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Bei Jia

Publications and source records attributed to Bei Jia.

15 recordsLinked to original sources
arXiv2019

Exact inference under the perfect phylogeny model

Motivation: Many inference tools use the Perfect Phylogeny Model (PPM) to learn trees from noisy variant allele frequency (VAF) data. Learning in this setting is hard, and existing tools use approximate or heuristic algorithms. An algorithmic improvement is important to help disentangle the limitations of the PPM's assumptions from the limitations in our capacity to learn under it. Results: We make such improvement in the scenario, where the mutations that are relevant for evolution can be clustered into a small number of groups, and the trees to be reconstructed have a small number of nodes. We use a careful combination of algorithms, software, and hardware, to develop EXACT: a tool that can explore the space of all possible phylogenetic trees, and performs exact inference under the PPM with noisy data. EXACT allows users to obtain not just the most-likely tree for some input data, but exact statistics about the distribution of trees that might explain the data. We show that EXACT outperforms several existing tools for this same task. Availability: https://github.com/surjray-repos/EXACT

q-bio.QM↗
arXiv2018

Efficient Projection onto the Perfect Phylogeny Model

Several algorithms build on the perfect phylogeny model to infer evolutionary trees. This problem is particularly hard when evolutionary trees are inferred from the fraction of genomes that have mutations in different positions, across different samples. Existing algorithms might do extensive searches over the space of possible trees. At the center of these algorithms is a projection problem that assigns a fitness cost to phylogenetic trees. In order to perform a wide search over the space of the trees, it is critical to solve this projection problem fast. In this paper, we use Moreau's decomposition for proximal operators, and a tree reduction scheme, to develop a new algorithm to compute this projection. Our algorithm terminates with an exact solution in a finite number of steps, and is extremely fast. In particular, it can search over all evolutionary trees with fewer than 11 nodes, a size relevant for several biological problems (more than 2 billion trees) in about 2 hours.

cs.DS↗
arXiv2016

Rigidly Supersymmetric Gauge Theories on Curved Superspace

In this note we construct rigidly supersymmetric gauged sigma models and gauge theories on certain Einstein four-manifolds, and discuss constraints on these theories. In work elsewhere, it was recently shown that on some nontrivial Einstein four-manifolds such as AdS$_4$, N=1 rigidly supersymmetric sigma models are constrained to have target spaces with exact Kähler forms. Similarly, in gauged sigma models and gauge theories, we find that supersymmetry imposes constraints on Fayet-Iliopoulos parameters, which have the effect of enforcing that Kähler forms on quotient spaces be exact. We also discuss general aspects of universality classes of gauged sigma models, as encoded by stacks, and also discuss affine bundle structures implicit in these constructions.

hep-th↗
arXiv2016

Topological Sigma Models On Supermanifolds

This paper concerns constructing topological sigma models governing maps from semirigid super Riemann surfaces to general target supermanifolds. We define both the A model and B model in this general setup by defining suitable BRST operators and physical observables. Using supersymmetric localization, we express correlation functions in these theories as integrals over suitable supermanifolds. In the case of the A model, we obtain an integral over the supermoduli space of "superinstantons". The language of supergeometry is used extensively throughout this paper.

hep-th↗
arXiv2016

Topological String Theory Revisited I: The Stage

In this note we reformulate topological string theory using supermanifolds and supermoduli spaces, following the approach worked out by Witten for superstring perturbation theory in arXiv:1209.5461. We intend to make the construction geometrical in nature, by using supergeometry techniques extensively. The goal is to establish the foundation of studying topological string amplitudes in terms of integration over appropriate supermoduli spaces.

hep-th↗
arXiv2016

Localization of twisted $\mathcal{N}{=}(0,2)$ gauged linear sigma models in two dimensions

We study two-dimensional $\mathcal{N}{=}(0,2)$ supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider $\mathcal{N}{=}(0,2)$ theories with an $R$-symmetry, which can always be defined on curved space by a pseudo-topological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of $\mathcal{N}{=}(2,2)$ GLSMs and retain a Coulomb branch, we consider the $A/2$-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the $\mathcal{N}{=}(2,2)$ locus. These correlation functions can be written in terms of a certain residue operation on the Coulomb branch, generalizing the Jeffrey-Kirwan residue prescription relevant for the $\mathcal{N}{=}(2,2)$ locus. For abelian GLSMs, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. For non-abelian GLSMs, our methods lead to new results. As an example, we briefly discuss the quantum sheaf cohomology of the Grassmannian manifold.

hep-th↗
arXiv2014

Orbifold Grand Unification: A Solution to the Doublet-Triplet Problem

To solve the doublet-triplet splitting problem in SU(5) grand unified theories, we propose a four dimensional orbifold grand unified theory by acting Z2 on the SU(5) gauge group. Without an adjoint Higgs, the orbifold procedure breaks the SU(5) gauge symmetry down to the standard model gauge group, and removes the triplet component of the fundamental SU(5) Higgs. In the supersymmetric framework, we show that the orbifold procedure removes two triplet superfields of the Higgs multiplets and leaves us with the minimal supersymmetric standard model, which also solves the hierarchy problem and realizes gauge coupling unification. We also discuss possible UV completions of the orbifold theories.

hep-ph↗
arXiv2013

Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$

Following recent work on GLSM localization, we work out curvature couplings for rigidly supersymmetric nonlinear sigma models with superpotential for general target spaces, describing both ordinary and twisted chiral superfields on round two-sphere worldsheets. We briefly discuss why, unlike four-dimensional theories, there are no constraints on Kahler forms in these theories. We also briefly discuss general issues in topological twists of such theories.

hep-th↗
arXiv2013

D-branes and $K$-homology

In this thesis the close relationship between the topological $K$-homology group of the spacetime manifold $X$ of string theory and D-branes in string theory is examined. An element of the $K$-homology group is given by an equivalence class of $K$-cycles $[M,E,ϕ]$, where $M$ is a closed spin$^c$ manifold, $E$ is a complex vector bundle over $M$, and $ϕ: M\rightarrow X$ is a continuous map. It is proposed that a $K$-cycle $[M,E,ϕ]$ represents a D-brane configuration wrapping the subspace $ϕ(M)$. As a consequence, the $K$-homology element defined by $[M,E,ϕ]$ represents a class of D-brane configurations that have the same physical charge. Furthermore, the $K$-cycle representation of D-branes resembles the modern way of characterizing fundamental strings, in which the strings are represented as two-dimensional surfaces with maps into the spacetime manifold. This classification of D-branes also suggests the possibility of physically interpreting D-branes wrapping singular subspaces of spacetime, enlarging the known types of singularities that string theory can cope with.

math.KT↗
arXiv2008

Angular Momentum of a Brane-world Model

In this paper we discuss the properties of the general covariant angular momentum of a five-dimensional brane-world model. Through calculating the total angular momentum of this model, we are able to analyze the properties of the total angular momentum in the inflationary RS model. We show that the space-like components of the total angular momentum of are all zero while the others are non-zero, which agrees with the results from ordinary RS model.

hep-th↗
arXiv2008

Energy-momentum of a Cosmological Brane Model and the Gauge Hierarchy

We analyze the general covariant energy-momentum tensor of the gravitational system in genreal five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the "visible" brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy.

hep-th↗
arXiv2007

Small Cosmological Constants from a Modified Randall-Sundrum Model

We study a mechanism, inspired from the mechanism for generating the gauge hierarchy in Randall-Sundrum model, to investigate the cosmological constant problem. First we analyze the bulk cosmological constant and brane vacuum energies in RS model. We show that the five-dimensional bulk cosmological constant and the vacuum energies of the two branes all obtain their natural values. Finally we argue how we can generate a small four-dimensional effective cosmological constant on the branes through modifying the original RS model.

hep-th↗
arXiv2007

Effective Field Theory, Renormalizability and Extra Dimensions

We discuss in this paper two ways of defining the concept of "effective field theory": effective field theory defined by low energy effectiveness and effective field theory defined by 4D effectiveness out of higher dimensions. We argue that these two views are actually equivalent, that effective field theories at low energy can in fact be regarded as field theories of higher dimensions confined on a 4D spcaetime. We examine this idea through comparing two different regularization schemes: Momentum Cutoff and Dimensional Regularization, and through analyzing how fields can be localized on branes.

hep-th↗
arXiv2007

Quantum States and Complex Projective Space

In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through analyzing some of the basic principles and concepts of quantum mechanics, including the principle of superposition, representations and inner product of quantum states, and give some interesting examples. Based on our point of views we are able to generate the evolution equation of quantum states -- the Heisenberg equation. We also discuss the act of dynamical operators on quantum states.

math-ph↗