) with advanced hardware, focusing on developing a general-purpose device designed for enhanced interaction with LLMs. Initially, we analyze the current landscape, where virtual assistants and LLMs are reshaping human-technology interactions, highlighting pivotal advancements and setting the stage for a new era of intelligent hardware. Despite substantial progress in LLM technology, a significant gap exists in hardware development, particularly concerning scalability, efficiency, affordability, and multimodal capabilities. This disparity presents both challenges and opportunities, underscoring the need for hardware that is not only powerful but also versatile and capable of managing the sophisticated demands of modern computation. Our proposed device addresses these needs by emphasizing scalability, multimodal data processing, enhanced user interaction, and privacy considerations, offering a comprehensive platform for LLM integration in various applications.

cs.AR↗

arXiv2024

Every type A quiver locus is a Kazhdan-Lusztig variety

The Zariski closures of the orbits for representations of type A Dynkin quivers under the action of general linear groups (i.e. quiver loci) exhibit a profound connection with Schubert varieties. In this paper, we present a scheme-theoretical isomorphism between a type A quiver locus and the intersection of an opposite Schubert cell and a Schubert variety, also known as a Kazhdan-Lusztig variety in geometric representation theory. Our results generalize and unify the Zelevinsky maps for equioriented type A quiver loci and bipartite type A quiver loci, as presented respectively by A. V. Zelevinsky in 1985 and by R. Kinser and J. Rajchgot in 2015. Through this isomorphism, we establish a direct and natural connection between type A quiver loci and Schubert varieties. We compute an explicit relationship between Zelevinsky permutations and the indecomposable factors of the corresponding representations. Additionally, we present three applications of our isomorphism with examples in order to justify its further potentials.

math.AG↗

arXiv2024

Large Language Models for Forecasting and Anomaly Detection: A Systematic Literature Review

This systematic literature review comprehensively examines the application of Large Language Models (LLMs) in forecasting and anomaly detection, highlighting the current state of research, inherent challenges, and prospective future directions. LLMs have demonstrated significant potential in parsing and analyzing extensive datasets to identify patterns, predict future events, and detect anomalous behavior across various domains. However, this review identifies several critical challenges that impede their broader adoption and effectiveness, including the reliance on vast historical datasets, issues with generalizability across different contexts, the phenomenon of model hallucinations, limitations within the models' knowledge boundaries, and the substantial computational resources required. Through detailed analysis, this review discusses potential solutions and strategies to overcome these obstacles, such as integrating multimodal data, advancements in learning methodologies, and emphasizing model explainability and computational efficiency. Moreover, this review outlines critical trends that are likely to shape the evolution of LLMs in these fields, including the push toward real-time processing, the importance of sustainable modeling practices, and the value of interdisciplinary collaboration. Conclusively, this review underscores the transformative impact LLMs could have on forecasting and anomaly detection while emphasizing the need for continuous innovation, ethical considerations, and practical solutions to realize their full potential.

cs.LG↗

arXiv2023

Symplectic conditions on Grassmannian, flag, and Schubert varieties

In this paper, a description of the set-theoretical defining equations of symplectic (type C) Grassmannian/flag/Schubert varieties in corresponding (type A) algebraic varieties is given as linear polynomials in Pl$\ddot{u}$cker coordinates, and it is proved that such equations generate the defining ideal of variety of type C in those of type A. As applications of this result, the number of local equations required to obtain the Schubert variety of type C from the Schubert variety of type A is computed, and further geometric properties of the Schubert variety of type C are given in the aspect of complete intersections. Finally, the smoothness of Schubert variety in the non-minuscule or cominuscule Grassmannian of type C is discussed, filling gaps in the study of algebraic varieties of the same type.

math.AG↗

arXiv2020

The defining equations of a class of Richardson and flag varieties on Sp$_{2n}(k)$

This paper aims to focus on Richardson varieties on symplectic groups, especially their combinatorial characterization and defining equations. Schubert varieties and opposite Schubert varieties have profound significance in the study of generalized flag varieties which are not only research objects in algebraic geometry but also ones in representation theory. A more general research object is Richardson variety, which is obtained by the intersection of a Schubert variety and an opposite Schubert variety. The structure of Richardson variety on Grassmannian and its combinatorial characterization are well known, and there are also similar method on quotients of symplectic groups. In the first part of this paper, we calculate the orbit of the symplectic group action, and then rigorously give a method to describe the corresponding quotient by using the nesting subspace sequence of the linear space, i.e. flags. At the same time, the flag is used to describe the Schubert variety and Richardson variety on quotient of symplectic group. The flag varieties of Sp_{2n}(k)/P_d can be viewed as closed subvarieties of Grassmannian. Using the standard monomial theory, we obtain the generators of its ideal, i.e. its defining equations, in homogeneous coordinate ring of Grassmannian. Furthermore, we prove several properties of the type C standard monomial on the symplectic group flag variety. Defining equations of Richardson varieties on Sp_{2n}(k)/P_d are given as well.

math.AG↗

arXiv2018

Tetris

Tetris is an Asynchronous Byzantine Fault Tolerance consensus algorithm designed for next generation high-throughput permission and permissionless blockchain. The core concept of Tetris is derived from Reasoning About Knowledge, which we believe to be the most appropriate tools for revealing and analyzing the fundamental complexity of distributed systems. By analyzing the states of knowledge that each participant attained in an unreliable system, we can capture some of the basis underlying structure of the system, then help us designing effective & efficient protocols. Plus the adoption of Full Information Protocol (FIP) with the optimized message traffic model, Tetris has finally got high performance, with proved safety. Tetris achieve consensus finality in seconds, means transactions can be confirmed greatly faster than other scheme like Pow/Dpos. Tetris also achieve fairness, which is critically important in some areas such as stock market etc.

cs.MA↗

arXiv2014

MultiModeCode: An efficient numerical solver for multifield inflation

We present MultiModeCode, a Fortran 95/2000 package for the numerical exploration of multifield inflation models. This program facilitates efficient Monte Carlo sampling of prior probabilities for inflationary model parameters and initial conditions and is the first publicly available code that can efficiently generate large sample-sets for inflation models with $\mathcal O(100)$ fields. The code numerically solves the equations of motion for the background and first-order perturbations of multi-field inflation models with canonical kinetic terms and arbitrary potentials, providing the adiabatic, isocurvature, and tensor power spectra at the end of inflation. For models with sum-separable potentials MultiModeCode also computes the slow-roll prediction via the $δN$ formalism for easy model exploration and validation. We pay particular attention to the isocurvature perturbations as the system approaches the adiabatic limit, showing how to avoid numerical instabilities that affect some other approaches to this problem. We demonstrate the use of MultiModeCode by exploring a few toy models. Finally, we give a concise review of multifield perturbation theory and a user's manual for the program.

astro-ph.CO↗

arXiv2011

Effective Field Theory and Decoupling in Multi-field Inflation: An Illustrative Case Study

We explore the effects of heavy degrees of freedom on the evolution and perturbations of light modes in multifield inflation. We use a simple two-field model as an example to illustrate the subtleties of integrating out massive fields in a time-dependent background. We show that when adiabaticity is violated due to a sharp turn in field space, the roles of massive and massless field are interchanged, and furthermore the fields are strongly coupled; thus the system cannot be described by an effective single field action. Further analysis shows that the sharp turn imparts a non Bunch-Davis component in each perturbation mode, leading to oscillatory features in the power spectrum, and a large resonantly enhanced bispectrum.

hep-th↗

arXiv2011

A Brachistochrone Approach to Reconstruct the Inflaton Potential

We propose a new way to implement an inflationary prior to a cosmological dataset that incorporates the inflationary observables at arbitrary order. This approach employs an exponential form for the Hubble parameter $H(ϕ)$ without taking the slow-roll approximation. At lowest non-trivial order, this $H(ϕ)$ has the unique property that it is the solution to the brachistochrone problem for inflation.

astro-ph.CO↗

arXiv2011

Duality Cascade in Brane Inflation

We show that brane inflation is very sensitive to tiny sharp features in extra dimensions, including those in the potential and in the warp factor. This can show up as observational signatures in the power spectrum and/or non-Gaussianities of the cosmic microwave background radiation (CMBR). One general example of such sharp features is a succession of small steps in a warped throat, caused by Seiberg duality cascade using gauge/gravity duality. We study the cosmological observational consequences of these steps in brane inflation. Since the steps come in a series, the prediction of other steps and their properties can be tested by future data and analysis. It is also possible that the steps are too close to be resolved in the power spectrum, in which case they may show up only in the non-Gaussianity of the CMB temperature fluctuations and/or EE polarization. We study two cases. In the slow-roll scenario where steps appear in the inflaton potential, the sensitivity of brane inflation to the height and width of the steps is increased by several orders of magnitude comparing to that in previously studied large field models. In the IR DBI scenario where steps appear in the warp factor, we find that the glitches in the power spectrum caused by these sharp features are generally small or even unobservable, but associated distinctive non-Gaussianity can be large. Together with its large negative running of the power spectrum index, this scenario clearly illustrates how rich and different a brane inflationary scenario can be when compared to generic slow-roll inflation. Such distinctive stringy features may provide a powerful probe of superstring theory.

hep-th↗

arXiv2010

Comment on Asymptotically Safe Inflation

We comment on Weinberg's interesting analysis of asymptotically safe inflation (arXiv:0911.3165). We find that even if the gravity theory exhibits an ultraviolet fixed point, the energy scale during inflation is way too low to drive the theory close to the fixed point value. We choose the specific renormalization groupflow away from the fixed point towards the infrared region that reproduces the Newton's constant and today's cosmological constant. We follow this RG flow path to scales below the Planck scale to study the stability of the inflationary scenario. Again, we find that some fine tuning is necessary to get enough efolds of infflation in the asymptotically safe inflationary scenario.

hep-th↗

arXiv2010

A Meandering Inflaton

If the cosmological inflationary scenario took place in the cosmic landscape in string theory, the inflaton, the scalar mode responsible for inflation, would have meandered in a complicated multi-dimensional potential. We show that this meandering property naturally leads to many e-folds of inflation, a necessary condition for a successful inflationary scenario. This behavior also leads to fluctuations in the primordial power spectrum of the cosmic microwave background radiation, which may be detected in a near future cosmic variance limited experiment like PLANCK.

hep-th↗

arXiv2009

Multi-field Inflation with a Random Potential

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.

hep-th↗

arXiv2008

Comparing Infrared Dirac-Born-Infeld Brane Inflation to Observations

We compare the Infrared Dirac-Born-Infeld (IR DBI) brane inflation model to observations using a Bayesian analysis. The current data cannot distinguish it from the \LambdaCDM model, but is able to give interesting constraints on various microscopic parameters including the mass of the brane moduli potential, the fundamental string scale, the charge or warp factor of throats, and the number of the mobile branes. We quantify some distinctive testable predictions with stringy signatures, such as the large non-Gaussianity, and the large, but regional, running of the spectral index. These results illustrate how we may be able to probe aspects of string theory using cosmological observations.

hep-th↗

arXiv2007

Comparing Brane Inflation to WMAP

We compare the simplest realistic brane inflationary model to recent cosmological data, including WMAP 3-year cosmic microwave background (CMB) results, Sloan Digital Sky Survey luminous red galaxies (SDSS LRG) power spectrum data and Supernovae Legacy Survey (SNLS) Type 1a supernovae distance measures. Here, the inflaton is simply the position of a $D3$-brane which is moving towards a $\bar{D}3$-brane sitting at the bottom of a throat (a warped, deformed conifold) in the flux compactified bulk in Type IIB string theory. The analysis includes both the usual slow-roll scenario and the Dirac-Born-Infeld scenario of slow but relativistic rolling. Requiring that the throat is inside the bulk greatly restricts the allowed parameter space. We discuss possible scenarios in which large tensor mode and/or non-Gaussianity may emerge. Here, the properties of a large tensor mode deviate from that in the usual slow-roll scenario, providing a possible stringy signature. Overall, within the brane inflationary scenario, the cosmological data is providing information about the properties of the compactification of the extra dimensions.

hep-th↗

arXiv2006

Is Brane Inflation Eternal?

In this paper, we show that eternal inflation of the random walk type is generically absent in the brane inflationary scenario. Depending on how the brane inflationary universe originated, eternal inflation of the false vacuum type is still quite possible. Since the inflaton is the position of the D3-brane relative to the anti-D3-brane inside the compactified bulk with finite size, its value is bounded. In DBI inflation, the warped space also restricts the amplitude of the scalar fluctuation. These upper bounds impose strong constraints on the possibility of eternal inflation. We find that eternal inflation due to the random walk of the inflaton field is absent in both the KKLMMT slow roll scenario and the DBI scenario. A more careful analysis for the slow-roll case is also presented using the Langevin equation, which gives very similar results. We discuss possible ways to obtain eternal inflation of the random walk type in brane inflation. In the multi-throat brane inflationary scenario, the branes may be generated by quantum tunneling and roll out the throat. Eternal inflation of the false vacuum type inevitably happens in this scenario due to the tunneling process. Since these scenarios have different cosmological predictions, more data from the cosmic microwave background radiation will hopefully select the specific scenario our universe has gone through.

hep-th↗