arXiv subjects

Abhinav Nellore

Publications and source records attributed to Abhinav Nellore.

12 recordsLinked to original sources

arXiv2021

Arbitrary-length analogs to de Bruijn sequences

Let $\widetildeα$ be a length-$L$ cyclic sequence of characters from a size-$K$ alphabet $\mathcal{A}$ such that the number of occurrences of any length-$m$ string on $\mathcal{A}$ as a substring of $\widetildeα$ is $\lfloor L / K^m \rfloor$ or $\lceil L / K^m \rceil$. When $L = K^N$ for any positive integer $N$, $\widetildeα$ is a de Bruijn sequence of order $N$, and when $L \neq K^N$, $\widetildeα$ shares many properties with de Bruijn sequences. We describe an algorithm that outputs some $\widetildeα$ for any combination of $K \geq 2$ and $L \geq 1$ in $O(L)$ time using $O(L \log K)$ space. This algorithm extends Lempel's recursive construction of a binary de Bruijn sequence. An implementation written in Python is available at https://github.com/nelloreward/pkl.

math.CO↗

arXiv2021

An invertible transform for efficient string matching in labeled digraphs

Let $G = (V, E)$ be a digraph where each vertex is unlabeled, each edge is labeled by a character in some alphabet $Ω$, and any two edges with both the same head and the same tail have different labels. The powerset construction gives a transform of $G$ into a weakly connected digraph $G' = (V', E')$ that enables solving the decision problem of whether there is a walk in $G$ matching an arbitrarily long query string $q$ in time linear in $|q|$ and independent of $|E|$ and $|V|$. We show $G$ is uniquely determined by $G'$ when for every $v_\ell \in V$, there is some distinct string $s_\ell$ on $Ω$ such that $v_\ell$ is the origin of a closed walk in $G$ matching $s_\ell$, and no other walk in $G$ matches $s_\ell$ unless it starts and ends at $v_\ell$. We then exploit this invertibility condition to strategically alter any $G$ so its transform $G'$ enables retrieval of all $t$ terminal vertices of walks in the unaltered $G$ matching $q$ in $O(|q| + t \log |V|)$ time. We conclude by proposing two defining properties of a class of transforms that includes the Burrows-Wheeler transform and the transform presented here.

cs.DS↗

arXiv2014

Recovery guarantees for exemplar-based clustering

For a certain class of distributions, we prove that the linear programming relaxation of $k$-medoids clustering---a variant of $k$-means clustering where means are replaced by exemplars from within the dataset---distinguishes points drawn from nonoverlapping balls with high probability once the number of points drawn and the separation distance between any two balls are sufficiently large. Our results hold in the nontrivial regime where the separation distance is small enough that points drawn from different balls may be closer to each other than points drawn from the same ball; in this case, clustering by thresholding pairwise distances between points can fail. We also exhibit numerical evidence of high-probability recovery in a substantially more permissive regime.

stat.ML↗

arXiv2009

Ground states of holographic superconductors

We investigate the ground states of the Abelian Higgs model in AdS_4 with various choices of parameters, and with no deformations in the ultraviolet other than a chemical potential for the electric charge under the Abelian gauge field. For W-shaped potentials with symmetry-breaking minima, an analysis of infrared asymptotics suggests that the ground state has emergent conformal symmetry in the infrared when the charge of the complex scalar is large enough. But when this charge is too small, the likeliest ground state has Lifshitz-like scaling in the infrared. For positive mass quadratic potentials, Lifshitz-like scaling is the only possible infrared behavior for constant nonzero values of the scalar. The approach to Lifshitz-like scaling is shown in many cases to be oscillatory.

hep-th↗

arXiv2009

Universal relations of transport coefficients from holography

We show that there are universal high-temperature relations for transport coefficients of plasmas described by a wide class of field theories with gravity duals. These theories can be viewed as strongly coupled large-Nc conformal field theories deformed by one or more relevant operators. The transport coefficients we study are the speed of sound and bulk viscosity, as well as the conductivity, diffusion coefficient, and charge susceptibility of probe U(1) charges. We show that the sound bound v_s^2 <= 1/3 is satisfied at high temperatures in these theories and also discuss bounds on the diffusion coefficient, the conductivity and the bulk viscosity.

hep-th↗

arXiv2009

A bound on the speed of sound from holography

We show that the squared speed of sound v_{s}^{2} is bounded from above at high temperatures by the conformal value of 1/3 in a class of strongly coupled four-dimensional field theories, given some mild technical assumptions. This class consists of field theories that have gravity duals sourced by a single scalar field. There are no known examples to date of field theories with gravity duals for which v_{s}^{2} exceeds 1/3 in energetically favored configurations. We conjecture that v_{s}^{2}=1/3 represents an upper bound for a broad class of four-dimensional theories.

hep-th↗

arXiv2009

Low-temperature behavior of the Abelian Higgs model in anti-de Sitter space

We explore the low-temperature behavior of the Abelian Higgs model in AdS_4, away from the probe limit in which back-reaction of matter fields on the metric can be neglected. Over a significant range of charges for the complex scalar, we observe a second order phase transition at finite temperature. The symmetry-breaking states are superconducting black holes. At least when the charge of the scalar is not too small, we observe at low temperatures the emergence of a domain wall structure characterized by a definite index of refraction. We also compute the conductivity as a function of frequency.

hep-th↗

arXiv2008

Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics

We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio zeta/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first order transition, we observe a sharp rise in zeta/s near T_c. For constructions that exhibit a smooth cross-over, like QCD does, the rise in zeta/s is more modest. We conjecture that divergences in zeta/s for black hole horizons are related to extrema of the entropy density as a function of temperature.

hep-th↗

arXiv2008

Mimicking the QCD equation of state with a dual black hole

We present numerical and analytical studies of the equation of state of translationally invariant black hole solutions to five-dimensional gravity coupled to a single scalar. As an application, we construct a family of black holes that closely mimics the equation of state of quantum chromodynamics at zero chemical potential.

hep-th↗

arXiv2004

Pion-Nucleon Scattering Relations at Next-to-Leading Order in 1/N_c

We obtain relations between partial-wave amplitudes for pi-N-->pi-N and pi-N-->pi-Delta directly from large N_c QCD. While linear relations among certain amplitudes holding at leading order (LO) in 1/N_c were derived in the context of chiral soliton models two decades ago, the present work employs a fully model-independent framework based on consistency with the large N_c expansion. At LO we reproduce the soliton model results; however, this method allows for systematic corrections. At next-to-leading order (NLO), most relations require additional unknown functions beyond those appearing at leading order (LO) and thus have little additional predictive power. However, three NLO relations for the pi-N-->pi-Delta reaction are independent of unknown functions and make predictions accurate at this order. The amplitudes relevant to two of these relations were previously extracted from experiment. These relations describe experiment dramatically better than their LO counterparts.

hep-ph↗

arXiv2004

The quantization of exotic states in SU(3) soliton models: A solvable quantum mechanical analog

The distinction between the rigid rotor and Callan-Klebanov approaches to the quantization of SU(3) solitons is considered in the context of exotic baryons. A numerically tractable quantum mechanical analog system is introduced to test the reliability of the two quantization schemes. We find that in the equivalent of the large N_c limit of QCD, the Callan-Klebanov approach agrees with a numerical solution of the quantum mechanical analog. Rigid rotor quantization generally does not. The implications for exotic baryons are briefly discussed.

hep-ph↗

arXiv2003

Excited Baryon Decay Widths in Large N_c QCD

We study excited baryon decay widths in large N_c QCD. It was suggested previously that some spin-flavor mixed-symmetric baryon states have strong couplings of O(N_c^{-1/2}) to nucleons [implying narrow widths of O(1/N_c)], as opposed to the generic expectation based on Witten's counting rules of an O(N_c^0) coupling. The calculation obtaining these narrow widths was performed in the context of a simple quark-shell model. This paper addresses the question of whether the existence of such narrow states is a general property of large N_c QCD. We show that a general large N_c QCD analysis does not predict such narrow states; rather they are a consequence of the extreme simplicity of the quark model.

hep-ph↗