645 research outputs found
A Spectral Bound on Hypergraph Discrepancy
No full textLet ℋ be a t-regular hypergraph on n vertices and m edges. Let M be the m × n incidence matrix of ℋ and let us denote λ = max_{v ∈ ^⟂} 1/‖v‖ ‖Mv‖. We show that the discrepancy of ℋ is O(√t + λ). As a corollary, this gives us that for every t, the discrepancy of a random t-regular hypergraph with n vertices and m ≥ n edges is almost surely O(√t) as n grows. The proof also gives a polynomial time algorithm that takes a hypergraph as input and outputs a coloring with the above guarantee
On the AC^0[oplus] Complexity of Andreev’s Problem
No full textAndreev’s Problem is the following: Given an integer d and a subset of S subset F_q x F_q, is there a polynomial y = p(x) of degree at most d such that for every a in F_q, (a,p(a)) in S? We show an AC^0[oplus] lower bound for this problem.
This problem appears to be similar to the list recovery problem for degree-d Reed-Solomon codes over F_q which states the following: Given subsets A_1,...,A_q of F_q, output all (if any) the Reed-Solomon codewords contained in A_1 x *s x A_q. In particular, we study this problem when the lists A_1, ..., A_q are randomly chosen, and are of a certain size. This may be of independent interest
Unbalanced Random Matching Markets with Partial Preferences
No full textProperties of stable matchings in the popular random-matching-market model have been studied for over 50 years. In a random matching market, each agent has complete preferences drawn uniformly and independently at random. Wilson (1972), Knuth (1976) and Pittel (1989) proved that in balanced random matching markets, the proposers are matched to their ln nth choice on average. In this paper, we consider competitive markets with n jobs and n+k candidates, and partial lists where each agent only ranks their top d choices. Despite the long history of the problem, the following fundamental question remains unanswered for these generalized markets: what is the tight threshold on list length d that results in a perfect stable matching with high probability? In this paper, we answer this question exactly - we prove a sharp threshold d₀ = ln n ⋅ ln (n+k)/(k+1) on the existence of perfect stable matchings when k = o(n). That is, we show that if d (1+ ε) d₀, then all jobs are matched in every stable matching with high probability. This bound improves and generalizes recent results by Kanoria, Min and Qian (2021).
Furthermore, we extend the line of work studying the effect of imbalance on the expected rank of the proposers (termed the "stark effect of competition"). We establish the regime in unbalanced markets that forces this stark effect to take shape in markets with partial preferences
On the List Recoverability of Randomly Punctured Codes
No full textWe show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound. In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound. It was previously known that there are Reed-Solomon codes that do not have this property. As an immediate corollary to our main theorem, we obtain better degree bounds on unbalanced expanders that come from Reed-Solomon codes
Error-Correcting Graph Codes
No full textIn this paper, we construct Error-Correcting Graph Codes. An error-correcting graph code of distance δ is a family C of graphs, on a common vertex set of size n, such that if we start with any graph in C, we would have to modify the neighborhoods of at least δ n vertices in order to obtain some other graph in C. This is a natural graph generalization of the standard Hamming distance error-correcting codes for binary strings.
Yohananov and Yaakobi were the first to construct codes in this metric. We extend their work by showing
1) Combinatorial results determining the optimal rate vs distance trade-off nonconstructively.
2) Graph code analogues of Reed-Solomon codes and code concatenation, leading to positive distance codes for all rates and positive rate codes for all distances.
3) Graph code analogues of dual-BCH codes, yielding large codes with distance δ = 1-o(1). This gives an explicit "graph code of Ramsey graphs".
Several recent works, starting with the paper of Alon, Gujgiczer, Körner, Milojević, and Simonyi, have studied more general graph codes; where the symmetric difference between any two graphs in the code is required to have some desired property. Error-correcting graph codes are a particularly interesting instantiation of this concept
A Spectral Approach to Approximately Counting Independent Sets in Dense Bipartite Graphs
No full textWe give a randomized algorithm that approximates the number of independent sets in a dense, regular bipartite graph - in the language of approximate counting, we give an FPRAS for #BIS on the class of dense, regular bipartite graphs. Efficient counting algorithms typically apply to "high-temperature" problems on bounded-degree graphs, and our contribution is a notable exception as it applies to dense graphs in a low-temperature setting. Our methods give a counting-focused complement to the long line of work in combinatorial optimization showing that CSPs such as Max-Cut and Unique Games are easy on dense graphs via spectral arguments.
Our contributions include a novel extension of the method of graph containers that differs considerably from other recent low-temperature algorithms. The additional key insights come from spectral graph theory and have previously been successful in approximation algorithms. As a result, we can overcome some limitations that seem inherent to the aforementioned class of algorithms. In particular, we exploit the fact that dense, regular graphs exhibit a kind of small-set expansion (i.e., bounded threshold rank), which, via subspace enumeration, lets us enumerate small cuts efficiently
Dentigerous Cyst
No full textDentigerous Cyst
Dental School Radiology Presentation : Dentigerous Cyst
Author : Tadinada, Aditya
Medical Subject : Dentigerous Cyst, Odontogenic Cysts
Clinical Presentation Description : Radiolucency arising from the CEJ of an unerupted tooth
Location of Abnormality : Posterior Mandible
Radiological Features : Radiolucency arising from the CEJ of an unerupted tooth
DDx Description : Dentigerous cyst, odontogenic keratocyst, ameloblastoma
Type of Image : Panoramic Radiograph
Digital Publisher : UCONN Health Center : Kilham, Jessica
Format : jpg
Date : 201
Design, modeling and real-time monitoring of continuous powder mixing processes
No full textContinuous processing is an advantageous alternative for the current methods used in the pharmaceutical manufacturing. Important advantages that it offers include smaller equipment footprint, reduced efforts in the scale-up work, and the potential to utilize already continuous processes to make the entire manufacturing more efficient. In the current pharmaceutical manufacturing environment, powder mixing process is carried out in the batch mode. The necessary methods and guidelines to design an equivalent continuous process are not well established. The work presented in this dissertation focuses on the characterization, design and optimization of a continuous powder mixing process for pharmaceutical powders. A systematic study was performed of the effects of process and design variables, and material properties involved in the continuous powder mixing process. The bulk powder flow behavior was characterized using the residence time distribution (RTD) measurement approach. Impeller speed, material bulk density and impeller design greatly influenced the mean residence time. With increasing impeller speed, mechanical fluidization was observed, which significantly affected axial dispersion coefficients. Intermediate rotation rates exerted maximum strain on the material, which leads to maximum homogenization. The strain measurements correlated well with the properties of tablets including content uniformity and tablet hardness. Mixing performance was largely dominated by the material properties of the mixture, and the blend uniformity measurement was affected by the sample size analyzed. An experimental protocol was developed to measure the blend uniformity in the in-line mode, and a methodology was further built to quantitatively relate the in-line NIR measurements with the off-line wet chemistry measurements. Considering the shear limitations of the continuous bladed mixer, alternative blending strategies, suitable for blending of cohesive materials were also demonstrated. A combination of a high-shear mixing followed by a low-shear mixing process provided the optimal mixing performance. The predictive understanding of the continuous powder mixing process developed in this dissertation can assist towards the design and development of a fully controlled continuous manufacturing process.Ph. D.Includes bibliographical referencesIncludes vitaby Aditya U. Vanaras
Crystal Dynamics and Anharmonic Properties of Bi-Pb-Tl Alloys
No full textTitle: Crystal Dynamics and Anharmonic Properties of Bi-Pb-Tl Alloys, Author: Aditya P. Roy, Location: ThodeThe crystal dynamics and anharmonic properties have
been investigated in disordered alloys of Bi-Pb-Tl using slow
neutron spectrometry. Damping of phonons caused by phonon-phonon
interaction and the effect of the force constant
disorder on the lifetime of the phonons have been studied in
the alloys. Measurements of the coefficients of thermal
expansion are reported. An experimental method of determining
the lattice frequency spectra by coherent inelastic scattering
of neutrons from polycrystalline materials is described.ThesisDoctor of Philosophy (PhD
On the two-potential constitutive modelling of rubber viscoelastic materials
No full textU of I Only Restriction Lifted for Item 93166 on 2018-07-08T09:15:36Z."This work lays out the specialization of the two-potential constitutive framework --- also known as the ""generalized standard materials'' framework --- to rubber viscoelasticity. Inter alia, it is shown that a number of popular rubber viscoelasticity formulations, introduced over the years following different approaches, are special cases of this framework. As a first application of practical relevance, the framework is utilized to put forth a new objective and thermodynamically consistent rubber viscoelastic model for incompressible isotropic elastomers. The model accounts for the non-Gaussian elasticity of elastomers, as well as for the deformation-enhanced shear thinning of their viscous dissipation governed by reptation dynamics. The descriptive and predictive capabilities of the model are illustrated via comparisons with experimental data available from the literature for two commercially significant elastomers."Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01The student, Aditya Kumar, accepted the attached license on 2016-04-21 at 16:42.The student, Aditya Kumar, submitted this Thesis for approval on 2016-04-21 at 17:40.This Thesis was approved for publication on 2016-04-25 at 13:53.DSpace SAF Submission Ingestion Package generated from Vireo submission #9421 on 2016-07-07 at 13:50:34Made available in DSpace on 2016-07-07T20:27:55Z (GMT). No. of bitstreams: 2
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Previous issue date: 2016-04-25Embargo set by: Seth Robbins for item 93166
Lift date: 2018-07-07T20:28:14Z
Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD systemEmbargo set by: Seth Robbins for item 93166
Lift date: 2018-07-07T20:35:34Z
Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD syste
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